ABSTRACT. are implemented on a reduced-order model of WECC, however, the underlying controller design

Transcription

1 ABSTRACT WEISS, MATTHEW DAVID. Wide-Area Monitoring and Control of Power Systems using Real-Time Hardware-in-the-Loop Simulations. (Under the direction of Aranya Chakrabortty.) In this research, wide-area damping control is achieved. The majority of these control schema are implemented on a reduced-order model of WECC, however, the underlying controller design and implementation could easily be translated to any arbitrary power system provided sufficient information and data. Firstly, a breakdown of methodology used to create a functional and accurate reduced-order model of a large and complex power system is presented. Next, the model is validated and several contingencies regarding renewable energy integration explored, and thus a major problem identified. This problem stems from the integration of renewable energy, particularly DFIG wind penetration, and thus resulting increase in transience swing intensity. Two wide-area controller designs are presented using PMU measurements. Finally, a hardware-in-the-loop test-bed is presented for implementation of control schema in a real-world setting for validation of performance. It is concluded the wide-area control schema presented in this work are successful at stabilizing otherwise unstable power-system conditions.

2 Wide-Area Monitoring and Control of Power Systems using Real-Time Hardware-in-the-Loop Simulations by Matthew David Weiss A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Doctor of Philosophy Electrical Engineering Raleigh, North Carolina 2016 APPROVED BY: Xiangwu Zhang Ning Lu Subhashish Bhattacharya Aranya Chakrabortty Chair of Advisory Committee

3 BIOGRAPHY Matthew Weiss completed his undergraduate degree in Electrical Engineering at North Carolina State University in May of After completion of his bachelors degree, he immediately began work on his Doctor of Philosophy in Electrical Engineering at North Carolina State University under the advising of Doctor Aranya Chakrabortty at the NCSU FREEDM Research Center with the financial support of the Deans Doctoral Fellowship. Focusing on the wide-area monitoring and control of power systems, several journal and conference papers were published on this topic. An en-route Masters Degree in Electrical Engineering was obtained May of 2014, and completion of his Doctor of Philosophy was achieved August of ii

4 TABLE OF CONTENTS List of Tables List of Figures vi vii Chapter 1 Introduction Introduction Chapter 2 Identification of Power System Models using Synchrophasors Introduction to Reduced-Order Modeling of Power Systems WECC Model Objective Motivation and Literature Review Problem Formulation Modal Extraction using Hankel Matrices Modal Decomposition Description of 5-Area model Model parameter estimation Identification of inter-area tie-line impedance Identification of intra-area Thevenin reactance Problem of non-identifiability Identification of Equivalent Inertia and Damping Chapter 3 Model Validation Model Validation Area 3 Tie-line Impedance Negative Voltage Tuning Fault Power Flow Matching via Resistive Load Swapping Phase Angle Tuning via Governors Inertias and Damping Values Sensitivity Analysis Contingencies Chapter 4 Impacts of Wind Penetration Wind Generation in the WECC Wind Penetration by Area Chapter 5 Wide-Area SVC Control Design SVC in the WECC SVC Nominal Controller Tuning SVC Local Measurement Delay Contingency Selection of Supplementary Control Input Choice of Control Metric Selection of an Input Signal iii

5 5.4.3 Residue Variances SVC Supplementary Controller Parameter Calculations SVC Controller Simulation Results SVC Required Capacity Explanation of Tests Test Results SVC WAC Validation WECC Test Cases Conclusion of Controller Performance Chapter 6 Wide-Area PSS Design using LQR LQR Wide-Area Control Power System Modeling Kron Reduction State-Space Equations Partial Derivatives Wide-Area Control Experimental Results Unstable Case Controller Comparison Test Feedback of Just Local Voltage State Variables Feedback of Just Local Frequency State Variables PSS Stabilizer on WECC Unstable Baseline Case Comparison of All Controllers Conclusion on LQR Implementation in RSCAD Chapter 7 Hardware-in-loop Implementation Hardware Integration Overview Hardware Introduction Hardware Test-Bed Components Hardware Setup GTAO Card Calibration Integration of Supplementary Controller in Hardware Differences Between Software and Hardware Controllers Differences in Model Performance Chapter 8 Wide-Area Control using Cloud Computing Introduction EXOGENI-WAMS Networked Cloud Computing Testbed Testbed Components Testbed Architecture Setup of ExoGENI-WAMS Testbed for Wide-Area Control Loop ExoGENI Lab Tests PMU with Loss of Synchronization iv

6 8.3.2 ExoGENI Implementation ExoGENI Packet Loss Chapter 9 Conclusion Chapter 10Future Work References v

7 LIST OF TABLES Table 2.1 Calculated inter-tie impedance values Table 2.2 Calculated intra-tie impedance values Table 3.1 Model parameters used for RTDS implementation Table 3.2 Calculated Intra-Tie Ompedance Values Table 3.3 Bus Voltages Table 3.4 Voltage Angle and Power Flow Change Across Major Tie-Lines Table 3.5 Voltage Angle Simulated v/s Real Values Table 3.6 Inertia and Damping Table 4.1 Power Outputs of Aggregate Machines Table 4.2 Power Outputs of Aggregate Machines Table 5.1 ERA Example Data Table 5.2 Variance Table 5.3 Variance without Extreme Case Table 5.4 Phase 3 and 4 Modal Data Table 5.5 Changes in Damping for Mode Table 5.6 Changes in Damping for Mode Table 6.1 Alteration of Load Reference Sliders for Case Table 6.2 Steady-State WECC Condition Table 6.3 Alteration of Load Reference Sliders for Case Table 6.4 Steady-State WECC Condition Table 7.1 Changes in Damping for Mode Table 7.2 Changes in Damping for Mode vi

8 LIST OF FIGURES Figure 2.1 A 5-area dynamic equivalent model for the WECC power system Figure 2.2 Electrical topology of WECC s 500kV network Figure 2.3 Slow mode component of Voltage angle difference between Station 2 and Station Figure 2.4 Phasor Diagram for the Aggregated Synchronous Generator Figure 3.1 Transience Modal Comparison Figure 3.2 Loss of Inertia Comparisons Figure 3.3 Impedance Comparisons Figure 4.1 WECC Transient Response with Wind on Area Four Figure 4.2 WECC Transient Response with Wind Figure 5.1 SVC PI Controller Figure 5.2 SVC Process Reaction Curve Figure 5.3 WECC Transient Response Improvement with SVC Figure 5.4 WECC Transient Comparison with Local Delay Figure 5.5 Supplementary Controller Input Figure 5.6 Decomposition of Transient Response Figure 5.7 Phase Angle Case Variation Figure 5.8 Phase Angle Transience of Randomized Tests Figure 5.9 Phase Angle Transience of Controller Tests Figure 5.10 SVC Output Data, Pre and Post-Filtered Figure 5.11 SVC For Different Fault Durations Figure 5.12 SVC For Different Droop Values Figure 5.13 SVC For Different Droop Values Figure 5.14 Case 1 Data Figure 5.15 Case 2 Data Figure 5.16 Case 3 Data Figure 5.17 Case 4 Data Figure 6.1 Electrical topology of WECC s 500kV network Figure 6.2 Example of Relative Phase Angles Figure 6.3 Impulse Response of State Space: Original K Figure 6.4 Impulse Response of State Space: Altered K Figure 6.5 Phase Angle Transience, With and Without WAC Figure 6.6 PMU Data Stream of Operation of Controller Figure 6.7 Phase Angle Transience, Local Voltage vs Wide-Area Control Figure 6.8 Phase Angle Transience, Local Frequency vs No Control Figure 6.9 Phase Angle Transience, PSS vs WAC Figure 6.10 Phase Angle Transience, PSS vs Local Voltage Feedback Figure 6.11 Phase Angle Transience, Controller Comparison vii

9 Figure 7.1 Hardware Open-Loop Test-Bed Figure 7.2 Hardware Closed-Loop Test-Bed Figure 7.3 Test-Bed with WECC Model and Supplementary Controller Figure 7.4 Work Functions of the Supplementary Controller Compared in Hardware and Software Figure 7.5 Phase Angle TransienceUsing Hardware vs Software Controllers Figure 8.1 Architecture of the ExoGENI-WAMS Testbed Figure 8.2 Setup of the ExoGENI-WAMS Testbed Figure 8.3 Flowchart of Wide-Area Controller Figure 8.4 WECC Response to Area 2 Measurement Delay of 8ms Figure 8.5 Phase Angle Transience, RSCAD vs ExoGENI Controller Implementation 126 Figure 8.6 Phase Angle Transience, Data Loss Contingency viii

10 Chapter 1 Introduction 1.1 Introduction In the coming decades, electric power grids are envisioned to become green and smart. Motivated by catastrophic failures such as the 2003 blackout in the Northeastern USA, Hurricane Katrina in 2005, the Energy Act of 2007, concerns over carbon emissions from fossil fuel based power generation, and the critical need for a cost effective electric energy system, the concept of smart grid has become almost ubiquitous across the world. It is both a socio-economic-regulatory concept and also a new engineering/technology vision. One key component of smart grid development over the past decade is the deployment of measurement and instrumentation systems, especially in the form of the Wide-Area Measurement System (WAMS) technology, also commonly referred to as the Synchrophasor technology [1]. Sophisticated digital recording devices called Phasor Measurement Units or PMUs are currently being installed at different points in the North American grid, especially under the smart grid initiatives of the US Department of Energy. Analogous deployment of PMUs is also underway in different regions of the world. These devices record and communicate GPS-synchronized, high sampling rate (6-60 samples/sec), dynamic power system data. Research platforms such as the North American Synchrophasor Initiative (NASPI) [2] and the Western Interconnection Synchrophasor Project (WISP) [3] have 1

11 been formed to investigate how Synchrophasors can be exploited to track the dynamic health of geographically dispersed large power networks [4]. Concerted efforts are currently being made to develop nationwide early warning mechanisms using PMU measurements that will enable power system operators to take timely actions against blackouts and other widespread contingencies. Excellent visualization tools, for example, in the form of Real Time Dynamics Monitoring System (RTDMS) developed by the Electric Power Group [5] and US-Wide Frequency Monitoring Network (FNET) developed at University of Tennessee [6] are currently being deployed across the US grid. This development has been complemented by an equally remarkable progress in data analysis methods and software platforms, some leading examples being the Dynamic System Identification (DSI) software developed by the Pacific Northwest National Laboratory [7, 8], wide-area oscillation detection by frequency-domain optimization methods [9], Hilbert-Huang transforms [10], and phasor-based state estimation [11--13]. However, most of the research done so far in this direction only addresses monitoring and observation. Relatively modest efforts have been made to explore how Synchrophasors can also be used for automatic feedback control [14--17]. More than 1700 PMUs are currently operating in the US West Coast power system (WECC), and close to 1000 PMUs in the Eastern Interconnect (EI), (and much larger numbers of PMUs expected in the coming years). As such, control by human operators is obviously not sustainable. An autonomous, highly distributed, bandwidth-efficient, real-time control system will be needed to fully utilize the value of wide spread Synchrophasor deployment. With the number of PMUs scaling up several hundreds, the control problem, in fact, is becoming more and more prominent, especially for small-signal stability. It is well-known that small-signal instabilities often occur in power grids with minor disturbances in the grid growing into devastatingly large events. These phenomena often occur while the grid operators [18] are unaware of the dynamic instability. For example, on August 10, 1996, two groups of equivalent generators, one in Alberta and the other in southern California, began 2

12 oscillating with respect to each other at an uncontrolled rate, resulting in the largest blackout in the US West coast power system. At that time technology did not permit the diverging oscillations to be observable to the grid operators due to the lack of high-resolution measurements, and the result was an unfortunate disintegration of the entire western interconnection into five separate islands [19]. Today, the WAMS technology offers the means to detect such instabilities. However, the critical question that we still need to answer is: can we design robust, distributed controllers using Synchrophasor feedback to stabilize and control the inter-area power/phase swings between various clusters of the network? Currently, the formulation of these important control problems is still somewhat qualitative. It is common for power engineers to learn about control designs using Power System Stabilizers (PSS) and Automatic Voltage Regulators (AVR). In terms of wide-area control, however, the power system must be viewed as a large interconnected dynamic system, which, for the sake of analyses, is typically represented by hypothetically aggregated clusters that represent the equivalent dynamics of numerous synchronous machines, voltage regulators, dynamic reactances, power electronic conditioners, and so on. If a PSS or AVR needs to be designed for each cluster then obviously the design becomes hypothetical as well with no clear solution on how the controller must be implemented in reality, or how these hypothetical controllers are going to exchange information between them to maintain global stability. No research has yet been done to address this challenging and exemplary control problem. Two seminal contributions in wide-area damping control [14], [15] also motivate similar questions of network partitioning and selection of optimal set of PMUs in order to meet a desired dynamic criterion for closed-loop control. These papers present experimental case studies on two very specific interconnections in North America - namely, the north-south Pacific AC Intertie transfer in the WECC [14], and the Hydro-Quebec internal grid [15]. Their methods for solving these problems are case-specific as well. In more recent years, phasor-based wide-area power flow control problems have been handled using model reference control [20], gain scheduling and observer based control [16], as well as by simulation based power electronic control methods 3

13 supported by field testing [17]. Several initiatives are also currently being taken, for instance, by EPRI and California Energy Commission, to frame the control problem more along the lines of wide-area protection [21]. The formulation of an overarching control framework for wide area control of power systems, however, remains an open question. In this research, wide-area damping control is achieved. The majority of these control schema are implemented on a reduced-order model of WECC, however, the underlying controller design and implementation could easily be translated to any arbitrary power system provided sufficient information and data. In chapter 2, a breakdown of methodology used to create a functional and accurate reduced-order model of a large and complex power system is presented. In chapter 3, the model is validated and several contingencies regarding renewable energy integration explored, and thus a major problem identified in chapter 4. This problem stems from the integration of renewable energy, particularly DFIG wind penetration, and thus resulting increase in transience swing intensity. Two wide-area controller designs are presented using PMU measurements in chapters 5 and 6. Finally in chapter 7, a hardware-in-the-loop test-bed is presented for implementation of control schema in a real-world setting for validation of performance, and this is carried out further in a cloud computing network in chapter 8. It is concluded in chapter 9 the wide-area control schema presented in this work are successful at stabilizing otherwise unstable power-system conditions and counteracting adverse effects of wind penetration on power grid stability. 4

14 Chapter 2 Identification of Power System Models using Synchrophasors 2.1 Introduction to Reduced-Order Modeling of Power Systems List of symbols A i : P i : ASG i : E i δ i : V i θ i : x i : r ij : x ij : p ij : i th area Pilot bus for the i th area Aggregated synchronous generator representing area A i Voltage Phasor of the internal EMF of ASG i Voltage Phasor at pilot bus P i Internal Thevenin reactance of ASG i Resistance of transmission line between P i and P j Reactance of transmission line between P i and P j Active power flow between buses P i and P j Ĩ i : Current Phasor injected at P th i bus by ASG i 5

15 2.1.1 WECC Model Objective The original objective of creation of a model of WECC was to develop an experimental framework for testing transient stability, frequency response and oscillation damping of the US Western Interconnection using a Real-time Digital Simulator (RTDS) though the ambitions of the model have grown much since then. A reduced-order, 5-machine dynamic equivalent model using Synchronized Phasor Measurements [1, 22] to represent the primary oscillation clusters of the WECC power system, starting from the major generation clusters in Alberta, Washington and Oregon to the load clusters in Southern California, Montana and Arizona with intermediate voltage support at appropriate points, as shown in Figure 2.1 referenced from [23] was constructed. This figure shows the so-called wide-area, clustered view of the WECC system [24, 25], breaking the entire interconnection into several well-defined, coherent generation/load clusters that oscillate with respect to each other in face of different disturbances. Such oscillations between aggregate clusters are typically referred to as inter-area oscillations, which is well-studied and well-understood for the traditional operating conditions of the WECC. However, with gradual expansion in transmission level infrastructure as well as tremendous penetration of renewable power including wind and solar photovoltaic in the west coast over the next decade, several dynamical properties of the WECC will change significantly, and so will the characteristics of the inter-area oscillations and their stability margins [2, 26, 27]. Such projected changes are neither well-understood from an analytical perspective nor well-established from an experimental or validation point of view. A goal is to bridge this gap by investigating how real-time changes in operating conditions, unforeseen contingencies, and intermittency of renewable generation have an impact on the inter-area oscillations in WECC, and validate those observations using an RTDS-based emulation framework. This model studied three major phases, and answered three major questions as follows: 1. How can Synchrophasor measurements of voltage, phase angle, and frequency collected from a set of critical buses in the WECC be used to construct a reliable dynamic equivalent model of the entire system capturing the significant inter-area modes of oscillation 6

16 Canada Washington Oregon Grand Coulee 1 Hanford Colstrip Montana Wyoming Utah Pacific AC Intertie 4 San Francisco Bay Area Table Mountain Vincent Malin 3 2 Pacific HVDC Intertie Intermountain HVDC Line Arizona New Mexico Los Angeles Baja CA (Mexico) Lugo PMU location Observable bus Pseudopoint Figure 2.1: A 5-area dynamic equivalent model for the WECC power system 2. How can the identified reduced-order model be implemented and validated using a hardware-in-loop real-time digital simulation framework integrated with Phasor Measurement Units 3. How does the implemented model react to different types of contingencies, and how utility companies operating over the different clusters of the WECC can predict their local phase angle responses and prepare for the worst-case contingency happening at any other cluster. In the following, we present a detailed description of the above three research problems. 7

17 2.1.2 Motivation and Literature Review Recent analyses of phase angle and frequency oscillations in the Western Electricity Coordinating Council (WECC) and the Eastern Interconnect (EI) have highlighted the importance of constructing real-time dynamic models of large power systems from Synchrophasor measurements [28]. For example, spectral analysis of phase angles in the California-Oregon Intertie [29], or frequency oscillations between New England and the Entergy grid in Florida [33] clearly indicate the potential use of such predictive models for critical applications such as oscillation monitoring, transient stability assessment, and voltage instability prediction. However, given the large size of any realistic power system, such as the WECC or EI, it is practically impossible to derive the pre-event or post-event dynamic model for the entire network in real-time. System operators are, rather, more interested in constructing reduced-order models of the power system that capture the dominant inter-area modes of oscillation, and, hence, can predict how the different parts of the system may oscillate with respect to each other in the face of a particular event. Such reduced-order models are often referred to as wide-area models [34--36]. Preliminary results for constructing wide-area models of two-area power systems using PMU measurements have recently been presented in [37]. The authors in this paper listed two main steps for deriving these models, namely 1. identification of the dynamic equivalent model for each area, and 2. identification of the topology of the equivalent reduced-order transmission network connecting these areas. The topology identification step was not addressed in [37] as the system under study was a simple two-area system connected by a single tie-line. For multi-area power systems, however, identifying the parameters of the equivalent topology as well as that of the individual equivalent generators becomes absolutely imperative. The topology graph captures the effective impedance between the areas, while the equivalent inertia indicates the relative strength of one area with respect to another, and thereby retains the modal frequencies and the mode shapes for the inter-area oscillations. One objective here is to identify this equivalent topology and inertial parameters for the five-area WECC model shown in Figure 2.1 with well-defined inter-area modes using PMU 8

18 measurements collected from the terminal buses of each cluster. Though this is done here primarily on WECC, the methodology is identical for any generic power system model. The uniqueness of our approach compared to traditional topology identification methods are as follows: First, the majority of network reduction methods used in the power system literature are model-based, such as the methods based on modal equivalencing [38], coherency [39], and decomposition algorithm assigning coupling factors to generators [40]. In contrast, our methods are completely measurement-based, and need only a few basic information about the underlying system model. Traditional methods such as SME [43] tend to capture the details of fast local oscillations that may not be necessary for wide-area monitoring but increases the computation time. Our methods, in contrast, are based on inter-area or slow oscillation only and, therefore, will be significantly faster. In computer science literature, topology identification of large complex networks is often formulated as a combinatorial optimization problem [44]. Our methods, however, are not based on combinatorial analysis, but follow from underlying system dynamics, thereby preserving all the system-level properties as reflected in the PMU measurements. Compared to recent works of [45--47] on topology identification of generic network dynamic systems using graph-theoretic methods, and of [48] where raw PMU data was used to estimate a Thevenin equivalent model of power systems in steady-state, our approach integrates model reduction with identification by considering separation of slow and fast dynamics. Once constructed, the inter-area topology can be used for useful applications such as transient stability assessment and voltage stability assessment. For example, a common tool for assessing transient stability of a multi-area power system is the transient energy function consisting of kinetic and potential energies. As shown in [49], the potential energy function is dependent on the inter-area topology. Similarly, this topology can also serve as a critical parameter for tracking loadabilty limits for voltage, wide-area protection, and islanding schemes. 9

19 It should be noted that while the methods applied here are only to the WECC model for illustration, they are applicable to any generic power system model other than WECC as well. 2.2 Problem Formulation We first recall the general ideas on how a multi-area power system model can be reduced to its dynamic equivalent via time-scale separation. For this, let us consider a power system network consisting of n synchronous generators and n l loads connected by a given topology. Without loss of generality, we assume buses 1 through n to be the generator buses and buses n + 1 through n + n l to be the load buses. Let P m denote the vector of the mechanical power injection at generator buses, P L be the vector of total active power consumed by the loads, and P N i be the total active power injected to the i th bus of the network (i = 1,..., n + n l ), where the superscript N indicates that this power is flowing in the network as opposed to the loads. This power is calculated as: P N i = n+n l k=1 ( V 2 i r ik /y 2 ik + V iv k sin(θ ik α ik )/y ik ), (2.1) where, V i θ i is the voltage phasor at the i th bus, θ ik = θ i θ k, r ik and x ik are the resistance and reactance of the transmission line joining buses i and k, y ik = rik 2 + x2 ik, and α ik = tan 1 (r ik /x ik ). Let P N G and P N L denote the vectors of P N i calculated for generators and loads, respectively. The electromechanical model of the power system can be described as a system of differential-algebraic equations (DAE) [50]: M δ = P m P N G Dω, (2.2a) P L P N L = 0, (2.2b) where δ is the vector of generator angles, ω is the vector of the speed deviation of the generators from synchronous speed, and M = diag(m i ) and D = diag(d i ) are n n diagonal matrices 10

20 of the generator inertias and damping factors, respectively. The DAE (2.2) can be converted to a system of pure differential equations by relating the algebraic variables V i and θ i to the system state variables (δ, ω) from (2.2b), and then substituting them back in (2.2a) via Kron reduction. The resulting system is a fully connected network of n second-order oscillators with l n(n 1)/2 tie-lines. Let the internal voltage phasor of the i th machine be denoted as Ẽ i = E i δ i. The electromechanical dynamics of the i th generator in the Kron s form, neglecting line resistances, can be written as: δ i = ω i, M i ω i = P mi k ( ) Ei E k sin(δ ik ) D i ω i, x ik (2.3a) (2.3b) where ω s = 120π (rad/sec) is the synchronous speed for the 60 Hz system, for i = 1,..., n. Linearizing (2.3) about the equilibrium (δ i0, 0) results in the small signal model: δ ω = 0 I n M 1 L M 1 D } {{ } A δ ω + 0 u, (4) e j }{{} B where, δ = [ δ 1 δ n ] T, ω = [ ω 1 ω n ] T, I n is the n-dimensional identity matrix, e j is the j th unit vector with all elements zero but the j th element that is 1, considering that the input is modeled as a change in the mechanical power in the j th machine. However, since we are interested only in the oscillatory modes or eigenvalues of A, this assumption is not necessary, and the input can be modeled in any other feasible way such as faults and excitation inputs. 11

21 The matrix L in (4) is the n n Laplacian matrix of the form: L ij = ( E i E j cos(δ i0 δ j0 ) ) /x ij i j, (5a) L ii = n k=1 ( Ei E k cos(δ i0 δ k0 ) ) /x ik. (5b) It is obvious that L ij = L ji. Let us denote the i th eigenvalue of the matrix M 1 L by λ i. The largest eigenvalue of this matrix is equal to 0, and all other eigenvalues are negative, i.e. λ n λ 2 < λ 1 = 0. Assuming the magnitude of D i /M i are small, the eigenvalues of A can be approximated by ±jω i (j = 1), where Ω i = λ i. Now, assuming that the entire network consists of r coherent areas that are sparselyconnected, and the i th area consists of m i nodes with connections defined by M 1 i L i, (i = 1,..., r), one can then rewrite (4) as shown in: δ 1 1. δ 1 m 1 δ 2 1. δ 2 m 2. δ r 1. δ r m r = M 1 1 L 1 + K 1 M 1 2 L 2 + K 2... M 1 r L r + K r }{{} M 1 L δ 1 1. δ 1 m 1 δ 2 1. δ 2 m 2. δ r 1. δ r m r M 1 D δ + e j u (2.5) where, δ i j means the angle of the jth machine in the i th area. Construction of matrices K i follows from the definitions of A and M 1 i L i for i = 1,..., r. The off-diagonal blocks of the 12

22 matrix M 1 L are shown by asterisks ( ). The (i, j) th off-diagonal block shows the connectivity between areas i and j in the Kron-reduced form. Due to the assumption of coherency following from the difference between the local and inter-cluster reactances and inertias, the oscillatory modes of the matrix A will be divided into sets of (r 1) inter-area modes with eigenvalues σ 1 ± jω 1 through σ r 1 ± jω r 1. The remaining (n r) modes will be characterized by intra-area modes representing the local oscillations inside areas. In fact, as shown in [38], if the inertias M i i = 1,..., n, are of the same order of magnitude, then from (5a) it is clear that L ij will be a large positive number for nodes i and j that are connected by a short tie-line with small reactance x ij while L ij will be a small positive number for nodes that are connected by a long transmission line with large reactance x ij, leading to a sharp separation of inter-area and intra-area frequencies. Our basic assumption for dynamic equivalencing is that the (r 1) inter-area modes can be attributed to r equivalent machines. Let E E k, δe k (t), and ωe k (t) δ E k (t) denote the voltage, angle, and frequency of the k th equivalent machine, respectively. The equivalent small-signal model for the inter-area dynamics of (4) is shown in: δ E 1 δ E 2. δ E r = (M E 1 ) 1 L E 11 (M E 2 ) 1 L E (M E r ) 1 L E rr }{{} (M E ) 1 L E δ E 1 δ E 2. δ E r (M E ) 1 D E δ E + e E j u E (2.6) 13

23 where δ E [ δ E 1... δ E 1 ]T, and M E and D E are (r r) diagonal matrices of equivalent machine inertias and equivalent machine dampings, respectively. L E represents the connectivity of the r areas in the equivalent topology whose elements are as follows: L E ij = ( Ei E Ej E cos(δi0 E δj0) E ) /x E ij, i j (2.7a) r L E ( ii = E E i Ek E cos(δe i0 δk0 E )) /x E ik, (2.7b) k=1 where, x E ij is the equivalent reactance of the tie-line connecting areas i and j in the reduced-order model. Our objective is to find the equivalent topology that connects these r equivalent machines using PMU data, which is equivalent to estimating the elements of the matrix L E. Given the measurements of δ and ω from (2.5), our first task, therefore, is to apply modal decomposition techniques by which we can extract the slow components of these outputs, i.e., δ E and ω E δ E respectively, as defined in (2.6), and, thereafter, use these slow components to estimate L E i,j i, j = 1,..., r. We next review a modal decomposition technique using Hankel matrices to achieve the first task. 2.3 Modal Extraction using Hankel Matrices Modal Decomposition As discussed in the previous section, the output measurements of (2.5) will contain the contribution of both inter-area and intra-area modes. The first step in topology identification of the dynamic equivalent model is to find the slow component of each measurement. Several methods for such modal extraction have recently been proposed both in the power system literature [8, 10, 51, 52], and in the control systems literature [53] with applications to real-world power system models such as the WECC system [54]. All of these methods have their own advantages and disadvantages depending on applications. Among them, subspace identification methods 14

24 such as Eigensystem Realization Algorithm (ERA) [52] have been shown to be very useful tools for identifying slow oscillation modes from PMU data. The choice of ERA also follows from the fact that it is computationally fast and can be implemented in real-time. We next summarize the basic ERA algorithm as follows. Let us consider a general continuous-time LTI system: ẋ(t) = Ax(t) + Bu(t), y(t) = Cx(t), (2.8) where A R n n, B R n p, and C R q n are unknown state space matrices and need to be identified from the output measurements y(t) and the input u(t). We assume the triplet (A, B, C) are controllable and observable. Also, u(t) is assumed to be persistently exciting. The discrete-time equivalent of (2.8) is written as x(k + 1) = A d x(k) + B d u(k), y(k) = Cx(k). (2.9) The impulse response of (2.9) will be y(k) = CA k 1 d B d. (11) Given measurement y(k) for k = 0,..., m, we next construct two l s Hankel matrices H 0 and H 1 as: [ H 0 [ H 1 y 0 0 y 0 1 y 0 s y 1 0 y 1 1 y 1 s ], (12a) ], (12b) where l and s are positive integers satisfying (n < l, n < s, s + l m), y j i = col(y(i + j)..y(i + j + l 1)) for j = 0, 1 and i = 1,..., s. It can be easily shown that H 0 = OC and H 1 = OA d C, where O and C are observability and controllability matrices for (2.9), respectively. We next 15

25 consider the truncated singular value decomposition of H 0 by retaining its largest n singular values as 1 Ĥ 0 = ˆR ˆΣ ŜT. (13) Defining E 1 [ I p 0 p (s p) ] T and E2 [ I q 0 q (l q) ] T, the estimates for the triplet (Ad, B d, C) up to a similarity transformation can be calculated as  d = ˆΣ 1/2 ˆRT H 1 Ŝ ˆΣ 1/2, (14) ˆB d = ˆΣ 1/2 Ŝ T E 1, Ĉ = E T 2 ˆR ˆΣ 1/2. (2.11) One can next convert (Âd, ˆB d, Ĉ) to their continuous-time counterpart (Â, ˆB, Ĉ) by zero-order hold. For our application, since the eigenvalues of A satisfy the two time-scale property of (2.5), the oscillatory components of the output response of (2.8) can be estimated as r 1 ŷ(t) = (α i ± jβ i )e ( σ i±jω i )t i=1 }{{} y E (t), inter-area modes (α k ± jβ k )e ( σ k±jω k )t, (16) n 1 + k=r }{{} y I (t), intra-area modes where σ i ±jω i are the eigenvalues of Â, and the residues α i±jβ i follow from the state-space structure of (Â, ˆB, Ĉ) for i = 1,..., n 1. Therefore, given PMU measurements y(t) one can easily construct y E (t) using (2.8)-(16). Note that if y(t) is corrupted by additive white Gaussian noise, one may use the stochastic variant of ERA [55] to preserve the accuracy of estimating y E (t). It is important to note that ERA alone cannot be used for solving the topology identification problem. This is because Âd will only be a similarity transform of A d and, therefore, may not capture the topology of the system through a Laplacian structure. Thus, we have to cast the 1 Note that ERA depends on the SVD of the Hankel matrix H 0, and therefore, does not depend on the diagonalizability of A d. 16

26 problem using a parameter estimation framework as presented in Section 5. Remark 1 The standard approach for doing modal decomposition, as shown in [51] is to assume the input to be an impulse function. Accordingly, in (2.9) we assumed u(k) to be an impulse input. In fact, since we are interested in identifying only the inter-area modes, even if u(k) is not an impulse, ERA will still give accurate results provided that its frequency content do not lie in the inter-area frequency range. Remark 2 In literature, ERA has been shown to be robust to noise. For example, in [55], it is shown that if both the process and measurement noise are zero mean white Gaussian and the stochastic process is zero mean stationary, then there exist stochastic variants of ERA which preserves the accuracy of the estimated modes. Remark 3 Here, we assumed a single output to describe the ERA algorithm. However, ERA algorithm can be generalized for multiple outputs as well. In our power system application, we assumed that we have at least one measurement from any area. Then, clearly the system will be observable. Also, we assume that the input u(t) will persistently excites all slow modes of system, i.e., the dynamic equivalent model to be identified is both controllable and observable. 2.4 Description of 5-Area model As mentioned before, the WECC system is divided into five separate areas which are connected in a linear topology through long 500 kv transmission lines following the example cited in [23]. These five areas are represented by five aggregated synchronous generators (ASG) with the interconnecting 500 kv lines between any two areas can be reduced to a single equivalent transmission line between those two areas. This reduction is shown in figure 2.2. Although the equivalent transmission lines are reduced versions of real-world transmission lines, they connect five real-world sub-stations on the 500 kv network to each other cyclically. 17

27 ASG2 A 2 A 1 E 2 δ 2 E 1 δ 1 ASG1 Ĩ2 jx2 r12 jx12 jx1 P 2 PMU p12 PMU Ĩ1 jx23 V 2 θ 2 V 1 θ 1 p23 P 1 ASG3 r23 A 3 Ĩ3 P 3 E 3 δ 3 V 3 θ 3 jx3 PMU jx34 jx45 V 5 θ 5 p34 PMU P 5 r34 r45 PMU Ĩ5 jx5 Ĩ4 P 4 p45 A 5 ASG4 jx4 V 4 θ 4 E 5 δ 5 ASG5 A 4 E 4 δ 4 Figure 2.2: Electrical topology of WECC s 500kV network These sub-stations, referred to as pilot buses, are selected from each area based on the following criteria and are shown in figure 2.2: -- The sub-station must have a PMU installed at it s location -- All generators within that area lie behind this sub-station The voltage phasor, V i θ i is known at each pilot bus owing to availability of PMU data at that bus. Furthermore, the current I i α i being injected at each pilot bus can be calculated from the difference in line currents flowing in and out of that pilot bus, which are known quantities from PMU data. Ĩ i = Ĩik Ĩji (2.12) The pilot bus of a particular area also acts as the terminal bus for the aggregated synchronous generator which represents that area. Looking from the pilot bus into the area, this generator is modeled as a Thevenin voltage source with internal EMF E i δ i and Thevenin reactance jx i. Due to non-identifiability, it is not possible to model it as an impedance of r i + jx i. This is further elaborated upon in section Each aggregated synchronous generator is modeled 18

28 as a second order damped oscillator described by the swing equation (2.2a)-(2.2b). Since these ASGs are fictitious generators, their model parameters are not known, and need to be identified using PMU measurements of voltage and phase angles measured at the corresponding pilot bus. Thus, the parameter identification for the five-area model is a three step process: -- Identification of long tie line impedance r ij + jx ij -- Identification of Thevenin reactance jx i of ASG -- Identification of inertia M i and damping D i of ASG Also, as indicated in Section 3, since the ASG is obtained by collapsing coherent areas of the network, the non-coherent modes or local modes must be removed from the PMU measurements before they can be used to identify the above three quantities for each ASG. In other words, the raw PMU data contains both fast local modes as well as slow inter-area modes, and must be passed through a band-pass filter to remove the faster modes. However, since such filtering typically adds a phase shift to the slow modes, distorting the data, an alternative time-domain approach of using modal decomposition method is applied, as described in Section 3. We next briefly describe the method adopted for this particular case, namely the Prony algorithm. Prony analysis, which is a time-domain based curve fitting technique, is used to determine frequency, amplitude, phase and damping components of the equivalent PMU measurement from the pilot buses. Essentially, any stream of PMU data can be formulated as M y(t) = x(t) + n(t) n(t) + R i e λ it i=1 (2.13) 19

29 Plot of θ 2 θ 1 v/s time Original Slow Mode Content Time (secs) Figure 2.3: Slow mode component of Voltage angle difference between Station 2 and Station 1 where y(t) is the observed time response x(t) n(t) R i λ i σ i is the reconstructed signal is noise is the complex amplitude of i th component = σ i + jω i is the damping coefficient of i th component ω i is the angular frequency of i th component Prony s method returns a set of exponential and damped oscillatory components, which when combined create x(t) that provides the best possible least-squares fit to y(t). The least-squares fit is constrained by the value of M. The obtained list of components are then subject to the constraint, ω i < 2π rad/s to obtain the slow modes. The voltage angle difference between pilot bus 1 and 2, and its slow mode component obtained from the Prony algorithm are shown in Figure 2.3. For the sake of completeness, we compare the results of the Prony algorithm with that of Matrix Pencil method. In the next section we outline the estimation process of the three essential model parameters listed above using the extracted slow mode components of the PMU 20

30 measurements. 2.5 Model parameter estimation Identification of inter-area tie-line impedance The reduced-order model assumes that each station S i is connected to the next station S j through a single equivalent transmission line. Since this line is a reduction of several long 500 kv transmission lines, the equivalent-π model of the transmission line must be used for analysis. In order to calculate the equivalent shunt admittance at the end of each line, we require the voltage at the pilot buses and the line charging current. However, the line charging current at any bus is not available from PMU data, and hence it is not possible to estimate the equivalent shunt admittance from PMU data alone. The following two alternative approaches can be adopted: -- The shunt admittance values of a transmission line of a given length can be estimated from typical values of admittance per mile values for 500kV transmission lines for a given conductor configuration, or -- The shunt admittance of the transmission lines can be merged with the shunt load present at the ASG, thus effectively eliminating them from analysis. To ensure that all parameters can be evaluated using PMU data alone, the second approach is adopted in this paper, and the long transmission lines are represented by pure series impedance. This series impedance can be calculated from the voltage phasors Ṽi and Ṽj available at the pilot buses from PMU data. Additionally, the physical 500 kv lines between the aforementioned two pilot buses are identified, and lines with substantially larger currents are selected for analysis. The net current I ij between the two pilot buses along the fictitious transmission line is taken as the phasor sum of the currents in the previously selected transmission lines. Using the voltages and currents thus obtained, the inter-tie impedance can now be calculated using Ohm s law as: Ṽ i Ṽj = Ĩij Z θ z (2.14) 21

31 Separating out real and imaginary parts, V i cos θ i V j cos θ j = I ij Z cos (θ z + α) (2.15) V i sin θ i V j sin θ j = I ij Z sin (θ z + α) (2.16) Each data-point has two equations with two unknown parameters Z and θ z. Thus the above set of equations can be solved algebraically using least squares technique for each data-point to calculate Z and θ z Identification of intra-area Thevenin reactance After the estimation of inter-tie impedances, the next logical step is to estimate the small intra-tie impedance values that connect the generator voltage source to the pilot bus. The estimation of internal voltage magnitude E i, internal voltage angle δ i and intra-tie impedance x i was approached from several directions, some of which are listed below. Before describing these approaches, the assumptions made in these techniques are listed. 1. Assumption 1: E i is assumed to be a constant magnitude This assumption is important because for every point of data, there are two equations. Thus there are 2N s equations overall. The unknowns in these equations are E i, δ i, r i and x i. If E is a varying quantity, then we will have 2N s + 2 variables and only 2N s equations. Thus the problem is not identifiable for varying E i. If E i is considered as a constant but unknown parameter, the number of variables in the problem reduces to N s + 3. Thus this case is theoretically identifiable for N s > 3. This is true for PMU data which is usually three to five minutes long sampled at 15 to 30 samples per second, making N s very large. It is also reasonable to take E i constant since the second order model for the generator is used for analysis. Field dynamics are ignored due to the absence of field currents and voltages for the ASG. 22

32 Unknown Angle E α δ V IZ Figure 2.4: I Phasor Diagram for the Aggregated Synchronous Generator Problem of non-identifiability From the figure below, it is clear that the phasors E, V and IZ form a triangle. The angles, δ and α are marked in the figure. Thus, in this triangle sine rule can be written as follows: a sin A = b sin B = c sin C (2.17) Here, a, b and c are the lengths of the sides opposite to the vertices A, B and C respectively. Thus: a = l(bc), b = l(ac), c = l(ab) (2.18) For the triangle above: E sin (θ z + α) = IZ sin δ = V sin (180 θ z α δ) (2.19) The above set of equations cannot be solved for unique values of E, Z and θ z. This is because none of the ratios are known and the sides of the triangle E and IZ cannot be uniquely determined. Another way to look at this is as follows. Both E and IZ are unknown. V is known, but E and IZ both can take an infinite pair of values so that they satisfy V = EIZ. Hence, to 23

33 make the system identifiable, the following assumptions are made: -- E i = 1 per unit, and -- r i = 0, or θ z = 90, or Z i = jx i. Using the above two assumptions, equation (1.11) reduces to: 1 sin (90 + α i ) = I ix i sin δ i = V i sin (90 α i δ i ) (2.20) or, 1 cos α i = I ix i sin δ i = V cos (α i + δ i ) (2.21) From the above equation, the following two equations can be written: δ i = cos 1 (V i cos α i ) α i (2.22) x i = sin δ i I i cos α i (2.23) Thus, the system is identifiable in the light of these two assumptions. It may be noted that these are all algebraic relationships and x i and δ i can be calculated for each and every data point Identification of Equivalent Inertia and Damping After the estimation of the inter-tie and intra-tie reactance values for the five-machine aggregated synchronous generator equivalent network for the WECC system, estimation of M i and D i from PMU data and reactance values is the next step. To estimate M i and D i for each ASG, filtered PMU data from the pilot buses as well as the reactance values estimated in the previous steps are used. For the i th generator ASG i, the sma--signal electro-mechanical dynamics using the 24

34 models of Section 2 can be represented by δ i ω i = Using the expression for P ei as ω s ω i 2D i M i ω i 1 M i P ei + 1 M i P mi (2.24) P ei = E iv i x i sin(δ i θ i ) (2.25) and linearizing we obtain, P ei = E i x i sin(δ i0 θ i0 ) V i + E iv i x i cos(δ i0 θ i0 )( δ i θ i ) (2.26) Moreover, I = Ȳbus V can be written using Kirchoff s Current law. But for the generators, from Kirchoff s Voltage law, I = Ȳg( E V ), where Ȳg = diag(1/jx i ). Combining these equations, we get V = Ȳ E, where Ȳ = (Ȳbus + Ȳg) 1 Ȳ g. Separating out real and imaginary parts, V R = V i cos θ i = Y R E i cos δ i Y I E i sin δ i (2.27) V I = V i sin θ i = Y I E i cos δ i + Y R E i sin δ i (2.28) Linearizing, V R = cos θ i0 V i + V i0 sin θ i0 θ = ( Y R E i sin δ i0 Y I E i cos δ i0 ) δ i (2.29) V I = sin θ i0 V i + V i0 cos θ i0 θ = ( Y I E i sin δ i0 + Y R E i cos δ i0 ) δ i (2.30) Through mathematical manipulation of (2.29) and (2.30), the following result is obtained: V θ = F G 0 5X5 0 5X5 δ ω (2.31) 25

35 where F G = diag(cos θ i0) diag(v i0 sin θ i0 ) diag(sin θ i0 ) diag(v i0 cos θ i0 ) 1 X Y Rdiag(E i sin δ i0 ) Y I diag(e i cos δ i0 ) Y R diag(e i cos δ i0 ) Y I diag(e i sin δ i0 ) Substituting (2.31) in (2.26), P ei can be expressed purely as a function of δ as follows, (2.32) P ei = L i δ (2.33) Substituting 2.33 in 2.24, the following result is derived: δ i ω i = ω s ω i 2D i M i ω i 1 M i L i δ i + 1 M i P mi (2.34) The above equation can be written in a generalized form for all five aggregated synchronous generators as follows: δ ω = 0 5X5 ω s I 5X5 diag ( 1 M i ) L diag ( ) 2Di M i δ ω + 0 5X5 ( ) diag 1 Mi P m (2.35) It can be seen that (2.35) and (2.31) are of the form Ẋ = AX + BU (2.36) Y = CX (2.37) where matrices A and B are unknown and are parameterized by M i and D i. C is known as the network structure and parameters are known from and Therefore, to formulate the least squares problem, M i, D i and P mi are given arbitrary initial values within certain upper and lower bounds, and the resulting matrices  and ˆB are calculated. These matrices are used to calculate ˆX(t), an estimate for X by solving the differential equation 2.36 for step 26

36 change in u(t). The computed value of ˆX(t) is then used to calculate an estimate of Y using Ŷ (t) = C ˆX(t). The least squares problem is finally formulated as the optimal solution of M i, D i and P mi obtained by minimizing the integral t t=0 Y (t) Ŷ (t) 2 2dt (2.38) where Y (t) is obtained from PMU measurements. For the purpose of simulation, Y (t) was restricted only to θ(t) to reduce computational burden. Line Reactance Station 1-Station j Station 2-Station j Station 3-Station j Station 4-Station j Table 2.1: Calculated inter-tie impedance values Machine Tie-line Reactance Calculated Used Station j j Station j j Station 3-3.4j j Station j j Station j j Table 2.2: Calculated intra-tie impedance values 27

37 Chapter 3 Model Validation 3.1 Model Validation After identification of the model parameters in 2, the next step was to validate these parameters by further tuning them until the predicted phase angle responses of the estimated model closely matched the inter-area component of the angles obtained from the measured PMU data. For the purpose of implementation in a real-time digital simulator, several other model parameters also needed to be used. These parameters include load resistances, governor power set points, internal machine voltage references, machine inertia, machine damping, and various reactance values in the model. Table 3.1 gives an overview of all the final values used in the model. In the coming sections it will be explained in detail how these values were calculated, tuned, and altered in order to allow the model to closely represent the real-world system. 3.2 Area 3 Tie-line Impedance Negative The least squares calculations from [66] produced a negative tie-line impedance at Area 3, as can be seen in Table 3.2. This is because of the existence of a large capacitor bank at this point in the real WECC system that helps to sustain the voltage at this bus. The least squares calculations do not account for the presence of capacitors, but merely try and calculate inter 28

38 Machine Area 1 Area 2 Area 3 Area 4 Area 5 Inertia MWs/MVA Damping (D) Rated MVA Machine Internal Voltage pu pu pu pu pu Bus Load Prefault MW Bus Load Postfault MW Pre-Fault Gov. Load Ref pu pu pu pu pu Post-Fault Gov. Load Ref pu pu pu pu pu Tie Line Z j j j j j Exciter Model (IEEE) Type ST1 Type ST1 Type ST1 Type ST1 Type ST1 Governor model Type 1 Type 1 Type 1 Type 1 Type 1 Bus Type PQ PQ Slack PQ PQ Table 3.1: Model parameters used for RTDS implementation and intra-area tie-line values to minimize the error integral in [66]. Area 3 is a very heavy load bus representing the San Francisco metropolitan area. Without a capacitor placed on this bus, the voltage would sag to unacceptably low levels. This was seen in the RSCAD model as well. Without considering negative tie-line impedance, the voltage at Area 3 was drooping very low in the model. The addition of a capacitor to the model allowed the voltage to become a more acceptable level while also better representing the real-world setting. The value of this capacitor was chosen such that the voltage on this bus remained in a reasonable range. Machine Tie-line Reactance Calculated Used Area j j Area j j Area 3-3.4j j Area j j Area j j Table 3.2: Calculated Intra-Tie Ompedance Values 29

39 Bus Voltage Simulated Real Data Area pu pu Area pu pu Area pu pu Area pu pu Area pu pu Table 3.3: Bus Voltages 3.3 Voltage Tuning Though the phase angles were of primary interest for matching, matching the voltages to a reasonable level was important as well. The voltages were matched during the load-flow calculations computed in RSCAD. Internal voltages on the buses inside the five machines were tuned so that load-flow compilation yielded a close match on bus voltage value. The voltages were matched to the last point of data immediately prior to the fault time in the set of PMU data received. Values were matched by repeated changing of voltage set points and recompilation of the draft. The voltages, however, did not match quite as well during run-time when the model was actually running. Table 3.3 lists the voltages viewed in run-time versus the voltages seen in the PMU data. The values are close, lying within two percent of the actual PMU data values, which was deemed to be close enough for the model s purpose. Further retuning of the internal bus voltages to match run-time values rather than load-flow values is also possible, but was not pursued for the sake of simplicity. 3.4 Fault Power Flow Matching via Resistive Load Swapping Observing the plots in Figure 3.1, one can see that at the instant of the fault i.e., at t = 1.5 seconds, the filtered PMU data demonstrated a sudden increase or decrease in phase angle. The actual values of these changes are shown in Table 3.4. Three of the four phase angles in the filtered PMU data displayed a large change in angle at the immediate time of the fault. Using 30

40 o Line Angle Power Flow in MW Pre-Fault Immediate Post-fault Difference Pre-Fault Post-fault Change Area 1-Area Area 2-Area Area 3-Area Area 4-Area Table 3.4: Voltage Angle and Power Flow Change Across Major Tie-Lines (3.1) in combination with the knowledge of the bus voltages and inter-area line reactances, it was possible to calculate the change in power necessary to recreate these instantaneous phase angle changes. The calculated change in power flow is shown in Table 3.4, and was modeled as the addition or subtraction of resistive loads on appropriate buses in the system. P ei = E iv i x i sin(δ i θ i ) (3.1) 3.5 Phase Angle Tuning via Governors Simply swapping out resistive loads during fault, as described in the previous section, was not enough to match pre and post-fault phase angles of the model up against the steady-state values of the PMU data collected from the real-world system. The pre and post fault steady-state phase angles were further tuned using the governor load reference set points during the RTDS run-time of the model. The governors of the machines allow changing the load reference set point of the machines during run-time. This allowed the exact tuning of the phase angle steady state values during run-time both pre and post-fault by tuning the power set-points of these machines both pre and post-fault. The model values of the steady-state phase angles pre and post-fault were compared against the PMU data in Table 3.5. Essentially, the machines have different power set-points post-fault than they do pre-fault, and this change in power set-point has allowed very close matching of the steady-state phase angles. The exact values used for these governor load reference set points are shown in Table 3.1. The reasoning behind separating 31

41 Line Pre-fault Angle Post-fault Angle Simulated Real Data Simulated Real Data Area 1-Area Area 2-Area Area 3-Area Area 4-Area Table 3.5: Voltage Angle Simulated v/s Real Values the swapping of resistors to model the instantaneous power changes across the lines and the changing of power set points in the governor is because changing the governor set point changes the phase angles across the lines on a much slower time scale than changing the immediate load at each bus. In order to recreate both the large, quick changes in phase angles of several degrees that occurs the instant the fault occurs as well as the gradual approach of the phase angles to a steady-state value, both of these methods were implemented together. 3.6 Inertias and Damping Values As described in 2, the original inertia and damping values were calculated using a least squares method to match the filtered PMU data. This method alone, however, yielded a poor result. The original inertia of Area 1 was calculated to be much smaller than the other areas. It was also very under-damped, reflecting a low calculated damping coefficient. The calculated inertia and damping of the machines are shown below in Table 3.6. The inertia and damping of Area 1 was altered such that the new transient response better matched the transient response of the filtered PMU data. Various values were attempted and gauged by how well the integration of the original dataset compared with that of the model dataset. The model response with Area 1 demonstrating changes in inertia and damping were compared against the filtered PMU data. The inertia of Area 1 was also deliberately altered such that the first major peak in phase angle occurred at the same time. Observing the plots in Figure 3.1, one can see the response between Area 1 and Area 2 has been significantly improved while the other three transient responses remain almost identical to the model response prior to changing the inertia and damping of 32

42 Area Sensitivity Analysis In order to test the model, a set of contingencies were simulated to observe oscillations and analyze them to validate the model. These include -- Generator tripping resulting in loss of generation and inertia -- Line tripping resulting in increase in intra-area reactance. 3.8 Contingencies There were three sets of contingencies tested on the model thus far. The first set of contingencies involved a case where ten percent of the inertia was lost on each bus. A separate case was run for each machine losing ten percent inertia. The simulated loss of 1300 MW of generation on Area 5 was used as a disturbance event and the phase angles on all four inter-area lines were recorded. The results are shown below in Figure 3.2. It can be seen that changing the inertia by a small amount has little effect on the model s transients and no effect on the steady-state values of the model. Next, the intra-area tie-line impedance of each machine was individually increased by integer multiples of itself until instability in the model occurred. The last point before instability was used as the new value for intra-area impedance. These values ended up being larger for some machines than others. Area 1 was able to be increased by a factor of ten Machine Inertia Damping Calculated Model Calculated Model Area Area Area Area Area Table 3.6: Inertia and Damping 33

43 19 18 Angle Between Area 1 and Area 2 Real Transient Response Model Transient Response Angle Between Area 2 and Area 3 Real Transient Response Model Transient Response Angle Between Area 4 and Area 3 Real Transient Response Model Transient Response Angle Between Area 5 and Area 4 Real Transient Response Model Transient Response Figure 3.1: Transience Modal Comparison 34

44 before instability, whereas merely doubling the intra-area impedance at Area 5 caused model instability. These plots are in Figure 3.3. Notice that in every case there is one phase angle that is almost completely undamped. This is where the instability would start when the intra-area impedance was increased by a small amount for any generator. Angle Between Area 1 and Area 2 Angle Between Area 2 and Area Original Area 1 10% Area 2 10% Area 3 10% Area 4 10% Area 5 10% Angle Between Area 4 and Area Original Area 1 10% Area 2 10% Area 3 10% Area 4 10% Area 5 10% Angle Between Area 5 and Area Original Area 1 10% Area 2 10% Area 3 10% Area 4 10% Area 5 10% Original Area 1 10% Area 2 10% Area 3 10% Area 4 10% Area 5 10% Figure 3.2: Loss of Inertia Comparisons 35

45 20 Angle Between Area 1 and Area 2 Angle Between Area 2 and Area Original Area 1 x10 Area 2 x5 Area 3 x5 Area 4 x3.5 Area 5 x Original Area 1 x10 Area 2 x5 Area 3 x5 Area 4 x3.5 Area 5 x Angle Between Area 4 and Area Angle Between Area 5 and Area Original Area 1 x10 Area 2 x5 Area 3 x5 Area 4 x3.5 Area 5 x Original Area 1 x10 Area 2 x5 Area 3 x5 Area 4 x3.5 Area 5 x Figure 3.3: Impedance Comparisons 36

46 Chapter 4 Impacts of Wind Penetration 4.1 Wind Generation in the WECC Wind penetration is on the rise, especially in the Western part of the US. As the level of wind penetration grows, the dynamics of the power system will change. An increase in wind penetration can cause contingencies on the power system related to a loss of inertia at the bus with wind penetration or an increase in intra-area impedance of the this bus. The ultimate purpose of this controller is to counteract the degradation of power system stability caused by bringing more wind penetration online. For this reason, a wind farm has been added to the model of the WECC. 500MW of wind penetration was added on area three. The turbine is a Doubly Fed Induction Generator (DFIG) type wind turbine with the necessary power electronics to interface with the grid frequency. The turbine is 2.0MW but the output current of the turbine was scaled up such that it will generate 500MW to the grid, representing a large aggregate of these turbines operating in parallel. Since intra-wind-farm dynamics are not within the scope of this model, it is acceptable to model a larger amount of wind penetration in this way. More information regarding the design of the turbine model can be found in [62], [63], and [64]. Information regarding the implementation of the model in RSCAD software can be found in [69]. 37

47 Since the machine on area three represents an aggregate, it is reasonable to assume a fraction of the generation on this bus coming from wind would subsequently result in some generation being brought offline in area three. An offline machine results in no additional inertia in the area, and thus this must be accounted for in the WECC model. A fractional portion of the inertia on area three was removed to represent this phenomenon. This fraction can be represented by Equation 4.1, where M 1 represents the new bus inertia, M 0 represents the original inertia calculated in [66], P 0 represents the generation on area three, and P w represents the amount of generation coming from wind power. M 1 = M 0 P 0 P w P 0 (4.1) Four test cases were ran and compared, plotted below in Figure 4.1. In all cases a four-cycle, three-phase line-to-ground fault was applied on area three exclusively to excite the system. The cases contained are a default, high inertia case where neither wind penetration nor inertia removal via (4.1) was conducted. This case was compared against a case where just inertia was removed from the bus, represented by a low inertia case. These two cases were then compared against cases where wind penetration was added at the expense of conventional power output on area three. The resulting power outputs of each aggregate machine are shown below in Table 4.1. Observing Figure 4.1, one can see removal of inertia and addition of wind penetration both have a negative influence on system transience, with both negative and positive swings reaching further and in greater discrepancy in the angle between areas two and three, closest in proximity to area three. The case where wind was added but no inertia is subtracted is akin to wind penetration causing heavy inertia plants such as coal-fired units running at a lower capacity or governor level without removal from the grid. Thus, their inertia is still present and aids in preventing more intense swings. The case where wind is added and inertia is subtracted as well from the conventional aggregate machine is representative of a reliable wind forecast allowing decommissioning of conventional, heavy inertia units with the expectation of wind replacing that generation in some plants. The next couple sections will explore a few more windy scenarios 38

48 Table 4.1: Power Outputs of Aggregate Machines Area 1 Power Output Area 2 Power Output Area 3 Power Output Area 4 Power Output Area 5 Power Output No Wind, Original 500MW Wind, No Wind, 500MW Wind, Inertia Lower Inertia Lower Inertia Original Iner- tia for WECC! 4.2 Wind Penetration by Area A test was conducted on WECC to examine the impact wind penetration has on each of the five areas. The purpose of this test was simple; to examine inter-area oscillations present in WECC and how these oscillations change when wind penetration is added. The test was conducted by adding 700MW of wind penetration on each area individually with the exception of Colstrip due to less than 700MW of generation coming from Colstrip originally. Subsequent with addition of wind penetration on a bus, inertia was subtracted from the corresponding aggregate synchronous generator on that bus via (refeqn:inertiaremoval). In order to perturb the model equally in all areas, the model was excited by a fault of duration four cycles and type three-phase line-to-ground on all five areas simultaneously. Pre-fault steady-state power from the corresponding aggregate synchronous generator was subtracted in quantity sufficient to match inter-area steady-state angle values to such that the state of power-flow was held constant. In general, 700MW of generation was subtracted from 39

49 Angle Between Area 1 and Area 2 Angle Between Area 2 and Area MW Wind Low Inertia 500MW High Inertia 0MW Wind High Inertia 500MW Wind Low Inertia MW Wind Low Inertia 500MW High Inertia 0MW Wind High Inertia 500MW Wind Low Inertia Angle Between Area 4 and Area MW Wind Low Inertia 500MW High Inertia 0MW Wind High Inertia 500MW Wind Low Inertia Angle Between Area 5 and Area MW Wind High Inertia 500MW Low Inertia 0MW Wind Low Inertia 500MW Wind High Inertia Figure 4.1: WECC Transient Response with Wind on Area Four 40

50 the corresponding generator, but the exact power values of the machines for each case are shown in Table 4.2. Table 4.2: Power Outputs of Aggregate Machines Area 1 Power Output Area 2 Power Output Area 3 Power Output Area 4 Power Output Area 5 Power Output No Wind Wind at Wind at Vincenlin Wind at Ma- Wind Palo Verde Grand Coulee at The results of these tests run on WECC can be seen plotted below in Figure 4.2. This is one of many contingencies run on WECC and by simply observing the plots it was immediately obvious area five was most sensitive to the addition of wind penetration. Intensity of the transient swing rose much more when wind was placed on area five than on any other area and damping decreased. Also, observing specifically the angle between areas five and four, one can see the most intense oscillation. In all cases, the most damped and least intense swing was observed when no wind penetration existed. 41

51 Angle Between Area 1 and Area 2 Wind Area 2 Wind Area 3 Wind Area 4 Wind Area 5 Default Case Angle Between Area 2 and Area 3 Wind Area 2 Wind Area 3 Wind Area 4 Wind Area 5 Default Case Angle Between Area 4 and Area Wind Area 2 Wind Area 3 Wind Area 4 Wind Area 5 Default Case Angle Between Area 5 and Area Wind Area 2 Wind Area 3 Wind Area 4 Wind Area 5 Default Case Figure 4.2: WECC Transient Response with Wind 42

52 Chapter 5 Wide-Area SVC Control Design 5.1 SVC in the WECC Earlier in Chapter 2, a reduced-order model of the Western Electricity Coordinating Council (WECC) power system using mathematically derived parameters from real Synchrophasor data was constructed. These parameters included inter and intra-area impedances, inertias, and damping factors for aggregate synchronous generators representing five geographical, and yet coherent, areas of WECC. In this chapter we use this reduced-order model as a tool to design a supplementary controller for a Static VAr Compensator (SVC). Wide-area feedback consisting of phase angle and frequency measurements from Phasor Measurement Units (PMUs) in the other areas is used to design this controller. The objective is to damp the inter-machine oscillation modes of the reduced-order model, which in the full-order system corresponds to inter-area oscillations. The controller input is chosen via statistical variance analysis, and its parameters are tuned to improve the damping factors of the slow modes. The model is implemented in a real-time digital simulator, and validated using a wide range of disturbance scenarios. The closed-loop system is observed to be highly robust to all of these disturbances as well as the choice of operating points. Detailed experimental analyses of the capacity of the SVC to satisfy the damping specifications of supplementary control are also presented via multiple contingencies. 43

53 The results are promising in aiding damping of inter-area modes in WECC, especially at a time of increasing penetration of wind and other renewable resources. We start from the reduced-order swing model of the WECC derived in Chapter 2 and design a wide-area supplementary controller for a Static VAr Compensator (SVC) sited between two areas. Following the Static VAr System installed in between southern California and Arizona regions of WECC [32], we choose the SVC location at an intermediate bus between areas 4 and 5, as shown in Figure 2.2. The objective is to damp the oscillation modes between all the aggregate machines, which in the actual system will correspond to inter-area oscillations, i.e., oscillations between all the areas. The interesting aspect of this design is that although it is based on a reduced-order model, the designed controller can be easily implemented in the actual WECC system since the pilot buses retain their identity. Note, however, that the structure of the model mandates the controller to be a in shunt configuration. For example, one will not be able to use this model to design a series controller such as a Thyristor Controlled Series Compensator (TCSC) along a transmission line connecting two areas [30, 31], simply because of the fact that the tie-lines retained in the model are equivalent tie-lines that do not exist in the actual system. Similarly, conventional damping controllers such as Power System Stabilizers (PSS) are also not permissible for this model since all the ASG s are aggregate generators. The basic approach for the control design presented here is twofold. First, a nominal PI controller is designed using local output feedback, and the gains are tuned for optimal closed-loop damping of the inter-area power flows. Thereafter, a supplementary controller is designed using remote feedback of voltages and phase angles from other pilot buses, thereby forming a wide-area control loop. This control strategy is especially suitable as wind penetration is on the rise in the WECC, causing the nominal dynamics of the grid to change in various ways as seen earlier in Section 3.8. Several studies have been done in recent past on FACTS/SVC design for oscillation damping [29]. Majority of these designs, however, need precise information about all the intra-area network and machine parameters surrounding the FACTS device. Our controller, in contrast, 44

54 only needs aggregate model information, and PMU data feedback from the pilot buses, and therefore is much easier to design, and simpler to implement, once the reduced-order model is estimated accurately. 5.2 SVC Nominal Controller Tuning A Static Var System (SVS) is defined as a combination of discretely and continuously switched Var sources that are operated in a coordinated fashion by an automated control system. Following the WECC SVC report in [32] we assume the SVS model for our control design to be comprised of a thyristor based SVC, coupled with coordinated mechanically switched shunts (MSSs). It is assumed that at least one thyristor controlled reactor (TCR) branch exists. Thus, for the purpose of positive sequence simulations, the SVC can be modeled as a smoothly and continuously controllable susceptance throughout its entire operating range. We consider a SVC located between areas 4 and 5 that includes a 117 MVAR variable inductive reactance, and two 91 MVAR switchable capacitor banks. A droop of 4% is necessary to allow the SVC to operate within limits during faults of desired excitation capabilities. The SVC s base controller is a PI controller. The input to the PI controller is a filtered voltage measurement on the local bus of the SVC, measured in per-unit. This voltage input signal is filtered and SVC droop is compensated for before the signal reaches the input of the PI controller. The output of this PI controller is responsible for controlling the reactive elements in the SVC, and some switching logic is responsible for activating or deactivating the capacitor banks of the SVC. Greater detail regarding the SVC controller is outside the scope of this thesis, but it can be described in greater detail in [68]. The two constants, k p and k i, must be tuned to appropriate values to optimize SVC performance. In order to tune these two constants, Zeigler-Nichols tuning method was used [67]. Zeigler-Nichols method for tuning PI controllers is a systematic method for tuning the controller that can be completed given the ability to experiment with the model and perform some simple tests. This method is particularly useful when the plant of interest for control is large, complex, 45

55 and unknown, as is the case for the WECC power system model, especially with both wind and an SVC integrated into the model. In order to use Zeigler-Nichols tuning method for PI controllers, a unit step input was applied to the SVC controller where the per unit voltage measurement would normally be applied. The resulting change in PI controller input, in this case filtered per unit voltage, was observed and the data needed for Zeigler-Nichols method collected using simulation software. Figure 5.1 shows the means by which the system was excited to collect the necessary data to complete Zeigler-Nichols method. Vref VPU Input PI - Controller SVC Reactors Figure 5.1: SVC PI Controller The PI controller input V P U was disconnected and a step input on Input3 was applied instead. The change in the normal PI controller input, V P U, was collected. The data collected is shown plotted in Figure 5.2. This data is known as the Process Reaction Curve for the plant [68] and allowed computation of PI controller parameters. The lag L, rise time T, and change in amplitude A were derived from the data shown in Figure 5.2. Using Equations 5.1 and 5.2 it was possible to calculate k p and k i for this PI controller. k p = 0.9T AL (5.1) 46

56 0.02 Step Response of SVC Voltage Voltage Reference Figure 5.2: SVC Process Reaction Curve k i = 0.3 L (5.2) The computed values for the SVC located between area four and area five in the WECC for the PI controller came to be k p = 5.18 and k i = These results were used as the tuned parameters for the PI controller in the SVC. Upon installing this SVC into the WECC model, power system slow-mode damping was improved as shown in Figure 5.3, however, significantly more improvement using wide-area control, i.e., by feeding back signals from the remote pilot buses, is possible. This motivates us to design an additional supplementary controller that works in conjunction with the local nominal controller. 5.3 SVC Local Measurement Delay Contingency A brief test was conducted on the reduced-order model with the purpose of investigating the impact measurement delay had on the performance of the SVC s ability to damp the inter-area oscillations during transience. For this particular set of tests, the SVC s droop value was held at four percent and the system was disturbed by a four-cycle line-to-ground fault on all five 47

57 Angle Between Area 1 and Area 2 Baseline Model Wind Online Angle Between Area 4 and Area Baseline Model Wind Online Angle Between Area 2 and Area 3 Baseline Model Wind Online Angle Between Area 5 and Area Baseline Model Wind Online Figure 5.3: WECC Transient Response Improvement with SVC 48

58 area buses simultaneously. It should be noted that during this test, no wide-area controller was implemented. The SVC was operating locally with local voltage control only. Four cases were tested. 1. Normal Operation Transient: SVC is operating optimally with no measurement delay. 2. Small Delay: SVC has 100ms of measurement delay between local bus voltage measurement and control input. 3. Medium Delay: SVC has 200ms of measurement delay between local bus voltage measurement and control input. 4. Unstable Delay: SVC has 350ms of measurement delay between local bus voltage measurement and control input. The transience seen across the four inter-area transmission lines are shown below in Figure 5.4. Regardless of delay, transience is identical with one exception. Increased delay causes instability on the SVC and causes it to oscillate. Figure 5.4 also shows the output reactive power from the SVC and displays this phenomenon nicely. The SVC, however, at least in this model, does not have the capacity to propagate this instability into the entire system. 5.4 Selection of Supplementary Control Input The supplementary controller for the SVC will require an additional input signal, shown by Input3 in Figure 5.1. This signal will be a measurement of some quantity in the power system model. The viable choices are rotor angles of generators, speed deviations of generators, electrical power of some machines, and electrical power on a branch [65]. In the WECC model only the five pilot buses exist in the real-world, the machines, loads, and intra-area impedance not actually having a real-world translation. This narrows down the choice to one viable option, which is to use the phase angle between two pilot buses as our input. 49

59 Angle Between Colstrip and Grand Coulee No Delay 100MS Delay 200MS Delay 350MS Delay Angle Between Vincent and Malin SVC Output (pu) No Delay 100MS Delay 200MS Delay 350MS Delay Output of SVC No Delay 100MS Delay 200MS Delay 350MS Delay (a) SVC Output for Delay Test Voltage (Volts) Angle Between Grand Coulee and Malin No Delay 100MS Delay 200MS Delay 350MS Delay Angle Between Palo Verde and Vincent No Delay 100MS Delay 200MS Delay 350MS Delay x Voltage at Devers 105 No Delay 100MS Delay MS Delay 350MS Delay (b) SVC Local Bus Voltage for Delay Test Figure 5.4: WECC Transient Comparison with Local Delay 50

60 Figure 5.5 shows the supplementary controller. The input to this controller for both branches has been selected by the process shown in Subsections The output of this controller is added to the voltage measurement of the local bus, in per unit. This summed quantity leads to the PI controller of the SVC which would normally only have the per unit local bus voltage, V P U, applied. Figure 5.5: Supplementary Controller Input Choice of Control Metric In order to measure the improvements made by a controller on the transient response of a power system, a metric needs to be defined. In previous sections, no metric has been defined by which to gauge improvements in transience and only visual observation of changes in the plotted transient response have been addressed. The WECC has five aggregate machines, of which inter-area modes are present. The system should contain four slow-mode frequencies, but each phase angle may not exhibit large components of each frequency. Eigensystem Realization Algorithm (ERA) is an algorithm that allows the extraction and separation of modal components of a transient response. Using ERA, 51

61 it is possible to take the phase angle transience data from the software simulation in RSCAD and break it down into separate frequencies, residues, and damping values, often shown as pairs of imaginary poles. It is often necessary to allow ERA to create a very high order system that accurately represents the response seen in the input data. For this particular decomposition, a system order of 500 was used. Only a few pairs of poles, however, are important. For example, a plot of one phase angle transience is shown below after having been passed through the bandpass filter, F (s), shown in Equation 5.3. When concerned with observing inter-area modes in a power system, typical values for this bandpass filter are w l = 2π 0.1, w u = 2π 1.0 to isolate frequencies between 0.1Hz and 1.0Hz. F (s) = (w u w l )s s 2 + (w u w l )s + w u w l (5.3) ERA reconstructs the A, B, C, D matrices for the state space that would have a matched impulse response as the data passed into the algorithm. The frequencies, residues, and damping of the slow-mode poles of the A matrix will be the metric used to observe improvement or degradation of system performance due to the controllers operation. An example of this pole finding technique will be shown below and will use the data present in Figure 5.3. Using the data for phase angle four before the SVC was implemented, ERA has identified three pairs of complex poles that shape the transient response. These are listed below in Table 5.1. Table 5.1 contains three modal components of the data, of frequencies Table 5.1: ERA Example Data Frequency Damping Residue

62 0.1489Hz, Hz, and Hz. These three components of the transient response are plotted in Figure 5.6 along with the sum. The red line in the plot represents the decomposed mode displayed, whereas the blue plot represents the original transient response that has been decomposed. Notice when summed, these three pairs of poles form a very close match with the original signal. This method of decomposing and observing frequencies, damping values, and residues will be used when necessary as a metric for observing the change in power system transient response. 1.2 selected system impulse response, selection number selected system impulse response, selection number (a) Decomposed Transient Response, Hz (b) Decomposed Transient Response, Hz 1.2 selected system impulse response, selection number selected system impulse response, selection number (c) Decomposed Transient Response, Hz (d) Original Transient Response Figure 5.6: Decomposition of Transient Response 53

63 5.4.2 Selection of an Input Signal Selection of which signal to use as the supplementary controller s input requires determining which signal is most robust to changes in system steady-state operating point [65]. An impulse input to the SVC controller will be applied and the resulting transient response of the inter-area phase angles will be decomposed using ERA described in Section This process will be repeated for many different randomized operating points on the WECC. These operating points will be determined by taking key parameters in the WECC and randomizing them. These key parameters are the load reference of each machine s governor and the amount of wind penetration present at Vincent. By randomizing these parameters, a randomized profile of power flows across the major transmission lines, and thus a randomized profile of the steady-state phase angles across the major transmission lines, will be created. The randomized parameters will fit the Gaussian profile described by Equation 5.4, where P k represents the updated, random parameter for test case k and P 0 represents the baseline parameter. Figure 5.7 shows the distribution of steady-state phase angles in degrees per ohm of impedance on the line to avoid some distributions appearing wider simply due to the angles being across lines of differing impedance values. Note that while they are not identical, the phase angle variations in the model due to these randomized parameters distribute across all four phase angles similarly. P k = e (x P 0 ) (5.4) The model was then excited using an impulse input at the SVC controller, at the location of Input3 in Figure 5.1, and the resulting transient response of the four inter-area phase angles of the model were collected and decomposed by ERA, described in Section Plots of the variation of transient response throughout the series of test cases can be seen in Figure 5.8. Each phase angle exhibited two dominant slow-mode frequencies that varied in residue as the steady-state operating point of the model was varied. Often there was a third sometimes 54

64 Phase Angle Case Variation 0.4 Angle(Degrees/Ohm) Angle Figure 5.7: Phase Angle Case Variation 0.15 Angle Between Area 1 and Area Angle Between Area 2 and Area Angle Between Area 4 and Area Angle Between Area 5 and Area Figure 5.8: Phase Angle Transience of Randomized Tests 55

65 a fourth identifiable mode of oscillation present that had residue values that were less than the dominant poles by an order of magnitude or greater. These poles were neglected due to their insignificance in shaping the transient responses of the WECC, and only the two most important pairs of poles were observed and compared, and were labeled M ode1 being the slowest oscillation and M ode2 being the relatively faster mode Residue Variances The residue R ijk, damping d ijk, and angular frequency ω ijk of mode i, phase angle j, and test number k were all extracted from the data using ERA described in Section ERA yields these values as pairs of poles in the form described by Equation 5.5, but it is desired to find the residues in the form described by Equation 5.7 for computation of controller parameters as described in [65]. The variance of each mode i on each phase angle j across all k test cases was calculated off the transformed residues, as shown in Equations P ijk = P ijk = P ijk = R ijk s 2 + 2d ijk ω ijk s + ω 2 (5.5) R ijk (s + C ijk )(s + C ijk ) (5.6) A ijk (s + C ijk ) + A ijk (s + C ijk ) (5.7) V ij = V ariance(a ij1...a ijk ) (5.8) Table 5.2 displays the variance V ij for both dominant modes present across each transmission line. One case, seen in Figure 5.8, was significantly less damped than the rest of the cases by a larger degree. Table 5.3 displays the result of the variance when this outlier case is omitted. In Table 5.2, phase angles one and two display a much poorer variance as compared to angles three and four. Table 5.3 shows that the extreme case has effected phase angle two, and has a variance more on par with angles three and four when it is removed from the analysis. Since the 56

66 SVC is actually located along the transmission line where phase angle four was measured, phase angle three was chosen first in the interest of having more of a wide-area control implementation for the controller. A further implementation of the controller using the phase angle between area four and five as well as the phase angle between areas three and four, shown in Figure 2.2, was constructed as well. This will allow comparison between a controller using two geographic areas for input to one using three geographic areas for input. Extending the geographic area of the controller is of interest. 5.5 SVC Supplementary Controller Parameter Calculations The methodology in [65] for calculating the parameters of the supplementary controller shown in Figure 5.5 requires knowledge of the residues, frequencies, and damping of the dominant oscillatory slow-modes that shape the controller input during transience. These slow-modes are extracted in [65] using a method of creating a system Fourier Transform, with experimental input signals of various frequencies applied. Using software simulations and ERA, it was possible to find these residues by collecting data in RSCAD of the phase angles transient response between the pilot buses to an input impulse. This data was then passed through ERA to decompose the transient response into modal components, complete with the frequency, residue, and damping of each mode. The supplementary controller for the SVC is composed of a sum of i transfer functions, each comprised of a low pass filter L 1i (s), a washout filter L 2i (s), and a lead-lag filter L 3i (s), shown in Figure 5.5. One set of filters must be created for each mode. In this case, there were i = 2 Table 5.2: Variance Mode Phase 1 Phase 2 Phase 3 Phase

67 modes for each phase angle input to the supplementary controller. This means each phase angle will pass through two transfer functions in parallel, The modal data for phase angles three and four are shown in Table 5.4. This data will be used to construct the parameters of the lead-lag filters, L 2 (s), using the mathematical relations shown below in Equations and in [65]. It should be noted the residue, A ij0, used in Equation 5.9 is the residue derived from separating the pair of poles, shown in Equations φ j = 180 o angle(a ij0 ) (5.9) α j = 1 sin( φ 2 ) 1 + sin( φ 2 ) (5.10) T 1 = 1 ω j α (5.11) T 2 = αt 1 (5.12) L 2 (s) = (1 + st 1) 2 (1 + st 2 ) 2 (5.13) The low pass filters, shown in Figure 5.5, are designed such that frequencies higher than the fundamental frequency of the slow-mode do not pass through the filter as easily. They are of type first order and are described by Equation The gain of these filters was set to be G = 1. The cutoff frequency of the filter was set to be 4 3 of the modal frequency ω ij0 L(s) was designed around, described by equation The fraction L 1 (s) = G 1 + st (5.14) Table 5.3: Variance without Extreme Case Mode Phase 1 Phase 2 Phase 3 Phase

68 Table 5.4: Phase 3 and 4 Modal Data Angle Mode Frequency Residue Damping j i ω ij0 R ij0 d ij T = ω ij0 (5.15) The gain of the controller was found experimentally through simulation. Many different values for controller gain were tried and the best gain in this case was found to be A simple procedure of trial and error allowed repeated testing to find the best gain for increasing modal damping of these slow-mode frequencies. The washout filter, shown in Figure 5.5, can be described by Equation Currently, no attempts have been made to improve controller performance by changing the washout filter parameter T w and T w = 1. L 3 (s) = st w 1 + st w (5.16) The transfer functions for phase angles three and four were calculated using Table 5.4 and Equations 5.13, 5.14, and The total transfer function L ij (s) for each mode i present in phase angle θ j where j = 3, 4 can be described by Equations The total input signal I(s) can be described by Equation 5.23 and is the input signal added to the ordinary input signal to the SVC PI controller. L 13 (s) = ( 0.05s 1 + s ) ( ) s 2 ( s s ) (5.17) 59

69 L 23 (s) = ( 0.05s 1 + s ) ( ) s 2 ( s s ) (5.18) L 3 (s) = L 13 (s) + L 23 (s) (5.19) L 14 (s) = L 24 (s) = ( 0.05s 1 + s ( 0.05s 1 + s ) ( ) s 2 ( s ) ( ) s 2 ( s s s ) ) (5.20) (5.21) L 4 (s) = L 14 (s) + L 24 (s) (5.22) I(s) = L 3 (s)θ 3 (s) + L 4 (s)θ 4 (s) (5.23) 5.6 SVC Controller Simulation Results The designed controller in Section 5.5 was implemented in RSCAD using the phase angle from area three to area four for the first case. For the second case, the angle between areas four and five was also included. It should be noted the actual SVC was located between area four and area five. These angles were chosen due to their low variance, shown in Tables 5.2 and 5.3. The model was then disturbed with an eight cycle, three phase line-to-ground fault on area three. The resulting phase angle disturbance was recorded for three cases. The first case used the SVC in the WECC with no supplementary controller. The second case used the supplementary controller designed in Section 5.5. The third case used supplementary controllers using two phase angle inputs from the model rather than just one, gathering data from areas three, four, and five to do so. The phase angles are plotted against one another in Figure

70 Table 5.5 and 5.6 display the damping values for each mode of each phase after having implemented the first controller with only the phase angle between areas three and four as an input, and then the controller with two relative phase angle inputs Phase Angle 1 Transience Baseline Case Phase 3 Active Phase 3 & 4 Active Phase Angle 2 Transience Baseline Case Phase 3 Active Phase 3 & 4 Active Phase Angle 3 Transience 3.5 Baseline Case Phase 3 Active Phase 3 & 4 Active Phase Angle 4 Transience Baseline Case Phase 3 Active Phase 3 & 4 Active Figure 5.9: Phase Angle Transience of Controller Tests During the table entries for phase angle three, the ERA decomposition of the signal was not showing the same frequencies being observed in the previous two tests, and the numerical decomposition was not directly comparable as in the other cases. Only one mode at a frequency between the previous two was showing up, and the damping of this new mode was recorded in Tables 5.5 and 5.6. Figure 5.9, however, visually reveals a similar improvement in the second 61

71 Table 5.5: Changes in Damping for Mode 1 Phase Mode 1 Mode 1 Mode 1 Angle Baseline Control 1 Control * Table 5.6: Changes in Damping for Mode 2 Phase Mode 2 Mode 2 Mode 2 Angle Baseline Control 1 Control * test was seen over that of the first test, and then over the baseline model with no supplementary controller at all. 5.7 SVC Required Capacity It has been shown in Section 5.6 that the SVC Wide-Area Controller has a strong, positive influence on the WECC. A question left unanswered, however, is just how much capacity is demanded from the SVC during transience. Just how much SVC capacity is required such that the SVC does not max out during transience? Explanation of Tests Three sets of tests are conducted on the WECC model and hardware-integrated WAC to determine the answer to this question. The three tests swept three separate variables that have an influence on behavior of the SVC and WECC. These three variables are fault duration, SVC 62

72 droop, and level of wind penetration in area four. The model is faulted, and the resulting phase angles across all four inter-area transmission lines are recorded from RSCAD. The reactive power injection from the SVC is also recorded during each test, such that the contribution of the SVC to the system can be seen. During these tests, however, the data collected from the SVC was filtered through a bandpass filter, H(s), using Equation In this filter, w l = 2π 0.01 and w u = 2π 2.5. This is necessary to remove much of the higher frequency noise present from the SVC and wind power electronics couplings. Figure 5.10 shows an example of a set of collected data from a WECC simulation, both pre and post-filtration. It should be noted the SVC work function in Figure 5.10 has two points of absolute importance. The maximum and minimum reactive power output the SVC delivers during transience occur at T ime = 1.45Seconds and T ime = 1.70Seconds respectively, and these points of interest will be used in future sections to determine the capacity requirement of the SVC. H(s) = (w u w l )s s 2 + (w u w l )s + w u w l (5.24) Reactive Power (Per Unit) Pre Vs Post Filtered SVC Output Pre Filtered Post Filtered Figure 5.10: SVC Output Data, Pre and Post-Filtered 63

73 Test 1 The first test involves testing the WECC with faults of differing duration. These faults were three phase line-to-ground faults located on area three of the WECC. The duration of fault was swept from one cycle to six cycles. Faults of duration longer than six cycles yielded results that caused the SVC to exceed capacity during transience. During this test, the other two variables of interest, SVC droop and wind penetration on area four, were held at 4% and 27% respectively. As seen Figure 5.11, one can observe a linear relationship between fault duration and SVC maximum and minimum reactive power injections during the transience. Reactive Power (Per Unit) Per Unit output of SVC 1 Cycle 2 Cycles 3 Cycles 4 Cycles 5 Cycles 6 Cycles SVC Peak Output (Per Unit) SVC Capacity Required as Fault Intensity Varies (a) Per-Unit Output of SVC for Different Fault Durations Fault Duration (Cycles) (b) SVC Capacity Required for Different Fault Durations Figure 5.11: SVC For Different Fault Durations Test 2 The second test involves testing the WECC with differing droop values in the inherent, local portion of the SVC. This droop has no connection with the Wide-Area Controller, and is present in a standard SVC configuration [68]. Droop was varied from 0% to higher values of 8%, in increments of 2% for each next test. During this test, the other two variables of interest, fault 64

74 duration and wind penetration on area four, were held at 4 cycles and 27% respectively. As seen in Figure 5.12, one can observe a weak linear relationship between SVC droop and SVC maximum and minimum reactive power injections during transience. Voltage has little effect on the WAC, and any variation in SVC behavior is likely due to local voltage and the effects droop has on SVC local voltage response. Reactive Power (Per Unit) Per Unit output of SVC 0% Droop 2% Droop 4% Droop 6% Droop 8% Droop SVC Peak Output (Per Unit) SVC Capacity Required as Droop Varies (a) Per-Unit Output of SVC for Different Droop Values Droop (Percentage) (b) SVC Capacity Required for Different Droop Values Figure 5.12: SVC For Different Droop Values Test 3 The third test involves testing the WECC with differing levels of wind penetration present on area four. Wind penetration was ranged from 0% to 54% on area four, and inertia was subtracted from the conventional machine present on area four as described by Equation 4.1. During this test, the other two variables of interest, SVC droop and fault duration, were held at 4% and 4 cycles respectively. As seen in Figure 5.13, there is little to no correlation between wind penetration present on area four and the intensity of the swing of reactive power injection from the SVC. 65

75 Reactive Power (Per Unit) Per Unit Output of SVC 13.5% Penetration 27.0% Penetration 40.5% Penetration 54.0% Penetration SVC Peak Output (Per Unit) SVC Capacity Required as Wind Penetration Varies (a) Per-Unit Output of SVC for Different Levels of Wind Penetration Wind Penetration (Percent Total Generation) (b) SVC Capacity Required for Different Levels of Wind Penetration Figure 5.13: SVC For Different Droop Values Test Results After having collected these test cases, a linear regression is fit to the data. This regression contains a mathematical equation predicting necessary SVC reactive power necessary in both the positive and negative direction to ensure clipping does not occur during transience and an active WAC. These equations are shown in Equation 5.25 and 5.26, where ˆ W is the percentage of wind power penetration on area four, ˆ F is fault duration given in cycles, ˆ D is the droop used on the SVC located between areas four and five, ˆ C max is the amount of VAR overhead the SVC would require to not clip, and ˆ C min is the amount of underhead the SVC would require to not clip. C max = W F D (5.25) C min = W F D (5.26) 66

76 These equations are verified by collecting many additional sets of tests from the WECC simulation with WAC. These tests are conducted at the corner points as the most extreme sets of data within test parameters, and well matched the regression but are not shown here. 5.8 SVC WAC Validation Observant readers may realize that up until this point every test that has been conducted on the WECC model in Chapter 5 has remained constant in power flow regarding the SVC. That is, the power flow across each line of the power grid has remained a constant whereas other variables such as SVC parameters, WAC parameters, wind penetration, etc, have varied. One may also be wondering about whether this controller would function if this finely tuned condition were to change, as it most certainly will in a real-world setting. Here, the WECC and WAC are tested for several test cases designed to deliberately alter this operating point, in some cases, into unstable regions of operation WECC Test Cases Four test cases have been created in the WECC with WAC. The power outputs of the machines in the RSCAD model were altered to create several different power flow scenarios in WECC. Line impedance, intra-area impedance, machine inertia, machine damping, and wind penetration were left constant. The only quantities varied were inter-area line power flows via alteration of the machine load reference values. The state of power flow can be observed at a glance in the top-left of Figures 5.14, 5.15, 5.16, and Level of stress in each machine and transmission line is color coded according to what fraction of per-unit loading the machine or line is experiencing. Absolute steady-state angles can be seen for each case in the individual plots for each figure, and line impedance for each transmission line are given in [66]. Each test case contains two sets of data. One set of data, plotted in green, was collected by faulting the model in RSCAD with the WAC disabled. Note the SVC is still enabled, and 67

77 simply is operating as an ordinary SVC with the local bus voltage as its sole input control signal. The other set of data plotted against the first set contains the case where the model was faulted, with the WAC online and adding to the control of the SVC. SVC per-unit reactive power output is plotted for each case, as is all four phase angle transient responses in WECC between each of the five areas. Case 1 Case one is the nominal case with no change in power flow in WECC. One can see large improvements in the transient responses of phase angles three and four. Case 2 Case two is designed to deliberately stress the Southern portion of the WECC, containing areas four and five particularly. In Figure 5.15, one can see the machines along the bottom are stressed and the angles across those transmission lines are larger than the nominal case. The third phase angle has switched direction, indicating power is now flowing from area four to area three, rather than the nominal case where power flows from area three to area four. This is a very interesting case. When the WAC is offline, the model is immediately unstable after fault. When the WAC is online, however, the model is not only stable but damped heavily. Case 3 Case three is designed to deliberately stress the Northern portion of the WECC, containing areas one, two, and three. In Figure 5.16, one can see the machines along the Northern part of WECC are stressed and the angles across the transmission lines in the Northern part of the WECC are larger than the nominal case. Power now flows the opposite direction in both angles three and four over the nominal case. This is also a very interesting case, as one can see the model is marginally unstable without the WAC, and marginally stable with the WAC. The machines distant from the SVC and WAC 68

78 are first to become asynchronous with the grid in this test case. While distant, the WAC and SVC were still capable of stabilizing this test case, while not to the dramatic extent of the previous case. Case 4 Case four is a bit less interesting than the previous cases, but serves an important purpose nonetheless. This case is similar, but not identical to the first case, and serves as an observation on controller performance when WECC is at a different steady-state, but one that s still similar to the nominal model. Figure 5.17 shows improvements similar to that of the first case, where there are larger improvements in transient phase angle swing closer to the SVC and its controller. 5.9 Conclusion of Controller Performance This wide-area controller draws upon PMU data areas three, four, and five to control a SVC located halfway between areas four and five. Figure 5.9 clearly shows improvements in damping for the signals in relatively close geographic proximity to the SVC. More distant signals have been less effected. Tables 5.5 and 5.6 display the changes in damping for both dominant slow modes in the model after the supplementary controller was implemented in RSCAD and expanded to have more than one relative phase angle input. With the exception of the most geographically distant phase, all modes became more damped. The angles between areas three and four, and areas four and five showed substantial improvement in damping. The angle between areas two and three showed modest improvements. The angle between angles one and two was slightly less damped. Overall, the controller using two relative phase angles as inputs has allowed a level of damping on the WECC model that greatly outweighed the degradation in damping seen in Figure 4.1. The supplementary controller designed and implemented is an effective way of counteracting the decreases in system stability seen by adding wind penetration on area four. Finally, in Section 5.8 the concern is addressed regarding tuning and computation of the 69

79 A3 A2 Wind A4 SVC A1 Very Low Stress Low Stress Moderate Stress Heavy Stress Very Heavy Stress Extremely Stressed Angle Between Area 1 and Area 2 A5 WAC On WAC Off Reactive Power (Per Unit) Per Unit Output of SVC WAC On WAC Off Angle Between Area 2 and Area WAC On WAC Off Angle Between Area 4 and Area WAC On WAC Off Angle Between Area 5 and Area 4 13 WAC On WAC Off Figure 5.14: Case 1 Data 70

80 A3 A2 Wind A4 SVC A1 Very Low Stress Low Stress Moderate Stress Heavy Stress Very Heavy Stress Extremely Stressed Angle Between Area 1 and Area 2 A5 WAC On WAC Off Reactive Power (Per Unit) Per Unit Output of SVC WAC On WAC Off Angle Between Area 2 and Area WAC On WAC Off Angle Between Area 4 and Area WAC On WAC Off Figure 5.15: Angle Between Area 5 and Area WAC On WAC Off Case 2 Data 71

81 A3 A2 Wind A4 SVC A1 Very Low Stress Low Stress Moderate Stress Heavy Stress Very Heavy Stress Extremely Stressed Angle Between Area 1 and Area 2 A5 WAC On WAC Off Reactive Power (Per Unit) Per Unit Output of SVC WAC On WAC Off Angle Between Area 2 and Area WAC On WAC Off Angle Between Area 4 and Area WAC On WAC Off Figure 5.16: Angle Between Area 5 and Area WAC On WAC Off Case 3 Data 72

82 A3 A2 Wind A4 SVC A1 Very Low Stress Low Stress Moderate Stress Heavy Stress Very Heavy Stress Extremely Stressed Angle Between Area 1 and Area 2 A5 WAC On WAC Off Reactive Power (Per Unit) Per Unit Output of SVC WAC On WAC Off Angle Between Area 2 and Area WAC On WAC Off Angle Between Area 4 and Area WAC On WAC Off Figure 5.17: Angle Between Area 5 and Area WAC On WAC Off Case 4 Data 73

83 controllers parameters around one specific point of power flow. Several test cases were created to address and test this issue by deliberately putting the WECC into a different point of steady-state operation. The results clearly indicate unanimous improvement in system stability regardless of the testing of several rather extreme cases. These methods and results can be a helpful resource for wide-area damping control of the WECC, especially given the high wind penetration in the US west coast grid. 74

84 Chapter 6 Wide-Area PSS Design using LQR 6.1 LQR Wide-Area Control A reduced-order five-machine dynamic equivalent model of the WECC has been developed in Chapter 2 to represent its interarea oscillation patterns [89]. In face of both small-signal and large-signal disturbances, these five areas oscillate with respect of each other thereby giving rise to inter-area oscillation modes. For the reduced-order system, these modes will be reflected in the inter-machine oscillations as every area now is represented by a unique generator. To damp these oscillations, we next design a linear quadratic regulator (LQR) state feedback controller u(t) = K x(t) using excitation voltage as the control signal. A third-order state-space model consisting of swing and excitation states is considered for each generator. The model is linearized at a chosen operating point and the gain matrix K is computed offline. PMUs are installed at every pilot bus, and the measured values of the bus angle, frequency, current and voltage are used for estimating the machine states. The estimated states of each machine are then passed to a dedicated VM in the cloud, whereafter the states are exchanged between the VMs over a shared yet secure network to compute u(t) in a distributed fashion. The control signals are then communicated back to the respective exciters to actuate the damping action. 75

85 6.2 Power System Modeling Consider a power system network consisting of n synchronous generators and n l loads connected by an arbitrary topology. Without loss of generality, we assume buses 1 through n to be the generator buses and buses n + 1 through n + n l to be the load buses. Let P m denote the vector of the mechanical power injection at generator buses, P L be the vector of total active power consumed by the loads, and P N i be the total active power injected to the i th bus of the network (i = 1,..., n + n l ), where the superscript N indicates that this power is flowing in the network as opposed to the loads. This power is calculated as: P N i = n+n l k=1 ( V 2 i r ik /y 2 ik + V iv k sin(θ ik α ik )/y ik ), (6.1) where, V i θ i is the voltage phasor at the i th bus, θ ik = θ i θ k, r ik and x ik are the resistance and reactance of the transmission line joining buses i and k, y ik = rik 2 + x2 ik, and α ik = tan 1 (r ik /x ik ). Let P N G and P N L denote the vectors of P N i calculated for generators and loads, respectively. The electromechanical model of the power system can be described as a system of differential-algebraic equations: M δ = P m P N G Dω, (6.2a) P L P N L = 0, (6.2b) where δ is the vector of generator angles, ω is the vector of the speed deviation of the generators from synchronous speed, and M = diag(m i ) and D = diag(d i ) are n n diagonal matrices of the generator inertias and damping factors, respectively. The differential algebraic system (6.2) can be converted to a system of pure differential equations by relating the algebraic variables V i and θ i to the system state variables (δ, ω, E) from (6.2b), and then substituting them back in (6.2a) via Kron reduction. 76

86 PMU ASG2 A 2 A1 E 2 δ 2 E 1 δ 1 ASG1 Ĩ2 jx2 r12 jx12 jx1 P2 PMU p12 Ĩ1 PMU jx23 V 2 θ 2 V1 θ1 p23 P1 ASG3 r23 A3 Ĩ3 P 3 E 3 δ 3 V 3 θ 3 jx3 PMU jx34 jx45 V 5 θ 5 p34 P 5 r34 r45 PMU Ĩ5 jx5 Ĩ4 P4 p45 A 5 ASG4 jx4 V 4 θ 4 E 5 δ 5 ASG5 A4 E 4 δ 4 Figure 6.1: Electrical topology of WECC s 500kV network 6.3 Kron Reduction The reduced-order model of WECC created in Chapter 2 has a topology shown in Figure 6.1. Note this topology includes five synchronous machines attached five different intermediate nodes through individual tie-line impedances. Each intermediate node is attached to one or two adjacent nodes by an inter-area impedance. The tie-line impedances are large enough to be significant, and thus it was necessary to perform Kron Reduction on this network. This allows formation of an equivalent network by which a set of state-space equations can be derived. The formation of this reduced network is shown below. Let the impedance of the line connecting buses i and k be z ik = r ik + jx ik. Its admittance is therefore, y ij = 1/z ij. The admittance of the load at the i th bus be denoted as y Li. These numerical values can be found in [66], and were derived from PMU data recorded during a disturbance event on WECC. Knowing these values, the admittance matrix Y R (n+n l) (n+n l ) of the network is therefore defined as: [Y ] i,k = y i,k, (6.3) n [Y ] i,i = y Li + y i,k, (6.4) k=1,k i Let V = [Ṽ1 Ṽ n ] T R n, ˆV = [Ṽn+1 Ṽ n+nl ] T R n l, I = [Ĩ1 Ĩ n ] T R n. 77

87 I 0 = Y 11 Y 12 Y 21 Y 22 } {{ } Y VˆV (6.5) I =(Y 11 Y 12 Y 1 22 Y 21) }{{} Y kron,1 V (6.6) I =Y kron,1 V (6.7) Let X = diag(jx di ) R n n, E = [Ẽ1 Ẽ n ] T R n. E = XI + V (6.8) Substituting V from (6.7) E = XI + Y 1 kron,1 I (6.9) I = (X + Y 1 kron,1 ) 1 }{{} Y kron E (6.10) I = Y kron E (6.11) Also, the relationship between E and V can be described as: E = XI + V (6.12) = (XY kron,1 + I n )V, (6.13) 78

88 where I n R n n is the identity matrix. Thus, one can write: V = (XY kron,1 + I n ) 1 E (6.14) }{{} K Here, Y kron represents the equivalent network impedance between each of the buses in the reduced order model of WECC, and thus is a 5x5 matrix. This will be used extensively in control design in following sections. 6.4 State-Space Equations The resulting system is a fully connected network of n = 5 third-order oscillators with excitation dynamics with l n(n 1)/2 tie-lines. Let the internal voltage phasor of the i th machine be denoted as Ẽi = E i δ i. The electromechanical dynamics of the i th generator in the Kron s form can be written as: δ i = ω i (6.15) M i ω i = P mi E 2 i G Li D i ω i n k=1,k i E i E k (G ik cos(δ i δ k ) B ik sin(δ i δ k )) (6.16) ( n ) τ i Ė i = x d i x d i E i + U i + x di x d i x d i k=1 K i,k E k cos(δ i δ k ) (6.17) where ω s = 120π (rad/sec) is the synchronous speed for the 60 Hz system, for i = 1,..., n. Linearizing (6.15)-(6.17) about the equilibrium (δ i0, 0, E i0 ) results in the small signal model: 79

89 δ(t) d δ d δ d δ dδ dω de δ(t) 0 M ω(t) = d ω d ω d ω dδ dω de ω(t) + 0 u (6.18) } τ Ė(t) dė dė dė dδ dω E(t) I dė {{}}{{}}{{}}{{} ẋ A x B where, δ = [ δ 1 δ n ] T, ω = [ ω 1 ω n ] T,, Ė = [ Ė1 Ėn] T, and I n is the n-dimensional identity matrix. The matrix A in (6.18) is composed of partial derivatives. 6.5 Partial Derivatives The A matrix from Equation 6.18 is composed of partial derivatives of each differential equation evaluated at the steady-state operating point of the WECC model in RSCAD. These partials are given below: d δ i dδ j = 0 (6.19) d δ i dω j = 0 i j, 1 i = j (6.20) d δ i de j = 0 (6.21) dω i = 1 E i E j (G ij sin(δ i0 δ j0 ) B ij cos(δ i0 δ j0 )), i j (6.22) dδ j M i dω i = dδ i 1 n E i E j (G ij sin(δ i0 δ j0 ) + B ij cos(δ i0 δ j0 )) (6.23) M i j=1, i dω i = D i i = j, 0else (6.24) dω j M i 80

90 dω i = 1 ( E i0 G ij cos(δ i0 δ j0 ) + E i0 B ij sin(δ i0 δ j0 )) (6.25) de j M i dω i = de i 1 n M i j=1, i E j (B ij sin(δ i0 δ j0 ) G ij cos(δ i0 δ j0 )) 2E i G Li (6.26) d E i dδ j = x d x d K ij E j0 sin(δ i0 δ j0 ) (6.27) τ i x d d E i dδ i = n j=1, i x d x d τ i x d K ij E j0 sin(δ i0 δ j0 ) (6.28) dė dω = 0 (6.29) d E i de j = x d x d + x d x d K ii (6.30) x d In the above mentioned partial differential equations, there are three state variables for each machine i. Here are the variables needed from the WECC model, and thus RSCAD. These values were not derived in [66] and were default values from RSCAD machine and excitation system models created by Schweitzer Engineering Laboratories. These are given below. ˆ x d : Machine impedance, default value in RSCAD ˆ x d : Machine impedance, default value in RSCAD ˆ τ : Machine excitation system IEEE-ST1 data from RSCAD Other parameters, however, were directly derived from the PMU data received from Southern California Edison in [66], and are shown below. 81

91 ˆ M : Machine inertia, derived value ˆ D : Machine damping, derived value ˆ Y kron : Impedance between full mesh bus, derived in 6.3 ˆ K : Derived in Equation 6.14 To evaluate the partials, the following steady-state parameters for the initial condition were necessary. ˆ δ 0 : Machine initial angle ˆ ω 0 : System initial frequency ˆ E 0 : Initial bus voltage It should be noted as well the initial angles are all compared to one another in pairs. Relative angles between two buses are relevant, whereas absolute stand-alone angles are not. The relative phase angles between buses are only needed, and thus the following relative angles were used from Figure 2.2. ˆ δ 10 δ 20 : The angle between ASG 1 and ASG 2 ˆ δ 20 δ 30 : The angle between ASG 2 and ASG 3 ˆ δ 40 δ 30 : The angle between ASG 4 and ASG 3 ˆ δ 50 δ 40 : The angle between ASG 5 and ASG 4 Once the partials were evaluated using all of the above values and constants, the completion of a linearized state-space, ẋ = Ax + bu has been done. 82

92 6.6 Wide-Area Control The controller designed was a simple feedback controller where u = Kx to transform the state-space in (6.18) from ẋ = Ax + Bu into ẋ = (A BK)x via use of the PSS stabilizer input on each machine. Observing (6.18), B includes control inputs to just the excitation state variables E. Careful selection of the matrix K was computed such that slow-mode oscillations during transience were damped. A Linear Quadratic Regulator algorithm (LQR) was used to calculate the matrix, K. An LQR choice for K will minimize: 0 inf (x T Qx + u T Ru)dt (6.31) With LQR control design, R and Q can prioritize certain state variables over others, allowing favoritism of reducing deviation of certain states over others during transience. For the purposes here, R = I 3n such that all state variables was equally considered. Selection of Q, however, was a bit more challenging. x contains n state variables representing each angle δ of each machine i, n state variables representing each frequency ω for each machine i, and n state variables for each machine voltage E for each machine i, represented by (6.32) and shown in (6.18). x = δ(t) ω(t) E(t) (6.32) This gives 3n state variables total but angles are only relevant and useful in relation to one another and are never considered as absolute quantities as a control input. This is because each angle is rotating with respect to a reference, and will rotate in value as seen in Figure 6.2. Power flow feedback is also desired, which relates to relative angle differences as seen in (6.16) and (6.17). For this reason, the product x T Qx must be composed entirely of relative phase angles to represent power flows. This product can be expanded, shown in (6.33). 83

93 Phase Angle 1 Phase Angle 2 Difference Figure 6.2: Example of Relative Phase Angles 84

94 x T Qx = δ(t) ω(t) E(t) T Q δ Q ω Q E δ(t) ω(t) E(t) (6.33) Note only the submatrix Q δ in (6.33) must be. To ensure the product only takes relative phase angles into account, the following matrix was used for Q δ : Q δ = nxn (6.34) The computation of K minimizing (6.31)was then done with Q and R, but another problem also was encountered regarding K and relative angle feedback. The resulting feedback matrix product Kx for the LQR controller contained feedback constants for each state variable including the absolute phase angle from each bus. Relative angles must be used for feedback. If the product Kx is observed and only terms with δ state variables are considered, the following series of feedback terms can be observed in (6.35). u i = n K ij δj + j=1 n K i,(j+n) ωj + j=1 n K i,(j+2n) Ej (6.35) j=1 Let s now assume we only observe the ith feedback variable, u i, from (6.35). Defining: 85

95 K i,1 = M 1 K i,2 = M 2 M 1 K i,n 1 = M n 1 M n 1 K i,n = M n 1 (6.36a) (6.36b) (6.36c) (6.36d),(6.35) can be rewritten as: u i = M 1 (δ 1 δ 2 ) + M 2 (δ 2 δ 3 ) + + M n 1 (δ n 1 δ n ) + ω and E terms (6.37) Rearranging (6.36) shows: M 1 = K i,1 M 2 = K i,2 + K i,1 M n 2 = K i,n 2 + K i,n K i,2 + K i,1 M n 1 = K i,n K i,2 + K i,1 = K i,n (6.38a) (6.38b) (6.38c) (6.38d) (6.37) is only true if (6.38d) is true, meaning: n K 1,j = 0 (6.39) j=1 The expression (6.39) will not be true for an arbitrary calculation. This condition, however, was forced by changing the K matrix the LQR algorithm computed. The alteration of K is 86

96 given in (6.40). K i,j = K i,j 1 n K i,j (6.40) n The reader may be wondering, however, how altering the feedback matrix K has changed performance of the system. A very brief test was conducted in MATLAB to observe if controller performance would degrade. The results are shown in Figure 6.3 and Figure 6.4. Four output variables are observed, including (δ 1 δ 2 ), (δ 2 δ 3 ), (δ 4 δ 3 ), and (δ 5 δ 4 ). Since it is the ultimate goal of the long-going research to damp these inter-area angles, they were chosen as the state-space output variables, and an appropriate C matrix corresponds with viewing these relative angles from the state-space. It can simply be observed no alteration in controller performance was suffered by altering K to meet the criteria of Equation Now that a proper controller has been designed, it would be of interest to describe the network that will be used to implement this controller. j=1 6.7 Experimental Results Many different test cases were performed on the controller described in the previous sections to gauge the performance of the LQR WAC. In order to test the performance of this controller, it was first necessary to create a scenario in WECC that was unstable without control Unstable Case Load Reference Settings The WECC model s steady-state condition was altered by adjusting the load reference sliders on the aggregate machines, thus altering power flow throughout the system. The new load reference values are shown in Table 6.1, and were found through trial and error running RSCAD and adjusting the sliders until a case was created that was unstable, but not greatly so. 87

97 Impulse Response 0.2 From: In(1) From: In(2) From: In(3) From: In(4) From: In(5) To: Out(1) Amplitude To: Out(2) To: Out(3) To: Out(4) Figure 6.3: Impulse Response of State Space: Original K Table 6.1: Alteration of Load Reference Sliders for Case Gen 1 Gen 2 Gen 3 Gen 4 Gen 5 Before After

98 Impulse Response 0.2 From: In(1) From: In(2) From: In(3) From: In(4) From: In(5) To: Out(1) Amplitude To: Out(2) To: Out(3) To: Out(4) Figure 6.4: Impulse Response of State Space: Altered K 89

99 Steady-State Variables The K matrix of the controller was tuned for a new operating point by recomputing the matrix parameters described in Section 6.6. The steady-state operating point was observed by running RSCAD without the controller active. The following operating point was found for tuning the k matrix in Table 6.2. All 70 K matrix values were reentered into RSCAD for manual controller tuning about this new steady-state point of operation. Table 6.2: Steady-State WECC Condition E 1 E 2 E 3 E 4 E pu 0.996pu 1.002pu 0.994pu 0.997pu δ 1 δ 2 δ 2 δ 3 δ 4 δ 3 δ 5 δ rad 0.405rad rad 0.708rad Controller Comparison Test A comparison of the transient response of WECC was conducted both with the RSCADimplemented LQR feedback controller on and off. A three phase fault of duration four cycles was applied to area three and the resulting phase angle differences between each aggregate machine recorded. The resulting transient response is shown in Figure 6.5. Note the difference in system performance with the controller switched on. The system is unstable without controller action, and is stable and damped with the controller s aid. Another experiment was also conducted. The system simulation was allowed to run for a while without controller action after being faulted such that the angle swing would become intense, risking loss of synchronization of the machines. After several minutes, the controller was switched on to damp the system. The resulting plot was observed in real-time from PMU data streaming from the RTDS, in Figure 6.6. It should be noted this case damps a swing of roughly 10 degrees peak to peak. 90

100 Angle Between Machines 1 and 2 ON OFF Angle Between Machines 2 and 3 ON OFF Angle Between Machines 4 and ON OFF Angle Between Machines 5 and ON OFF Figure 6.5: Phase Angle Transience, With and Without WAC 91

101 Figure 6.6: PMU Data Stream of Operation of Controller Feedback of Just Local Voltage State Variables If one observes the K feedback matrix for voltages, each control input has a very large local term for voltage, which could essentially provide a built-in PSS out of the WAC. The controller s performance will be again tested with these voltage state variables enabled locally, but all other variables and feedback pathways disabled. Figure 6.7 displays the resulting transient response on WECC from a four-cycle three-phase line-to-ground fault on area three. One can observe that the controller gives a superior transient response if wide-area control is enabled rather than just the local voltage feedback terms. Though not as extreme of an improvement as Figure 6.5, wide-area control has still proved here to greatly aid in damping system during transience. 92

102 Angle Between Machines 1 and 2 Wide Area Local Angle Between Machines 2 and 3 Wide Area Local Angle Between Machines 4 and Wide Area Local Angle Between Machines 5 and Wide Area Local Figure 6.7: Phase Angle Transience, Local Voltage vs Wide-Area Control 93

103 6.7.4 Feedback of Just Local Frequency State Variables As in the previous subsection, another test will be conducted here. The only feedback enabled from the controller will be measurement of local bus frequency. This is an attempt to simulate a frequency-based PSS. The system with just local frequency feedback was stable, but barely so compared to the unstable case without controller action. The plots are shown in Figure 6.8. Marginal improvement was noted. 22 Angle Between Machines 1 and 2 25 Angle Between Machines 2 and Angle Between Machines 4 and Angle Between Machines 5 and Figure 6.8: Phase Angle Transience, Local Frequency vs No Control 94

104 6.7.5 PSS Stabilizer on WECC A case was then conducted with a power system stabilizer added to each machine in WECC. Default recommended values in RSCAD were used for the PSS, as is true for the governor and excitation system local controllers. The purpose of this test is two-fold. One, a comparison between WAC controller performance and PSS only performance was observed in Figure 6.9. Second, a comparison between PSS and local voltage feedback was compared in Figure The PSS is capable of stabilizing a previously unstable system, but the WAC is still more effective here Angle Between Machines 1 and 2 WAC PSS Angle Between Machines 2 and 3 WAC PSS Angle Between Machines 4 and WAC PSS Angle Between Machines 5 and WAC PSS Figure 6.9: Phase Angle Transience, PSS vs WAC 95

105 Angle Between Machines 1 and 2 Local Voltage PSS Angle Between Machines 2 and 3 Local Voltage PSS Angle Between Machines 4 and Local Voltage PSS Angle Between Machines 5 and Local Voltage PSS Figure 6.10: Phase Angle Transience, PSS vs Local Voltage Feedback 96

106 6.7.6 Unstable Baseline Case Comparison of All Controllers As in Subsection 6.7.1, another unstable case was created. The difference, however, is now the WECC will be unstable with the assistance of a PSS. The new operating point is shown in Table /reftable:point2. Table 6.4 shows the new operating point by which the system was tuned Table 6.3: Alteration of Load Reference Sliders for Case Gen 1 Gen 2 Gen 3 Gen 4 Gen 5 Before After around for calculation of new K matrix values. Figure 6.11 shows the transient responses of Table 6.4: Steady-State WECC Condition E 1 E 2 E 3 E 4 E 5 δ 1 δ 2 δ 2 δ 3 δ 4 δ 3 δ 5 δ pu 0.995pu 1.002pu 0.994pu 0.995pu 0.357rad 0.423rad rad 0.859rad various controllers when a four-cycle three-phase line-to-ground fault was applied on area three. The case with no control at all was very unstable, losing synchronization almost immediately. The case with only PSS on the system was unstable. The case with Wide-Area Control, however, was stable, proving WAC is being much more effective than PSS at providing stability to this power system under these conditions. The older case where an SVC-based Wide-Area Controller was also tested at the same operating point shown in Table 6.3, and it also was capable of damping this unstable system. Both WAC methods were effective at doing so where a PSS was not. 97

107 Angle Between Machines 1 and 2 NONE SVC WAC PSS Angle Between Machines 4 and NONE SVC WAC PSS Angle Between Machines 2 and 3 NONE SVC WAC PSS Angle Between Machines 5 and NONE SVC WAC PSS Figure 6.11: Phase Angle Transience, Controller Comparison 98

108 6.8 Conclusion on LQR Implementation in RSCAD Our experiments here show the LQR controller s performance is superior to local control and capable of damping otherwise unstable power system conditions in WECC. Subsection shows the controller is able to stabilize an otherwise unstable system and Subsection shows that this implementation of wide-area control is more robust than a local power-system stabilizer. It should be realized, also, this system represents aggregate machines that indeed did have power system stabilizers operating locally so addition of a second in RSCAD was redundant and optimistic. This only further proves the worth of this wide-area control method. Finally, a test case was conducted and set such that the system was not stable even with PSS use. The LQR controller was seen to be fully capable of providing a stable power system where local PSS could not. The SVC controller described in Chapter 5 was also shown to be stable as well. Two wide-area control schema were shown here to be fully capable of providing stability in an otherwise unstable system, even when redundant, double PSS was applied to fictitious aggregate machines. 99

109 Chapter 7 Hardware-in-loop Implementation 7.1 Hardware Integration Overview This section presents a description of a hardware-in-loop simulation framework for verifying and validating critical wide-area monitoring applications in large power systems using Synchronized phasor measurements. The set up employs both software and hardware layers that interact over a secure communication network, and both oben-loop and closed-loop simulations are considered. Continuous-time models of power systems are simulated in the software layer using a series of real-time digital simulators, while the voltage and phase angles at the buses in the models are captured in discrete-time using hardware Phasor Measurement Units (PMUs). To demonstrate open-loop operation, we first discuss how the PMUs and their associated Phasor Data Concentrators (PDCs) operate symbiotically with the real-time simulations in this set up with mutual time-stamping from a common reference GPS. Thereafter, we demonstrate the effectiveness of the software-hardware interactions by simulating the 4-machine 11-bus Kundur power system model, and employing the PMUs to capture its voltage and phase angle oscillations. Finally, we modify this model to include a wind turbine, and analyze the bus voltage oscillations available from the PMUs using detailed modal analysis. Our results demonstrate how the slow oscillation spectrum of the model changes with increasing wind power injection, thereby 100

110 facilitating the formal methods of wide-area oscillation monitoring in a realistic power system control center. Closed-loop operation includes creation of real-time simulation of a single-machine infinite-bus power system with a layer of hardware integration and control implemented to control the generators governor. The model will demonstrate differences in the hardware and software simulations that are critical to accurately modeling wide-area control in a laboratory setting. 7.2 Hardware Introduction Over the past few years several catastrophic phenomena such as cascade failures and blackouts in different parts of the North American power grid have forced power systems researchers to look beyond the traditional approach of analyzing power system functionalities in steady-state, and instead pay serious attention to their dynamic characteristics, and that too in a global or wide-area sense. This mindset has been particularly facilitated by the recent outburst of measurement and instrumentation facilities provided by the Wide-area Measurement System (WAMS) technology, which uses sophisticated digital recording devices called Phasor Measurement Units (PMUs) to record and export GPS-synchronized, high sampling rate (1-240 samples/sec), dynamic power system data [70], [71], [72]. Research platforms such as the North American Synchropasor Initiative (NASPI) [73] have been formed to investigate ways by which PMU measurements from different parts of the United States power system can be possibly exploited to gain insight about their dynamic inter-dependence indicating how events in one area of the grid can cascade and have significant impact on the other remote areas. However, in current state-of-art almost all PMU data analysis for research purposes are contingent on accessing the real data from specific utility companies that own the PMUs at locations of interest. Gaining access to such data may not always be an easy task due to privacy and non-disclosure issues. More importantly, in many circumstances even if real PMU data are obtained they may not be sufficient for studying the detailed operation of the entire system because of their limited coverage. For example, in many studies on the WECC dynamic analysis, researchers have faced observability issues due to lack 101

111 of PMU data at certain buses in the system that decide system connectivity. To circumvent this problem, in this paper we describe a hardware-in-loop simulation framework where high fidelity detailed models of large power transmission systems can be simulated in real-time, and the dynamic responses can be captured via real hardware; Phasor Measurement Units that are synchronized with the time-scale of the simulations via a common GPS reference. We describe how the hardware and the software layers of this test-bed are integrated with each other to create a substation-like environment within the confines of the research laboratory, and how they symbiotically capture power system dynamic oscillations as if these measurements were made by real PMU data installed at the high voltage buses of a real transmission substation. Our analysis covers inter-area oscillation modeling of a 2-area power system, integrated with a wind turbine. Dynamic analysis of synchronized phasor data obtained in realistic manifestations of such systems, for example the United States West Coast system, from disturbances and stage tests has focused on low-frequency inter-area damping calculation [74], transfer function analysis [75], and the validation of system models and parameters [76]. This paper shows how all of these analytical methods can be reproduced in the lab environment using PMU-based hardware-in-loop simulations in real-time. The model is extended to control different parts of the model with hardware rather than having these components controlled via software. Examples of these components are the governor and exciter models controlling the generators in various models. Other researchers have developed various control structures and methods for the control of Doubly Fed Induction Generators (DFIG) in wind turbines. A common problem, however, is the fidelity and accuracy of a non-integrated, completely theoretical and mathematical approach to modeling these systems. Observing the current state of research in this area, models to observe this phenomenon have been developed using MATLAB and other mathematical tools [77], [78]. One may question the true value of a model that does not include errors and uncertainties present in a real system, such as quantization error, propagation delay of data, measurement error, and noise. This hardware-in-the-loop test-bed will by default include all of these real-world 102

112 modification sources on the phasor data, thus increasing the fidelity of the models with respect to how they would behave in a real-world scenario. 7.3 Hardware Test-Bed Components This section describes the separate parts required to create the lab setup that will be used for setting up this test-bed. A Phasor Measurement Unit (PMU) is an instrument that allows the measurement of the voltages, currents, and relative phase angles present in a power system via the hooking up of the PMU using external voltage and current transformers, and will be one of the most crucial components of this hardware-in-the-loop test-bed. Most PMUs contain many more functionalities than just measurement of voltages, currents, and phase angles that will not be used in this experiment. Two separate varieties of PMUs were used in this lab setup. The PMUs that will be used in this setup are the SEL-421 and SEL-487 PMUs. Both of these PMUs have the capability of accepting an IRIG-B signal from the GPS clock and outputting data at a rate of at least 60 samples per second and have multiple current and voltage channels accessible [80], [81]. The PMUs will require satellite synchronization in order to operate. While this will also provide a timestamp for the data that will be collected, it is insignificant for current experiments. To fulfill this role the SEL-2407 Satellite-Synchronized Clock was used in this setup. The SEL-2407 provides the IRIG-B signal the PMUs require to function [79]. The PMUs also require a Phasor Data Concentrator (PDC) in order to operate correctly. The PDC chosen for this test-bed is the SEL-3373 Station Phasor Data Concentrator. The PDC collects the data from many PMUs at once via Ethernet communications and EIA-232 protocol messages and concentrates it into one block of data the computer either request directly via C communications protocol or have archived for later access. The user will be able to view the phasor data on a computer screen using the SynchroWAVE PDC Assistant software and the computer will be requesting data from this PDC [83]. The Real Time Digital Simulator (RTDS) is a power system simulator tool that allows the 103

113 real-time simulation of a system with a time-step of 50 microseconds. The RTDS comes with software known as RSCAD which allows the user to develop models for the RTDS to simulate. The RTDS also comes with various cards that allow external hardware to interface with the simulation. The card of interest for this case is the Gigabit Transceiver Analog Output (GTAO) card, which will allow the user to view low level signals proportional to what voltages and currents lay on different buses of the system in real time [82]. The entire test-bed will be centered on the RTDS. The GTAO card inside the RTDS will be generating voltage and current waveforms to send to the PMUs. The PMUs will measure these voltage and current waveforms and send the resulting digitized phasor data calculations to the PDC. The PDC will timestamp and collect the data from all of the PMUs and send the resulting data to the computer when it is requested. The computer will be able to retrieve archives of data as well as display the data in real time on the screen. A high level diagram of the entire test-bed is shown in Figure 7.1. RTDS GTAO Card PMU1 GPS PMU2 PDC PMU3 To Computer Figure 7.1: Hardware Open-Loop Test-Bed The RTAC (Real-Time Actuated Controller) will be used to close the loop and allow feedback 104

114 from the PMUs to be reintroduced into the real-time simulation as an analog data stream. The controller designed in Section 5.5 will also be constructed inside the RTAC computer. Figure 7.2 displays what the test-bed looks like after this has been implemented. RTDS GTAO Card RTAC PMU1 GPS PMU2 PDC PMU3 To Computer Figure 7.2: Hardware Closed-Loop Test-Bed 7.4 Hardware Setup For the purposes of this experiment, the voltage and current measurement channels will be accessed through the low-level test interface inside the PMUs rather than by the back of the PMU conventionally. This allows the application of small signals generated by the RTDS GTAO card to be directly applied to the PMU for measurement rather than requiring an external amplifier to step up these low level voltages [80], [81]. Both the SEL-421 and SEL-487 have a low level test interface located internally, but the pin-out differs. The pin-outs of both PMUs are located in [80] and [81]. 105

115 The current and voltage channels of these ribbon cable sockets will be attached to the outputs of the GTAO card. There is some scaling that must be done to ensure the voltage on the ribbon cable does not exceed the voltage that will cause damage to the device and to ensure the voltage or current ultimately measured by the PMU is the same as the voltage or current of the point of measurement in the simulation. The GTAO card must also be calibrated by following the instructions in the card manual [82]. The SEL-421 PMU low level signal interface must not exceed 2.33 Volts RMS and the SEL-487 PMU low level signal interface must not exceed Volts RMS. Exceeding these voltages can cause undesirable operation. Both PMUs have the same input scale, where 446 millivolts RMS on the low level signal interface will cause the PMU to read 67 Volts or 66.6 millivolts RMS will be read as 1 amp [80], [81]. The PMUs also have an internally programmable potential transformer turns ratio which will scale these voltages or currents by the factor set. These will be called T P MUV and T P MUI. This means the voltage on the ribbon cable can be related to what the PMU will read and display on the console by Equations 7.1 and 7.2, where V P MU and I P MU are the voltages and currents of the phasors the PMU will be measuring, V GT AO is the RMS Voltage on the GTAO card output wires, and the fractions and come from the PMU manuals [80], [81]. It is important for T P MU to be an appropriate value so that the level of the voltages on the GTAO card are sufficient to remain below the limits described in the previous section. V P MU = V GT AOT P MUV (7.1) I P MU = V GT AOT P MUI (7.2) The GTAO card in RSCAD will have a scaling constant, k, which needs to be calculated in order for the voltage or current on the GTAO card output, V GT AO, to match that of the bus voltage or current in the real time simulation. The voltage coming out of the GTAO card will be related to the voltage applied in the real-time simulation by Equation 7.3, where V RT S is 106

116 the RMS voltage applied to the GTAO component in the real-time simulation draft and k is the configurable constant in the component settings [82] Equations 7.3 and 7.1 yield: V GT AO = V RT S 5 k V = I RT S 5 k I (7.3) V P MU = V RT S 5 k V T P MU V (7.4) 5 1 I P MU = I RT S k I T P MU I (7.5) Assuming the user wishes V P MU = V RT S as well as I P MU = I RT S, solving for the two k constants yields: k V = T P MU V (7.6) k I = T P MU I (7.7) 7.5 GTAO Card Calibration The setup of the current hardware test-bed is almost complete. There is, however, one small step that must be taken to ensure the results are as accurate as possible. The values measured by the different voltage and current ports of the PMUs will differ slightly even when the same node in the real time simulation is being measured. Before use, one must calibrate this by slight adjustment of the k constants. In order to do this, a GTAO port was instructed to a voltage node in the real-time simulation model. The model was ran and allowed sufficient time to reach a steady-state value. The resulting phasor data was archived over a period of time and the average value of the phasor voltage, V A V G, calculated off of this archived data. The resulting 107

117 V A V G value differed slightly from that of the simulation and calibration is required to make them match exactly. Equations 7.8 and 7.9 relate the new calibrated k constants to the old ones where V S IM is the correct value of the voltage in the real-time simulation. k V = V AV G V SIM k V (7.8) k I = I AV G I SIM k I (7.9) This must be done for each channel for voltages and for currents in order for the most accurate results to be obtained. 7.6 Integration of Supplementary Controller in Hardware Until this point, the WECC model and the accompanying supplementary controller have all been simulated in a strictly software setting. The supplementary controller was designed and implemented in RSCAD using an input source of data generated in the RSCAD simulation. It is of interest to actually implement this controller using realizable hardware that one may find in a real-world setting. Sections explain in detail the creation of a hardware-in-the-loop test-bed within the laboratory setting. This section explains how this test-bed will be combined with the WECC model to implement the supplementary controller in a hardware setting. Areas three, four, and five from WECC were used and integrated with the hardware-in-the-loop test-bed in Figure 7.3. Notice that the transfer function described in Section 5.5 was in the continuous time, or s domain. The hardware based controller must be designed in the discrete, or z domain as it is operating off of PMU data sampled at a rate of 60Hertz. A zero order hold using a sample time of 1 60 Seconds was used to transform L(s) into L(z). Equations display L ij(z) for both modes 1 and 2 for angles θ 3 and θ 4. Equation 7.16 reveals the SVC controller supplementary input signal in the discrete domain, and will be the output signal of the hardware-in-the-loop 108

118 SVC Model DATA RTDS GTAO Card L(z) PMU1 GPS PMU2 PDC PMU3 To Computer Figure 7.3: Test-Bed with WECC Model and Supplementary Controller test-bed that is reintroduced into the software simulation. L 13 (z) = z z z z z z z (7.10) L 23 (z) = z z z z z z z (7.11) L 3 (z) = L 13 (z) + L 23 (z) (7.12) L 14 (z) = z z z z z z z (7.13) L 24 (z) = z z z z z z z (7.14) 109

119 L 4 (z) = L 14 (z) + L 24 (z) (7.15) I(z) = L 3 (z)θ 3 (z) + L 4 (z)θ 4 (z) (7.16) 7.7 Differences Between Software and Hardware Controllers It is expected that there be differences between the software based controller and angle measurement performance and those measured through the hardware-in-the-loop test-bed. After all, this was in part the inspiration for creating this test-bed in the first place. The hardware must measure an analog quantity through the use of PMUs, digitally filter this data through a discrete representation of the designed continuous controller, and reintroduce the data back into the simulation. This can cause several differences between the software based controller and the hardware based controller. These differences include measurement error, analog noise, discretization error, error stemming from the difference between the continuous and discrete representations of the transfer function, and signal delay. This section investigates the differences between the software and hardware based SVC supplementary controllers. The WECC model with the SVC active was faulted in the same manner as in Section 5.5 with an eight cycle line-to-ground, three phase fault on area three. The output of the Supplementary Controller was observed both in software and as the output of our hardware-in-the-loop test-bed. The two controller functions were plotted against one another, shown in Figure 7.4. Observing the figure, it can be seen that the software and hardware controllers are indeed behaving differently as expected. It is visually obvious there is some delay in the hardware controllers output, there is clear discretization as the hardware signal is refreshed at a rate of 60 Hertz, and the hardware signal s magnitude is slightly larger. The delay created by the hardware-in-the-loop test-bed was calculable using the data from Figure 7.4. One signal is a delayed version of the other. The cross correlation between the 110

120 Supplementary Controller Output (pu) Work Functions Software Controller Hardware Controller Figure 7.4: Work Functions of the Supplementary Controller Compared in Hardware and Software 111

121 controller outputs was calculated and the resulting delay between the two signals found. This delay was found to be 75ms, as a combination between network delays and discrete filter delays. Considering the supplementary controller consists of several 4th order discrete filters in parallel, each with a sampling rate of 16.67ms, the delay from the filter alone would equate to about 67ms. This leaves 8ms to network communication and computational delays within the other components of the hardware-in-the-loop test-bed. Considering this test-bed has been created in one room within a local-area network, small communication delays are expected. The hardware-in-the-loop test-bed has also created a variation of magnitude between the two signals, seen as differences in peak work function magnitude in Figure 7.4 at times t = 0.5 seconds and t = 0.8 seconds. Simply observing the differences in magnitude between the two peaks at both of these times, the peak magnitude of the work function sourced from the hardware controller was found to be 6.2% larger than the software based work function. The hardware-in-the-loop test-bed contains PMUs that sample the data at a rate of 60 Hertz. Though the frequencies of interest for slow-mode damping lie between 0.1 and 1.0 Hertz and are well below the Nyquest rate, discretization is still clearly visible in the hardware signal in Figure 7.4. The PMUs sample and hold until new data arrives, hence the stair-step looking nature of the hardware work function. The next section will answer how these cumulative differences in software and hardware control signals translate to degradation (or improvement!) in system performance. 7.8 Differences in Model Performance In the previous section, the SVC supplementary controller was implemented both in software and in hardware. There were many differences immediately obvious between the two controllers, as expected, and these were graphically shown and numerically calculated. It is known that one can expect a 75ms delay between the two signals when running locally, and likely more if implemented in a wide geographic region rather than on a local area network. This section will investigate the performance of the WECC using both controllers and the results will be compared 112

122 using the modal composition method ERA as a metric for system performance increases or decreases. Figure 7.5 displays the transient response of the four inter-area phase angles in the WECC as similar to previous tests when the model was excited by an eight cycle, three phase line-to-ground fault on area three. Two sets of data have been plotted, including the transient response of the model when the SVC supplementary controller was implemented in software and the transient response of the model when the SVC supplementary controller was implemented in hardware Phase Angle 1 Transience Software Controller Hardware Controller Phase Angle 2 Transience Software Controller Hardware Controller Phase Angle 3 Transience 3.5 Software Controller Hardware Controller Phase Angle 4 Transience 13 Software Controller Hardware Controller Figure 7.5: Phase Angle TransienceUsing Hardware vs Software Controllers Visually, it appears that the controller performance has not been significantly altered by 113

123 its presence in hardware versus software. Like in Section 5.6, however, the data collected will be decomposed using ERA in order to numerically investigate the change in damping of the dominant slow-modes of all phase angles. The resulting damping values of both dominant modes are shown below in Tables 7.1 and 7.2. Table 7.1: Changes in Damping for Mode 1 Phase Mode 1 Mode 1 Mode 1 Angle Software Hardware No Controller Table 7.2: Changes in Damping for Mode 2 Phase Mode 2 Mode 2 Mode 2 Angle Software Hardware No Controller The phase angle in closest proximity to the controller, angle four, has been negatively influenced by migration of the supplementary controller from software to hardware in both slow modes. The hardware controller, however, still improved damping of both inter-area modes substantially above the baseline case with no supplementary controller for phases two, three, and four, while only slightly decreasing damping across phase angle one. 114

124 Chapter 8 Wide-Area Control using Cloud Computing 8.1 Introduction It is now proposed to use cloud-computing platforms and virtual network laboratories such as GENI (Global Environment for Network Innovations), together with high-speed software defined networks such as Internet2 to combat various cyber-physical implementation challenges for wide-area control of large power systems using Synchrophasors. Experimental results from a cloud-in-the-loop testbed environment are reported to support our proposed architecture. The Wide-area Measurement Systems (WAMS) technology using GPS-synchronized Synchrophasor measurements is an ideal way to control instabilities in large power systems [1, 2, 84]. The challenge, however, is the bottleneck in data communication and computation, which cannot be handled by today s Internet [85--88]. Here we propose the use of cloud-computing platforms such as GENI [90] together with high-speed software defined networks such as Internet2 to combat this challenge. We consider a five-area reduced-order model of the Western Electricity Coordinating Council (WECC), i.e. transmission grid of the US west coast as our test system. This system is first implemented in Real-time Digital Simulators (RTDS), and integrated with 115

125 hardware Phasor Measurement Units (PMU), which are further connected to the ExoGENI cloud. PMUs are assigned to the terminal bus of every area of the WECC model. The states measured by the PMUs are then communicated to unique sets of virtual controllers constructed in the cloud. The virtual machines (VMs) share the state information between each other in the cloud over Internet2, and cooperatively compute a state-feedback LQR control algorithm for small-signal oscillation damping of the five-area model. The control signals from each VM are thereafter communicated back to the excitation system of every generator in the RTDS for actuation. A cloud-in-the-loop control system is thereby created. In the following sections we describe different parts of this closed-loop system in more details. 8.2 EXOGENI-WAMS Networked Cloud Computing Testbed As a complementary system, a Wide-Area Monitoring and Control (WAMC) system is expressly designed to enhance the operator s real-time situational awareness that is necessary for safe and reliable grid operation. The envisioned WAMC system is a typical cyber-physical system due to the tight coupling between information, communication, and computation technologies, as well as physical power systems. The increasing deployed synchrophasor measurement units and highresolution measurement data requires to switch current state-of-the-art centralized information processing architecture to the completely distributed architecture. Toward this envisioned distributed WAMC architecture, we already theoretically designed the wide-area controller based on LQR technology for the improvement of inter-area transience in the above sections. The cyber-physical networked cloud computing testbed is next needed to implement this innovative distributed wide-area control algorithm. The research objective of this cyber-physical networked cloud computing testbed is to verify and validate critical distributed wide-area monitoring and control applications in large power systems using synchronized phasor measurement. The remainder of this section will introduce the testbed components, architecture, and setup, as well as controller implementation in the cyber system. 116

126 8.2.1 Testbed Components From the point of view of the hierarchy of the future power grid, the ExoGENI-WASM testbed consists of three main components: 1) Real-time digital simulator (RTDS) at the physical power grid layer; 2) PMU-based Wide-Area Measurement System (WAMS) at the information layer; 3) ExoGENI networked cloud computing platform at the Wide-Area Monitoring and Control application layer. The RTDS is used to simulate the large power system and perform analogue/digital input/output (I/O). The PMU-based WAMS system is allowed to measure the voltage, currents, and phase angles present in the simulated power system. The ExoGENI testbed enables data virtualization and implementation of innovative distributed wide-area monitoring and control applications. 1) RTDS: Real-time digital simulator (RTDS) is specifically designed for real time simulating power systems. Various I/O cards with numerous analogue and digital channels enable the Hardware-In-Loop (HIL) feature to be implemented easily. Furthermore, the GTNETx2 card supports various protocols (e.g. GSE, SV, DNP, PMU, Socket) based on the data format defined in IEC standards. 2) PMU-based WAMS: PMU-based WAMS consists of advanced measurement technology and information tools that lay down the foundation for the understanding and management of the increasing complex behaviors of dynamic charaterestics exhibited by large power systems. The Phasor Measurement Unit (PMU) is used to measure the voltage, currents, and phase angles, synchronize these measurements with the GPS signal, and output data at a rate of at least 60 samples per second. The applications located in either the real computer or virtual machine can request synchrophasor data directly via C communication protocol. 3) ExoGENI: ExoGENI platform provides the powerful networking and cloud computing services. It enables the real-world deployment of innovative distributed wide-area monitoring and control applications. The System-in-the-Loop (SITL) feature enables researchers to evaluate the performance of a monitoring and control network that is comprised of virtual networking, virtual computing nodes/machines, and physical networking PMU machines in real time. Rich 117

127 Figure 8.1: Architecture of the ExoGENI-WAMS Testbed visualization and user-friendly operability through web-start applications make experiments developed in ExoGENI easy to understand, thus suitable for training and education Testbed Architecture The architecture of the ExoGENI-WAMS cyber-physical testbed that is comprised of the components introduced above is shown in Figure 8.1. The data exchange between cyber and physical is time-critical and should be done in real time. The blocks in Figure 8.1 is described as below. 1) Physical System Modeler: Physical System Modeler consists of a power system modeler, corresponding controllers, and physical PMU-based WAMS/physical IEDs. The power system modeler implemented in RTDS includes all the modeling components that represent a physical power system, such as generators, transformers, lines, loads and wind turbines. The controller (e.g. exciter, governor) collects the measurement data from the power system model and sends 118

128 back control commands. Similarly, the physical PMU-based WAMS system can stream needed data from the power system model. The data can either be exchanged within the physical system modeler, or be exchanged through the cyber system modeler, depending on whether a controller or the WAMS system is connected to the communication and computation network. RTDS can easily model a large power system and its controllers using its user interface software RSCAD. The GTNET card, GTAO card, and PMU machines enable RTDS to communicate with the cyber system modeler through ethernet or analogue/digital I/O ports. 2) Cyber System Modeler: Cyber system modeler for this specific testbed pertains the ExoGENI networked cloud computing platform, and it can interact with physical system modeler by emulating the reconfigurable virtual communication and computation network. The WAMS applications and its networks can be implemented in the cyber system modeler. The ExoGENI platform consists of 5 circuit providers and 14 cloud sites at the physical layer and corresponding Open Resource Control Architecture (ORCA) control software including Aggregate Manager (AM) and Slice Manager (SM) at the software layer. The ORCA AM configured in each site, either cloud site or circuit provider, comprises a cloud handler plugin to invoke the cloud service and an image proxy server to obtain VM s images through the URL address. A slice refers to an experiment/application run in ExoGENI and thus the ORCA SM is to create, maintain, and delete an experiment/slice. The ExoGENI sites and control software enable the software-defined networking using OpenFlow, thus ExoGENI offers a powerful unified hosting platform for deeply networked, data-intensive cloud computing applications, such as distributed synchrophasor applications for the WAMC. Flukes, a web-start GUI application, is used to run the WAMS applications on ExoGENI. 3) Data Exchange Socket Data exchange socket enables data to be exchanged between the cyber system modeler and the physical system modeler. The analogue and the digital signals generated by the GTAO card are converted into packets that are streamed by PMU machines and further transferred into the cyber system modeler. On the other hand, the packets from the cyber system modeler will be formatted and converted to analogue or digital signals through the 119

129 Figure 8.2: Setup of the ExoGENI-WAMS Testbed 120