Power Systems Oscillations Damping with Regard the Finite Speed of Propagation the Electromechanical Waves

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1 International Journal of Energy and Power Engineering 15; 4(): Published online March 14, 15 ( doi: /j.ijepe ISSN: X (Print); ISSN: 36-96X (Online) Power Systes Oscillations Daping with Regard the Finite Speed of Propagation the Electroechanical Waves Oleg Agaalov Tashlyk Pup Storage Power Plant, Yuzhnoukrainsk, Ukraine Eail address: To cite this article: Oleg Agaalov. Power Systes Oscillations Daping with Regard the Finite Speed of Propagation the Electroechanical Waves. International Journal of Energy and Power Engineering. Vol. 4, No., 15, pp doi: /j.ijepe Abstract: Daping of the power syste electroechanical oscillations with agnitude-phase excitation controller (MPH-EC), which is responsive to the deviations of the agnitude and phase of the terinal voltage phasor, and taking into account the finite speed of propagation the electroechanical waves, caused perturbation the power balance are considered in this paper. The structure of an integrated excitation control syste of synchronous achines (IECS SM) using a reote phasor easureent units (PMU s) to identify the cross-sections (tie lines) of electroechanical oscillations and putting into operation the function of power syste stabilizer, installed on the revealed cross-sections of electroechanical oscillations has been proposed. A significant advantage of the proposed ethod and technology of daping the low-frequency electroechanical oscillations in the power syste is its selectivity in relation to the ain odes, with the lowest daping ratio, aking the greatest contribution to the developent of the power syste instability, due to the action of the optial nuber of MPH-EC located taking into account the given grid topology. Keywords: Power Syste, Synchronous Generator, Terinal Voltage Phasor, Autoatic Voltage Regulator, Power Syste Stabilizer, Synchrophasor Vector Processor, Mode of Electroechanical Oscillation 1. Introduction The ajor blackouts in large extended power systes of the world occurred in the recent past [1] show the need to continue work on the developent, as a atheatical odel of occurring transients, and practical applications to ensure safe, reliable and efficient operation of the interconnected systes. Contributes to this goal recently active developent of reote easureent, onitoring, protection and control systes: WAMS - wide area easureent syste, WAPS - wide area protection syste, WACS - wide area control syste, WAMPC - wide area onitoring, protection, and control syste [-4], which are based on phasor easureent unit (PMU). At the sae tie, currently with sufficient hardware developent of the above systes, the ain obstacle to their further developent is the lack of control algoriths based on the use of phasors easureents [4]. Application of the above systes in the United States [3, 5-7] allowed the practice to reveal the existence of electroechanical wave s propagation in the power syste with a finite speed, uch less than the speed of electroagnetic waves propagation. Experients with load shedding, conducted in the United States [5] revealed a delay of about.5 s with the easured values of the frequency in the transient (with the help of PMU) between the nearest and reote power syste buses. This is allowing estiating the propagation speed of the electroechanical waves about 5-1 k/s, as a uch saller copared to the speed of electroagnetic waves, depending on the tie lines paraeters and the inertia of synchronous generators. Distribution of electroechanical waves in the event of disturbances in the power syste is not considered as a classical odel of electroechanical oscillations of synchronous achines in a power syste, and the developent of protection and control. At the sae tie, accounting of this physical phenoenon, and the use of reote easureent systes (WAMPC) allow, as shown in the paper, to develop an integrated excitation control syste of synchronous achines (IECS SM), revealing the cross-sections of electroechanical oscillations (CSEO), and the selective introducing the function of power syste stabilizer on the synchronous achines, located in the CSEO. This allows us to suppress the ain electroechanical

2 International Journal of Energy and Power Engineering 15; 4(): oscillation odes, with the lowest daping ratio, that ake the greatest contribution to the developent of the instability of the power syste. Thus, an effective daping of electroechanical oscillations and better dynaic properties of the power syste is attained by the action of an optial aount of ECS SM, located with account the grid topology. This paper presents the sections with the following contents. In the second section consider the ain existing odels of electroechanical wave propagation in large power systes. The key assuptions used in these odels and it ain conclusions are given. The attention is focused on the applicability of the obtained results for the developent of IECS SM. Section three presents the ain eleents of WAMPC. The structural and functional diagras of this syste are presented. Discussed in detail the synchrophasor vector processor (SVP), those obtain the input data fro PMU s. SVP provides the calculation of CSEO with the subsequent foration of the necessary control signals to ECS SM for daping the ost dangerous electroechanical odes. In the fourth section, we consider a block diagra and the algorith of IECS SM with agnitude-phase excitation controller (MPH-EC), which receives the control signals fro SVP. In the fifth section shows an exaple the design of IECS SM for 6-achines power syste odel, in which we investigate the static and dynaic stability of the SM. In the conclusions suarizes the ain points and results of this paper.. Main Provisions of the Existing Models of Electroechanical Wave Propagation in Large Power Systes Operating experience has revealed that the perturbations in the large extended power systes caused by an ibalance of power consuption and generation propagate with finite speed. Obviously, the speed boundedness of electroechanical waves propagation in the power syste with values 5-1 k/s, uch lower than the speed of electroagnetic wave propagation, was identified with the use of PMU s, synchronized in tie with the help of global positioning syste GPS [, 5-7]. This fact is not reflected in the classical theory of electroechanical oscillations, based on ordinary differential equations (ODE) the otion of synchronous achine rotor, depending only on the tie [8, 9]. Therefore, the odels, that describe the otion of the synchronous achines rotors depending on the tie, and the spatial coordinates, based on partial differential equation (PDE) have been developed [6, 7, 1-1]. These odels are based on the representation of the basic paraeters of the power syste as continuous variables, distributed in a certain spatial coordinate syste. For exaple, defined by the distributed inertia of synchronous achine rotor per unit length. Directly hoogeneous odel of power syste for study the electroechanical wave propagation represented as a grid of connected nodes, shown on Figure 1: Figure 1. Diagra of siulated grid node with the coordinates (X, Y). Each node can be odeled in two-diensional space (X, Y) of grid coordinate syste, that characterized by a certain constant voltage E ( X, Y) with phase δ and conductivity Y. At displaceent relative to the given node along the selected axes (X, Y) paraeters of transission lines linking it with other nodes receive an increent ( R + jx). Connecting a set of nodes (Figure 1) in ring, was exained the physical processes of electroechanical wave propagation in the event of disturbances in the hoogeneous 64-achines power syste odel [6, 7, 1-1]. In equation of otion the synchronous achine rotor: Hɺɺ δ + ωdɺ δ = P Pe = Pa, (1) ω where H - inertia constant, s, ω - angular rotor speed of SM, rad/s, D - daping coefficient, s, P, Pe, Pa - echanical, electrical, and accelerating power, p. u. In equation (1) its paraeters are also considered as distributed paraeters that

3 73 Oleg Agaalov: Power Systes Oscillations Daping with Regard the Finite Speed of Propagation the Electroechanical Waves depend on the spatial coordinates (X, Y): H h ( X, Y ), D d ( X, Y ), ( X, Y ), P p ( X, Y ), P p ( X Y ) P p e e a a, Passing to the liit, the equation (1) reduces to the for [6]: where v ωv sin Θ =, u hz ( δ ) P () ɺ δ + γδɺ v δ + u = (3) ωv cosθ ω =, P = hz ω d γ =, z = R + jx, G = Re[ Y], = h ( P GV ) X h i + Y Equation (3) is a hyperbolic wave equation of nd order in partial derivatives. Local frequency easured on the tie line or any bus of power syste is defined as: 1 dδ 1 dδ f = f +, f = f f = (4) π dt π dt Accordingly, when the electroechanical wave passes through the PMU location (the bus of power syste, tie line, etc.), a local phase angle of the voltage in this location will vary depending on the tie. The velocity of electroechanical wave propagation, and accordingly the phase angle change in the local voltage in this location depend on the agnitude voltage, power syste frequency, inertia of synchronous achines, and ipedance of tie lines. For the above hoogeneous odel of grid in the for of a ring was deterined the speed estiate of electroechanical wave propagation: v V sin Θ = ω, (5) h z where ω - power syste noinal frequency, V - voltage agnitude, Θ - phase angle of the tie line ipedance ( Θ 9 sin Θ 1), h - inertia constant per unit length, z - ipedance of the tie line per unit length. In the above power syste hoogeneous odel the spatial distribution the inertia constant of SM, and the ipedance of tie lines (links) along the coordinate axes X-Y assued to be identical. The orientation of branches, connecting the nodes deterined º or 9º with respect to the chosen coordinate syste X-Y. In a heterogeneous power syste odel for study the electroechanical waves propagation the distributions of paraeters (inertia constants, tie lines ipedances, and others), as well as the spatial arrangeent of branches relative to the selected coordinate syste is assued to be arbitrary. For this odel in [1], the electroechanical wave in power syste described by a syste of equations siilar to the, j telegraph equations: ω t p ( x, t) ( x, t) t 1 = = b ( x) ( x) 1 x b x ( x) ( x) ω x ( x, t) ( x, t) p x where ( x) - inertia constant, p. u., b ( x) - susceptance of tie lines per unit length, p. u., ω ( x,t) - angular rotor velocity, p. u., p ( x, t) - electric power, p. u., x - 1-diensional spatial j t coordinate. This syste of equations for ω( x t) = Ω( x) e jωt p( x, t) = P( x) e where ( x ), P( x) has an analytical solution: ω p ( x, t) = Ω ( x ) ( x, t) = P ( x ) v v v v, (6) ω,, Ω - coplex functions, x ( x) 1 exp jω ( ) t x v( ξ ) x ( x) 1 exp jω ( ) t x v( ξ ) x x dξ, dξ where v ( x) - speed of electroechanical wave propagation. Effective daping of power syste oscillations can be significantly iproved if the algoriths of power syste stabilizers will take into account the liitation of speed (5) of distribution the electroechanical waves (and hence the delay) in the event of disturbances to deterine the optial ipacts of ECS SM. The following section describes the ain eleents of WAMPC syste, necessary for the solving given proble. 3. Wide area Measureent, Protection and Control Syste Currently, the synchronized phasor easureents have been widely used in power systes around the world for checking the accuracy of developed power systes odels, transient analysis, and paraeters estiation in real tie. However, the synchrophasor easureents are still significant untapped potential to provide a safe, reliable and econoic operation of power systes by it control taken into account the phase relations between their operation ode paraeters, which can be easured and processed in real tie. Synchrophasor easureent based on the use of PMU. For counication between PMU s and their top-level devices using protocol by standard IEEE C [13]. Processing of synchrophasor easureents and their use for controlling includes the next steps: 1. Sending the synchrophasor easureents data fro PMU;. Tie coordination for received synchrophasor easureents data taking into account the delays in each of the counication channels; (7)

4 International Journal of Energy and Power Engineering 15; 4(): Perfor the vector coplex atheatical operations for processing synchronized data; 4. Perfor the prograed logic operations based on the synchrophasor easureents data; 5. Foration and sending the control coands to the corresponding output relay, or control unit of power syste in a tie short period to ensure control in real tie. Block diagra of the power syste control in real tie using synchrophasor easureent data is shown in Figure : Figure. Block diagra of real tie synchrophasor power syste control. Task of synchrophasor vector processor (SVP) [3, 14] is to collect data fro PMU s, reception of digital input signals fro the protection relays and syste autoation, the ipleentation of vector and scalar calculations, the foration of the control signals, and sending the to the actuating eleents, recording and archiving of power syste data in transients. For exaple, one of the SVP tasks ay be collect data fro PMU s, established at the tie line ends, the coparison of the voltage phase angles at its ends, and the foring the alar, and control signals to reduce the active power flow above a certain critical value. An iportant issue to ensure the correct control of the power syste in real tie, using the synchrophasor easureent data, is accuracy of the tie easureent. So, for exaple, one electrical degree (1º el.) for frequency 5 Hz corresponds to the tie interval in 55.5 µs. Therefore, the error in the tie easureent, approxiated to 1- µs, ay be considered acceptable. Working with such sall tie intervals for processing the synchrophasor easureent data defines the requireents for the data transission. Considered as acceptable the speed that deterines at least one packet data transission over the period. In soe cases the use of a serial data transission protocol at speed 96 bit/s answered for these requireents. For applications requiring higher data rates need to use the Ethernet protocol, or siilar. A block diagra of the SVP inputs-outputs shown in Figure 3. [3]: Figure 3. SVP Input/Output Block Diagra.

5 75 Oleg Agaalov: Power Systes Oscillations Daping with Regard the Finite Speed of Propagation the Electroechanical Waves The appointent of SVP inputs and outputs described in [3, 14]. Software SVP based on the standard IEC , which includes the functions for perforing atrix and coplex calculations, can be used for the following tasks: 1. Monitoring the dynaics of the power syste states by calculating the difference between the voltage phasors angles in its ain reference points (buses), the slip frequency, and acceleration in order to predict the state of the angular grid instability.. Modal analysis in real tie based on synchrophasor easureents data for identification the undaped electroechanical oscillation odes in order to perfor the necessary copensation actions to prevent violations of the power syste stability. One of these actions can be coordinated excitation control of synchronous achines using SVP deterining the cross-sections of electroechanical oscillations (CSEO), as will be discussed below. 3. Develop and ipleent a differential buses protection, covering several switching power supply syste to ensure the axiu perforance and selective clearance of faults. 4. Identification and copensation the data easureent error fro PMU s. Next, consider the hardware functional block diagra of the SVP [3, 14], is shown in Figure 4.: Figure 4. SVP Hardware Functional Block Diagra. The ain eleents of SVP are [3]: Protocol Conversion and Tiestap. This block translates IEEE C37.118, serial data, IP/Ethernet protocols, and input coands into a coon data forat/structure. For protocols that do not support tie inforation, a tiestap for the data is added. Exaples of protocols that do not have tie inforation are Modbus, and SEL Fast Message. IEEE protocols such as C37.118, IEC 6185, and SEL Synchrophasor Fast Message already have a tiestap. Data Tie Alignent. Data ay be easured at the sae tie but delayed during counication. The Data Tie Alignent block correlates data blocks based on tie to copensate for unequal counications delays. Logic Engine. The Logic Engine is a soft-core prograable logic controller (PLC) with vector and

6 International Journal of Energy and Power Engineering 15; 4(): coplex ath capabilities. Data inputs to the Logic Engine are fro the Data Tie Alignent block. The Logic Engine can also access the Database Manager to retrieve stored data, as required for logic processing. Protocol Generator. Outputs fro the Logic Engine are sent to the Protocol Generator. It converts the results into appropriate protocols such as IEEE C37.118, DNP3 LAN/WAN, Modbus RTU, SEL MIRRORED BITS counications, SEL Fast Message, etc. Database Manager. The Database Manager interfaces to the Data Tie Alignent block and the output of the Logic Engine. The Database Manager forats data for storage, perfors the OPC Client query, and provides OPC Server responses. It also provides data to the Logic Engine for use in control algoriths. OPC Client. The OPC Client perfors OPC requests for data as defined by user setting or the Logic Engine. OPC Server. The OPC Server serves data to external OPC clients. The data ay be raw data fro the Data Tie Alignent block, Logic Engine, or Data Archive block. Configuration Manager and Control (CMC). The CMC provides a user interface to configure the various counications inputs, Logic Engine algoriths, counications output forat configurations, database anageent, and other various configuration duties. As entioned above, an object of the SVP is fast execution of atheatical operations by coplex vectors for control of the power syste ode. For it the coputation cycle should not exceed one period of the frequency. Algorithic functional diagra of SVP shown in Figure 5: Figure 5. SVP Algorithic Functional Block Diagra. In addition to the above given hardware functional block diagra of the SVP in this figure arked the following algorithic function blocks, that can be odified or expanded: Power Calculation: the calculation of active P and reactive Q power using the voltage U and current I phasors. Monitoring of Phase Angle Difference: the calculation of the phase angle difference for voltage phasors between two points (buses) of controlled grid, and foring alar when it exceeds a predeterined value for a given cross-section to prevent angular instability. Modal Analysis (MA): the calculation in real tie the paraeters of the observed electroechanical oscillation odes, based on data received fro the PMCU s. Synchronous Machine and Grid Topology States Estiation Processor: receiving inforation fro the previously entioned algorithic function blocks, this processor calculates the integral state of a synchronous achine with regard to its stability, theral and vibration conditions, work of power syste autoation, liiters (OEL overexcitation liiter, UEL underexcitation liiter, etc.), and generates the control inputs to ECS SM and turbine controller. One of these actions ay be the control of power syste stabilizer (PSS) of ECS SM, using SVP that defining the cross-sections of electroechanical oscillations (CSEO), enable or disable

7 77 Oleg Agaalov: Power Systes Oscillations Daping with Regard the Finite Speed of Propagation the Electroechanical Waves the fro working on corresponding synchronous achines. It is thus possible to provide an integral selective stabilizing effect of PSS, ounted on all ECS SM. Foration of output signals and coands: SVP, using fast protocols and counication cannels, sends coands to the reote and local control devices of the power syste (such as ECS SM, turbine controllers, copensators, shunt reactors and other). As an exaple of the odern SVP, can be considered the unit SEL-3378 [14], anufactured by Schweitzer Engineering Laboratories (USA). This SVP provides for the collection of inforation fro PMU s with all the above entioned protocols for data transfer, the transfer of control coands and processing of algorithic probles, except for the above-described the processor for synchronous achine and grid topology states estiation. In concluding this section, it should be noted that the ipleentation of such a control principle is based on the previously discussed concepts, defining the electroechanical oscillations as electroechanical wave in power syste, having a finite, and a uch lower speed of propagation copared with an electroagnetic wave. 4. Daping of Low-Frequency Electroechanical Oscillations in the Power Syste Using a Coplex "PMU s SVP ECS SM" Using devices PMU s and SVP, taking into account the finite speed propagation of electroechanical waves, allows to execute a odal analysis of eerging electroechanical oscillations in the power syste in real tie. Identifying the dangerous oscillation odes, and ways of their distribution is possible optially provide the necessary control actions (signals) for their daping. The traditional approach to prevent and daping of electroechanical oscillations in the power syste is based on the odal analysis (MA) ipleentation, studying the dynaic properties of the grid odel at the stage of it design (not in real tie). The inaccuracy of the constructed grid odel, and therefore a reflection of its dynaic properties, the inability to coplete the odeling of all perturbations and odes of operation that ay occur in the power syste, liited the ethod of MA. Using the PMU s and SVP is possible to identify and optially dapen the electroechanical oscillations in real tie, due to selectively chosen ECS SM for the identified cross-section(s) of power syste oscillations. For it in SVP used the algorith of odified Prony analysis (MPA). At the core of the MPA is the superposition principle by which the initial easureent signal (phasor voltage, current, power, or another physical quantity) is replaced by a linear cobination of a set of exponential oscillation odes in a finite tie interval. To saple the easured data { x [ ], x[ ],... x[ N] } the value xˆ [ n] accordingly both for <n< 1 MPA estiates 1 N [3]: xˆ M σ [ ] ( 1) T n = A e cos( πf ( 1) T + ϕ ) = 1 where: T - sapling interval, s; A - aplitude of th exponential function, p. u.; σ- daping constant for the th exponential function, s -1 ; f- frequency, Hz; ϕ - initial phase, rad.; M - nuber of odes. An iportant paraeter that deterines the objectivity of the calculations is the SNR signal-to-noise ratio : (8) N [ ] x n n= SNR = 1 log 1 (9) N ( [ ] [ ]) x n xˆ n n= Since MPA is based on a linear superposition of the odes, it has a low SNR, if the saple data contain the results of nonlinear perturbations (for exaple, the on-off generators or loads, tie lines, or the like). The SNR has a sufficient value (~ 8 db), if the disturbances of this kind are not included in the reporting sapling interval, corresponding to the ode of the following electroechanical oscillations in the power syste. Electroechanical oscillations (waves) in the power syste can be observed in the paraeters deviations of the operation ode, such as bus voltage V i, the difference of buses voltage angles δ ij, flows of active P and reactive Q power in tie lines. In MA used the synchrophasor easureents data as input signals. As result, MA deterinates the ain existing (or observed by MPA) electroechanical oscillation odes, and their value SNR. Each detected ode of electroechanical oscillations characterized by a structure which is based on the following key paraeters [3]: 1. Aplitude of ode A (naed or relative units of corresponding physical paraeter);. Frequency of ode f, Hz; 3. Daping constant σ, s -1 ; 4. Daping ratio ς, p. u. or %; 5. Initial phase of ode ϕ, º or rad. The daping ratio ςcalculated fro the known values daping constant σ and frequency f : ς σ = σ + ( πf ) (1) The negative value of the daping ratio ς (positive daping constant σ ) characterizes that the corresponding ode leads to an instability the power syste. Since the MPA uses a nuerical approxiation (8), the calculated values of

8 International Journal of Energy and Power Engineering 15; 4(): the observed frequencies of the odes in various places of the grid ay be different at frequency ain, ost dangerous ode of the electroechanical oscillation. Therefore, to identify a coon syste ode of electroechanical oscillation, that ust be dapening priarily, used a predeterined threshold Π deviation of frequency i ode fro the average frequency value f of observed electroechanical oscillation odes: SNR f M M f i (11) i= = 1 + SVP calculates the total electroechanical oscillation ode, if the difference between the calculated average value of the frequency f and the frequency f i i ode is less Π : f f i Π (1) In accordance with the above, in SVP is ipleented the logic unit for detection, and daping the dangerous ode of electroechanical oscillations in the power syste, Figure 6. [3]: SNR Π f H + f + f L A A Π + ς Π ς + Figure 6. Logic unit for the detection and daping of dangerous ode of electroechanical oscillations in the power syste. For generating a control signal fro the SVP to ECS SM ust satisfy the following conditions ( Π - lower index for a given threshold): "Signal to noise" ratio SNR >SNRΠ; The upper f H and lower f L values define a predeterined frequency range of electroechanical oscillation typical for given power syste. The frequency of the observed dangerous ode fl f fh ; If the structure of observed ode of electroechanical oscillation with frequency f is characterized by the paraeters: aplitude A AΠ, and daping ratio (DR) ς ς Π, control signal fro SVP activates the power syste stabilizers in those ECS SM, which are located at the buses of power syste, connectable the

9 79 Oleg Agaalov: Power Systes Oscillations Daping with Regard the Finite Speed of Propagation the Electroechanical Waves CSEO. Let us now consider how to ensure optiu daping effect of low-frequency electroechanical oscillations in the power syste using the coplex "PMU-SVP-ECS SM". To solve the probles of voltage regulation and daping of electroechanical oscillations in ECS SM used the structure of agnitude-phase excitation controller (MPH-EC) [15-17]. Block diagra of the proposed coplex "PMU-SVP-ECS SM" is shown in Figure 7: Figure 7. Daping of low-frequency electroechanical oscillations in the power syste through an integrated excitation control syste of synchronous achines (IECS SM) "PMU SVP ECS SM". SVP, using the inforation fro PMU s, deterines the cross-section (-s) of power syste in which it extends a dangerous for the stability electroechanical oscillation ode, assue this cross-section k n as shown in Figure 7. For it cross-section detects the conditions: f A ς L f k n k n k n A, ς Π Π f H, (13) In deterining the conditions (13), SVP generates the control signals for ECS SM, connected to the k th and n th buses of power syste, connected the cross-section k n (this can be one or ore tie-lines). When receiving these control signals in ECS SM k and ECS SM n introduced the power syste stabilizers fro the angles deviations at the ends of the cross-section in accordance with the law of MPH-EC: V V f f k n = K = K V V V V k n sec sec ( N δk n ), δk n = δk δn, ( N δ ), δ = δ δ, n k n k n k (14) or gain N changes to enhance the action on angles deviations δ k n, δn k. A significant advantage of the proposed ethod and technology of daping the low-frequency electroechanical oscillations in the power syste is its selectivity in relation to the ain odes, with the lowest daping ratio, aking the greatest contribution to the developent of the power syste instability, due to the action of the optial nuber of ECS SM, located taking into account the given grid topology. 5. Exaple of Construction the Integrated ECS SM to Study the Steady-State and Transient Stability To estiate the stability and dynaic properties of ulti-achine power syste with integrated ECS SM consider a odel of 6-achine syste, Figure 8:

10 International Journal of Energy and Power Engineering 15; 4(): In each of the areas 1-3, connected by tie lines 3 kv, installed two synchronous turbogenerator with paraeters Figure 8. 6-achine power syste odel. given in Table 1: Table 1. Paraeters of the odels of synchronous turbogenerators in 6 - achine syste. Paraeter Value G1 G G3 G4 G5 G6 x d, p. u. 1.8 x' d, p. u..3 x '' d, p. u..5 x q, p. u. 1.7 x' q, p. u..55 x '' q, p. u..5 x l, p. u.. T ' d, s. 8 T '' d, s..3 T ' q, s..4 T '' q, s..5 R S, p. u..5 Н, s K F (friction gain), p. u. р (nuber of poles pairs) 4 f, Hz 6 Paraeters of the initial steady state d ω, % δ, I s, p. u ϕ a, ϕ b, ϕ c, V f, p. u

11 81 Oleg Agaalov: Power Systes Oscillations Daping with Regard the Finite Speed of Propagation the Electroechanical Waves In ECS SM odelled MPH-EC with paraeters K V = 3.3, N = In the initial steady-state ode, the loads of power syste areas are: P 1 = 967 МW, Q 1 = - 87 МVAr; P = 1767 МW, Q = МVAr; P 3 =1767 МW, Q 3 = МVAr that causes the active power flow 75 MW between the first and second areas. To study the steady-state and transient stability of power syste under consideration are siulated following perturbations: 1. Subission a step signal.5 p. u. at the input of voltage setting V ref1 of the first turbogenerator duration s at s of siulated transient;. The three-phase short circuit on the tie line, connecting area 1 and area, in a tie oent t = 5 s, and duration. 33 s. After the appearance of dynaic disturbance (three-phase short-circuit), and the identification of a dangerous ode of electroechanical oscillations siulated different cobinations of control actions fro SVP in the tie interval s (taking into account the delays in data transission fro the PMU, and the coputation tie of the SVP for conditions (13)), increases the gain of MPH-EC on the deviation rotor angle N =1 18. In this case, as a result of coputational experients, it was deterined that the stability of the siulated ultiachine power syste at a Annex given hard dynaic perturbation is provided only for the case of increasing the gain N =1 18 of MPH-EC for SM G1 and G, installed on the revealed cross-section of the power syste oscillations between area 1 and area, fro the sending area 1. For other cobinations of control actions fro SVP, the stability of siulated ultiachine power syste is not guaranteed. In the annex Figure 9 and 1 shows the obtained transients in the tie doain. 6. Conclusions Modern state developent of power systes is characterized by intensive introduction the reote easureent data syste, such as WAMPC, allowing the use, in addition to the agnitude of state paraeters, their angle (phase) inforation. These systes allow in practice to identify the existence of electroechanical waves propagating with finite speed in power systes at its perturbations. Using this fact, offer an integrated ECS SM, to identify the electroechanical oscillation odes with the lowest daping ratio, akes the greatest contribution to the developent of the power syste instability. Putting into operation the power syste stabilizers of ECS SM with MPH-EC, located in the arising cross-sections of electroechanical oscillations fro the transitting side, allows achieving an optial daping of power syste. Coputational experients carried out on the odel, have shown the effectiveness of the proposed integrated ECS SM to increase the stability, and dynaic properties of the power syste.

12 International Journal of Energy and Power Engineering 15; 4(): Figure 9. Transient in the 6-achine power syste odel, K v = 3.3, N = 18 is inputted to the SM G1 and G in the area 1.

13 83 Oleg Agaalov: Power Systes Oscillations Daping with Regard the Finite Speed of Propagation the Electroechanical Waves Figure 1. Transient in the 6-achine power syste odel, K v = 3.3, N = 18 is inputted to the SM G3-G6 in the areas, 3. New York: McGraw-Hill, p. References [1] U.S.-Canada Power Syste Outage Task Force, Final Report on the August 14, 3 Blackout in the United States and Canada: Causes and Recoendations, April 4, Available at [] Phadke A. G., Thorp J. S., Synchronized Phasor Measureents and Their Applications, Springer Science + Business Media LLC, 8, p. 48, ISBN [3] Schweitzer E. O. Advanced Real-Tie Synchrophasor Application / E. O. Schweitzer, III, D. Whitehead, A. Guzan, Y. Gong, M. Donolo// Journal of Reliable Power. 11. Vol... May. p [4] Machowski J., Bialek J. W., Buby J. R., Power Syste Dynaics: Stability and Control, nd Edition, John Wiley & Sons, Ltd., 8, p. 69. [5] Faulk D., Murphy R. J., Coanche peak unit no. 1% load rejection test underfrequency and syste phasor easureent across TU electric syste, Proc. Annu. Conf. Protective Relay Engineers, March, 1994, College Station, TX, USA. [6] Thorp J. S., Seyler C. E., Phadke A. G., Electroechanical Wave Propagation in Large Electric Power Systes, IEEE Transactions on Circuits and Syste-I: Fundaental Theory and Applications, Vol. 45, 6, pp , June [7] Huang L., Parashar M., Phadke A., Thorp J., Ipact of electroechanical wave propagation on power syste protection and control, Cigre Session, Paris, France, no. 34, pp. 1-6, August. [8] Kundur P. Power Syste Stability and Control / P. Kundur. [9] Analysis and Control of Power Syste Oscillations: CIGRE TF , Brochure 111, p. [1] Selyen, A., Analysis of Disturbance Propagation in Power Systes Based on a Hoogeneous Dynaic Model, IEEE Transactions on Power Apparatus and Systes, Vol. 93,, pp , [11] Lesieutre B. C., Scholtz E., Verghese G. C., A Zero-Reflection Controller for Electroechanical Disturbances in Power Networks, 14 th PSCC, Seville, 4-8 June, p. 7. [1] Xu Y., Wen F., Ledwich G., Xue Y., Electroechanical Wave in Power Syste: Theory and Applications, Journal Modern Power Syste Clean Energy, 14, no. (), p [13] IEEE Standard for Synchrophasor for Power Systes, IEEE Standard C Available at [14] SEL-3378 Synchrophasor Vector Processor Data Sheet, Schweitzer Engineering Laboratories, available at [15] Agaalov O. N. Magnitude-Phase Controller (MPHC) / O. N. Agaalov // The 1 International Conference on Control Engineering and Counication Technology (ICCECT 1), Shenyang, China, 1. [16] Agaalov O. Control systes structures of synchronous achines excitation / O. Agaalov. Labert Acadeic Publishing, p. ISBN: [17] Agaalov O. Physical Processes in the Daping of Electroechanical Oscillations of the Synchronous Machine with Magnitude-Phase Excitation Controller / O. Agaalov // International Journal of Energy and Power Engineering. ISSN: 36-96X (Online) 13. Vol.. 4. p