Power System Stability Enhancement Using Adaptive and AI Control

Transcription

1 Power System Stability Enhancement Using Adaptive and AI Control O.P. Malik University of Calgary Calgary, Canada 1

2 Controller Design Requirements Selection of: System model Control signal Scaling of signals Eliminate the effects of unpredictable errors (use of filters) Sampling period (for discrete implementation) Conventional Controller Design Obtain a limited order system model Linearize the system model around a prespecified operating point [y(s) = G(s)u(s)] or [Y(z) = H(z)U(z)] The linear model has fixed parameters -θ s is constant Using linear control theory, design a controller off-line The controller is implemented with fixed parameters 2

3 Control Computation u(t) = f[θ s (t), y(t), u(t-t)] where: θ s (t) is the system (Plant) parameter vector y(t) is the output vector [y(t) y(t-t) ] u(t-t) is the control vector [u(t-t) u(t-2t) ] denotes the transpose T is the sampling period, and f[.] denotes a function Conventional Controller How to select a proper controller transfer function for satisfactory performance over full frequency range of interest How to effectively tune the controller parameters How to automatically track the variation of system operating conditions How to consider the interaction between various machines 3

4 Characteristics of Conventional Controller Designed for each specific application Settings are a compromise that provide acceptable, though not optimal, performance over a wide range of operating conditions Needs to be tuned during commissioning Needs retuning if the system configuration has changed. Power System Operation Characteristics Power systems are non-linear Their characteristics and parameters depend upon the operating conditions System variables may execute large excursions under disturbance conditions System configuration and parameters may change with time -θ s (t) 4

5 Desirable Controller Features for Power Systems Desirable to have control that takes into account the true operating conditions Track the system parameters on-line during operation Determine the control based on actual parameters Computations in real-time. Thus should be simple to compute Adaptive Control Changing of controller parameters on-line based on changes in the system operating conditions Whenever changes in system operating conditions are detected, an adaptive controller responds by determining a new set of control parameters 5

6 Adaptive Controller Functions of the Adaptive Controller Identification of unknown parameters or measurement of a performance index Decision of the control strategy On-line modification of the controller parameters 6

7 Adaptive Control Techniques Two approaches -Direct Adaptive Control Parameters of the controller adjusted directly -Indirect Adaptive Control Parameters of the plant estimated and controller parameters vector adapted based on estimated plant parameters Direct Adaptive Control General Configuration Reference Model ω _ u c FL Controller System + ω r e Steepest Gradient MRAC PSS Structure 7

8 This image cannot currently be displayed. Reference Model A reference model provides the desired response of the controlled system Objective: Overall controlled system responds dynamically as the specified reference model Example of a second order reference model Transfer function G RM = s ζω s +ω n 2 n -percent overshoot related to damping ratio ζ -settling time related to ζ and natural frequency ω n 8

9 Reference Model Selection Apply a perturbation to the plant (generating unit) viewed as a second order system For various operating conditions, estimate pole locations and get an average set of pole locations Shift the chosen poles by a certain amount with the consideration of the limitation of control Characteristics of MRAC Reference model such that actual system can match its performance Not always easy to select proper model If performance not achieved, delay of inputs will occur causing reference model response substantially different from actual system Actual system responds to disturbances immediately but not the reference model 9

10 Indirect Adaptive Control General Configuration System System Model Model Parameter Identification Controller Self-tuning Adaptive Control Estimate the parameters of the plant model at any instant in time, say k, using an appropriate identification technique Adapt the controller parameters based on the estimated plant parameters vector and the control strategy chosen, assuming the identified model is the true description of the controlled system 10

11 Self-tuning Adaptive Control (Contd.) Ability to self-adjust control parameters to the system conditions Based on certainty equivalence principle of stochastic control theory A stochastic control problem can be solved in the following two steps -A system identification -A deterministic control problem Main Functions of Identification Not expected to obtain an exact mathematical description of the system Stress only the important features of the system A model fit for the specific application 11

12 System Identification Evaluation of a system model representing the essential aspects of an existing system and representing the knowledge of that system in a useful form -Model identification -Parameter identification Parameter (Explicit) Identification Identification algorithms always in discrete time-domain Parameter estimates updated every sampling interval For correct identification, there must always be some variation in the system output, i.e. the system has to be excited 12

13 Identification Techniques Analytical techniques Recursive Least Squares (RLS) Extended Recursive Least Squares (ERLS) Recursive Maximum Likelihood (RML) Ŷ(t)=-A(q -1 )y(t-t)+b(q -1 )u(t-t)+ζ(q -1 )ε(t-t) ε(t)=y(t)-ŷ(t) = prediction error Artificial Intelligence based- Fuzzy logic, NN RLS Identifier more popular due to: Relatively low computational requirements Fairly straightforward to understand Can provide very good results for: high signal to noise ratio, and noise affecting the system is white. For S/N ratio <10, bias in parameter estimates 13

14 Model Parameter Identification Using the actual output and input, determine the transfer function (model) of the system Because computers are used, the system is described by a discrete model A( z ) y( t) = B( z ) u( t) + C( z ) e( t), where A( z B( z C( z n b n ) = 1+ a z ) = b z 1 ) = c z a a z b z c nc i b and e( t) is white noise. i z i nc i a nb z na nb z na CLOSED LOOP SYSTEM Σ u(t) B A 1 ( Z ) 1 ( Z ) y(t) G F 1 ( Z ) 1 ( Z ) 14

15 Identification Algorithm Compute A and B parameters on-line using Analytical or AI based algorithm To track the system, the parameters must be updated continuously at an interval consistent with the frequency of the system dynamics. Three main points: appropriate model proper test (input) signal identification scheme In practice use a fixed order structure (generally a third order) Y(t)= -a 1 y(t-t)-a 2 y(t-2t)-a 3 y(t-3t) +b 1 u(t-t)+b 2 u(t-2t)+b 3 u(t-3t) ˆT = θ ( t). φ( t) + e( t) ˆT θ = [ a, a 1 2, a 3, b, b 1 2, b 3 ] T φ = [ y( t T),..., y( t 3T ), u( t T),..., u( t 3T )] Determine a 1,a 2,a 3,b 1,b 2,b 3 by an identification algorithm 15

16 Recursive Least Squares Algorithm P( t 1) φ( t) K( t) = T 1+ φ ( t) P( t) φ( t) T P( t + T) = [ P( t) K ( t) P( t) φ( t)] Θˆ ( t + T) = Θ( t) + K( t)[ e( t) eˆ( t)] K(k)- gain matrix; P(k)- error covariance matrix Forgetting Factor As time increases, the estimated parameter vector, converges towards its true value and covariance matrix, P(t), tends to zero. In time varying systems, this affects the parameter tracking. A forgetting factor is used to improve tracking of parameters. 16

17 Forgetting Factor, λ, (Contd.) Forgetting factor <1 gives more emphasis on recent data during parameter updating while old data is considered obsolete This provides better tracking of time varying parameters by exponential inflation of the covariance matrix, P(t), and hence the estimator gain, K(t). Forgetting Factor (Variable) Problem of blow-up can be overcome by employing time-varying forgetting factor, λ(t). [1 λ ( t ) = 1 Σ 0 = σ 2. N 0 φ T ( t 1). K Σ 0 ( t )] ε 2 ( t ) where, σ 2 is the expected noise variance N 0 controls the speed of adaptation 17

18 Control Strategies Control strategy is based on the assumption that the parameters, A and B, of the system are known. Thus control strategies for the deterministic control problem can be used in the self-tuning control. Both analytical and AI based control techniques can be used. ANALYTICAL TECHNIQUES Optimal Control Theory - Linear Quadratic Gaussian - Minimum Variance Control - Generalized Minimum Variance control Classical Control Techniques - Pole-zero Assignment Control - Pole Assignment Control - Pole Shifting Method 18

19 Pole Assignment Specify desired system closed-loop poles Freedom to place poles at any desired locations Similar to MRA as desired response is specified Controller parameters updated based on explicit identification Pole Assignment (Contd.) Most basic advantages of PZA Simple to realize No specific guidelines for the selection of desired locations of poles Considering only the closed-loop poles can guarantee stability, but cannot guarantee good system response 19

20 Desirable Controller Requirements Controller should not be unstable under nonminimum phase conditions Controller should not saturate under transients Pre-selection of required performance be avoided Trade-off between the best control effort and control action made on as few parameters as possible. These requirements satisfied by Pole Shift control algorithm MAPPING FROM s DOMAIN TO z DOMAIN Im Im x Re x x Re x s z 20

21 Pole Shift Control Basic Principles: 1.Theoretically, as the closed-loop poles are shifted towards the center of the unit circle in the z-domain, the closed-loop system becomes more stable. 2. Practically, as the poles are shifted towards the center of the unit circle, more control effort is required. 3. The control variable has output limits. Pole Shift Control (Contd.) Characteristics - In essence a PA controller but the closed-loop poles are obtained by shifting open-loop poles radially towards the center of the unit circle by a factor α<1. - Always guarantees closed-loop system has greater margin of stability for α<1. - Reduces the number of tuning parameters of the regulator 21

22 Analytical Self-tuning Adaptive Poleshift PSS Recursive least-squares identification algorithm to determine the system model parameters, A(z -1 ) and B(z -1 ). Open-loop poles of the system are the characteristic roots of A(z -1 ) = 0. Pole-shifting control shifts the roots towards the origin of unit circle by a factor α. Positioning The Closed Loop Poles r i αr i Open loop poles Closed loop poles 22

23 This image cannot currently be displayed. Self-Adjusting Pole Shift Control Strategy Shift the closed-loop poles of the controlled system towards the center in the z-plane by a factor, α, less than 1. In open-loop transfer function the poles are 1 given by A( z ). 1 In closed-loop, poles become Aαz ( ).. Vary the pole-shift factor, α, on-line to always produce maximum damping contribution without exceeding the control limits. 23

24 Efdo + Efd + G Δω AVR Vr + u CPSS - Vt AFPSS Single Machine Infinite Bus System Commonly Used PSS (CPSS) An illustrative example: Take IEEE type PSS1A PSS Its transfer function is TF = K s 1 st5 1+ st1 1+ st..[. 1+ st6 1+ st5 1+ st2 1+ st 3 4 ] 24

25 Comparison of APSS & CPSS For P = 1.26pu, pf = 0.94 lag Dynamic Stability Improvement by APSS Active power deviation (p.u.) Time (sec) Active power deviation (p.u.) Time (sec) 25

26 Transient Stability Margin Results Maximum Clearing Time Without PSS 120 ms With CPSS 150 ms With pole shift APSS 165 ms 3-Machine System Configuration #5 T5 11.5kW #4 T kW 5 3 T3 #3 18.5kW 10kW j0.92pu 20kW 0.11+j1.84pu 0kW Response of Gen. #4 with 0.8 Hz Forced Oscillations on Gen. #3 Power deviation kw Power deviation kw s 5s 10s 15s 20s AER on Gen. #4-3 0s 5s 10s 15s 20s AER on Gen. #4 26

27 Test on a 400 MW Thermal Unit 27

28 Practical Application of an APSS A self-tuning APSS with RLS identifier and selfadjusting pole shift control has been implemented on a commercial platform. Initially tested in the laboratory with a real-time system model that includes a governor, turbine, synchronous generator, unit transformer and grid models. 28

29 Practical application (Contd.) Tested in the field on a 45 MVA salient pole hydro-generator at Feistritz hydro power station in Austria Installed on a 100 MVA gas turbine driven solid-pole machine since September 1997 at Mainz Power Station, Germany 29

30 Other Installations Retrofitted on eleven 280 MW hydrogenerators at Porto Primavera hydrostation in Brazil and in operation since One turbo-generator in a nuclear generating station in Latvia Observations Based on Practical Experience with APSS Able to improve the natural damping for all possible operating conditions Does not need specific tuning for each machine on which it is installed No need to calculate the parameter settings or further tuning during commissioning 30

31 Observations (Contd.) APSS can be used with every type and size of generator In simulation studies, same APSS was used on a salient pole machine and on a solid rotor machine without any change or further tuning. In each case it provided effective performance APSS Applications The APSS is especially well suited for use in networks characterized by a high variability of system configuration or by high system impedances, such as: - Weak power systems with low short circuit capacity - Systems in which drastic changes in network configuration are usual 31

32 Applications (Contd.) - Systems subjected to strong load fluctuations - Systems operated as isolated networks - Systems with long feeder lines from the generating station to the distribution centers The APSS is able to improve and ensure a good damping for all system configurations and conditions. Artificial Intelligence Techniques Out of the various Artificial Intelligence (AI) techniques, artificial neural networks and fuzzy logic offer the possibility of realtime implementation. Neural networks and fuzzy logic can be used for both identification and control. 32

33 Various types of identification and control techniques can be combined to form a variety of controllers. Fully analytical Fully artificial intelligence based Mixed analytical and artificial intelligence based Adaptive PSS With Simple NN Identifier and PS Controller An adaptive linear element (ADALINE) based identifier to identify ARMA model parameters Pole shift controller Implemented on a commercial AVR/PSS platform Experimental studies 33

34 ADALINE Network Model Power System Model Structure 34

35 Plant and ADALINE Response 0.1 pu Torque Step Change (P=0.6 pu, pf=0.92 lead, V=0.99 pu) 35

36 Stability Margin Test Neuro Adaptive PSS 36

37 Neuro-Adaptive PSS Response to a three phase to ground fault, p=0.7 pu, pf=0.62 Table 1:Dynamic Stability Margin * for Different Stabilizers. OPEN CPSS NAPSS Maximum Power 2.65 pu 3.35 pu 3.60 pu Maximum Rotor Angle 1.55 rad 2.14 rad 2.36 rad * Dynamic Stability Margin is defined as the maximum power output at which the generator loses synchronism while input torque reference is gradually increased RBF Identifier applicable for on-line application - Hidden layer created as a competitive layer wherein the center closest to the input vector is the winner. - Scalar weights from the hidden layer to the output node are modified as a vector θ, whose size equals the size of the input vector θ (t)= [a 1,,a n,b 1,,b m ] - By linearizingthe output of the RBF at each sampling instant, θ has a one to one relationship with the system parameters. 37

38 Stability Margin Test APSS CPSS APSS Five Machine System Configuration 38

39 Identified System Oscillation Frequency Time after disturbance s Identified frequency Hz APSS Installed on G 1 & G 3, CPSS Installed on G 2, G 4 & G 5 39

40 Functional module ofafuzzy fuzzy controller Domain Expert Fuzzy Knowledge Base and inference Engine Fuzzification Pre-Processing Defuzzification Post-Processing Power System Controller A self-learning fuzzy logic controller with two inputs-speed deviation and its derivative Each input represented by seven membership functions The center points, i.e. weights of the fuzzy controller, are updated depending upon the error, e, using the standard back-propagation algorithm 40

41 Results APSS CPSS No PSS APSS CPSS Power Angle [rad] Power Angle [rad] time [s] time [s] 0.05 p.u. step increase in torque and return to initial condition (Power 0.95 p.u., 0.9 pf lag) 3 phase to ground fault, middle of one transmission line and successful reclosure (Power 0.9 p.u., 0.9 pf lag) Simple Fuzzy PSS SFPSS output: Control action sign: Fuzzy Rule Base: Normalized distance: s V pss =K s u 1 1 if ω + ω N 0 N = if ω + ω N < 0 d n ZO S M B u d n = ω N + ω N N 41

42 Study system -MIS Nort-South oscillation mode: λ= 0.011±j2.016 f = 0.32 Hz ζ= % SYC, SYD, CBD, ENO vs. LAV, MDP, VAD CPSS Mixed Power angle at CBD generators ( ) Time (s) 3 phase fault at one 400 kv bus and trip of one 400 kv line with CPSSs on units 1 and 2, and SFPSS on unit 3. 42

43 Adaptive Takagi-Sugeno PSS (ATSPSS) Results 0.05 p.u. step increase in torque and return to initial condition (power 0.95 p.u., 0.9 pf lag) 3 phase to ground fault at the middle of one transmission line and successful reclosure (power 0.9 p.u., 0.9 pf lag) 43

44 Fuzzy Adaptive Control PSS u(t) AVR & Exciter Mamdani FLC ^ y(k+1) + _ z-1 y(t) TL Grid RLS identifier APSS RLS identifier and a self-learning Mamdani fuzzy logic controller. Results 0.1 p.u. step increase in torque and return to initial condition (power 0.30 p.u., 0.9 pf lead) 3 phase to ground fault at the middle of one transmission line and successful re-closure -adaptive Mamdani fuzzy logic PSS (AMFLPSS ----fixed centers FLPSS (power 0.9 p.u., 0.9 pf lag) 44

45 SVC with supplementary adaptive controller Adaptive Control Scheme D - + ANFC u(k) Plant y(k) D + D e i D D RLS Identifier ŷ (k) D D e c - + y d 45

46 Control Structure for a SVC device in a SMIB System G SVC Device V m - + u(t) V ref Infinite Bus P svc Adaptive Controller Control Parameters System Identification Example of membership functions before and after adaptation Before adaptation, After adaptation 46

47 Concluding Remarks Successful application of a number of modern control and AI techniques to design PSSs has been demonstrated. Extensive work has shown quite clearly the advantages offered by these techniques. Each technique has its unique characteristics. Advantages of an Adaptive PSS Does not require to be redesigned for each new application. Needs no tuning during commissioning. Provides optimal response to suit the system operating conditions. Tracks the system characteristics. Therefore, needs no retuning over time. 47

48 Thank you 48