Summary of Engineering doctoral thesis: Study on stabilization and optimization of a large-scale system applying for power systems

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The objectives of the thesis are to study on a method to analyze a large-scale system into a number of relatively independent subsystems (interconnected subsystems). Then, the dissertation will focus on designing a decentralized control method for the large-scale system which has been decomposed into the interconnected subsystems.

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Nội dung Text: Summary of Engineering doctoral thesis: Study on stabilization and optimization of a large-scale system applying for power systems

MINISTRY OF VIETNAM ACADEMY OF EDUCATION AND SCIENCE AND TRAINING TECHNOLOGY GRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY ……..….***………… VU DUY THUAN Study on stabilization and optimization of a large-scale system applying for power systems Major: Control theory and Optimization control Code: 62.52.60.05 SUMMARY OF ENGINEERING DOCTORAL THESIS Hà Nội – 2018
INTRODUCTION The urgency of the thesis Study on large-scale systems have been facing a lot of challenges. One of the most difficulties is the increasing complexity of the mathematical models of the systems. This is due to a mutual influence of complex technology processes, environments and society on the system. In addition, calculation increase of each system cannot be compared to the increase of its size. These difficulties make the design of an efficient control strategy to deal with the stability and reliability of a large-scale system, especially for a multi-machine interconnected power network highly challenging. 2. The objectives, ranges, objects and research methods of the thesis a, The objectives The objectives of the thesis are to study on a method to analyze a large-scale system into a number of relatively independent subsystems (interconnected subsystems). Then, the dissertation will focus on designing a decentralized control method for the large-scale system which has been decomposed into the interconnected subsystems. The proposed control strategy has been applied for a multi-machine electric power system, which is a typical example of the large-scale systems. With the above objectives, the dissertation consists of the following contents: - Study on large-scale systems characterized by a number of nonlinearities and uncertainties. 1
- Design two control problems for a large-scale power system, including decentralized control for transient stability issue and hybrid control strategy for load-frequency control. - Design simulation model in MATLAB/Simulink package to demonstrate the accuracy and feasibility of the proposed control strategies. b, Range and object of research Relying on the previous studies about the large-scale systems, the author decided to design two control strategies to stabilize a multi-machine electric power grid which is considered to be a typical example of the large-scale systems under uncertainties and nonlinearities. The research range of this thesis is to build a mathematical model for a large-scale electric power network consists of more than three station areas under uncertainties as well as nonlinear constraints. The author applied analytical methods to propose a novel control strategy using modified Riccati equations in dealing with the transient stability problem of the three-machine electric power system. The author also suggested a hybrid control scheme applying a PD-like fuzzy logic controller and superconducting magnetic energy storage devices to tackle the load- frequency control of a five-machine interconnected power network. Although the research results are obtained by numerical simulation demonstrations, this study is completely significant in practical applications. c, Research methods - Theoretical research: Analyze the theory, build theoretical basis for control problems under uncertainties with a number of given laws 2
and constraints. The goal is to maintain the system frequency at the nominal value and bring the stability back to the power grid. - Tools: Lyapunov’s stability theory, Riccati equation, linear algebra, fuzzy logic control, etc. - Based on the above tools, this thesis presented a control strategy applying modified Riccati equations to find an optimal feedback control law with a state gain vector. The goal of this control scheme is to damp instantaneous fluctuations caused by noises, thereby ensuring the stability of the system. The next part of the study focuses on designing an intelligent control strategy applying a PD-type fuzzy logic controller and superconducting magnetic energy storage (SMES) to maintain the network frequency at the nominal value. The control performances obtained in this study are verified through numerical simulations using MATLAB/Simulink package. It is supposed that these research achievements are able to be a fundamental study for the further studies of large-scale systems under uncertainties, then they can be applied for the reality. 3. Scientific and practical significances - Reaffirm the correctness of several theories which have been applied for studies on the control engineering of optimization and fuzzy logic. - Propose a simplest and best method for calculation to obtain good control performances satisfying acceptable tolerances. Then, this method has been applied for two typical control problems of the large-scale power system: transient stabilization and load-frequency control problems. 3
- Practical significances: There is no doubt that the power system plays an extremely important role for a nation, thus the stability and reliability of power transmission need to be seriously considered. The control strategies proposed in this study are able to enhance the control performances and ensure the stability and economy of the power network. The main contents of the thesis The thesis includes four chapters: Chapter I. Overview of large-scale systems: generally analyze large-scale systems with domestic and foreign studies which were reported in the past. Chapter II. The theory of distributed systems and decentralized control. This chapter mainly focused on building a mathematical model for the large-scale power networks and evaluating the stability of the systems. The author proposed two control problems, i.e. transient stability and load-frequency control for whole the multi- machine electric power plant. Chapter III. Study on an effective decentralized control strategy to stabilize a large-scale power grid. The proposed control method using improved Riccati equations has been applied for a three-machine power system. Simulation results implemented in MATLAB/Simulink environment were presented to demonstrate control quality of the proposed strategy. Chapter IV. Study on load-frequency control of an interconnected power system. In this chapter, the author presented a novel control scheme to maintain the network frequency at a nominal value (50Hz). The proposed control method is a hybrid integration of 4
PD-like fuzzy logic controllers and SMES devices. Good simulation achievements clarified the feasibility of the control strategy studied in this chapter. Conclusion and discussion: Conclude studied results and present discussions for future work. CHAPTER 1: OVERVIEW 1.1 Characteristics of large-scale systems 1.2. Related work 1.2.1. Domestic studies 1.2.2. Foreign studies 1.3. Brief conclusions relating to the thesis 1.4. Conclusion for chapter I - Study on stability of the large-scale systems under uncertainties is a new research in Vietnam and in the world. In fact, the electric power grid in Vietnam is considered to be a typical example of the large-scale systems, so that this study plays an important role in reality. - There have been a number of studies on the large-scale systems, especially the interconnected power networks. In dealing with the stability of a multi-machine electric power grid, there exist a lot of control strategies, such as PID, fuzzy logic, neural network, optimal and adaptive control methods. However, each control strategy still needs to be further improved to design the best control method in dealing with the stability of a large-scale power system. 5
CHAPTER 2: DISTRIBUTED SYSTEMS AND DECENTRALIZED CONTROL FOR LARGE-SCALE POWER SYSTEMS 2.1. Introduction A multi-machine power grid is considered to be a typical example of large-scale systems. Such a power system normally consists of several generation areas; each area is considered to be a control area which includes three basic components: a governor, a turbine and a synchronous machine with electrical load. Figure 2.1. A large-scale power system model consists of N interconnected areas In this study, the author proposes two stability control problems for a multi-machine power system. The first one is a transient stability problem, and the second one is load-frequency control problem which is the key for automatic generation control (AGC) of a power grid. 2.2. Mathematical model of a multi-machine power system Consider a n-machine electric power system with an equation describing rotor motion of the ith generator as follows: Mii  Dii  Pmi  Pei , i = 1, 2,…, n (2.1) 6
n Where: Pei   j 1 Ei E jYijcos( i   j  ij ) In (2.1), M i , Pmi và Ei are constant for each synchronous generator. Let: Di   , i = 1, 2,…, n (2.2) Mi Let a vector x  R 2( n 1) be: x  (1n ,2n ,...,n1,n ,1n  10n ,..., n1,n   n01,n )T (2.3) where      ,      ,    and  are solved from 0 in in n in i n i i ij the power balance: Pei (ij0 )  Pmi với i = 1, 2,…, n – 1 (2.4) The Lur’e-Postnikov function as:  x  Ax  Bf ( y)  T (2.5)  y C x Equation (2.5) can be rewritten as:    0   1  xi    xi    i ( yi )  h i ( x)   1 0 0 , i = 1, 2,…, n – 1  yi   0 1 xi  (2.10) The system given by (2.10) presenting interconnected Lur’e – Postnikov subsystems. These subsystems are given by: s xi  Ai xi  bii (  i )   eij hij ;  i  ciT xi , i  1, 2,..., s j 1 2.2.2. Analysis of subsystems Each subsystem can be modelled by the following equation: 7
   0   1  xi    xi    1 ( yi )   1 0 0 (2.13)  y  [0 1] x  i i Based on Walker and McClamroch (1967), we select a Lyapunov candidate as: ciT xi T Vi ( xi )  x H i xi  i i   ( y )dy i i i (2.18) 0 Where Hi is a constant matrix, and i is a scalar number. According to [20], the Popov constraint as: i1  Re(1  ji )cTi (A j I)1 bi    0 (2.19) . 2 V i ( xi ) (7.15)   i1/ 2i ( yi )  gTi xi    i (2.20) Now we carry out stable area as xi*  0. Based on a procedure proposed by Walker and McClamroch, let  i1  0 and consider the following condition: i  ( i  1) 2 2 0   0 (2.22) i   2    2 2 An approximation i of the stable region i (  i   i ) . We get: i   xi : Vi ( xi )  Vi 0  , i  1, 2,..., n -1 (2.36) where Vi 0 is determined from (2.35). 2.2.3. Stable region With each given value i , we can select a positive number  i (0   i  cosij0 ) given in (2.30)  yik'  sin( yik'   in0 )  sin  in0 , k = 1, 2  i  1   i i (2.52) Where, m (Gi )   i  i is combined with (2.51), one can be obtained below: 8
 n 1   i M ( H i )  1 i  2 M n  M i1 Ain cos in sin  in0  M i1  Aij sin( ij0  ij0 )  i m ( H i )  j 1   j i  i = 1, 2,…, n – 1 (2.53) From (2.53) it is possible to recognize that the smaller Aịj is, the easier the value of εi can be selected. This means that the decomposition of the power system model should be performed in such a way that the resulting subsystems are weakly coupled. This is also the general principle to analyze a large-scale electric power system. 2.3. Control strategies to stabilize a power system 2.3.1. Introduction 2.3.2. Transient stability problem Recall a N-machine electric power system with the following mathematical [18-20]:  xi (t )  Ai xi (t )  Bi ui (t )  fi (t , x(t )), t  t0  (2.60)  xi (t0 )  xi 0 , i  1, 2,3,..., N In dealing with the nonlinearities of the system, the author suggested using a two-step method based on Riccati equations to establish the linear decentralized control law as follows. Step 1: Establish the modified algebraic Riccati equations in a form as follows: 9
 N  AiT Pi  Pi Ai  Pi   pij Gij GijT  Pi  PB T 1 i i Ri Bi Pi  j 1, j i  (2.64) N   pij Wi Wi  W W ji   Qi  0 T T ji j 1, j  i where Ri > 0 and Qi(ni x ni) and Pi(ni x ni) are defined matrices. Step 2: Solve the above Riccati equations to find the control law as follows: ui (t )   K i xi (t )  1 T (2.65)  K i  Ri Bi Pi The feedback control law mentioned in (2.65) is capable of recovering the stability of a large-scale system after presence of disturbances. Hence, it is also applied to an interconnected electric power system, particularly the three-machine network. In this perspective, the corresponding control law can be given below: ui (t )   Ki xi (t )     K i  i (t )   i 0   Ki i (t )    K Pi  Pmi (t )  Pmi 0   K Xi  X ei (t )  X ei 0   K  R 1 BT P  i i i i (2.66) The effectiveness of this control law will be specifically demonstrated in the following section through a number of numerical simulations using MATLAB/Simulink package. 10
2.3.3. Fuzzy logic applied for load-frequency control 2.3.3.1 Definition of fuzzy logic control 2.3.3.2. Principles and steps to design a fuzzy logic controller 2.3.4. Fuzzy logic controllers 2.4. Conclusions for Chapter 2 The main objective of this study is to analyze the large-scale nonlinear and uncertain systems with a typical example of interconnected power networks. The author also presented an approach to evaluate the stability region for such a power system in a case of considering it as a set of weakly interconnected subsystems by applying Lyapunov theory. For the stability issue of a large-scale power system, the author proposed two problems: transient stability and load-frequency control. To each control problem, the author presented a particular control strategy which will be discussed in the following chapters. Chapter 3: Decentralized control strategy to stabilize a power system 3.1. Introduction 3.2. Structure of a multi-machine electric power system Figure 3.1: Typical structure of a power system 11
3.3. Mathematical model of a power system Figure 3.2. Three-machine electric power system model 3.4. A control strategy to stabilize an interconnected power system Assuming that this model consists of N subsystems, its corresponding mathematical representation is as follows1:  xi (t )  Ai xi (t )  Bi ui (t )  fi (t , x(t )), t  t0   xi (t0 )  xi 0 , i  1,2,3,..., N (3.23) where, fi(t, x(t)) = fi(x) denotes the interconnected components which represent all nonlinear characteristics of the ith subsystem. Such terms should satisfy the Lipshitz conditions as:  f i ( x )  c x  x, y n (3.24)  f i ( x )  f i ( y )  h x  y 12
N f i ( x)   j 1, j  i Gij gij ( xi , x j ), i  1, 2,3,..., N . (3.25) Where gij(xi, xj) is a nonlinear function, which must satisfy the following constraint: n gij (xi , x j )  Wi xi (t)  Wij x j (t) , xi ni , x j  j (3.26) xi* (t )  0 ui (t )   K i .xi (t ) xi (t ) Figure 3.3. Feedback control model for the control area #i 3.5. Simulation and discussion In this chapter, the author presents three simulation cases to demonstrate the effectiveness of the proposed control strategy. First, three steps need to be implemented as follows : Step 1: Design of the control plant, a typical example of an interconnected electric power grid. Using the simulation parameters given in the two reports, the following equations can be obtained for the first and second machines: N xi (t )  Ai xi (t )  Bi ui (t )   pij Gij gij ( xi , x j ), i  1, 2,3,..., N . (3.30) j 1, j  i 13
Step 2: Find the solution of the algebraic Riccati equations given in (3.23). Using MATLAB environment, solving the Riccati equations presented in (2.64) with the given simulation parameters, the control law, especially the following two gain vectors (computed from (3.26)), can be obtained:  K1  [ K1 K1 K P1 K X1 ]    [174.7398  42.2510  10.7218  5.2562]  . (3.31)  K 2  [ K 2 K2 K P2 K X 2 ]   [174.2508  29.2102  10.7003  5.4231]  Step 3: Carry out the necessary numerical simulations to demonstrate the feasibility of the proposed control method. In this step, we give two simulation cases with the initial conditions indicated in Table. 1 4 Machine 1 Machine 1 1,2 (rad/s)  1,2 (rad) Machine 2 2 Machine 2 0.5 0 0 -2 0 1 2 0 1 2 time (s) time (s) (a) (b) 0.5 1 Machine 1 Pm1,2 (p.u.) Machine 1 Xe1,2 (p.u.) Machine 2 0.5 Machine 2 0 0 -0.5 -0.5 0 1 2 0 1 2 time (s) time (s) (c) (d) Figure 3.4: Dynamic responses of the first and second machines in the simulation case #1 14
1 4 Machine 1 Machine 1 1,2 (rad/s)  1,2 (rad) Machine 2 2 Machine 2 0.5 0 0 -2 0 1 2 0 1 2 time (s) time (s) (a) (b) 0.5 2 Machine 1 Machine 1 Pm1,2 (p.u.) Xe1,2 (p.u.) Machine 2 1 Machine 2 0 0 -0.5 -1 0 1 2 0 1 2 time (s) time (s) (c) (d) Figure 3.5: Dynamic responses of the first and second machines in the simulation case #2 0.7 0.5   0.6   Pm 0.4 Pm 0.5 Xe Xe Settling time(s) Settling time(s) 0.3 0.4 0.3 0.2 0.2 0.1 0.1 0 0 Machine 1 Machine 2 Machine 1 Machine 2 (a) (b) Figure 5: Comparative results of settling times for four state parameters 15
3.6. Conclusions for Chapter 3 This Chapter has studied an effective linear decentralized control strategy to find an optimal solution for the stabilization issue of the large-scale system. A three-machine electric interconnection model representing a typical case study of the large-scale systems has also been taken into account. First, this model is mathematically formulated then the linear decentralized control scheme is applied to recover the stability of the network after the presence of the disturbances. Numerical simulation results obtained have demonstrated the feasibility and superiority of the proposed control method. For future work, with the diversity and complexity of the practical electric power systems, modern control techniques, such as fuzzy logic and neural network should be considered to further improve the effectiveness of the studied regulation strategy. In this aspect, a robust control scheme can be built in an efficient integration with the decentralized control methodology proposed in the present paper. 16
CHAPTER 4: LOAD-FREQUENCY CONTROL OF A LARGE-SCALE POWER SYSTEM 4.1. Introduction 4.2. Mathematical model of a large-scale power system in LFC 4.2.1. Introduction to large-scale power systems 4.2.2. Mathematical model of a large-scale power system PD ,i U i ( s) PG ,i ( s ) PTnr ,i ( s ) Fi ( s ) GG ,i ( s) GT ,i ( s) GP , i ( s ) Ptie,i Figure 4.2. A typical model of a generation area From Figure 4.2, a mathematical model of the above system can be described as follows: Fi ( s )  GP ,i ( s )  PTnr ,i ( s )  PD ,i ( s )  Ptie,i ( s)  , (4.1) PTnr ,i (s)  GTnr ,i (s).PG,i (s), (4.2)  1  PG ,i (s)  GG ,i (s) U i (s)  Fi (s)  . (4.3)  Ri   2 n   Tij Fi (s)  Fj ( s) ,areas #i & #j are connected directly . Ptie,i ( s)   s j 1, j  i  0, otherwise  (4.4) 17
4.2.3. A model of superconducting magnetic energy storage - SMES Figurer 4.3. A model of SMES unit The output voltage of the converter is: Ed ,i  U d 1  U d 2  Vd 0 .cos  V 'd 0 .cos  ' (4.11) where Vd0 and V’d0 , α and α’ denote the ideal no-load DC voltages and firing angles of converter R1 and R2, respectively. Assuming that such two 6-pulse AC/DC thyristor – based converters are completely symmetrical, the DC output of the 12-pulse converter can be calculated as follows    Ed ,i  0 if   2 rectifying mode Ed , i  2Vd 0,i .cos  with   E  0 if    inverting mode  d ,i 2 (4.12) In terms of using the SMES as an efficient part of the LFC strategy, it is necessary to mathematically model such an SMES device. According to the tie-line bias control idea, ACE signals must be collected, and then they are taken to both the LFC regulator and the SMES. It means that each generating power should be equipped with an LFC controller and an SMES. The control idea is that the load changes can be compensated by charging or discharging of the inductor, thus the DC current Id,i should become a controlled 18
quantity. (a) Tie-line mn PD ,m PD ,n PD ,i PG ,i ( s ) PT ,i (s ) Fi ( s ) 1 PSM ,i SMES Ri Ptie ,i Model Ptie ,i ( s) Fi ( s) Calculation F j ( s ) Figure 4.7. SMES model in MATLAB/Simulink 4.3. LFC controllers 4.3.1 Conventional controllers 4.3.2. PD-like fuzzy logic controllers Control system using a PD-like fuzzy logic controller is shown in Figure 4.8. 19