Applications of FACTS devices for improving power system transient stability

TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K6- 2015 Applications of FACTS devices for improving power system transient stability . Dang Tuan Khanh . Nguyen Van Liem Ho Chi Minh city University of Technology, VNU-HCM, Vietnam (Manuscript Received on July 15, 2015, Manuscript Revised August 30, 2015) ABSTRACT As the power demand has been applicable in shunt connection Static Var increasing rapidly, today’s modern power Compensator (SVC), in series connection system becomes to be more complex and Thyristor-Controlled Series Capacitor faces many challenges. It is envisaged that (TCSC), or in the combination of both. transient stability will play the important role Mathematical models of power systems in ensuring the steady state operation of having FACTS devices are set of Differential power systems in the event of three phases - Algebraic Equations (DAEs). Trapezoidal fault or switching of lines. This paper rule and Newton - Raphson method are investigates models of Flexible AC applied to solve DAEs. The simulation results Transmission Systems (FACTS) and of rotor angles demonstrate the effectiveness applications of FACTS devices for improving and robustness of proposed the SVC and the rotor angle stability. FACTS devices are TCSC on transient stability enhancement of power systems. Keywords: Angle stability, FACTS, power system, power system stability, transient stability, SVC, STATCOM, TCSC, UPFC 1. INTRODUCTION Stability is always the important issue in controlling the power flow in very fast manner, today’s modern power system. Power system they can improve transient stability. stability may be broadly defined as that property The paper is recognized as follows: Models of power system that enables it to remain in a state of power system components and FACTS of operating equilibrium under normal operating devices’ models are represented in section 2. conditions and to regain an acceptable state of Section 3 discusses about models of power equilibrium after being subjected to a disturbance systems having SVC and TCSC. The [1]. This paper concentrates the rotor angle on mathematical model of power system having SVC analyzing transient stability. Rotor angle stability and/or TCSC is presented in section 4. The is the ability of interconnected synchronous simulation results in section 5 prove that FACTS machines of power systems to remain in devices used in power system are possibility of synchronism. As FACTS devices are capable of improving transient stability. Trang 47 SCIENCE & TECHNOLOGY DEVELOPMENT, Vol.18, No.K6 - 2015 2. MODELS OF POWER SYSTEMS mechanical power from the prime‐mover to COMPONENTS AND FACTS DEVICES reduce speed deviations. Accurate modelling of 2.1 Synchronous generator model the prime mover and governor which control the input mechanical power to the synchronous In this paper, the synchronous generator is generator and the rotor speed is very important, represented by fifth-order model in the d-q axes especially in the stability studies. The inputs having the rotor frame of reference [2]. comprise the machine speed, its reference value ψ r A m ψ r  F m I S  V r  and the initial power. The output is the machine  PPm e  power. The first-order differential equation set for  r  (1)  M describing the dynamics of the prime-mover and       r r R governor controller can be arranged in the following form [3, 4]. Where ψ r ,  r and r are rotor flux linkage x  A x  C   B ref  D P 0 (3) vector, rotor angular frequency and rotor angle g g g g r g g m Where is the state vector the prime-mover and respectively; Vr is the rotor voltage vector; Pm x g and P are the mechanical and electrical power ref 0 e governor controller;  , Pm are the speed respectively; M is the machine inertia constant; reference and the initial power respectively; A g , R is the synchronous speed; IS is the stator B g , C g , and D g are matrices of constant values current vector and E is the field voltage; A and fd m which depend on the gains and time constants of F are the matrices depending on machine m the controller. parameters. 2.2 Power System Stabiliser (PSS) As excitation systems of synchronous The PSS has been the most common generators play an vital role in their operation and stabilizer to damp out oscillations. The machine can affect the systems dynamic response, it is speed, terminal frequency and power can be used necessary to model the excitation systems as the input signals to the PSS. Figure 1 shows the accurately in transient stability analysis. The general structure of a PSS [5]. inputs comprise the terminal voltage magnitude, its reference value and supplementary signal from power system stabilizer (PSS). The output of excitation is the field voltage. The excitation system dynamics can be represented by the set of first-order differential equation as follows [3, 4]. Figure 1. PSS control block diagram ref Here, the rotor speed is used for the PSS x e A ee x  C esVVV  B ePSS  D es (2) input. The PSS output is added to the exciter Where x e is the state vector for the ref voltage error signal and served as a supplementary excitation system; Vs , V PSS , V s are the signal. The differential equation set for synchronous machine terminal voltage, representing the PSS controller can be arranged in supplementary signal from the PSS and voltage the following form. reference respectively. A e , B e , Ce and De are x  A x  C  (4) matrices of constant values which depends on the p p p p r Where is the vector of state variables of gains and time constants of the controller. x p the PSS; A and C are matrices the elements of Governor is responsible for sensing the speed p p deviations in rotor, and then adjusting the Trang 48 TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K6- 2015 which depend on the gains and time constants of system of SVC used in this paper is shown in the PSS controller. figure 3 [6, 11]. 2.3 Supplementary Damping Controller (SDC) model Block diagram of the SDC is shown in figure 2 [6, 7, 8, 9, 10]. The SDC block provides a modulation for power oscillation damping or Figure 3. Control block diagram of SVC small-disturbance stability improvement control. The inputs comprise the terminal voltage |VT |, The SDC block contains a gain, a washout, lead- ref its reference value V T and supplementary lag blocks and limiter. Many different power signal XSDC . The output is the SVC susceptance system quantities have been proposed or used for B c . The state equations for SVC can be arranged the input signal to the SDC. They include voltage as follows: phase angle, frequency, line current and active x  A x  CVXV  B  D ref (6) power flow. The principal SDC function is to s ss sT sSDC sT Where x is the state vector for the improve the inter-area mode damping. As there is s SVC; A , B , C and D are matrices the a strong interaction between active power and S S S S electromechanical oscillations, the use of active elements of which depend on the gains and time power flow input appears to be most common one, constants of the controller. which is also used in this paper. 2.5 Thyristor-Controlled Series Capacitor (TCSC) model The series counterpart of the shunt-connected SVC is a TCSC, which is connected in series with transmission line. TCSC was introduced in 1986. Figure 2. Control block diagram of SDC TCSC is a FACTS device that can provide fast The state equation for SDC can be described and continuous changes of transmission line in compact form as follows: impedance, and can regulate power flow in the line. The possibility of controlling the x  A x  C P (5) su su su su T transmittable power also implies the potential T Where xsuXXX S1 S2 SDC is the vector application of this device for the improvement of power system stability [12, 13, 14]. of state variables of SDC; Asu and Csu are matrices the elements of which depend on gains and time Figure 4 is shown in block diagram form the constants of the SDC controller. control system of TCSC [7, 8, 9, 13]. 2.4 Static Var Compensator (SVC) model SVC has been in use since the early 1960s. In addition to the main function of voltage or reactive power control, SVC can provide auxiliary control of active power flow through a Figure 4. Control block diagram of TCSC transmission line. The possibility of controlling The inputs are composed of active power of ref the transmittable power implies the potential transmission line PT and its reference value P application of this device for improving stability . The output is the reactance of TCSC X t . The in power system. Block diagram form the control Trang 49 SCIENCE & TECHNOLOGY DEVELOPMENT, Vol.18, No.K6 - 2015 state equations for SVC can be arranged as corresponding d-q components IsM and V sM follows: [15]. x  A x  BXPPP  C  D  E ref t tt tSDC tT tT t YTVTIYVSS MsM  MSM  SL LN  0 (13) (7) YTVYVLS M sM LL LN  0 (14) Where x t is the state vector for the TCSC; Where TTTTMdiag  1 ,  2 ,...,  ,NG  ; Ti is A t , B t , C t , D t , E t are matrices the elements of which depend on the gains and time constants the transform matrix [15]. of TCSC. Complete power system model need Section 2 has the focus on models for following algebraic equation. Equation (15) is individual components in power system such as relationship between the stato current vector and synchronous generator, PSS, SDC, SVC, and the stator voltage vector. TCSC. VPsM Mψ rM  Z M I sM  0 (15) 3. POWER SYSTEM HAVING FACTS Algebraic Equations (13), (14) and (15) are DEVICES represented power system’s model. V sM , IsM and V are algebraic variables of network model. Section 3 presents models of power systems LN having each of FACTS devices. 3.2 Power system with SVCs model 3.1 Power system model Power system with NS SVCs is considered in NB-node power system is considered in this this section. In D-Q frame, the network model for paper. It is to be assumed that NG generators are power system with SVCs can be described by: connected to the power system. The network IYYVSN   SS SL   SN        (16) nodal current vector and voltage vector are related                 as follows: I YV IYYYVLN0   LS LL  FS   LN  (8) YFS is also separated into real and imaginary In general, all of the quantities in (8) are parts. YFS and Y LL are the same dimension [15]. complex numbers. Separating (8) into real and Based on (16), the following equations is imaginary parts and rearrange: obtained: IYVNNN (9) YVYYVLS SN LL  FS LN 0 (17) IYYV      SN SS SL SN Transforming V in (17) into its           (10) SN       corresponding d-q components V leads to:       sM IYYVLN 0   LS LL   LN  YTVYYVLS M sM LL  FS LN 0 (18) Where S is set of generator nodes; L is set of non-generator nodes. Algebraic Equations (13), (15) and (18) are described power system with SVCs. These Based on (10), the following equations are equations contain non-state variables. obtained: 3.3 Power system with TCSCs model IYVYVSN SS SN  SL LN (11) Power system with NT TCSCs is discussed in 0 YVYV  (12) LS SN LL LN this section. In D-Q frame, the network model for I and V in (11) and (12) are in the SN SN power system with TCSCs can be described by: network D-Q frame of reference. The variables ISN and V SN are transformed into their Trang 50 TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K6- 2015 Where x is the vector of state variables; w IYYVSN   SS SL   SN  is the vector of non-state variables; f , g are       (19)           nonlinear vector functions. IYYYV0       LN   LS LL FT   LN  In order to validate the performance of power As each TCSC is connected in series with the system under transient conditions, it is always transmission line, the TCSC reactance augment desirable to carry out the time-domain simulations both the diagonal and off-diagonal of the network for the power system to investigate stability nodal admittance matrix for nodes which are analysis. The time-domain solutions are connected to TCSC. YFT is also separated into real implemented by solving simultaneously the set of and imaginary parts [15]. DAEs (22) and (23). The set of differential equation in (22) is solved by using the Trapezoidal Based on (19), the following equation is of integration as follows: obtained: x(n 1) x (n)  YVYYVLS SN LL  FT LN 0 (20) t (24) Transforming V in (20) into its SN f x(n 1),, w (n  1)  f x (n) w (n)  2   corresponding d-q components V sM becomes: Where t is the time step length and n is the YTVYYV  0 (21) LS M sM LL FT LN time step counter. Algebraic Equations (13), (15) and (21) are Equation (24) is rearranged to give: described power system having TCSCs. These x x  equations contain non-state variables.  (n 1) (n)  (25) t 4. THE SET OF DIFFERENTIAL - f x(n 1), w (n  1)  f x (n) , w (n)   0 ALGEBRAIC EQUATIONS (DAES) 2 Combining equations (23) and (25), we have: The main outcome of this section is the  x x  composite set of DAEs of the power system  ( n 1) (n )  having FACTS devices.  t (26)  f x(n1), w (n1)    f x (n) , w (n)   0  2 Differential equations of the model of power g x, w   0 system having FACTS devices comprise (1), (2),  (3), (4), (5), (6), and (7) in section 2. Depending Using Newton-Raphson method, the on the types of FACTS devices connected the solutions for x and w are found by power system, the set of state equations is simultaneously solving DAEs (26). In this paper, augmented with those for individual FACTS rotor angle results are necessary to study stability devices. These equations can be written in analysis. Next section will present results of compact equation (22). Equations (13), (14), (15), simulation in some cases. (18), and (21) in section 3 are algebraic equations 5. SIMULATION of the power system having FACTS devices. The computer programming is necessary to These equations can be also written in compact simulate power systems having FACTS devices. equation (23). This programming is helpful to students, (22) x  f x, w  engineers who do research in power system g x, w  0 (23) stability because of the expensive commercial   software. Trang 51 SCIENCE & TECHNOLOGY DEVELOPMENT, Vol.18, No.K6 - 2015 5.1 Case 1 5.2 Case 2 Case 1 considers the two-generator power Disturbances such as three phases fault or a system with or without FACTS devices as figure switching of line are discussed in case 2 as figure 5. The shunt FACTS device SVC is equipped at 8. The series FACTS device TCSC is equiped bus 4 while TCSC is connected between bus 3 and between bus 5 and bus 2 and the shunt FACTS bus 4. device SVC is equieped at bus 4. 2 3 ~ 5 1 4 ~ Figure 5. Power system in case 1 The disturbance is a three phases fault at bus Figure 8. Power system in case 2 3. The fault is initiated at time t = 0.5 s and the fault clearing time is 0.2 s. Figure 6 and figure 7 show the transient of power sytem. Figure 9. Relative rotor angle response to three phases fault at bus 5 Figure 6. Relative rotor angle response to transient The three phases fault is initiated at bus 5 at distubance in case1 with SVC at bus 4 time t = 0.0 s, and the clearing time fault is 0.2 s. Figure 9 presents the transient of power sytem. The three phases fault happens near bus 4 on the line between bus 4 and bus 3. The fault is initiated at time t = 0.0 s, and the clearing time fault is 0.2 s. Following the fault clearance, line between bus 4 and bus 3 is lost. Figure 10 shows the transient of power system. Figure 7. Relative rotor angle response to transient distubance in case 1 with TCSC between bus 3 and bus 4 It can be observed that if properly used FACTS devices, both SVC and TCSC can improve power system stability. Trang 52 TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K6- 2015 angles of the power system having FACTS devices recover faster than those of the power system without FACTS devices. 6. CONCLUSION In this paper, the power system stability enhancement of two-generator power system by SVC and TCSC is considered. The transient of rotor angles is compared with or without the present of FACTS devices in power system in the Figure 10. Relative rotor angle response to three event of a three phases fault or switching of lines. phases fault on line between bus 4 and bus 3 The above simulation results of rotor angles From results in figures 6-7 and figures 9-10, demonstrate the effectiveness and robustness of it can be seen that, FACTS devices are capable of proposed the SVC and TCSC on transient stability improving power system stability. Relative rotor enhancement of power systems. Ứng dụng các thiết bị FACTS cải thiện ổn định động trong hệ thống điện . Đặng Tuấn Khanh . Nguyễn Văn Liêm Trường Đại học Bách Khoa, ĐHQG-HCM, Việt Nam TÓM TẮT Hệ thống điện ngày nay ngày càng phức (Flexible AC Transmission Systems) và ứng tạp và đối diện với nhiều vấn đề về ổn định dụng các thiết bị FACTS để nâng cao tính ổn do nhu cầu sử dụng điện tăng cao. Cho nên, định của hệ thống điện. Các thiết bị FACTS ổn định động đóng vai trò rất quan trọng cho có thể được dùng trong hệ thống như SVC việc đảm bảo chế độ vận hành của hệ thống (Static Var Compensator) bù shunt, TCSC khi có sự cố ngắn mạch hay loại trừ đường (Thyristor-Controlled Series Capacitor) bù nối dây bị sự cố. Nội dung bài báo này tiến hành tiếp hoặc bù kết hợp cả hai shunt và nối tiếp. nghiên cứu mô hình của các thiết bị FACTS Mô hình toán của hệ thống điện có thiết bị Trang 53 SCIENCE & TECHNOLOGY DEVELOPMENT, Vol.18, No.K6 - 2015 FACTS là hệ phương trình vi phân đại số. Để các trường hợp hệ thống điện có thiết bị SVC giải cùng lúc hệ phương trình vi phân đại số và TCSC. Kết quả mô phỏng chứng minh các này thì phép lập Newton-Raphson và qui tắc thiết bị FACTS có khả năng cải thiện và nâng Trapezoidal được áp dụng. Chương trình cao tính ổn định của hệ thống, cụ thể trong phần mềm được lập trình và mô phỏng cho bài báo này là ổn định góc roto. 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