A new coordination strategy of SSSC and PSS controllers in power system using SOA algorithm based on Pareto method

Electrical Power and Energy Systems 67 (2015) 462–471

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

A new coordination strategy of SSSC and PSS controllers in power system using SOA algorithm based on Pareto method Eskandar Gholipour ⇑, Seyyed Mostafa Nosratabadi Department of Electrical Engineering, Faculty of Engineering, University of Isfahan, Isfahan, Iran

a r t i c l e

i n f o

Article history: Received 27 October 2013 Received in revised form 2 December 2014 Accepted 5 December 2014 Available online 24 December 2014 Keywords: Power system stability Seeker Optimization Algorithm (SOA) SSSC PSS Pareto method Coordination design

a b s t r a c t Along with the development of power grids and increasing the use of Flexible AC Transmission System (FACTS) devices, complex and unexpected interactions will be increased in power system. With considering to the non-linearity of power system, operating point changes and reaction between power system and FACTS devices, using of linear methods are not suitable for controller design. Therefore, the nonlinear model to design of Power System Stabilizer (PSS) and Static Synchronous Series Compensator (SSSC) coordinated controllers is considered here. In this paper, a new multi-objective function as an optimization problem is proposed for this coordination process. Also a beneficial strategy to solve this optimization problem using Seeker Optimization Algorithm (SOA) based on Pareto optimum method with high convergence speed is presented. In order to evaluate the performance of the proposed method, coordination strategy is applied on a four-machine system under different contingencies. The results of the proposed multi-objective function are obtained and compared with others in this system and finally, superior ability of the proposed method is observed. Ó 2014 Elsevier Ltd. All rights reserved.

Introduction Problem statement and literature review One of the most important issues in power system analysis is power system stability [1]. Long heavy loaded tie-lines in the wide spread interconnected power systems could be a source of different stability problems [2]. Thus, in recent decades, different methods have been used to design a suitable stabilizer. Due to the increasing the application of FACTS devices and their impact on improving the damping of power system oscillations, coordination of their controllers with Power System Stabilizer (PSS) is required. Since the power system is a nonlinear system, the design method for stabilizing and controlling parameters of FACTS devices must be performed for nonlinear models [1–3]. One of the most important FACTS devices that can be used to compensation process in the system is Static Synchronous Series Compensator (SSSC). When using this device and PSS at the same time in the power system, investigation of their coordination and introducing a suitable function to do this process is necessary. It ⇑ Corresponding author at: Department of Electrical Engineering, University of Isfahan, Isfahan 8174673441, Iran. Tel.: +98 3137935605; fax: +98 3137933071. E-mail addresses: [email protected] (E. Gholipour), sm.nosratabadi@eng. ui.ac.ir (S.M. Nosratabadi). http://dx.doi.org/10.1016/j.ijepes.2014.12.020 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved.

usually can be an optimization procedure to obtain parameter of their controllers simultaneously. In this regard, in recent years, definition of different functions to coordinate different types of FACTS devices and PSS controller together and with other parts of the system is considered. Also using of heuristic algorithms in order to solve optimization problems in this field is considered. Intelligent algorithms such as genetic algorithms (GA) [4], particle swarm optimization (PSO) [5], simulated annealing [6], modified particle swarm optimization (MPSO) [7]; are used to design and set-out the PSS parameters. Also, in [8] PSS design using bacterial foraging algorithm (BFA) and PSO are performed and the results are compared. A methodology for the synthesis of PSSs and speed governors in order to satisfy some objectives and constraints imposed by the evolution of large-scale interconnected power systems is presented in [9]. In [10] modeling of TCSC based damping controller in coordination with automatic generation control (AGC) is presented to damp the oscillations and thereby, improve the dynamic stability. The AGC and TCSC parameters are optimized simultaneously using an improved particle swarm optimization (IPSO) algorithm through minimizing integral of time multiplied squared error (ITSE) performance index. Coordinated design of PSS and TCSC has been studied in [11–14]. To this end, neuro-fuzzy inference system in [11] and BFA in [12,13] are applied to tune the controller parameters of PSS and TCSC. The main objective in [12] is to maximize the margin of loading in the

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system before the occurrence of the Hopf Bifurcation. The coordination design in [14] is performed using the PSO algorithm. In [15] the simultaneously design of PSS and SSSC using dynamic multi-objective scheduling are discussed. Coordinated design of PSS and SVC using probabilistic theory in [16] and using a bacterial-foraging oriented by particle swarm optimization (BFPSO) algorithm in [17] is proposed and in [18], the Seeker Optimization Algorithm (SOA) is used to coordinate the parameters of PSS and STATCOM. In [19], to compensation process, the dynamic power flow control of SSSC in coordination with superconducting magnetic energy storage (SMES) is proposed. Gains of the integral controllers and parameters of SSSC are optimized with an improved version of PSO. A coordination scheme to improve the stability of a power system by optimal design of multiple and multi-type damping controllers of PSS and SSSC is presented in [20]. The differential evolution (DE) algorithm is employed to search for the optimal controller parameters. In [21] a coordination scheme to improve the stability of a power system by optimal design of PSS and SSSC controller is presented. The coordinated design problem is formulated as an optimization problem and hybrid bacteria foraging optimization algorithm and particle swarm optimization (hBFOA–PSO) is employed to search for the optimal controller parameters. Paper contribution and layout As it has been described in the field of multi-objective way for coordination, there are a few works specifically in the field of PSS and SSSC coordination in a power system. In recent years, as can be seen in previous subsection, Refs. [19–21] have taken into account coordination of SSSC controller with elements of system like PSS but all of them introduce a way for single-objective consideration with a specific method. In Ref. [15] a multi-objective function is introduced for the coordination of PSS and SSSC but it does not consider important items of overshoot, undershoot and settling time of rotor speed to have a suitable solution with lower oscillations to reach the steady state solution. In this paper, a multi-objective method is proposed for coordinated design of the PSS and SSSC controllers to damp the oscillations and improve system stability. For this purpose, three different objective functions- two single-objective function and one multi-objective function- are proposed. The rotor speed, rotor angle and tie-line power deviations and the values of characteristics of the speed curve variations such as overshoot, undershoot and settling time are employed as input of the method. In the multi-objective function, mentioned parameters as two objective functions are taken into account with weighting factors. Then for optimal solving the single-objective and multi-objective functions, optimization strategies based on Seeker Optimization Algorithm (SOA) and also SOA algorithm based on Pareto optimum method are proposed for them respectively. To demonstrate the effectiveness of the proposed method coordinated design of PSS and SSSC regarding the actual and complete model of the power system, four-machine system is taken into consideration. Also to show the effectiveness of the proposed method in multi-objective condition against single-objective one, different contingency case studies are considered too. Simulation results show the capability of the multi-objective proposed algorithm comparing with single-objective one for coordination of SSSC and PSS to improve the stability of the system.

in Fig. 1 is considered at the first instance. The generator is equipped with hydraulic turbine and governor (HTG), excitation system and a Power System Stabilizer (PSS) [21,22]. In Fig. 1, VT and VB are the generator terminal and infinite-bus voltages respectively; V1, V2 and V3 are the bus voltages; VDC and Vconv. are the DC voltage source and output voltage of the SSSC converter respectively; I is the line current and PL is the total real power flow in the transmission line. Power System Stabilizer (PSS) Power System Stabilizers (PSSs) are complementary controllers in the excitation system in order to increase damping of generator rotor oscillations. This is necessary as high gain AVRs can contribute to oscillatory instability in the power systems, which are determined by low frequency oscillations (0.2–2.0 Hz). The washout circuit is considered to delete the steady state bias in the output of the PSS [23]. The dynamic compensator has the following transfer function:

TðsÞ ¼ K s

1 þ sT 1 1 þ sT 2

ð1Þ

where the constant gain Ks and time constants T1 and T2 are chosen depending on the required compensation for damping. Static Synchronous Series Compensator (SSSC) A Static Synchronous Series Compensator (SSSC) provides the virtual compensation of transmission line impedance by injecting the controllable voltage (Vq) in series with the transmission line. Vq is in quadrature with the line current, and emulates an inductive or a capacitive reactance so as to influence the power flow in the transmission lines. The variation of Vq is performed by means of a voltage sourced converter (VSC) connected on the secondary side of a coupling transformer. A capacitor connected on the DC side of the VSC acts as a DC voltage source. To keep the capacitor charged and to provide transformer and VSC losses, a small active power is drawn from the line [24–27]. The VSC using IGBT-based PWM inverters is used in this study. Therefore the equations applicable for the network power flow in presence of SSSC are given below [28]:

Pq ¼

V2 V2  sin d sin d ¼  X eff X L 1  X q =X L

ð2Þ

Qq ¼

V2 V2  ð1  cos dÞ ð1  cos dÞ ¼  X eff X L 1  X q =X L

ð3Þ

where V, Xeff, and d are bus voltage, effective reactance of the transmission line, and phase angle respectively. Also XL and Xq are transmission line reactance and compensating reactance of SSSC respectively.

VT

Transformer

V2

V1 PL

I Vq

Generator

Vconv. SSSC

V3

VB

Transmission Line

Infinite Bus

VSC

Power system modeling To design the PSS and SSSC-based damping controllers coordinately, a single-machine infinite-bus power system depicted

VDC Fig. 1. Single-machine infinite-bus power system with SSSC.

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Subject to

Proposed coordination design Structures of the PSS and SSSC damping controller The SSSC controller structure is shown in Fig. 2. The input signal of the presented controller is the speed deviation (Dx), and the output one is the injected voltage Vq. The structure includes a gain block with KS value, a signal washout block and two-stage lead-lag block. The signal washout block acts as a high-pass filter, with the time constant TW. With considering to the washout actions, the value of TW is not critical and it can be in the range of 1–20 s. The lead-lag blocks which are modeled by time constants T1S, T2S, T3S, and T4S provide the suitable lead characteristics for phase to compensate for the phase lag between input and the output signals. In Fig. 2, Vqref represents the reference injected voltage as desired one by the steady state value in control loop. So, the desired value of compensation is obtained according to the change in the SSSC injected voltage DVq which is added to Vqref. Fig. 3 shows the structure of the PSS used in this paper. The PSS including a gain block with KPS value, a signal washout block and two-stage lead-lag block. The input signal to the PSS is the speed deviation Dx of target generator where the PSS is installed. The output signal is the voltage VS which can be added to the reference voltage of the excitation system (Vref). For PSSs and SSSC controller a time constant of 15 ms for sensors is considered too [21].

K min 6 K S 6 K max S S

max K min P;i 6 K P;i 6 K P;i

max T min 1S 6 T 1S 6 T 1S

max T min i;1 6 T i;1 6 T i;1

T min 2S

T max 2S

max T min i;2 6 T i;2 6 T i;2

max Tmin 3S 6 T3S 6 T3S

max T min i;3 6 T i;3 6 T i;3

max Tmin 4S 6 T4S 6 T4S

max T min i;4 6 T i;4 6 T i;4

6 T 2S 6

As it can be seen in (5), gains and time constants amounts are limited between two minimum and maximum introduced values. The second single-objective function introduced by (6) is so considered to reduce the values of characteristics of the speed curve variations such as overshoot, undershoot and settling time.

min J 2 ¼ ð4000  OSÞ2 þ ð1000  USÞ2 þ T 2s Subject to : Constraintsð5Þ

min J 3 ¼ W 1  J 1 þ W 2  J 2 In this subsection, a new multi-objective method to coordinate PSS and SSSC functions is proposed. At first two single-objective functions those will contribute into multi-objective process are introduced. In the first objective function (J1), the coordination design problem as an optimization one in which the PSS and SSSC coefficients (KS, T1S, T2S, T3S, T4S, KP,i, T1P,i, T2P,i, T3P,i, and T4P,i) will be determined. In this objective function introduced in (4), the deviations of rotor speed, the deviations of power angle, and also the deviation of tie-line power will be minimized. For this purpose one performance index should be selected. The Integral Time Absolute Error (ITAE) criterion tries to minimize time multiplied absolute error of the considered deviations in control system. In this single-objective function, two set of constraints are considered as (5) those are related to parameters of PSS and SSSC.

min J 1 ¼

t 2 ¼t sim t1 ¼0

( ) n n X X jDdi jþjDPtie j  t  dt j Dx i j þ i¼1

sTw 1 + sTw

Ks

In this paper, with introducing the multi-objective function (7), it is expected that this function have all characteristics of mentioned single-objective functions. This anticipation will be tested in simulation and results section. To solve the mentioned single-objective and multi-objective functions in an optimal condition, optimization strategies based on SOA algorithm and SOA algorithm based on the Pareto optimum method are proposed respectively which are introduced in the next section. Proposed strategy for multi-objective optimization Seeker optimization algorithm

ð4Þ

Seeker Optimization Algorithm (SOA) is a relatively new intelligent algorithm that may be used to find optimal (or near optimal)

1 + sT1s 1 + sT2 s

Gain Block Washout Block

ð7Þ

Subject to : Constraintsð5Þ

i¼1

Δω

1 + sT3 s 1 + sT4 s

ΔVq

Ʃ

+

Vq max

Vq min

+

Two Stage Lead-Lag Blocks

Vqref

Vq

Limiter Block

Fig. 2. Structure of SSSC damping controller.

Δω

KP

sTWP 1 + sTWP

Gain Block Washout Block

ð6Þ

where OS, US and Ts are overshoot, undershoot and settling time of rotor speed respectively. To consider these parameters with different values, normalization numbers of 4000 and 1000 are allotted to overshoot and undershoot parameters. Also in this function constraints of (5) will be considered to set the limitations for gains and time constants values of PSS and SSSC. To incorporate the functions of the first and second objective functions at the same time to optimize the control parameters, two objective functions are taken into consideration like (7) with the weighting factors W1 and W2.

Proposed coordination method

Z

ð5Þ

1 + sT1P 1 + sT2 P

1 + sT3 P 1 + sT4 P

Two Stage Lead-Lag Blocks

Fig. 3. Structure of power system stabilizer.

VS max

VS min

Limiter Block

VS

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465

solutions to numerical and qualitative problems [29]. The results of simulations in [29–32] indicate the robustness of this algorithm, in rapid convergence in reaching the global optimum. The algorithm has the additional advantage of being easy to understand, simple to implement, so that it can be used for a wide variety of design and optimization tasks [29]. The seekers exchange their information with those defined in their neighbors to negotiate the quickest way to reach the best solution [30]. Seeker optimization algorithm parameters In SOA, the position of each seeker i, update on each dimension j is given by the following equation:

xij ðt þ 1Þ ¼ xij ðtÞ þ aij ðtÞdij ðtÞ

ð8Þ

where aij(t) and dij(t) are step length and search direction of each seeker i on each dimension j for time step t, where aij(t) P 0 and dij(t) 2 {1, 0, 1}. In (8) if dij(t) = 1, this means the ith seeker goes to the positive orientation of the coordinate axis on the dimension j, if dij(t) = 1 means the seeker goes to the negative orientation, and if dij(t) = 0 means the seeker stays at the current position [29]. In order to avoid the convergence of subpopulations to local minimums, if there are k seekers in search space, the positions of the worst k  1 seekers of each subpopulation are combined with the best one in each of the other k  1 subpopulations using the following binomial crossover operator:

 xkn j;worst ¼

xlj;best

if Rj 6 0:5

xkn j;worst

else

ð9Þ

where Rj is a uniformly random real number within [0, 1], xkn j;worst is denoted as the jth dimension of the nth worst position in the kth subpopulation and xlj,best is the jth dimension of the best position in the lth subpopulation with n, k, l = 1, 2, . . . , k  1 and k – l [33]. Search direction In SOA, the search direction of each seeker is specified based on several empirical gradients (EGs) by comparing the current or epochal positions of himself or his neighbors [33]. The corresponding EG can be involved:

  ~ di;ego ðtÞ ¼ sign ~ pi;best ðtÞ  ~ xi ðtÞ

ð10Þ

  ~ di;alt1 ðtÞ ¼ sign ~ g i;best ðtÞ  ~ xi ðtÞ

ð11Þ

  ~ di;alt2 ðtÞ ¼ sign ~li;best ðtÞ  ~ xi ðtÞ

ð12Þ

di;ego ðtÞ is egotistic direction, ~ di;alt1 ðtÞ and ~ di;alt2 ðtÞ are altruistic where ~ directions of seeker i, ~ pi;best ðtÞ, ~ g i;best ðtÞ and ~li;best ðtÞ are the personal historical best position, the historical best position of neighbors and the current best position of neighbors, respectively, sign(.) is a signum function on each dimension of the input vector and ~ xi ðtÞ ¼ ½~ xi2 ; . . . ; ~ xiD  is the position of the ith seeker at time step xi1 ; ~ t. In this algorithm, each seeker i can earn an EG by appraising his latest positions as follows.

~ di;pro ðtÞ ¼ signð~ xi ðt1 Þ  ~ xi ðt 2 ÞÞ

ð13Þ

xi ðt 1 Þ is better than ~ xi ðt2 Þ. Every where t1, t2 2 {t, t  1, t  2} and ~ dimension j of the search direction of the ith seeker, di(t), is selected applying the following proportional selection rule:

Fig. 4. Flowchart of the used SOA algorithm [33].

8 ð0Þ 0 if r j 6 pj > > < ð0Þ ð0Þ ðþ1Þ þ1 if pj < rj 6 pj þ pj > > : ð0Þ ðþ1Þ 1 if pj þ pj < rj 6 1

ð14Þ

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where rj is a uniform random number in [0, 1], pj(m) (m 2 {0, 1, 1}) is the percent of number of m from the set n o ~ ~ ~ ~ dij;ego ðtÞ; dij;alt1 ðtÞ; dij;alt2 ðtÞ; dij;pro ðtÞ on each dimension j of all the

Start

the number of m . four empirical directions, i.e., pm j ¼ 4

Initialization of SOA Parameters (ω, μmin, μmax, IterMax)

Step length In SOA algorithm, the fitness values of all the seekers are at descending state which are sorted and converted to the sequence numbers from 1 to s as the inputs of Fuzzy reasoning [33]. This work prepares a fuzzy system to a wide range of optimization problems. One can consider:

Initial Population Iter=1

li ¼ lmax 

ð15Þ

where Ii is the sequence number of ~ xi ðtÞ after sorting the fitness values, lmax is the maximum membership degree value which is equal to or a little less than 1. Then Bell membership function lðxÞ ¼ ex2 =2~d2 is used in the action part of fuzzy reasoning. ~d is the parameter of the Bell membership function that is determined by the following:

Calculation of Sub-functions J1 and J2 in Objective Function J3

~ d ¼ x  absð~ xbest  ~ xrand Þ

Best Solutions (x1,x2,…,xn)

Iter=Iter+1

 s  Ii  l  lmin s  1 max

Pareto Front (non dominated solutions)

where abs(.) produces an output vector. The parameter x is used to decrease the step length with time step increasing, so the accuracy of search is gradually improved. The ~ xbest and ~ xrand are the best seeker and a randomly selected seeker from the same subpopulation to which the ith seeker belongs, respectively [30,32]. Step length is earned as follow:

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

aij ¼ dj  lnðlij Þ Population Update by Seeker Optimization Mechanism

ð16Þ

ð17Þ

where

lij ¼ RANDðli ; 1Þ

ð18Þ

So using the mentioned steps and formulations of SOA, its flowchart can be expressed as Fig. 4.

No

?

Pareto optimum method

Iter=Iter ? Max Yes Print Optimized Parameters for Controllers Considering J1 and J2 Weightings

End

Fig. 5. Flowchart of the proposed strategy using SOA algorithm based on Pareto optimum method.

The most appropriate solution for a multi-objective optimization would have to be selected among the spectrum of solutions considering treatment carried out and aims expressed [34]. In multi-objective optimization, a vector of decision variables, say, xj, j = 1, . . . , N which satisfies constraints and optimizes a vector function {say f = (f1(x), . . . , fM(x))} whose elements represent M objective functions. They form a mathematical description of a performance criteria expressed as computable functions of the decision variables. Hence, means are optimized to find a solution which would give the values of all objective functions acceptable to the treatment planner [35]. The constraints define the feasible region X and any point x in X, defines a feasible solution. The vector function f(x) is a function that maps the set X in the set F that represents all possible values of the objective functions. Normally, we never have

Fig. 6. Two-area power system with SSSC [3].

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E. Gholipour, S.M. Nosratabadi / Electrical Power and Energy Systems 67 (2015) 462–471 Table 1 Optimized controller parameters for four-machine power system using proposed methods. Element

Parameters

J1

J2

J3 W1 = 0.3, W2 = 0.7

W1 = 0.5, W2 = 0.5

W1 = 0.7, W2 = 0.3

PSS1

K1 T11 T21 T31 T41

12.8530 0.3298 0.1495 0.1598 0.1296

23.0235 0.0067 0.7542 0.2736 0.6230

24.0521 0.3525 0.0979 0.8362 0.2104

25.5733 0.0185 0.0967 0.1077 0.7649

37.5989 0.0185 0.0967 0.1077 0.7552

PSS2

K2 T12 T22 T32 T42

10.2790 0.2587 0.6021 0.2876 0.0693

18.1417 0.8204 0.7295 0.4016 0.5237

12.4728 0.0745 0.7638 0.7405 0.5223

13.5607 0.8426 0.8562 0.8835 0.6687

13.5705 0.84263 0.8572 0.8835 0.6683

PSS3

K3 T13 T23 T33 T43

5.3486 0.1833 0.6424 0.2921 0.9682

16.3899 0.9452 0.5856 0.7853 0.0534

12.3582 0.2017 0.2339 0.6586 0.2925

17.8616 0.5157 0.5416 0.3028 0.1295

17.8524 0.5157 0.5416 0.3028 0.1373

PSS4

K4 T14 T24 T34 T44

17.9116 0.9996 0.2087 0.4196 0.4512

25.0012 0.0185 0.0967 0.1077 0.9524

22.2675 0.5041 0.0344 0.7321 0.4320

19.8616 0.9066 0.4810 0.3974 0.2341

25.0989 0.0185 0.1123 0.1077 0.7552

SSSC

KS TS1 TS2 TS3 TS4

48.9561 0.2909 0.4828 0.7410 0.3856

73.6716 0.3428 0.7576 0.7228 0.9922

63.7559 0.1856 0.9065 0.6262 0.3450

71.5645 0.5157 0.5416 0.3028 0.1295

71.6622 0.9066 0.4811 0.3975 0.2341

a situation in which all the fi(x) values have an optimum in X at a common point x. We therefore, have to establish certain criteria to determine an optimal solution. So x1 dominates x2 if and only if the two following conditions are true:

-3

x 10

1.6

SOA GA PSO BFOA

 x1 is no worse than x2 in all objectives, i.e., fj(x1) 6 fj(x2) for j = 1, . . . , M.  x1 is strictly better than x2 in at least one objective, i.e., fj(x1) < fj(x2) for at least one j 2 f1; . . . ; Mg. More details related to gain the Pareto front can be found in [36]. Parameter setting and proposed flowchart for the used method

Fitness Function Value

1.4 1.2 1 0.8 0.6 0.4

0

10

20

30

40

50

60

70

80

90

100

Iteration

In the present study, SOA parameters are selected as: x = 0.9, lmin = 0.011 and lmax = 0.97 [33]. Also, the maximum iterations to find the optimal solutions is chosen as Itermax = 100. So using the proposed strategy which is illustrated in Fig. 5, the optimized parameters for PSS and SSSC controllers considering multi-objective method can be achieved. Simulation results and discussion The proposed approach of coordinated design of PSS and SSSC based damping controller is applied to a modified four-machine twelve-bus power system shown in Fig. 6 [3]. The system consists of four generators divided into two areas and are connected through an intertie. To improve the stability the line is sectionalized and a SSSC is assumed on the mid-point of the tie-line between two areas. Also, PSSs are installed with each machine. The relevant information of the test system is given in Appendix. The SimPower-Systems (SPS) toolbox [37] is used for all simulations and designs. The ‘Powergui’ block of SPS supplies beneficial graphical user interface tools for the analysis of models. To find the best values of the PSS and SSSC-based controller parameters, three mentioned objective functions in

Fig. 7. Convergence characteristics of SOA, BFOA, PSO and GA algorithm for J1.

Section;‘Proposed coordination design’ are used. In all of them SOA algorithm is used with parameter settings corresponding to the presented settings in previous section. The optimized controller parameters for PSSs and SSSC components in four-machine power system using proposed methods are shown in Table 1. Fig. 7 shows the typical convergence characteristics of the SOA, BFOA, PSO and GA algorithms for the first mentioned objective function (J1). It is quite clear from this figure that among the four techniques the convergence of SOA is the fastest and the final value of fitness function is minimized. In multi-objective condition, using J3 optimization process is done with the proposed SOA based on Pareto method. Fig. 8 shows the Pareto front in this condition. For a comparison, NSGA-II [38] is used and its results have been illustrated in this figure too. As it is clear from that, results of the proposed method (red1 dots) have a better performance and minimum values against results of the

1 For interpretation of color in Fig. 9, the reader is referred to the web version of this article.

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NSGA-II application (blue stars). Then to choose the performance of the system in multi-objective condition, weighting factors with three different points of view are considered by a typical user. In Fig. 9, three best points selected by three different weighting factors (W1 = 0.3, W2 = 0.7, W1 = 0.5, W2 = 0.5 and W1 = 0.7, W2 = 0.3) have been shown.

900 800 700

J2

600 500

Investigation of different contingencies

400 300 200

In the next step to demonstrate the performance of the proposed method in tuning of controllers, three cases are studied, in another word, three different contingencies are investigated. In these cases, W1 and W2 values are selected equal to 0.5.

by SOA Based on Pareto Method by NSGA-II

200

300

400

500

600

700

800

900

J1 Fig. 8. Pareto front in multi-objective condition.

Case 1: Three-phase fault disturbance In this condition, a 3-phase self-clearing fault with duration 200 ms, is applied at one of the line sections between bus 7 and bus 8 near bus 8 at t = 1 s. The initial system will be restored after

0.3

by J1

900 by SOA Based on Pareto Method by NSGA-II

800

by J2

0.2

by J3

700

500

0.1

Vq (pu)

J2

600 W1=0.7, W2=0.3

0

400 W1=0.5, W2=0.5

300 200

-0.1

W1=0.3, W2=0.7

200

300

400

500

600

700

800

-0.2

900

0

1

2

3

4

J1

5

6

7

8

Fig. 9. Optimal solutions for multi-objective condition considering different weighting factors.

-3

0.01

by J1 by J

by J

0.005

3

ω2-ω4 (pu)

2

ω1-ω4 (pu)

by J1

by J2

4

0 -2

by J

2 3

0

-0.005 -4 0

1

2

3

4

5

6

7

8

9

-0.01

10

0

2

3

4

5

6

Time (sec)

(a)

(b)

7

8

9

10

16 by J2 by J3

40 30

35 34.5

20

1

2

3

4

34 0

2

5

6

4

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8

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2

by J1

12

by J3

10 8

10.6

6

10.5 10.4 0

4

10

9

by J

14

1

δ 4-δ 2 (deg)

by J

50

δ 4-δ 1 (deg)

1

Time (sec)

60

10 0

10

Fig. 11. SSSC injected voltage for a 200 ms self-clearing fault by three proposed methods.

6 x 10

-6

9

Time (sec)

2

0

1

2

3

4

5

6

Time (sec)

Time (sec)

(c)

(d)

2

4

7

Fig. 10. System responses for a 200 msec self-clearing fault: (a) x1–x4, (b) x2–x4, (c) d4–d1 and (d) d4–d2.

6

8

8

10

9

10

469

E. Gholipour, S.M. Nosratabadi / Electrical Power and Energy Systems 67 (2015) 462–471 0.003

0.002

by J1 0.002

by J2

by J3

by J3

ω2 - ω4 (pu)

ω1- ω4 (pu)

by J1

by J2

0.001 0

0.001

0

-0.001 -0.002

0

1

2

3

4

5

6

7

8

9

-0.001 0

10

1

2

3

4

5

6

7

Time (sec)

Time (sec)

(a)

(b)

8

9

10

Fig. 12. System responses for one line outage contingency: (a) x1–x4 and (b) x2–x4.

8

x 10

-3

0.004

6

by J1

by J1

by J2

by J2 by J3

by J3

ω2-ω4 (pu)

ω1-ω4 (pu)

4 2 0

0.002

0

-2 -4

0

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2

3

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6

7

8

9

10

-0.002

0

1

2

3

4

Time (sec)

5

6

7

8

9

10

Time (sec)

(a)

(b)

Fig. 13. System responses for load curtailment at bus 7: (a) x1–x4 and (b) x2–x4.

Voltage Magnitude at Bus 1 (pu)

1.25 Scenario 3 Scenario 2 Scenario 1

1.2 1.15 1.1 1.05 1 0.95 0.9

0

1

2

3

4

5

6

Time (sec)

(a)

Voltage Magnitude at Bus 3 (pu)

1.25

Scenario 3 Scenario 2 Scenario 1

1.2

the fault clearance. The system responses are illustrated in Fig. 10. It is clear in the figures that the proposed controllers considering multi-objective condition significantly improve the power system stability by repressing the oscillations by modulating the injected voltage of SSSC and stabilizing signals of PSSs. As it is shown in Fig. 11, SSSC injected voltage for this contingency type by three proposed methods is illustrated. It is clear from the figure that using J3 objective function more SSSC injected voltage is done comparing with other objective functions (J1 and J2). However, the third proposed method provides much more suitable damping specifications to oscillations and rapidly stabilizes the system by adjusting the SSSC injected voltage and stabilizing signal of PSS. Case 2: Line outage contingency To investigate the operation of the test system under an important contingency, line outage contingency is considered. Because of Table 2 Comparison of objective functions solution with different items.

1.15 1.1 1.05 1 0.95 0.9

0

1

2

3

4

5

6

Time (sec)

(b) Fig. 14. System response to uncertainty of SSSC parameters in 3 scenarios: (a) at bus 1 and (b) at bus 3.

Presented single objective function in Ref. [21] Proposed single objective function of Eq. (4) Proposed multiobjective function of Eq. (7)

Run time to obtain convergence (s)

Overshoot of Vq (pu)

Undershoot of Vq (pu)

Settling time of Vq (s)

5430

0.19

0.14

1.63

6258

0.17

0.09

1.31

8342

0.22

0.17

0.9

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E. Gholipour, S.M. Nosratabadi / Electrical Power and Energy Systems 67 (2015) 462–471

Table A1 Information of used power system components. Component

Parameter

Generator

VB = 20 kV, Xd = 1.8, Xq = 1.7, Xl = 0.2, X 0d ¼ 0:3; X 0q ¼ 0:55; X 00d ¼ 0:25; X 00q ¼ 0:25; Ra ¼ 0:0025; T 0d0 ¼ 8; T 0q0 ¼ 0:4; T 00d0 ¼ 0:03; T 00q0 ¼ 0:05; Asat ¼ 0:015; Bsat ¼ 9:6 H = 6.5 (for G1 and G2), H = 6.175 (for G3 and G4), KD = 0 P1 = 700 MW, Q1 = 185 MVar, P2 = 700 MW, Q2 = 235 MVar P3 = 719 MW, Q3 = 176 MVar, P4 = 700 MW, Q4 = 202 MVar

Transformer

900 MV A; 20/230 kV; 60 Hz; R1 = R2 = 0.002; L1 = 0; L2 = 0.15; D1/Yg connection; Rm = 500, Lm = 500

Transmission line

Vnom = 230 kV, line length: L1 = 25 km, L2 = 10 km, L3 = 110 km R = 0.0001 pu/km, XL = 0.001 pu/km, BC = 0.00175 pu/km

Load

PLoad1 = 967 MW, QLoad1 = 100 MVar, PLoad2 = 1767 MW, QLoad2 = 100 MVar

SSSC

Converter rating: Snom = 100 MVA; system nominal voltage: Vnom = 230 kV; frequency: f = 60 Hz; converter impedances: R = 0.00533, L = 0.16; DC link nominal voltage: VDC = 40 kV; DC link equivalent capacitance CDC = 375 ⁄ 106 F; injected voltage regulator gains: KP = 0.00375, KI = 0.1875; DC voltage regulator gains: KP = 0.1 ⁄ 103, KI = 20 ⁄ 103; injected voltage magnitude limit: Vq = ±0.25

symmetry in test network and choosing a line to cut in this situation of study, the transmission lines between buses 7 and 8 and also the transmission lines between buses 9 and 10 can be selected for this purpose in a worst situation. In this case, one of the transmission lines between buses 7 and 8 is selected to trip off at t = 1 s. The initial system is restored after three cycles and then the line is reclosed. Fig. 12(a) shows speed difference of generators 1 and 4 and depicts the inter-area mode response using three mentioned methods. Fig. 12(b) shows speed difference of generators 2 and 4 that illustrates the local mode response using three methods. From these figures, it can be found that the multi-objective proposed function has better and effective results in two operating modes. Case 3: Load curtailment In this section the performance of the presented controllers is also considered under load curtailment. The load at bus 7 is disconnected at t = 1 s until t = 3 s for 2 s. Fig. 13 shows the system response for the load curtailment contingency. Fig. 13(a) shows speed difference of generators 1 and 4 and depicts the inter-area mode response using three mentioned methods. Fig. 13(b) shows speed difference of generators 2 and 4 that illustrates the local mode response using mentioned methods. It is clear from these figures that the multi-objective proposed method for tuning the controllers is robust and provides efficient and better damping in this condition. Investigation of parameter uncertainty effect In this subsection, change in SSSC controller parameters is performed related to investigate the effect of parameter uncertainty on the performance. For this purpose, parameters of SSSC have been set in three scenarios as below:  Scenario 1: parameters setting are equal to values in Table 1 where W1 and W2 values are equal to 0.5.  Scenario 2: parameters setting are equal to 10% upper than values in Table 1 where W1 and W2 values are equal to 0.5.  Scenario 3: parameters setting are equal to 10% lower than values in Table 1 where W1 and W2 values are equal to 0.5. The reaction of voltage magnitude at buses 1 and 3 for a 200 ms 3-phase fault at bus 8 is obtained for the mentioned cases. The results for these situations have been illustrated in Fig. 14. As can be seen, based on the sensitivity of the proposed method, uncertainty of the parameters can affect on the performance of the system in reaction to the disturbance. So the best performance

is when the setting is based on the obtained values for the parameters using the proposed method and it is clear from these figures that in this situation, reaching to rated value the performance will be more suitable. Comparison of approaches To prove the effectiveness of the proposed multi-objective method for coordination of SSSC and PSS controllers, in this section a comparison in different aspects has been prepared with Ref. [21]. In this reference, only two speed deviations of local and inter-area modes of oscillations have been considered while in our proposed multi-objective formulation speed, angle of local and inter-area modes and tie-line power with consideration to overshoot, undershoot and settling time minimization. To have a reasonable comparison three different objective function in single and multi-objective ones have been compared considering application of SOA algorithm to solve single objective functions and SOA algorithm to solve multiobjective one. These functions have been solved for four-machine power system that has shown in Fig. 6. Here the items those have been considered to prepare the comparison are run time to obtain convergence, overshoot, undershoot and settling time of Vq. As can be seen in Table 2, with comparing to the mentioned objective functions, the presented function in [21] has a better run time to convergence. However other items have better results especially the settling time for the proposed multi-objective function (7) that is less than others while it has more complexity in formulation with comparing to others. In our opinion, formulation complexity and much run time comparing to suitable and optimum results benefit are negligible to obtain the best one. Conclusion In this paper, a new method is presented to coordinate the PSS and SSSC controllers to damp the oscillations and improve the system stability. Three different objective functions are proposed. The first and second objective functions are single-objective and the third one is multi-objective. In the first objective function considering desired power system, speed and angle deviations for local and inter-area modes and tie-line power deviation between two areas are employed as input to ITAE method. In the second objective function the values of characteristics of the speed curve variations such as overshoot, undershoot and settling time are minimized. In the third objective function to incorporate the functions of the first and second objective functions at the same time to optimize the control parameters, two objective functions are taken into account

E. Gholipour, S.M. Nosratabadi / Electrical Power and Energy Systems 67 (2015) 462–471

with weighting factors. So to solve optimally the single-objective and multi-objective functions, optimization strategies based on SOA algorithm and SOA algorithm based on the Pareto optimum method are proposed for single and multi-objective functions respectively. To demonstrate the effectiveness of this approach to solve the desired optimization problems, the proposed method has been tested on a four-machine power system, and different cases such as fault occurrence in line, line outage and load change or curtailment has been studied too. In these conditions, it is illustrated that the control system with proposed method is robust against these contingencies and depicted its adaption as well. Appendix An information list of used parameters those are considered in simulation of four-machine power system is shown in Table A1. All data are in pu unless specified otherwise. References [1] Hingorani NG, Gyugyi L. Understanding FACTS – concepts and technology of flexible AC transmission systems. IEEE Press; 2000. [2] Gholipour E, Isazadeh G. Design of a new adaptive optimal wide area IPFC damping controller in Iran transmission network. Electr Pow Energy Syst 2013;53:529–39. [3] Kundur P. Power system stability and control. McGraw-Hill; 1994. [4] Bomfim ALB, Taranto GN. Simultaneous tuning of power system damping controllers using genetic algorithms. IEEE Trans Power Syst 2000;15:163–9. [5] Shayeghi H, Shayanfar HA, Safari A, Aghmasheh R. A robust PSSs design using PSO in a multi-machine environment. Energy Convers Manage 2010;51:696–702. [6] Abido MA. Robust design of multimachine power system stabilizers using simulated annealing. IEEE Trans Energy Convers 2000;15:297–304. [7] Eslami M, Shareef H, Mohamed A, Khajehzadeh M. An efficient particle swarm optimization technique with chaotic sequence for optimal tuning and placement of PSS in power systems. Electr Pow Energy Syst 2012;43:1467–78. [8] Das TK, Venayagamoorthy GK, Aliyu UO. Bio-inspired algorithms for the design of multiple optimal power system stabilizers: SPPSO and BFA. IEEE Trans Ind Appl 2008;44:1445–57. [9] Marinescu B, Petesch D. Three-level coordination in power system stabilization. Electr Pow Syst Res 2014;111:40–51. [10] Zare K, Tarafdar Hagh M, Morsali J. Effective oscillation damping of an interconnected multi-source power system with automatic generation control and TCSC. Electr Pow Energy Syst 2015;65:220–30. [11] Gandhi PR, Joshi SK. Smart control techniques for design of TCSC and PSS for stability enhancement of dynamical power system. Appl Soft Comput 2014;24:654–68. [12] Tripathy M, Mishra S. Coordinated tuning of PSS and TCSC to improve Hopf Bifurcation margin in multimachine power system by a modified Bacteria Foraging Algorithm. Electr Pow Energy Syst 2015;66:97–109. [13] Ali ES, Abd-Elazim SM. Coordinated design of PSSs and TCSC via bacterial swarm optimization algorithm in a multimachine power system. Electr Pow Energy Syst 2012;36:84–92. [14] Shayeghi H, Safari A, Shayanfar HA. PSS and TCSC damping controller coordinated design using PSO in multi-machine power system. Energy Convers Manage 2010;51:2930–7.

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