Scholarly article on topic 'A modified GWO technique based cascade PI-PD controller for AGC of power systems in presence of Plug in Electric Vehicles'

A modified GWO technique based cascade PI-PD controller for AGC of power systems in presence of Plug in Electric Vehicles Academic research paper on "Electrical engineering, electronic engineering, information engineering"

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Abstract of research paper on Electrical engineering, electronic engineering, information engineering, author of scientific article — Sasmita Padhy, Sidhartha Panda, Srikanta Mahapatra

Abstract A Modified Grey Wolf Optimization (MGWO) based cascade PI-PD controller is suggested in this paper for Automatic Generation Control (AGC) of power systems in presence of Plug in Electric Vehicles (PEV). The modification in original Grey Wolf Optimization (GWO) algorithm is introduced by strategy which maintains a proper balance between exploration and exploitation stages of the algorithm and gives more importance to the fittest wolves to find the new position of grey wolves during the iterations. Proposed algorithm is first tested using four bench mark test functions and compared with original GWO, Differential Evolution (DE), Gravitational Search Algorithm (GSA), Particle Swarm Optimization (PSO) to show its superiority. The proposed technique is then used to tune various conventional controllers in a single area three-unit power system consisting of thermal hydro and gas power plants for AGC. The superiority of proposed MGWO algorithm over some recently proposed approaches has been demonstrated. In the next step, different controllers like PI, PID, and cascaded PI-PD controller are taken and Plug in Electric Vehicles (PEVs) are assumed. The proposed approach is also extended to a two-area six-unit power system. Lastly, a five unequal area nonlinear power system with PEVs and dissimilar cascade PI-PD controller in each area is considered and proposed MGWO technique is employed to optimize the controller parameters in presence of nonlinearities like rate constraint of units, dead zone of governor and communication delay. It is observed that PEVs contribute in the AGC to control system frequency.

Academic research paper on topic "A modified GWO technique based cascade PI-PD controller for AGC of power systems in presence of Plug in Electric Vehicles"

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A modified GWO technique based cascade PI-PD controller for AGC of power systems in presence of Plug in Electric Vehicles

Sasmita Padhya, Sidhartha Panda a,*> Srikanta Mahapatrab

a Department of Electrical Engineering, VSSUT, Burla 768018, Odisha, India b School of Electrical Engineering, KIIT University, Bhubaneswar 751024, Odisha, India

ARTICLE INFO

Article history: Received 8 December 2016 Revised 26 February 2017 Accepted 11 March 2017 Available online xxxx

Keywords:

Automatic Generation Control Cascade PI-PD controller Grey Wolf Optimization Modified Grey Wolf Optimization Plug in Electric Vehicles

ABSTRACT

A Modified Grey Wolf Optimization (MGWO) based cascade PI-PD controller is suggested in this paper for Automatic Generation Control (AGC) of power systems in presence of Plug in Electric Vehicles (PEV). The modification in original Grey Wolf Optimization (GWO) algorithm is introduced by strategy which maintains a proper balance between exploration and exploitation stages of the algorithm and gives more importance to the fittest wolves to find the new position of grey wolves during the iterations. Proposed algorithm is first tested using four bench mark test functions and compared with original GWO, Differential Evolution (DE), Gravitational Search Algorithm (GSA), Particle Swarm Optimization (PSO) to show its superiority. The proposed technique is then used to tune various conventional controllers in a single area three-unit power system consisting of thermal hydro and gas power plants for AGC. The superiority of proposed MGWO algorithm over some recently proposed approaches has been demonstrated. In the next step, different controllers like PI, PID, and cascaded PI-PD controller are taken and Plug in Electric Vehicles (PEVs) are assumed. The proposed approach is also extended to a two-area six-unit power system. Lastly, a five unequal area nonlinear power system with PEVs and dissimilar cascade PI-PD controller in each area is considered and proposed MGWO technique is employed to optimize the controller parameters in presence of nonlinearities like rate constraint of units, dead zone of governor and communication delay. It is observed that PEVs contribute in the AGC to control system frequency. © 2017 Karabuk University. Publishing services by Elsevier B.V. This is an open access article under the CC

BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4XI/).

1. Introduction

For stable and reliable operation of power systems, Automatic Generation Control (AGC) is necessary. AGC maintains balance between load and generation and hence minimizes frequency errors [1-3]. In present day power system, the generation is usually made up of a combination of thermal units, hydro units as well as gas units. Gas bad units are suitable for supplying peak demands as they can be put into service quickly. When generation capacity is not sufficient to meet the increased load demand, other alternatives could be used to minimize the imbalance. Plug in Electric Vehicles (PEV) are projected to be used vigorously in the near future because of their low charging cost and less co2 emission level and low noise pollution and hence environment friendly [4,5]. PEVs offer an opportunity to use small distributed energy storage systems while they are plugged in [6,7]. Large numbers of PEV with V2G technology and the communications and sensing

* Corresponding author. E-mail address: panda_sidhartha@rediffmail.com (S. Panda). Peer review under responsibility of Karabuk University.

associated with the power grid, could offer ancillary services for the power grid. It can act as controllable energy storage device for the operation of power system. Frequency control is an ideal capability for PEV as the duration of energy supply is short and at the same time it is the highest priced ancillary service on the market which offers greater economic returns for vehicle owners [8-11]. Thus, PEVs have potential to contribute in the AGC to preserve the system frequency as per the load variations [12].

In this paper, a lumped EV model is employed bearing in mind EV users' convenience and vagueness. Furthermore, a frequency control scheme based on the lumped model is used. In addition, a dispatching method of the control signal (LFC signal) to the EVs, which enables the State of Charges (SOCs) of all the EVs to be synchronized, is employed. For the operation of Plug in Electric Vehicles in the LFC scheme, there is two way communications between PEVs and the power system. A third party like Local Control (LC) centers are assumed to be acting as the mediator between Central Load Dispatching Center (CLDC) and the Plug in Electric Vehicles. The command (LFC signal) is sent by CLDC to PEV and the information like EV specific meter data, percentage of SOC from the PEVs is given to CLDC via LC centers. CLDC calculates the LFC

http://dx.doi.org/10.1016/j.jestch.2017.03.004

2215-0986/® 2017 Karabuk University. Publishing services by Elsevier B.V.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

signal from the frequency fluctuation and decides when and how the EVs are going to participate in LFC. The SOC of the PEV is highly dependent on the command signal it receives from CLDC. The SOC of the participating PEVS in LFC is assumed to be within 80% to 90% in this paper. The Electric vehicles are assumed to participate in LFC only after completing the sufficient level of charging of batteries, they have. The Electric vehicles are assumed to be into three states [13] i.e. driving state (when EV is plugged out and on the road), charging state (EV is plugged-in for charging the battery but don't respond to the control signal), controllable state (EV is control in i.e. ready to respond to the command signal sent by power system). Electric vehicles are highly efficient for settling the frequency deviation and load instability. Hence it is practicable for the plugged in Electric vehicles (PEVs) to involve in LFC for quick settle of frequency due to load variation [14].

Numerous control approaches have been proposed in literature for AGC of traditional interconnected systems. In this regard, Fuzzy Logic Controller (FLC) [15] and Adaptive Neuro Fuzzy Inference System (ANFIS) [16] based approaches have been suggested for AGC. However, these controllers require skilled operator for the design as well as application. Hence, these approaches are susceptible to the operator's understanding and skills. The classical Proportional Integral (PI) controller are still extensively used in industrial systems in spite of the substantial advances in recent years in modern control system as PI controllers provides satisfactory results for a variety of plants with varied operating conditions. Besides, PI controllers can be realized and are well known to engineers. For improved system performance, a PD feedback loop can be added to a PI controller to modify the poles of the plants to required locations.

Many traditional approaches pertaining to the tuning of PID controllers and its variants are available in literature [17-20]. However, these methods are time consuming and optimal parameters may not be obtained. Modern heuristic optimization approaches [21-24] have been recently proposed for AGC. Frequency control in multi-source power systems by optimal controller [25], Differential Evolution (DE) [23,26] and Teaching Learning Based Optimization (TLBO) [22,27] have been reported in literature. As per 'no-free-lunch' theorem, no meta-heuristic method is well suited for all problems and there is scope for improvement [28]. Grey Wolf Optimization (GWO) is a recent meta-heuristic optimization technique proposed in 2014 [29]. The technique follows the social ladder and hunting actions of grey wolves. Their hunting strategy is followed by this algorithm to search and hunt a prey (solution). The chief advantage of GWO algorithm compared to other well- established meta-heuristic algorithms is that the GWO algorithm implementation needs no specific input parameters. In addition, it is simple and free from

computational complication. Moreover, GWO can be easily programmed and ease to understand. Though the original GWO is easily understood and programming is simple but it has a limitation that it sacrifices half of its iteration for exploration and the other half for exploitation, overlooking the impact of correct balance among them to provide a precise estimate of global optimum. In [30], a grouped GWO technique is proposed to tune the parameters of PID controllers of doubly-fed induction generator based wind turbine where a trade-off between exploration and exploitation is achieved by two independent groups of grey wolves, in which the cooperative hunting group employs four types of grey wolves for a deep exploitation, while the random scout group adopts multiple scouts for a wide exploration. A hybrid GWO technique has been presented in [31] for solving nonlinear, non-convex and discontinuous economic dispatch problems with numerous equality and inequality constraints. In the present paper, a strategy has been adopted to change the exploration and exploitation stages of original GWO to get an improved solution. In case of original GWO, all four category of wolves irrespective of their fitness are given equal importance to calculate the new position of wolves during the iterations but in the proposed modified version, the Alpha category wolves are given more importance as their fitness is more in comparison to other category wolves.

In this paper, Modified Grey Wolf Optimization (MGWO) based cascade PI-PD controller is suggested for AGC of power systems in presence of PEVs. Initially, a single area thermal-hydro-gas units based power system is considered and MGWO is used to tune the gains of conventional Integral (I) controller. The advantage of suggested MGWO algorithm over conventional optimal controller, DE, TLBO techniques is also established by comparative result analysis for the identical power system with identical controller. Then cascade PI-PD controller is employed and the superiority of cascade PI-PD controller over, I, PI, PID controller is demonstrated. Then, PEVs are incorporated and the effect of PEVs in AGC is accessed. Finally, the study is extended to a five area interconnected non-linear power system with PEVs with dissimilar cascade PI-PD controller in each area.

2. System under study

At the first instance, a single area three-unit power system illustrated in Fig. 1 is assumed. The system compromises of a hydro unit, a thermal and a gas unit. Initially integral controllers are considered for each unit. The individual generating units have their distinct regulation parameter and participation factor. According to these parameters the total load on the system is distributed among the units. The participation factors of all units should add

Controller 1 UT

Controller 2 Uh

Therma^power plant with reheat turbine

-JL i* 1 + STSG

1 "I"s KrT r 1 + sTr

1 + s_Tt

Hydrol power plant with governor

\ 1 1 + STRS ^ sTw Kh

) ^ sTGH 1 + sTrh 1 + .5sTw

cg+sbg

1 + si, !+STCR 1 Kg

1 + syc 1 + sfp 1 + sTcd

Gas turbine power plant Fig. 1. Single area three-unit power system.

Controller 3

up to unity. The details of each parameter can be found in reference [26,27] and also provided in Appendix A.

3. Modeling of Plug in Electric Vehicle

Since a large number of PEVs are going to run on the road in near future, a lumped PEV model is considered in the present study. Each PEV is modeled as per its inverter capacity. The detail model of lumped PEV is provided in Fig. 2 [10] where DUE is the Load Frequency Control (LFC) signal given as an input to PEV and charging/discharging power of one PEV is the output. The capacity of battery is represented by ±BkW. The complex frequency is symbolized by s, the time constant of PEV is symbolized by T. The present energy of the battery is symbolized by E and controllable energy of battery is represented by limits Emax and Emin. The PEV energy remains within the maximum and minimum limit of 90% and 80% of the controllable energy respectively. K1 and K2 are calculated as K1 = E - Emax, K2 = E - Emin, as the energy differences. The PEV do not participate in AGC when the charge is above the maximum limit (Emax) of 90% and below the minimum limit (Emin) of 80%. The stored energy model in Fig. 2 computes the net energy stored in the batteries in one local control center. Local

control center can act as a communicating link between power grid and the electric vehicles which control several EVs.

The stored energy model of one PEV is shown in Fig. 3. The controllable EVs (Nconcrouabie) is varied as per the added number of the control in and plug out of the EVs (NcontrolinNplugout) shown in Eq. (1). The number of controllable EVs providing energy to the grid Ncontrollable (t) is given by:

Ncontrollable(t) = Ninitial(t) — Nplugout(t) + Ncontrolin(t)

Ninitial = Initial number of controllable EVs Nplugout = Number of EVs moving from controllable state to driving state

Ncontroiin = Number of EVs moving from charging state to controllable state

The energy expression is written as:

Econtrol(t) = Einitial(t) + Econtrolin(t) — Eplugout(t) — ELFC(t)

where, Einitial(t) is the initial energy, Econtmlin(t) is the increase in energy because of the EVs. This increase in energy results in the

Energy of oneEV

Fig. 2. Model of Lumped Plug in Electric Vehicle.

PLFc(t)

N , (0

i- * control m v '

NinUiaff)

ELFC(0

Econtrolin (0 +

Einitial (0 /

Econtrol (0

AJ Plug OMi^)

Eplugout

Ncontrol

Fig. 3. Stored energy model of one local control center.

change in the state of PEVs to controllable state from the charging state which is found by multiplying Ncontrolin(t) by the average charging energy (Ckwh).The expression for Econtroun(t) can be written as:

Econtrolin(t) ~ 0-8-BKW'Ncontrolin [kWh] (3)

Eplugout(t) is the reduction in energy as a result of plug out.

In Fig. 3, ELFC is the energy corresponding to the load frequency control signal and found by integrating local center power (PLFC). ELFC can be expressed as:

Elfc (t)= ft Plfc (t)dt (4)

4. The proposed approach

Hence ITAE is chosen as objective function in the present study which is written as:

i" tsim

J = ITAE = / |AF|.t.dt (5)

where, AF is deviation in frequency and tsim is simulation time. 5. Optimization technique

Grey Wolf Optimizer (GWO) is a typical swarm-intelligence algorithm which is inspired from the leadership hierarchy and hunting mechanism of grey wolves in nature. In this section, an overview of original GWO technique and its improved version have been provided.

The performance of the power system depends on the controller structure and selection of objective function. The details about controller structure and objective function employed in the present study are presented in this section.

4.1. Controller structure

In AGC, integral based controllers are generally used to minimize the Area Control Errors (ACE). However, the disadvantage of using only integral controller is that it might produce a closed loop system with significantly slower response times. Proportional Integral (PI) improves the system dynamic response and also offers the additional advantages like simple design, small cost, and their usefulness when designed for systems which are linear and stable process. At the same time, conventional PI controllers are generally not efficient when the higher order nonlinear unstable systems are involved.

Cascade control is one of the approaches used to enhance the system performance. As the number of tuning nubs are more in a cascade controller than a non-cascade controller, improved system performance is expected with cascade control system [32]. Because of its advantages, cascade PI-PD controller for control systems have been proposed in recently in literature [33]. Because of its improved system performance, a cascade PI-PD controller shown in Fig. 4 is chosen in the present study for AGC. The control input signals are the respective ACEs and controller output are the reference power settings of individual generating units.

4.2. Objective function

For controller design employing optimization methods, the objective function is generally specified depending on some performance criteria such as Integral of Time multiplied Absolute Error (ITAE), Integral of Absolute Error (IAE), Integral of Squared Error (ISE) and Integral of Time multiplied Squared Error (ITSE). Detailed expression of these objective functions, their comparison on the system performance are available in literature [21-24,26,27]. It has also been shown in several studies that ITAE objective function offers improved system response than other alternatives [30,31].

5.1. Overview of Grey Wolf Optimization

Grey Wolf Optimization (GWO) is a recently proposed meta-heuristic optimization technique motivated by the social ladder and hunting behavior of grey wolves [29]. The hunting strategy grey wolves are imitated by GWO to search and hunt a solution or pray. There are three main steps in hunting.

1. Tracking (following), chasing (dashing) and approaching the prey.

2. Surrounding and annoying the prey till it halts.

3. Attacking the prey.

Mathematically, GWO algorithm is expressed as follows:

5.1.1. Social hierarchy

Just like the social ladder of grey wolves (to live in groups), four groups are defined; namely Alpha (a), Beta(p), Delta(S), and Omega (ra) in GWO algorithm, During the designing stage the social hierarchy of wolves is modeled. Alpha is the fittest solution; following Beta and Delta as the second and third best solutions. The rest of the solutions are least important and considered as Omega.

Alpha category wolves are present at the top of the hierarchy are the leader of the whole group. They have the decision making power which are followed by the group. Beta category wolves are present in second level of the hierarchy and they are subordinate of alpha wolves. Beta category wolves help alpha wolves in the decision-making process as well as other group actions. They transform into the alpha category wolves when alpha wolves die or become very old. Omega wolves are present in the lowest stage of hierarchy and always follow the decision made by other dominant wolves. Delta types of wolves always follow the alphas and betas but dominate omegas.

5.1.2. Encircling prey

The encircling behavior of grey wolves around the pray are expressed as:

D = |C • D(t)-X(t)|

—►

-► Input

signal —►

Fig. 4. Structure of cascaded PI-PD controller.

X(t + 1) =Xp(t) — A ■ D

where t is the current iteration, A and C are coefficient vectors, XP is the position vector of the prey and X is the position vector of wolf. The coefficient vectors are calculated as:

A = 2 a ■ r1 — a

C = 2 ■ ?2

(8) (9)

where r1 and r2 are random numbers in the range 1 to 0 and vector a is linearly decreased during iterations from 2 to 0.

5.1.3. Hunting

The hunting phase is guided by the best wolves i.e. alphas wolves but beta and delta wolves also participate in hunting phase. The optimum position are obtained by saving three best positions corresponding to alpha, beta and delta wolves and remaining solutions including omega are competed. The updated wolf positions around the prey are determined by:

Da = C ■ Xa — X|, D/j = |C2 ■ Xb - XI, Dd = |C3 ■ Xd — X|

X1 = Xa — A! ■ (Da), X2 = Xb — A2 ■ (Db), X3 = Xd — A3 ■ (Dd) (11) X1 + X2 + X3

X(t +1)=-

5.1.4. Attacking prey

This phase enables the algorithm to exploit the search process. The grey wolves end the hunt by attacking the prey when it stops moving. This process is mathematically expressed by decreasing a which also decreases the variations in A. So initially, A is a random value in the interval [-a, a] and over the course of iterations a is decreased from 2 to 0. When |A| < 1, wolves move towards the prey for attacking.

5.1.5. Searching the prey

This phase enables the algorithm to explore the search process. Grey wolves search based on the position of the alpha, beta, and delta wolves. The wolves move away from each other to search for the prey and come together to attack the prey. When the values of A lie outside the range -1 to 1, the wolves diverge from the prey which incorporates the exploration capability in GWO algorithm. When |A| >1, wolves move away from the prey to search for a better pray. The component C also assist in exploration process. This component which lies in the range 0 to 2, assigns random weights for prey to define the distance. After each iteration, the GWO algorithm allows its search agents to update their position based on the location of a, b, d and attack towards the prey.

Before starting the main objective of any meta-heuristic population based algorithm; two basic parameters are required to be initialized. The first and foremost parameter is the ''maximum number of search agents" or ''grey wolfs". The number of search agents may vary according to the application. In this application this value is taken as 30. The second important parameter is the ''number of iterations". This also depends upon the type of application and varies in a broad range. The less the number of iterations; less the evaluation time. In this study this value is taken as 500. The pseudo code of GWO algorithm is given in Table 1.

5.2. Modified Grey Wolf Optimization

In all population based optimization methods there are mainly two phases to reach the global solution. During the initial stages of

Table 1

Pseudo code of GWO algorithm.

Initialize the algorithm parameters and generate the initial populations (positions

of the wolves or agents) Determine the fitness of each agent

Estimate Xa, Xp and Xd, the position of a, b and d wolves (the, the three best search agents)

while (t < Max number of iterations) for each search agent

Update the position of current search agents end for

Update search agents Calculate the fitness of all search agents Update the position of a, b and d wolves Increase the iteration count end while

Display the best wolves Xa

the algorithm, the individuals should explore the whole search space. During the final stages, the individuals should exploit the information collected to converge on the global optimum. In the original GWO [29], the changeover between exploration and exploitation phase is made by the adaptive values of a and A. In the original GWO, the first half of iterations are dedicated to exploration when |A | p 1 and the second half of iterations are dedicated to exploitation when |A | < 1. Too much exploration of search space may result in lower probability of getting trapped in local optima. At the same time higher exploration introduces more randomness and the optimal solution may not be obtained. At the same time, excess exploitation is related to less randomness and the algorithm may not reach the global optima. Hence, a balance between exploration and exploitation phases should be maintained during the iterations. In the original GWO algorithm, the value of a decreases linearly from 2 to 0 as follows:

a = 2(1 — T-

where tc is the current iteration and Tm is the maximum number of iterations.

In the present MGWO algorithm, more number of iterations are dedicated to the exploration phase and less number of iterations are dedicated to the exploitation stage. In the proposed MGWO, the value of a is decreased from 2 to 0 by the following equation.

a = 2 1-

(■—D

iterations.

In the original GWO algorithm, the position vector of a grey wolf is equally guided by position of a, b and d wolves as given by Eq. (12). As the most dominating member among the group is a followed by b and d, in the proposed modified GWO, more weigh-tage is given to the a followed by b and d to find the position vector of a grey wolf as givenbelow:

X(t + 1) =

3X1 + 2X2 + X3 6

6. Performance analysis of algorithm

In the current study, the performance analysis of MGWO algorithm was carried out by fitting to some standard benchmark functions [29]. The benchmark functions include some unimodal and some multimodal function as these functions prove the exploration and exploitation capability of the algorithm and used by many researchers. These functions expressions, dimensions (Dim), ranges

where tc is the current iteration and Tm is the maximum number of

Table 2

Test function details.

Test Functions

Function Type

f i(x) = E n=! x? f?(x) = EHi I xiI + E[¡Li Ixil

fs(x) = E¡Li - xi ^(^l) f4(x) = E¡Li [x? - 10cos(2pxi) + 10]

Unimodal Unimodal Multimodal Multimodal

30 30 30 30

[-100,100] [-10,10] [-500,500] [-5.12,5.12]

-418.9829x5

Table 3

Statistical result of proposed modified GWO and comparison with other techniques [28].

Average

Std. Dev.

Average

Std. Dev.

Average

Std. Dev.

Average

Std. Dev.

Average

Std. Dev.

F1 F2 F3 F4

0.1150e-37 0.1899e-22 -5766.8 0.0758e-13

0.2729e-37 0.2322e-22 829.9

0.1965e-13

6.59e-28 7.18e-17 -6123.1 0.310521

6.34e-05 29.01e-3 -4087.44 47.35612

1.36e-4 42.14e-3 -4.84e + 3 46.70423

2.02e-4 45.4e-3 1152.814 11.62938

2.53e-16 55.65e-3 -2821.07 25.96841

9.67e-17 19.4e-2 493.0375 7.470068

8.2e-14 1.5e-09 -11080 69.2

5.9e-14 9.9e-10 574.7 38.8

uT 10"'

GWO mGWO

100 200 300 400 500 Iteration

(a) Benchmark test function/;

100 200 300 400

Iteration (b) Benchmark test function

~ -3000 x,

Li." -3500

H -4000 m

-4500 -5000 -5500 -6000

100 200 300 400 Iteration

(c) Benchmark test function/3

■GWO ■mGWO

200 300 Iteration (d) Benchmark test function^

Fig. 5. Comparison of convergence curves of original GWO and modified GWO for benchmark test functions.

and optimum solutions (fmin) are given in the Table 2. After implementing the proposed algorithm to the benchmark functions, the obtained results are compared with some recent metaheuristic techniques like GWO, PSO, GSA and DE. The statistical results like average and standard deviations are gathered in the Table 3. While performing the test the search agents are chosen as 30, maximum number of iterations are taken as 500 and the algorithm is made to run for 30 as proposed in the original GWO. In all population based algorithms, the optimization process is divided into two conflicting stages: exploration and exploitation. Exploration encourages potential solutions to change abruptly and stochastically thus improving the diversity of the solutions. On the other hand, exploitation aims for improving the quality of solutions by

searching locally around the obtained promising solutions in the exploration stage. In original GWO, the transition between exploration and exploitation is generated by the component a which decreases linearly as given in Eq. (13). Greater exploration of search space may result in getting struck in local optima as too much exploration introduces randomness. To enhance the exploration rate, exponential functions are used to decrease the component a as given in Eq. (14). Using this exponential decay function, the numbers of iterations used for exploration and exploitation are 75% and 25%, respectively.

In the original GWO algorithm, the position vector of a grey wolf is guided by position of all four category of wolves i.e. original GWO move the wolves pack toward prey by updating position

Table 4

p-values produced by Wilcoxon's rank sum test comparing MGWO and GWO algorithms.

Wilcoxon p-value

F1 F2 F3 F4

7.3555 e-47 1.081e-28 -4882.976 0

17788e-47 9.067e-22 -3188.033 13.5219

4.71e-28 1.8467e-17 -7406.742 0

123.38 e-28 6.32 e-16 -3162.569 18.351

3.0199e-11 3.0199e-11 5.5727e-10 1.4214e-06

Table 5

Integral controller parameters and performance of single area system with various optimization techniques

Controller parameters/performance/technique

TLBO [26]

DE [25]

Optimal Controller [24]

Parameter value

ITAE x 10—2 IAE x 10—2 ITSE x 10—3 ISE x 10—3

Settling time (sec)

Ki1 Kl2

0.0423

0.0141

0.2191

0.0511

0.0041

0.1847

0.0516

0.0071

0.1701

0.1514

0.0131

0.0708

Table 6

Controller parameters and performance of single area system with different controllers.

Parameters/ITAE

With PI Controller

With PID controller

With PIPD controller

With EV & PIPD controller

Parameter values

Unit 1: Thermal

KP = 1.9995 KI = 0.2391 Unit 2: Hydro Kp = 0.0189; KI = 0.0048 Unit 3: Gas Kp = 0.0507 KI = 0.9633

ITAE x 10-

Unit 1: Thermal

KP = 1.9995 KI = 0.1637 KD = 0.4633 Unit 2: Hydro KP = 0.4779 KI = 0.0906 KD = 0.9258 Unit 2: Hydro KP = 0.1918 KI = 1.9995 Kd = 0.1192

Unit 1: Thermal

KP1 = -0.2828 KI = -1.7898 KD = -1.9978 KP2 = 0.0084 Unit 2: Hydro KP1 = 0.1610 KI = -0.5022 KD = -0.4581 KP2 = -0.6917 Unit 3: Gas KP1 = 0.0115 KI = -1.9978 Kd = -0.1134 KP2 = -1.9978 2.92

Unit 1: Thermal

KP1 = 1.9996 KI = 1.9992 KD = 1.6298 KP2 = 1.9978 Unit 2: Hydro KP1 = 0.1361 KI = -1.7691 KD = -1.9978 KP2 = -0.0427 Unit 3: Gas KP1 = 0.0023 KI = 1.9986 KD = 1.9421 Kp2 = 1.9752 2.39

vector as given by Eq. (12). This strategy of using average of best positions of the pack may introduce randomness in the algorithm. As the most dominating member among the group is a followed by b and d, in the proposed MGWO, weighted sum of best locations is used instead of just a simple average to find the position vector of a grey wolf as given in Eq. (15).

It is clear from Table 3 that proposed MGWO gives significantly improved results compared to original GWO, PSO, GSA and DE algorithms. As unimodal functions are suitable for testing exploitation capability of the algorithms, therefore, the results given in Table 3 gives evidence of high exploitation capability of the proposed MGWO algorithm. At the same time, multimodal functions have large number of local optima. Results given in Table 3 show that proposed MGWO algorithm is able to explore the search space extensively and find promising regions of the search space. In addition, high local optima avoidance of this algorithm is another finding that can be inferred from these results. The convergence curves of unimodal and multimodal benchmark functions for original GWO and proposed MGWO algorithms are given in Fig. 5 for all benchmark test functions. It is clear from Fig. 5 that proposed MGWO algorithm provides better convergence characteristics compared to that of original GWO algorithm.

Wilcoxon's rank-sum test is carried out between MGWO and GWO and p-values along with the best and worst values are reported in Table 4. It can be seen from Table 4 that all the

p-values are less than 0.05 (5% significance level). This is strong evidence against the null hypothesis, indicating that the better median values of the performance metrics produced by MGWO is statically significant and has not occurred by chance.

To further investigate the superiority of the algorithm it is applied to single area system, two-area six unit interconnected system and five unequal interconnected area system with nonlinearities.

7. Application of MGWO for AGC

The model of the system under study has been developed in MATLAB/SIMULINK environment and optimization program has been written (in .mfile). The developed model is simulated in a separate program (by .m file using initial population/controller parameters) considering a step load disturbance. The objective function is calculated in the .m file and used in the optimization algorithm.

7.1. Single area power system

Initially, a single area three-unit power system without PEVs illustrated in Fig. 1 is considered. Each source of power thermal, hydro and gas units are assigned a participation factor which

Time (s)

Fig. 6. Frequency deviation of single-area power system under 1% SLP.

Fig. 7. Two-area six-unit power system with PEVs.

decide the contribution to the nominal loading, summation of participation factor of each control being equal to 1. Participation factor for thermal, hydro and gas units are assumed to be 55%, 32% and 12% respectively. Integral controllers are initially chosen for better illustration of advantage of proposed optimization technique over some of the recently proposed technique such as optimal controller [25], DE [26] and TLBO [27]. It is worthwhile to mention here that for a fair comparison of optimization techniques, identical system and controller should be used. The integral gains are tuned using ITAE objective function by applying a 1% Step Load Perturbation (SLP) employing MGWO algorithm. The ranges

of the gains are chosen as (2, -2). For the execution of MGWO technique the same parameters as given in Section 7 are selected. The final solutions for single area power system with integral controller as well as their performance are shown in Table 3 for MGWO algorithm. For comparison, the corresponding values with TLBO [27], DE [26] and optimal control [25] for the identical system and controller are also given in Table 5. It is obvious from Table 5 that MGWO outperforms TLBO [27], DE [26] and optimal control [25] approaches as less ITAE value is found by MGWO algorithm (ITAE = 45.14 x 10-2) compared to TLBO (ITAE = 51.35 x 10-2), DE (ITAE = 51.65 x 10-2) and optimal

Table 7

Various controller parameters and performance of two area system with MGWO optimization technique.

Parameters/ PID Controller PID Controller PIPD Controller

performance/ without EV with EV with EV

technique

Parameter values Unit 1: Thermal Unit 1: Unit 1:

Thermal Thermal

KP = 1.7502 KP = 1.9995 KP1 = -1.7585

Ki = -0.0087 Ki = 0.3211 Ki = -1.7218

KD = 0.7499 KD = 1.3629 KD = -1.9997

Unit 2: Hydro Unit 2: Hydro KP2 = -1.5747

K2 = 0.311 Kp = 0.0256 Unit 2: Hydro

Ki = 0.3102 Ki = 0.0358 KP1 = 0.0554

KD = 0.0034 KD = 0.2676 KI = 0.3241

Unit 3: Gas Unit 3: Gas Kd = -0.0038

Kp = 0.0091 Kp = 0.1328 KP2 = -0.4726

^ = 1.2409 ^ = 1.5027 Unit 3: Gas

Kd = 0.6901 Kd = 0.4916 Kp1 = 0.3682

Ki = 0.0269

Kd = 0.1706

KP2 = 0.3462

ITAE x 10-2 91.97 50.51 45.41

IAE x 10-2 24.47 17.27 10.61

ITSE x 10-4 78.75 41.74 11.92

ISE x 10-4 47.82 30.51 8.92

technique compared to other techniques. To further improve the system performance PI, PID and cascade PI-PD controllers are assumed and the parameters are tuned by MGWO algorithm. The results are gathered in Table 6 from which is obvious that less ITAE value is got by MGWO optimized cascade PI-PD controller (ITAE = 2.92 x 10~2) compared to PID (ITAE = 3.75 x 10~2) and PI (ITAE = 5.72 x 10~2) controllers. In the next step cascade PI-PD controllers are tuned by proposed MGWO algorithm in presence of PEVs. Participation factor for PEVs are assumed to be 10% and the same for thermal, hydro and gas units are assumed to be 45%, 32% and 12% respectively. The optimized parameters and ITAE value are given in Table 6 from which it is evident that ITAE value is decreased to 2.92 x 10~2 by the dynamic support of PEVs during the disturbance.

To examine the time-domain performance, a SLP of 1% is assumed and system frequency response with proposed MGWO optimized cascade PI-PD controller is provided in Fig. 6. It can be seen from Fig. 6 that, for the case of system without PEV, better dynamic response is obtained with proposed cascade PI-PD controller structure than conventional structured PI and PID controllers. The dynamic response is significantly improved with the inclusion of PEVs as evident from Fig. 6.

control (ITAE = 99.34 x 10~2). Consequently, minimum settling time in frequency deviation (5% band) is attained with MGWO compared to other approaches. It is also evident from Table 5 that less IAE, ITSE and ISE values are acquired with proposed MGWO

7.2. Extension to 2-area 6-unit multi-source power system

The proposed controller strategy is also applied in a two-area six-unit multi-source power system as shown in Fig. 7. The

0.01 0

-0.01 -0.02 -0.03 -0.04 -0.05

/ .*/ is,

/w Ih" I h I h

\U \h --PID without EV

«V V -PIPD with EV

Time (s)

Fig. 8. Frequency deviation of area 1 for two-area power system under 2% SLP in area 1.

^.«.«■^■■-■-""a'ui'ui-ui-

PID without EV

■ PID with EV

■ PIPD with EV

Time (s)

Fig. 9. Frequency deviation of area 2 for two-area power system under 2% SLP in area 1.

x 10"'

V;" ............ *

1/ /i / ✓ * / /

\r i.i

i? £ --F ........F 'ID without EV 'ID with EV >IPD with EV 1 -

5 10 15 20 25 30 35 40 45

Fig. 10. Tie line power deviation for two-area power system under 2% SLP in area 1.

x 10""

irrrrr

■ A PpEV of Area-1

■ AP ofArea-2

0 5 10 15 20 25 30 35 40 45 50

Time (s)

Fig. 11. Variation of PEV output power for two-area power system under 2% SLP in area 1.

x 10"'

10 15 20 25 30 Time (s)

Fig. 12. Power variation of PEV for two-area power system under different SLPs.

-2% SLP SLP SLP -

- - 10°/

ü 1 ' \\

nominal system parameters are taken from [26,27] and given in Appendix B.

The objective function in this case is defined as:

J = ITAE = 1 + |AF2| + IDPTiel) • t • dt

where, AF1 and AF2 deviations in frequency of teach areas; AP^ is the tie line power deviation; tsim is the simulation time.

In this case PID, PID controller with EV and cascade PI-PD controllers are considered and the parameters are tuned employing MGWO algorithm as explained earlier. The optimized controller parameters along with various errors for a 2% step load disturbance

S. Padhy et al. /Engineering Science and Technology, an International Journal xxx (2017) xxx-xxx

Fig. 13. Five unequal area power system with GRC, dead band and transport delay (PEV in area 1).

Table 8

Various controller parameters and performance of five area system with MGWO

optimization technique.

Parameters/ PID Controller PID Controller PIPD Controller

performance/ without EV with EV with EV

technique

Parameter values AREA 1: AREA 1: AREA 1:

KP = 0.1989 KP = 1.5961 KP1 = 1.5767

KI = 0.5162 KI = 1.5108 KI = 1.9998

KD = 0.1190 KD = 0.6316 KD = 1.7824

AREA 2: AREA 2: Kp2 = 0.5224

KP = 0.2992 KP = 0.5639 AREA 2:

KI = 0.0272 KI = 0.5672 Kp1 = 1.9999

KD = 0.3214 Kd = 0.1346 Ki = 0.8375

AREA 3: AREA 3: KD = 0.3291

Kp = 0.1604 Kp = 1.527 Kp2 = 1.1032

Ki = 0.4011 Ki = 0.6237 AREA 3:

KD = 0.0860 KD = 0.73 KP1 = 0.7216

AREA 4: AREA 4: KI = 0.4813

Kp = 0.1939 Kp = 1.9986 Kd = 1.5674

KI = 0.4642 ^ = 0.2199 KP2 = 0.7114

KD = 0.5077 KD = 1.0041 AREA 4:

AREA 5: AREA 5: Kp1 = 1.3860

Kp = 0.5161 Kp = 0.631 KI = 0.6059

KI = 0.3250 KI = 0.4592 KD = 1.3167

KD = 0.5116 KD = 0.8349 KP2 = 1.4274

AREA 5:

KP5 = 0.6462

KI5 = 1.2263

Kd5 = 1.7012

KP55 = 1.982

ITAE x 10~2 99.27 40.49 39.41

in area 1 are given in Table 7. It is evident from Table 7 that lower ITAE value is attained with MGWO optimized PID controller with PEV (ITAE = 50.51 x 10~2) compared to PID controller without

PEV (ITAE = 91.97 x 10~2) and the ITAE value is further reduced to 45.41 x 10~2 when cascaded PI-PD controller along with PEVs are included in the system model. It is also seen from Table 7 that less 1AE, ITSE and ISE values are obtained with cascade PI-PD controller in presence of PEVs compared to individual PID controller without and with PEV.

A 2% SLP is assumed at t = 0 s in area 1 and the results are provided in Figs. 8-10. It can be seen from Figs. 8-10 that better dynamic response is obtained with cascade P1-PD controller than conventional P1D controller and the best system response is obtained with the inclusion of PEVs as shown in Figs. 8-10. The Variation of PEV output power under 2% SLP in area 1 is shown in Fig. 11 from which it is obvious that PEVs contribute in the LFC to maintain the system frequency as per the load variations Fig. 12.

To show the contributions made by PEVs, different step load disturbances are applied and power variation of PEVs are shown in Fig. 11. It is seen from Fig. 11 that as the size of load disturbance increases, PEVs contribute more real power during transient period to minimize the real power imbalance in that period.

7.3. Extension to five area unequal power system with nonlinearities

Lastly, to validate the effectiveness of suggested controller to deal with unequal areas and nonlinearities, a five unequal area thermal power system has been considered [34] for investigation as shown in Fig. 13. The ratings of areas 1 to 5 are taken as 2000 MW, 4000 MW, 8000 MW, 10,000 MW and 12000 MW respectively. The PEV is assumed in area-1. 1t is necessary to consider the basic physical constraints and include the system model to acquire a proper understanding of the generation control

Time (s)

Fig. 14. Frequency deviation of area 1 for five unequal-area nonlinear power system under 1% SLP in area 1.

Fig. 15. Frequency deviation of area 2 for five unequal-area nonlinear power system under 1% SLP in area 1.

/ ■w >

„ ... X

\(0 S \

V, , 1

--PID without EV -PIPD with EV

II >1 '

0 5 10 15 20 25 30

Time (s)

Fig. 16. Frequency deviation of area 3 for five unequal-area nonlinear power system under 1% SLP in area 1.

problem. The major physical constraints which have an influence on the performance of AGC are generation rate constraint, governor dead band nonlinearity and time delay. A GRC of 3%/min, GBD of 0.036 Hz and time delay of 20 ms are considered in this paper [35].

The objective function is calculated by assuming a 1% SLP in area-1. The optimized parameters of controllers found using MGWO technique along with the ITAE values are provided in the Table 8. It is evident from Table 8 that less ITAE values is attained

i A / 1 BV ' -if ^ /

if ' If 1

--PID without EV -

V -PIPD with EV 1

0 5 10 15 20 25 30

Time (s)

Fig. 17. Frequency deviation of area 4 for five unequal-area nonlinear power system under 1% SLP in area 1.

/ A <> N .............*

i /V \\n / At / 11 / ✓

f --PID without EV

1 " 1» -PIPD with EV

0 5 10 15 20 25 30

Time (s)

Fig. 18. Frequency deviation of area 5 for five unequal-area nonlinear power system under 1% SLP in area 1.

0 5 10 15 20 25 30

Time (s)

Fig. 19. Tie-line power deviation of area 1 for five unequal-area nonlinear power system under 1% SLP in area 1.

when cascade PI-PD controllers are used with PEVs. The dynamic response with proposed MGWO tuned cascade PI-PD structure with PEV in area-1 is evaluated by applying a 1% SLP in area-1 at t = 0 s and the results are gathered in Figs. 14-23. For assessment

of improvement with proposed MGWO tuned PIPD structure with PEV in area-1, the dynamic response with MGWO tuned PID structure with PEV in area-1 and MGWO tuned PID structure without PEV are also given in Figs. 14-23. It is clear from Figs. 14-23 that

Time (s)

Fig. 20. Tie-line power deviation of area 2 for five unequal-area nonlinear power system under 1% SLP in area 1.

_ 6 3 4

0 5 10 15 20 25 30

Time (s)

Fig. 21. Tie-line power deviation of area 3 for five unequal-area nonlinear power system under 1% SLP in area 1.

Time (s)

Fig. 22. Tie-line power deviation of area 4 for five unequal-area nonlinear power system under 1% SLP in area 1.

significant improvement in system dynamic response is obtained with MGWO tuned PIPD structure with PEV in area-1 compared MGWO tuned PID structure with PEV in area-1 and MGWO tuned PID structure without PEV.

To evaluate the contribution of PEVs in frequency control under different SLPs, the power variation of PEV under different SLPs in area 1 is shown in Fig. 24. The power variation of PEV under 1% SLPs in different areas is shown in Fig. 25. It is clear from Figs. 24

--PID without EV

........PID with EV

-PIPD with EV

.......

Time (s)

Fig. 23. Tie-line power deviation of area 5 for five unequal-area nonlinear power system under 1% SLP in area 1.

HI 0. CL

0.025 0.02 0.015 0.01 0.005 0

-0.005

1» 1» III1 r «- — 1 % SLP in area-1

- - 3 % SLP in area-1

•A t\ y » 1 \ i : »

f v" V,» ■ J 't

Time (s)

Fig. 24. Power variation of PEV under different SLPs in area 1for five unequal-area nonlinear power system.

........1 % SLP in area-2

- - 1 % SLP in area-3

----1 % SLP in area-4

-1 % SLP in area-5

.iTitWI ■ L ■ ■ 'U"U"M' ""

i««"1" „ •» ""

Fig. 25. Power variation of PEV under 1% SLPs in different areas for five unequal-area nonlinear power system.

and 25 that in both the above cases, PEVs contribute in the AGC to restore the system frequency.

8. Conclusion

Automatic Generation Control (AGC) of power systems with Plug in Electric Vehicles employing Modified GWO (MGWO) optimized cascade PI-PD controller is presented in this study. In the

proposed MGWO, the exploration and exploitation stages of the algorithm are modified and more weightage is given to the fittest wolves to find the new position of grey wolves during the iterations. Proposed algorithm is first applied to four bench mark unimodal and multimodal test functions designed to test the exploration and exploitation capability of an algorithm. It is found from the statistical results that the proposed MGWO outperform original GWO, DE, GSA and PSO algorithms. In the next stage, AGC of a single area three-unit power system is considered and

the superiority of MGWO algorithm over some recently proposed approaches such as optimal control, DE and TLBO is demonstrated. Then PEVs are considered and a cascaded PI-PD controller is suggested. The controller parameters are tuned employing proposed MGWO technique. It is demonstrated that best system performance is attained with cascade PI-PD controller in presence of PEVs. The approach is then applied in a two area six-unit interconnected power system with PEVs in each area. It is found that improved system response is obtained with MGWO optimized cascade PI-PD controller in presence of PEVs than some recently proposed approaches like DE and TLBO. Finally, a five unequal area power system with PEVs in area 1 and appropriate nonlinearities such as GRC, GBD and time delay is considered. It is seen that the proposed MGWO optimized cascade PI-PD controller structures offer better system response compared to the conventional PID controllers in this case also. In all cases, it is observed that, PEVs participate in the AGC to improve the system frequency response.

Appendix A. Single area three-unit system [25-27] & stored energy model of one local center

B = 0.4312 p.u. MW/Hz; Prt = 2000 MW; PL = 1840 MW; Rj=R2 = R3 = 2.4 Hz/p.u.; TSG = 0.08 s; TT =0.3s; KR = 0.3 p.u.; TR = 10 s; KPS = 68.9566 Hz/p.u. MW; TPS = 11.49 s; T12 = 0.0433; a12 = —1; TW =1s; TRS = 5s; TRH = 28.75 s; TGH = 0.2s; XC = 0.6s; YC = 1 s; cg =1; bg = 0.05 s; TF = 0.23 s; TCR = 0.01s; TCD = 0.2s; KT =0. 543478 p.u.; KH = 0.326084 p.u.; KG = 0.130438 p.u.; Ncontoiin(t) = 12; Ninittai(t) = 90;NplUgOJt)=20;Ncontroiiabie(t) = 82;

Appendix B. Two area six-unit interconnected power system [26,27]

Bj=B2 = 0.4312 p.u. MW/Hz; Prt = 2000 MW; PL = 1840 MW; Rj=R2 = R3 = 2.4 Hz/p.u.; TSG = 0.08 s; TT =0.3s; KR = 0.3 p.u.; TR = 10 s; KPSI = KPS2 = 68.9566 Hz/p.u. MW; TPS1 = TPS2 = 11.49 s; T12 = 0.0433; a12 = —1; TW = 1 s; TRS = 5 s; TRH = 28.75 s; TGH = 0.2 s; XC = 0.6 s; YC = 1 s; cg =1; bg = 0.05 s; TF = 0.23 s; TCR = 0.01s; TCD = 0.2 s; KT =0. 543478 p.u.; KH = 0.326084 p.u.; KG = 0.130438 p.u.; KDC = 1; TDC = 0.2 s.

Appendix C. Five unequal area thermal power system with generation rate constraints, governor dead band & transport delay [34,35]

Ratings: Area 1 = 2000 MW, Area 2 = 4000 MW, Area 3 = 8000 MW, Area 4 = 10000 MW, Area 5 = 12000 MWBi = B2 = B3 = B4 = B5 = 0.425 p.u. MW/Hz; R1 = R2 = R3 = R4 = R5 = 2.4 Hz/p.u.

MW; Tg1 = TG2 = Tg3 = Tg4 = Tg5 = 0.08 s;Trt = Tr2 = Tr3 = Tr4 = Tr5 = 10.0 s; Tt1 = Tt2 = Tt3 = Tt4 = Tt5 = 0.35 s; Kr1 = Kr2 = KR3 =

KR4 = KR5 = 0.5 s; TR1 = TR2 = TR3 = TR4 = TR5 = 5 s; KPS1 = KPS2 =

Kps3 = Kps4 = Kps5 = 120 Hz/p.u. MW; Tps1 = Tps2 = Tps3 = Tps4 = Tps5 = 20 s; T12 = T23 = T34 = T45 = T51 = 0.544 p.u.; Td1 = TD2 = TD3 = TD4 = TD5 = 20 ms; Frequency = 50 Hz; Loading = 50%.

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