Comparative study using soft computing techniques for the reactive power compensation of a hybrid power system model

Ain Shams Engineering Journal xxx (xxxx) xxx

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Electrical Engineering

Comparative study using soft computing techniques for the reactive power compensation of a hybrid power system model Pabitra Kumar Guchhait a, Abhik Banerjee a,⇑, V. Mukherjee b a b

Department of Electrical Engineering, National Institute of Technology, Arunachal Pradesh, India Department of Electrical Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, India

a r t i c l e

i n f o

Article history: Received 15 March 2019 Revised 11 June 2019 Accepted 16 July 2019 Available online xxxx Keywords: Hybrid power system model Reactive power compensation STATCOM-PIDF controller Symbiosis organism search algorithm Voltage stability

a b s t r a c t Reactive power discrepancy has caused brief disturbance in the Hybrid Power System Model (HPSM), resulting into voltage fluctuation in the system. This fluctuation has impact in the HPSM both for the steady state and the transient stability. The objective of this paper is to compensate this reactive power and find solution to overcome the problems of not being able to maintain a flat voltage profile of a winddiesel HPSM. Therefore, the study employs a Proportional-Integral-Derivative Controller with Derivative Filter (PIDF) along with a Static Synchronous Compensator (STATCOM) controller. It also proposes an effectiveness of symbiosis organism search algorithm to optimize the various controller parameters of the studied HPSM and compares the results with other reported stochastic and heuristic algorithms. Ó 2019 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/ by-nc-nd/4.0/).

1. Introduction Shrinkage of fossil fuels like coal, petroleum etc have drawn much attention of the renewable energy sources. Solar, wind, PV and others have come into consideration as potential replenishing energy derivation in the world. Clean nature, less maintenance and sustainability have made these renewable energies very popular and favourable [1]. Currently, the large scale power generation facilities have been supplemented by small distributed generation (DG) technologies. To minimize the cost component associated with the transmission of power, the DG systems are incorporated in the distribution network located nearer to the load centres [2,3]. So, a proper system approach is necessary to deploy a DG unit for a flawless distribution networks. This led to a new concept (i.e., micro grid concept) which views a set of DGs and their associated loads as a subsystem. The micro grid is linked with the host power system at a single point and can be operated in both gridconnected and autonomous (islanded) modes [4,5]. In the islanded

⇑ Corresponding author. E-mail address: [email protected] (A. Banerjee). Peer review under responsibility of Ain Shams University.

Production and hosting by Elsevier

mode, the operation of micro grid is a difficult task. The voltage and frequency of the micro grid should be regulated with the help of suitable DG controllers and at the same time, balance of total generation and demand should be maintained. The power management of an islanded micro grid is very much difficult to control as the loads connected in micro grid are of different uncertainties. As such, the autonomous (islanded) mode requires sophisticated control strategies for the reliable and robust operation of micro grid. It also gives the secure operation and desirable performance in a wide range of operating conditions [6]. In [7], a new optimal control strategy has been discussed for efficient operation of the autonomous micro grid. To provide continuous power supply in a system, it is very much difficult for a single generating source. It is pertinent if the energy generating systems are hybrid in nature [8] where combination of two or more sources generates the power needed. It might be an amalgamation of one renewable and one conventional energy sources or other possible combinations of wind-diesel, PV-wind, wind-diesel-micro hydro etc. In this paper, a wind-diesel model is particularly taken into consideration as a hybrid system. The detailed description of this model and its functionality have been discussed in the succeeding sections of the paper [9–12]. For healthy and smooth operation of any type of hybrid power system, synchronisation is very much important between the two generating sources as well as the balancing of active and reactive power is also an essential criterion. Due to variable nature of loads and intermittent nature of renewable energy sources like wind generator system, a reactive power mismatch

https://doi.org/10.1016/j.asej.2019.07.012 2090-4479/Ó 2019 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article as: P. K. Guchhait, A. Banerjee and V. Mukherjee, Comparative study using soft computing techniques for the reactive power compensation of a hybrid power system model, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2019.07.012

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has been occurred in the isolated HPSM [13]. This reactive power imbalance in the isolated hybrid power system may cause a voltage fluctuation in the terminals. It also produces transient in the system. To overcome such hazardous situation of the isolated HPSM, reactive power adjustment is definitely deemed to be crucial. Though many dedicated researchers have been working on this field, scope of this paper remains exclusive and progressive. The concept of flexible ac transmission systems (FACTS) was first introduced by Hingorani [14–15] for controlling active and reactive power-system for redistribution of power into the system to prevent an overall congestion. Various FACTS controllers like static VAR compensator (SVC), Static Synchronous Compensator (STATCOM) and thyristor controlled switch capacitor are used in the literature (see [16–19]) to ensure speedy and continuous power supply responsive towards the system. Regulation of reactive power into a system is essential for stabilizing a transient voltage profile in any type of imbalance with load or input power. This transient voltage response is the most effective characteristic of a power system considering the fast-acting dynamic behaviour of load. Therefore, a dynamic compensation is required for the system to stabilize the voltage profile within a short span of time. FACTS devices like SVC, STATCOM may be helpful in mitigating this complication. However, the STATCOM seems to be appropriate for overcoming this problem once and for all [20]. The required amount of reactive power release or absorbed by a system may be achieved by controlling the firing angle of the STATCOM [21]. Moreover, in presence of high amplitude disturbances, tuning of STATCOM proves to be very important [22]. In the literature, various tuning methods of STATCOM are available. Though a PI controller is used for minimizing the performance index, its results may not be satisfactory when an uncertain disturbance occurs into the power system [22]. Various attempts with diverse approaches like Genetic Algorithm (GA), Artificial Neural Networks (ANNs) and many others are applied to stabilize the voltage profile [23]. Taking into consideration all these previous works, this paper explains the use of a STATCOM with Proportional-Integral-Derivative (PID) Controller with Derivative Filter (PIDF) controller for better realisation of reactive power of a wind-diesel HPSM by using a novel Symbiosis Organism Search (SOS) optimizing technique. Several types of advanced controllers and their structures have been proposed in the literature for stabilizing the voltage of HPSM [24–26]. But, these different controllers are not suitable to get good voltage profiles. The classical PID controllers are preferred for its structural simplicity and minimum cost. In PID controller, derivative mode improves the stability of the system by increasing the speed of the controller response. However, it produces unreasonable noise in the system which may cause a big problem in the hybrid system during practical applications. This problem is handled by incorporating a filter with derivative term of the PID controller where low frequency noise does not affect the system [27]. Therefore, a STATCOM with a PIDF controller has been proposed in this paper for better understanding of reactive power and the voltage stability of the studied wind-diesel HPSM. Existing literature survey indicates a controller structure is valuable for better performance. It will be more appropriate when the controller parameters are being optimised by various techniques used for the same. A controller for voltage stability and reactive power compensation of the HPSM, high performance optimising algorithms are always acceptable for power system operation and control. Miscellaneous stochastic and heuristic algorithms like GA [30,34], ANN [29], seeker optimization algorithm [26], gravitational search algorithm (GSA) [28], oppositional based GSA [24] etc have been used earlier in many papers. In this paper, SOS algorithm is used for its well optimizing capability than the others as discussed earlier. SOS is a meta-heuristic algorithm that works upon the concept of living organisms’ interaction with nat-

ure [31]. Another merit of SOS algorithm is that, during the operation, it requires less number of algorithmic factors as compared to the other existing algorithms. For simplicity of this algorithm, different complicated works have been solved by using SOS technique in power system optimization problems. It has also been observed in [32], that the dynamic response of automatic generation control has been improved with the help of SOS based PID controller in an interconnected power system. In the studied hybrid system, Power System Stabilizer (PSS) is incorporated with generator. Fundamentally, it overcomes the local area oscillation problems [33]. To reduce the oscillation of the power system, different parameters of the PSS are to be tuned properly. In order to tune the parameters of the PSS, the algorithms like GA [34], GA-fuzzy [34], SOA-SFL [35] and PSO [36] are applied recently. Due to complexity burden, insufficient memory storage and non adaptive tuning under various operating conditions, these algorithms are always not very suitable. Moreover, simultaneous tuning of the devices like STATCOM and PSS is a challenging task for the power system utility houses and practicing engineers. Predominant contributions of this paper are to: (a) design a new controller for reactive power compensation of the studied wind-diesel HPSM, (b) optimize various parameters of the PIDF and the STATCOM controller with the help of a novel SOS algorithm, (c) study various HPSM performance parameters (like transient response, performance indices, steady state error, maximum overshoot and convergence profiles etc.), (d) compare the performance of SOS algorithm based results with binary GA (BGA) based technique, (e) compare the convergence profiles and transient responses of studied HPSM with different other algorithms and (f) compare the efficacy of reactive power compensation in the studied HPSM by using two different test cases i.e., model with STATCOM-PIDF and model with STATCOM-PIDF along with PSS. 2. Theory A wind-diesel HPSM has been designed in Fig. 1. At normal operating condition, the real and reactive power balance equation may be represented as,

DPig þ DPsg ¼ DPload

ð1Þ

DQ sg þ DQ com ¼ DQ load þ DQ ig

ð2Þ

where the termsDPig , DP sg , DQ sg and DQ com are the real power delivered by the induction generator (IG), synchronous generator (SG) and reactive power delivered by the SG and STATCOM, respectively.

Fig. 1. Block representation of the studied wind-diesel HPSM.

Please cite this article as: P. K. Guchhait, A. Banerjee and V. Mukherjee, Comparative study using soft computing techniques for the reactive power compensation of a hybrid power system model, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2019.07.012

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the SG and FACTs devices. The amount of reactive power supply by the SG device (refer [22]) due to its change in voltage of HPSM may be formulated as in (5).

DQ sg ¼ K 2 DVðsÞ þ K 3 DEq ðsÞ

ð5Þ

SG parameters related to the HPSM reactive power compensation have been described in Appendix A.1 whereas, the parameters value are also put in Appendix section. The other related HPSM parameters values are given in Appendix A.2. 2.1. STATCOM-PIDF controller structure

Fig. 2. Transfer model diagram of the studied wind-diesel HPSM.

The termsDP load ,DQ load andDQ ig represent the real power drawn by the load, reactive power drawn by the load and that of the IG. When a small input disturbance occurs in the described HPSM, then the system stability may be affected but, there is a certain limitation to bring back the system to its normal operating situation [37]. The voltage fluctuations to the HPSM has been derived from the transfer function (TF) model i.e., Fig. 2 (refer [22]) as in (3).

DVðsÞ ¼ ðK V =1 þ sT V Þ½DQ sg þ DQ com  DQ load  DQ ig 

ð3Þ

Due to the changes in load voltage of the system, the overall reactive power demand of the HPSM may also change. The amount of reactive power surplus of each component of HPSM may be stated as follows. The reactive power surplus/demand to the IG for its operation under a certain slip (s) condition may be modified as in (4) (see [22]).

DQ ig ¼ K 1 DVðsÞ

The need for reactive power for the system cannot be fulfilled by the SG components only. Therefore, the requirement of a reactive power supply device is necessary for the smooth operation of the HPSM. The STATCOM is used to provide the requisite amount of reactive power to the HPSM and make the voltage profile flat after sensing short disturbances of any kind [22]. The STATCOM controller structure is given in Fig. 3. Conventional PID controllers are often preferred in the majority of power systems due to their straight forward designs, convenient accomplishment, low-price and effectiveness from the view-point of their potential use into the domain of engineering. Their impacts upon the dynamic treatments of large scale power systems become relatively inefficient to provide an appropriate level of flexibility to perform in different operating conditions. In order to overcome this type of situation, in this paper, a PIDF controller has been used and properly justified for voltage stability of the studied winddiesel HPSM [27]. The reactive power provided by the STATCOM controller (refer [23]) is given here in the form of (6).

DQ com ¼ G1 DaðsÞ þ G2 DVðsÞ

ð6Þ

In this controller, the controller parameters are T c and T d which are to be optimized within the range of 0:01 6 T c 6 1:02 and 0:01 6 T d 6 1:02. Different controller parameters of PIDF are K p ; K i ; K d ; N and T. The transfer function of the PIDF controller is presented in (7)

TF ¼ K p þ

Ki sK d þ s ðT=NÞs þ 1

ð7Þ

where N and T are, in order, the derivatives, the filter coefficients. The ranges of the derivative filter co-efficient are as follow:

ð4Þ

The various IG parameters associated with reactive power demand devices are formulated in Appendix A.1 and its various constant components may also be found in Appendix A.2. Due to variation of load components, the requirements of reactive power could be enhanced. The change in reactive power demand to the load components may depend on type of load conditions. The deficit/surplus of reactive power to the HPSM due to its enhancement of demand by IG and load may be fulfilled both by

Fig. 4. Power system stabilizer transfer function block representation.

Fig. 3. STATCOM-PIDF controller model for small signal stability analysis.

Please cite this article as: P. K. Guchhait, A. Banerjee and V. Mukherjee, Comparative study using soft computing techniques for the reactive power compensation of a hybrid power system model, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2019.07.012

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[33]. Due to meager oscillation in the rotor of the SG, system stability has got affected and this oscillation might cause severe faults into the system. PSS block is used to overcome such oscillations. Here, in this HPSM, a PSS3B is used for its better control capability than PSS2B [35]. The model of PSS3B controller has been depicted in Fig. 4 and its various components (i.e., K s1 ; K s2 ; T d1 ; T d2 ; T d3 and T d4 ) with their limiting values are as follows. 10 6 K s1 6 10; 10 6 K s2 6 100; 0:001 6 T di 6 0:005 ði ¼ 1; 2; 3; 4Þ 3. Problem formulation Fig. 5. D-shaped sector.

3.1. Design of objective function 1 6 N 6 20;0:01 6 T 6 10 The range of other controller parameters values of the PIDF controller are: 1 6 K p 6 10; 10 6 K i 6 100; 1 6 K d 6 10 2.2. PSS block A PSS block is also used along with the HPSM to damp out the local oscillations and enhance the system’s relative stability

To minimize the reactive power gap between demand and generation of the HPSM, adjustment of various HPSM parameters are being appropriated in such a way that the transient response of the HPSM is to be in a satisfactory level; impling smooth, fast functioning. Here, the damped oscillation process ensures that the dynamic stability of the system is excellent. To fulfil the above objectives of the HPSM, an objective function needs to be defined. Desired transient response specifications which means rise time (t r ), settling time (ts ), maximum overshoot

Fig. 6. SOS-algorithm flowchart.

Please cite this article as: P. K. Guchhait, A. Banerjee and V. Mukherjee, Comparative study using soft computing techniques for the reactive power compensation of a hybrid power system model, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2019.07.012

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(M p ) are to be minimized. Therefore, to fulfil these specifications, an objective function has been formulated in the shape of (8) [35].

error (ITSE) to verify the system’s performance in a better way. These performance index parameters [38] are defined as:

J ¼ J 1 þ 10  J 2 þ 0:01  J 3 þ J 4

ISE ¼

ð8Þ

Z

1

0

e2t ðtÞdt

ð9Þ

In this equation, J 1 ; J 2 ; J 3 and J 4 are known as the weighting factors. Here, the termJ 1 is related to the real part of the eigenvalues. It is responsible to determine the relative stability of the system. The J 2 term determines the maximum overshoot of the system. By proper choosing of this weighting factor (i.e.,J 2 ), maximum overshoot can be minimized. The weighting factorJ 3 is chosen to enhance the damping of the system. Finally, the factorJ 4 is considered as a high arbitrary value. If any unreasonable oscillation has come into the system due to any model parameters, then it rejects the particular parameters [35]. So, these weighting factors have chosen in a manner that, during the optimizing process, all the closed loop poles of the HPSM are in the negative half of jw-axis. During the optimizing process, the closed loop poles are to be within the D-shaped sector (Fig. 5) [35] by enhancing the relative stability and by increasing the damping ratio (ri  r0 ; n  n0 ) of the system as well.

SOS algorithm was invented taking an idea from existing living organisms and their interactions in nature [31]. It is an algorithm like BGA [39], bacteria foraging optimization [40], ant lion optimization [41] etc. SOS algorithm is widely used to solve various kinds of optimization problems which are mostly occurred in power system engineering. It is a preferable optimization technique over the others for its excellent controlled behaviour [42].

3.2. Measure of various performance parameters

4.2. Basic theory of the SOS algorithm

This paper also includes the measurement of two performance indices i.e., integral square error (ISE) and integral time square

Symbiosis means interaction between the living organisms of an ecosystem. Depending on their relationships, symbiotic interac-

Z ITSE ¼ 0

1

ð10Þ

te2t dt

4. Brief description about SOS algorithm 4.1. Literature survey of the algorithm

Table 1 SOS-algorithm based optimized parameters and optimal fitness values under the different test cases. Input V and Xeq conditions in p.u.

Considered test systems

Optimal parameters values

0.97;0.4752

Model + STATCOM + PIDF

0.0010 0.0010 9.0078 0.0167 8.8417 0.0112 0.0010 0.0017 0.0100 0.0174 10.5777 0.0010 0.0010 0.0010 5.3655 0.0143 10.2782 0.2278 0.0010 0.0010 5.5795 0.0055 14.6243 0.1897 0.0010 0.0010 0.0104 0.0076 12.4717 0.0010 0.0010 0.0010 3.4392 0.0087 28.1160 0.0010 0.0010 0.0137 0.0100 0.0272 33.8637 0.0015

Model + STATCOM + PIDF + PSS

0.99;1.08

Model + STATCOM + PIDF Model + STATCOM + PIDF + PSS

1.0;0.93

Model + STATCOM + PIDF Model + STATCOM + PIDF + PSS

1.0;1.08

Model + STATCOM + PIDF Model + STATCOM + PIDF + PSS

1.01;0.752

Model + STATCOM + PIDF Model + STATCOM + PIDF + PSS

1.01;0.97

Model + STATCOM + PIDF Model + STATCOM + PIDF + PSS

1.01;1.08

Model + STATCOM + PIDF Model + STATCOM + PIDF + PSS

Optimal fitness value (J)

1.0000 0.0032 4.1036 2.5974 0.7364

0.0010 0.0010 0.0010 0.0100 0.0124

1.0000 0.0466 3.8756 0.3561 0.0010

0.0010 0.0058 0.0010 0.0135 0.0010

4.8426 0.0065 6.2275 2.3074 0.0039

0.0010 0.0010 0.0010 0.0100 0.1535

1.0000 0.0794 3.7398 1.4651 0.0011

0.0010 0.0094 0.0010 0.0100 0.0666

3.9871 0.3827 3.4922 0.4001 0.0021

0.0010 0.0584 0.0010 0.0100 0.0010

1.0000 0.1047 7.6119 1.8297 0.0010

0.0010 0.0223 0.0010 0.0100 0.0011

1.0000 0.0827 3.0815 3.3347 0.0010

0.0010 0.0200 0.0010 0.2486 0.0030

0.0256

566.4984

0.0167 9.46963 0.0320

181.0912

0.0010

566.4984

0.0083 8.1896 0.0011

176.3837

0.0010

566.4984

0.0191 3.4694 0.0174

181.0636

0.001

566.4984

0.0248 5.7471 0.8789

181.0676

0.0010

566.4984

0.0131 4.0365 0.0011

180.9821

0.0010

566.4984

0.0238 1.1991 0.0011

181.0243

0.0010

566.4984

0.0026 4.6820 0.0012

176.3573

Please cite this article as: P. K. Guchhait, A. Banerjee and V. Mukherjee, Comparative study using soft computing techniques for the reactive power compensation of a hybrid power system model, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2019.07.012

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tions are categorized into three types (namely, mutualism, commensalism and parasitism). In the first kind of interaction, two different species of organism are acted and both the organisms get benefitted. One of examples of this type of relationship is between Oxpecker and Zebra. In commensalism, the symbiotic relationship between two different species of organisms in the ecosystem has been described in which one is getting benefitted while the other is, effectively, unaffected. This type of relationship is observed between the organism tree and spider. In parasitism relationship, one gets benefit from the ecosystem and the other is harmfully affected. One of the major examples of this type of relationship is human body and plasmodium parasite. Therefore, through the process of symbiotic relationships, the living organisms adapt and increase their fitness value to stay alive over long time in the ecosystem. Equations under these three processes are given below chronologically: For mutualism, if X i and X j are the two interacting organisms in the ecosystem, then after their interaction the new X i and X j will be as in (11) and (12) respectively.

X inew ¼ X i þ randð0; 1Þ  ðX best  Mutual v ector  bf 1 Þ

ð11Þ

X jnew ¼ X j þ randð0; 1Þ  ðX best  Mutual v ector  bf 2 Þ

ð12Þ

In these two equations, the Mutual v ector which represents a common relationship between X i and X j . It has been defined as:

Mutual v ector ¼

Xi þ Xj 2

Here, in (11) and (12), randð0; 1Þrepresents any random number that varies between 0 and 1 and X best describes the maximum degree of adaptation. The values of bf 1 and bf 2 are either 1 or 2. When the organisms are fully benefitted by their interactions, it is 2 otherwise, for any partial benefit, it will be considered as 1 [42]. In case of commensalism, the new fitness value of the benefitted organisms (i.e., X i and X j ) is given by (13)

  X inew ¼ X i þ randð1; 1Þ  X best  X j

ð13Þ

  where X best  X j represents the aid provided by the X i to help X j in increasing its fitness or adaptation value for the survival in the ecosystem. 4.3. Algorithm flowchart The flowchart of the SOS algorithm is given in Fig. 6. 5. Results and discussions All the simulations are carried out under different sort disturbances in the HPSM. The simulation has been executed on MATLAB 2010a software in core i5 processor. Various simulation parame-

Table 2 BGA based optimal parameters values and fitness value under the two considered test case. Input V and Xeq conditions in p.u.

Considered test systems

Optimal parameters values (BGA) Algorithm

0.97;0.4752

Model + STATCOM + PIDF

99.6484 0.6596 70.4688 0.3011 100.0000 1.1000 99.6484 1.3766 10.0000 0.4804 100.0000 1.1000 99.6484 1.3688 43.7500 1.1739 100.0000 1.1000 99.6484 1.2519 59.2188 0.4024 100.0000 1.1000 99.6484 1.1272 82.7734 1.1506 100.0000 1.1000 99.6484 1.2519 88.7500 0.5427 100.0000 1.1000 99.6484 1.7506 43.7500 0.9635 100.0000 1.1000

Model + STATCOM + PIDF + PSS

0.97;1.08

Model + STATCOM + PIDF Model + STATCOM + PIDF + PSS

0.99;1.08

Model + STATCOM + PIDF Model + STATCOM + PIDF + PSS

1.0;0.93

Model + STATCOM + PIDF Model + STATCOM + PIDF + PSS

1.01;0.752

Model + STATCOM + PIDF Model + STATCOM + PIDF + PSS

1.01;0.97

Model + STATCOM + PIDF Model + STATCOM + PIDF + PSS

1.01;1.08

Model + STATCOM + PIDF Model + STATCOM + PIDF + PSS

88.3984 99.6529 10.0000 71.1129 1.2100

13.5156 0.0050 12.8125 1.3688 1.0500

88.3984 99.6529 10.0000 10.4447 1.2100

44.1016 0.0050 94.3750 1.9454 1.0500

99.6484 99.6534 10.0000 44.1899 1.2100

32.5000 0.0050 95.7813 1.2441 1.0500

94.0234 99.6532 10.0000 59.6840 1.2100

32.8516 0.0050 91.9141 1.1194 1.0500

99.6484 99.6534 10.0000 83.3672 1.2100

32.5000 0.0050 38.1250 1.9299 1.0500

94.0234 99.6532 10.0000 89.2054 1.2100

32.8516 0.0054 55.3516 1.9922 1.0500

99.6484 99.6534 10.0000 44.2241 1.2100

62.3828 0.0050 63.4375 1.7740 1.0500

Optimal fitness value (J) 1.2207

656.8861

0.3401 10.0000 1.0600

347.9533

1.9221

656.8784

1.3454 10.0000 1.0600

359.9740

1.2363

656.8323

0.5583 10.0000 1.0600

359.3145

1.5013

656.6698

1.5324 10.0000 1.0600

359.8794

1.5013

656.7778

0.2154 10.0000 1.0600

358.7044

1.5013

656.8762

0.6986 10.0000 1.0600

360.4391

1.8753

656.8446

0.4336 10.0000 1.0600

358.7104

Please cite this article as: P. K. Guchhait, A. Banerjee and V. Mukherjee, Comparative study using soft computing techniques for the reactive power compensation of a hybrid power system model, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2019.07.012

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P.K. Guchhait et al. / Ain Shams Engineering Journal xxx (xxxx) xxx Table 3 Comparison of applied algorithms (BGA and SOS) in the verge of optimization process under test case II i.e., Model + STATCOM + PIDF + PSS. Input V and Xeq conditions in p.u.

Considered algorithms

Optimal parameters values

0.97;0.4752

BGA

70.4688 71.1129 1.0500 9.0078 2.5974 0.0124 10.0000 10.4447 1.0500 0.0320 0.2102 0.0010 43.7500 44.1899 1.0500 0.0100 0.3561 0.0010 59.2188 59.6840 1.0500 5.3655 2.3074 0.1535 24.0625 24.4996 1.0500 5.5795 1.4651 0.0666 82.7734 83.3672 1.0500 0.0104 0.4001 0.0010 43.7500 44.2241 1.0500 0.0100 3.3347 0.0030

SOS

0.97;1.08

BGA

SOS

0.99;1.08

BGA

SOS

1.0;0.93

BGA

SOS

1.0;1.08

BGA

SOS

1.01;0.752

BGA

SOS

1.01;1.08

BGA

SOS

Table 4 Performance indices parameters under different load disturbances and different applied algorithms for Model + STATCOM + PIDF + PSS. Input conditions in p.u.

Algorithms

ISE

ITSE

1.01;1.08

BGA SOS BGA SOS

16.9472 11.0598 26.4718 22.1028

74.1923 73.1699 82.1564 80.5930

0.97,1.08

Table 5 Comparison within the various power system transient voltage parameters. Input conditions in p.u.

Applied algorithms

Overshoot (Mp)

Steady state error (Ess)

V = 1.0, Xeq = 1.08 V = 1.01, Xeq = 1.08

BGA SOS BGA SOS

0.0275 0.0080 0.0333 0.0100

0.0087 0.0077 0.0109 0.0089

10.0000 1.3688 1.0600 4.1036 0.0100 0.0320 10.0000 1.9454 1.0600 6.0029 0.0105 0.0010 10.0000 1.2441 1.0600 3.8756 0.0135 0.0011 10.0000 1.1194 1.0600 6.2275 0.0100 0.0174 10.0000 0.6830 1.0600 3.7398 0.0100 0.8789 10.0000 1.9299 1.0600 3.4922 0.0100 0.0011 10.0000 1.7740 1.0600 3.0815 0.2486 0.0012

Optimal fitness value (J) 12.8125 10.000 1.1000 0.0010 9.4696 0.0112 94.3750 10.000 1.1000 0.0011 0.9837 0.0010 95.7813 10.0000 1.1000 0.0010 8.1896 0.0010 91.9141 10.0000 1.1000 0.0010 3.4694 0.2278 88.7500 10.0000 1.1000 0.0010 5.7471 0.1897 38.1250 10.0000 1.1000 0.0010 4.0365 0.0010 63.4375 10.0000 1.1000 0.0010 4.6820 0.0015

0.3401 100.000

0.3011 1.2100

347.9533

0.0167 38.8417

0.0167 0.7364

181.0912

1.3454 100.000

0.4804 1.2100

359.9740

0.0148 23.1656

0.0142 0.0011

176.414

0.5583 100.000

1.1739 1.2100

359.3145

0.0083 10.5777

0.0174 0.0010

176.3837

1.5324 100.000

0.4024 1.2100

359.8794

0.0191 10.2782

0.0143 0.0039

181.0636

0.4960 100.000

1.1817 1.2100

361.7838

0.0248 14.6243

0.0055 0.0011

181.0676

0.2154 100.0000

1.1506 1.2100

358.7044

0.0131 12.4717

0.0076 0.0021

180.9821

0.4336 100.0000

0.9635 1.2100

358.7104

0.0026 33.8637

0.0272 0.0010

176.3573

cases i.e., (i) Model + STATCOM + PIDF and (ii) Model + STATCOM + PIDF + PSS. For different test cases, the state differential vector (X_ ¼ ADX þ BDU þ C DP) components are defined as (i) For case I i.e., Model + STATCOM + PIDF:

DX ¼ ½Dxr Dd DEfd DEq DV t DV DY 1 DaT DU ¼ ½DV ref DT m T DP ¼ ½DQ ref T

(ii) For case II i.e., Model + STATCOM + PIDF + PSS:

DX ¼ ½DX 1 DX 2 DX 3 DX 4 Dxr Dd DEfd DEq DV t DV DY 1 DaT ters are optimized using a novel meta-heuristic algorithm, namely, SOS algorithm. The results are compared with other heuristic algorithms like BGA. The algorithm parameters are taken during testing cases for the sake of comparison. For the algorithms, chosen number of iterations equals to 500 and number of populations equals to 60. The simulation has been carried out under two different test

DU ¼ ½DV ref DT m T DP ¼ ½DQ ref T After the input perturbation, various parameters are observed. Results and observations are discussed below.

Please cite this article as: P. K. Guchhait, A. Banerjee and V. Mukherjee, Comparative study using soft computing techniques for the reactive power compensation of a hybrid power system model, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2019.07.012

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Fig. 7. Convergence profiles comparison between two test cases under SOS-algorithm.

the two different applied algorithms (SOS and BGA). The optimal convergence values (J) under different input operating conditions like simultaneous change in input voltage (V), equivalent reactance (Xeq) or both in the HPSM are also given. From the convergence values (J) of the Tables 1 and 2, it may be concluded the J value converges at a lower level for the test case II, than the test case I. It also implies that the controller parameters of the studied HPSM model are being well optimized for Model along with STATCOM-PIDF and PSS3B (i.e. case II) while using SOS-based meta-heuristic algorithm. In the HPSM, lower value of J indicates that the system under PIDF and PSS3B acquired more stable one that also confirms that the system has attended a stable state quickly. The lower values of J make it possible for the system closed loop poles to stay left in the negative jw-axis.

Fig. 8. Convergence curves under two different algorithms for test condition I.

5.2. Efficiency of SOS algorithm on the verge of optimisation Table 3 shows the optimal values of the parameters under various kinds of applied algorithms considering all input parameters of the HPSM as same. It is seen from the Table 3 that the power system parameters for wind-diesel HPSM are better optimised for the SOS algorithm where the convergent values are lessened. From Table 3, it also becomes evident that for stability responses of the HPSM, application of SOS algorithm is more effective than the others. 5.3. Performance indices based analysis

Fig. 9. Convergence curves under two different algorithms for test condition II.

Table 4 replicates the values of ITSE and ISE. The values of these performance indices for particular input conditions are lower for the Model along with PIDF controller and PSS3B blocks. For quick transient stability of the system, the performance indices must be low. So, from the performance indices values, it may be concluded that the system transient responses could be achieved more quickly for the said algorithm. Therefore, reactive power of the HPSM is compensated with the help of SOS algorithm than BGA. Also, the system operation may become healthier and supportive after the use of SOS-based soft computing technique.

5.1. The objective function based analysis of the HPSM 5.4. Compare of various transient voltage parameters Tables 1 and 2 show the optimal parameter values for Model along with STATCOM and PIDF (K p ; K i ; K d ; T c ; T d ; N and T) and the Model along with STATCOM-PIDF and PSS3B for (K p ; K i ; K d ; T c ; T d ; N; T; K s1 ; K s2 ; T d1 ; T d2 ; T d3 and T d4 )

The system transient voltage parameters values are given in Table 5 under different applied algorithm for the test case II. It is observed from Table 5 that the main transient response specifica-

Please cite this article as: P. K. Guchhait, A. Banerjee and V. Mukherjee, Comparative study using soft computing techniques for the reactive power compensation of a hybrid power system model, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2019.07.012

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Fig. 10. Transient voltage profiles for the applied SOS-algorithm under different test cases.

Fig. 11. Transient voltage responses for test case II under BGA and SOS algorithm.

tions i.e., maximum overshoot and steady state error are less for the applied SOS algorithm. Therefore, the system is more stable for the said controller design than the others under any sort of disturbances. 5.5. Convergence profile based analysis Fig. 7 represents the convergence profiles of HPSM under different conditions. Lower convergence value implies better reactive power optimisation. Fig. 7 shows the objective function convergent at a lower value for test case II. The convergent rate is faster for the test case II and it is also shown in Figs. 8 and 9. It has also been observed that the convergence profiles are better for the applied SOS-algorithm than the other compared algorithms as given in the said figure. 5.6. Transient responses based analysis The system transient stability analysis is one of the most important tasks for HPSM under any type of disturbances. It also gives a better voltage profile by proper reactive power compensation of the HPSM with a very transparent manner. The system transient response profiles are given in Fig. 10 and Fig. 11 under different input conditions of input voltage (V) and equivalent reactance

Fig. 12. Comparison voltage profiles under different applied algorithms.

(Xeq). Fig. 10 shows the modelled transient responses under different test cases and the different applied algorithms under the test case II are depicted in Fig. 11. It may be noted from Fig. 10 that the voltage profile for test case II undergoes its steady state very quickly than the test case I, where the system response achieves its voltage profile flat after a long time. To verify the efficiency of SOS algorithm in the optimization process, the results of various other existing algorithms are taken into consideration for the sake of comparison. The comparison is being done with BGA [41], ALO [41] and GSA [28]. The input parameters of the various compared algorithms are listed below:  For BGA [41]: population size = 60, no. of iterations = 500, runtime = 10, cross-over rate = 80%, mutation probability = 0.001, number of bits = (number of parameters) * 8(for BGA).  For ALO [41]: population size = 60, no. of iterations = 500 and run time = 10  For GSA [28]: population size = 60, no. of iterations = 500, runtime = 10, Go = 100, t = 20, rNorm = 2, rPower = 1 ande0 = 0.0001.

Please cite this article as: P. K. Guchhait, A. Banerjee and V. Mukherjee, Comparative study using soft computing techniques for the reactive power compensation of a hybrid power system model, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2019.07.012

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Fig. 12 also indicates transient voltage response profiles of the studied HPSM under 1% step change in reference voltage and in load demand. This figure is obtained for Model + STATCOM + PIDF + PSS for an input operating conditionV = 0.97p.u., X eq = 0.4752p.u. From this figure, it may be said that the optimal response has been achieved for SOS-based algorithm and it is faster than the other different optimization algorithms. It also explains in other way that reactive power is supported by the STATCOM and stabilizing impact is supported by the PSS3B controller. Also the response error profiles should be minimized by the use of PID controller with a derivative filter. The comparative convergence profile of J values for all applicable algorithms to test case II are given in Fig. 13 at an operating conditionV = 1.01 p.u., X eq =1.08 p.u. From the figure it may also be established that the SOS-based algorithm offers minimum value of J than the other optimized algorithm. Fig. 13. Comparison of fitness value curves under different applied algorithms.

Fig. 14. Various model parameters of the HPSM under test cases I and II.

Please cite this article as: P. K. Guchhait, A. Banerjee and V. Mukherjee, Comparative study using soft computing techniques for the reactive power compensation of a hybrid power system model, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2019.07.012

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P ig ¼ 0:6p:u: kW,

5.7. Various HPSM parameters responses

Q ig ¼ 0:291p:u: kVAR,

Pin ¼ 0:667p:u: kW,

g ¼ 90%, power factor in IG = 0.9, Psg ¼ 0:4p:u: kW, Q sg ¼ The different parameters response of the HPSM under two test cases for the effective SOS-algorithm are given in Fig. 14 and it is observed that the responses are in better order for the test case II. 6. Conclusion

Appendix A.1. IG, SG, STATCOM-PIDF and load parameters The termsK 1 , K 2 , K 3 , K 4 , K 5 and T g related to the Eqs. (1)–(3) are further elaborated as

2VX eq ðR2ig

þ X 2eq Þ

ðA1Þ

K2 ¼

Vcosd X 0d

ðA2Þ

K3 ¼

ðEcosd  2VÞ X 0d

ðA3Þ

K4 ¼

X 0d Xd

ðA4Þ

K5 ¼

ðX 0d  X d Þcosd X 0d

ðA5Þ

T g ¼ T 0d0

X 0d Xd

ðA6Þ

In the Eq. (A1), the denominator parameters i.e.,Rig and X eq again interrelated with the other IG parameters and may written as

Rig ¼

r 02 ð1  sÞ þ ðr1 þ r02 Þ s

X eq ¼ ðx1 þ x02 Þ

Q load ¼ 0:75p:u: kVAR,

power

factor

of

load = 0.8,

Q com ¼

0:841p:u: kVARand a ¼ 53:320 . Appendix A.2. Simulink model based power system data

It may be concluded that the reactive power is properly controlled in smooth way for the wind diesel hybrid power system model under study. The reactive power has effectively controlled by using a STATCOM-PIDF with PSS controller. The transient voltage as well as reactive power optimisation of the system is achieved at its best position when the system control parameters are optimized by the use of a novel soft computing technique, namely SOS algorithm. The results of interest also compared with the different test cases firstly, with STATCOM-PIDF controller i.e., test case I and secondly, in test case II i.e. STATCOM-PIDF with PSS controller. Thereafter, the different heuristic algorithms have also been applied in the cases under study (i.e. test case I and test case II). It can also be concluded that the proposed model (i.e. in test case II, STATCOM-PIDF with PSS controller) gives faster transient response and is more effective for truly compensating the reactive power in the proposed hybrid power system model. The application of SOS algorithm is successfully implemented and best results are achieved in the proposed model as compared to other optimization techniques under study.

K1 ¼

0:2p:u: kVAR, Eq ¼ 1:12418p:u:, E0q ¼ 0:9804p:u:, P load ¼ 1:0p:u: kW,

ðA7Þ ðA8Þ

The different IG and SG parameters value in Eqs. (A1)–(A8) are given as [23] For IG: s = 3.5%, r 1 ¼ r 02 ¼ 0:19p:u:, x1 ¼ x02 ¼ 0:56p:u: For SG: V ¼ 1:0p:u:, d ¼ 17:24830 , T 0d0 ¼ 5:0sec, X d ¼ 1:0p:u: andX 0d ¼ 0:15p:u: The other considered data of the proposed STATCOM-PIDF based wind-diesel HPSM as [23,24]

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Abhik Banerjee was born in 1986 at Burnpur, Burdwan, West Bengal, India. He received his B.Tech degree in electrical engineering from Asansol Engineering College (under West Bengal University of Technology), Asansol, Burdwan, India and M. Tech. in Power System from Dr. B. C. Roy Engineering College (under West Bengal University of Technology), Durgapur, Burdwan, India, respectively. He has done his Ph.D. degree from Indian Institute of Technology (Indian School of Mines) Dhanbad, Jharkhand, India. Previously, he was working in the capacity of assistant professor in the department of electrical engineering, Asansol Engineering College, Asansol, West-Bengal, India. Currently, he is assistant professor in National Institute of Technology, Arunachal Pradesh, Yupia, India. His research interest includes reactive power control, distributed generation, load tracking. Dr. Banerjee is an Associate member of The Institution of Engineers (India).

V. Mukherjee was born in 1970 at Raina, Burdwan, West Bengal, India. He received his graduation in electrical engineering and post graduation in power system from B.E. College (IIEST), Shibpur, Howrah, India and B.E. College (Deemed University), Shibpur, Howrah, India, respectively. He received his Ph.D. degree from NIT, Durgapur, India. Presently, he is an associate professor in the department of electrical engineering, Indian Institute of Technology (Indian School of Mines) Dhanbad, Jharkhand, India. His research interest is application of soft computing intelligence to various fields of power systems. Dr. Mukherjee is a member of The Institution of Engineers (India).

Pabitra Kumar Guchhait was born in 1991 at Paschim Medinipur, West Bengal, India. He received his B.Sc (Physics Hons.) degree from R.K.Mission Vivekananda Centenary College (under W.B.S.U) at 2011. Thereafter, he received his B.Tech and M.Tech degree from University of Calcutta, India in 2014 and 2016, respectively. Now, he is pursuing Ph.D from National Institute of Technology, Arunachal Pradesh, India.

Please cite this article as: P. K. Guchhait, A. Banerjee and V. Mukherjee, Comparative study using soft computing techniques for the reactive power compensation of a hybrid power system model, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2019.07.012