Whale Optimization Algorithms-based PI controllers of ... · Whale optimization algorithm (WOA) is one of the modern optimization techniques used in many power systems ap-plications

ISSN 1 746-7233, England, UKWorld Journal of Modelling and Simulation

Vol. 16 (2020) No. 1, pp. 26-40

Whale Optimization Algorithms-based PI controllers of STATCOM forRenewable Hybrid Power System

Mohammed I. Mosaad1*

Yanbu Industrial College (YIC), Alnahdah, Yanbu Al Sinaiyah, Yanbu 46452, Saudi Arabia

(Received October 01 2019, Accepted November 20 2019)

Abstract. This paper introduces whale optimization algorithm (WOA) of PI controllers for controlling STAT-COM. This WOA-PI controllers of SATCOM is applied for a renewable hybrid system to improve the per-formance of the entire system. This hybrid power system consists of wind energy conversion system (WECS)based- switched reluctance generator (SRG) and photovoltaic (PV) system. The primary thought behind thispaper is to enhance the system performance through regulating the reactive power injected to the system bySTATCOM to beat the anomalous operating conditions in the system including three-phase fault taken place atthe point of common coupling (PCC) between the grid and the hybrid renewable energy system. This accord-ingly increases the fault ride through (FRT) capability of the system. Two conventional PI controllers, optimallytuned by WOA, are used to drive the STATCOM. The results show the capability of the controlled WOP-PI forSTATCOM to improve the PCC voltage profile and the system performance. Moreover keep the WECS and PVsystems in service without disconnecting from the network during abnormal operating conditions. To investi-gate the WOA performance for optimal tuning of the controller parameters, another optimization technique,particle swarm optimization is introduced.

Keywords: hybrid power systems, wind energy conversion system, Photovoltaic System (PV), fault ridethrough, STATCOM, whale optimization algorithm.

1 Introduction

Renewable energy sources (RES) play a significant role in the electric power generation in the last decades.These RES are integrated into the electrical grid to fulfill the expanding need for energy and decrease theharmful emissions that arises as a result of using classical fuel [4, 28]. Many RES had appeared as doablesolutions, each one of them has their own positive and negative characteristics. As a whole, RES offer theway that their fuel is essentially free and they produce negligible to no waste. These factors are the primarymotivation for countries to integrate RES in the classical electric power generation [20, 27].

Hybrid power systems based on wind energy conversion system (WECS) and photovoltaic (PV) systemscannot supply the needed reactive power during disturbances applied to the system. Consequently, the voltageprofile at the point of common coupling (PCC) will fluctuate and this fluctuations have negative effects on thepower system performance including system stability, power factor and power quality. Moreover these voltagefluctuations, if not properly controlled, will range to undesirable levels based on some grid codes [1]. These gridcodes were developed for fault ride through (FRT) during fault events to determine the continuous operation andtrip zones. Nordal grid code, as an example is given in Fig. 1, [1]. These grid codes determine the acceptablevoltage levels during faulty events for the RES to be in continuous operation without disconnection from thegrid (continuous operation zone). On the other hand, there is another zone for the unacceptable voltage ranges(trip zone) in which the RES will be disconnected from the grid.

∗ Corresponding author. E-mail address: m i [email protected]

Published by World Academic Press, World Academic Union

World Journal of Modelling and Simulation, Vol. 16 (2020) No. 1, pp. 26-40 27

The disconnection from the grid will lead to extreme inrush of reactive power from the grid, which isunfortunate. Many flexible controlled devices are used to inject the required reactive power for the renewablehybrid systems to regulate the voltage levels at PCC during faulty operating conditions and fulfill the contin-uous operation especially for WECS based self-excited induction generators (SEIG) and switched reluctancegenerators (SRG).

SEIG as an example of WECS generators than desperately need for reactive power either in the abnormaloperating conditions for support the self-excitation or as reactive power support and consequently improvementof the voltage profile at disturbances applied to such generators. Some flexible and controllable devices are usedfor support the reactive power for such generators. SVC, as one of the flexible devices was used for reactivepower support and consequently improve the voltage regulation of SEIG as in [23]. Another flexible device,STATCOM was introduced for voltage support and performance enhancement of WECS as in [9, 17]. Dynamicvoltage restorer is also presented for performance enhancement of hybrid power system as in [20]. The staticsynchronous series compensator (SSSC), the unified power flow controller (UPFC) and superconductors (SC)were also used for renewable energy system’s performance improvement [9, 10, 19].

Till now the classical PI controllers are still used in many applications related to the electrical generatingfield. This is due to their simplicity and ease of implementation. PI controllers were used for power qualityenhancement of fuel cell (FC) system connected to the grid [19]. They were also used for WECS integrated tothe grid as in [17]. In spite of all the previous features of PI controllers, if their parameters are not determinedproperly they would not play the role assigned to them. This opened the way for the presence of modernoptimization methods for optimal tuning of PI controller parameters.

Many optimization techniques were presented in many application in electrical systems [6, 7, 22, 24]. Ge-netic algorithm (GA) was early used for optimal tuning of PI control parameters [6, 12, 25]. GA is considerednow as the benchmark for the optimized PI control parameters. Particle swarm optimization (PSO), harmonysearch and follower pollination were introduced for the optimal tuning of PI control parameters for FC con-nected to the electrical network [16]. These three optimization techniques were utilized for optimal tuning ofPI controllers parameters driving the inverter used to connect RES in the form of fuel cell to the grid. Whaleoptimization algorithm (WOA) is one of the modern optimization techniques used in many power systems ap-plications. WOA is utilized for optimal tuning of FOPI controllers to control SSSC and prove efficient resultsthan PSO [26]. WOA is used for optimal tuning of PID control parameters for automatic voltage regulator(AVR) as in [15]. WOA proves better performance than other seven optimization techniques [15].

In this paper, a new optimization technique namely WOA is introduced to determine the optimal controlparameters of two PI controllers. These two PI controllers are used to drive STATCOM in order to supportthe reactive power of hybrid power system including WECS and PV system. This reactive power support fromSTATCOM for the hybrid power system aimed at regulating the PCC voltage during grid side disturbance.Moreover, the STATCOM is introduced for improving the system performance and complies with grid codesand keep the continuous operation of these renewable sources even with fault events. A comparison betweenthe system performance using PSO and WOA for tuning PI controller is introduced.

The paper is organized as follows: In section 2, the system under study is indicated. In section 3, modellingof the WECS, PV, STATCOM, the design of the controller and the optimization techniques used are presented indetails. In section 4, the simulation results and discussions about these results are given. Finally, the conclusionsin section 5.

2 System under study

The studied system consists of two RES, WECS- based SRG and PV systems. These two RES are connect-ed to the system at the PCC between the grid and the hybrid renewable energy system. This common couplingbus is connected to the grid through two transformers and two transmission lines. STATCOM is connected tothe system at PCC to improve the system performance. The system is depicted in Fig. ??. The system dataalong with the STATCOM data are given in the appendix.

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28 M. I. Mosaad: Whale Optimization Algorithms-based PI controllers of STATCOM

Fig. 1: Nordal grid code

3 System modelling

3.1 Switched reluctance generator

The manufacture of SRG is modest as related to other kinds of electric generators. The stator windingsare of concentrated type and they have simple structure. In a typical structure, diametrically opposite statorwindings are connected in series to form a two-pole field pattern. The rotor has no winding, no magnets andcan be made to have low inertia. The SRG has a doubly salient pole construction (stator and rotor are salient)excited by asymmetric bridge converter. In this study four phases 8/6 poles SRG with the construction given inFig. 2a is used. Fig. 2b illustrates the converter structure of a four-phase 8/6 SRG [14, 21].

The phase currents of the SRG can be independently controlled by feeding the four-phase using asymmet-rical power converter. A rotor position is sensed so that the turn-on (α) and turn-off (β) angles of each phasecan faultless performed. The four independent hysteresis controller is used to control the currents in statorphases [14]. The magnetic flux linkage to the windings is determined by integrating the difference between theinput voltage and the voltage drop across the stator resistance Rs w.r.t time as [20]:

λ (t) =

∫ t

0(V − isRs)dt (1)

Where, V is the terminal voltage and is is the phase current respectively.A lockup table ITBL, is used to describe the nonlinear function of the currents is(λ, θ). Another table

TTBL is used also for describing the nonlinear function of the torque created by stator phases Te(is, θ) .Then the total torque of the SRG is the summation of torque of all phases;

Te =

Ns∑j=1

Tj (θ, is) (2)

The average electric power of SRG phases Pout is the summation of output power of each phase in oneelectric cycle.

Pout =1

T

Ns∑j=1

∫ t

0vjisjdt (3)

Where Ns is are the number of phases. T is the conduction period of one phase. Vj and is, are the voltageand current of Phase j, respectively.

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Fig. 2: four-phase 8/6 SRG

3.2 Photovoltaic system

Solar photovoltaic (PV) become gradually important as a RES since they compromise numerous benefitssuch as, incurring no fuel costs, no pollution, requiring little maintenance, and producing no noise, among otherRES. There are contrasting mathematical models that can be used to model a PV array. From the solid-statephysics attitude, the cell is commonly a wide area p-n diode with the junction situated near to the top surface[2, 29]. So a practical solar cell may be modeled by a current source in parallel with a diode that mathematicallydescribes the I-V characteristic.

The equivalent Circuit of PV module presented in Fig. 3. Where Rs is the array series resistance, Rp is thearray parallel resistance [2, 29]. Ns and Np are the number of series and parallel modules respectively, I and Vare the output current and voltage of the array and Im is the module current.

Fig. 3: Equivalent Circuit of PV module.



The currentCvoltage (VCI) characteristic of a solar photovoltaic cell is given by :

I0 =Iscn +Ki∆T

exp(Vocn+Kv∆T

αVt

)− 1

(4)

Ipv = (Ipvn +Ki∆T )G

Gn(5)

Im = IpvNp − I0Np

expV +Rs

(NsNp

)I

VtαNs

− 1

(6)

Where a is the diode ideality constant, Vt is the thermal voltage of the array and can be obtained from thefollowing equation [2, 29]:

Vt=NcskT

q(7)

Ncs is the number of cells connected in series, q is the electron charge, k is Boltzmann constant and Tis the temperature of the P − N junction in Kelvin’s. Ipv is the photovoltaic current, Io is the reverse leakagecurrent of the diode, Ipvn is the generated current at 25oC and 1000 W/m2 (nominal conditions). Ki,Kv thecurrent and voltage temperature confident respectively, G is the irradiance and Gn is the irradiance at nominalconditions, Iscn, Vocn are the short circuit current and open circuit voltage respectively at nominal conditionsand ∆T is the difference between the actual and the nominal temperatures in Kelvin’s [2]. KC200GT moduleis used in this paper. Maximum power point tracking (MPPT) technique based incremental conductance is usedin this paper [3, 8, 18].

3.3 Principle of operation and control of statcom

STATCOM is a static shunt compensator whose capacitive or inductive output current can be controlledbased on the PCC voltage. The operation principle of STATCOM can be described through STATCOM singleline diagram and control block diagram shown in Fig. 4a and b respectively.

STATCOM comprises of a VSC, a DC energy storage device (capacitor), and a coupling transformer whichconnects the VSC in shunt to the power network at PCC, Fig. 3. The VSC generates a group of controllablevoltages with the frequency of the AC power system. STATCOM has the ability to operate in capacitive andinductive modes based on the PCC voltage [17]. If the amplitude of the PCC voltage is decrease, a leadingcurrent is injected from STATCOM to the grid at PCC, i.e. the STATCOM generates reactive power (capacitivemode).While in the inductive mode, a lagging current is injected from STATCOM to the grid at PCC and theSTATCOM absorbs the reactive power when the PCC increases. If the PCC voltage is not changed, no powerexchange takes place. This controllable injected current from STATCOM support the PCC voltage fluctuationsduring fault events. Two PI controllers are presented in this paper to drive the STATCOM to support the voltagefluctuations and consequently improve the hybrid system performance. Tuning the parameters of the two PIcontrollers is performed by WOA [15]. WOA is used to minimize the minimize integral of square of error(ISE) between the reference voltage and the PCC voltage. The STATCOM block diagram along with the twooptimized PI controllers are shown in Fig. 3b. The block diagram contains d-q frame transformation of the three-phase PCC voltages and currents. The two proposed controllers are utilized to drive the STATCOM [11, 13].The first controller (controller 1) is used to update the reference quadrature axis current, Iqref , based on thedifference between the vector of measured and reference voltages. While, the second controller (controller 2)is used to drive the angle α that is added to the phase angle of the terminal voltage of the PCC, Θ. SPWMtechnique is introduced to generate switching pulses of the three-level inverter of STATCOM used to controlthe inverter voltage injected to the system based on the phase angle control [17].

WOA is used to determine the optimal PI controller parameters for STATCOM. PSO, another optimizationtechnique, is also used to compare the system performance with the two PI controllers for STATCOM whenusing WOA technique.



Fig. 4: STATCOM circuit representation.

A. Particle Swarm for Tuning PI Control ParametersPSO is used to find the optimum PI control parameters for controlling reactive power flow between the

hybrid system and the grid based on STATCOM. Two PI controllers are introduced to drive STATCOM. Eachcontroller has two parameters (Kp,KI) as given Fig. 4b. The optimization process using PSO is introducedto determine the optimal PI controllers parameters while minimizing the objective function J during any faultevents.

The objective function, J , can be defined as:

J =

∫ t

0(ev(t)2)dt (8)



where ev represents the error between PCC and reference voltages.Initial pollution for the two controller’s parameters is assumed and the objective function is calculated

based on this initial values. The velocity and position of each particle are updated and the new objective functionis determined. This process is repeated till the maximum number of iteration is reached, and lastly the bestpopulation consistent to the minimum objective function obtained is calculated. The PSO flowchart for optimaltuning of tuning the two PI controller’s parameters is depicted in Fig. 5, [5].

3.4 Wale optimization algorithm for tuning pi control parameters

WOA is anew optimization technique as the wale is one of the most intelligent animals as their brain havesome cells common to the human brain cells [13-14]. As in all optimization techniques the solution starts byassuming random solutions for the optimized parameters (four parameters of the two PI controllers) and thecorresponding objective function J , introduced in Eq. 8 is determined. In WOA, search agents updated theposition at each iteration and the objective function is determined based on this update. The process is repeatedtill react the maximum number of iterations and the best solution is stored. The flow chart of WOA for optimaltuning of PI control parameters is given in Fig. 6.

The optimization process based WOA can be divided into three steps:1- Surrounding prey whalesAt first, humpback whales perceive the location and after that circle the prey. First, the calculation of WOA

expects the present best solution as the solution close to the best one. When the best solution is characterized,other whales (search operators) will attempt to update their individual positions towards the best arrangement.The mathematical presentation of the whales surrounding prey methodology can be defined as:

−→H =

∣∣∣∣−→E .−→Y P (i)−−→Y (i)

∣∣∣∣ (9)

−→Y (i+ 1) =

−→Y P (i)−

−→D.−→H (10)

where i indicates the current iteration,−→Y is the position vector for the currently best solution obtained and−→

Y P is the best position vector.The two vector coefficients D and

−→E are determines as:

−→E = 2r2 (11)

−→D = 2

−→d .r1 −

−→d (12)

The value of D is decreasing from 2 to 0, the vector−→D ranges from [

−→−d,−→d ]. The two random values r1

and r2 take the value between 0 and 1.2- Assaulting instrument of the WOA (bubble-net chasing)/ exploitation stageIn this bubble-net chasing step, two methodologies are defined, shrinking encircling mechanism and spiral

updating position. The whales’ shrinking attitude is performed by reducing the value of−→d . While the second

methodology is based on updating the position attitude and can be defined as:

−→Y (i+ 1) =

−→F ′.bel(2πr) +

−→Y P (i) (13)

During chasing, whales use to swim around the prey in the previously mentioned two strategies at the sametime. So as to update the position of whales, 50% probability is considered for these two strategies as follows:

−→Y (it+ 1) =

−→Y P (i)−

−→D.−→H p < 0.5

−→F ′.bel(2πr) +

−→Y P (i) p ≥ 0.5

(14)

Where F ′ represents the best position between whale and prey.



Fig. 5: Flow Chart of optimal tuning PI controller’s parameters using PSO.

3- Prey Searching stepThe searching step is manly relies on the fluctuation of the vector. Based on each other’s position, hump-

back whales search the best position randomly. For optimal global position,

−→F =

∣∣∣∣−→D.

−−−→Y rand −−→

Y (i)

∣∣∣∣ (15)

−→Y (i+ 1) =

−−−→Y rand −−→

D.−→H (16)

Where Y rand is a random whale position vector selected from the current population.

4 Results and discussions

The MATLAB/SIMULINK is used to simulate the hybrid model integrated to the grid and the STATCOM.The WOA and PSO are used for optimal tuning of the two PI controllers parameters used to drive STATCOMto enhance the system performance during abnormal operating conditions including three-phase fault at PCC.

In this case three-phase to ground fault is applied to the system at PCC between 2 and 2.25s. Both PSO andWOA are used for optimal tuning of the controller parameters and the system performance will be investigated



Fig. 6: Flow Chart of optimal tuning PI controller’s parameters using WOA

with and without STATCOM. The convergence of the objective function, J introduced in Eq. (8) when usingPSO and WOA is indicated in Fig. 7.

The PI controllers parameters using PSO and WOA are given in Table 1.

Table 1: Control parameters using PSO and GWO.

PSO GWOController 1 Controller 2 Controller 1 Controller 2

Kp 9.76 15.7 12.6 20.8Ki 3.8 9.6 14.8 16.2

The PCC voltage with and without STATCOM is depicted in Fig. 8a. Without STATCOM, the PCC voltageranges out of the continuous operating zone (for both Spain and US codes) that will call the RES includingWECS and PV to be disconnected from the grid. The reconnection of these RES to the grid is not easy issue,as it requires some complicated steps and procedures. Adding the controlled STATCOM to the system hadimproved the PCC voltage profile with the superiority of using WOA-PI than PSO-PI. The PCC voltage reachto 0.35 and 0.4 pu when using PSO-PI and WOA-PI respectively. Adding the proposed controlled STATCOMto the system at PCC will the RES in service during the three-phase fault as the PCC voltage ranges within thecontinuous operating zone. Consequently, WECS and PV system will be in service during this fault event.

Without using STATCOM, the PCC current increased by 3.2 pu that will call the protection devices todisconnect the RES from the grid [14]. When using the STATCOM, the RES will not be disconnected from thegrid as slightly increase in the PCC current to 1.45 and 1.32 pu when using PSO-PI and WOA-PI respectively,Fig. 8b.



Fig. 7: Convergence of the objective function using PSO and WOA

Fig. 8: PCC voltage and current with and without STATCOM



The WECS performance through the SRG in this three-phase fault will be investigated. The DC voltageof the SRG is increased to 480 V and this voltage cannot return to the steady state value of 230V without usingSTATCOM after clearing the fault at 2.25s. When the controlled STATCOM proposed was connected to thePCC, the SRG DC voltage profile is improved and the DC voltage can come back to the steady state value as inFig. 9a. If the SRG is still connected to the grid, the increase in the DC voltage will damage the DC link. Thesame scenario was happened for the SRG current as in Fig. 9b. The SRG current reached to a steady state valueof 151A rather than 111 when using STATCOM. These results and discussions emphasis the disconnection ofthe WECS from the grid as investigated from the PCC voltage profile and the grid codes as in Fig. 8a.

Fig. 9: SRG performance

The PV system performance is indicated in Fig. 10. The PV system is slightly affected by the three-phasefault applied at the PCC as the MPPT used in this study for the PV system.

5 Conclusion

This paper introduced WOA, as a new optimization technique for optimal tuning of PI control parametersof STATCOM. The main role of controlled STATCOM is to support the reactive power for the system duringfault events. The controlled STATCOM succeeded at enhancing the performance of a hybrid grid-connected



Fig. 10: PV performance

power system consists of WECS and PV system. The controlled STATCOM also succeed in increasing the FRTcapability of the system and keep the RES connected to the grid during abnormal operating conditions withoutdisconnection. WOA for optimal tuning introduced in this paper proved better performance when compared toPSO.



Appendix

Table 2: SRG parametersα = 10, β = 16

DC bus o/p Voltage Vo 230 VDC bus o/p Current Idc 99.2 AOutput power Pout 24.8 KW

Table 3: Add captionQuantity ValueI max power 7.61 AV max power 26.3 VP max 200.143 WI short circuit 8.21 AV open circuit 32.9 VI leakage 9.825*10-8 AI photovoltaic 8.211 ADiode ideality constant (a) 1.3Parallel resistance 415.406 ΩSeries resistance 0.221 Ω

Table 4: STATCOM dataSTATCOM rating 48 KVASeries line resistance 0.34 ΩSeries line reactance 3.63 ΩDC- link capacitance 250 µF



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Whale Optimization Algorithms-based PI controllers of ... · Whale optimization algorithm (WOA) is one of the modern optimization techniques used in many power systems ap-plications