Electrical Power and Energy Systems 53 (2013) 742–751

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Electrical Power and Energy Systems

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Voltage and frequency regulation based DG unit in an autonomousmicrogrid operation using Particle Swarm Optimization

0142-0615/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.ijepes.2013.06.002

⇑ Corresponding author. Tel.: +61 8 6304 5318; fax: +61 8 6304 5811.E-mail addresses: walsaedi@our.ecu.edu.au (W. Al-Saedi), s.lachowicz@ecu.

edu.au (S.W. Lachowicz), d.habibi@ecu.edu.au (D. Habibi), o.bass@ecu.edu.au(O. Bass).

Waleed Al-Saedi ⇑, Stefan W. Lachowicz, Daryoush Habibi, Octavian BassSchool of Engineering, Edith Cowan University, 270 Joondalup Drive, Joondalup, Western Australia 6027, Australia

a r t i c l e i n f o

Article history:Received 19 February 2013Received in revised form 31 May 2013Accepted 1 June 2013

Keywords:MicrogridAutonomous operationPower controllerCurrent controllerParticle Swarm Optimization (PSO)

a b s t r a c t

This paper presents an optimal power control strategy, for an inverter based Distributed Generation (DG)unit, in an autonomous microgrid operation based on real-time self-tuning method. This research seeksto improve the quality of power supplied by DG units connected to the grid. Voltage and frequency reg-ulation, dynamic response, steady-state response, and harmonic distortion are the main performanceparameters considered, particularly when the microgrid is islanded or under the load change condition.The controller scheme comprises an inner current control loop and an outer power control loop based ona synchronous reference frame and conventional PI regulators. The power controller is designed for volt-age-frequency (Vf) power control mode. Particle Swarm Optimization (PSO) is an intelligent searchingalgorithm that is applied for real-time self-tuning of the power control parameters. In this paper, the pro-posed strategy is that when the microgrid is islanded or under load change condition, the DG unit adoptsthe Vf control mode in order to regulate the system voltage and frequency. The simulation results showthat the proposed controller provided an excellent response to satisfy the power quality requirementsand proved the validity of the proposed strategy.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

A microgrid is a cluster of DG units that interface with an elec-trical distribution network using power electronic devices such asthe Voltage Sourced Inverter (VSI). This scenario represents a com-plementary infrastructure to the utility grid due to the rapidincrease of the load demand. The microgrid can operate in twomodes: grid-connected and islanding. Moreover, the high marketpenetration of the micro-sources such as wind, photovoltaic,hydro, and fuel cell emerge as alternatives which provide greenenergy and a flexible extension to the utility grid [1]. However,these sources are usually interconnected by widely usedPulse-Width-Modulation (PWM)-VSI systems which have nonlin-ear voltage-current characteristics of semiconductor components,and produce high switching frequency, both of which affect thequality of the power supply for the end user [2].

Fig. 1 shows an example of the microgrid. In such systems, arobust control strategy is required to achieve high performanceoperation and to meet power quality requirements, allowing theDG units to be connected to the grid. Therefore, the current controlstrategy of the PWM-VSI system is one of the most important

aspects of the modern electronic power converters. There aretwo main categories for current controllers: nonlinear, based onclosed loop current type PWM; and linear, based on open loop volt-age type PWM, and both are applied using the inner current feed-back loop [3].

In the nonlinear controller, hysteresis current control (HCC) iscommonly used for a 3-phase grid-connected VSI systems. TheHCC compensates the current error and generates PWM signalswith acceptable dynamic response. While the current is controlledindependently with a control delay, zero voltage vectors cannot begenerated, resulting in a large current ripple with high total har-monic distortion (THD) [4]. The linear current controller, basedon space vector PWM (SVPWM), is an adequate controller, whichcompensates the current error either by the proportional-integral(PI) regulator or predictive control algorithm while the compensa-tion and PWM generation can be done separately. This controlleryields an excellent steady-state response, low current ripple, anda high-quality sinusoidal waveform. In addition, the SVPWM canhelp to improve the controller behavior because it has positivefeatures such as constant switching frequency, optimum switchingpattern, and excellent DC-link voltage utilization [5].

Furthermore, an outer power control loop is usually integratedwith the current control loop to release the reference voltage signalsto the PWM module. In a synthetic control scheme, the power con-trol strategy plays a key role to satisfy the power quality require-ments. The DG unit can use one of the two typical power control

Grid

Micro -

source

Line 1

Load 1

DG 1

VSI

Micro -

source

Line 2

Load 2

DG 2

VSI

Load 3

STS

Fig. 1. An example of microgrid system.

W. Al-Saedi et al. / Electrical Power and Energy Systems 53 (2013) 742–751 743

strategies: active-reactive power control strategy in grid-connectedmode, and voltage-frequency control strategy in islanding mode. Inthis case, the DG unit is expected to supply maximum power andmaintain system stability [6].

Recently, researchers have investigated power controllers basedon an inner current control loop for better microgrid configuration.In [7], a controller is described which seeks to ensure the system’sdynamic stability and provide all information needed for analysisand design. In [8,9], the power control strategy is applied for amicrogrid system which can analyze and compare the two powercontrol strategies. The dynamic performance and load sharing areconsidered and the controller is described in detail, but the processlacks automatic control parameter tuning to optimize the opera-tion during abrupt changes.

To solve optimization problems, many techniques have emergedto address the nonlinear problems. These techniques are classifiedbased on the type of search space and the objective function as fol-lows. First, the simple method is the Linear Programming (LP) thatuses only the linear objective function and linear equality orinequality constrains [10]. Second, the Nonlinear Programming(NLP) is introduced for nonlinearity objective function and con-strains, but the researchers have noticed that it is a difficult field,and also valuable results are only achieved when all constrainsare linear, so it is referred as Linearly Constrained Optimization[11]. Third, Stochastic Programming is another technique that pro-vides the probability functions of various variables in order to solvethe problems that involve the uncertainty. It also has an alternativename which is called Dynamic Programming (DP) [12]. Although thismethod is widely used for optimization problems, the numericalsolution requires more computational process which increasesthe probability of suboptimal results because of the dimensionalityproblem.

Genetic Algorithm (GA) and Particle Swarm Optimization (PSO)are computational-intelligence based techniques that proposed tosolve the above problems. GA is a search method that emulatesthe evolutionary biology to find the approximate optimal solutions[13]. Although a good solution can be located rapidly, it also hassome negative aspects, namely: (1) the convergence moves towardthe local solution rather than the global solution because only goodgenetic information can be passed , (2) it is difficult to run with setsof the dynamic data, and (3) in a particular optimization problemsand computation time, simple optimization technique may givesbetter results than GA.

The PSO is also an evolutionary computation technique thatsimulates the social behavior of the swarm of bird or school of fish.The main aspect of this technique is that the size and nonlinearityof the problems do not largely affect the solution [14]. As reportedin [15,16], the best results are achieved by the PSO algorithm

compared to other optimization techniques. This is because it out-performs other methods, especially GA in some positive aspectsnamely:

1. The PSO is easier to implement with less parameters for tuning.2. The memory capability of the PSO is more effective than the GA

because of each particle is able to remember its own previousbest position and its neighbors’ best too.

3. The PSO is more efficient to maintain the diversity of theswarm. This is because the swarm uses the most successfulinformation to move toward the best which is similar to thecommunity social behavior. While, the GA neglects the worsesolution and passes only the good ones.

Moreover, using PSO to solve the optimization problems is onlyemerging technology for power systems. In [17–19], PSO algorithmwas used to address the size and the location of the DG unit in or-der to minimize the installation costs and the line losses. In [20],the design of the microgrid was proposed using PSO algorithm tooptimize control parameters, filter components, and power sharingcoefficients. The results obtained from the optimization techniquewere used to run the model and enhance its stability, while systemfrequency was not considered, and neither was a self-tuning meth-od utilized for real-time operation. In [21,22], PSO algorithm wasemployed for both microgrid operation modes: grid-connectedand islanding, and the control parameters were optimized regard-less of the controllers type. This may increase the complexity of theoptimization technique and the probability of the error when themicrogrid contains several DG units.

In this paper, a power controller based on real-time optimiza-tion is proposed for an inverter based DG unit in an autonomousmicrogrid. This controller is interfaced with the current controlloop based on a synchronous reference frame. Conventional PI reg-ulators are used in this scheme, and feed-forward compensation isapplied to the inner control loop to achieve high dynamic response.In this work, whether the microgrid switches to the islanding modeor is under load change condition, the Vf control mode based PSOalgorithm is adopted by the DG unit in order to regulate the systemvoltage and frequency. The PSO algorithm is utilized for real-timeself-tuning parameters, with Integral Time Absolute Error (ITAE) asan objective function that calculates Simpson’s 1/3 rule. The aimof this work is to improve the quality of the power supply byachieving acceptable limits of the voltage and frequency.

The remaining part of this paper is divided into five sections.Section 2 presents a mathematical foundation of a three-phasegrid-connected VSI model. In Section 3, the power control strategyis demonstrated for power quality requirements in a microgrid.Section 4 describes the proposed control strategy in detail. In

Fig. 2. 3-Phase grid-connected VSI model.

Fig. 3. VSI based Vf power controller.

744 W. Al-Saedi et al. / Electrical Power and Energy Systems 53 (2013) 742–751

Section 5, the simulation results are analyzed to verify the aims ofthis work. Finally, the conclusions are outlined in Section 6.

2. Modeling of the three-phase grid-connected VSI system

A typical model of the three-phase grid-connected VSI with anLC filter is depicted in Fig. 2, where Rs and Ls represent the equiva-lent lumped resistance and inductance of the filter, the couplingtransformer if applicable, and the grid as detected by the inverter.C is the filter capacitance and Vs is the grid voltage.

In the abc reference frame, the state space equations of the sys-tem equivalent circuit are given by [21]:

ddt

ia

ib

ic

264

375 ¼ Rs

Ls

ia

ib

ic

264

375þ 1

Ls

Vsa

Vsb

Vsc

264

375�

Va

Vb

Vc

264

375

0B@

1CA ð1Þ

Using Park’s transformation, Eq. (1) can be expressed in the dq ref-erence frame as:

ddt

id

iq

� �¼� Rs

Lsx

�x � RsLs

" #id

iq

� �þ 1

Ls

Vsd

Vsq

� ��

Vd

Vq

� �� �ð2Þ

where x is the coordinate angular frequency, and the Park’s trans-formation can be defined as:

idq0 ¼ Tiabc ð3Þ

where;

idq0 ¼id

iq

i0

264

375; iabc ¼

ia

ib

ic

264

375 ð4Þ

T ¼ffiffiffi23

r cosh cos h� 2p3

� �cos hþ 2p

3

� ��sinh �sin h� 2p

3

� ��sin hþ 2p

3

� �1ffiffi2p 1ffiffi

2p 1ffiffi

2p

264

375 ð5Þ

h = xst + ho is the synchronous rotating angle, ho represents the ini-tial value.

3. Vf control strategy

In contrast to large generators, DG units can be classified intothree energy source types, namely: variable speed (variable fre-quency) source such as wind energy, high speed (high frequency)

source such as micro-turbine generators, and direct energy conver-sion source such as photovoltaic and fuel cells. For this reason, it isnecessary to use a VSI to interface the DG unit to the grid and pro-vide flexible operation [23]. As shown in Fig. 2, the power circuit ofthe VSI based DG unit is associated with the control structure, sothe controlled operation of the DG unit relies on the inverter con-trol mode. For instance, in the grid-connected mode, the DG unitoperates as a PQ generator and the inverter should follow the ac-tive-reactive power (PQ) control mode, while voltage and fre-quency regulation are not required because the grid voltage isfixed. However, in the islanded mode, the DG units are expectedto meet the load demand with respect to the quality of power sup-ply. In this case, the voltage and frequency are not fixed, and theinverter should follow the Vf control mode taking into accountthe inverter power rating for power sharing issues [24]. Therefore,an appropriate power control mode can result in the high perfor-mance operation of the DG unit.

For reliable microgrid’s operation, it is necessary to ensure theseamless transition between the microgrid operation modes, andalso keep a stable operation during the islanding mode in termsof regulating the microgrid voltage and frequency with respect tothe load demand. In this case, the DG units must follow the loaddemand and maintain the voltage and frequency within thresholdlimits, so the Vf control mode has to be adopted by one or more DGunits in order to satisfy the above requirements [9]. The block dia-gram of this application is shown in Fig. 3. Since the reference volt-age and frequency values can be defined locally or by the MicrogridControl Centre (MGCC), the frequency can be measured by thePhase-Locked-Loop (PLL) application, and the Vrms is given by [7]:

Vrms ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2

d þ V2q

qð6Þ

4. Proposed control strategy

This section presents the proposed power controller for a three-phase grid-connected VSI system. As shown in Fig. 4, the controller

Fig. 4. The proposed power controller scheme.

W. Al-Saedi et al. / Electrical Power and Energy Systems 53 (2013) 742–751 745

scheme consists of three main blocks, namely: power controller,linear current controller, and PSO algorithm for real-time self-tun-ing of the power control parameters. The following subsections de-scribe the functionality of each block in more detail.

4.1. Power control strategy

The purpose of using this strategy is to improve the quality ofpower supply in terms of the control objective mode. As shownin Fig. 4, the left side depicts the block diagram of the proposedpower controller based on two PI regulators. This controller repre-sents the outer control loop which is employed to generate the ref-erence current vectors i�d and i�q. Consequently, a relatively slowchange of the reference current trajectory would ensure high qual-ity of the inverter output power, indicating that the control objec-tive has been achieved. In this paper, the Vf control strategy basedon the PSO algorithm is proposed for the VSI based DG unit; thesystem voltage and frequency are the main control objectiveswhich must be achieved during the islanding operation mode. Thisstrategy is designed to respond to sudden changes such as startingthe islanding operation mode, or at load change condition. In thiscase, the controller regulates the voltage and frequency based ontheir reference values (Vref and fref), and the PSO is an intelligentprocess which provides optimum control parameters in order torelease qualified reference current vectors. Accordingly, in a dq ref-erence frame and based on two PI regulators, the reference currentvectors can be expressed as:

i�d ¼ ðVref � VÞðKpv þ Kiv=sÞ ð7Þi�q ¼ ðfref � f ÞðKpf þ Kif =sÞ ð8Þ

4.2. Current control strategy

The objective of this controller is to ensure accurate trackingand short transients of the inverter output current. As shown inFig. 4, the right side depicts the block diagram of the current con-trol loop the design of which is based on a synchronous referenceframe. This controller is usually used in a way that the voltage isapplied to the inductive R � L impedance, so that an impulse cur-rent in the inductor has a minimum error. The PLL block is requiredto detect the voltage phase angle in order to implement Park’stransformation in the control scheme. Two PI regulators are usedto eliminate current error, and both the inverter current loop andthe grid voltage feed-forward loop are employed to improve thesteady state and dynamic performance. Consequently, the outputsignals of the controller represent the reference voltage signals inthe dq frame. It is followed by the inverse Park’s transformationand Clarke’s transformation, so that the controller generates the

reference voltage signals in ab stationary frame, synthesizing sixpulses for the SVPWM in order to fire the Insulated-gate BipolarTransistor (IGBT) inverter. Moreover, use of the SVPWM techniqueensures that the controller provides the desired output voltagevectors with less harmonic distortion.

In the synchronous dq frame, based on Eq. (2), the referencevoltage signals can be expressed as:

V�dV�q

" #¼�Kp �xLs

xLs �Kp

� �id

iq

� �þ

Kp 00 Kp

� �i�di�q

" #þ

Ki 00 Ki

� �Xd

Xq

� �þ

Vsd

Vsq

� �

ð9Þ

where the superscript ‘‘⁄’’ denotes the reference values,

dXd

dt¼ i�d � id; and

dXq

dt¼ i�q � iq:

Using Clarke’s transformation, Eq. (9) can be transformed into abstationary frame, as shown in the following equation:

Va

Vb

V0

264

375 ¼ 2

3

Va

Vb

Vc

264

375

1 �12

�12

0ffiffi3p

2�ffiffi3p

212

12

12

264

375 ð10Þ

Furthermore, the inductor current is obtained using a Low Pass Fil-ter (LPF) [7]. In this work, the LPF is presented as a first-order trans-fer function which is given by:

f1

1þ sTi¼ fl ð11Þ

where f is the filter input value, fl is the filtered value, and Ti is thetime constant.

4.3. Particle Swarm Optimization (PSO) algorithm

The Particle Swarm Optimization (PSO) algorithm was proposedby Kennedy and Eberhart in 1995 [25]. It can be defined as an Evo-lutionary Computation (EC) technique that simulates the socialbehavior of the swarm in nature, such as schools of fish or flocksof birds where they find food together in a specific area. In otherwords, PSO is an iterative algorithm that searches the space todetermine the optimal solution for an objective function (fitnessfunction) [26]. The PSO algorithm evaluates itself based on themovement of each particle as well as the swarm collaboration.Each particle starts to move randomly based on its own bestknowledge and the swarm’s experience. It is also attracted towardthe location of the current global best position Xgbest and its ownbest position Xpbest [27]. Fig. 5 shows the flowchart of the imple-mented PSO algorithm. The basic rules of this algorithm can be ex-plained in three main stages:

Fig. 5. Flowchart of the applied PSO algorithm.

746 W. Al-Saedi et al. / Electrical Power and Energy Systems 53 (2013) 742–751

1. Evaluating the fitness value of each particle.2. Updating local and global best fitness and positions.3. Updating the velocity and the position of each particle.

The search process can be expressed by simple equations, usingthe position vector Xi = [xi1, xi2, . . . , xin] and the velocity vectorVi = [vi1, vi2, . . . , vin] in the specific dimensional search space. Inaddition, the optimality of the solution in the PSO algorithm de-pends on each particle position and velocity update using the fol-lowing equations [28]:

Vkþ1i ¼ w � Vk

i þ c1 � r1 Xkpbest � Xk

i

h iþ c2 � r2 Xk

gbest � Xki

h ið12Þ

Xkþ1i ¼ Xk

i þ Vkþ1i ð13Þ

where i is the index of the particle; Vki ;X

ki are the velocity and posi-

tion of particle i at iteration k, respectively; w is the inertia constantand it is often in the range [01]; c1 and c2 are coefficients which areusually between [02]; r1 and r2 are random values which are gener-ated for each velocity update; Xgbest and Xpbest are the global best po-sition that is achieved so far based on the swarm’s experience, andthe local best position of each particle that is achieved so far, basedon its own best position, respectively. Moreover, each term in Eq.(12) can be defined according to its task as follows:

� The first term w � Vki is called the inertia component; it is respon-

sible to keep the particles search in the same direction, the lowvalue of the inertia constant w accelerates the swarm’s conver-gence toward the optimum position, while the high value dis-covers the entire search space.� The second term c1 � r1 Xk

pbest � Xki

h iis called the cognitive compo-

nent; it represents the particle’s memory. The particle tends toreturn to the field of search space in which it has high individualfitness and the cognitive coefficient c1 affects the step size of theparticle to move toward its local best position Xpbest.

� The third term c2 � r2 Xkgbest � Xk

i

h iis called the social component;

it is responsible to move the particle toward the best regionfound by the swarm so far. The social coefficient c2 affects thestep size of the particle to find the global best position Xgbest.

According to Eq. (13), the position of each particle updates itselfby using the new velocity and its previous position. In this case, anew search process starts over the updated search space in order tofind the global optimum solution. This process repeats itself until itmeets the termination criterion such as the maximum number ofiterations or the required fitness value. Consequently, regeneratingthe swarm through a stochastic velocity term and the ability ofunderstanding, the search process produce high performance oper-ation to find the global optimum solution. Therefore, the PSO algo-rithm has more advantages than other iterative searching methodssuch as the Genetic Algorithm (GA), which passes only good genet-ic information to the descendants.

A confined search space is the only significant limitation of thePSO algorithm. A fast solution can be achieved by selecting limitedsearch space, but the optimality of the solution will be influenced ifthe global optimum value is located outside the boundaries. Ex-tended boundaries however allow finding global optimum results,but need more time to determine the global optimal value in thesearch space. Therefore, more information about the limits of theparameters will help to determine the search boundaries.

4.4. Fitness function

The fitness function is a particular criterion that is used to eval-uate an automatic iterative search such as PSO or GA. When con-sidering the control objectives, the minimization of error-integrating function is the most relevant function of the four errorcriterion techniques, namely: (1) Integral Absolute Error (IAE), (2)Integral Square Error (ISE), (3) Integral Time Squared Error (ITSE),and (4) Integral Time Absolute Error (ITAE) which; offered the bestresults in the previous study [29]. In this work, the controller’sobjective function is based on ITAE, which is calculated using Simp-son’s 1/3 rule [30]. For instance, the ISE and ITSE are very aggressivecriterions because of squaring the error produces unrealistic eval-uation for punishment. The IAE is also inadequate compared withthe ITAE which represents more realistic error index because the

3.0053.01

3.0153.02

0 5 10 15 20 25 30 35 408.5

9

9.5

10

10.5

11 x 10−5

Iterations

ITA

E−vo

ltage

con

trol

obj

ectiv

e

Load change

Islanding mode

Fig. 7. Fitness values of the voltage control objective.

W. Al-Saedi et al. / Electrical Power and Energy Systems 53 (2013) 742–751 747

error multiplies by time. An examples of using the ITAE index canbe found in [31–33].

The mathematical expression of the ITAE performance index isdefined by the following equation:

ITAE ¼Z 1

0tjeðtÞjdt ð14Þ

where t is the time and e(t) is the difference between the referenceset point and the controlled signal.

4.5. Termination criteria

In general, the termination criteria of a PSO algorithm can beeither when the algorithm completes the maximum number ofiterations, or else when it achieves an acceptable fitness value. Inthis work, the minimization of the objective function is consideredwith the maximum number of iterations to find the optimumpower control parameters. Table 1 shows the parameters of the ap-plied PSO algorithm, while the number of particles and iterationsare set to 50, and the search spaces of the parameters of the voltagecontrol loop Kpv and Kiv are limited to [0�20] and [05e�3], respec-tively. Also, the search boundaries of the parameters of the fre-quency control loop Kpf and Kif are set to [030] and [05e�3],respectively. In this model, the PSO algorithm and its objectivefunction are individually constructed for each control objectivefor one DG unit. This allows dealing with more than one DG unitunder the supervision by the MGCC. In this work, the performanceof the implemented PSO search process can be described asfollows:

1. The ITAE performance index is separately implemented oneach control objective (voltage and frequency). As shownin Figs. 6 and 7, the results are related to the differencebetween the set-value and the computed area of the con-trolled signals over the limited time; which are calculatedusing Simpson’s 1/3 rule. It can be seen that the errordecreases rapidly with the number of iterations, and thesolution steady toward the end.

Table 1The applied PSO parameters.

PSO parameters description Kpf Kif Kpv Kiv

Acceptable violation (p.u.) ±0.01 ±0.01 ±0.1 ±0.1Initial velocity (V) 0 0 0 0Initial fitness value (best so far) 800 800 800 800Inertia constant (w) 0.05 0.5 0.05 0.5Cognitive coefficients (c1 and c2) 0.09 0.1 0.09 0.1

0 5 10 15 20 25 30 35 409.569.579.589.59

9.69.619.629.639.649.65 x 10−5

Iterations

ITA

E−fr

eque

ncy

cont

rol o

bjec

tive

Islanding mode

Load change

Fig. 6. Fitness values of the frequency control objective.

2. The PSO algorithm is executed in three phases. First, thealgorithm sequentially injects 50 particles, thus the systemreacts to each one as a control parameter value, and simul-taneously the fitness value is calculated for each controlobjective. Second, after the particles have been injected,the PSO algorithm runs to evaluate and compare the fitnessvalue of each particle with the current values to select thelocal best position Xpbest. Third, the algorithm updates theparticle’s position according to Eqs. (12) and (13), in orderto repeat the process until the global optimum parameterXgbest is found. In this work, for both cases starting the islan-ding mode and at load change, Figs. 8–15 depict the move-ment behavior of the particles. The results show that the

0.65 0.7 0.75 0.8 0.85 0.90

0.5

1

1.5

2

2.5

3

3.5

4 x 10−3

Time (s)

Kif

Fig. 9. Search process of Kif when the microgrid is islanded.

0.65 0.7 0.75 0.8 0.85 0.92.9752.98

2.9852.99

2.9953

Time (s)

Kpf

Fig. 8. Search process of Kpf when the microgrid is islanded.

1.8 1.85 1.9 1.95 2 2.05 2.1 2.150.5

1

1.5

2

2.5

3

3.5

4 x 10−3

Time (s)

Kiv

Fig. 15. Search process of Kiv at the load change condition.

Table 2Power control parameters.

Control parameters Islanding operation mode Load change condition

Kpf 3.010859051739 2.561841587350Kif 3.779371678977e�04 3.778269709488e�04Kpv �0.993692883859 �1.012858708331Kiv 0.003377691047 0.0031963506784

1.8 1.85 1.9 1.95 2 2.05 2.1 2.15

−1.03

−1.025

−1.02

−1.015

−1.01

−1.005

−1

−0.995

Time (s)

Kpv

Fig. 14. Search process of Kpv at the load change condition.

1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.93.77723.77743.77763.77783.778

3.77823.77843.77863.77883.779 x 10−4

Time (s)

Kif

Fig. 13. Search process of Kif at the load change condition.

0.604 0.605 0.606 0.607 0.608 0.609 0.61 0.611 0.612 0.6130

0.5

1

1.5

2

2.5

3

3.5

4 x 10−3

Time (s)

Kiv

Fig. 11. Search process of Kiv when the microgrid is islanded.

1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.92.558

2.56

2.562

2.564

2.566

2.568

Time (s)

Kpf

Fig. 12. Search process of Kpf at the load change condition.

0.604 0.605 0.606 0.607 0.608 0.609 0.61 0.611 0.612 0.613−1.002

−1

−0.998

−0.996

−0.994

−0.992

−0.99

−0.988

Time (s)

Kpv

Fig. 10. Search process of Kpv when the microgrid is islanded.

748 W. Al-Saedi et al. / Electrical Power and Energy Systems 53 (2013) 742–751

particles finish their movement above the best positions,and the power control parameters stay at the optimum glo-bal values which are indicated in Table 2.

In conclusion, it can be noticed that the PSO algorithm providesa logical process and high performance operation. For this reason,it is necessary to summarize the implementation advantages asfollows. First, few particles are required to tune the parametersthat provide high speed optimization process and robust conver-gence. Second, the so far best parameters can be used as initial val-ues. Third, the algorithm can be individually constructed for eachcontrol objective, so precise results are greatly expected. Conse-quently, it can be proven that the PSO algorithm is implementedeasily.

5. Simulation results

The model of a three-phase grid-connected VSI system and theproposed controller are simulated using MATLAB/Simulinkenvironment, and are depicted in Fig. 2. The PSO algorithm isimplemented through a MATLAB/M-file program, and the model

1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2−6

−4

−2

0

2

4

6

Time (s)

Cur

rent

(p.u

.)

Fig. 20. The dynamic response when the load is changed at 1.8 s.

0.5 0.55 0.6 0.65 0.7 0.75−6

−4

−2

0

2

4

6

Time (s)

Volta

ge a

nd c

urre

nt (p

.u.) Voltage

Current

Fig. 21. Transient and steady-state responses in islanding mode.

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8−6

−4

−2

0

2

4

6

Time (s)

Cur

rent

(p.u

.)

Fig. 19. The dynamic response when the microgrid is islanded at 0.6 s.

0.6 1 1.5 2 2.50.98

0.984

0.988

0.992

0.996

1

1.004

1.008

Time (s)

Freq

uenc

y (p

.u.)

Fig. 18. The microgrid frequency regulated by Vf controller.

0.6 1 1.5 2 2.5 30.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

Time (s)

Volta

ge (p

.u.)

Fig. 17. The microgrid voltage regulated by Vf controller.

0.6 1 1.5 2 2.5 34

4.2

4.4

4.6

4.8

5

Time (s)

Act

ive

load

pow

er (p

.u.)

Fig. 16. The active load power.

W. Al-Saedi et al. / Electrical Power and Energy Systems 53 (2013) 742–751 749

parameters are defined as follows: Ls = 5 mH, Rs = 1.4 X, f = 50 Hz,filter capacitance C = 1500 lF, and the input capacitor of the dcside is set to 5000 lF. One DG unit with rating 50 kW is used. Typ-ically, the current control parameters are set to Kp = 12.656 andKi = 0.00215. For the SVPWM-based current controller, switchingand sampling frequency are fixed at 10 kHz and 500 kHz, respec-tively. All results are in a per-unit (p.u.) system, and the followingobjectives are investigated:

5.1. Voltage and frequency regulation

To evaluate the proposed controller scheme, the simulationstarts in the grid-connected mode, so the microgrid voltage andfrequency are mainly established by the grid which is responsibleto maintain their profiles.

At 0.6 s, the microgrid switches to the islanding operationmode. As shown in Fig. 16, the load power is considered to be ac-tive power for simplicity and set to 4.65 (p.u.). The DG unit adoptsthe Vf power control mode based on PSO algorithm in order to mit-igate the voltage drop and avoid a severe deviation of the fre-quency caused by a sudden move to the islanding mode or loadchange. In this mode, and as presented in Eqs. (7) and (8), the Vref

and fref of the proposed controller are set to 1 (p.u.). As a result,since the PSO algorithm and its results are discussed in Section 4,Figs. 17 and 18 depict the results of the controlled voltage and fre-quency. These figures are resulted from the reaction between theproposed power controller and the applied PSO technique. Forexample, at 0.6 s, the system is islanded and Fig. 18 shown thatthe frequency is going to fall around 0.7 s. At this time, the PSOalgorithm started searching on new power control parameters

1.7 1.75 1.8 1.85 1.9 1.95−6

−4

−2

0

2

4

6

Time (s)

Volta

ge a

nd c

urre

nt (p

.u.)

CurrentVoltage

Fig. 22. Transient and steady-state responses during load change.

750 W. Al-Saedi et al. / Electrical Power and Energy Systems 53 (2013) 742–751

(see Figs. 8 and 9), because the frequency is decreased and reachedthe threshold limit (±0.01 p.u.). This process occurs even throughthe transient period. Thus, the frequency restored to be withinthe acceptable limits, and Fig. 18 is a consequence of an automatic

0.66 0.7 0.75

−5

0

5Selected

T

−50 0 50 100 10

5

10

15

Frequ

Fundamental (50

Mag

(% o

f Fun

dam

enta

l)

Fig. 23. Spectrum of the VSI line curren

0 50 100 1500

1

2

3

4

Freque

Fundamental (50

Mag

(% o

f Fun

dam

enta

l)

1.86 1.9 1.95

−5

0

5Selected

T

Fig. 24. Spectrum of the VSI line cu

response of the proposed power controller. Consequently, the pro-posed controller reacts to starting the islanding mode and providesvoltage and frequency equal to 0.96 p.u. and 0.9914 p.u.,respectively.

At 1.8 s, the active load power is decreased to 4.55 p.u., so thePSO algorithm searches again to find the optimal parameters ofthe Vf power controller based on minimum error of the fitnessfunction. As shown in Figs. 17 and 18, the proposed controller stilloffers an excellent behavior and maintains the system voltage andfrequency equal to 1.067 p.u. and 1.0018 p.u., respectively.

Consequently, according to the acceptable limits which are out-lined in Table 1, it can be noticed that the proposed strategy re-stores the microgrid voltage and frequency close to theirreference values within ±0.1 and ±0.01 (0.5 Hz), respectively.

5.2. Dynamic and steady state response

In order to verify the dynamic response of the proposed control-ler, the inverter output current is stepped two times. First, whenthe microgrid is islanded at 0.6 s, then once the load is changed

0.8 0.850.85 0.9

signal: 12 cycles

ime (s)

50 200 250 300 350ency (Hz)

Hz) = 2.967, THD= 1.79%

t of the islanding operation mode.

200 250 300 350ncy (Hz)

Hz) = 2.818 , THD= 0.44%

2 2.05 2.1

signal: 12 cycles

ime (s)

rrent during the load change.

W. Al-Saedi et al. / Electrical Power and Energy Systems 53 (2013) 742–751 751

at 1.8 s. Figs. 19 and 20 show the simulation results of the inverteroutput line current. For both cases, it can be seen that the transienttime is short and the current reaches steady state within twocycles.

For the steady-state response, Figs. 21 and 22 depict the micro-grid phase voltage and the inverter output line current of the islan-ding operation mode and load change condition, respectively. Inthis work, since the inverter output filter is utilized to bypassswitching harmonics, and a LPF with low enough cut-off frequencyto ensure sufficient attenuation for the harmonic content of the dqcurrent vectors is used, the results show that the waveforms arehigh-quality sinusoids with a unity power factor. Also, Figs. 23and 24 show the spectrum of the line current when the microgridis islanded and during the load change, respectively. The THD val-ues are 1.79% and 0.44% which are well below the 5% THD allowedin IEEE Std 1547-2003 [34].

6. Conclusion

In this paper, an optimal power control strategy has been pro-posed for an inverter based DG unit in order to improve the qualityof the power supply in an autonomous microgrid operation. Theproposed controller scheme consists of an inner current controlloop and an outer Vf power control loop. The PSO algorithm hasbeen incorporated into the Vf control mode to implement a real-time self-tuning method in order to regulate the microgrid voltageand frequency, especially when the microgrid transits to the islan-ding operation mode or during load change. In addition, the con-troller is designed to investigate the dynamic response, steady-state response, and driving the harmonic currents through the in-verter. The simulation results show that the proposed controlleroffers an excellent response for regulating the microgrid voltageand frequency, and achieves short transient time with a satisfac-tory harmonic distortion level. Consequently, this controller canbe used by more than DG unit in a microgrid scenario, consideringthe power sharing issue.

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