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Electric Power Systems Research 125 (2015) 164–173

Contents lists available at ScienceDirect

Electric Power Systems Research

j o ur nal ho me page: www.elsev ier .com/ lo cate /epsr

odeling and control of quasi Z-source inverters for parallel operationf battery energy storage systems: Application to microgrids

asem Khajesalehi, Mohsen Hamzeh, Keyhan Sheshyekani ∗, Ebrahim Afjeiepartment of Electrical and Computer Engineering, Shahid Beheshti University, Tehran, Iran

r t i c l e i n f o

rticle history:eceived 29 November 2014eceived in revised form 4 April 2015ccepted 7 April 2015

eywords:attery energy storage systemurrent sharingicrogridsuasi Z-source inverternbalanced loads

a b s t r a c t

In this paper, a quasi Z-source Inverter (qZSI) is presented for the application in parallel operation ofBattery Energy Storage Systems (BESSs) in microgrids. The qZSI is a single stage converter with twocontrollable DC ports. In the proposed control method to parallel battery stacks, in islanded mode ofmicrogrid operation, the BESS supplies the load power, while the shoot-through duty cycle of inverterlegs is utilized to fulfill the current sharing between the battery systems with different voltage and powerratings. In this mode, the inverter modulation index is used to control the microgrid voltage while otherdistributed energy resources (DERs) operate in power control mode. Furthermore, thanks to the proposedcurrent sharing method, the oscillatory power due to the unbalanced loads is also appropriately sharedbetween the battery systems. In the grid-connected mode of operation in which the microgrid voltage isdictated by the main grid, the current of each battery system can be independently regulated by adjustingthe inverter modulation index and the shoot-through duty cycle. The performance of the proposed control

strategy in both charging and discharging modes of the BESS operating in the grid-connected mode isevaluated. Moreover, in the islanded mode, the suitability of the proposed method for current sharingbetween the battery systems is investigated. Simulations are conducted in MATLAB/Simulink for thecase of a typical microgrid involving two battery systems characterized by different current and voltageratings.

© 2015 Elsevier B.V. All rights reserved.

. Introduction

With the increasing penetration of renewable energy resources,he Energy Storage Systems (ESSs) are becoming an integral part ofhe future electrical systems bringing many technical and financialenefits to these systems. Usually, to integrate ESSs into con-entional electricity grids, one needs to design special topologiesnd/or controllers for almost each particular case. The ESSs havehe capability to operate either in charging mode to store elec-rical energy or in discharging mode to supply the excessive loademands. There are many applications for ESSs including micro-rids [1–3], electrical vehicles (EVs) [4], uninterruptible powerupplies (UPSs) [5], and power system stabilizers [6]. In micro-

rid applications, ESSs aim at improving the efficiency and stability7], integrating renewable energy resources (RERs) [8], and poweruality improvement [9], etc.

∗ Corresponding author. Tel.: +0098 912 214 21 90.E-mail address: k sheshyekani@sbu.ac.ir (K. Sheshyekani).

ttp://dx.doi.org/10.1016/j.epsr.2015.04.004378-7796/© 2015 Elsevier B.V. All rights reserved.

Power Electronic Interfaces (PEIs) associated to Battery EnergyStorage Systems (BESSs) are responsible for exchanging powerbetween battery units and loads or the AC-side source. These PEIsystems must be bidirectional converters with the capability tooperate in both charging and discharging modes. To design a BESSwith higher level of power and energy capacity, the parallel andseries arrangements of battery systems have been proposed in Ref.[10]. The parallel battery systems may have different current andvoltage ratings; therefore the PEI system must allow the batterysystems to operate under their nominal voltage and current. To thisaim, it is usually required to use more than one controllable con-verter stage which, in turn, increases the volume and the cost ofthe PEI, while reducing the efficiency of the BESS. Although for bat-tery systems working in series, the need to multi-converter stageis obviated, the reliability of the BESS is decreased. In fact, in seriesarrangement when one of the battery systems fails, the operation

of the entire system is interrupted.

The quasi Z-source inverter (qZSI) proposed in [11] is adouble-port converter in its DC side taking the advantage of theshoot-through duty cycle of the inverter legs to boost the DC source

Systems Research 125 (2015) 164–173 165

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J. Khajesalehi et al. / Electric Power

oltage to a desirable value. Resorting to this feature of the qZSI, in12–14] a dispatchable photovoltaic (PV) system equipped with aESS has been presented. Therefore, the qZSI is a suitable choice

or parallel operation of two battery stacks, while each stack mightonsist of different batteries working in series. In this arrangement,he operation of the entire BESS is not disrupted by the failure ofn individual battery thus increases the system overall reliability.

As known, the batteries connected to the qZSI might not haveecessarily the same voltage and current ratings. Therefore, theZSI must be controlled such that the batteries operate under theiroltage and current ratings. In non-controlled qZSI, the load currents shared inversely proportional to the equivalent impedance of thearallel battery banks. Therefore, considering a certain value for the

nverter shoot-through duty cycle, the battery system with lowerquivalent impedance supplies a greater portion of the load currenthat can overload this battery system.

In this paper, a control strategy is proposed so that the batteryystems paralleled by a qZSI, share the load current in proportiono their power ratings in the islanded microgrid. Moreover, the pro-osed control system is able to share the oscillatory power due tohe unbalanced loads. Furthermore, in the grid-connected mode,he BESS can operate both in charging and discharging modes. Inhis condition, for charging the battery currents to a certain statef charge (SOC), their currents must be separately regulated. In theroposed control strategy, the output current of one of the batter-

es can be regulated by adjusting the modulation index while theutput current of the other battery is regulated using the shoot-hrough duty cycle. The design of the current controller for theattery systems is based on the average state space model of theZSI impedance network [15,16].

This paper is organized as follows: the proposed system config-ration and its operation are investigated in Section 2. The controltrategy for both islanded and grid-connected modes of operation isroposed in Section 3. In Section 4, the performance of the proposedEI system and its current sharing control strategy is evaluated byimulations conducted in MATLAB/Simulink.

. System configuration and modeling

Two battery systems are connected to the microgrid through aZSI as the PEI system. The host microgrid in general could involvether DERs such as dispatchable and non-dispatchable sourcesnd different type of loads with the capability to work in bothrid-connected and islanded modes, Fig. 1, [17]. The microgrid isonnected to the main grid through static transfer switch (STS)

t the point of common coupling (PCC). In our study however, ashe BESS accounts for the control of voltage and frequency of the

icrogrid in the islanded mode, we only focus on this unit and itserformance in different microgrid operation modes. The proposed

Fig. 2. The proposed PEI system for

Fig. 1. A typical microgrid structure.

system configuration for making a BESS is shown in Fig. 2. Each ofbattery systems can consist of different number of battery cells con-nected in series. Since the qZSI has two independent controllableports in its impedance network, two battery systems with differ-ent current and voltage ratings can be connected to this converter.The PEI system can operate either in charging mode when the BESSis connected to the main grid or in the discharging mode (provid-ing the load demand) in the islanded mode. The qZSI regulates itsAC-side current by adjusting the inverter modulation index.

With reference to Fig. 3, two different states namely the shoot-through state and the nonshoot-through state are defined for theqZSI. The battery system is modeled by a resistance in series withan ideal voltage source of E1 and E2 that is the no-load battery volt-age [18], while the dynamic of the battery systems is not takeninto account. Moreover, the voltage drops caused by the batterycurrents are modeled by Rb1 and Rb2. The series inductor Lb inbattery “2” is used to eliminate the high frequency ripples on thecurrent of battery “2”. In the shoot-through state, the impedancenetwork equivalent circuit is shown in Fig. 3(a). In this state, theswitch S that models the shoot-through condition, is ON, while theswitch S′ is OFF blocking current flowing from capacitors in theimpedance network to the short-circuited inverter legs. Alterna-tively, in shoot-through duration, switch S is OFF, while switch S′

is ON and conducts as shown in Fig. 3(b). In discharging mode ofbattery “1”, during nonshoot-through state, the inverse paralleleddiode of switch S’ is forward biased and conducts the current, there-fore switch S′ is turned ON in zero voltage condition. In the chargingmode of battery “1”, the current of L1 is negative and must flowto battery “1” through switch S′ in nonshoot-through condition.

It should be noted that, for proper operation of the qZSI shown inFig. 3(a) and (b), switches S and S′ cannot be turned ON or OFF simul-taneously. When switches are OFF, the power conversion process

paralleling battery systems.

166 J. Khajesalehi et al. / Electric Power Syste

Fc

iCotOp

wdtta

t(⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

ˆ

ˆ

in

ig. 3. The qZSI equivalent circuit: (a) shoot-through, and (b) nonshoot-throughondition.

s degraded. When switches are ON, a shoot-through occurs across1 and C2, destroying the devices. Therefore, for reducing the riskf simultaneously turning ON of both switches during switchingransients, a dead time is considered over which both switches areFF. However, the dead time intervals must be short enough torevent degradation of power conversion process.

It is worth noting that, according to the qZSI impedance net-ork model shown in Fig. 3, the currents of L1 and L2 increase andecrease simultaneously during the shoot-through and nonshoot-hrough conditions, respectively. The same approach can be appliedo the case of coupled inductors. In this paper it is assumed that L1nd L2 are two inductors with separate cores without any coupling.

The dynamic model of the qZSI impedance network in shoot-hrough and nonshoot-through states can be expressed by (1) and2), respectively.

Rb1 Cpdib1(t)

dt= −ib1(t) + iL1(t)

Lbdib2(t)

dt= −Rb2ib2(t) − �b2(t) + E2

L1diL2(t)

dt= −Rb1ib1(t) − rL1iL1(t) + �b2(t) + E1

L2diL2(t)

dt= −rL2iL2(t) + �c1(t)

C1d�C1(t)

dt= −iL2(t)

d�b2(t)dt

= ib2(t) − iL1(t)

(1)

Rb1 Cpdib1(t)

dt= −ib1(t) + iL1(t)

Lbdib2(t)

dt= −Rb2ib2(t) − �b2(t) + E2

L1diL2(t)

dt= −Rb1ib1(t) − rL1iL1(t) + �C1(t) + E1

L2diL2(t)

dt= −rL2iL2(t) + �b2(t)

d�C1(t)

(2)

C1 dt= iL2(t) − iload(t)

d�b2(t)dt

= ib2(t) + iL2(t) − iload(t)

ms Research 125 (2015) 164–173

Using the average state space method and linearizing it arounda given operating point, the dynamic model of the system can beobtained as follows:

F × x = A × x + B × u (3)

where

x =[ib1(t)ib2(t)iL1(t)iL2(t)vC1(t)vb2(t)

]T, u =

[iload(t)d

]T

A =

⎡⎢⎢⎢⎢⎢⎢⎣

−1

0

−Rb10

0

0

0

−Rb2

00

0

1

1

0

−rL10

1

0

0

0

0−rL2

0

1

0

0

−10

0

0

0

−1

0−1

0

0

⎤⎥⎥⎥⎥⎥⎥⎦

(4)

B =

⎡⎢⎢⎢⎢⎢⎢⎢⎣

0

0

00

D − 1

D − 1

0

0

V11V11

I11

I11

⎤⎥⎥⎥⎥⎥⎥⎥⎦

(5)

F = diag(Rb1 × CP Lb L1 L2 C1 C2)T (6)

where D is the inverter shoot-through duty cycle in the steady-state condition. Moreover, iload (t) and d are the input variables,which represent the small signal variation of the load current andthe inverter shoot-through duty cycle around the operating point.Without losing any generality, we assume that L = L1 = L2, C = C1 = C2,and rL = rL1 = rL2.

In (3), all variables indicate the small signal variation around agiven operating point. VC1 and Vb2, are, respectively, voltage acrossthe C1 and voltage of battery “2”; Ib1, Iload and Ib2, respectively,represent the current of battery “1”, the load current, and the cur-rent of battery “2” in the steady-state, while V11 = VC1 + Vb2 andI11 = Iload − 2Ib1 + Ib2.

The state space equations in (3) are used for the calculation oftransfer functions as follows:

ib2 = [0 1 0 0 0 0] × (FsI − A)−1B × u = Gib2iload

iload + Gib2d

d (7)

ib1 = [1 0 0 0 0 0] × (FsI − A)−1B × u = Gib1iload

iload + Gib1d

d (8)

In the steady-state, the left side of (3) is zero; hence the followingequations can be obtained

VC1 = 1 − D

1 − 2DVb1 + −rL (1 − D) Iload + rLDIb2

1 − 2D(9)

Vb2 = D

1 − 2DVb1 − −rL (1 − D) Iload + rLDIb2

1 − 2D(10)

Vpn = 11 − 2D

Vb1 (11)

Ib1 = 1 − D2

1 − 2DIload − D

1 − 2DIb2 (12)

where Vb1 represents the voltages of battery “1” in the steady-state,while Vpn is the peak value of the inverter DC-link voltage (vpn)in the steady-state. Moreover, amplitude of the phase to neutralvoltage (v ) in the AC-side is obtained as follows:

vin = m

2vpn (13)

with m being the inverter modulation index.

J. Khajesalehi et al. / Electric Power Syste

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wcMstw⎧⎪⎪⎨⎪⎪⎩

wAVc

˛

w

bit

i

Fig. 4. Battery currents ratio versus shoot-through duty cycle.

Eqs. (7) and (8) indicate that, parameters of the qZSI impedanceetwork and the batteries (i.e., L, C, Rb1, Rb2, Lb, CP and rL) as wells D, are the factors which determine the system dynamic charac-eristics. Referring to (10), the value of D is determined in order todapt the battery system voltages; therefore it is not considered as

parameter for improving the dynamic of the qZSI network. More-ver, decreasing in L and increasing in parasitic resistances can besed to obtain a higher damping ratio, while reducing in C is usedo decrease the settling time [19]. Although small values of L and Cre preferred for improving dynamic characteristics of the system,ecreasing them below a critical values, increases the steady stateoltage and current ripples affecting the proper operation of theZSI [20]. Thus, tradeoffs need to be made for proper operation inransient and steady states. Moreover, the values of CP and Lb arenly designed to reduce the battery current ripples.

As known, in the qZSI, the shoot-through duty cycle and theodulation index are dependent on each other. This means that

he boost capability of the qZSI is achieved by partially or fullyeplacing of conventional null switching vectors of (0 0 0) and (1 1 1)ith shoot-through state, leaving active vectors unchangeable [19].

herefore, (14) must be fulfilled in the different control methodsresented in [21–23],

SBC : M ≤ 1 − D

MCBC : M ≤ 2√3

(1 − D)

MBC : M ≤ 2�

3√

3(1 − D)

(14)

here SBC, MCBC and MBC stand for the simple boost, maximumonstant boost and maximum boost control methods, respectively.oreover, M represents the inverter modulation index in the

teady-state. By neglecting the parasitic resistances of the induc-ors in the impedance network and referring to (9), (11) and (13),e can rewrite (14) as

SBC : VC1 ≥ 2Vin

MCBC : VC1 ≥√

3Vin

MBC : VC1 ≥ 3√

3�

Vin

(15)

here Vin is the amplitude of the phase to neutral voltage in theC-side in the steady-state. From (10) and (12), and consideringb1 = E1 − Rb1 × Ib1 and Vb2 = E2 − Rb2 × Ib2, the following equationan be obtained:

= rL (1 − 2D) iload − D(1 − D)2Rb1Iload − (1 − 2D) E

DE − (1 − 2D)(

1 − D2)

Rb2Iload − D2rLIload(16)

here = Ib2/Ib1, and E = (1 − 2D)E2 − DE1.

Considering rL = 0.1 �, Rb1 = Rb2 = 0.2 �, and E1 = E2 = 200 V, the

attery current ratio ˛, versus D for a certain load current is shownn Fig. 4. As it can be seen in this figure, the inverter shoot-hrough duty cycle can be considered as a current sharing control

ms Research 125 (2015) 164–173 167

variable when the BESS operates in the islanded microgrid. More-over, according to (13), the microgrid voltage is regulated usingm.

In the steady-state condition, VC1 can be obtained as

VC1 = Vb1 + Vb2 (17)

According to (17), for the proper operation of the qZSI modula-tion algorithm, the rating voltage of the batteries must satisfy theinequalities expressed by (15).

3. Description of the proposed controller

The transfer functions obtained in (7) and (8) are used in this sec-tion to design the current controllers. From (16), is determinedby the shoot-through duty cycle for a certain value of load cur-rent. Therefore, the control system can provide current sharing byadjusting the shoot-through duty cycle d, in the allowable regionexpressed by (15). The proposed controller configuration is shownin Fig. 5. As shown in this figure, the AC-side controller operates instationary reference frame (˛ˇ), therefore, the proportional res-onant (PR) controller can be used to track the reference valueswith zero steady-state error providing a suitable dynamic behavior[24,25]. Utilizing PR controller, the AC current controller can com-pensate for the negative sequence component of the unbalancedload currents. The PR controller transfer function is as follow:

PR = kP + kRs

s2 + �s + ω2(18)

where ω (rad/s) is the microgrid frequency, � is the cut-off fre-quency used for limiting the controller gain in resonance frequencyω. kP and kR are the PR controller parameters, which are obtained bythe stability analysis of the controller system. The Laplace domainmodel of the employed multi-loop controller for the AC-side of theinverter is shown in Fig. 6. In the islanded mode of operation, the ACloads are considered as resistive-inductive (RL) loads. The mason’sgain rule is used for calculating the closed-loop transfer functions.In the grid-connected mode, the dynamic of Cf and loads are notconsidered. Moreover, the grid voltage is fed forward to eliminatethe disturbance effect of the grid voltage on the current controller.

Assuming Cf = 45 �F, Lf = 2 mH, and rf = 0.1 �, and consideringdynamic model of the LC filters of the inverter shown in Fig. 6, theAC current controller is designed with the bandwidth of 0.7 kHz inwhich kP and kR of the current controller are 4.5 and 2000, respec-tively. Moreover, the bandwidth of the outer voltage controller isabout 350 Hz with kP = 1 and kR = 400.

3.1. Islanded microgrid

In the absence of the main grid, the control switch is in posi-tion “0” and the reference current for the AC current controlleris provided by the AC voltage controller. In this mode, the bat-tery currents are dictated by the load power demand. Fig. 5 showsthe proposed scheme to provide the appropriate current sharingbetween the battery systems. To share the load current betweenthe batteries with the ratio of (i.e. ib2 = ˛ib1), the current of bat-tery “1” is multiplied by and used as the reference current forthe current controller of battery “2”. Moreover, a low-pass filter(LPF2(is)) is used to eliminate the switching ripples on the currentof battery “1”.

The current sharing controller model in Laplace domain isshown in Fig. 7. The current controller of battery “2” is designedconsidering a certain bandwidth and stability margins using the

current controller model and the transfer function G b2d

obtained

from (7). Considering the BESS parameters listed in Table I, the cur-rent controller of battery “2” is designed with kpb2 = −3.3 × 10−3

and kib2 = −0.67 providing a bandwidth of 310 Hz with the phase

168 J. Khajesalehi et al. / Electric Power Systems Research 125 (2015) 164–173

Fig. 5. The structure of the proposed BESS controller.

Fig. 6. The Laplace-domain model o

Table IThe BESS parameters.

Circuit parameters Values

Inductances of quasi Z-source, (L) 400 �HSeries inductance of battery “2” 20 �HParasitic resistance of inductance L, (rL) 0.1 �Capacitances of quasi Z-source, (C) 600 �FAC side inductances, (Lf) 1.5 mHParasitic resistance of Lf , (rf) 0.05 �AC side inductance, (Cf) 45 �FSwitching frequency, (fs) 10 kHz

aAtchc

Parallel capacitor of battery “1” (CP) 400 �FEquivalent resistance of batteries, (Rb1 & Rb2) 0.2 �

nd gain margins of 33◦ and 21 dB, respectively, as shown in Fig. 8.s known, unbalanced loads absorb oscillatory power which leads

o ripples at double microgrid frequency on the battery current. Theurrent controller of battery “2” is characterized by a bandwidthigher than 120 Hz enabling it to track 120 Hz oscillatory referenceurrent with a zero steady-state error. Hence, the DC and oscillatory

Fig. 7. The Laplace-domain model of the battery current controllers.

f the AC-side control systems.

currents of battery systems, for a 60 Hz microgrid, can be appropri-ately shared in the presence of unbalanced loads. It should be notedthat the cut-off frequency of LPF2(is) is 1 kHz, which is well above120 Hz, thus, not affecting the performance of the current sharingcontroller.

As discussed earlier, the shoot-through duty cycle is the keyparameter in the proposed current sharing algorithm, therefore thevariation of d during the transient conditions leads to the varia-tion of the peak value of the DC-link voltage (see (11)). As shownin Fig. 5, the inverter voltage reference provided by the AC-sidecurrent controller is divided to vpn/2 to eliminate the effect of theimpedance network on the AC-side current and voltage controllers.Since the DC-link voltage is pulsed shape, its peak value cannot bemeasured directly, therefore it is calculated by measuring othervariables in the impedance network. Using the average state spacemodel of the system obtained in (3), in nonshoot-through condi-

tion, the input voltage of the inverter is (vb1 + vb2)/(1 − d), thereforethe voltages of the battery systems are used to calculate the valueof vpn.

100

10 1

10 2

10 3

10 4

10 5

04590

135180225270315

Frequency (Hz)

Phas

e (d

eg)

−100

−50

0

50

Mag

nitu

de (d

B)

Fig. 8. Bode plot of the current controller of battery “2”.

Syste

3

rilobtc

lilbt(ai

dasctA7tcboiT

3

tccftn

⟨

shown in Fig. 10. Since the power rating of both battery systems isequal, the current sharing controller must equally share the loadcurrent between the two battery systems. Initially, the total loadof the microgrid is supposed to be 5.5 kW and 4.2 kVar. At t = 0.06 s,

J. Khajesalehi et al. / Electric Power

.2. Grid-connected microgrid

In the grid-connected mode, the BESS must operate in the cur-ent control mode. In this mode, the selector switch shown in Fig. 5s in position “1” and the output current of battery systems is regu-ated to their references provided by the BESS management systemr microgrid tertiary control system [26]. To this aim, the current ofattery “1” is regulated by adjusting the inverter AC current, whilehe current of battery “2” is regulated using the shoot-through dutyycle.

In the current control mode, the current of battery “1” is regu-ated using direct component of the reference current (id(ref)). Sinced is related to the real power injected to the grid, any increase in ideads to increase of the current of battery “1”, while the current ofattery “2” is fixed to its reference by the current controller of bat-ery “2”. Moreover, the quadratic component of reference currentiq(ref)) is related to reactive power injected to the grid and does notffect the battery currents. Thus for reducing the inverter losses, its set to zero.

The model of the current controller of battery “1” in Laplaceomain is shown in Fig. 7. In this figure, iload = g × id, with g being

constant value associated with a certain modulation index andhoot-through duty cycle. The frequency response of the currentontroller loop of battery “1”, in grid connected mode, for the par-icular choice of g = 1, kpb1 = 0.1 and kib1 = 500 is shown in Fig. 9.s shown in this figure, the bandwidth of the current controller is2.6 Hz having phase and gain margins of 83◦ and 6.2 dB, respec-ively. Due to the mutual disturbance effect of battery currentontrollers, any sudden change in the reference current of eachattery leads to an unwanted overshoot in the current of anotherne. The low-pass filters LPF1 and LPF2(gc) are considered to min-mize the disturbance effect of current controllers on each other.he cut-off frequency of both low-pass filters is 50 Hz.

.3. Synchronization

In control of microgrids, before transferring from islanded modeo the grid-connected mode, the microgrid voltage must be syn-hronized with the main grid. Considering operation of BESSontrollers in ˛ˇ-frame, for synchronizing with the main grid, weollow the same procedure presented in [27]. In this scheme, whenhe grid voltage (v˛ˇg) and microgrid voltage (v˛ˇm) are synchro-ized, it can be assumed that:

vˇg v˛m − v˛g v˛m

⟩= 0 (19)

101

10 2

10 3

10 4

10 5

−315−270−225−180−135−90

Frequency (Hz)

Phas

e (d

eg)

−200

−100

0

100

Mag

nitu

de (d

B)

Fig. 9. Bode plot of the current controller of battery “1”.

ms Research 125 (2015) 164–173 169

where 〈x〉 denotes the average of x in half period of microgrid volt-age (�/ω). Thus, the synchronizing frequency (ωsynch) which mustbe added to the frequency of BESS can be calculated as

ωsynch =(vˇgv˛m − v˛gvˇm

)× ωC

s + ωC× kPs + kIs

s(20)

where kPs and kIs are coefficients of PI compensator for synchro-nization, and ωC is cut-off frequency of a low-pass filter. SelectingkPs = 0.02, kIs = 0.1, and ωC = 8� rad/s results in synchronizing ofmicrogrid with the main grid in about 0.2 s when the initial phasedifference between the microgrid and the grid is �

9 rad.

4. Simulation results

The proposed qZSI system is simulated in MATLAB/Simulink toverify its performance. The system parameters are listed in Table I.The nominal phase to neutral voltage of the considered systemis 120 V(RMS) with a frequency of 60 Hz. In addition to the BESS,the studied microgrid consists of both balanced and unbalancedresistive-inductive loads, DERs, and lines. Moreover, it is assumedthat the BESS is connected to the microgrid bus through a line withequivalent impedance of Zline = 0.07 + j0.07 �. We first investigatethe operation of the current sharing controller in the absence ofthe main grid for various voltage and current ratings of battery sys-tems. In this mode, the load demand is supplied by the BESS. Wethen investigate the battery current regulation in the presence ofthe main grid. It is noted that the qZSI PWM algorithm in all casestudies is based on the simple boost control method. In a separatecase, the operation of the PEI system is investigated when the volt-age level of the battery systems violate the allowable region. In caseVIII, the performance of the BESS during changes in DERs’ powergeneration is evaluated. Moreover, the effectiveness of the BESS inproviding generation and consumption balance in islanded mode isalso investigated. Finally, the operation of the BESS in synchroniz-ing microgrid with the main grid as well as transferring betweenislanded and grid-connected modes are evaluated.

4.1. Case I. Equal voltage and current ratings

The operation of the proposed controller when two battery sys-tems have the same voltage rating of 200 V with Rb1 = Rb2 = 0.2 � is

Fig. 10. The battery systems with equal voltage and current ratings: (a) current ofbattery systems, (b) load voltage, and (c) inverter current.

170 J. Khajesalehi et al. / Electric Power Systems Research 125 (2015) 164–173

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connection of this single-phase load, results in battery current oscil-lations. However, since the bandwidth of the current controller ofbattery “2” is well above 120 Hz, both of the battery currents takeequal values in case of oscillatory currents imposed by unbalanced

ig. 11. The battery systems with equal voltage and different current ratings: (a)urrent of battery systems, (b) load voltage, and (c) inverter current.

he total load power is increased to 11 kW and 8.4 kVar, and finallyt t = 0.12 s, the load power is decreased to its initial value. The cur-ent of the battery systems are shown in Fig. 10(a). As it can beeen in this figure, the load current in any load condition is equallyhared between the battery systems. The voltage and the currentf the load are shown in Fig. 10(b) and (c), respectively. During thisoad changes, the voltage controller maintains the AC voltage equalo its reference value, while the current sharing controller equallyhares the load current between the battery systems.

.2. Case II. Equal voltage rating with different current ratings

In this case, the operation of the current sharing controller whenhe battery systems have similar voltage ratings of 200 V, whilehe current ratings are different is evaluated. The current rating ofattery “1” is two times more than that of battery “2”. Moreover,b1 and Rb2 are 0.1 � and 0.2 �, respectively. At first, the microgridotal load is 5.5 kW and 4.2 kVar, while at t = 0.06 s, the load powers doubled. Subsequently, at t = 0.12 s, the load power is broughtack to its initial value. The currents of both batteries are shown

n Fig. 11(a) showing an appropriate current sharing between thewo batteries with respect to their ratings. The load voltage and thenverter current are shown in Fig. 11(b) and (c), respectively.

.3. Case III. Different voltage rating with equal current ratings

In this case, the operation of the current sharing controller whenhe battery systems have similar current ratings and different volt-ge ratings is evaluated. The equivalent resistance for both batteriess 0.2 �, while the voltage ratings of battery “1” and battery “2” aref 200 V and 300 V, respectively. The load variation in this case isdentical to that of Case I for which the battery currents is shown inig. 12(a). It is clearly seen from this figure that, despite differentoltage ratings, the current controller succeeds in equally sharinghe load current between the two battery systems. For this loadhange, the inverter output voltage is shown in Fig. 12(b) whoseoltage follows the reference provided by the AC voltage controller.he qZSI current during these load changes is shown in Fig. 12(c).

.4. Case IV. Different voltage and current ratings

To further study the performance of the proposed control sys-em, we consider two battery systems with different voltage ratingsimilar to Case III, while the current rating of battery “1” is twoimes more than that of battery “2”. The equivalent resistance of

Fig. 12. The battery systems with different voltage rating and equal current ratings,(a) current of battery systems, (b) load voltage, and (c) inverter current.

both batteries is 0.2 �. The load variation scenario is identical tothe previous case. Subsequent to the considered load change, thebattery currents are determined by the current controller, whichadequately shares the load current proportional to the battery cur-rent ratings, Fig. 13(a). The load voltage is shown in Fig. 13(b)showing a desirable phase to neutral voltage of 120 V in all loadconditions. As shown in Fig. 13(c), the amplitude of the qZSI cur-rent is doubled to supply the load connected at t = 0.06 s and bringsback it to its initial value, while the same load is disconnected att = 0.12 s.

4.5. Case V. Unbalanced load

In this case, it is assumed that the battery systems have similarvoltage and current rating (Eb1 = Eb2 = 200 V). According to Fig. 14,the BESS initially supplies a three-phase balanced load, whosereal and reactive powers are, respectively 5.5 kW and 4.2 kVar. Att = 0.08 s, a single-phase load of 1.8 kW and 1.4 kVar is connectedbetween phases “b” and “c”. As it can be seen from Fig. 14(a), the

Fig. 13. The battery systems with different voltage and current ratings: (a) currentof battery systems, (b) load voltage, and (c) inverter current.

J. Khajesalehi et al. / Electric Power Systems Research 125 (2015) 164–173 171

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load while DERs have no generation. At t = 0.2 s, the power ofDERs gradually increases to 10 kW during about 0.4 s shown in

ig. 14. Operation of BESS in the presence of unbalanced load: (a) current of batteryystems, (b) load voltage, and (c) inverter current.

oads. The microgrid voltage is shown in Fig. 14(b) which shows desirable balanced voltage in the presence of unbalanced loads.s it can be seen from Fig. 14(c), following the connection of theingle-phase load, the qZSI current is not balanced. Since the volt-ge and current controllers in the AC side are based on PR controller,he negative sequence current of unbalanced load can be providedy the BESS keeping the microgrid voltage balanced as shown inig. 14(b).

.6. Case VI. Grid-connected mode

In this case, the BESS operates in the grid-connected mode. Inhis mode, the control switch shown in Fig. 5 is in position “1” andhe current of both battery systems can be independently regulatedo their references. Based on the proposed control strategy, the cur-ent of battery “1” is regulated by means of the AC-side currentontroller using the modulation index, while the current of battery2” is regulated by the adjustment of the shoot-through duty cycle.he battery systems are supposed to have the same voltage ratingsf 200 V. It is assumed that initially, both battery systems operate inhe charging mode with a charging current of −20 A (see Fig. 15). At

= 0.05 s, the reference current of battery “2” is changed to +20 A,nd at t = 0.1 s, the reference current of battery “1” is changed to20 A. The reference current of both batteries is brought back to the

nitial value of −20 A at t = 0.15 s and t = 0.2 s for battery “2” and bat-ery “1”, respectively. As it can be seen from Fig. 15(a), the currentsf both batteries are regulated to their references in both chargingnd discharging modes. The inverter current injected to the main

ig. 15. The variation of the battery current references in the grid-connected mode,a) current of battery systems, and (b) inverter current.

Fig. 16. Load voltage when battery systems operate under unallowable voltageratings.

grid is shown in Fig. 15(b). According to Fig. 15(b), any increase inthe current of battery systems increases the inverter current in theAC-side. At intervals (0.05–0.1) s and (0.15–0.2) s, the charging cur-rent of one battery is provided by another one, thus the qZSI currentis almost zero.

4.7. Case VII. BESS operation with unallowable voltage rating

In this simulation case, we evaluate the performance of the pro-posed system when the BESS is faced with different voltage levelseither in the allowable or unallowable region expressed by (15).The qZSI switching is based on simple boost control method. To thisaim, the BESS is equipped with batteries with voltage ratings listedin Table II. Considering 120 V voltage in the AC side (i.e., amplitudeof 170 V), VC1 = Vb1 + Vb2 in (15) must be at least 340 V. As it can beseen from Table II, the voltage THD is significantly affected by thevoltage of the batteries. The load voltage when the batteries arecharacterized by equal voltage ratings of 200 V (Vb1 + Vb2 > 340 V)supplying the same portion of the load demand has been alreadyshown in Fig. 10(b). As it can be seen from Table II, operating in theallowable voltage region results in a sinusoidal load voltage withan acceptable THD of about 0.15%. In case of operating within theunallowable voltage region i.e., 100 V and 200 V for battery ‘1’ andbattery ‘2’, respectively (Vb1 + Vb2 < 340 V), the load voltage wouldbe contaminated by harmonics with an unacceptable THD, Fig. 16and Table II.

4.8. Case VIII. BESS operation in absorbing surplus of microgridpower

In this case, we evaluate the performance of the BESS when itabsorbs power from the islanded microgrid to provide the localgeneration and consumption balance while regulating the micro-grid voltage. The batteries’ characteristics are similar to Case I.It is assumed that initially, the BESS supplies a 5.5 kW + 4.2 kVar

Fig. 17(a). Subsequent to the DERs’ power variations, the BESS startsto change its power generation in order to keep generation and

Fig. 17. Operation of the BESS during increasing of DERs’ power generation, (a) DERsand BESS powers, and (b) battery currents.

172 J. Khajesalehi et al. / Electric Power Systems Research 125 (2015) 164–173

Table IIOperation of the BESS with different voltage ratings.

Voltage of battery 1 (V) Voltage of battery 2 (V) Operation region Voltage THD (%)

200 120 Unallowable 1.08Allowable 0.15Allowable 0.15Unallowable 11.3

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are equal during the islanded mode while they are set to their ref-erences in the grid-connected mode. Then, at t = 0.6 s, the microgridagain gets disconnected from the main grid. From t = 0.6 s on, the

200 200

100 300

100 200

onsumption balance. According to Fig. 17(a), at t = 0.27 s, the BESStarts to absorb power from the microgrid to charge its batteries.he BESS battery currents during the variation of DERs’ power gen-ration are shown in Fig. 17(b). As it can be seen from this figure,he battery current sharing controller properly shares the batteryurrents between both BESSs in both charging and discharging con-itions. The inverter current and the microgrid voltage are shown

n Fig. 18(a) and (b), respectively. According to Fig. 18, the BESS reg-lates the microgrid voltage to its reference in both BESS chargingnd discharging conditions.

.9. Case IX. Synchronization and mode transitions

In this case, operation of the microgrid during transferring fromhe islanded mode to the grid-connected mode and vice versas evaluated. The microgrid total load power is assumed to be.5 kW + 4.2 kVar while the voltage ratings of batteries are 200 Vith equal current ratings. At first, it is assumed that microgrid

perates in the islanded mode with a voltage phase difference of0◦ with the main grid. At t = 0.2 s, the microgrid starts to be syn-hronized with the main grid. Fig. 19 shows the synchronizationrocess. It can be seen from Fig. 19(a) that the synchronizationrror, defined by (19), approaches to zero after about 0.2 s. Theoltages of the microgrid and the main grid in phase “a” are shownn Fig. 19(b). The left figure shows the voltages at the start of theynchronization process with about 20◦ phase difference while theight figure shows the voltages when they are synchronized at

= 0.3 s. At this time, the STS can be closed to connect the microgrido the main grid. Having connected to the main grid, the selectorwitch shown in Fig. 5 rapidly changes to state “1”, the BESS rapidlyakes over the responsibility of regulating battery currents to theireferences of −10 A for battery “1” and −20 A for battery “2”. Theicrogrid voltage during closing the STS is shown in Fig. 20(a). Since

he microgrid is synchronized with the main grid, its voltage expe-iences a smooth transition. Fig. 20(b) shows the inverter current.

he BESS power and the grid power are shown in Fig. 20(c). As it cane seen from this figure, in the islanded mode, the BESS generatesower while in the grid-connected mode it absorbs power from the

ig. 18. Operation of the BESS during increasing of DERs’ power generation, (a)nverter current, and (b) microgrid voltage.

Fig. 19. Operation of the BESS in regulating the microgrid voltage during synchro-nization with the main grid, (a) synchronization Error defined by Eq. (19), and (b)voltages of the microgrid and the main grid before and after synchronization.

main grid. As expected, the battery currents, shown in Fig. 20(d),

Fig. 20. Operation of the BESS in regulating the microgrid voltage during mode tran-sitions, (a) microgrid voltage, (b) inverter current, (c) main grid and BESS powers,and (d) battery currents.

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ESS starts to regulate the microgrid voltage as shown in Fig. 20(a).he inverter current shown in Fig. 20(b), increases at t = 0.6 s toeep the microgrid voltage stable during the transition from therid-connected to the islanded mode. From Fig. 20(d), at t = 0.6 s,he batteries switch to the discharging mode with a dischargingurrent of 13 A to supply the islanded microgrid.

. Conclusion

A quasi Z-source Inverters (qZSI) was presented for the applica-ion in parallel operation of Battery Energy Storage Systems (BESS)n microgrids. The modeling and control of quasi (qZSIs) for thearallel operation of Battery Energy Storage Systems (BESS) wasresented. In the proposed control strategy, the shoot-through dutyycle of the qZSI is utilized to share the load current between theattery systems operating in the islanded mode. In this mode, the

nverter modulation index is used to control the inverter AC-sideoltage. Furthermore, by virtue of the proposed current sharingethod, the oscillatory power due to the unbalanced loads is also

ppropriately shared between the battery systems with differentoltage and power ratings. In the grid-connected mode of opera-ion, the proposed control method relies on the inverter modulationndex and the shoot-through duty cycle to independently reg-late the currents of both battery systems. The performance ofhe proposed control strategy was evaluated for different volt-ge and current ratings of the battery systems operating in bothrid-connected and islanded modes of operation as well as moderansitions. In particular, in the grid-connected mode of operation,he current of each battery system was independently regulatedy adjusting the inverter modulation index and the shoot-throughuty cycle. Simulations were conducted in MATLAB/Simulink forhe case of a typical microgrid involving two battery systems char-cterized by different current and voltage ratings.

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