A power sharing scheme for voltage unbalance and harmonics compensation in an islanded microgrid

Electric Power Systems Research 155 (2018) 153–163

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A power sharing scheme for voltage unbalance and harmonics compensation in an islanded microgrid A. Ranjbaran, M. Ebadian ∗ Faculty of Electrical and Computer Engineering, University of Birjand, Birjand, 971175-615, Iran

a r t i c l e

i n f o

Article history: Received 11 June 2017 Received in revised form 18 September 2017 Accepted 27 September 2017 Keywords: Distributed generation Microgrid Droop control Power sharing Voltage unbalance and harmonic compensation Critical load

a b s t r a c t In this paper, a hierarchical control structure with voltage unbalanced compensation scheme in ac islanded microgrid is proposed to improve Critical Load Bus (CLB) voltage quality and address inaccurate power sharing problems. The hierarchical scheme includes primary and secondary control levels. The primary control mainly contains the power droop controllers, voltage and current controllers, selective virtual impedance loop, and voltage unbalanced compensation. The virtual impedance loop includes virtual positive- and negative-sequence impedance loops at fundamental frequency and virtual variable harmonic impedance loop at harmonic frequencies. The secondary control is designed to restore frequency and amplitude of the CLB voltage. In order to compensate the CLB voltage, an unbalanced compensation is proposed to change the voltage reference of the distributed generation (DG) units. This strategy also employs the low bandwidth communication (LBC) technique to send the proper signals of the secondary control from the microgrid control center (MGCC) to the primary control. To evaluate the performance of the proposed control strategy, simulations are conducted on two islanded microgrid prototype. The results demonstrate the effectiveness of the proposed control structure in the unbalance and harmonic compensation of the CLB voltage and proper power sharing of reactive, unbalanced and harmonic powers among the DG units. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Unbalanced and nonlinear load conditions are the common case in low voltage microgrids, where the most of the loads are single phase [1]. The voltage unbalance mainly emerges through the connection of single-phase loads between two phases or between one phase and the neutral [2]. The unbalance and harmonic-distorted voltage have some negative impacts on critical loads that are sensitive to voltage deviations, such as electronic loads, adjustable speed drives and induction motors. Therefore, a control strategy should be designed for the DG units to improve the performance of microgrids under unbalanced and nonlinear load conditions. One major method for compensation of voltage unbalance and harmonics is the use of series active power filter in series with the distribution line by injecting negative sequence and harmonic voltage [3]. Also, in Refs. [4–6], shunt compensation is provided to mitigate voltage unbalanced and harmonic distortion. In this method, unbalanced load voltage is compensated by balancing the line currents. However, for the islanded microgrid conditions, it is

∗ Corresponding author. E-mail address: mahmoud [email protected] (M. Ebadian). https://doi.org/10.1016/j.epsr.2017.09.026 0378-7796/© 2017 Elsevier B.V. All rights reserved.

uneconomic to install extra series/parallels active power filter for each of the DG. Several control strategies have been presented to improve the quality of ac microgrid. In Ref. [7] a control strategy based on droop control method is proposed for a microgrid. The method improves the power quality and proper power sharing in the presence of unbalanced and nonlinear loads. In Refs. [8–12], the virtual impedance is proposed to balance load voltage and share the nonlinear load among DG units. However, in this study, the unbalanced voltage drop of the virtual impedance is not considered, which eventually lead to unbalance of the output voltage. In Refs. [13–15], hierarchical control structure is proposed for voltage unbalance compensation at sensitive loads. However, in most proposed methods, the compensation of voltage harmonics at the DG terminal is investigated, while the power quality at PCC is usually the main concern due to critical loads, which may be connected to PCC [16]. Furthermore, power quality problems under unbalanced and nonlinear loads and power sharing problems with mismatch feeder impedance are scarcely considered. Therefore, in this paper, a hierarchical control structure consisting of several electronically-interfaced three-wire DG units is proposed for an islanded microgrid that includes primary and secondary control levels. It has been supposed that DG capacities can be different. In

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the primary control, the P–f/Q–V droop method has been used. In order to compensate the CLB voltage, a voltage unbalance compensation is proposed to change the voltage reference of the distributed generation (DG) units. In this method, voltage drop across the feeders is estimated for each phase and added to voltage reference generated by the Q–V droop control method. The reactive power sharing is sensitive to the impacts of mismatched feeder impedance. In the proposed control strategy, the mismatch in voltage drops across feeders is compensated. Moreover, in order to avoid the active and reactive power control coupling and also, due to reduction of the fundamental negative sequence circulating current, the virtual positive- and negative-sequence impedance loops with voltage and current control loops have been utilized. Also, the virtual variable harmonic impedance loop at specific harmonic frequency has been used for proper sharing of harmonic power among all the DGs. Furthermore, for performance improvement of the Q–V droop control method; the voltage drop of the virtual positive sequence impedance has been considered. The second order generalized integrator (SOGI) has been implemented to extract the fundamental positive- and negative-sequence currents in order to calculate voltage drop on the fundamental positive- and negativesequence virtual impedance. The secondary control is designed to restore frequency and amplitude of CLB voltage. The performance of the proposed strategy in microgrids with two parallel DGs is evaluated and reported in this paper. The main novelties of this paper are summarized as follows. 1) Balance of the CLB voltage by voltage drop estimation across the feeder impedance. In order to compensate the CLB voltage, a voltage unbalance compensation is proposed to change the voltage reference of the distributed generation (DG) units. 2) Enhancement of the accuracy of reactive power sharing of the islanded microgrid. In the proposed control strategy, the mismatch in voltage drops across feeders is compensated. 3) Improvement performance of the Q–V droop control method by considering the voltage drop of the virtual positive sequence impedance.

Fig. 1. Equivalent circuit of a DG connected to a load bus.

is disrupted, the primary control autonomously compensates voltage unbalance and harmonics and properly share the active and reactive power according to the local measurements unless total load changes, in the case of which, the sharing accuracy is reduced, but the proposed control method still outperforms the traditional droop control method. In this paper, a three-phase three-wire islanded microgrid is considered. The proposed control strategy of an individual DG unit is shown in Fig. 2. 2.1. The primary control The primary control is designed to: (1) satisfy decentralized adjustment of the voltage and frequency of the microgrid and properly shared power load between DGs based on its capacity in islanding mode, (2) compensate voltage unbalance and harmonics, (3) minimize the fundamental and harmonic circulating current between DG units, and (4) compensate the mismatch in voltage drops across feeders. 2.1.1. The P–f/Q–V droop control method The droop control method can be studied by considering an equivalent circuit of a DG connected to load bus, as shown in Fig. 1. The DG unit modeled as an AC source, with the voltage of VS ∠ı. The load bus voltage is VL ∠0. The real and reactive power delivered to load bus is given by P =

  V S2 VS VL cos  + ı cos  − Z Z

(1)

Q =

  V S2 VS VL sin  + ı sin  − Z Z

(2)

The rest of this paper is organized as follows. The structure of the proposed hierarchical control strategy is analyzed in detail in Section 2, including calculation of the active and reactive power for each phase, P–f/Q–V droop control method, voltage unbalanced compensation, voltage and current control loops and secondary control. The controller performance with/without control strategy is evaluated and compared in Section 3. Finally, conclusions are drawn in Section 4.

P =

2. Microgrid hierarchical control strategy

If the phase difference between the DG output voltage and load bus, ␦, is small, it is reasonable to suppose, cos ı ≈ 1 and sin ı ≈ ı. Then, the frequency and amplitude of the DG output voltage reference can be expressed as follows:

The hierarchical control structure consists of two control levels: primary and secondary level. The primary control comprises DG local controllers. The local controllers, including power droop controllers, voltage and current controllers, selective virtual impedance loop and unbalance voltage compensators, balance the PCC voltage and share power load between DGs based on their capacity. Furthermore, unbalance voltage compensators can compensate the mismatch in voltage drops across feeders by voltage drop estimation without requiring knowledge of the feeder impedances. The central secondary control level is designed to restore the PCC frequency and voltage amplitude deviations by sending proper reference signals to each of the DGs. The LBC is used for sending the data communication of the secondary controllers and active and reactive power references from the MGCC to the local controller. The MGCC provides the individual power and voltage reference for each local controller. If communication

If the effective line impedance is purely inductive,  = 90◦ and Z = jX, then (1), (2) can be reduce to

Q =

VS VL sin(ı) X VS2 X

−

VS VL cos( ı) X

(3) (4)

f = f0 − Dp (P0 − P)

(5)

V = V0 − Dq (Q0 − Q )

(6)

where f0 , V0 are the frequency and voltage magnitude references, Dp , Dq are droop coefficients and P0 and Q0 represent the real and reactive power references. The P0 and Q0 from each DG are set by the MGCC. For determining the Q–V droop coefficient, the voltage drop across virtual impedance should also be taken into consideration [17]. As a result, droop coefficient is modified as follows Dqi new =

V0i new − Vi min new − Io max |Zv i | Q0i − Qi max

(7)

where |Zv | is virtual positive-sequence impedance and Iomax is output current at full load.

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155

Fig. 2. Block diagram of the proposed voltage control strategy. a) Per phase fundamental active and reactive power of DG output, b) the voltage drop estimation, c) droop control method, d) selective virtual impedance loops, e) the secondary control. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

2.1.2. Calculation of P and Q for each phase The active and reactive power for each phase of the DG units’ output have been obtained based on the stationary and orthogonal ␣␤ reference frame per phase. In this scheme, each phase of the original three-phase system can be considered as three independent two-phase systems. Therefore, for each phase, a second fictitious phase should be generated by a given phase shift of ␲/2 lead or ␲/2 lag [18]. For the purpose of generating the fictitious phase, the SOGI [19] has been implemented. The actual DG output voltages and currents have been considered as ␣-axis quantities, whereas the ␲/2 lag voltages and ␲/2 lag currents of the DG output have been considered as ␤-axis quantities. For phase-a, the DG output voltage and current in ␣–␤ coordinates can be represented by ␲/2 lag as:





voa

˛

voa

ˇ

 =

voa (ωt) voa (ωt − /2)



 =

Vom cos(ωt) Vom sin(ωt)

 (8)





ioa

˛

ioa

ˇ

 =

ioa (ωt + ϕi ) ioa (ωt + ϕi − /2)

 (9)

where voa (ωt) and Vom represent the reference DG output voltage and desired DG output voltage magnitude, respectively. Considering phase-a, by using the voltage (voa ˛ˇ ) and current (ioa˛ˇ ) of phase-a in the ˛ˇ-axis, the instantaneous active power (pa ) and reactive power (qa ) can be represented by Ref. [20]. pa = voa

˛ ioa ˛

+ voa

ˇ ioa ˇ

(10)

qa = voa

ˇ ioa ˛

− voa

˛ ioa ˇ

(11)

Subsequently, pa and qa are processed by low pass filter in order to eliminate the double frequency ripples of the power components. Similarly, for phase-b and phase-c can also be defined as a two-phase system in ␣–␤ coordinates and instantaneous active and reactive power can be calculated for each phase separately.

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2.1.3. Voltage unbalanced compensation Voltage reduction, due to the voltage drop across the feeder impedance, is known as one of the problems with the Q–V droop method, which, consequently, results in a noticeable reduction in load voltage and reactive power sharing accuracy. Under the unbalanced loading conditions, single-phase loads’ power demand may not be the same in the given microgrid and therefore, the load current drawn by each phase may be different. In the traditional droop control method, DG output voltage is balanced, and due to the presence of unbalanced voltage drop throughout the feeder’s impedance, load voltage becomes unbalanced. Therefore, in this paper, for the purpose of balancing load voltage, voltage drop across the feeders has been estimated for each phase and added to voltage reference generated by the Q–V droop control method, which leads to a balanced load voltage. Furthermore, this method can improve accuracy reactive power sharing, which affect by the feeder impedance mismatch. The Eq. (4) can be represented by Q =

VS (VS − VL ) VS V = X X

X V = Q VS

(12) (13)

Therefore, there is linear relevance between the DG output reactive power and the voltage magnitude difference (between DG output voltage and PCC voltage). This linear relevance can be expressed as Ref. [21]. KQ =

V X = Q VS

Fig. 3. Block diagram voltage drop calculation of the virtual impedance with fundamental positive sequence, fundamental negative sequence, and harmonic frequencies. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

the phase-a voltage drop across the feeder impedance is presented as follows V a = K Q ·Q a

(14)

where V, Q are the DG output voltage magnitude difference and the DG output reactive power, respectively. As presented in Eq. (14), the KQ is related to the system voltage, and the inductance between the DG output and the PCC. The inductance is often not readily available. Therefore, this coefficient(KQ ) must be estimated without the knowledge of the feeder impedance. According to Eq. (6), if reactive power output of the DG with the reactive power reference (Q0 ) is equal, so, the DG output voltage and the voltage magnitude reference (V0 ) will be equal. Therefore, the difference between the DG output voltage and PCC voltage is actually the PI controller’s output (Q0 –Q). The V/Q coefficient can be achieved as (KQ = (Q0 –Q)/Q0 ). A LPF with the cut-off frequency 5 Hz is used to smoothen the achieved coefficient (KQ ), which is subsequently applied to estimate the voltage drop across feeder impedance between the output DG and PCC. The reactive power reference from each DG has been set by the MGCC. Through the communication link, each DG unit sends information to MGCC regarding generation capacity. The MGCC based on this information, and the data regarding forecasts and historical data calculate the proper share of reactive power for each DG unit and send it back to each unit, along with a controller enable signal. To avoid constantly varying power reference values, a sampler with 5 Hz sampling rate was used. The power references with time delay transmit to the local controller, due to the fact that reference Q0 is updated periodically, will have no effect on the power sharing at the steady state. This time delay is called the information update delay [22]. The proposed strategy only requires that the MGCC exchange data periodically at a slow rate, low-bandwidth communication links are sufficed for this application. It should be noted that the proportional coefficient of PI controller is selected according to the required response time such that with the increase of this coefficient, the response time is reduced, but the control system becomes more prone to instability [23]. The response time should be much longer than the information update period (an information update period is 0.2 s). Therefore,

(15)

where Qa is the phase-a output reactive power of DG unit i. Similarly, the voltage drop on the feeder for phase-b and phase-c can also be calculated. Vb = KQ · qb

(16)

Vc = KQ · qc

(17)

Finally, the voltage drops have been added to the reference voltage achieved by the Q–V droop control method. Hence, the new reference voltage can be defined as follows: new V0a = V0 + Va

(18)

new V0b = V0 + Vb

(19)

new V0c = V0 + Vc

(20)

2.1.4. The virtual positive/negative-sequence impedance loops In the presented paper, unbalanced and nonlinear loads are supplied in the microgrid. In this situation, the PCC current includes fundamental positive and negative sequences as well as positive and negative sequences at harmonic frequencies. The presence of such components in PCC current generates respective distortion in the output voltage of DG unit, which should be properly mitigated. On the other hand, these current components should be shared among DG units [8]. Therefore, in this paper, the virtual positive- and negative-sequence impedance and harmonic virtual impedance are presented in order to achieve these goals. This positive-sequence virtual impedance is considered to enhance the performance of the droop controllers. The inductive part contributes in reducing the circulating current and decoupling control of the active and reactive power, and the resistive part improves the system damping. The negative-sequence virtual impedance for negative sequence of the PCC current fundamental component is proposed to compensate voltage distortion of the PCC voltage and minimize the negative sequence circulating currents among the DGs and the virtual variable harmonic impedance loop for the better sharing of harmonic power [10]. As shown in Fig. 3,

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the voltage drop of the virtual positive- and negative-sequence and harmonic sequence impedance in ␣␤ axis are derived as Ref. [11].



Vv ˛ + j Vv ˇ = Rv + + jωLv +

 

Rv − − jωLv −

 

Rv h − jhωLv h

+

i0˛ + j ioˇ −

i0˛ + j ioˇ



+ −

h

i0˛ + j ioˇ

 

h



+ + (21)

Table 1 System parameters with their values. System parameter

Value

LCL filter DC link voltage Grid voltage amplitude Grid frequency DG feeder

Lf = 1.8 mH, Cf = 25 ␮F, Lo = 1.8 mH 650 V 380 V (line to line RMS) 50 Hz RDG1 = 0.6, LDG1 = 3 mH RDG2 = 0.2, LDG2 = 1 mH Value

Primary control level

Vv ˛ = Rv + · i0˛

+

+

− ωLv + ioˇ + Rv − · i0˛

h

+Rv h · i0˛ + hωLv h · ioˇ Vv ˇ = Rv + · i0ˇ

+

−

+ ωLv − ioˇ

Frequency droop slopes Voltage loop PR parameters

−

Current loop PR parameters

h

+

+ ωLv + i0˛ + Rv − · i0ˇ

−

− ωLv − io˛

Virtual resistance

−

(22) h

+ Rv h · ioˇ − hωLv h · io˛

h

where Rv + and Lv + are the virtual resistance and inductance for fundamental positive sequence. Similarly, Rv − and Lv − are the virtual resistance and inductance for fundamental negative sequence, Rv h and Lv h represent the virtual harmonic-frequency resistance and inductance, h denotes the dominant harmonic components as −5, 7, −11, 13, etc., and  represents the system fundamental frequency [24]. For the decomposition of the DG output currents and extraction of the fundamental positive- and negative-sequence currents as well as the dominant harmonic components, the DSC-SOGI is utilized [25]. 2.1.5. Voltage and current control loops The voltage and current controllers are implemented on the stationary frame and the proportional resonant (PR) controllers are employed in the ˛–ˇ frame by using the following transfer function [26]. GV (s) = kpv +



2kih ωc s

h=1,5,7

Gi (s) = kpi +

s2 + 2ωc s + (2hf )

 h=1,5,7

2

2kiIh ωc s s2

+ 2ωc s + (2hf )

2

(23)

(24)

where kPV and kpi are the proportional gains, kih and kiIh respectively represent the voltage and current resonant controller coefficients for the hth order harmonic component (including fundamental component as the first harmonic) and ωc represents cutoff frequency for resonant bandwidth control. 2.2. Secondary control The secondary control level restored amplitude and frequency of the PCC voltage to nominal values [27]. The angular frequency and amplitude levels in the PCC voltage ωPCC and VPCC are measured and compared with the references ref and Vref . Then, the error signals are processed by the PI controllers as in Eq. (25); the resulting signals (ωsec and Vsec ) are sent to the primary control level of each DG unit to restore the PCC voltage.



ωsec = kpω (ωref − ωPCC ) + kiω



V

sec

= kpe (Vref − VPCC ) + kie

(ωref − ωPCC )dt (25) (Vref − VPCC )dt

where kp , ki , kpe , and kie are the control parameters of the secondary control compensator.

157

Virtual inductance Cut-off frequency for resonant bandwidth control Cut-off frequency of power calculation Secondary control level

Dp = −2.612 × 10−4 rad/s/W kpv = 0.25 kih = 15 (h = 1) and 10 (h = 5,7,11,13) kpI = 75 kiIh = 550 (h = 1), 50 (h = 5), 40 (h = 7) and 20 (h = 11, 13) Rv − = 6, Rv 5 = 1, Rv 7 = 2,Rv 11 = 8 and Rv 13 = 4  Lv + = 6, Lv 5 = 2 and Lv 7 = Lv 11 = Lv 13 = 1.5 mH ωc = 1 ωf = 5 Value

Frequency proportional and integral term Load parameters

kp = 0.75, kI = 7.5

Unbalanced load Nonlinear load

RUL = 230  RNL = 460 , LNL = 84 ␮H, CNL = 235 ␮F

Value

3. Simulation results Simulation results have been carried out in Matlab/Simulink environment. In order to verify the effectiveness of the proposed control strategy, two case studies are conducted. A microgrid with two DG units has been chosen, shown by Fig. 4. 3.1. Simplified microgrid A single-phase load between the phase a and b together with a three-phase diode rectifier load is connected to PCC as unbalanced and nonlinear loads, respectively. The system parameters used for simulation are demonstrated in Table 1. In this paper, all the three-phase waveforms shown by the colors blue, red and green represent the phase-a, phase-b and phase-c, respectively. 3.2. Case-1: DG units with equal rating In this study, DG1 and DG2 capacities are equal with identical system parameters. Based on the data provided in Table 1, it can be observed that the value of the feeder impedance of DG1 is thrice that of the DG2. The three-phase voltage and current waveforms of the output DG1 , DG2 and PCC using the traditional droop control method are shown in Fig. 5. In the case of traditional droop control, the virtual negative impedance at fundamental frequency and virtual harmonic impedance at harmonic frequencies and the unbalanced compensation are not activated and only the virtual positive impedance at fundamental frequency is activated. Fig. 5 presents that the currents of DG1 and DG2 are not identical, and DG2 produces higher harmonic currents because of a smaller series feeder impedance. By using the proposed control strategy, the power sharing performance is improved as illustrated in Fig. 6. From Fig. 6, it is clearly shown that the current outputs of the DG1 and DG2 are identical, and the current sharing errors are effectively decreased. In addition, the active and reactive power sharing among the DG units has been illustrated in Figs. 7 and 8. As it can be seen, the

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Fig. 4. Islanded microgrid with two DGs and unbalanced and nonlinear load. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 5. Results of the microgrid system with traditional droop control method. (a) Output voltages of DG1 . (b) Output currents of DG1 . (c) Output voltages of DG2 (d) Output currents of DG2 . (e) PCC voltages. (f) PCC currents. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

capacity of the DG units is equal and therefore, the active power is equally distributed among the DG units with the traditional droop control method and proposed control strategy. However, in the traditional droop control method, reactive powers generated by the two DG units are not the same due to unequal feeder impedance of each DG unit. As it can be seen in Fig. 8, the reactive power sharing is accurate with the proposed control method.

It can be observed in Fig. 10, by proposed control strategy, the active and reactive powers are properly shared among DG units based on their capacity, and the amount of the P2 and Q2 supplied by DG2 are accurately twice of the supplied by DG1 .

3.4. Evaluation of the proposed scheme performance in a multibus microgrid system with two paralleled DG unit

3.3. Case-2: DG units with unequal rating In this study, the rating DG2 is twice that of DG1. The value of the positive-sequence virtual impedance of DG1 is twice of DG2. The control and system parameters are same as that of previous study. The three-phase voltage and current waveforms of the output DG1 , DG2 and PCC using the proposed control strategy are shown in Fig. 9. As shown, it is clearly shown that the current output of the DG2 is twice that of DG1 and the current sharing errors are effectively decreased.

A microgrid with two DG units has been chosen, shown by Fig. 11. The microgrid including two source buses, one critical load bus and non-critical load bus. A balanced three-phase load with star connection (with an impedance ZL ) and a three-phase diode rectifier load is connected to CLB as unbalanced and nonlinear loads, respectively. In order to create unbalanced voltage distortion, one phase of nonlinear load 2 is disconnected. The system parameters for simulation have been demonstrated in Table 2. The details of the voltage unbalance factor (VUF) calculation are illustrated in Fig. 12.

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Fig. 6. Results of the microgrid system with using the proposed control strategy. (a) Output voltages of DG1 . (b) Output currents of DG1 . (c) Output voltages of DG2 (d) Output currents of DG2 . (e) PCC voltages. (f) PCC currents. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Table 2 System parameters with their values. System parameter

Value

LCL filter DC link Voltage Grid voltage amplitude Grid frequency DG feeder (Z1 , Z2 , Z3 ) Nonlinear loads tie lines (Z) Primary control level

Lf = 1.8 mH, Cf = 25 ␮F, Lo = 1.8 mH 650 V 380 V (line to line RMS) 50 Hz R = 0.1 , L = 1.8 mH 0.1 , 1.6 mH Value

Frequency droop slopes Voltage loop PR parameters

Dp = −5.236 × 10−5 rad/s/W kpv = 0.56 kih = 15 (h = 1) and 100 (h = 3), 50 (h = 5) and 100 (h = 7,11,13) kpI = 35 kiIh = 5550 (h = 1), 200 (h = 3), 50 (h = 5), and 100 (h = 7,11, 13) Rv + = 0.3/0.6, Rv − = 1.5/3, Rv 3 = 2/4 Rv 5 = 4/8,Rv 7 = 4/8, Rv 11 = 4/8 and Rv 13 = 4/8  Lv + = 2.5/5 mH ωc = 1

Current loop PR parameters

Virtual resistance (DG1 /DG2 )

Virtual inductance (DG1 /DG2 ) Cut-off frequency for resonant bandwidth control Cut-off frequency of power calculation Secondary control level

ωf = 5 Value kp = 0.75, kI = 15

Frequency proportional and integral term Load parameters

Value

Linear load (ZL ) Nonlinear load 1 Nonlinear load 2

50 , 20 mH RNL =50 , LNL = 0.084 ␮H, CNL = 235 ␮F RNL = 200 ,LNL = 0.084 ␮H,CNL = 235 ␮F

Fig. 7. Power sharing performance with traditional droop control method. (a) Active power sharing. (b) Reactive power sharing.

Table 3 VUF at CLB and DGs output. VUF (%)

DG1

DG2

CLB

With traditional droop control method With using the proposed control strategy

0.077 2.37

0.145 0.675

1.23 0.152

As shown in Table 3, the VUF of the CLB voltage with traditional droop control method is about 1.23%, whereas the proposed control strategy shows values about 0.152%. As a result, CLB voltage unbalance is decreased, while the DG voltage output becomes unbalanced. Furthermore, the VUF of the DG1 is higher than the DG2 value, because of, the feeder impedance between SB1 and CLB is relatively high, also, capacity of DG1 is twice DG2 , and in order to compensate the voltage drops on the feeder impedance and balance CLB voltage; DG1 output voltage should be noticeably distorted.

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Fig. 8. Power sharing performance with proposed control strategy. (a) Active power sharing. (b) Reactive power sharing.

It can be observed in Fig. 13, by proposed control strategy, the active and reactive powers are properly shared among DG units based on their capacity, and the amount of the Q2 supplied by DG2 is accurately twice of the supplied by DG1 . The three-phase voltage and current waveforms of the output DG1 , DG2 and CLB using the traditional droop control method are shown in Fig. 14. In the case of traditional droop control, the virtual positive impedance at fundamental frequency is activated. In traditional droop control method, the output voltage of DG units is balanced, due to the presence of unbalanced voltage drop throughout the feeder’s impedance, CLB voltage will be unbalanced, that in

Fig. 10. Power sharing performance with proposed control strategy. (a) Active power sharing. (b) Reactive power sharing.

Fig. 14, is shown. By using the proposed control strategy, voltage drop across the feeder impedance for each phase is compensated and added to voltage reference generated by the Q–V droop control method, which will lead to unbalance DG units’ output voltage and finally CLB voltage is balanced, that in Fig. 15, is shown. Furthermore, given that the rating DG1 is twice DG2, but the total current supplied by DG units is not properly shared in traditional droop control method. Whereas, by using the proposed control strategy, the power sharing performance is improved as illustrated in Fig. 15. It is clearly shown that the current output of

Fig. 9. Results of the microgrid system with using the proposed control strategy. (a) Output voltages of DG1 . (b) Output currents of DG1 . (c) Output voltages of DG2 . (d) Output currents of DG2 . (e) PCC voltages. (f) PCC currents. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

A. Ranjbaran, M. Ebadian / Electric Power Systems Research 155 (2018) 153–163

161

Fig. 11. Two paralleled DG units in a multibus microgrid system.

Fig. 13. Power sharing performance with proposed control strategy. (a) Active power sharing. (b) Reactive power sharing.

Fig. 12. Block diagram of VUF calculation.

the DG1 is significantly higher, and the current sharing errors are effectively decreased. 3.4.1. Effect of communication delay In this section, performance of the control system in the presence of delays in communication is investigated. For this purpose, communication delays of 0.1 s, 0.2 s and 0.3 s have been investigated. In Fig. 16, the VUF of the CLB voltage for different communication delays is shown. It is obvious that the time delays do not affect the VUF and difference in the transient behavior is negligible.

4. Conclusion and future work This paper presents a novel power control strategy for voltage unbalance and harmonic compensation in an islanded microgrid consisting of the power-electronics-interfaced DG units. The proposed strategy uses the hierarchical control, including primary and secondary control. The primary control is comprised of the droop control method, unbalanced compensation and virtual impedance loop. The virtual impedance loop consists of virtual positiveand negative-sequence at fundamental frequency and the virtual variable harmonic impedance loop at harmonic frequencies. This positive-sequence virtual impedance is considered to enhance the performance of the droop controllers. The negative-sequence virtual impedances compensate voltage distortion of the load voltage

Fig. 14. Results of the microgrid system with traditional droop control method. (a) Output voltages of DG1. (b) Output voltages of DG2. (c) Voltages of CLB. (d) Output currents of DG1. (e) Output currents of DG2. (f) Currents of CLB. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 15. Results of the microgrid system with proposed control strategy. (a) Output voltages of DG1. (b) Output voltages of DG2. (c) Voltages of CLB. (d) Output currents of DG1. (e) Output currents of DG2. (f) Currents of CLB. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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[10] Fig. 16. Effect of communication delay on the VUF of the CLB voltage. [11]

and minimize the negative sequence circulating currents among the DGs. The virtual variable harmonic impedance loop is used for better sharing of harmonic power. The DSC-SOGI is utilized for the decomposition of the DG output currents and extraction of the fundamental positive- and negative-sequence currents as well as the dominant harmonic components. The secondary control level restored amplitude and frequency of the PCC voltage to nominal values. Simulations have been performed and the results show that the proposed strategy is effective to use in microgrid implementations. In respect to the future work, we aim to further evaluate the proposed control method in the real microgrid to validate its effectiveness.

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