A review of droop control techniques for microgrid

Renewable and Sustainable Energy Reviews 76 (2017) 717–727

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Renewable and Sustainable Energy Reviews journal homepage: www.elsevier.com/locate/rser

A review of droop control techniques for microgrid a,⁎

a

MARK a

Usman Bashir Tayab , Mohd Azrik Bin Roslan , Leong Jenn Hwai , Muhammad Kashif a b

a,b

University Malaysia Perlis, Malaysia University Malaysia Sawarak, Malaysia

A R T I C L E I N F O

A BS T RAC T

Keywords: Distributed generation Microgrid Inverter Droop control technique Renewable resources

Coordination of different distributed generation (DG) units is essential to meet the increasing demand for electricity. Many control strategies, such as droop control, master-slave control, and average current-sharing control, have been extensively implemented worldwide to operate parallel-connected inverters for load sharing in DG network. Among these methods, the droop control technique has been widely accepted in the scientific community because of the absence of critical communication links among parallel-connected inverters to coordinate the DG units within a microgrid. Thus, this study highlights the state-of-the-art review of droop control techniques applied currently to coordinate the DG units within a microgrid.

1. Introduction Non-renewable resources, such as diesel, coal, and gas, are major energy sources of electrical energy produced by traditional power generators worldwide. However, the increasing demand for electrical energy, depletion of reserves of non-renewable resources, and generation of electrical energy from non-renewable resources have resulted in environmental pollution [1–3]. Therefore, the development of a distributed generation (DG) system that utilizes renewable resources to generate electricity is necessary [4,5]. DG systems are suitable for providing highly reliable electric power [6]. Several types of energy resources, such as solar thermal panels, photovoltaic panels, fuel cells, and microturbines, are currently available [7,8]. These renewable resources are difficult to connect directly to a utility grid. A microgrid is an interface between distributed renewable resources and the utility grid. This interface is a low-voltage distribution system consisting of DG units, energy storage devices, and load. Furthermore, a microgrid can be operated separately or connected to a main distribution system [9–11]. Fig. 1 illustrates the general architecture of a microgrid [12]. In addition, compared with a single DG unit, a microgrid has high capacity and control flexibility to fulfill power-quality requirements [13]. By contrast, the electric power generated from several renewable resources is in direct current (DC) form and converted to alternating current (AC) by an inverter [14]. Thus, an inverter is a crucial component of a microgrid. Furthermore, an inverter acts as an interface between the DG unit, load, and grid [15]. Inverters are also used parallel to a microgrid to improve performance. Parallel operation of

⁎

inverters often provides high reliability, because the remaining modules can still deliver the required power to the load in case an inverter fails [16]. Several control techniques have been proposed for proper operation of parallel-connected inverters in microgrid. Among these methods, voltage and frequency droop control has gained popularity and is considered as a well-established method [17–19]. Thus, this paper presents an overview of recent studies on the droop control technique. Section 2 provides an overview of the conventional droop control technique. Section 3 presents the virtual impedance loop-based droop control technique. Thereafter, Section 4 discusses the working principle of the adaptive droop and robust droop control technique. Section 5 focuses on simulations to support the analysis. Section 6 provides a discussion on different methods and future work. Finally, Section 7 concludes this report. 2. Conventional droop control The inverter output impedance in the conventional droop control [20–22] is assumed to be purely inductive because of its high inductive line impedance and large inductor filter. The equivalent circuit of two inverters connected in parallel to a point of common coupling bus is shown in Fig. 2(a), and the phasor diagram is shown in Fig. 2(b). In an inductive system, the active and reactive power drawn to a bus from each inverter can be expressed as follows [23,24]:

P=

Corresponding author. E-mail address: [email protected] (U.B. Tayab).

http://dx.doi.org/10.1016/j.rser.2017.03.028 Received 13 May 2016; Received in revised form 22 November 2016; Accepted 8 March 2017 1364-0321/ © 2017 Elsevier Ltd. All rights reserved.

EV sin α , X

(1)

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PV PV

DG Static transfer Main switch AC Grid

DG

Microturbine

DG DG

DG

Microturbine

Gas turbine

Fig. 1. General architecture of a microgrid. (a) Grid-connected microgrid (b) Islanded microgrid.

Fig. 2. (a) Equivalent model of two inverters connected in parallel to point of common coupling bus. 2 (b) Phasor diagram.

Q=

EV cos α − V 2 , X

(2)

where E and V are the amplitudes of the inverter output voltage and the common bus voltage, respectively, α is the power angle, and X is the output reactance of the inverter. Based on Eqs. (1)–(2) and small power angle α(sin α ≈ α and cos α = 1) , the active power injected from the inverter to the common bus is predominantly influenced by the power angle. By contrast, the reactive power is strongly dependent on the amplitude difference between E and V. In addition, the inverter output voltage phase can be changed by altering the inverter output voltage frequency. Consequently, the wireless control of the parallel-connected inverters primarily uses the frequency droop and output voltage droop to control the output power of the inverter. A block diagram of the conventional droop control is shown in Fig. 3. Moreover, the equations of the droop characteristics of P − ω and Q − E in Fig. 4(a) and (b) can be written as follows:

ωΚ = ω• − mΚ PΚ ,

(3)

EΚ = E • − nΚ QΚ ,

(4)

Fig. 3. Block diagram of conventional droop control.

Increasing the droop coefficients results in good power sharing but degraded voltage regulation [25]. The inherent trade-off of this controller is the selection of the droop coefficient value. The main advantage of the droop control technique is its avoidance of critical communication links among parallel-connected inverters. The absence of communication links between parallel-connected inverters provides significant flexibility and high reliability [26]. However, the conventional droop technique has several drawbacks [27–30], such as slow transient response, inherent trade-off between voltage regulation and load sharing, poor harmonic load sharing between parallel-connected inverters in the case of non-linear loads, line impedance mismatch between parallel-connected inverters that affect active and reactive power sharing, and poor performance with renewable energy resources.

where PK , QK , mK , and nK are the real active power output, real reactive power output, frequency droop coefficient, and voltage droop coefficient of the K th inverter, respectively. Furthermore, ω• is the rated frequency, and E • is the rate voltage amplitude. The frequency and voltage droop coefficient are designed from Eqs. (3) and (4), as follows:

mΚ =

Δω , PΚ max

(5)

nΚ =

ΔE , QΚ max

(6)

3. Virtual impedance loop-based droop control The conventional droop control cannot provide a balanced reactive power sharing among parallel-connected inverters under line impedance mismatch. Therefore, the imbalance in reactive power sharing is a serious problem in an AC microgrid. Several studies have achieved balanced reactive power sharing implementing virtual output impedance in droop control method through a fast control loop which emulates the line impedance (Fig. 6) [31,32]. Thus, the reference voltage from each inverter can be modified, as follows:

where ∆ω and ΔE are the maximum allowed deviation of frequency and voltage, respectively. PKmax and QKmax are the nominal active and reactive power supplied by the system, respectively.

Vref = Vo* − Z vIo, 718

(7)

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Fig. 4. (a) P-ω and (b) Q-E droops.

Fig. 5. (a) Equivalent model of a virtual impedance and (b) Phasor diagram.

parallel connected inverters, respectively. In the summation approach, one virtual output impedance is set to zero, and another virtual output impedance is set to emulate the line impedance. Based on Eq. (8) and considering that one line impedance is larger than another, that is, Zl1 > Zl 2 , which permits the selection of Z v1=0 , and Eq. (8) can be simplified as follows:

where Z v is the virtual output impedance. The equivalent model of virtual impedance and the phasor diagram of Z v > Zl are illustrated in Fig. 5(a) and (b), respectively. The virtual output impedance is generally selected to dominate line impedance [33]. Thus, the virtual output impedance can be chosen through the summation approach, in which balanced reactive power sharing is achieved if the voltage drop from every inverter to AC bus is as follows [34]:

Vdrop1 = (Zl1 + Z v1)Il1 = Vdrop2 = (Zl 2 + Z v2 )Il 2,

Z v 2 = Zl 1 − Zl 2 ,

(9)

The value of the virtual impedance is reduced using the summation approach, which minimizes the degradation of voltage regulation. Reactive power sharing is improved if the change in output voltage is markedly higher than the voltage drop across the line than the reactive power.

(8)

Hence, Z v1 and Z v2 are the virtual output impedance of two parallel connected inverters. Furthermore, Zl1 and Zl2 are line impedance of two

3.1. Virtual impedance loop-based droop control for single-phase inductive microgrid Several droop control techniques have been proposed to overcome the limitations of the conventional droop control technique and improve the performance of parallel-connected inverters in DG systems. In [35], an improved droop control is introduced in which an integral-derivative term and virtual output impedance using a highpass filter are added to the conventional static droop technique. This technique achieves good transient response and effectively shares the non-linear load. However, the suitable coefficients of an integralderivative term and filter gain are difficult to choose. In addition, voltage regulation is poor. Voltage regulation is improved by designing a controller using three main loops, namely, inner, intermediate, and outer loops [36,37]. The inner loop is developed using a proportional-integral-derivative controller that can well-regulate voltage. Meanwhile, the intermediate and outer loops are designed based on the droop control technique using a virtual impedance loop. This technique provides proper transient response and excellent active and reactive power sharing without frequency or amplitude steady-state deviations. However, the droop control technique cannot avoid the initial current peaks and provide the hot-swap operation. In [38,39], a modification of the droop control technique is presented. This technique involves a control method that uses adaptive virtual output impedance to achieve effective reactive power sharing. A

Fig. 6. Virtual impedance loop-based droop control.

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soft-start operation is also included to avoid initial current peaks and provide hot-swap operation. In addition, a current harmonic loop is added to properly share the linear and non-linear loads. This loop is often tested to consider different line impedances of two DG units without considering the distinct power capacities of these DG units. In [40], an improved droop control technique using virtual complex impedance is proposed to consider the effects of complex line impedance. This technique provides excellent current sharing and minimizes harmonic circulating currents. However, Q sharing is not presented. Another modified droop control technique that uses voltage amplitude droop loop with zero steady-state error control and virtual impedance loop is presented in [41]. These loops are effective in avoiding frequency deviation and improving the accuracy of the sharing and control of reactive power. However, these loops can increase the total harmonic distortions of voltage components. Therefore, in [42], a voltage amplitude correction method is included to improve the quality of output voltage. The proposed techniques in [35–42] are implemented for islanded microgrid. However, some cases of autonomous operation are required. Thus, an enhanced droop control technique was developed in [43] to achieve the autonomous operation of a parallel-connected inverter. This strategy can accomplish a tight P and Q regulation performance and proper transient response. In [44–46], an improved droop control strategy is implemented in parallel-connected inverters by including a virtual impedance loop, feeder current-sensing loop, and a second-order general-integrator scheme. The accuracy of reactive power sharing and inability to perform the time-derivative function are some issues of these strategies. Furthermore, these strategies can achieve fast transient response, improved current harmonic sharing, and lowest total harmonic distortion of output voltage. Brabandere et al., proposed a virtual impedance droop utilizing a virtual power frame transformation to avoid the coupling between active and reactive power. This method provides excellent voltage and frequency control as well as mitigation of voltage harmonics [47,48].

Fig. 7. Resistive virtual impedance loop-based droop control.

vitiating of Q share performance [59]. However, in [60], the reactive power sharing is improved by including the R-C virtual impedance loop in the conventional droop control. 3.4. Virtual impedance loop-based droop control for three-phase resistive microgrid In [61,62], an enhanced droop control technique was designed by adding a virtual negative impedance to the conventional droop control approach. The enhanced droop control technique can achieve accurate active power sharing although two DG units have different power capacities. Furthermore, voltage double-loop control is added to avoid voltage deviation caused by the P-E droop. 4. Adaptive and robust droop controls The conventional droop control involves several issues to be solved, such as line impedance dependency, inaccurate power sharing, and slow transient response [63]. Consequently, variants of the conventional droop control have been proposed to address these problems.

3.2. Virtual impedance loop-based droop control for three-phase inductive microgrid In [49–52], another novel structure of droop controller utilizing virtual impedance loop is presented. The proposed techniques can generally achieve accurate reactive power sharing and perform stable operation of parallel-connected inverters. The virtual power transformation frame is another interesting structure to implement the droop control with virtual impedance [53]. A transformation frame dependent on R/X value of lines is used to calculate the virtual powers. The P/Q is decoupled if the distributed system is purely inductive or estimation of R/X value is known. Similar to [53], a virtual frequency and voltage frame is proposed [34,54–56]. This strategy also effectively decouples power control and enhances the system stability and transient response. If the line impedance of parallel-connected DG inverters are mismatched, then the transformation angles will vary, and the reference frame will not be synchronized. These phenomena are common drawbacks of a virtual transformation-based controller.

4.1. Adaptive droop control Kim et al., proposed the adaptive droop control strategy in 2002 to considerably maintain the voltage amplitude with accurate reactive power sharing [64]. In this technique, the maximum reactive power Qmax drawn from each unit is stored and compared with reference value of reactive power Qref . If the maximum reactive power is less than the reference value, then the voltage amplitude follows the traditional Q/E droop equation. However, when the maximum reactive power exceeds the reference value, then the voltage amplitude will become as follows [65]:

E = E * − nQ − nadd (Q − Qref ),

(10)

Hence, Q > Qref. The basic concept of adaptive droop control is shown in Fig. 8. The difference between the output reactive power Q and reference value of reactive power Qref is utilized as an additional value to set the desired voltage amplitude. When Q > Qref , the voltage amplitude turns from lines 10 and 20 to lines 11 and 21. The maximum reactive power is stored, and nadd (Qmax − Qref ) is subtracted from the voltage amplitude as a constant value. Therefore, when Q becomes lower than Qref again, the voltage amplitude does not revert to lines 10 and 20 but to lines 12 and 22. This phenomenon can be expressed as Eq. (11).

3.3. Virtual impedance loop-based droop control for single-phase resistive microgrid Droop control for resistive line impedance that uses resistive virtual output impedance and harmonic power-sharing loop is introduced in [57] and shown in Fig. 7. This strategy is based on P-E and Q-ω droops that afford improved dynamic response and active power sharing and often obtains automatic harmonic sharing. In addition, active power sharing can be further improved by applying a new control algorithm presented in [58]. The downside of resistive droop control is the

E = E * − nQ − nadd (Qmax − Qref ), 720

(11)

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Fig. 8. Basic concept of adaptive droop control.

Fig. 11. Parallel-connected inverters in islanded microgrid. Fig. 9. Block diagram of closed-loop system with adaptive droop control.

lel-connected inverters in DG systems is improved by including the following derivative term in the adaptive droop control in [70]

ωK = ωref + kP(PK − PK , ref ) + kP, d

dPK , dt

VK = Vref + kQ(QK − QK , ref ) + kQ, d

dQK , dt

(12)

(13)

The change in the output voltage of an inverter increases the power oscillation in transient conditions. Thus, adaptive transient derivative droops are used in [70] to decrease power oscillation. In [71], a modified derivative controller-based control technique is presented to enhance the performance of the proposed controller in [70]. The proposed control strategy equations that work are defined as follows:

ωK = mK (PK , ref − PK ) + kd

d (PK , ref − PK ), dt

(14)

VK = nK (QK , ref − QK ) + ki

∫t (Qg,ref − Qg)dt,

(15)

Fig. 10. Robust droop control.

4.1.1. Adaptive droop control for single-phase inductive microgrid The adaptive droop control is one of the interesting strategies among several variations of the traditional droop control. Several studies have proposed different approaches to determine the adaptive droop coefficient in adaptive droop control. In [65], a second-order filter and a modified equation of voltage droop were adapted to improve the reactive power sharing and transient response. In [66– 68], the adaptive integral loop technique was implemented to improve power-sharing dynamic response and remedy the effects of line impedance on circulating current, but the control parameters are too complex to determine. In [69], the adaptive droop parameters were predetermined by calculating the microgrid impedance. This technique ensures effective power sharing and reduces line losses.

In [72], another derivative-term-based technique is presented. This technique ensures active damping of power oscillation. In addition, this control strategy yields the desired transient response to avoid the circulating current under different operating conditions. The equations for frequency [Eq. (12)] and voltage [Eq. (13)] droops based on the derivative term in [72] are defined as follows:

ωK = ωn − mpP − mdP

VK = VK − nqQ + nnP

4.1.2. Adaptive droop control for three-phase inductive microgrid

dP dQ + mdQ , dt dt

dP dQ − nnQ , dt dt

(16)

(17)

In addition, the proposed control method decreases the oscilla-

1. Derivative-term-based Technique: The transient response of paral721

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Fig. 12. Active and reactive power.

tolerance. In [76], an optimization-based technique is proposed in which the control parameters are adjusted by compromising between reactive power sharing and voltage regulation. The adaptive droop constants were derived by solving a specific optimization issue. In [77], the optimization-based strategy in [76] is presented, but the adaptive droop constants are determined based on a small signal analysis of the system. This technique improves the stability of the microgrid operation. However, the power sharing performance is not presented. Power sharing is improved using the genetic algo-

tion frequencies and stable power-sharing performance. However, power sharing can be improved using the proposed strategy in [73], as depicted in Fig. 9. 2. Algorithm and Optimization-based Technique: In [74], an algorithm is presented to modify the adaptive droop coefficient based on operating conditions. This technique can improve the active power sharing but does not consider the reactive power sharing. An algorithm to achieve a good reactive power sharing is presented in [75]. However, this algorithm is complex and sensitive to parameter 722

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Fig. 13. Frequency restoration of inverter 1 and 2.

rithm [78], imperialist competitive algorithm [79], and particle swarm optimization [80] to obtain the adaptive droop coefficient, but the improvement is not significant. 3. Theory-based technique: The bifurcation theory is used in [81] to schedule the adaptive droop coefficient. The Kuramoto oscillator non-linear model for determining the optimal droop constants is presented in [82]. These approaches can improve voltage and frequency regulation, as well as produce stable operation in certain cases. However, both approaches are only verified through simulation.

Vo = E * −

(22)

where nP / KeE *is the voltage drop ratio and can be chosen within the required range by selecting a large Ke . The right hand side of Eq. (21) will be same for all parallel connected inverter, as long as the same Ke is selected, which guarantees proper active power sharing. The robust droop constant m and n are calculated using Eqs. (23) and (24), as follows:

n=

Ke ΔE , Pmax

(23)

m=

1 Δω, Qmax

(24)

4.2. Robust droop control The robust droop control is also proposed to eliminate the inherent limitations of conventional droop control.

The active power sharing error is inversely proportional to n / Ke , and voltage drop is directly proportional to n / Ke . For instance, the voltage drop at rated power is nP / KeE *=5%, and the error in the RMS voltage is ∆E / E * =0.5%. Then, the error in the active power sharing is ∆V KeE */(nS*)( E*)o =2.5%, which is acceptable.

4.2.1. Robust droop control for single-phase resistive microgrid The conventional voltage droop can be rewritten as follows:

ΔE = E − E * = nP,

n nP * P = E* − E , Ke KeE *

(18)

where ∆E is zero under grid-connected mode [83]. However, ∆E cannot be zero for islanded mode, because the active power could not be zero. Another problem is the voltage drop caused by the droop and load changing effects. Smaller voltage drop can be achieved by selecting a smaller droop coefficient. However, a larger droop constant need to be selected to achieve fast response. The voltage drop can be obtained by adjusting E * − Vo by a certain way through basic principle of control theory. This strategy is accomplished using the improved droop controller presented in [84], and the strategy is also known as robust droop control. This technique is a control strategy that modifies the droop equation by deducting the RMS of the inverter output voltage from the voltage set point as shown in Fig. 10. This method compensates the voltage drop because of the droop and load effect. Furthermore, it maintains the load voltage within the rated value but with poor reactive power sharing. The robust droop control can be expressed as follows:

4.2.2. Robust droop control for single-phase inductive microgrid Shuai et al., proposed a robust droop controller for single-phase inductive microgrid [85]. This controller considers the impact of line impedance and designed base on signal detection on the high voltage side of the coupled transformer [85]. This strategy can improve voltage regulation and significantly mitigate the line impedance impact on power sharing. McFarlane H infinity synthesis method [86], universal droop controller theory [87,88], small-gain theorem and bounded droop controller theory [89,90] have been applied to robust droop control to ensure stability, yield high robustness, frequency and voltage regulation, and improve the reactive power sharing. In addition, bounded droop controller theory based on robust droop control can yield high load sharing during linear and non-linear loads.

E = Ke(E * − Vo ) − nP,

(19)

ω = ω* + mQ,

(20)

After reviewing the different droop control techniques, we performed a comparative analysis among virtual impedance loop-based droop control, adaptive droop control and conventional droop control through simulation. Fig. 11 presents a block diagram of two parallelconnected inverters in islanded microgrid which is simulated using MATLAB/Simulink. The microgrid consists of two 5KVA inverters those are connected to a common AC bus based on the assumption that the load is connected to a common AC bus. Each inverter consisted of a single

5. Simulation and results

In steady-state form, Eq. (19) can be rewritten as follows:

nP = Ke(E * − Vo ),

(21)

The output voltage can be obtained using Eq. (21) which is described as follows: 723

724

Robust Droop

Adaptive Droop

● ● ● ● ● ●

● Voltage amplitude droop loop+virtual impedance+conventional droop.

● Modified the droop equation by subtracting RMS output voltage value to the voltage set point ● Glover McFarlane H infinity synthesis method, universal droop control theory, small gain theorem and bonded droop controller theory is applied to robust droop for enhance the performance

● Bifurcation theory and Kuramoto Oscillator non-linear model is used to determine the adaptive droop constants

● Algorithm & optimization+adaptive droop control

● Derivative term+adaptive droop control

● Integral loop+adaptive droop control

● Virtual impedance loop through virtual power frame transformation, virtual frequency and voltage frame transformation+conventional droop control ● P/E and Q/ω ● Resistive virtual impedance and harmonic power sharing loop introduced ● R/C virtual output impedance loop+conventional droop control

● Virtual impedance loop+conventional droop control

● Proportional-derivative term, Feeder current sensing loop+virtual output impedance loop+conventional droop control ● Virtual impedance loop through virtual power frame transformation +conventional droop control

● Compensate voltage drop due to load and droop effect ● Ensure the stability ● Good frequency and voltage regulation ● Improve reactive power sharing

● Good transient response ● Excellent power sharing ● Active damping of power oscillations ● Avoid circulating current ● Good transient response ● Improve power sharing performance and system stability ● Good frequency and voltage regulation ● Perform stable operation in certain cases

● Fast dynamic response ● Good active power sharing ● Improve reactive power sharing

● ● ● ● ●

● ● ● ●

● Virtual impedance loop+derivative term+conventional droop control

Virtual Impedance LoopBased Droop

● Virtual complex impedance loop+conventional droop control

● Avoid critical communication link ● Great flexibility ● High reliability

● P/ω and Q/E

Conventional Droop

Fast dynamics response Good power sharing Excellent current sharing Minimize harmonics circulating currents Improve reactive power sharing Prevent frequency deviation Excellent power sharing Perform autonomous operation Decoupled P/Q sharing control Excellent Voltage and frequency control Better voltage harmonic sharing Accurate reactive power sharing Perform stable operation Good dynamics response Decoupled P/Q power control

Advantage

Concept

Control

Table 1 Summary of different droop control methods.

[70–73]

● Virtual reactance need to used minimize the circulating power ● The magnitude and phasor angle of output impedance is difficult to control because the virtual reactance is too dependent on voltage bandwidth ● Improvement is not significant ● Complicated ● Authors did not present experimental validation ● Complicated ● Poor power sharing

[84,85] [86–90]

● Reactive power sharing is poor ● High total harmonic distortion of current components

[81,82]

[74–80]

[65–69]

[60]

● Increase total harmonic distortion ● Virtual reactance need to used minimize the circulating power

[57–59,61,62]

[53–56]

● Difficult to ensure the same transformation angle for all DGs

● Poor reactive power sharing

[49–52]

[47,48]

[43–46]

[41,42]

[40]

● Poor active power sharing

● Difficult to select the proper coefficient of proportionalderivative term for stable operation ● Difficult to implement

● Active power sharing is not considered

● Difficult to choose the suitable coefficient for integral-derivative term and filter gain ● Reactive power sharing is not presented

[31–39]

[25–30]

● ● ● ● ● Slow dynamics response Poor harmonic load sharing Line Impedance mismatch affect power sharing Poor voltage regulation Poor performance with renewable energy resources

Reference

Disadvantage

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metal-oxide-semiconductor field-effect transistor (MOSFET) fullbridge with a switching frequency of 4000 Hz and an LC output filter with the following parameters: L=1 mH, C=20 µF, and Vin =250 V. The rated voltage and system frequency are 118 V RMS and 50 Hz, respectively. However, the line impedances are Z1=0.12+j0.028 and Z 2 =0.24+j0.046. The droop coefficients m1 and m 2 are 0.0008 rad/W.s, while n1 and n 2 are 0.001 V/VAr. The droop coefficients are the same for conventional droop control, and virtual impedance loop-based droop control. However, the concept of design and calculation of virtual impedance proposed by the authors of [37] is used to simulate the virtual impedance loop-based droop control. According to [37], the equation for calculation of virtual impedance is expressed as follows:

Vref = Vo* − L vIo.

previously proposed methods. Thus, these methods can still be improved further. ● Stability issue: Existing droop control methods cannot achieve system stability in case of complex loads, such as induction motor, electric vehicles, and pulsed loads. Thus, control strategies should be proposed to solve the frequency, voltage, and power angle stabilities for these complex loads. ● Trade-off between frequency and active power sharing: The reviewed droop control strategies cannot mitigate the trade-off between frequency and active power sharing. Thus, a hybrid droop control method can be derived to resolve this issue. ● Integration of renewable energy resources: The droop control method has poor performance with renewable energy resources, such as photovoltaic and wind turbine. Existing droop control methods can be modified to mitigate this problem.

(25)

Based on Eq. (25), the value of virtual impedance for the given system parameter is L v =j0.010. The concept of adaptive droop control presented by the authors of [73] is chosen for the simulation. The adaptive droop constants mp, mi , md , np , and ni are 0.0015 W/rad, 0.0018 W.s/rad, 7x10−7 W/rad.s, 0.0004 VAr/V, and 0.15 VAr.s/V, respectively. The simulation result in Fig. 12 shows the waveforms of active (P1, P2, PLoad ) and reactive power (Q1, Q2 , QLoad ) of two parallel-connected inverters and load, which were obtained by applying conventional droop control, virtual impedance loop-based droop control, and adaptive droop control. It can be seen from Fig. 12 that the virtual impedance loop-based droop control and adaptive droop control minimize the effects of impedance mismatch and improve power sharing compared with the conventional droop control. In addition, the adaptive droop control provides the highest active and reactive power among the simulated techniques. Fig. 13. depicts the frequency restoration of two parallel-connected inverters. As seen, the virtual impedance loop-based droop control and adaptive droop control achieves good frequency restoration of two parallel-connected inverters, while the conventional droop control results in a static frequency deviation.

7. Conclusion In this paper, a comprehensive review of recent studies on droop control technique is presented and discussed. Based on the preceding discussion, the variations of the droop control technique eliminates the inherent limitations of the conventional droop control (i.e., effect of impedance mismatch on active and reactive power sharing, frequency deviation, and dynamic response). In addition, the review shows that adapting a single control strategy for all applications or improving the weakness of conventional droop control by one variation is difficult. However, a deep understanding of the variations of the droop control technique can help to address their weaknesses and enhance the design and implementation of a microgrid. Basic simulation results are also presented to support the analysis. Furthermore, the different droop control methods are summarized in Table 1. References [1] Carreras BA, et al. Evidence for self-organized criticality in a time series of electric power system blackouts. IEEE Trans Circuits Syst: Regul Pap 2004;51:1733–40. [2] Nichols DK, et al. Validation of the CERTS microgrid concept the CEC/CERTS microgrid testbed. In: Proceedings of the 2006 IEEE power engineering society general meetin"g. 2006. [3] Barklund E, et al. Energy management in autonomous microgrid using stabilityconstrained droop control of inverters. IEEE Trans Power Electron 2008;23:2346–52. [4] Su S, et al. Self-organized criticality of power system faults and its application in adaptation to extreme climate. Chin Sci Bull 2009;54:1251–9. [5] Satish B, Bhuvaneswari S. Control of microgrid: a review. In: Proceedings of the 2014 international conference on advances in green energy (ICAGE). 2014. pp. 18– 25. [6] Lassetter R, et al. Integration of distributed energy resources: the CERTS microgrid concept. CERT Rep 2002. [7] Kyoungsoo R, Rahman S. Two-loop controller for maximizing performance of a grid-connected photovoltaic-fuel cell hybrid power plant. IEEE Trans Energy Convers 1998;13:276–81. [8] Lasseter R, Piagi P. Providing premium power through distributed resources. In: Proceedings of the 33rd annual hawaii international conference on system sciences. 2000. pp. 1–9. [9] Katiraei F, Iravani MR. Power management strategies for a microgrid with multiple distributed generation units. IEEE Trans Power Syst 2006;21:1821–31. [10] Piagi P, Lasseter RH. Autonomous control of microgrids. In: Proceedings of the 2006 IEEE power engineering society general meeting. 2006. [11] Zeng Z, et al. Study on small signal stability of microgrids: a review and a new approach. Renew Sustain Energy Rev 2011;15:4818–28. [12] Chicco G, Mancarella P. Distributed multi-generation: a comprehensive view. Renew Sustain Energy Rev 2009;13:535–51. [13] Li YW, Kao CN. An accurate power control strategy for power electronics-interfaced distributed generation units operating in a low-voltage multibus microgrid. IEEE Trans Power Electron 2009;24:2977–88. [14] Osika O. Stability of microgrids and inverter-dominated grids with high share of decentralized sources. Kassel University Press; 2005. [15] Vandoor TL, et al. A control strategy for islanded microgrids with DC-link voltage control. IEEE Trans Power Deliv 2011;26:703–13. [16] Mohd A, et al. Review of control techniques for inverters parallel operation. Electr Power Syst Res 2010;80:1477–87. [17] Reza M, et al. Dynamic stability of power systems with power electronic interfaced DG. In: Proceedings of the 2006 IEEE PES power systems conference and exposition. 2006. pp. 1423–1428.

6. Discussion of different methods and future work From the previous discussion, it can be concluded that each of the proposed control strategy has its own characteristics, advantages, drawbacks, and applications. The droop control techniques are based on local measurements of network state variables. These variables totally distribute the DG and provide redundancy, because they avoid critical communication link for reliable operation. The absence of communication link provides high flexibility, expandability, modularity, and redundancy. In contrast, the conventional droop control displays several drawbacks, and these issues are listed in Table 1. Different variations, such as virtual impedance loop-based droop, adaptive droop, and robust droop, have been proposed to overcome the limitations of conventional droop. The virtual impedance loopbased droop control can provide accurate reactive power sharing among parallel-connected DG inverter. However, this control presents some limitations, such as degradation of voltage regulation and increase in no load voltage. The adaptive and robust droop control method provide excellent voltage regulation and reactive power sharing. However, these methods result in poor active power and load harmonic sharing. Therefore, based on the overall discussion on the control strategies for an AC microgrid, reports on the following topics can resolve the presented issues: ● Harmonic load sharing: Droop control methods guarantee accurate active and reactive power sharing in case of non-linear load. However, desired harmonic load sharing cannot be achieved from

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