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# Open Physics

### formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina

IMPACT FACTOR 2018: 1.005

CiteScore 2018: 1.01

SCImago Journal Rank (SJR) 2018: 0.237
Source Normalized Impact per Paper (SNIP) 2018: 0.541

ICV 2017: 162.45

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2391-5471
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Volume 15, Issue 1

# An accurate reactive power control study in virtual flux droop control

Aimeng Wang
• Corresponding author
• State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Baoding, China
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• Other articles by this author:
/ Jia Zhang
• State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Baoding, China
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Published Online: 2017-12-29 | DOI: https://doi.org/10.1515/phys-2017-0116

## Abstract

This paper investigates the problem of reactive power sharing based on virtual flux droop method. Firstly, flux droop control method is derived, where complicated multiple feedback loops and parameter regulation are avoided. Then, the reasons for inaccurate reactive power sharing are theoretically analyzed. Further, a novel reactive power control scheme is proposed which consists of three parts: compensation control, voltage recovery control and flux droop control. Finally, the proposed reactive power control strategy is verified in a simplified microgrid model with two parallel DGs. The simulation results show that the proposed control scheme can achieve accurate reactive power sharing and zero deviation of voltage. Meanwhile, it has some advantages of simple control and excellent dynamic and static performance.

PACS: 88.05.Ec

## 1 Introduction

Due to environmental, social and geographical constraints, traditional power supply is almost saturated. In recent years, microgrid technology has developed rapidly, which provides a new choice for traditional power grid [1]. There are two main modes of operation in microgrid: grid connected mode or islanded mode. When faults occur, microgrid will automatically separate from the large power grid, which ensures the flexibility and reliability of power supply [2].

Reactive power sharing among DGs is an important research field of microgrid. Virtual impedance is introduced to decouple active and reactive powers in low voltage microgrid. However, the drop of voltage will be increased with the adoption of virtual impedance [3,4]. Ref. [5] uses the high reactive power droop gain, which reduces the error of reactive power sharing at the expense of system stability. Ref. [6] improves the accuracy of reactive power allocation by injecting small real power disturbances. But in this method active and reactive powers affect each other, and the control performance is sensitive to the load change. In [7], an adaptive voltage droop control strategy is proposed with the consideration of voltage drop across transmission line and reactive power sharing. Nevertheless, the strategy needs to know the parameters of lines and system stability can be affected by some small errors.

All the aforementioned control schemes are based on voltage-frequency droop method, which requires multiple feedback loops and PI regulations. Ref. [8] proposes a novel virtual flux droop control method, where flux and angle can be controlled by a direct flux controller without complex multiple feedback loops and PI regulations. The control strategy is very simple and has excellent static and dynamic performance.

This paper proposes a novel reactive power control strategy based on virtual flux droop. The paper is organized as follows: In section 2, flux droop control method is introduced briefly for further study. In section 3, the factors influencing reactive power sharing are analyzed. On this basis, a new reactive power droop controller is designed with the consideration of accurate reactive power sharing and voltage recovery. In section 4, a simulation is conducted in a microgrid model to verify the effectiveness of the proposed control strategy.

## 2 Virtual flux droop control

The equivalent circuit of an inverter in microgrid is shown in Figure 1. In Figure 1, L and R are the line parameters; V, E and I denote inverter side voltage, load side voltage and the line current respectively; ϕV and ϕE represent the phase angle of V and E; P and Q are the average real and reactive powers.

Figure 1

Equivalent circuit of an inverter in microgrid

The following relations can be obtained for highly inductive transmission line

$V=LdIdt+E$(1)

$S=P+jQ=I∗E$(2)

ΨV and ΨE are the inverter side flux and load side flux which are obtained by the time integration of V and E. They satisfy

$ψV=∫−∞tVdt$(3)

$ψE=∫−∞tEdt$(4)

Combining (1) (3) (4), the following formula can be obtained $I=ψV−ψEL$(5)

By substituting (4) (5) into (2), powers supplied to the load can be obtained

$P=wψVψELsin⁡δ$(6)

$Q=wψEL(ψVcos⁡δ−ψE)$(7)

Considering the value of δ is typically small, active and reactive powers can be controlled by δ and |ΨV|, respectively. Thus the virtual flux droop formulas can be obtained

$δ=δn−m(P−Pn)$(8)

$ψV=ψVn−n(Q−Qn)$(9)

where δn and |ΨV|n are the nominal flux angle difference and amplitude of inverter flux; Pn and Qn are the rated active and reactive powers; m and n are the droop coefficients of the P - δ and Q — |ΨV|.

Figure 2 is the overall control structure of flux droop method, which consists of two parts: flux droop controller and direct flux controller. As shown in Figure 2, |ΨV|refand δref from flux droop controller are compared with their actual values to get deviation signals. Then, deviation signals combined with the current position of inverter flux are used to select the proper voltage vectors according to a switching table during each period [9]. The control system is simple and has excellent control performance.

Figure 2

The overall control block diagram of flux droop control

## 3.1 Factors affecting reactive power distribution

Figure 3 shows the equivalent circuit of power sharing between two parallel DGs. In Figure 3, |ΨVi| and ϕfVi are the inverter flux amplitude and angle (i = 1, 2); PL and QL are the load demand powers.

Figure 3

The power sharing circuit of two parallel DGs

When the voltage drop of transmission line is considered (Note that the line resistance can be neglected in this paper), the relationship between V and E can be expressed as $V−E=QXV≈QXE$(10)

According to (3) (4), the relation between the amplitude of flux and voltage is $V=wψV,E=wψE$(11)

Substituting (11) into (10), the difference between |ΨVi|and |ΨE| is $ψVi−ψE=nLiQi$(12)

where nLi = Li/(w |ΨE|), and it can be seen from the expression of nLi that nLiLi(i = 1,2).

According to (9), the flux amplitude difference can be obtained with the assumption of n1Q1 = n2Q2 $ψV1−ψV2=n2Q2−n1Q1$(13)

According to (12), the flux amplitude difference can be $ψV1−ψV2=nL1Q1−nL2Q2$(14)

Combining (13) (14), the reactive power distribution formula can be obtained $Q1Q2=n2+nL2n1+nL1$(15)

It can be seen from (15) that the accuracy of reactive power sharing is affected by droop gains as well as line impedance. Due to the disperse geographical locations of DGs, the line impedance usually does not satisfy the inverse proportional relationship to DGs’ rated capacities, so the reactive power sharing error is usually unavoidable.

## 3.2 The novel reactive power droop controller

Figure 4 is the principle diagram of the proposed power control strategy, which includes active power control and the novel reactive power control. The novel reactive power controller consists of three parts: reactive power compensation control, flux droop control and voltage recovery control, which ensures accurate power sharing and voltage recovery simultaneously. Because the main purpose of this paper is the allocation of reactive power, active power control is not discussed here.

Figure 4

The novel control structure of the proposed power control strategy

Reactive power compensation control is mainly to implement accurate reactive power sharing without affecting system stability. In reactive power compensation control, the reactive power deviation from rated power of i-th DG is given by $ΔQi=Qi−Qin$(16)

The sum of reactive power deviation is $ΔQtot=∑i=1NΔQi$(17)

where N represents the number of DG units participating in reactive power distribution.

Correction value of reference flux amplitude can be obtained $ΔψViref1=kc∫(ciΔQtot−ΔQi)$(18)

where compensation coefficient kc is all the same for DGi, and its value is closely related to the stability of system, so it should be properly selected. ci is the partition coefficient, which is determined by droop gains $ci=1/ni∑j=1N(1/nj)$(19)

The main purpose of voltage recovery control is to maintain the value of output voltage at rated level. Its expression is $ΔψViref2=kv∫(En−Ei)dt$(20)

where voltage recovery coefficient kv is also the same for every DG, |En| and |Ei| denotes the amplitude of nominal and actual output voltage.

By combining these three control modules, the expression of the novel reactive power controller can be obtained $ψViref=ψVn−ni(Qin−Qi)+kc∫(ciΔQtot−ΔQi)dt+kv∫(En−Ei)dt$(21)

After obtaining the values of |ΨVi|ref and δiref, they are sent to direct flux controller and controlled directly by two hysteresis comparators, which is as shown in Figure 2. The proposed control scheme can implement accurate reactive power sharing as well as voltage recovery. Meanwhile, it has some advantages of simple control and excellent control performance.

## 4 Simulation and analysis

To verify the effectiveness of the novel reactive power control strategy, a simplified microgrid model with two parallel DGs is built by Matlab/Simulink, as shown in Figure 5 [10]. The parameters of two parallel DGs are all the same except for the line inductance, which are listed in Table 1.

Figure 5

Simplified microgrid model with two parallel DGs

Table 1

Simulation parameters

Figures 6(a) and 6(b) show the reactive power sharing before and after adopting the novel reactive power controller. In the example studied in this paper, reactive power sharing among two parallel DGs should be identical. However, there is reactive power allocation error in traditional flux droop control due to the mismatch of line inductance. In the proposed control strategy, compensation control can help eliminate reactive power sharing error and achieve accurate power sharing.

Figure 6

Reactive power sharing under two control strategies. (a) adopting traditional flux droop method. (b) adopting the proposed control strategy

In the novel reactive power control strategy, voltage recovery control can make the voltage deviation caused by droop control to be zero. Figure 7 shows the voltage amplitudes of two parallel inverters. It can be seen from Figure 7 that the output voltages of two parallel inverters are stabilized at the rated value.

Figure 7

The voltage amplitudes of two parallel inverters after adopting voltage recovery control

In order to further verify the effectiveness of the novel reactive power controller, the output frequency and voltage are analyzed. Figure 8(a) is the output frequency, whose value is fixed around the rated value due to the adoption of angle droop instead of direct frequency droop control. From Figure 8(b), it can be seen that the output voltage is very stable and sinusoidal. Figure 8(c) is the Fourier analysis of the output voltage. It shows that the output voltage has good steady performance with only 0.47% of total harmonic distortion.

Figure 8

The voltage amplitudes of two parallel inverters after adopting voltage recovery control

## 5 Conclusion

To solve the problem of inaccurate reactive power sharing in flux droop control, a novel reactive power control scheme is proposed in this paper. The following conclusions can be drawn by analyzing simulation results:

1. In the novel reactive power controller, compensation control can effectively eliminate reactive power sharing error caused by the line inductance mismatch. Meanwhile, the voltage recovery control can maintain the output voltage at the rated value.

2. The novel control strategy based on flux droop method is very simple which replaces complicated multiple feedback loops with direct flux control. What’s more, the proposed control scheme has better characteristics of voltage and frequency, where zero deviations of frequency and voltage can be obtained and voltage has excellent static performance as well.

## Acknowledgement

The Open Subject of State Key Laboratory of Alternative Electrical Power System with Renewable Energy Sources (LAPS16023); Beijing Natural Science Foundation (3172037).

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Accepted: 2017-11-12

Published Online: 2017-12-29

Citation Information: Open Physics, Volume 15, Issue 1, Pages 948–953, ISSN (Online) 2391-5471,

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