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 . 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 .
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.  uses the high reactive power droop gain, which reduces the error of reactive power sharing at the expense of system stability. Ref.  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 , 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.  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.
The following relations can be obtained for highly inductive transmission line
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
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
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 . The control system is simple and has excellent control performance.
3 The novel reactive power control strategy based on virtual flux droop method
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.
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 (10)
where nLi = Li/(w |ΨE|), and it can be seen from the expression of nLi that nLi ∝ Li(i = 1,2).
According to (9), the flux amplitude difference can be obtained with the assumption of n1Q1 = n2Q2 (13)
According to (12), the flux amplitude difference can be (14)
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.
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 (16)
The sum of reactive power deviation is (17)
where N represents the number of DG units participating in reactive power distribution.
Correction value of reference flux amplitude can be obtained (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 (19)
The main purpose of voltage recovery control is to maintain the value of output voltage at rated level. Its expression is (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 (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 . The parameters of two parallel DGs are all the same except for the line inductance, which are listed in Table 1.
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.
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.
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.
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:
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.
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.
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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About the article
Published Online: 2017-12-29
Citation Information: Open Physics, Volume 15, Issue 1, Pages 948–953, ISSN (Online) 2391-5471, DOI: https://doi.org/10.1515/phys-2017-0116.
© 2017 Aimeng Wang and Jia Zhang. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0