# An Improved Fuzzy Voltage Compensation Control Strategy for Parallel Inverter

Authors: Guangyu Song; Xinghua Liu; Jiaqiang Tian; Peng Wang
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

With the rapid development of microgrids, voltage drop has become one of the focuses on the research of microgrid stability and grid-connected operation. In this article, an improved fuzzy voltage compensation control strategy (FVCC) is proposed to solve the bus voltage drop problem. This method takes the influence of feeder impedance into account, and there is no need to accurately measure the feeder impedance value. Since droop control and feeder impedance can lead to voltage drop and bus voltage instability, fuzzy control is applied to compensate bus voltage. Specifically, aiming at the voltage drop caused by droop control, an adaptive fuzzy controller is designed to automatically find suitable gain parameters to reduce the voltage difference. In addition, bus voltage gain module is added to compensate the voltage consumed by feeder impedance. The compensation only needs to measure the voltage at both ends of the line, without testing the line parameters. Finally, the simulation results show that the control strategy achieves the expected effect.


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## Body

## 1. Introduction

With the development of the power industry in the past decades, the conventional power generation modes based on nonrenewable energy such as coal are gradually replaced by distributed generation (DG) technologies based on renewable energy [1, 2]. Green energy and clean energy better meet the development trend of modern society. In particular, distributed generation, represented by photovoltaics and wind energy, forms a microgrid, which is connected to the public grid [3, 4]. The microgrid is connected to the public grid in parallel with the load. It is generally built on the load side. This power generation way reduces the problems of voltage loss, power mass defect, power oscillation [5], and power shortage caused by long-distance power transmission [6]. There must be a large number of electronic interface devices in the microgrid [7], such as inverter [8, 9]. Thus, the inverter and its characteristics have become one of the hotspots of scholars' research [10–12].Due to the limitation of the communication network control mode, droop control without communication technology is widely used in parallel systems to enhance the power quality and stability of the system [13]. Conventional droop control [14] simulates the characteristics of synchronous generators. By controlling the power P and Q of the system, they form a linear decoupling relationship with voltage and frequency, respectively [15, 16]. However, due to the limitations of conventional droop control, when there are differences among the parameters of line impedance [17–19], power electronic equipment [20], and filter device [7, 13] in a parallel system, it can lead to system voltage quality drop and power instability. In [17], the inaccurate power distribution between DGs is caused by the difference in line impedance. In [18], the difference between different lines is compensated by combining virtual impedance (VI) and droop control, but the voltage loss and errors are large. Hu et al. [19] use voltage information to control the rational distribution of output power in real time, but the addition of a communication network and processor increases the complexity and instability of the system.To solve the voltage quality drop and power distribution problems of the parallel system, different improvement schemes are put forward. In [21], in order to compensate voltage deviation, an event-triggered microgrid control strategy is proposed. A multiagent model with consistent characteristics is established through nonlinear state-space equation (SSE) to track voltage deviation and achieve power balance. However, the designed network has communication requirements, which is prone to control delay. The calculation process is also complicated. From the research and analysis of [22], peak cutting and valley filling of the DC bus voltage can be realized through the mode of on-off between the thermal storage system (TSS) and the bus, but this control mode has limitations; that is, the efficiency and reliability of communication can affect the voltage control. In the research design of [23], the output voltage is replaced by a virtual voltage to reduce the voltage deviation, and the droop coefficient is set by increasing the inverse ratio factor. However, this design takes the unknown line impedance parameters into account too simply, and the setting of the droop coefficient does not have a reasonable fitness. Only the coefficient is reduced without considering the influence of this reduction on power. Dam and Lee [24] propose a scheme of power control and voltage recovery for DC microgrid. The shift voltage is introduced to compensate the bus voltage drop caused by the droop controller, but it ignores the voltage consumption caused by the impedance of DC line, which is not small. In [25], a control strategy to enhance the stability and power sharing of the DC/AC converter is proposed. Virtual impedance is set to adjust the output impedance value of the converter. The power distribution effect of the load is good, but the voltage loss of the whole system cannot be reasonably considered. In the existing work of [26], under the condition of no communication, the range of parameters can be tracked and power sharing can be realized by adjusting the VI value. However, for the voltage balance and unknown feeder impedance, setting the VI value is a huge challenge.With the shortcomings of existing work, a fuzzy voltage compensation control strategy is designed to solve the voltage drop problem in this article. This approach compensates voltage loss without the assistance of communication devices. The main contributions of this article are summarized as follows:(1)
With the voltage drop from source to load in a microgrid system, the leading cause of voltage loss is analyzed, and then, an improved fuzzy voltage compensation control strategy is proposed. Compared with [23, 24, 26], instead of ignoring the influence of the line impedance or calculating its value, a voltage gain module is developed to compensate the voltage loss on the line. The voltage is improved from 177.94 V to 210.69 V, and the stability of power sharing is greater.(2)
Fuzzy control theory is applied to droop gain, and an adaptive variable coefficient fuzzy controller is designed, which makes droop gain change automatically within the allowable range. In contrast, it is not necessary to restore the voltage by reducing the droop coefficient without restriction, which leads to increased power loss in [23]. What’ more, compared with [19, 21], the performance of the system is no longer limited by communication.(3)
With the comparison of other existing control methods and parameter sensitivity, the simulation tests are carried out to verify the voltage recovery ability and stability under various conditions. The Case comparison results prove the effectiveness and good performance of the system.The remainder of this article is organized as follows. Section2 contains definitions, models, and main analysis. It can be obtained from Section 3 that voltage gain and fuzzy intelligent control are introduced to achieve voltage compensation and reduce the voltage deviation. Section 4 indicates the comparison results of different cases. Finally, conclusion and prospect are given in Section 5.


## 2. Analysis of Power Characteristic

With the inspiration from [27, 28], the equivalent circuit of an inverter system is shown in Figure 1. Udc represents analog photovoltaic, and LC filters (passive filter) are applied to the system. The inverter and the power supply can be regarded as a whole. Then, referring to Thevenin's theorem, inverter output current (IOC) is(1)I˙o=Uo∠φ−UB∠0ZL∠θ.Figure 1
Equivalent circuit of an inverter system.Uo and φ are the amplitude and phase angle of the inverter output voltage (IOV), respectively, and θ is the phase angle of feeder impedance. With the definition of apparent power, the active power and reactive power output by the parallel inverter can be presented as follows:(2)S=U˙BI˙o∗=U˙BUo∠−φ−UB∠0ZL∠−θ=UBUocosφcosθ+UBUosinφsinθ−UB2cosθZL+jUBUocosφsinθ−UBUosinφcosθ−UB2sinθZL.In a low-voltage microgrid, the line impedance is usually resistive. Therefore, there isRL >> XL. The impedance phase angle θ  ˜  0. Since the output voltage phase shift angle φ is relatively small in the system, it can be obtained that sinφ ≈ φ and cosφ ≈ 1. Equation (2) can be simplified as(3)P=UBUo−UBRL,Q=−UBUoφRL.In the resistive line (θ ˜ 0°), the output power of the inverter is mainly determined by output voltage Uo and phase shift angle φ. Furthermore, the output power is also affected by line impedance and bus voltage. Hence, compensating the bus voltage is also helpful to ensure the power quality.Similar to [29], the equivalent circuit model (ECM) of the ith and jth parallel inverters is shown in Figure 2. Ei∠δi is the no-load voltage of the inverter, and Zoi is the equivalent output impedance of the inverter.Figure 2
ECM of parallel inverters.With the relationship between power angleδ and angular frequency ω (ω = dδ/dt), the conventional droop control equation can be given as(4)ωi=ω∗+miQi,(5)Ei=E∗−niPi,where E∗ is the reference value of DG no-load voltage, and Ei and ωi are the measured voltage and angular frequency. Combining equation (3) with equations (4) and (5), the output power of the ith DG is further obtained as follows:(6)Pi=UBE∗−UBRsi+RLi+niUB.(7)Qi=ωB−ω∗UBEisRsi+RLi+miUBEi,where Rsi is the filter inductance resistance. The reactive power distribution is not affected by the equivalent impedance due to the integration link. Only the active power sharing, which is determined by equivalent impedance, needs to be considered.In equation (5), the voltage deviation ∆Ei of the inverter system is smaller when the droop gain coefficient ni is smaller. Consequently, to reduce the voltage loss, the gain coefficient should be selected as small as possible. However, the power difference can be shown as(8)ΔPi=P∗−Pi=1niΔEi.Under the condition of constant voltage difference, the power loss ∆Pi depends on the gain coefficient ni. The power loss is smaller when the gain coefficient is larger. There is a contradiction about ni between equations (6) and (8). The system needs to choose an appropriate gain coefficient ni.For conventional droop control, it mainly reflects the relationship between power, voltage, and frequency. During the system dynamic operation, whether it is the system error or the external environment disturbance, both the IOV and the system frequencyf can result in the output power loss (∆P, ∆Q). Uo can be regarded as Ei here. Furthermore, the power change rate can be greatly presented as(9)ΔPi=UBZLcosφicosθi+sinφisinθiΔEi+Eicosφisinθi−sinφicosθiΔφi,ΔQi=UBZLcosφisinθi−sinφicosθiΔEi−Eicosφicosθi+sinφisinθiΔφi.Then, it can be simplified to the equation of state as follows:(10)ΔPΔQ=UBZLcosφ−θEisinφ−θsinφ−θ−Eicosφ−θΔEΔφ.Now, with the deviation of the system, there is the following relationship:(11)ΔEi=niΔPi,Δωi=−miΔQi.Only the system deviation is considered here, and the other interferences and errors are ignored. Applying the low-pass filter (LPF), it can be indicated as follows:(12)ΔEi=niUBZLicosφi−θiΔEi+Eisinφi−θiΔφiwns+wn,sΔφi=−miUBZLisinφi−θiΔEi−Eicosφi−θiΔφiwns+wn.Then, the system with deviation can be expressed as(13)s3+cs2+bs+a=0,where(13a)c=−2ZLi2wn+niUBZLiwncosφi−θi−ZLi2,(13b)b=−niUBZLiwn2cosφi−θi+miUBZLiwnEicosφi−θi−ZLi2wn2ZLi2,(13c)a=−A+B+CZLi2,where(13d)A=miUBEiZLiwn2cosφi−θi,B=−miniUB2Eiwn2cos2φi−θi,C=−miniUB2Eiwn2sin2φi−θi.Combined with the system root locus diagram and the corresponding parameters in Table1, the system stability and the model characteristics can be analyzed. Figures 3(a) and 3(b) exhibit system root locus diagrams. When the system parameter, that is, droop gain, changes, the system stability is gradually reduced or even the system is in an unstable state. A set of appropriate gain coefficients is particularly more important for the system stability, and it is not allowed to be too large or too small. By setting the poles needed, the most reasonable parameters can be obtained. The optimal performance of the system can be achieved with this approach.Table 1
Parameters of the control system.
ParametersValuesUnitsOutput reference voltageE311VLine impedance amplitudeZline0.1ΩLine impedance angleθ45°Active power gain coefficientni2 × 10−4—Reactive power gain coefficientmi3 × 10−5—Effective value of bus voltageUB220VOutput reference voltage phase angleφ36.9°Cut-off frequency of low-pass filterωn31.4rad/sFigure 3
System root locus diagram. (a) 3 × 10−4 ≤ ni ≤ 3 × 10−6, mi = 3 × 10−5. (b) 3 × 10−4 ≤ mi ≤ 3 × 10−6, ni = 3 × 10−4.
(a)(b)In Figure3, the variables ni and mi are both selected from 3 × 10−4 to 3 × 10−6. With the decrease of ni and mi, the poles move rapidly to the negative half axis of the horizontal axis, and the root locus gain also increases rapidly. More importantly, the system remains stable all the time.


## 3. The Proposed Improved Fuzzy Voltage Compensation Control Strategy

In the power system, it is difficult to accurately measure the line impedance. Although the difference between lines can be compensated by VI in [18], it is not considered either. In [23], the proposed VI droop control method eliminates the voltage difference by setting VI to guarantee each IOV is the average of all parallel VSI voltages. However, the premise of this method is the fact that the line impedance and local load can be ignored. Reference [23] achieves the purpose of reducing voltage drop by decreasing the droop coefficient, but the specific range of coefficient is not designed. Similarly, reference [24] ensures the same IOV by setting VI. However, in order to keep the constant output voltage of the bus, the equivalent line impedance r’ is also ignored, as follows:(14)VLO=Vvir−iorL′.Based on [23, 24], their characteristics can be used to develop ideas, make improvements, and achieve the purpose of compensating voltage loss without involving line impedance. In this section, note that all factors, which are much comprehensive and concrete than those in [23, 24], resulting in voltage loss have been found and considered. They consist of two parts:(15)ΔEi=E∗−Ei=niPi,ΔUZ=ZiIoi=Ei−UB,where ∆Ei means the voltage difference generated by droop control and ∆UZ means the voltage deviation consumed by equivalent impedance.Therefore, an improved FVCC strategy is proposed to compensate the voltage drop of the bus. This strategy can improve the bus voltage level, making it more conducive to grid-connected operation at any time. It also has both rapid response capability and intelligence. The control strategy consists of two parts. One is the compensation of the voltage consumed by the equivalent impedance. The other is to improve the voltage drop caused by the conventional droop effect. On the one hand, to significantly reduce the voltage loss, the impedance voltage compensation (E∗ − UB) is added in the active power control link. The voltage gain is introduced together. On the other hand, to guarantee the output voltage within a certain expected range, the fuzzy controller is designed to dynamically adjust droop gain. Controller’s droop parameters can auto-revise to adjust voltage appropriately when the condition due to the external environment and electronic devices changes uncontrollably. The proposed improved FVCC is depicted in Figure 4.Figure 4
The improved FVCC.In the power calculation module, the instantaneous values of active powerp and reactive power q are obtained by the linear operation of voltage and current. A low-pass filter (LPF) is used to filter out harmonics and output fundamental power values (P¯, Q¯). The power calculation process is expressed in Figure 5.Figure 5
Power calculation process.The integrator in the reactive power loop ensures that the output reactive power is not controlled by equivalent impedance. Since this method can reduce the calculation error and noise interference, the controller has better robustness. In this controller, the control equation can be described as(16)ωi=ω∗+miQi,Ei=kpE∗−UB−niPi.In the fuzzy process of the proposed FVCC, as depicted in Figure6, voltage difference eE(t) and the rate of change of voltage difference ecE(t) are selected as two input variables of the controller, and ∆ni is selected as the output variable of the controller. eE(t) and ecE(t) are defined as(17)eEt=E∗−Ei,ecEt=dE∗−Ei.dtFigure 6
Fuzzy process of FVCC.The gain coefficient has the following relationship:(18)ni=ni∗+Δni.


### 3.1. Fuzzification Process

Based on the national voltage standard that the fluctuation range of the generator output voltage should be ±5% of the rated value, the allowable range of output voltageEi is set as [209, 231] V. Therefore, set the domain XeE of eE(t) as [−11, 11] V. The domain XecE of ecE(t) is [−11, 11] V/s. The interval X∆ni of ∆ni is [−2 × 10−4, 2 × 10−4]. Then, the discrete fuzzy sets Y are selected as {-3, -2, -1, 0, 1, 2, 3}. To unify the dimensions, the input and output variables are normalized. The quantization factors k1 of eE(t) and k2 of ecE(t) and the proportion factor ku of ∆ni are calculated accordingly the following formula:(19)k1=yxeE=311=0.2727,k2=yxecE=311=0.2727,ku=xΔniy=2×10−43=6.6×10−5,where xeE, xecE, and x∆ni and y are the absolute value of the interval boundary.Note that the input and output variables are all within the fuzzy subsets {−3, −2, −1, 0, 1, 2, 3}. The fuzzy subsets divided into seven equal parts can be defined as {NB, NM, NS, ZO, PS, PM, PB}. In language form, the meanings of these elements are as follows {negative big, negative middle, negative small, zero, positive small, positive middle, positive big}. The variables of FVCC adopt a triangular membership function. Figure7 shows membership function images of MfeE(t), MfecE(t), and Mf∆n.Figure 7
Membership functionMfeE(t), MfecE(t), and Mf∆n.


### 3.2. Fuzzy Reasoning Process

A fuzzy toolbox has been increasingly applied to make fuzzy rules and select calculation methods in MATLAB. Its four basic steps such as “and, or, implication and aggregation,” all adopt the max-min method. With the engineering experience, the fuzzy rules with two inputs and one output are established. The fuzzy control rules table ofeE(t), ecE(t), and ∆ni is shown in Table 2.Table 2
Fuzzy control rules.
ecE(t)eE(t)NBNMNSZOPSPMPBNBPBPBPMPMPSZOZONMPBPBPMPSPSZONSNSPMPMPMPSZONSNSZOPMPMPSZONSNMNMPSPSPSZONSNSNMNMPMPSZONSNMNMNMNBPBZOZONMNMNMNBNBThe fuzzy statement is defined as “ifeE(t) = NB and ecE(t) = NB then ∆ni = PB.” Accordingly, the fuzzy rule surface diagram of the FVCC is depicted in Figure 8.Figure 8
Fuzzy rule surface diagram.


### 3.3. Defuzzification Process

The output results have no dimension in this stage. The values required by the system must be handled by the proportion module. At last, the developed controller applies the Mamdani method to fuzzy reasoning calculation and the Centroid method to the defuzzification process.The application of the fuzzy controller can effectively reduce the calculation amount of complex models and the difficulty of model analysis. The complex nonlinear problems are transformed into language form that is easy to understand or mathematical form that is easy to model. The optimized step of this idea can be concluded as shown in Figure9.Figure 9
The overall framework of the proposed FVCC.


## 3.1. Fuzzification Process

Based on the national voltage standard that the fluctuation range of the generator output voltage should be ±5% of the rated value, the allowable range of output voltageEi is set as [209, 231] V. Therefore, set the domain XeE of eE(t) as [−11, 11] V. The domain XecE of ecE(t) is [−11, 11] V/s. The interval X∆ni of ∆ni is [−2 × 10−4, 2 × 10−4]. Then, the discrete fuzzy sets Y are selected as {-3, -2, -1, 0, 1, 2, 3}. To unify the dimensions, the input and output variables are normalized. The quantization factors k1 of eE(t) and k2 of ecE(t) and the proportion factor ku of ∆ni are calculated accordingly the following formula:(19)k1=yxeE=311=0.2727,k2=yxecE=311=0.2727,ku=xΔniy=2×10−43=6.6×10−5,where xeE, xecE, and x∆ni and y are the absolute value of the interval boundary.Note that the input and output variables are all within the fuzzy subsets {−3, −2, −1, 0, 1, 2, 3}. The fuzzy subsets divided into seven equal parts can be defined as {NB, NM, NS, ZO, PS, PM, PB}. In language form, the meanings of these elements are as follows {negative big, negative middle, negative small, zero, positive small, positive middle, positive big}. The variables of FVCC adopt a triangular membership function. Figure7 shows membership function images of MfeE(t), MfecE(t), and Mf∆n.Figure 7
Membership functionMfeE(t), MfecE(t), and Mf∆n.


## 3.2. Fuzzy Reasoning Process

A fuzzy toolbox has been increasingly applied to make fuzzy rules and select calculation methods in MATLAB. Its four basic steps such as “and, or, implication and aggregation,” all adopt the max-min method. With the engineering experience, the fuzzy rules with two inputs and one output are established. The fuzzy control rules table ofeE(t), ecE(t), and ∆ni is shown in Table 2.Table 2
Fuzzy control rules.
ecE(t)eE(t)NBNMNSZOPSPMPBNBPBPBPMPMPSZOZONMPBPBPMPSPSZONSNSPMPMPMPSZONSNSZOPMPMPSZONSNMNMPSPSPSZONSNSNMNMPMPSZONSNMNMNMNBPBZOZONMNMNMNBNBThe fuzzy statement is defined as “ifeE(t) = NB and ecE(t) = NB then ∆ni = PB.” Accordingly, the fuzzy rule surface diagram of the FVCC is depicted in Figure 8.Figure 8
Fuzzy rule surface diagram.


## 3.3. Defuzzification Process

The output results have no dimension in this stage. The values required by the system must be handled by the proportion module. At last, the developed controller applies the Mamdani method to fuzzy reasoning calculation and the Centroid method to the defuzzification process.The application of the fuzzy controller can effectively reduce the calculation amount of complex models and the difficulty of model analysis. The complex nonlinear problems are transformed into language form that is easy to understand or mathematical form that is easy to model. The optimized step of this idea can be concluded as shown in Figure9.Figure 9
The overall framework of the proposed FVCC.


## 4. Simulation Examples

To show the superiority of the control strategy proposed in this article, the FVCC strategy is compared with the conventional droop control through MATLAB/Simulink simulation tests. The parallel system, which has two DG with equal capacity, is modeled on the MATLAB/Simulink platform, as shown in Figure10. The simulation model simulates Figure 2. The rated capacity of the inverter is 3 kVA, and the rated frequency of the system is 50 Hz. In the process of the simulation design, the following parameters are shown in Table 3. Parameters are obtained through referring to [17] and from the laboratory.Figure 10
System simulation wiring diagram.Table 3
Cases parameters.
ParametersInverter 1 valuesInverter 1 valuesDC source voltageUdc800 V800 VFilter inductanceL5 mH5 mHFilter capacitanceC50μF50μFFilter inductance resistanceRs0.01 Ω0.01 ΩBus voltageUB220 V220 VLine impedanceZline0.1 +j 0.13 Ω0.1 +j 0.26 ΩActive power gain coefficientni2 × 10−42 × 10−4Reactive power gain coefficientmi3 × 10−53 × 10−5No-load angular frequencyω∗314 rad/s314 rad/sVoltage gainkp33Fuzzy proportion factorku6.6 × 10−56.6 × 10−5Fuzzy quantization factork1 and k20.27270.2727System frequencyf50 Hz50 HzIn the process of running in Case 2, the system initially has two loads running in parallel. After the system runs for 0.5 s, a load is connected to the system. Then, when the system runs for 1 s, another small load connects to the system.When the system is stable and continues to run for 1.5 s, part of the loads of the system are separated from the common bus. Finally, the system runs to 2 s.


### 4.1. Case 1: Comparison Results of Inverter Switching-On and Switching-Off with Constant Active Load

The number of inverters in the system cannot be invariable, which means that the switching process of inverters is very important, resulting in many significant influences on the system. Figure11 shows the comparative simulation test results of two inverters switching-on and switching-off. In order to study its characteristics, with different methods, simulation is carried out. The left side of Figure 11 is the curve of adopting the conventional droop method, and the parameters of all strategies are from Table 3. The controller uses the same gain parameters as the previous method but adds the voltage gain module. The related results are displayed in the middle part of Figure 11. The third group of simulation tests adopts the improved FVCC proposed in this article. Other parameters are the same. A controller with two compensation mechanisms is added, and the results are given on the right side of Figure 11. Then, the compensation coefficient of two parallel inverters is selected as 3 to ensure the consistency of parameters.Figure 11
Case comparisons of inverter in parallel operation switching-on and switching-off with constant active load. (a) Output voltage and current of inverter 1. (b) Output voltage and current of inverter 2. (c) Effective value of IOV. (d) Effective value of IOC. (e) The output power of two inverters. (f) System frequency and effective value of load terminal voltage.
(a)(b)(c)(d)(e)(f)Compared with the results, three groups of cases can ensure the voltage stability during operation, and the voltage fluctuation of the proposed controller is not obvious, as shown in Figures11(a) and 11(c). The minimum voltage of inverter 2 on the left side of Figure 11(c) is 202.67 V, the peak voltage of inverter 2 in the middle part of the figure reaches 424.4 V, and the maximum voltage of FVCC is 221.21 V, which is the closest to rated voltage 220 V. The dynamic process of a conventional controller is slow. Especially on the left side of Figure 11(d), the current of inverter 1 is slowly reduced to half of the original current, whereas the current of inverter 2 also has an obvious jump and change process. On the contrary, the other two sets of simulation results show good performance in the inverter conversion process. Their dynamic response is rapid. Nevertheless, the strategy of adding only voltage gain module shows a significant jump phenomenon at the initial stage of system operation. The instantaneous voltage reaches 691 V, which even exceeds the allowable rated maximum value. The convergence process to stability is long. It cannot quickly track near the stable value, whereas the improved controller can. When the conventional control strategy is added to the inverter, the power cannot be shared quickly. For the only active load, inverter 1 always fails to reach the rated output active power, and the reactive power appears in the system. In contrast, other strategies have a better power sharing effect. Under the condition of adopting the improved FVCC strategy, the bus voltage can be stabilized at 218.5 V (effective value), and the deviation error is small. The voltage level is greatly improved.


### 4.2. Case 2: Comparison Results of Parallel Inverters with Different Types of Load Conversion

Figure12 shows a comparative simulation case of two inverters with changing loads. The conventional droop strategy curves are shown on the left side of Figure 12. The results of adding only one voltage compensation strategy are depicted in the middle part of Figure 12. The right side of Figure 12 exhibits the results of the FVCC strategy. Figure 12(a) depicts the output voltage and current of the inverters. Figure 12(b) shows the effective value of the IOV connected in parallel. In Figures 12(a) and 12(b), since the equivalent impedance value of the inverter is relatively small, the output voltage of the inverter drops slightly. In terms of stability, it is obvious that the proposed strategy has great superiority. When the load is switched, it has no obvious fluctuation and the curve is smooth. Although the performance of the second group in simulation examples is better than those of conventional control, the system stability at the beginning of operation is poor, which has a huge jump that seriously affects the system security. In the process of load switching, the conventional droop strategy has been unable to share the power, especially in the active power P. There is a difference between the output power and the load, which reveals that the system parameter errors and device factors can result in power loss. It will make the load unable to work at full load.Figure 12
Case comparisons of parallel inverters with different types of load conversion. (a) Output voltage and current of the inverters. (b) The effective value of IOV. (c) The output power of two inverters. (d) Single-phase load terminal output voltage. (e) System frequency and effective value of the bus voltage. (f) THD of the microgrid.
(a)(b)(c)(d)(e)(f)Figures11 and 12 show that the power of the FVCC strategy has no obvious extra consumption, and the power-sharing effect is excellent. In the curves of Figure 12(d), the single-phase bus output voltage drops obviously with the conventional strategy and the second group of simulation examples, and the former is particularly prominent. With the conventional strategy, the peak voltage of the bus can only reach 226.84 V, which is far from the national voltage standard (−10% ∼ +7%). However, the voltage boost effect of adding only one control part is still not ideal. The instantaneous value far exceeds the system safety margin. In Figure 12(e), the effective value of bus voltage with conventional way is 177.94 V, which shows that the voltage drops far from the rated value due to various factors when the load changes. Compared with the left part, the voltage with FVCC finally stabilizes at 218.81 V.The proposed compensation strategy greatly reduces the deviation from the rated voltage and improves the voltage quality. It meets the voltage requirements of the load. Moreover, in three simulation examples, the fluctuation of voltage waveform on the right part of the figure is the smallest when the load is connected or disconnected. The system voltage total harmonic distortion (THD) of the FVCC strategy is 1.88%, which is the smallest in Figure12(f). Figure 13 describes the input variables diagram of FVCC.Figure 13
Diagram of input variableseE(t) and ecE(t) of FVCC.Compared with the cases, the proposed FVCC method obviously improves the output voltage stability, while reducing the voltage jump when conditions change. Then, it significantly reduces the bus voltage drop caused by impedance and inverter parameters. It maintains the stability of load voltage, while improving the voltage quality. Furthermore, as the system power distribution is better proportionate, the action time is accelerated. By comparing Figure12(f), the proposed strategy not only compensates the voltage but also reduces the THD from 3.54% to 1.88%. These indicate that the proposed strategy has achieved the expected goal.


### 4.3. Case 3: Comparison Results of the Performance with Different Control Methods

In this case, in order to test the ability of voltage compensation and power distribution of the proposed control scheme, under the same conditions, the FVCC scheme is compared with the method in [23] by simulation. In [23], ni is set to 2 × 10−10, and the output voltages of different inverters are kept the same. There are two parallel inverters in the system. The initial loads are LOAD1 = (1.1 + j0.6) kVA, LOAD2 = (1.1 + j0.6) kVA. When t = 0.5 s, 1 s, and 1.5 s, different types of loads are added or disconnected to the system. Figure 14 shows the results of the voltage control method in [23]. Figure 15 illustrates the results of the proposed voltage compensation strategy. Figure 16 is a comparison chart of THD with two methods.Figure 14
Case results of the voltage control method in [23]. (a) The output power of two inverters. (b) Load power. (c) The effective value of IOV. (d) The per unit of bus three-phase voltage.
(a)(b)(c)(d)Figure 15
Case results of the proposed voltage compensation strategy. (a) The output power of two inverters. (b) Load power. (c) The effective value of IOV. (d) The per unit of bus three-phase voltage.
(a)(b)(c)(d)Figure 16
Comparison chart of THD of two methods.
(a)(b)By comparison, the voltage control method in [23] has good recovery ability for bus voltage, while making the parallel branches have the same IOV. However, when the capacity of parallel inverters is the same, its output power cannot be balanced and the output power loss increases due to its improper reduction in droop gain, as shown in Figures 14(a) and 14(b). Even if the system is running in a stable state, Pi cannot be kept constant, especially in the fourth stage of system operation. Figure 15(a) is in sharp contrast with Figure 14(a). The power sharing performance of the proposed control strategy is excellent. When the system is steady, the power can be kept constant without obvious fluctuation. Figures 14(a) and 14(b) reveal that when t = 1.5 s, P1 and P2 achieve 1450 W and 2000 W, respectively, but PLO at the load terminal is only 3125 W, a part of which is consumed during transmission. The proposed voltage compensation strategy has better advantages. In Figures 15(a) and 15(b), when t = 1.5 s, P1 and P2 are both 1730 W and PLO is 3460 W. Comparing the curves of (c) and (d) in Figures 14 and 15, both methods can restore the output voltage, which is within the allowable range, but the results obtained by FVCC are better than those of the other method. Table 4 lists the data comparison results of simulation tests with different methods.Table 4
Case 3 data comparison results with different methods.
ParametersProposed strategyVoltage control methodt = 0.5 st = 1 st = 1.5 st = 2 sP1 (W)1060102015101400173014501200610P2 (W)10601080151016201730200012001780Q1 (var)5715908408709501020629760Q2 (var)571550840800950880629500PLO (W)21201940302027453460312524002180QLO (var)11421055168015001900167012581145UVSI (V)219.1218.5218.4218218217.8219218.9ULO (p. u.)0.9790.9770.9690.9660.97640.9620.97650.974THD (%)2.162.34


### 4.4. Case 4: Comparison Results of the Proposed Voltage Compensation Strategy withkp = 2 and kp = 10

In order to test the adaptability of the designed system to different parameters, in this subsection, the sensitivity analysis of its voltage gainkp is carried out through case simulation. When other parameters of the system are the same, kp = 2 and kp = 10 are discussed. Figure 17 shows the system output results of kp = 10. Figure 18 shows the system output results of kp = 2.Figure 17
The system output results ofkp = 10. (a) The output power of parallel inverters. (b) THD. (c) Single-phase output voltage of VSIs. (d) System frequency and effective value of bus voltage. (e) Three-phase voltage and current at the load terminal.
(a)(b)(c)(d)(e)Figure 18
The system output results ofkp = 2. (a) The output power of parallel inverters. (b) THD. (c) Single-phase output voltage of VSIs. (d) System frequency and effective value of bus voltage. (e) Three-phase voltage and current at the load terminal.
(a)(b)(c)(d)(e)By comparing different values of parameters, despite the output power sharing of the inverter, the dynamic response speed of the power is slow in Figure17(a). It takes 0.05 s for the system to complete the dynamic process, which is not conducive to the rapid switching of the system. More importantly, in the steady state, the power is not stable. It shows the characteristics of oscillation and fluctuation. Rapid fluctuations will greatly reduce the service life of the system and devices. However, when kp = 2, the power not only is evenly distributed, but also shows good stability without obvious fluctuation in Figure 18(a). Due to kp = 10, the compensated voltage is too large, which leads to the distortion of inverter voltage waveform. The peak voltage reaches 337.5 V in Figure 17(c), which is beyond the normal voltage range stipulated by the state, and can do great damage to the microgrid in a long time. In Figures 17(d) and 17(e), despite the voltage compensation, the voltage distortion is too serious. Especially at 0∼0.3 s, the peak value of bus voltage reaches 366 V, which is far greater than the rated value of 220 V. Moreover, the system cannot reach the stable state for a long time with obvious fluctuation. When kp = 2, however, the system performance is good and the voltage curve is smooth. In addition, the bus voltage fluctuates only at 0.02∼0.022 s and 1.50∼1.53 s, with the peak value of 226 V and the minimum value of 212 V. Table 5 lists the data comparison results when the parameters kp take different values.Table 5
Case 4 data comparison results with differentkp.
Parameterskp = 2kp = 10Pi fluctuation range (W)±4.456±124.55Qi fluctuation range (var)±7.555±83.9Distortion of IOVSmallGreatDistortion of IOCSmallGreatUB fluctuation peak (V)226366UB fluctuation minimum value (var)212212.5Bus voltage (V)218.9239.9THD (%)2.444.41


## 4.1. Case 1: Comparison Results of Inverter Switching-On and Switching-Off with Constant Active Load

The number of inverters in the system cannot be invariable, which means that the switching process of inverters is very important, resulting in many significant influences on the system. Figure11 shows the comparative simulation test results of two inverters switching-on and switching-off. In order to study its characteristics, with different methods, simulation is carried out. The left side of Figure 11 is the curve of adopting the conventional droop method, and the parameters of all strategies are from Table 3. The controller uses the same gain parameters as the previous method but adds the voltage gain module. The related results are displayed in the middle part of Figure 11. The third group of simulation tests adopts the improved FVCC proposed in this article. Other parameters are the same. A controller with two compensation mechanisms is added, and the results are given on the right side of Figure 11. Then, the compensation coefficient of two parallel inverters is selected as 3 to ensure the consistency of parameters.Figure 11
Case comparisons of inverter in parallel operation switching-on and switching-off with constant active load. (a) Output voltage and current of inverter 1. (b) Output voltage and current of inverter 2. (c) Effective value of IOV. (d) Effective value of IOC. (e) The output power of two inverters. (f) System frequency and effective value of load terminal voltage.
(a)(b)(c)(d)(e)(f)Compared with the results, three groups of cases can ensure the voltage stability during operation, and the voltage fluctuation of the proposed controller is not obvious, as shown in Figures11(a) and 11(c). The minimum voltage of inverter 2 on the left side of Figure 11(c) is 202.67 V, the peak voltage of inverter 2 in the middle part of the figure reaches 424.4 V, and the maximum voltage of FVCC is 221.21 V, which is the closest to rated voltage 220 V. The dynamic process of a conventional controller is slow. Especially on the left side of Figure 11(d), the current of inverter 1 is slowly reduced to half of the original current, whereas the current of inverter 2 also has an obvious jump and change process. On the contrary, the other two sets of simulation results show good performance in the inverter conversion process. Their dynamic response is rapid. Nevertheless, the strategy of adding only voltage gain module shows a significant jump phenomenon at the initial stage of system operation. The instantaneous voltage reaches 691 V, which even exceeds the allowable rated maximum value. The convergence process to stability is long. It cannot quickly track near the stable value, whereas the improved controller can. When the conventional control strategy is added to the inverter, the power cannot be shared quickly. For the only active load, inverter 1 always fails to reach the rated output active power, and the reactive power appears in the system. In contrast, other strategies have a better power sharing effect. Under the condition of adopting the improved FVCC strategy, the bus voltage can be stabilized at 218.5 V (effective value), and the deviation error is small. The voltage level is greatly improved.


## 4.2. Case 2: Comparison Results of Parallel Inverters with Different Types of Load Conversion

Figure12 shows a comparative simulation case of two inverters with changing loads. The conventional droop strategy curves are shown on the left side of Figure 12. The results of adding only one voltage compensation strategy are depicted in the middle part of Figure 12. The right side of Figure 12 exhibits the results of the FVCC strategy. Figure 12(a) depicts the output voltage and current of the inverters. Figure 12(b) shows the effective value of the IOV connected in parallel. In Figures 12(a) and 12(b), since the equivalent impedance value of the inverter is relatively small, the output voltage of the inverter drops slightly. In terms of stability, it is obvious that the proposed strategy has great superiority. When the load is switched, it has no obvious fluctuation and the curve is smooth. Although the performance of the second group in simulation examples is better than those of conventional control, the system stability at the beginning of operation is poor, which has a huge jump that seriously affects the system security. In the process of load switching, the conventional droop strategy has been unable to share the power, especially in the active power P. There is a difference between the output power and the load, which reveals that the system parameter errors and device factors can result in power loss. It will make the load unable to work at full load.Figure 12
Case comparisons of parallel inverters with different types of load conversion. (a) Output voltage and current of the inverters. (b) The effective value of IOV. (c) The output power of two inverters. (d) Single-phase load terminal output voltage. (e) System frequency and effective value of the bus voltage. (f) THD of the microgrid.
(a)(b)(c)(d)(e)(f)Figures11 and 12 show that the power of the FVCC strategy has no obvious extra consumption, and the power-sharing effect is excellent. In the curves of Figure 12(d), the single-phase bus output voltage drops obviously with the conventional strategy and the second group of simulation examples, and the former is particularly prominent. With the conventional strategy, the peak voltage of the bus can only reach 226.84 V, which is far from the national voltage standard (−10% ∼ +7%). However, the voltage boost effect of adding only one control part is still not ideal. The instantaneous value far exceeds the system safety margin. In Figure 12(e), the effective value of bus voltage with conventional way is 177.94 V, which shows that the voltage drops far from the rated value due to various factors when the load changes. Compared with the left part, the voltage with FVCC finally stabilizes at 218.81 V.The proposed compensation strategy greatly reduces the deviation from the rated voltage and improves the voltage quality. It meets the voltage requirements of the load. Moreover, in three simulation examples, the fluctuation of voltage waveform on the right part of the figure is the smallest when the load is connected or disconnected. The system voltage total harmonic distortion (THD) of the FVCC strategy is 1.88%, which is the smallest in Figure12(f). Figure 13 describes the input variables diagram of FVCC.Figure 13
Diagram of input variableseE(t) and ecE(t) of FVCC.Compared with the cases, the proposed FVCC method obviously improves the output voltage stability, while reducing the voltage jump when conditions change. Then, it significantly reduces the bus voltage drop caused by impedance and inverter parameters. It maintains the stability of load voltage, while improving the voltage quality. Furthermore, as the system power distribution is better proportionate, the action time is accelerated. By comparing Figure12(f), the proposed strategy not only compensates the voltage but also reduces the THD from 3.54% to 1.88%. These indicate that the proposed strategy has achieved the expected goal.


## 4.3. Case 3: Comparison Results of the Performance with Different Control Methods

In this case, in order to test the ability of voltage compensation and power distribution of the proposed control scheme, under the same conditions, the FVCC scheme is compared with the method in [23] by simulation. In [23], ni is set to 2 × 10−10, and the output voltages of different inverters are kept the same. There are two parallel inverters in the system. The initial loads are LOAD1 = (1.1 + j0.6) kVA, LOAD2 = (1.1 + j0.6) kVA. When t = 0.5 s, 1 s, and 1.5 s, different types of loads are added or disconnected to the system. Figure 14 shows the results of the voltage control method in [23]. Figure 15 illustrates the results of the proposed voltage compensation strategy. Figure 16 is a comparison chart of THD with two methods.Figure 14
Case results of the voltage control method in [23]. (a) The output power of two inverters. (b) Load power. (c) The effective value of IOV. (d) The per unit of bus three-phase voltage.
(a)(b)(c)(d)Figure 15
Case results of the proposed voltage compensation strategy. (a) The output power of two inverters. (b) Load power. (c) The effective value of IOV. (d) The per unit of bus three-phase voltage.
(a)(b)(c)(d)Figure 16
Comparison chart of THD of two methods.
(a)(b)By comparison, the voltage control method in [23] has good recovery ability for bus voltage, while making the parallel branches have the same IOV. However, when the capacity of parallel inverters is the same, its output power cannot be balanced and the output power loss increases due to its improper reduction in droop gain, as shown in Figures 14(a) and 14(b). Even if the system is running in a stable state, Pi cannot be kept constant, especially in the fourth stage of system operation. Figure 15(a) is in sharp contrast with Figure 14(a). The power sharing performance of the proposed control strategy is excellent. When the system is steady, the power can be kept constant without obvious fluctuation. Figures 14(a) and 14(b) reveal that when t = 1.5 s, P1 and P2 achieve 1450 W and 2000 W, respectively, but PLO at the load terminal is only 3125 W, a part of which is consumed during transmission. The proposed voltage compensation strategy has better advantages. In Figures 15(a) and 15(b), when t = 1.5 s, P1 and P2 are both 1730 W and PLO is 3460 W. Comparing the curves of (c) and (d) in Figures 14 and 15, both methods can restore the output voltage, which is within the allowable range, but the results obtained by FVCC are better than those of the other method. Table 4 lists the data comparison results of simulation tests with different methods.Table 4
Case 3 data comparison results with different methods.
ParametersProposed strategyVoltage control methodt = 0.5 st = 1 st = 1.5 st = 2 sP1 (W)1060102015101400173014501200610P2 (W)10601080151016201730200012001780Q1 (var)5715908408709501020629760Q2 (var)571550840800950880629500PLO (W)21201940302027453460312524002180QLO (var)11421055168015001900167012581145UVSI (V)219.1218.5218.4218218217.8219218.9ULO (p. u.)0.9790.9770.9690.9660.97640.9620.97650.974THD (%)2.162.34


## 4.4. Case 4: Comparison Results of the Proposed Voltage Compensation Strategy withkp = 2 and kp = 10

In order to test the adaptability of the designed system to different parameters, in this subsection, the sensitivity analysis of its voltage gainkp is carried out through case simulation. When other parameters of the system are the same, kp = 2 and kp = 10 are discussed. Figure 17 shows the system output results of kp = 10. Figure 18 shows the system output results of kp = 2.Figure 17
The system output results ofkp = 10. (a) The output power of parallel inverters. (b) THD. (c) Single-phase output voltage of VSIs. (d) System frequency and effective value of bus voltage. (e) Three-phase voltage and current at the load terminal.
(a)(b)(c)(d)(e)Figure 18
The system output results ofkp = 2. (a) The output power of parallel inverters. (b) THD. (c) Single-phase output voltage of VSIs. (d) System frequency and effective value of bus voltage. (e) Three-phase voltage and current at the load terminal.
(a)(b)(c)(d)(e)By comparing different values of parameters, despite the output power sharing of the inverter, the dynamic response speed of the power is slow in Figure17(a). It takes 0.05 s for the system to complete the dynamic process, which is not conducive to the rapid switching of the system. More importantly, in the steady state, the power is not stable. It shows the characteristics of oscillation and fluctuation. Rapid fluctuations will greatly reduce the service life of the system and devices. However, when kp = 2, the power not only is evenly distributed, but also shows good stability without obvious fluctuation in Figure 18(a). Due to kp = 10, the compensated voltage is too large, which leads to the distortion of inverter voltage waveform. The peak voltage reaches 337.5 V in Figure 17(c), which is beyond the normal voltage range stipulated by the state, and can do great damage to the microgrid in a long time. In Figures 17(d) and 17(e), despite the voltage compensation, the voltage distortion is too serious. Especially at 0∼0.3 s, the peak value of bus voltage reaches 366 V, which is far greater than the rated value of 220 V. Moreover, the system cannot reach the stable state for a long time with obvious fluctuation. When kp = 2, however, the system performance is good and the voltage curve is smooth. In addition, the bus voltage fluctuates only at 0.02∼0.022 s and 1.50∼1.53 s, with the peak value of 226 V and the minimum value of 212 V. Table 5 lists the data comparison results when the parameters kp take different values.Table 5
Case 4 data comparison results with differentkp.
Parameterskp = 2kp = 10Pi fluctuation range (W)±4.456±124.55Qi fluctuation range (var)±7.555±83.9Distortion of IOVSmallGreatDistortion of IOCSmallGreatUB fluctuation peak (V)226366UB fluctuation minimum value (var)212212.5Bus voltage (V)218.9239.9THD (%)2.444.41


## 5. Conclusion

By analyzing the causes of voltage loss, an improved fuzzy voltage compensation control strategy has been put forward in this article. Under the condition of no communication, the fundamental factors of voltage loss including load effect and droop effect have been found. The main conclusions have been as follows:(1)
Voltage gain module has been developed based on the voltage loss of feeder impedance, which does not need to calculate the feeder impedance value. Comparing FVCC and conventional control, the bus voltage is 210.69 V and 177.94 V, respectively. The voltage of conventional control is far beyond the safe allowable range of national voltage standard (−10% ∼ +7%). The load voltage peak is 298.49 V and 226.84 V.(2)
An adaptive fuzzy controller has been designed based on droop effect, which can adaptively adjust droop parameters to compensate voltage difference. Comparing FVCC and the reference method, the bus voltage recovery effect is obvious, with the bus voltage of 281.81 V and 214.28 V, respectively. THD is 2.16% and 2.34%.(3)
When the system load has been equal, the proposed control strategy has faster response speed and superior stability. Multigroup simulation cases have presented that FVCC has better voltage compensation performance and robustness by comparison. These cases have achieved the expected goal.The FVCC strategy has greatly restored the voltage and improved the voltage quality. The parallel inverter has achieved power sharing while having good stability. The system characteristics, however, after grid connection have been not considered. Hence, connecting parallel inverters to the grid will be the further research direction of the authors. Furthermore, as a complete microgrid, energy storage equipment will also be our future development and research direction.



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*Source: 5185028-2022-02-10.xml*