# Optimization of Voltage Dynamic Performance at Inverter Output with Machine Learning and Intelligent Virtual Impedance

Authors: Lu Wang
Journal: Mobile Information Systems
 (2022)

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## Abstract

With the continuous improvement of industrial production and manufacturing level, all kinds of equipment are developing in the direction of refinement and precision, especially the equipment manufacturing industry such as automobile manufacturing, equipment, integrated circuits, chip manufacturing, and other semiconductor industries. An intelligent virtual resistance control strategy based on machine research is proposed for rational power distribution and cycle suppression when multiple inverters are operated in parallel in low-voltage microgrids. Based on this, the control strategy of temporary power reduction of inverters is improved to improve the parallel inverter power distribution accuracy and ensure the reliable dynamic response of the constrained current in the circuit between parallel inverters. Finally, a multi-inverter parallel system model is established to verify the correctness and effectiveness of the proposed control strategy. The voltage waveform under nonlinear load conditions is improved and high-frequency harmonics are suppressed, which has obvious advantages compared with the general virtual impedance design method.


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## Body

## 1. Introduction

A large number of precision equipment with CPU, PLC, and other cores, these modern precision instruments, production equipment, etc. have very high requirements for power quality [1], sometimes just a momentary voltage dip may lead to very serious consequences, such as causing interruptions in the production process or equipment failure, thus causing enterprises to suffer huge economic losses, as shown in Figure 1 for a variety of high-end manufacturing equipment characteristics and the impact of power quality [2, 3]. These power quality problems can directly or indirectly cause serious economic losses to the national economy and seriously affect the safe, stable, and efficient operation of electric power.Figure 1
High-end manufacturing industry is affected by the power quality map.IEEE standard 22 coordinating committee pointed out that the main power quality problems include voltage unbalance overvoltage, undervoltage, voltage dips, voltage surges, power supply interruptions, flicker current harmonics, or ground fault. Among them, voltage dip refers to the phenomenon that the square root mean value of frequency voltage suddenly drops to 90%∼10% of the rated value at a certain moment, with a duration of 10 ms∼1 min, and then rises back to near the rated value. Through a large number of survey data, it is found that the grid voltage dip is the most probable and serious power quality problem.Voltage dips in the power grid have caused very serious effects on the normal operation of equipment [4, 5]. Siemens, Germany, has studied the voltage sensitivity of power electronics widely used in daily life and has given the effects of voltage dips on some important power electronics, as listed in Table 1. Many devices are affected by voltage dips, and the impact is so great that it seriously affects the safe and stable operation of the equipment. Therefore, it is of great practical significance to carry out comprehensive management of voltage dips [6].Table 1
Effect of voltage dips on some equipment (rated at 100%).
Device nameEffects caused by voltage dipsProgrammable controllerThe PLC will stop when the voltage is less than 50%Precision machine toolsIt will be tripped when there are 2 to 3 cycles of voltage value below the threshold valueDC motorTripped when the voltage is less than 80%ComputerIf the voltage is less than 60% and lasts for more than 12 cycles, data loss will occurSpeed control motorIf the voltage is less than 70% and lasts for more than 6 cycles, the speed control motor will be cut offFor the voltage dips in the power grid, the existing main governance solutions are mainly divided into two aspects: active governance and passive governance. Active management is to optimize the system operation by changing the system structure and connection, such as transformer tap regulator, magnetic resonant transformer CVT, and static switch switching STS. However, this kind of management can only mitigate the impact of voltage dips to a certain extent, and the cost is high and not universal. With the development of power electronics technology, the passive governance method has been widely developed and applied. Table2 compares and analyzes the treatment effects of the above power quality management devices. Among them, DVR is a series-type power quality controller, which ensures the voltage on the sensitive load side to maintain stability by injecting a compensating voltage with adjustable amplitude and phase in series between the system and the load [3, 7]. It not only can economically and effectively solve the power quality problems caused by voltage dips [8] but also can manage a variety of power quality problems through reasonable design and control, which has very good application prospects and is one of the most effective and economical devices recognized to solve the voltage dips of the power grid [9].Table 2
Treatment effect of different power quality treatment devices.
Name of governance deviceProblems that can be governedTreatment effectSTATCOMTransient problems, voltage fluctuations, voltage flicker, power oscillation dampingGoodAPFHarmonics, reactive power, unbalanceGoodUPQCVoltage dips/surges, voltage flicker, voltage unbalance, harmonics, power factor, load harmonic current, load unbalanceGoodUPSTransient power interruptionNot goodDVRVoltage dip/sudden riseGood


## 2. Related Work

The conventional DVR topology mainly consists of a DC-side energy storage unit, an inverter unit, an LC filter unit, a series-coupled transformer, and a bypass switch [10]. When the grid voltage does not dip, the DVR works in standby mode, when the DVR has no effect on the system and the losses are low. When a dip in the grid voltage is detected, the DVR is quickly connected to the system in series, and the DC-side voltage is passed through the voltage source inverter to produce a compensating voltage Udvr, and the compensating voltage vector Udvr is superimposed on the system voltage US to keep the load-side voltage UL balanced and stable.When the DVR detection module detects a grid voltage dip fault on the system side or a voltage dip fault on other lines at the bus due to a fault on a nearby line, the control module subtracts the load voltage reference value from the grid voltage value after the fault to obtain the voltage vector to be compensated by the device and then controls the inverter to output the compensation voltage with the required amplitude and phase through the corresponding control strategy. The DVR can output the compensated voltage in a very short time and thus has a fast compensation speed and good dynamic performance [11].Inverters with virtual impedance have been well developed because of their good dynamic performance and cost advantages [12]. Following the installation of the world’s first DVR device by Westinghouse in 1996, a series of in-depth analysis and research works on DVRs have been carried out by universities, research institutes, and companies in many countries one after another. The IGBT-based DVR device was announced to be developed by ABB in 1998 and attracted a lot of discussions. Since then, ABB has further upgraded the DVR products step by step, significantly increasing the capacity of the DVR and making it possible for the DVR products to obtain the required energy from the DC side directly from the grid [13]. In addition, research institutions such as Wisconsin and Cutler-Hammer have also researched and developed DVR devices and applied them to various research areas. These research institutions have not only achieved fruitful research results in the theoretical study of DVR but also have several devices that have been put into use and have achieved better operational results and experience. Some development history of DVR is listed in Table 3.Table 3
Some development history of DVR.
YearCapacity classCountry of developmentNumber of inverter levelsSeries transformer199912.47 kVUnited States2Yes2 MVA200110 KVAUK2Yes100 V2002250 KVANetherlandsMultilevelNone220 V2003220 VTaiwan2Yes20041 KVASingapore2None200 V2005200 KVADenmark2Yes10 KVAustralia200650 VUnited StatesMultilevelYes200710 KVCanada2YesSingaporeDenmark20085 KVAChinaMultilevelNone110 VAt present, 10 kVA/380 V DVR experimental prototype has been successfully developed by Tsinghua University, while the Chinese Academy of Sciences, Hunan University and other research institutions and universities have also concentrated their research efforts on DVR devices to carry out in-depth research, and has made many research results [14]. But whether from the capacity, voltage level, or engineering applications, there is still a large gap between the domestic development results on DVR compared to foreign countries [15].As can be seen from the development history of DVRs, the inverters used in DVRs are mostly two-level structures with simple circuit structures and control methods, but the equivalent switching frequency is low and the inverter output harmonics are large. Multilevel converters are widely used in the prestage structure of DVRs because of their large capacity, easy expansion, and good output voltage harmonic characteristics. There are three main basic circuit topologies of multilevel converters: (1) diode-clamped type, (2) fly-across capacitor type, and (3) cascaded H-bridge type. Among them, the cascaded H-bridge type multilevel converter has similar multiswitch combinations as the fly-span capacitor type structure compared to the first two structures, flexible control, easy-to-realize multilevel output, simple structure, easy modularization, and relatively independent DC power supply; therefore, it is widely used in DVRs to constitute a cascaded H-bridge type virtual impedance inverter (cascaded H-bridge-dynamic voltage restorer, CHB-DVR).The topology, control strategy, and modulation strategy of the CHB-DVR have been studied in depth as follows:(1)
Topology. Literature [16–19] proposed a cascaded H-bridge converter topology for high system voltage and power in medium and high voltage systems, which was applied to DVR and effectively extended the capacity of DVR compensation device; literature [20] eliminated the expensive series transformer for CHB-DVR structure; literature [21] made a detailed analysis and introduction for different topology characteristics of DVR. Literature [22] provides a detailed analysis and introduction of different topologies of DVRs.(2)
Control. The overall control strategy of CHB-DVR is divided into two aspects: compensation strategy and control strategy. The commonly used DVR compensation strategies are as follows: in-phase compensation, complete compensation, and minimum energy compensation, and the compensation capacity and compensation effect of the three compensation strategies are compared in Table 4. Literature [23] proposes a DVR control strategy based on minimum energy compensation, which can greatly reduce the active injection of DVR and extend the compensation time of DVR; literature [24] proposes a control strategy that can manage the harmonics of the grid system based on the original DVR control strategy for the harmonic problem in the grid.Table 4
Comparison table of DVR compensation strategies.
Compensation strategyCompensating voltage amplitudePhase angle jumpOutput active powerSame phase compensationMin.LargerLargerFully compensatedLargeMin.LargerMinimum energy compensationLargeLargeMin.


## 3. Method

The system consists of two resonance inductors that are receiving coil and transmission coil, which are denoted as Rx and Tx respectively, according to Figure2.Figure 2
Concise diagram of system on basis of magnetically coupled resonators.The system is denoted by the circuit component, which is lumped (L, C, and R), according to the Figure 3.Figure 3
The circuit equivalent for system. Each coil is considered as a train of resonators in the modeling.A common topology of inverter is shown in Figure3. This inverter supplies a three-phase resistive load consisting of a series inductor Lo, a resistor Ro, and a counter-electromotive force eo, and the three-phase output current is io.From Figure4, it can be observed that the WPT may exist multiple resonant frequencies. The Resonance frequency is randomly tracked by using the traditional frequency-tracking method.Figure 4
The frequency-tracking method.The gating signalg2=ioα∗k+1−ioαk+1+ioβ∗k+1−iok+1,ioa,iob,ioc=10A,Roa=Rob=Roc=0.1Ω,Loa=Lob=Loc=20mHTs=50μs10io∗k−1−20io∗k−2+15io∗k−3−4io∗k−4° determines the switching state of the converter.(1)Sy=1,Switch closed,0,Switch open,where Y=a,b,c. It can be expressed in vector form as follows:(2)Sy=23Sa+aSb,a2Sc,where a=e−j2π/3,Sg are the switching state vectors.The load voltage vector generated by the inverter is defined as follows:(3)UO=23UaN+aUbN,a2UcN,where UaN,UbN,UcN are the voltages between each phase of the inverter and the neutral point N.The relationship between the load voltage vectorUO and the switching state vector Sg is as follows:(4)UO=UdcSg,where Udc is the DC bus voltage.Substituting equation (3) into equation (4), we get that the relationship between the switching state variable (Sa,Sb,Sc) and the load voltage vector UO as follows:(5)UO=23UdcSa,aSb,a2Sc.According to the different combinations of (Sa,Sb,Sc), the inverter output voltage space vector is shown in Figure 5.Figure 5
Inverter output voltage space vector.When multiple inverters are operated in parallel, the multiinverter parallel system is first analyzed, as shown in Figure6.Figure 6
Block diagram of parallel inverter output characteristics control.In general, the switching frequency of the inverter is so high that the instantaneous values of the variables can be considered to be equal to their average values in one switching cycle. For the control of the inverter, the virtual impedance-basedv method is used, and its specific control block diagram is shown in Figure 7.Figure 7
Block diagram of virtual impedance-based control.TheU0 can be expressed as follows:(6)u0=u0refsGInvs−ZInvs+LvsTfs+1GInvs,i0su0refsGInvs−ZInvEsi0s.GInvs,ZInvs are based on capacitor-current feedback control; ZInvEs is obtained by the following equation:(7)ZInvEs=ZInvs+LvsTfs+1GInvs.They are reduced byR after introducing a certain virtual inductance Lv, so that the fundamental frequency output impedance ZInvE is approximately purely inductive. Therefore, the system inductance can be designed by changing Lv, and then, the system impedance of each parallel inverter unit can be matched.Low-voltage lines generally existLLine much larger than RLine, and it is assumed that the low-voltage line impedance ZLine is as follows:(8)ZLine=RLine+sLLine.The fundamental system impedanceZLine of the parallel inverter is as follows:(9)Z=ZInvE+ZLine=Rs+jLs.ZInvE is approximately purely inductive, and ZLine is purely resistive, which is easy to cause power coupling and output voltage landing when the size of Rs and Ls is comparable. In this regard, by introducing virtual negative resistance to reduce the resistive component of the system impedance, the coupling degree between the output power is reduced, and the virtual negative impedance is obtained as follows:(10)Zvs=−Rv+LvsTfs+1.The system impedance can be expressed as follows:(11)Zs=ZInvs+LvsTfs+1−RvGInvs+RLine+sLLine=R+jX.A suitable virtual negative resistanceRv is chosen to meet the impedance matching requirement. Considering that the power decoupling makes the system impedance at the fundamental frequency R=X, the filtering time constant Tf is very small and can be neglected, GInvs=1,ZInvs=0, and thus, the total system impedance can be simplified as follows:(12)Zs=RLine−Rv+sLLine+Lv.From equation (12), it can be seen that only Rv=RLine needs to be satisfied under the condition of fundamental impedance to achieve completely independent decoupling from the inverter. The ideology of segmentation frequency-tracking algorithm is shown in Figure 8.Figure 8
Flowchart of segmentation frequency-tracking algorithm.CNNs have been widely used in classification problems for power system stability analysis, but their applications in regression problems are rarely explored. In this section, the advantages of CNN in classification and regression problems are fully utilized to develop the inverter output-time voltage dynamic performance of virtual impedance and quantitative risk classification. First, the traditional stability classification result is replaced by a binary combination of stability classification result and plausibility metric as the output of the classification model, so that the plausibility of the classification result can be grasped intuitively. Then, by setting the confidence threshold, the stability prediction results of the samples are divided into four sets: stable set, unstable set, missed unstable set, and misclassified unstable set. For the misclassified destabilization set and the stable set, the voltage stability margin at output is quickly predicted by the CNN regression model; for the missed destabilization set and the destabilization set, the stability margin is set to −1 according to the constructed voltage stability margin at output index, and the specific analysis process is shown in Figure9. The method improves the confidence of the inverter output-time voltage dynamic performance of virtual impedance, solves the problem of mishandling the omission/misjudgment cases, and realizes a reasonable quantitative evaluation of the output-time voltage stability, which is fully applicable to practical rapid evaluation applications [25, 26].Figure 9
The process of analyzing the dynamic performance and confidence with virtual impedance.After softmax processing, for each test sample, the predicted result of the CNN classification model corresponds to a probabilistic output [27]. In this section, the above two are combined to obtain a binary indicator to replace the traditional single classification result indicator, whose expression is as follows:(13)y=C,P.C is the stability discriminant result, and the value of C is 0 for destabilization and 1 for stability; P is the probability corresponding to the stability discriminant result.The confidence threshold can be set by an iterative search of the training samplesT1,T0. In the training phase, the confidence threshold is determined based on the samples obtained from the system historical data or time domain simulation results T1,T0; in the evaluation phase, the set of prediction results of the samples is divided using the confidence threshold determined in the phase, and the set is updated immediately if there is an error in the set division due to the possible difference in the confidence threshold corresponding to the training samples and the test data. In this stage, the confidence threshold T1,T0 is readjusted by analyzing the cases of division errors so that it can be correctly divided for the test data set. Through the update learning process of CNN, the confidence thresholds can perform better on unknown data and substantially improve the generalization ability.As shown in Figure9, the probability of judging as stable is expressed by PC=1, and the probability of judging as unstable. If PC=1>T1, the prediction result is considered credible and classified into the stable set; on the contrary, the prediction result is not credible and classified into the unstable set. On the contrary, if PC=1<PC=0, the prediction result is initially judged as unstable. If PC=0>T0, the prediction result is considered credible and is classified into the unstable set; on the contrary, the prediction result is considered untrustworthy and is classified into the misjudged unstable set.Based on the above principles, the prediction results are classified into stable set, unstable set, missed unstable set, and misjudged unstable set. For the unstable set and the missed unstable set, they are directly fed back to the dispatching operators for early warning; while for the stable set and the misjudged unstable set, the CNN regression model-based method proposed in the next section is used to predict the voltage stability margin at output to achieve quantitative and graded risk assessment of voltage stability at output [28, 29].


## 4. Experiments

For the intention of checking the validity of the approach, we have built a prototype model for the system. It contains a DC voltage source, an H-bridge inverter, a transfer resonant coil, a receiving resonant coil, and a load. For the voltage source of DC, its value is 30 V. The H-bridge inverter is arranged to realize AC excitation, which is presented in Figure10(b). It consists of four Si C MOSFETs (C2M0080120D). Figure 10(c) shows the transmission resonant coil. Its outer diameter is 60 cm with a pitch of 0 cm for 17 turns. Figure 10(d) shows the receiving resonant coil. Its outer diameter is 55 cm with a pitch of 0 cm for 13 turns. The circuit of phase detection is displayed in Figure 10. Through the circuit, the input electric tension and the input current are converted to signal of square wave. Then, we can work out the value of θ by comparing the two values, that is, the forward position for the square wave signal of input voltage, and the forward position for the square wave signal of input current, with the aid of DSP28335 ECAP. Every coil is made of AWG 38Litz-wire with 300 strands. The parameters of every coil range from 20 to 22. Their parameters can be calculated [19–21]. We can compute the parameters in equations (2) and (1) by adopting the impedance analyzer. We set the primary resonant frequency as 85.0 kHz and the resistance of load as 15.8Ω. The distance of transmission equals 15 cm. Table 5 lists the resonant coils and their parameters. The receiver’s travelling direction is denoted as Y axis. We simulated the mutual induction between Rx and Tx by ANSYS Maxwell and measured it by adopting an impedance analyzer. The simulated and calculated results of mutual induction are presented in Figure 9. It is easy to see that the mutual induction changes from 66.2 µH to 29.6 µH, while the misalignment is varied from 0 cm to 25 cm.Figure 10
Experimental setup. (a) Setup. (b) H-bridge inverter. (c) Tx. (d) Rx.
(a)(b)(c)(d)Table 5
Detailed parameters of every coil.
SymbolValueL1 (μH)353.68L2 (μH)216.02C1 (nF)9.86C2 (nF)16.09R1 (Ω)0.438R2 (Ω)0.281f0 (kHz)85.0The start frequency is set as 76 kHz. Meanwhile, the WPT system works in a nonresonant condition as shown in Figure11(a). However, when using this frequency-tracking algorithm, the system is in a resonance condition. It is found that the input voltage has same phase with the input current, as presented in Figure 11(b). According to Figure 11b, we see that the resonant frequency is 77.56 kHz.Figure 11
Input voltage and Input current with Δ = 0 cm. (a) Input voltage and current without frequency-tracking algorithm. (b) Input voltage and current with frequency-tracking algorithm.
(a)(b)Figure12 presents the output power as well as the DC-DC efficiency measured versus misalignments. From Figure 12(a), we can see that the efficiency is changed from 82.0% to 81.2% with frequency-tracking; whereas, the efficiency is changed from 81.0% to 75.4% with fixed frequency. The efficiency with frequency-tracking is nearly the same as that with fixed frequency when Δ = 25 cm because the frequency at the highest efficiency point is equal to 85.298 kHz, which is close to 85 kHz. From Figure 12(b), we can see that the output power ranges from 33.2 W to 25.6 W when there is frequency tracking; the output power ranges from 33.2 W to 6.7 W when the frequency is fixed. Apparently, the efficiency of frequency tracking is greater than that of fixed frequency tracking. Meanwhile, the output power of frequency tracking is larger than that of fixed frequency. Interestingly, output power and efficiency in frequency-tracking method remain almost invariable as the misalignment changes from 0 to 20 cm. But in the presence of fixed frequency approach, output power varies greatly under the circumstance that the misalignment changes from 5 to 25 cm.Figure 12
Measured efficiency and output power versus misalignment. (a) Measured DC-DC efficiency versus misalignment. (b) Measured output power versus misalignment.Vref.
(a)(b)The reference voltageVref is given by the following equation:(14)VfilVref=Gvs=LspTs2+Lsp+TRis+RoLspTs2+Lsp+T+RiTs+Ro=1−TsLspTs2+Lsp+T+RiTs+Ro.It is known that the magnitude of the virtual resistance and virtual inductance changes the pole distribution of the output transfer function, i.e., the adjustment of the virtual impedance. The output gainGinv=1 can be obtained and the inverter control parameters in the steady-state condition, but only determined by the reference voltage, so the output voltage can maintain good stability when the load condition is changed. Table 6 gives the virtual impedance parameters of resistive, inductive, and resistive inductance respectively in the industrial frequency state, according to which the step signal response can be obtained with the parameter.Table 6
Control parameters of different virtual impedances.
Output impedanceαβλT/msRi/ΩLi/mHPurely inductive0.20.961.010.635106.35Purely resistive1.26−0.51.0115.80.46.35Resistive inductive10.961.013.1926.35To check the accuracy of results obtained by equations (7) and (12), the simulation is conducted. The result of simulation is presented in Figure 13. Figure 13(a) presents the characteristic angle of input impedance versus ω/ω0 when the lateral misalignments are varied.Figure 13
Input impedance characteristic angle, efficiency, and output power. (a) Characteristic angle of input impedance versusω/ω0. (b) Efficiency versus ω/ω0. (c) Output power versus ω/ω0.
(a)(b)(c)To verify the effectiveness of the algorithm, a system model of the voltage inverter FCS-MPC is built in this study, as listed in Table7.Table 7
Model prediction controller parameters table.
Parameter nameParameter valueDC voltageUdc/V520Load counter-electromotive forceeo/V100Sampling timeTs/μs50Reference currentio∗/A10/10-20Load resistanceRo/Ω0.1Load inductanceLo/mH20The simulation results of the model predictive control system considering different scenarios for the steady state and transient cases at sampling timeTs=50μs are shown below. With delay time and compensation case, the objective function is g2=ioα∗k+1−ioαk+1+ioβ∗k+1−iok+1,ioa,iob,ioc=10A,Roa=Rob=Roc=0.1Ω,Loa=Lob=Loc=20mH, sampling time Ts=25μs.The CNN-based output-time voltage stability evaluation process can be divided into two phases, training and evaluation, as shown in Figure14.Figure 14
Voltage stability evaluation flow at output.The training phase includes the following steps:(1)
Fully consider the key factors, develop a reasonable equivalence scheme, and scale down the studied AC-DC large system significantly with the same transient response characteristics to obtain the equivalence postsystem.(2)
A two-stage partitioning method based on the system structure and output-time voltage similarity is used to partition the AC-DC equivalent system, and each partition is subsequently evaluated separately for output-time voltage stability.(3)
Set different operation modes and fault scenarios, simulate the equivalent system in time domain to obtain the sample set, construct the input feature set based on the steady-state features and fault features, and carry out data normalization preprocessing; according to the basis for judging the voltage stability at output and the calculation results of the voltage stability margin at output, label the samples one by one to form two kinds of labels of stability category and margin.(4)
Generate CNN classification model and regression model corresponding to each partition, classify and predict the voltage stability at output and quantitative risk classification for the input samples, test the evaluation effect according to the evaluation index, and apply it to the evaluation if it meets the requirements.Evaluation Stage. Steady-state features are obtained from actual system data, while a number of expected accident sets are generated to obtain fault features, which together constitute the input feature set and are fed into the CNN model of each partition obtained from training for output-time voltage stability prediction and quantitative risk grading evaluation. If the risk levels are 3 and 4, the scheduling and operation personnel are required to take preventive control measures in time to avoid serious damage to the system caused by voltage instability at output.The equivalent switching frequencies of the compensated voltage FFT and H-bridge under CPS-SPWM modulation and HPWM modulation are compared in Table8.Table 8
Comparison of compensation voltage FFT and H-bridge equivalent switching frequency.
Modulation strategyCPS-SPWM modulationHPWM modulationCompensation voltage THD (%)0.431.33Switching frequency3 × 2k2 × 50 + 2kThe load voltage can be stabilized at the target value after CHB-DVR compensation in the case of 30% drop in grid voltage within 0.2 to 0.4 s time.


## 5. Conclusion

The control strategy of CHB-DVR is a method for the design of the control loop as well as the steady-state and dynamic performance analysis, which is mainly responsible for the improvement of the response speed and compensation accuracy of the DVR. In order to make the DVR device achieve the ideal compensation effect, its detection module should be sensitive and accurate enough to have a faster voltage tracking capability. The corresponding compensation strategy can be used to obtain a more accurate and appropriate compensation reference signal. The tracking performance of the DVR device for the compensation reference signal is determined by the control strategy adopted by the DVR, so the selection of a suitable control strategy can make the DVR device have a better compensation effect. The virtual impedance output voltage performance optimization method proposed in this study not only ensures the dynamic and steady-state characteristics but also improves the voltage waveform under nonlinear load conditions and suppresses high-frequency harmonics, which has obvious advantages over the general virtual impedance design method.



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