Harmonic State Space Based Impedance Modeling and Virtual Impedance Based Stability Enhancement Control for LCC-HVDC Systems

Line commutated converter based high-voltage direct-current(LCC-HVDC)transmissions are prone to harmonic oscillation under weak grids.Impedance modeling is an effective method for assessing interaction stability.Firstly,this paper proposes an improved calculation method for the DC voltage and AC currents of commutation stations to address the complex linearization of the commutation process and constructs an overall harmonic state-space(HSS)model of an LCC-HVDC.Based on the HSS model,the closed-loop AC impedances on the LCC-HVDC sending and receiving ends are then derived and verified.The impedance characteristics of the LCC-HVDC are then analyzed to provide a physical explanation for the harmonic oscillation of the system.The effects of the grid strength and control parameters on system stability are also analyzed.To improve the impedance characteristics and operating stability of the LCC-HVDC system,a virtual impedance based stability enhancement control is proposed,and a parameter design method is considered to ensure satisfactory phase margins at both the sending and receiving ends.Finally,simulation results are presented to verify the validity of the impedance model and virtual impedance based stability enhancement control.

Adaptive Harmonic Virtual Impedance Control for Improving Voltage Quality of Microgrids

The effects of nonlinear loads on voltage quality represent an emerging concern for islanded microgrids.Existing research works have mainly focused on harmonic power sharing among multiple inverters,which ignores the diversity of different inverters to mitigate harmonics from nonlinear loads.As a result,the voltage quality of microgrids cannot be effectively improved.To address this issue,this study proposes an adaptive harmonic virtual impedance(HVI)control for improving voltage quality of microgrids.Based on the premise that no inverter is overloaded,the main objective of the proposed control is to maximize harmonic power absorption by shaping the lowest output impedances of inverters.To achieve this,the proposed control is utilized to adjust the HVI of each inverter based on its operation conditions.In addition,the evaluation based on Monte Carlo harmonic power flow is designed to assess the performance of the proposed control in practice.Finally,comparative studies and control-in-the-loop experiments are conducted.

Power quality enhancement in islanded microgrids via closed-loop adaptive virtual impedance control

The high proportion of nonlinear and unbalanced loads results in power quality issues in islanded microgrids.This paper presents a novel control strategy for harmonic and unbalanced power allocation among distributed genera-tors(DGs)in microgrids.Different from the existing sharing strategies that allocate the harmonic and unbalanced power according to the rated capacities of DGs,the proposed control strategy intends to shape the lowest output impedances of DGs to optimize the power quality of the microgrid.To achieve this goal,the feasible range of virtual impedance is analyzed in detail by eigenvalue analysis,and the findings suggest a simultaneous adjustment of real and imaginary parts of virtual impedance.Because virtual impedance is an open-loop control that imposes DG to the risk of overload,a new closed-loop structure is designed that uses residual capacity and absorbed power as feedback.Accordingly,virtual impedance can be safely adjusted in the feasible range until the power limit is reached.In addi-tion,a fuzzy integral controller is adopted to improve the dynamics and convergence of the power distribution,and its performance is found to be superior to linear integral controllers.Finally,simulations and control hardware-in-the-loop experiments are conducted to verify the effectiveness and usefulness of the proposed control strategy.

Circulating Current Suppression Method with Adaptive Virtual Impedance for Multi-bidirectional Power Converters Under Unbalanced Conditions

Multi-paralleled bidirectional power converters(BPCs)are commonly used to improve the power capacity and reliability in an AC/DC hybrid microgrid.However,circulating current through multi-BPCs has been one of the challenges and it can be aggravated in the presence of non-ideal operating conditions,such as unbalanced AC voltages,and the mismatch of hardware parameters.In order to suppress the circulating current,this paper proposes a distributed method based on adaptive virtual impedance,which also employs positive sequence power droop control and voltage deviation compensation control.The traditional positive sequence power droop control is adopted to only regulate the positive components of the BPCs output voltage.The negative sequence power term is fed to an adaptive virtual impedance generator to modify the damping characteristics of the BPCs.Also,an adaptive virtual impedance-based voltage deviation compensation method is proposed to recover the fluctuated output voltage of the BPCs due to droop action and the power fluctuations.The fully distributed regulation of adaptive virtual impedance enables the load power to be shared accurately among BPC modules and thus the circulating current can be effectively suppressed.The proposed control strategy does not require an additional communication system and the precise parameters of hardware equipment and line impedance.Furthermore,the effectiveness of the proposed method is verified by the experimental results.

Joint Limiting Control Strategy Based on Virtual Impedance Shaping for Suppressing DC Fault Current and Arm Current in MMC-HVDC Systems

This paper proposes a joint limiting control strategy for suppressing DC fault current and arm current in modular multilevel converter-based high-voltage direct current(MMC-HVDC) systems, which includes two target-oriented current limiting controls. To limit the DC fault current in the early fault stage, an equivalent modular multilevel converter(MMC) impedance is obtained, and its high-frequency part is reshaped by introducing virtual impedance, which is realized by adjusting the inserted submodules adaptively. Following the analysis of MMC control characteristics, the arm current limiting strategy is investigated, with results showing that the inner-loop control has significant effects on arm current and that a simple low-pass filter can reduce the arm current in the fault period. Finally, by combining the virtual impedance shaping and innerloop control, the fault currents of DC lines and MMC arms can be suppressed simultaneously, which can not only alleviate the interrupting pressure of the DC circuit breaker, but also prevent the MMC from being blocked by the arm overcurrent. Theoretical analysis conclusions and the proposed strategy are verified offline by a digital time-domain simulation on Power Systems Computer Aided Design/Electromagnetic Transients including DC platform, and experiment on a real-time digital simulator platform.

A virtual lock-in amplifier,spectrum analyzer,impedance meter and semiconductor analyzer implemented on an SR7265 hardware target

Lock-in amplifiers are used to detect and measure very small alternating current(AC)signals down to the range of nVs.Accurate measurements can be made even when the small signals are buried by noise thousands of times larger.With the digital signal processing(DSP)technology involved in modern instrumentation,a lock-in amplifier is more versatile in sensing and recovering small signals.Combining the virtual instrumentation technology,we reorganize the functional blocks of a programmable lock-in amplifier and build it as a virtual spectrum analyzer,virtual impedance meter,virtual network analyzer,virtual semiconductor parameter analyzer,signal generator,etc.A 4 layer model is used to implement these virtual instruments.The same virtual instrument can also be implemented on a general purpose FPGA developing board.

Coordinated Control of Parallel Three-phase Four-wire Converters in Autonomous AC Microgrids

The coordinated control of parallel three-phase fourwire converters in autonomous AC microgrids is investigated in this paper.First,based on droop control,virtual impedance is inserted in positive-,negative-and zero-sequences to enhance system damping and imbalance power sharing.Then,to facilitate virtual impedance design,small signal models of the three-sequence equivalent circuits are established respectively.Corresponding indexes are proposed to comprehensively evaluate the impact of sequence virtual impedance on current sharing accuracy,voltage quality at the point of common coupling(PCC)and system stability.In addition,constraint of DClink voltage is also considered to avoid over modulation when subjected to unbalanced loads.Furthermore,to address the PCC voltage degradation resulting from virtual impedance,a voltage imbalance compensation method,based on low-bandwidth communication,is proposed.Finally,simulation and experimental results are provided to verify the correctness of the theory model,indicating that the proposed method can achieve PCC voltage restoration while guaranteeing the current sharing accuracy with desirable dynamics.

Dynamic Improvement of DC Microgrids Using a Dual Approach Based on Virtual Inertia

In this paper,inspired by the concept of virtual inertia in alternating current(AC)systems,a virtual impedance controller is proposed for the dynamic improvement of direct current microgrids(DCMGs).A simple and inexpensive method for injecting inertia into the system is used to adjust the output power of each distributed generation unit without using additional equipment.The proposed controller consists of two components:a virtual capacitor and a virtual inductor.These virtual components can change the rate of change of the DC bus voltage and also improve the transient response.A small-signal analysis is carried out to verify the impact of the proposed control strategy.Numerical simulation studies validate the effectiveness of the proposed solution for increasing the inertia of DCMGs.

A Finite-time Distributed Cooperative Control Approach for Microgrids

Reactive power sharing cannot be achieved using many existing microgrid(MG)control methods,but the convergence speed of these methods is slow.To solve these problems,a finite-time distributed control approach is proposed in this paper,which is based on the hierarchical control structure.The hierarchical control structure consists of a dual loop control,a droop control used as a primary control and a secondary control.First,the secondary controller is modeled,and the MG system composed of distributed generators(DGs)is considered as a multi-agent system.The secondary controller consists of a frequency regulator,voltage regulator and power regulator.Secondly,the adaptive virtual impedance module is established,using the output of the reactive power regulator as its input.Thirdly,a dual loop controller is combined with a primary controller and secondary controller to generate a pulse width modulation(PWM)signal to control the power and voltage of the MG.In order to reduce the fluctuation of the MG,a damping module is introduced when the structure of the system changes.Finally,the stability of the proposed control strategy is proved by the related theorems.A simulation system is established in the Matlab environment,and the simulation results show that the proposed method is effective.

A Harmonic Compensation Approach for Interlinking Voltage Source Converters in Hybrid AC-DC Microgrids with Low Switching Frequency

In recent years,the hybrid AC-DC microgrid has been well accepted as it combines the advantages of both AC and DC systems.As the microgrid contains both DC sub-grids and AC sub-grids,interlinking DC-AC converters are essential.Meanwhile,considering the nonlinear AC loads may deteriorate the voltage quality of the AC bus,embedding an ancillary harmonic compensation function to the interlinking converters is promising.However,the conventional harmonic control methods used for active power filters(APFs)may not be suitable for the interlinking converters due to the main purpose of it is to exchange real and reactive power between the DC and AC sub-grids.The switching frequency is preferred to be lower than the APFs when the capacity of the microgrid is large.At low switching frequency,harmonic compensation performance or even the system stability may be affected.In this paper,a harmonic compensation approach suitable for hybrid AC-DC interlinking converters at low switching frequency is proposed.Through feeding the PWM reference signal with the harmonic compensation component directly to avoid the multi-loop control path of the fundamental component,the proposed method can achieve the effective harmonics compensation without being limited by the closed-loop control bandwidth.The proposed method,modeling approaches,stability analysis,as well as detailed virtual impedance design are presented.Experimental verification is also provided.

Analysis and Optimization of Boost Converter Parameters in Internal Model Control for Voltage Source Converter-based AC Microgrids

This paper investigates integration of distributed energy resources(DERs)in microgrids(MGs)through two-stage power conversion structures consisting of DC-DC boost converter and DC-AC voltage source converter(VSC)subsystems.In contrast to existing investigations that treated DC-link voltage as an ideal constant voltage,this paper considers the non-ideal dynamic coupling between both subsystems for completeness and higher accuracy,which introduces additional DC-side dynamics to the VSC.The analysis shows parameters of the boost converter’s power model that impact stability through the DC-link.Carefully selecting these parameters can mitigate this effect on stability and improve dynamic performance across the DC-link.Hence,an optimization framework is developed to facilitate in selecting adequate boost converter parameters in designing a stable voltage source converter-based microgrid(VSC-MG).The developed optimization framework,based on particle swarm optimization,considers dynamic coupling between both subsystems and is also effective in avoiding inadequate boost converter parameters capable of propagating instability through the DC-link to the VSC.Simulations are performed with MATLAB/Simulink to validate theoretical analyses.