^{*}

Under complex grid conditions, the grid voltage usually has an imbalance, low order harmonics, and a small of DC bias. When the grid voltage contains low order harmonics and a small amount of DC bias component, the inverter's output current cannot meet the grid connection requirements, and there is a three-phase current imbalance in the control strategy of common VSG under unbalanced voltage. A theoretical analysis of non-ideal power grids is carried out, and a VSG control strategy under complex operating conditions is proposed. Firstly, the third-order generalized integrator (TOGI) is used to eliminate the influence of the DC component of grid voltage. An improved delay signal cancellation (DSC) method is proposed to control the balance current and power fluctuation under unbalanced voltage based on the method of common VSG positive and negative sequence separation, It also eliminates the harmonic of command current. Then, the improved quasi proportional resonant controller (QPR) cascaded PI is used to suppress the harmonic current further so that the harmonic content of grid-connected current can meet the grid-connected requirements and achieve the three-phase current balance. Finally, the proposed strategy is verified by simulation under the control objectives of the current balance, active power, and reactive power constant.

With the rapid development of new energy and high level accesses to the distribution network, the damping and inertia of the power system also decrease accordingly. The common grid-connected inverter has defects in providing frequency and voltage support for the power grid. Therefore, it cannot meet the power system's frequency, and voltage regulation performance with a large number of distributed generation penetration. As a result, the stability problem of power system is becoming increasingly serious. Therefore, when the distributed generation is connected to the grid, it should also support the grid voltage and frequency actively. In recent years, the application of virtual synchronous generator (VSG) grid-connected inverter control in the field of new energy has attracted attention [

However, most of the research on VSG is based on the condition of three-phase voltage balance. However, in the actual operation of the power system, the grid voltage is usually affected by various factors, resulting in three-phase voltage imbalance, DC bias component and harmonic content. When the grid voltage is unbalanced, including DC component and harmonic content, VSG will have grid-connected current distortion and output active power and reactive power oscillation just like an ordinary inverter. In reference [

The control strategies proposed in the above literature do not consider the unbalanced grid voltage, harmonic and DC components. Considering the above situation, this paper takes the three-phase balance of output current and constant power as the control objectives when the grid voltage of VSG grid-connected inverter is unbalanced and contains harmonics and a small DC components. It proposes a pre-third-order generalized integrator to eliminate DC components. The improved DSC achieves the current command balance and harmonic elimination based on the VSG control strategy under common voltage imbalance [

Assuming that the grid voltage is not ideal, that is, including DC offset component, three-phase voltage imbalance, and each harmonic component, the three-phase grid voltage can be expressed as
_{0k} is DC component; _{h}^{+} (_{h}^{−}) is the positive (negative) sequence voltage amplitude; _{hk}^{+}( _{hk}^{−}

The third-order generalized integrator can eliminate the DC component of the non-ideal grid voltage in the three-phase static coordinate system. After eliminating the DC component, the non-ideal grid voltage can be expressed as

It can be seen from reference [

When the grid voltage is unbalanced, the expressions of instantaneous active power and reactive power are as follows:

where:
_{dq} is the component of grid voltage in the dq coordinate system, the superscript “-” represents negative sequence component, and the superscript “+” represents the positive sequence component.

The essence of fractional VSG is to simulate the output characteristics of a synchronous generator, so that the grid-connected inverter can have the characteristics and advantages of a synchronous generator. The overall block diagram of the main circuit of fractional VSG is shown in _{dc}_{s} is inverter side impedance, C is filter capacitor, and Z_{g} is grid side impedance. _{a}, i_{b}_{c}_{a}, u_{b}_{c}^{*}^{*}

During grid-connected operation, the VSG power frequency and excitation control loop transmits power to the grid according to the initial set of active and reactive power.To calculate the reference phase and frequency, the active power loop of VSG simulates the primary frequency modulation, damping and inertia of SG. As the power system frequency must be within the allowable range, to meet this requirement, the VSG power frequency control loop must analyze the influence of frequency deviation on VSG. As a virtual synchronous motor, the frequency can be adjusted as long as the mechanical torque is controlled. In terms of power, the frequency can also be adjusted by controlling the output power and the given power, as shown in _{0} _{f}

VSG excitation control loop adjusts the output reactive power and voltage amplitude of grid-connected inverter, as shown in _{ref}_{q}^{*} is the initial given value of inverter reactive power, _{u}_{ref}_{0} is the voltage reference value.

According to

According to

The output voltage _{abc} of the inverter side is decomposed into dq by the d-axis orientation of the grid voltage, and the relationship between voltage and current in the dq coordinate system is as follows:

If _{ref}_{d} and _{ref}_{q} are d-axis and q-axis components of voltage command _{ref}

The positive and negative sequence separation control of grid voltage is adopted to nsure the three-phase current balance. The TOGI module is added before the positive and negative sequence separation module of grid voltage to eliminate the influence of the DC component. A modified DSC after the positive sequence current command is used to obtain a new current command and to eliminate the harmonic component in the current command. The calculation block diagram of the improved positive sequence current command is shown in

Assume that the input signal is

Then the output of the third-order generalized integrator (TOGI) is

It can be seen from _{1∞}(t) is eliminated, and the amplitude and phase are consistent with the AC quantity of the input signal. Thus, the influence of the DC component on the current command calculation can be eliminated according to TOGI. The structure of TOGI is shown in

The transfer function of traditional DSC in s domain is

To eliminate harmonics, traditional DSC usually consists of multiple DSC_{n} in series [

The modified DSC function has _{s}_{s}

Its implementation in the time domain can be simplified as shown in

The Bode diagram of MDSC is shown in

It can be seen from

In order to make the output current follow the current reference value mentioned above, the output current of VSG will keep balance. At this time, the negative sequence current instructions _{d}^{-*}and _{q}^{-*} are all zero.

When the active power must be constant, it can be seen from _{s2} and _{c2} need to be zero

Then when the active power is constant, the negative sequence current command can be obtained from

When the reactive power must be constant, the amplitudes of the reactive power fluctuation components _{s}_{2} and _{c}_{2} need to be zero

When the reactive power is constant, the negative sequence current command can be obtained from

The ideal proportional resonance (PR) regulator has infinite gain at the resonance frequency, and can realize the static error-free tracking of AC signal, but it has a certain influence on the system's stability. Therefore, this paper adopts the QPR regulator. The transfer function of QPR is as follows
_{QPR}_{r}_{0} represents the resonant frequency; _{c}

QPR at resonant frequency _{0} The gain is

It can be seen from _{0} The gain of _{QPR}_{r}

For AC input, at resonant frequency _{0} When only PI regulator is used in the current controller, the gain is

This paper adopts the improved QPR cascade PI control strategy with harmonic control to eliminate the 5th, 7th, 11th, and 13th harmonics in a three-phase static coordinate system, that is, the 6th and 12th harmonics in the dq coordinate system. The structure block diagram is shown in

The proportional term of the fundamental control part QPR is removed to reduce the gain of the non-resonant point,. According to

where:

The bode diagram corresponding to

Similarly, the negative sequence current inner loop control block diagram is consistent with the positive sequence current inner loop control block diagram, and the control quantity is the negative sequence component.

The simulation results show that the traditional current control strategy and the improved balanced current control strategy proposed in this paper are simulated by Matlab/Simulink software. The simulation parameters are as follows (

First, the balance current control is taken as the goal. The simulation duration is 2 s. The grid voltage is normal within 0∼0.5 s, the voltage amplitude of phase A drops to 240 V within 0.5∼1 s, and the grid voltage contains 5 times, 7 times, and 11 times. Sub-harmonics within 1∼1.5 s, the power grid A phase contains 15 V DC component within 1.5∼2 s.

It can be seen from

Parameter name | Value and unit | Parameter name | Value and unit |
---|---|---|---|

DC power supply _{dc} |
800 V | Inverter side resistance _{s} |
0.1 Ω |

Effective value of AC phase voltage | 220 V | Grid side resistance _{g} |
0.1 Ω |

Inverter side inductance _{S} |
5 mH | Filter capacitor C | 20 uF |

Grid side inductance _{g} |
3 mH | _{r} |
100 |

_{6r} |
200 | _{12r} |
250 |

_{6} |
1 | _{12} |
1 |

Given value of active power |
15 Kw | ^{*} |
0 Kvar |

When the A-phase voltage amplitude drops to 240 V, the common VSG control balanced current under unbalanced voltage can still maintain the current balance, and the current amplitude is 34.3 A. When the grid voltage contains harmonics, the output current of common VSG control balanced current under unbalanced voltage will contain harmonics. The harmonic distribution of the three-phase current is shown in

It can be seen from

When the grid voltage contains a small amount of DC component, it can be seen from

Under the same simulation conditions, the output three-phase current waveform of the proposed VSG control strategy under complex conditions is shown in

It can be seen from

The harmonic distribution of VSG control strategy under complex conditions is shown in

According to the harmonic distribution diagram 13, the output current harmonics can be completely suppressed by the VSG control strategy under complex conditions when the grid voltage has harmonics. The current THD of phase A, phase B, and phase C is reduced from 7.58% to 1.08%, 28.43% to 1.09%, and 24.25% to 1.07%, respectively. The harmonic content is greatly reduced to meet the requirements of the grid-connected harmonic content standard.

Under the current balance control target, the power waveforms of the traditional balance current control strategy and the comprehensive control strategy under complex conditions are shown in

It can be seen from

Under the same simulation conditions as the current balance control objective, the proposed scheme is verified with the a constant active power control objective.

According to

Under the target of constant reactive power, the reactive power waveforms under the two control strategies are shown in

It can be seen from

In this paper, VSG control strategy is proposed in the complex condition to realize grid-connected current to meet the grid connection requirements under complex voltage conditions, in the case of unbalanced three-phase voltage, harmonic and small DC components. The harmonic current is controlled by using TOGI to eliminate DC components, improve DSC and QPR cascade pi to control harmonic current. The harmonic content and unbalance degree meet the grid connection standard when grid-connected current balance is used for control purposes under the non-ideal grid voltage. Compared with the common VSG control balanced current under unbalanced voltage, VSG control under complex conditions can be applied in the multi-operation condition of power grid voltage. Finally, the control strategy can still achieve the control target under the condition that the power is constant for the control purpose.