https://doi.org/10.6113/JPE.2019.19.6.1554

ISSN(Print): 1598-2092 / ISSN(Online): 2093-4718

Comprehensive Coordinated Control Strategy of Virtual Synchronous Generators under Unbalanced Power Grid

Shuhuan Wang^*, Li Han^†, and Kai Chen^*

^†,*School of Electrical and Power Engineering, China University of Mining and Technology, Xuzhou, China

Abstract

When grid voltage is unbalanced, the grid-connected output current and power of Virtual Synchronous Generators (VSGs) are distorted and quadratic. In order to improve the power quality of a grid connected to a VSG when the grid voltage is unbalanced, a comprehensive coordinated control strategy is proposed. The strategy uses the positive sequence current reference command obtained by a VSG in the balanced current control mode to establish a unified negative sequence current reference command analytical expression for the three objectives of current balance, active power constant and reactive power constant. In addition, based on the relative value of each target's volatility, a comprehensive wave function expression is established. By deriving the comprehensive wave function, the corresponding negative sequence current reference value is obtained. Therefore, the VSG can achieve the minimum comprehensive fluctuation under the premise that the three targets meet the requirements of grid connection, and the output power quality is improved. The effectiveness of the proposed control strategy is verified by simulation and experimental results.

Key words: Grid-connected control, Power fluctuation, Virtual synchronous generator, Voltage imbalance

Manuscript received Mar. 7, 2019; accepted Aug. 12, 2019

Recommended for publication by Associate Editor Huiqing Wen.

^†Corresponding Author: dannyli717@163.com Tel: +86-13852092048, China University of Mining and Technology

^*School Electr. Power Eng., China Univ. Mining Tech., China

Ⅰ. INTRODUCTION

An increase of the installed capacity of renewable energy, such as photovoltaic power generation, reduces the rotational standby capacity in the power system, and poses a serious challenge to the safe and stable operation of the power grid [1]-[3]. Based on VSG photovoltaic grid-connected inverters, a relatively stable DC-side voltage can be obtained through maximum power point tracking control (MPPT) and a DC- DC converter circuit in the DC-side photovoltaic array. Thus, the VSG on the inverter side can simulate the active/frequency control and reactive/voltage control characteristics of synchronous generators from the external characteristics, which can provide certain inertia and damping for the grid. This is of great significance for stabilizing the grid voltage and improving the anti-disturbance capability [4]-[7].

The VSG control strategy was first proposed by the European VSYNC Project. Based on the VSYNC study, the University of Leuven in Belgium, the Netherlands Energy Research Center, the Delft University of Technology, the German Lloyd's Technical Universities and other institutions have proposed current type VSG control strategies with the external characteristics of controlled current sources [8], [9]. To compensate for the defects of current VSGs, scholars from the University of Liverpool, the Hefei Institute of Technology and the University of Toronto, have proposed voltage-type VSG control strategies with the external characteristics of controlled voltage sources [10], [11]. The voltage type VSG is suitable for the application of grid-connected operation and isolated island mode in weak power grid environments with high permeability. A mathematical model of an inverter based on VSG control was established, and the active and reactive power control strategy of a VSG in the droop mode was designed [12]. On this basis, an adaptive control method of the moment of inertia was proposed. This method changed the moment of inertia according to the acceleration and slip difference of a VSG, and reduced the overshoot in the dynamic process by reducing the speed and frequency [14]- [16]. In addition, improvements of the VSG control strategy in terms of low voltage ride through capability was studied, and the idea of a VSG was applied to the wind power field [17], [18]. On the other hand, the constant power control of a VSG when the grid frequency and voltage change has been proposed [19]. In this control, the constant active and reactive power can be output. However, when the grid voltage is unbalanced, the proposed control strategy becomes invalid.

The above studies on VSG are all in the environment of the three-phase balance of grid voltage. However, in actual operation, the distribution network voltage is susceptible to three-phase voltage imbalance due to factors such as load imbalance, short-circuit faults and non-full-phase operation. In these cases, the VSG experiences grid-connected current distortion, grid-connected active and reactive power oscillations, and other problems. For the control of a traditional VSG under an unbalanced voltage, a VSG balanced current control method based on negative sequence current suppression was proposed to achieve three-phase current balance [20], [21]. However, the power fluctuation problem was not considered. On this basis, starting from the three goals of achieving a grid-connected current balance, active power constant and reactive power constant, the positive and negative sequence current reference values are obtained in three cases [22], [23]. However, the three targets can only be switched among one another. They cannot be balanced with each other. For the three targets of a traditional inverter, the power reference value is used to establish a unified reference current analytical formula, and a real-time optimization algorithm is added. Since a VSG is essentially a voltage-controlled inverter, the current value reference value cannot be directly calculated from the power reference value. Therefore, this method cannot be used in VSGs. In addition, adding an optimization algorithm makes the system complex and difficult to implement in engineering [24], [25].

Therefore, this paper establishes a unified negative sequence reference current expression according to different control objectives, quantitatively expresses the relative fluctuation value, establishes a comprehensive wave function, and obtains a suitable negative sequence current reference value under the condition of minimum integrated fluctuation. Through the coordinated control of the output current, active power and reactive power of a VSG, the power quality of the VSG’s overall output is improved.

Ⅱ. MODELING OF A VSG UNDER AN UNBALANCED POWER GRID

A VSG simulates the rotor equation of a synchronous generator, introduces virtual inertia and damping in the active- frequency control, and simulates the excitation regulation of the synchronous generator in the reactive power-voltage control. The control equations are displayed in equations (1)-(3).

         (1)

         (2)

         (3)

Where: P_ref and P_e are the given active power and the electromagnetic power of the VSG; ω and ω₀ are the angular frequency of the VSG and the angular frequency of the grid; J and D are the moment of inertia and damping coefficient of the VSG; Q_ref and Q are the reactive set value and actual value; V₀ and V are the rated voltage value and measured voltage value; and D_q is reactive power-voltage droop coefficient.

An overall control block diagram of a VSG is shown in Fig. 1. In this figure, U_dc is the DC side voltage; R, L and C are the filter inductor internal resistance, filter inductor and filter capacitor; i_a, i_b and i_c are the output currents of the VSG; e_a, e_b and e_c are the three-phase voltage of the grid; and L_g is the inductance of the line. The amplitude and phase angle of the reference voltage are obtained by P_ref and Q_ref through the VSG control algorithm, and the three-phase modulation wave is obtained after the current instruction calculation and the current closed-loop control.

Fig. 1. Overall block diagram of a VSG.

If the three-phase power grid is unbalanced and only the fundamental wave electromotive force is considered, the grid electromotive force can be described as a combination of the positive sequence electromotive force, negative sequence electromotive force and zero sequence electromotive force. For a three-phase VSG without a midline connection, since there is no zero-sequence current channel, the zero-sequence electromotive force has no effect on the power. Therefore, the zero-sequence electromotive force is not considered.

When the grid voltage is unbalanced, the VSG output instantaneous complex power is:

         (4)

Where: and are the positive and negative sequence grid voltage complex vectors; and and are the positive and negative sequence output current complex vectors.

The instantaneous active power and reactive power expressions can be represented as:

         (5)

Where: P₀ and Q₀ are the instantaneous active power and reactive power average components; P_s and Q_s are peaks of the active and reactive power fluctuations according to the sinusoidal distribution; and P_c and Q_c are the peaks of the active power and reactive power fluctuations according to the cosine distribution.

Since the instantaneous active and reactive mean components are given values, only power fluctuation calculations are given here. The values are given by:

         (6)

Where: e and i are the instantaneous values of the grid voltage vector E and the current vector I.

When the grid voltage is unbalanced, the output current contains positive and negative sequence components. The VSG output instantaneous active and reactive power includes 2 times the frequency of the active and reactive power fluctuation components in addition to the average power P₀ and Q₀ components. Therefore, when the grid voltage is unbalanced, it is necessary to realize the three control targets of the output current balance, and the active power and reactive power fluctuation suppression. The corresponding positive and negative sequence current reference values can be calculated in the following two aspects under dq coordinates.

1) The VSG output current balance, i.e. the output current, only contains the positive sequence current component, while the negative sequence current component is zero. The output instantaneous average active power and reactive power is substituted into the reactive-voltage and active-frequency control loop of the VSG to obtain a constant reference voltage amplitude V and a phase angle θ. This results in obtaining the three-phase reference voltage v^* of the VSG. In addition, v^* is subjected to dq decomposition and positive and negative sequence separation to obtain the positive sequence components and . Since v^* is the three-phase equilibrium voltage, the negative sequence component is zero, and the reference value of the output current positive sequence component is calculated as shown in equation (7).

         (7)

At this time ; where, , and the grid voltage imbalance state is determined. Then and are unchanged. Since the current only has a positive sequence component and the voltage contains a negative sequence component, it definitely causes fluctuations in the VSG output power.

2) The output active and reactive power of the VSG are constant, i.e. twice the grid frequency fluctuations of the active and reactive power are eliminated. At this time, equivalent to adding a certain component of the negative sequence currents and , the active and reactive constant negative sequence current reference can be obtained. This value is calculated as shown in equation (8).

         (8)

Since there is a negative sequence current, the fluctuations of the active power or reactive power are correspondingly reduced, and the imbalance of the output current increases accordingly. Therefore, a comprehensive equilibrium point needs to be found between the three control targets to improve the output power quality of the VSG when the grid voltage is unbalanced.

Ⅲ. COMPREHENSIVE COORDINATED CONTROL STRATEGY OF A VSG

The current reference values calculated in equations (7) and (8) are obtained by the realization of a single target. The negative sequence current is zero, the power is very large, and when the active or reactive power fluctuation is zero, it leads to an increase in the output current imbalance. Therefore, based on the establishment and derivation of integrated wave function expressions of the current imbalance, the active power fluctuation value and the reactive power fluctuation value, this paper analyzes the mutual constraint relationships among the three, and designs a VSG integrated control strategy to minimize the fluctuations of a VSG under grid voltage imbalance.

It can be seen from equations (7) and (8) that when the grid voltage is unbalanced and the imbalance parameter has been determined, the positive sequence balance current reference value is also determined. However, at this time, only the current balance problem is considered. To take the power fluctuations into account, it is necessary add an appropriate amount of negative sequence current to make the power fluctuations relatively small.

By adding the comprehensive adjustment coefficient λ, the calculation method of the negative sequence reference current value is unified into:

         (9)

The adjustment coefficient in equation (9) is λ∈[0,2]. When λ=1, the negative sequence current component is zero, and the output current is a three-phase equilibrium; when λ=0, the active power fluctuation component is zero, and the output active power is constant; and when λ=2, the reactive power fluctuation component is zero, and the output reactive power is constant. Therefore, the VSG comprehensive control strategy is to achieve the comprehensive equilibrium of 3 goals to determine the specific value of λ.

Substituting equation (9) into equation (6), the maximum expression of the active and reactive power fluctuations according to the sine and cosine distribution is:

         (10)

According to the principle of grid voltage orientation, the d⁺ axis and the d^- axis of the synchronous rotating coordinate system coincide with the positive and negative sequence vectors of the grid voltage, respectively. Thus, at this time: , that is:

         (11)

However, the peak value of the active and reactive power fluctuations according to the sine and cosine distribution cannot accurately reflect the relative fluctuation of the power. Therefore, the relative value of the power fluctuation is compared with the power reference value to calculate the power fluctuation, as in equations (12) and (13). For the same reason, the relative imbalance of the current is calculated using the relative value, as in equation (14).

         (12)

         (13)

         (14)

Since a balance of the three targets is to be achieved, the relative fluctuations of the respective targets need to be integrated into one expression. Thus, the comprehensive wave function is constructed as follows:

         (15)

Where: indicates the relative fluctuation of the active power; indicates the relative fluctuation of the reactive power; indicates the relative imbalance of the current; ξ_i、ξ_p、ξ_q are the coefficients of the weight distribution.

Equations (12), (13) and (14) are integrated into equation (15), that is:

         (16)

It can be seen from equation (16) that F(λ) is a one-element one-time equation with an unknown number λ. Next, this function is deductively analyzed to obtain a suitable λ to minimize the value of F(λ).

When λ∈[0,1]:

         (17)

When λ∈[1,2]:

         (18)

According to the requirements of the grid operation specifications, an asymmetry state with an imbalance of less than 4% is allowed in the power grid. At this time, a constraint condition is added, that is . It is known that .

As can be seen from equations (17) and (18), the monotonicity of F(λ) can be discussed in the following 3 cases:

The 1st case:

         (19)

At this point, take

.         (20)

The 2nd case:

         (21)

At this point, take

.         (22)

The 3rd case:

         (23)

At this point, take

.         (24)

Due to fluctuation of the power grid voltage, formulas (19) ~ (24) are in a dead-zone state when is zero. In order to solve this problem, a threshold m is added to the simulation and experimental program design. When the ratio of to is less than m, it was decided that λ = 1. That is to say, it is kept in the balanced current control mode. The value of m is determined by a national standard for the unbalance of negative sequence voltage.

In summary, a block diagram of the VSG integrated control strategy is shown in Fig. 2. The traditional VSG control in Fig. 2 refers to the generation of the three-phase voltage modulation signal in Fig. 1, which is the process of generating the voltage signal amplitude V and the reference phase θ. By using the adaptive notch filter (ANF) positive and negative sequence separation method to obtain the reference value of the positive and negative sequence voltage in the dq coordinate system, the voltage and current detection on the grid side is obtained. Through the comprehensive control strategy, the value of λ is obtained, and the corresponding positive and negative sequence current reference value is obtained. Then, the positive and negative sequence current reference values are tracked by a PI, and finally the switching signal is obtained by SVPWM modulation.

Fig. 2. Block diagram of the integrated control strategy based on a VSG.

The transfer function of the notch filter used above is:

         (25)

Where: ω_n is the notch angular frequency; and Q is the quality factor.

It is known from the derivation and analysis of the comprehensive wave function F(λ) that the calculation logic of the above VSG integrated control strategy is simple. The value of λ can be obtained to minimize the F(λ) value without adding an online optimization algorithm, which improves the response speed of the system. At the same time, it does not depend on the specific parameters of the line or the type of voltage imbalance, and it does not need to switch the control mode, which improves the engineering practicability of the system.

Ⅳ. SIMULATION RESULTS

The comprehensive coordinated control strategy proposed in this paper is simulated in the MATLAB/Simulink software environment. The main parameters are shown in Table I.

TABLE I SIMULATION PARAMETERS OF SYSTEM

Parameter name	Value and unit
Udc	600 V
E	220 V
L、R	4.8 mH、0.1 Ω
Lg	1.2 mH
C	50
J	0.05 kg·m2
D	10
Dq	0.001
fs	6.4 kHz

Simulation conditions: The phase A voltage amplitude is reduced by 20%, and the power reference value is divided into three stages:

Stage 1: 0.2~0.4 s the active and reactive power are 5 kW and 0.5 kvar, respectively.

Stage 2: 0.4~0.6 s the active and reactive power are 3 kW and 3 kvar, respectively.

Stage 3: 0.6~0.8 s the active and reactive power are 1 kW and 5 kvar, respectively.

According to the actual operation of a power grid and multiple simulations, the weight coefficients ξ_i=0.5, ξ_p=0.3 and ξ_q=0.2 are selected.

According to the comprehensive coordinated control strategy proposed in Section 3, the value of λ is related to the grid voltage imbalance state, and to the given active and reactive power values. Judging by equations (19), (21) and (23), the value of λ can be obtained. In stage 1, according to the case of equation (21), λ=1.56 is obtained from equation (22); in stage 2, according to the case of equation (19), λ=1 is obtained from equation (20); in stage 3, according to the case of equation (23), λ=0.44 is obtained from equation (24).

Fig. 3 and Fig. 4 show simulation results of the output current, active power and reactive power in different control modes. Fig. 5 shows variation results of the integrated wave function values under different control modes.

Fig. 3. Simulation results of output current under different control modes. (a) Traditional balanced current control. (b) Traditional active power constant control. (c) Traditional reactive power constant control. (d) Comprehensive coordination strategy control.

(a)

(b)

(c)

(d)

Fig. 3(a) shows an output current waveform under the traditional balanced current control. According to the control principle, the value of λ in the three stages is always 1. A number of things can be seen by combining the power waveform under the balanced current control in Fig. 4. In stage 1, the output current imbalance is 0.4%, the active and reactive fluctuations are 180 W and 170 var, and the relative fluctuations are 3.6% and 34%, respectively. In stage 2, the output current imbalance is 0.5%, the active and reactive fluctuations are 160 W and 125 var, and the relative fluctuations are 5.3% and 4.2%, respectively. In stage 3, the output current imbalance is 0.4%, the active and reactive fluctuations are 175 W and 150 var, and the relative fluctuations are 17.5% and 3%, respectively. It can be seen from Fig. 5 that in the balanced current control mode, the relative fluctuations of the reactive power and active power in stage 1 and stage 3 are 34% and 17.5%, resulting in a large value of the integrated wave function, and a control effect that is not ideal.

Fig. 4. Simulation results of output active power and reactive power under different control modes.

Fig. 5. Variation results of synthetic wave function values under different control modes.

Fig. 3(b) shows an output current waveform under the traditional active constant control. According to the control principle, the value of λ in the three stages is always 0. A number of things can be seen by combining the power waveform under active constant control in Fig. 4. In stage 1, the output current imbalance is 7.4%, the active and reactive fluctuations are 40 W and 350 var, and the relative fluctuations are 0.8% and 70% respectively. In stage 2, the output current imbalance is 6.9%, the active and reactive fluctuations are 30 W and 250 var, and the relative fluctuations are 1% and 8.3%, respectively. In stage 3, the output current imbalance is 6.6%, the active and reactive fluctuations are 40 W and 310 var, and the relative fluctuations are 4% and 6.2%, respectively. A number of things can be seen from Fig. 5 in the active constant control mode. In stage 1, since the relative fluctuation of the reactive power is very large, it reaches 70%, resulting in the maximum value of the integrated wave function. In stage 3, due to the large reactive power value, the reactive power fluctuation is small, and its impact on the value of comprehensive fluctuation is reduced. The value of comprehensive fluctuation function is the smallest at this stage. However, the current imbalance is 6.6% at this stage, which is not conducive to the normal operation of a power grid.

Fig. 3(c) shows output current waveforms under the traditional reactive constant control. According to its control principle, the value of λ in the three stages is always 2. A number of things can be seen by combining the power waveform under balanced current control in Fig. 4. In stage 1, the output current imbalance is 7.5%, the active and reactive fluctuations are 350 W and 30 var, and the relative fluctuations are 7% and 6% respectively. In stage 2, the output current imbalance is 7.8%, the active and reactive fluctuations are 300 W and 35 var, and the relative fluctuations are 10% and 1.2% respectively. In stage 3, the output current imbalance is 7.6%, the active and reactive fluctuations are 350 W and 30 var, and the relative fluctuations are 35% and 0.6%, respectively. As can be seen from Fig. 5, in the reactive power constant control mode, since stage 2 and stage 3 have relatively large fluctuations in active work, they reach 10% and 35%, resulting in the largest comprehensive wave function value of the two stages. In stage 1, because the active setpoint is large, the active relative fluctuation is small, and its influence on the comprehensive fluctuation value is reduced. The comprehensive fluctuation function value is the smallest at this stage. However, the current imbalance is too high at 7.5%, which is harmful to the normal operation of a power grid.

Fig. 3(d) shows output current waveforms under the control of the comprehensive coordinated strategy in this paper. According to the grid state and the active and reactive power setting values, the values of the three stages of the control strategy are 1.56, 1 and 0.44, respectively. A number of things can be seen by combining the power waveform under the comprehensive coordinated strategy control in Fig. 4. In stage 1, the output current imbalance is 3.7%, the active and reactive fluctuations are 250 W and 85 var, and the relative fluctuations are 5% and 17%, respectively. In stage 2, the output current imbalance is 0.5%, the active and reactive fluctuations are 160 W and 125 var, and the relative fluctuations are 5.3% and 4.2%, respectively. In stage 3, the output current imbalance is 3.5%, the active and reactive fluctuations are 80 W and 230 var, and the relative fluctuations are 8% and 4.6%, respectively. From Fig. 5, it can be seen that in the comprehensive coordinated control mode of this paper, when stage 1 (stage 3) satisfies a current imbalance of less than 4%, the relative fluctuation of the active (reactive) increases slightly while the relative fluctuation of the reactive (active) is significantly reduced.

TABLE II COMPARISON OF RESULTS FOR THREE STAGES

Control method	3 stages	Value of λ	Relative imbalance of current relative	Relative fluctuation of active power	Relative fluctuation of reactive power
Balanced current control	Stage 1	1	0.4%	180 W(3.6%)	170 var(34%)
	Stage 2	1	0.5%	160 W(5.3%)	125 var(4.2%)
	Stage 3	1	0.4%	175 W(17.5%)	150 var(3%)
Active constant control	Stage 1	0	7.4%	40 W(0.8%)	350 var(70%)
	Stage 2	0	6.9%	30 W(1%)	250 var(8.3%)
	Stage 3	0	6.6%	40 W(4%)	310 var(6.2%)
Reactive constant control	Stage 1	2	7.5%	350 W(7%)	30 var(6%)
	Stage 2	2	7.8%	300 W(10%)	35 var(1.2%)
	Stage 3	2	7.6%	350 W(35%)	30 var(0.6%)
Integrated strategy control	Stage 1	1.56	3.7%	250 W(5%)	85 var(17%)
	Stage 2	1	0.5%	160 W(5.3%)	125 var(4.2%)
	Stage 3	0.44	3.5%	80 W(8%)	230 var(4.6%)

The value of the integrated wave function is kept minimal in all three stages.

Table II shows specific comparison results of the three stages under different control modes.

Therefore, when compared with the traditional control strategy of taking a fixed value of λ, the comprehensive coordinated control strategy proposed in the paper can obtain a comprehensive adjustment coefficient λ through a comprehensive wave function judgment derivation analysis according to the grid imbalance parameter, and the active and reactive setpoints. A large fluctuation of active or reactive power is suppressed at the cost of a small amount of current imbalance, and the integrated equalization control of the current balance, active power constant and reactive power constant is realized, so that the VSG outputs a good power quality.

Ⅴ. EXPERIMENTAL RESULTS

In order to verify the effectiveness of the VSG comprehensive coordinated strategy control, an experimental platform based on a DSP control board is built, using TI's TMS320F28335 as the core controller. In addition, the DC side adopts a regulated DC source, and the AC measurement uses two sets of autotransformers to generate unbalanced voltage. The main circuit of the experimental platform is shown in Fig. 6. The experimental system parameters are shown in Table III.

Fig. 6. Picture of the experimental platform. (a) Main circuit and control circuit board of the experimental platform. (b) DC-side power supply and transformer.

(a)

(b)

TABLE III SYSTEMATIC EXPERIMENTAL PARAMETERS

Parameter name	Value and unit
Udc	600 V
E	220 V
L、R	4.8 mH、0.1 Ω
Lg	1.2 mH
C	50 μF
fs	6.4 kHz

As stipulated in the national standard “GB/T 15543-2008 Power Quality Three-phase Voltage Unbalance”, the allowable value of normal voltage unbalance at the public connection points of a power system must be 2% and should not exceed 4% in a short time. Therefore, the experimental conditions are set to reduce the voltage of phase C by 6%, and the unbalance of the three-phase voltage is 4%, which meets national standards. A voltage waveform of the power grid is shown in Fig. 7.

Fig. 7. Experimental waveform of grid voltage.

Fig. 8 is a graph showing experimental results of the grid-connected point current output under the traditional VSG control without any control strategy in the experimental grid voltage conditions.

It can be seen from Fig. 8 that the three-phase amplitudes of the grid-connected currents at this time are 2.42 A, 4.43 A and 4.54 A, respectively, and that the current imbalance is 35%, which far exceeds the national grid-connected current standard. It is necessary to add appropriate control strategies to make the current imbalance meet national standards.

Fig. 8. Experimental results of the current of a VSG control without any control strategy

Fig. 9 shows experimental results of the current added to the traditional control strategy and that added to the comprehensive coordinated control strategy of this paper. Set the value of λ to 0 at 0.3~0.5 s. Set the value of λ to 1 at 0.5~0.7 s. Set the value of λ to 2 at 0.7~0.9 s. At 0.9~1.3 s, according to this comprehensive coordinated control strategy, the value of λ is 1.58.

Fig. 10 shows experimental results of the power added to the traditional control strategy and that added to the comprehensive coordinated control strategy. The active power and reactive power are set to 2 kW and 200 var at 0.3~1.1 s, and the active power and reactive power are increased to 3 kW and 300 var at 1.1~1.3 s.

It can be seen from Fig. 9(a) that the three-phase grid- connected current amplitudes under the control of the conventional active power constant (λ= 0) are 4.68 A, 4.436 A and 4.417 A, and that the grid-connected current unbalance is 3.7%. It can be seen from Fig. 10 that the active power and reactive power fluctuations under the control of the conventional active power (λ = 0) are 165 W and 266 var, and that the relative fluctuations are 8.25% and 133%, respectively.

It can be seen from Fig. 9(b) that the amplitudes of the three-phase grid-connected current under the control of the conventional current balance (λ=1) are 4.471 A, 4.524 A and 4.489 A, and that the grid-connected current unbalance is 0.8%. It can be seen from Fig. 10 that the active power and reactive power fluctuations under the control of the conventional current balance (λ=1) are 200 W and 170 var, and that the relative fluctuations are 10% and 85%, respectively.

Fig. 9. Experimental results of the current added to the traditional control strategy and that added to the comprehensive coordinated control strategy of this paper.

(a)

(b)

(c)

(d)

(e)

Fig. 10. Experimental results of the power added to the traditional control strategy and that added to the comprehensive coordinated control strategy of this paper. (a) Active power. (b) Reactive power.

(a)

(b)

It can be seen from Fig. 9(c) that the three-phase grid- connected current amplitudes under the control of the conventional reactive power constant (λ=2) are 4.325 A, 4.596 A and 4.534 A, and that the grid-connected current unbalance is 3.56%. It can be seen from Fig. 10 that the active power and reactive power fluctuations under the control of the conventional reactive power (λ=2) are 270 W and 140 var, and that the relative fluctuations are 13.5% and 70%, respectively.

It can be seen from Fig. 9(d) that the three-phase grid- connected current amplitudes under the control of the comprehensive coordinated strategy (λ=1.58) are 4.421 A, 4.577 A and 4.511 A, and that the grid-connected current unbalance is 1.8%. It can be seen from Fig. 10 that the active power and reactive power fluctuations under the control of the comprehensive strategy (λ=1.58) are 230 W and 145 var, and that the relative fluctuations are 11.5% and 72.5%, respectively.

From Fig. 9(e) and Fig. 10, it can be seen that after 1.1s power changes, the grid-connected current reaches a stable state within two cycles under the control of the comprehensive coordinated strategy in this paper (λ=1.58). The active and reactive power also follow set values within 0.05s.

The above experimental results show the VSG control added to the comprehensive coordinated control strategy of this paper when compared with the VSG control with the traditional balanced current control strategy (λ=1). The current imbalance is slightly increased by 1%, the relative fluctuation of the active power is increased by 1.5%, and the relative fluctuation of the reactive power is reduced by 12.5%. While paying the price of a small increase in the current imbalance and active power fluctuations, the system suppresses large fluctuations in the reactive power. Thus, the VSG output power quality is optimal while considering current balance and power fluctuations. In addition, it can track power changes very well. Similarly, the VSG control added to the comprehensive coordinated control strategy of this paper when compared with two other traditional control strategies (λ=0 or 2) has the same results. It can be seen that the experimental results are consistent with the simulation results.

Ⅵ. CONCLUSION

Aiming at the problem where the VSG control cannot simultaneously achieve the three control objectives of output current balance, active power constant and reactive power constant under the condition of an unbalanced power grid, this paper proposes a VSG comprehensive coordinated control strategy by deriving and analyzing three comprehensive fluctuations. Through simulation and experimental verification of the proposed control strategy, the following conclusions have been drawn.

1) When compared with the traditional inverter multi- objective coordinated control method, the reference value of the current positive sequence and negative sequence is directly calculated from the power. The method of this paper uses the reference value of the positive sequence current to unify the value of the corresponding negative sequence current reference command. The calculation logic is simple and does not require mode switching.

2) A comprehensive wave function is constructed, deducing the influence of the current imbalance, active fluctuation and reactive fluctuation on the integrated wave function, while suppressing large fluctuation targets by slightly increasing the fluctuation of other targets, and minimizing the fluctuation of the whole system. In addition, it can track power changes very well. Therefore, the integrated equalization control between the three targets is realized, and the overall control performance of the VSG is effectively improved.

ACKNOWLEDGMENT

This work was supported by National Natural Science Foundation of China (61703404).

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Shuhuan Wang was born in Henan Province, China, in 1993. He received his B.S. degree in Agricultural Electrification from the Henan University of Technology, Luoyang, China, in 2017. He is presently working towards his M.S. degree in Electrical Engineering at the China University of Mining and Technology, Xuzhou, China. His current research interests include control strategies of virtual synchronous generators and grid-connected photovoltaic control.

Li Han was born in Jiangsu Province, China, in 1977. She received her M.S. degree in Measurement Technology and Instruments, and her Ph.D. degree in Power Machinery and Engineering from Southeast University, Nanjing, China, in 2002 and 2005, respectively. She is presently working as a Professor in the School of Electrical and Power Engineering, China University of Mining and Technology, Xuzhou, China. She is the author or coauthor of more than 30 technical papers. Her current research interests include renewable energy systems, power system automation and wind power dispatching.

Kai Chen was born in Henan Province, China, in 1991. He received his B.S. degree in Biomedical Engineering from Nanjing Medical University, Nanjing, China, in 2015. He is presently working towards his M.S. degree in Electrical Engineering at the China University of Mining and Technology, Xuzhou, China. His current research interests include power system dispatching.