A Virtual Synchronous Machine Control Method for Grid-Connected Equipment to Eliminate Grid-Connected Voltage Harmonic Disturbances

Abstract

A virtual synchronous machine control method for grid-connected equipment to eliminate grid-connected voltage harmonic disturbances, comprising the following steps: designing a VSG power outer-loop controller, and using the output of the VSG power outer-loop controller as the input of the VSG voltage inner-loop; establishing a state-space mathematical model of the grid-side converter GSC of the grid-connected equipment, designing a state feedback SF controller adopted by the VSG voltage inner-loop, and obtaining a VSG voltage inner-loop SF control closed-loop system; establishing a generalized integral GI controller based on a harmonic disturbance signal model; selecting a compensator for the GI controller. If the control gain of the GI controller meets the judgment condition, adding the GI controller to the control loop of the VSG voltage inner-loop SF control closed system can make the control system still remain stable. It can better cope with the impact of large-scale new energy access on the power grid and enhance the dynamic support ability of the grid-forming flexible grid-connected equipment.

Description

Technical Field

[0001] The present invention relates to a control method for a virtual synchronous machine of a grid-connected device for eliminating grid-connected voltage harmonic disturbances. Background Art

[0002] With the large-scale, high-penetration, and high-density access of distributed new energy generating units (DGs) with power electronic converter grid-connected interfaces and various loads to the power grid, the penetration rate of conventional thermal power units based on synchronous generators (SGs) has been continuously decreasing. However, power electronic grid-connected interfaces do not have the characteristics of a rigid body moment of inertia. When a small disturbance occurs in the system and there is a power deficit, DG units cannot provide additional power dynamic support; while conventional SG units can respond to this process in real time due to their large moment of inertia. The decreasing penetration rate of SG units means that the power system will experience deteriorated operating stability due to the lack of sufficient inertia support. To address the lack of system inertia and damping brought about by the high-density and high-penetration access of new energy, and to improve the power grid frequency, voltage support capabilities, and system stability, the grid-forming control technology based on virtual synchronous generators (VSGs) has emerged. By simulating the dynamic regulation characteristics of synchronous generators, VSGs can provide necessary inertia and damping during system disturbances to suppress the fluctuations of the power grid frequency and output power.

[0003] Virtual synchronous generator (VSG) control provides grid-forming control functions such as power grid frequency support and droop control by simulating the virtual inertia and droop characteristics of synchronous generators to enhance the operating stability of the power system. VSG control includes an outer-loop power control loop and an inner-loop voltage control loop. The inner-loop voltage control loop of conventional VSG control mostly uses a synchronous rotating coordinate system (SRF) proportional-integral (PI) controller, which cannot guarantee high-quality grid-connected (PCC) voltage under harmonic distortion disturbances, such as nonlinear rectifier charging loads, distorted grid voltages, etc. The distorted PCC voltage will increase the risk of oscillation of grid-forming wind turbines. In addition, the parameter design and tuning of the PI controller are usually completed by trial and error, and the parameter optimization and debugging process of the voltage controller is very time-consuming. Summary of the Invention

[0004] The purpose of the present invention is to solve the above-mentioned deficiencies of the prior art, and thus provide a control method for a virtual synchronous machine of a grid-connected device for eliminating grid-connected voltage harmonic disturbances, which can better cope with the impact of large-scale new energy access on the power grid and enhance the dynamic support capabilities of grid-forming flexible grid-connected devices.

[0005] A control method for a virtual synchronous machine of a grid-connected device for eliminating grid-connected voltage harmonic disturbances includes the following steps:

[0006] Step 1: Design the virtual synchronous generator (VSG) power outer-loop controller, and use the output of the VSG power outer-loop controller as the input of the VSG voltage inner-loop.

[0007] Step 2: Establish the state-space mathematical model of the grid-connected device's grid-side converter (GSC). Based on the state-space mathematical model of the GSC, design the state feedback (SF) controller adopted by the VSG voltage inner-loop, and obtain the VSG voltage inner-loop SF control closed-loop system.

[0008] Step 3: Establish a generalized integral (GI) controller based on the harmonic disturbance signal model.

[0009] Step 4: Select the compensator of the GI controller to fully compensate the phase delay of the VSG voltage inner-loop SF control closed-loop system at the hth harmonic frequency. If the control gain of the GI controller meets the judgment condition, adding the GI controller to the control loop of the VSG voltage inner-loop SF control closed-loop system can make the control system still remain stable.

[0010] The virtual synchronous generator (VSG) power outer-loop controller is as follows:

[0011] (1)

[0012] (2)

[0013] Formula (1) represents the relationship between the active power P of the VSG and the frequency where P ref is the input active power signal of the VSG power outer-loop, P is the active power output signal of the grid-connected device, J is the moment of inertia of the VSG, and D is the damping coefficient; is the mechanical angular frequency of the VSG, is the grid angular frequency; Formula (2) represents the droop characteristic of the reactive power Q of the VSG and the voltage v m where v m is the grid connection point voltage reference value in the synchronous rotating dq-axis coordinate system, v0 is the rated voltage, k q is the droop coefficient, Q ref is the input reactive power signal of the VSG power outer-loop, and Q is the reactive power output signal of the grid-connected device;

[0014] Using the output of the VSG power outer-loop controller as the input of the VSG voltage inner-loop, specifically:

[0015] The grid connection point voltage reference quantity v m output by the VSG power outer-loop is converted into the three-phase grid connection point voltage reference quantity v ref,j (k) in the stationary abc coordinate system through the dq / abc coordinate transformation, where the voltage phase number j = a, b, c, and the three-phase grid connection point voltage reference quantity vref,j (k) will be the reference input quantity of the inner loop of the VSG voltage.

[0016] Step 2 specifically includes the following steps:

[0017] Establish the following mathematical model of the differential equation of the GSC of the wind turbine:

[0018] (3)

[0019] Discretizing (3) can obtain the following discrete state-space mathematical model of the GSC:

[0020] (4)

[0021] Where is the state variable, is the control variable, , and are coefficient matrices, i 1,j (k) is the inductor current of phase j on the GSC side, v o,j (k) is the voltage of phase j at the grid connection point, u j (k) is the control signal of phase j of the GSC, i o,j (k) is the output current flowing from the GSC to the grid;

[0022] Based on the discrete state-space mathematical model of the GSC, the SF controller adopted by the inner loop of the VSG voltage is as follows:

[0023] (5)

[0024] Where , j is the number of voltage phases, j = a, b, c;

[0025] Substituting Equation (5) into Equation (4), the SF control closed-loop system of the inner loop of the VSG voltage can be obtained as:

[0026] (6)

[0027] By selecting the feedback coefficient matrix F and , the SF controller can directly configure the poles of the SF control closed-loop system of the inner loop of the VSG voltage, and obtain a SF control closed-loop system of the inner loop of the VSG voltage with good rapidity and stability by optimizing the pole configuration within the unit circle;

[0028] For the SF control closed-loop system of the inner loop of the VSG voltage, the transfer function from the voltage reference quantity of the grid connection point voltage to the grid connection point voltage v o,j (k) is denoted as .

[0029] The GI controller is:

[0030] (7)

[0031] Wherein, is the h-th harmonic disturbance signal with a frequency of and is expressed as:

[0032] , (8)

[0033] k h is the control gain of the GI controller for the h-th harmonic disturbance with a frequency of , F h (z) is the compensator for the h-th harmonic disturbance with a frequency of , is the phase compensation angle at the frequency , T S is the sampling frequency of the control system.

[0034] Select the compensator of the GI controller to completely compensate for the phase delay of the VSG voltage inner-loop SF control closed-loop system at the h-th harmonic frequency, which is expressed as:

[0035] .

[0036] The judgment condition for the control gain of the GI controller is:

[0037] .

[0038] The grid-connected device VSG control method proposed by the present invention can quickly, robustly and accurately regulate the grid-connected voltage, eliminate the grid-connected voltage harmonic distortion caused by harmonic disturbances, reduce the risk of system oscillation that may be caused by the VSG control method, and better meet the development requirements of future new energy-friendly grid-connected technologies.

[0039] The present invention is directed to a grid-forming grid-connected device, and proposes a virtual synchronous machine voltage inner-loop controller composed of a state feedback (SF) controller based on a grid-side converter (GSC) model and a generalized integral (GI) controller based on a harmonic disturbance signal model, which is used to quickly, robustly and accurately regulate the grid-connected voltage and eliminate the harmonic distortion caused by harmonic disturbances, thereby improving the power quality of the grid-connected device output and the system stability;

[0040] The present invention provides a simple and easy method for designing and selecting controller parameters for the virtual synchronous machine voltage inner-loop controller proposed, which is composed of a state feedback controller based on a grid-side converter model and a generalized integral controller based on a harmonic disturbance signal model. Description of the Drawings

[0041] Figure 1 It is the topology diagram of the grid-forming wind turbine VSG control system under the condition of harmonic distortion disturbance;

[0042] Figure 2 It is the control block diagram of the VSG power outer loop controller;

[0043] Figure 3 It is the control block diagram of the conventional VSG voltage inner loop PI controller;

[0044] Figure 4 It is the control block diagram of the VSG voltage inner loop state feedback SF controller based on the GSC model;

[0045] Figure 5 It is the waveform diagram of the grid-connected point voltage and current of the GSC with a PI voltage controller in the VSG voltage inner loop;

[0046] Figure 6 It is the waveform diagram of the grid-connected point voltage and current of the VSG voltage inner loop with an SF+GI composite voltage controller designed by the present invention. Specific implementation manner

[0047] The virtual synchronous machine control method of the grid-forming grid-connected device (such as a wind turbine) for eliminating grid-connected voltage harmonic disturbance of the present invention includes the steps:

[0048] Step 1, design the VSG power outer loop controller as follows:

[0049] (1)

[0050] (2)

[0051] In the above formula, formula (1) is used to design the relationship between the active power (P) - frequency ( ) of the VSG, where P ref is the input active signal of the power outer loop, P is the active output signal of the GSC, J is the moment of inertia of the VSG, and D is the damping coefficient; is the mechanical angular frequency of the VSG, is the grid angular frequency; formula (2) is used to design the reactive power (Q) - voltage (v m ) droop characteristic. Where v m is the reference value of the grid-connected point voltage, v0 is the rated voltage, k q is the droop coefficient, Q ref is the input reactive signal of the VSG power outer loop, and Q is the reactive output signal of the GSC.

[0052] The grid-connected point voltage reference quantity v output by the VSG power outer loopm , after the dq / abc coordinate transformation, it will be converted into the three-phase grid connection point voltage reference quantity v in the stationary abc coordinate system ref,j (k), where the voltage phase number j = a, b, c. The three-phase grid connection point voltage reference quantity v ref,j (k) will be used as the reference input quantity of the VSG voltage inner loop

[0053] Step 2: Establish the mathematical model of the grid-side grid-connected converter GSC of the grid-connected equipment, and then design and establish the state feedback SF controller of the VSG inner-loop voltage loop based on the mathematical model of GSC, and obtain the VSG voltage inner-loop SF control closed-loop system;

[0054] Establish the differential equation mathematical model of the wind turbine GSC as follows:

[0055] (3)

[0056] Discretize (3) to obtain the discrete state-space mathematical model of GSC as follows::

[0057] (4)

[0058] Among them, is the state variable, is the control variable, , and are coefficient matrices, i 1,j (k) is the inductor current of phase j on the GSC side, v o,j (k) is the j-phase PCC voltage, u j (k) is the control signal of phase j of GSC, i o,j (k) is the output current flowing into the power grid

[0059] Based on the state-space mathematical model of GSC, the VSG inner-loop voltage loop adopts the SF controller as follows:

[0060] (5)

[0061] Among them is the grid connection point voltage reference quantity of phase j = a, b, c

[0062] Substitute Equation (5) into Equation (4), and the VSG voltage inner-loop closed-loop system using the SF controller can be obtained as

[0063] (6)

[0064] By selecting the feedback coefficient matrix F and , the SF controller can directly and arbitrarily configure the poles of the VSG voltage inner-loop SF control closed-loop system, and obtain a VSG voltage inner-loop SF control closed-loop system with good fastness and stability by optimizing the pole configuration within the unit circle. For the VSG voltage inner-loop SF control closed-loop system, from the grid-connected point voltage reference to the grid-connected point voltage v o,j (k), the transfer function is denoted as .

[0065] Step 3, establish a General Integrator (GI) controller based on the harmonic disturbance signal model as follows:

[0066] (7)

[0067] where is the following model of the h-th harmonic disturbance signal with frequency

[0068] , (8)

[0069] k h is the control gain of the GI controller for the h-th harmonic disturbance with frequency , F h (z) is the compensator for the h-th harmonic disturbance with frequency , is the phase compensation angle at frequency , T S is the sampling frequency of the control system.

[0070] Step 4, design and select F h (z) to completely compensate for the phase delay of the voltage inner-loop SF control closed-loop system at the h-th harmonic frequency, that is . If the control gain of the GI controller satisfies

[0071] ,

[0072] then after adding the GI controller to the VSG voltage inner-loop SF control closed-loop system, the control system will still remain stable.

[0073] The VSG voltage inner-loop composite controller composed of the SF controller based on the GSC model and the GI controller based on the harmonic disturbance signal model will be able to eliminate the grid-connected point voltage distortion caused by harmonic disturbances while maintaining the fastness and robustness of the SF controller, thereby reducing a series of risks such as system harmonic oscillations.

[0074] Example:

[0075] ​The present invention will implement and verify the effectiveness of the VSG voltage inner-loop voltage control method designed according to the present invention in the case where there are nonlinear rectifier load disturbances at the grid connection point of grid-forming grid-connected equipment (such as wind turbines) and harmonic distortions in the grid voltage. The present invention selects the conventional PI control method for the VSG voltage inner loop as a comparison scheme to verify the superiority of the control method proposed by the present invention. The specific situation is as follows:

[0076] Figure 1 In (a) is the block diagram of the VSG control system of the grid-forming wind turbine. Figure 1 In (b) is the circuit topology diagram of the VSG control system of the grid-forming wind turbine. The wind turbine includes a wind wheel, a permanent magnet synchronous generator, a machine-side converter RSC, and a grid-side converter GSC. The RSC is a three-phase AC / DC converter, and the GSC is a three-phase DC / AC converter. The permanent magnet synchronous generator is connected to the AC side of the machine-side converter. The wind wheel is installed on the input shaft of the permanent magnet synchronous generator. The permanent magnet synchronous generator and the wind wheel form a wind turbine. Capacitors are connected in parallel on the DC sides of the RSC and the GSC. The AC side of the three-phase GSC is connected to the grid. A nonlinear rectifier load is connected at the grid connection point (PCC). The equivalent inductance of the grid line is L g,j , j = a, b, c the grid voltage v g,j , j = a, b, c contains harmonic distortions.

[0077] When the wind turbine operates in the grid-forming mode, the GSC adopts the VSG control method. The VSG control includes an outer-loop power control loop and an inner-loop voltage control loop.

[0078] As Figure 2 shown, the outer-loop power control loop defines the grid-forming control functions such as the grid frequency support and droop control of the GSC by simulating the virtual inertia and droop characteristics of the synchronous generator as follows

[0079] (1)

[0080] (2)

[0081] As Figure 3 shown, the conventional inner-loop voltage control loop mostly adopts a model-free dq coordinate system PI controller.

[0082] Since the PI controller cannot effectively suppress the harmonic distortion of the PCC voltage, and it takes time and effort to design and tune the parameters of the model-free PI controller by trial and error and it is difficult to optimize the controller performance. Therefore, according to the method proposed in the present invention, making full use of the model information of the GSC and the harmonic disturbance signal information at the PCC point, a VSG voltage inner-loop controller based on the system model is designed and constructed.

[0083] First, establish the differential equation mathematical model of the GSC of the wind turbine as follows:

[0084] (3)

[0085] Discretizing (3) can obtain the discrete state - space mathematical model of the GSC as follows:

[0086] (4)

[0087] Wherein, is the state variable, is the control variable, , and are coefficient matrices, i 1,j (k) is the inductor current of phase j on the GSC side, v o,j (k) is the voltage of phase j at the grid connection point, u j (k) is the control signal of phase j of the GSC, i o,j (k) is the output current flowing into the grid.

[0088] Based on the discrete state - space mathematical model of the GSC, the VSG voltage inner - loop adopts a state - feedback (SF) controller as follows:

[0089] (5)

[0090] Where is the PCC reference voltage.

[0091] As Figure 4 shown, substituting Equation (5) into Equation (4), the VSG voltage inner - loop SF - controlled closed - loop system can be obtained as

[0092] (6)

[0093] By selecting the feedback coefficient matrix F and , the SF controller can directly and arbitrarily configure the poles of the VSG inner - loop SF - closed - loop feedback voltage - loop control system within the unit circle. By optimizing the pole configuration, a VSG inner - loop voltage - feedback control loop with good fastness and stability can be obtained. For example, by selecting F and such that the poles of the SF control system are configured at the origin, that is, = 0 and H = 1, then , that is, a fast control response without dead - beat is achieved . And since the poles of the dead - beat control system are configured at the origin, far from the stable boundary of the unit circle, the SF control system generally has good robust stability.

[0094] Furthermore, to eliminate the PCC voltage distortion caused by harmonic disturbances, a voltage inner-loop additional General Integrator (GI) controller based on the harmonic disturbance signal model is constructed as follows:

[0095] (7)

[0096] where h ∈ N represents the order of the main harmonics in the harmonic distortion disturbance; is the following model of the h-th harmonic disturbance signal with frequency

[0097] , (8)

[0098] k h is the control gain of the GI controller for the h-th harmonic disturbance with frequency , F h (z) is the compensator for the h-th harmonic disturbance with frequency , is the phase compensation angle at frequency , T S is the sampling frequency of the control system.

[0099] Design and select F h (z) to completely compensate for the phase delay of the SF control system at the h-th harmonic frequency, so that when , if the control gain of the GI controller satisfies

[0100] ,

[0101] then the control system can remain stable after adding the GI controller to the VSG inner-loop SF voltage control loop.

[0102] The following system parameters are used for simulation analysis:

[0103] TABLE Ⅰ. Test System Parameters

[0104] Item Value <![CDATA[DC bus voltage V dc > 400 V <![CDATA[Filter inductor L1]]> 3.4 mH <![CDATA[Filter capacitor C f > 10 uF Rectifier load resistance 150Ω Rectifier load current-limiting inductor 1mH Rectifier load filter capacitor 1000uF <![CDATA[Switching frequency f s > 20 kHz <![CDATA[Grid frequency f0]]> 50 Hz <![CDATA[Line inductance L g > 15mH <![CDATA[Grid voltage v g > 110V Grid voltage harmonic distortion Harmonic amplitudes of the 3rd and 5th orders are 1.5% of the fundamental wave

[0105] When the VSG adopts a conventional PI voltage inner-loop controller, the waveforms of the PCC voltage and current are as shown in Figure 5 , Figure 5 in which (a) is the waveform diagram of the GSC grid connection point voltage when adopting a conventional PI voltage inner-loop controller, Figure 5 in which (b) is the waveform diagram of the GSC grid connection point current when adopting a conventional PI voltage inner-loop controller, where the total harmonic distortion (THD) of the PCC voltage is as high as 7.26%, exceeding the 5% specified by the grid connection standard.

[0106] ​When the VSG adopts the voltage controller based on the system model proposed by the present invention, the waveforms of the PCC voltage and current are as Figure 6 shown, Figure 6 In (a) of Figure 6 is the grid-connected point voltage waveform diagram of the GSC adopting the method proposed by the present invention, Figure 6 In (b) of Figure 6 is the grid-connected point current waveform diagram of the GSC adopting the method proposed by the present invention, where the total harmonic distortion (THD) of the PCC voltage is only 1.8%, far lower than 5% specified by the grid connection specification.

Claims

1. A virtual synchronous machine control method for grid-connected equipment to eliminate grid-connected voltage harmonic disturbances, characterized in that, It includes the following steps: Step 1: Design a virtual synchronous generator (VSG) power outer-loop controller, and use the output of the VSG power outer-loop controller as the input of the VSG voltage inner-loop; Step 2: Establish the state-space mathematical model of the grid-connected device grid-side converter (GSC). Based on the state-space mathematical model of the GSC, design the state feedback (SF) controller adopted by the VSG voltage inner-loop, and obtain the VSG voltage inner-loop SF control closed-loop system; Step 3: Establish a generalized integrator (GI) controller based on the harmonic disturbance signal model; Step 4: Select the compensator of the GI controller to completely compensate the phase delay of the VSG voltage inner-loop SF control closed-loop system at the hth harmonic frequency. If the control gain of the GI controller meets the judgment condition, adding the GI controller to the control loop of the VSG voltage inner-loop SF control closed-loop system can make the control system still remain stable.

2. The virtual synchronous machine control method for a grid-connected device to eliminate grid-connected voltage harmonic disturbances according to claim 1, characterized in that, The virtual synchronous generator (VSG) power outer-loop controller is: (1) (2) Equation (1) represents the active power P of the VSG and the frequency relationship, where P ref is the input active signal of the VSG power outer loop, P is the active output signal of the grid-connected device, J is the moment of inertia of the VSG, and D is the damping coefficient; is the mechanical angular frequency of the VSG, is the grid angular frequency; Equation (2) represents the reactive power Q of the VSG and the voltage v m droop characteristic, where v m is the grid connection point voltage reference value in the synchronous rotating dq-axis coordinate system, v0 is the rated voltage, k q is the droop coefficient, Q ref is the input reactive signal of the VSG power outer loop, and Q is the reactive output signal of the grid-connected device.

3. A virtual synchronous machine control method for grid-connected equipment to eliminate grid-connected voltage harmonic disturbances according to claim 1, characterized in that, Using the output of the VSG power outer-loop controller as the input of the VSG voltage inner-loop, specifically: The grid connection point voltage reference quantity v output by the VSG power outer loop m , after dq / abc coordinate transformation, it will be converted into the three-phase grid connection point voltage reference quantity v in the stationary abc coordinate system ref,j (k), where the voltage phase number j = a, b, c, and the three-phase grid connection point voltage reference quantity v ref,j (k) will be used as the reference input quantity of the VSG voltage inner loop.

4. A virtual synchronous machine control method for grid-connected equipment to eliminate grid-connected voltage harmonic disturbances according to claim 1, characterized in that Step 2 specifically includes the following steps: Establish the differential equation mathematical model of the wind turbine GSC as follows: （3） Discretizing (3) can obtain the discrete state-space mathematical model of the GSC as follows: (4) Among them, is a state variable, is a control variable, , and are coefficient matrices, i 1,j (k) is the inductor current of phase j on the GSC side, v o,j (k) is the grid-connected point voltage of phase j, u j (k) is the control signal of phase j of the GSC, i o,j (k) is the output current flowing from the GSC to the power grid; Based on the discrete state-space mathematical model of the GSC, the SF controller adopted by the VSG voltage inner-loop is as follows: (5) Among them , j is the number of voltage phases, j = a, b, c; Substituting Equation (5) into Equation (4), the VSG voltage inner-loop SF control closed-loop system can be obtained as: (6) By selecting the feedback coefficient matrix F and , the SF controller can directly configure the poles of the closed-loop system of the VSG voltage inner-loop SF control. By optimizing the configuration of the poles within the unit circle, a VSG voltage inner-loop SF control closed-loop system with good rapidity and stability can be obtained. For the VSG voltage inner loop SF control closed-loop system, from the grid connection point voltage reference to the grid connection point voltage v o,j (k), the transfer function is denoted as .

5. A virtual synchronous machine control method for grid-connected equipment to eliminate grid-connected voltage harmonic disturbances according to claim 1, characterized in that, The GI controller is: (7) Among them, is the h-th harmonic disturbance signal with a frequency of and is expressed as: , (8) k h is the control gain of the GI controller for the h-th harmonic disturbance with frequency , F h (z) is the compensator for the h-th harmonic disturbance with frequency , is the phase compensation angle at frequency , T S is the sampling frequency of the control system.

6. The virtual synchronous machine control method for grid-connected equipment to eliminate grid-connected voltage harmonic disturbances according to claim 1, characterized in that Select the compensator of the GI controller to completely compensate the phase delay of the VSG voltage inner-loop SF control closed-loop system at the hth harmonic frequency, expressed as: 。 7. A virtual synchronous machine control method for grid-connected equipment to eliminate grid-connected voltage harmonic disturbances according to claim 1, characterized in that, The judgment condition for the control gain of the GI controller is: 。

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