CN104993495B - Suitable for the Active Power Filter-APF Direct Current Control method under weak grid conditions - Google Patents

Abstract

The invention discloses an active power filter direct current control method suitable for weak grid conditions, which is implemented as follows: step 1, collecting the voltage at the PCC point of the weak grid system, the DC side voltage of the inverter, and the instantaneous value of the load current, and the instantaneous value of the current sent by the inverter; Step 2, the collected instantaneous value and the instantaneous value of the current sent by the inverter are processed by the conditioning circuit and then input into the DSP processor to convert them into digital signals; Step 3, DSP The processor processes the digital signal to obtain the command current signal of the active power filter; step 4, the DSP processor compares the command current signal with the digital signal in a hysteresis loop, and controls the DSP to send out a PWM wave; step 5, sends out The PWM wave is sent to the driving circuit of the IGBT module of the inverter, and the inverter is controlled to follow the command current signal. The invention effectively and accurately compensates the reactive power and harmonic current of the load.

Description

Active Power Filter Direct Current Control Method Applicable to Weak Grid Conditions

technical field

The invention belongs to the technical field of power electronics, and relates to a direct current control method of an active power filter suitable for a weak power grid.

Background technique

With the increasing scarcity of fossil energy and the seriousness of environmental problems, more and more attention has been paid to clean and renewable energy. Therefore, as one of the main application methods of renewable energy, the distributed power generation system has continuously increased its proportion in the power grid. According to the grid structure, the impedance of the grid is mainly determined by the low power converter and the impedance of the distribution line. The increase of distributed power makes the grid impedance not negligible and changes in a wide range under different operating conditions, and the grid presents the characteristics of a weak grid. At the same time, the wide application of power electronic devices will bring increasingly serious power pollution to the power grid, which is usually treated by Active Power Filter (APF). For a weak power grid, since the voltage of the Point of Common Coupling (PCC) contains background harmonics caused by the harmonic current flowing through the grid impedance, the PCC voltage usually appears as distortion and imbalance. Therefore, the application of APF to control power quality in weak power grids needs to solve the problem that APF can accurately detect and compensate harmonics and reactive currents in real time when PCC voltage distortion is unbalanced and frequency deviation occurs.

For the real-time detection of harmonics and reactive currents, the most widely used ones are Instantaneous Reactive Power Theory (IRP Theory) and its extension method and Synchronous Reference Frame (SRF Method). But the IRP theory is not suitable for the state of PCC voltage distortion imbalance. Although the extended method of IRP and the SRF method are not affected by voltage distortion or unbalanced state, they need to detect the real-time phase of the positive sequence fundamental voltage. The distortion and imbalance of PCC voltage brings great difficulty to detect the real-time phase of the positive sequence fundamental voltage. Although the current relatively advanced phase-locking technologies can meet the above conditions to a certain extent, they are mostly complicated to implement, require precise parameter design, and have a certain delay, which is not conducive to practical application in engineering.

Improving compensation dynamics by eliminating detection delay is another major research direction of APF. Adaptive nonlinear control is used to eliminate the influence of system detection delay on compensation effect. The automatic correction of the repeated controller is used to eliminate the influence of delay, but its dynamic response speed is slow, and it cannot meet the compensation requirements when the system current fluctuates. Intelligent algorithms such as fuzzy logic controller and synovial film controller are used for predictive control to eliminate the influence of detection delay. Although the above method effectively eliminates the influence of the delay on the compensation effect, it is relatively complicated to implement.

Contents of the invention

The purpose of the present invention is to provide an active power filter direct current control method suitable for weak grid conditions, which solves the problem that traditional direct current control cannot accurately compensate harmonics and reactive power under weak grid conditions.

The technical solution adopted in the present invention is to apply to the direct current control method of the active power filter under the condition of weak power grid, and implement according to the following steps:

Step 1, collect the instantaneous values of the voltages e _a , e _b and e _c at the PCC point of the weak grid system, the instantaneous values of the inverter DC side voltage v _dc , the instantaneous values of the load currents i _La , i _Lb and i _Lc , and Instantaneous values of currents i _ca , i _cb and i _cc sent by the inverter;

Step 2, the collected instantaneous values of e _a , e _b , e _c , v _dc , i _La , i _Lb and i _Lc , and the instantaneous values of current i _ca , i _cb and i _cc sent by the inverter are adjusted After the circuit is processed, it is input to the DSP processor and converted into digital signals e _a , e _b , e _c , v _dc , i _La , i _Lb , i _Lc , i _ca , i _cb and i _cc through the A/D module;

Step 3, the DSP processor processes the digital signals e _a , e _b , e _c , v _dc , i _La , i _Lb and i _Lc to obtain the command current signals i _refa , i _refb , i of the active power filter _refc ;

Step 4, the DSP processor performs a hysteresis comparison of the command current signals i _refa , i _refb , i _refc and digital signals i _ca , i _cb and i _cc , and controls the PWM module of the DSP to send out PWM waves;

Step 5: Send the PWM wave sent by the DSP processor to the driving circuit of the IGBT module of the inverter, control the inverter to send current according to the command current signals i _refa , i _refb , and i _refc , and compensate the weak grid system according to the sent current Harmonics and reactive power.

The present invention is also characterized in that,

In step 3, the command current signal of the active power filter is obtained according to the following steps:

1) The instantaneous values of system PCC point voltage and load current are:

In formulas (1) and (2): m and n are harmonic times, + means positive sequence, - means negative sequence; ω is angular velocity, t is time, is the positive sequence m harmonic voltage amplitude, is the amplitude of the negative sequence mth harmonic voltage, is the initial phase angle of negative sequence m harmonic voltage, is the initial phase angle of the positive sequence mth harmonic voltage, is the positive sequence nth harmonic current amplitude, is the negative sequence nth harmonic current amplitude, is the initial phase angle of the negative sequence nth harmonic current, is the initial phase angle of positive sequence nth harmonic current;

2) Convert the instantaneous values of the voltage and load current at the PCC point into a two-phase stationary coordinate system;

The coordinate value of the voltage of PCC point on the two-phase stationary coordinate system is:

In formula (3), (4):

3) According to the spatial position conversion between the two-phase stationary coordinate system and the rotating coordinate system, the coordinate values of the voltage vector and the current vector on the rotating coordinate system are obtained;

The coordinate value of the voltage vector on the rotating coordinate system is:

In formula (5), γ is the initial phase angle of the xy coordinate system;

The coordinate value of the current vector on the rotating coordinate system is:

4) Use a low-pass filter to extract the coordinate value of the voltage vector on the rotating coordinate system, and obtain the coordinate values of the PCC point voltage and the positive sequence component of the fundamental wave of the load current on the rotating coordinate system:

In formula (7), is the magnitude of the fundamental positive sequence voltage and current, is the initial phase angle of the fundamental positive sequence voltage and current, and γ is the initial phase angle of the xy coordinate system;

5) According to the coordinate values of the fundamental positive sequence component of the voltage and current obtained in 3) and 4) on the rotating coordinate system in the same direction and at the same speed as the fundamental positive sequence voltage, the fundamental positive sequence component of the voltage and the current The angle between the positive sequence components of the fundamental wave is

Then according to the definition of active current, the active current is obtained, and the specific expression is as follows:

In formula (8),

Then the coordinate value of the active current on the rotating coordinate system in the same direction and at the same speed as the fundamental positive sequence voltage is:

6) According to the deviation between the DC side voltage and the expected value, apply the PI controller to obtain the active current i _pdc required for voltage control, and then according to the positive sequence component of the PCC point voltage fundamental wave obtained in 3) and 4) on the rotating coordinate system Coordinate values, i _pdc is also projected to the xy coordinate system, and its coordinate values are:

Add the component of i _pdc on the xy coordinate system to the component of the load active current on the xy axis coordinate respectively, then the coordinate value of the active current consumed by the system in the xy coordinate system is:

7) Perform matrix inverse transformation on the coordinate values of the active current on the rotating coordinate system in the same direction and at the same speed as the fundamental positive sequence voltage to obtain the three-phase instantaneous values of the active current as follows:

In formula (12), γ is the initial phase angle of the xy coordinate system;

8) Subtract the three-phase instantaneous value of the system active current obtained in 7) from the collected three-phase instantaneous value of the load current to obtain the command current signal of the active power filter,

When the PCC voltage frequency is shifted from ω to ω', the instruction current signal of the active power filter obtained in step 3 is implemented according to the following steps:

1) The instantaneous values of system PCC point voltage and load current are:

In formulas (14) and (15), m and n are harmonic times, + means positive sequence, - means negative sequence; ω ₀ is angular velocity, t is time, is the positive sequence m harmonic voltage amplitude, is the amplitude of the negative sequence mth harmonic voltage, is the initial phase angle of negative sequence m harmonic voltage, is the initial phase angle of the positive sequence mth harmonic voltage, is the positive sequence nth harmonic current amplitude, is the negative sequence nth harmonic current amplitude, is the initial phase angle of the negative sequence nth harmonic current, is the initial phase angle of positive sequence nth harmonic current;

2) Convert the instantaneous values of the voltage and load current at the PCC point into a two-phase stationary coordinate system;

The coordinate value of the voltage of PCC point on the two-phase stationary coordinate system is:

In formula (16), (17),

3) According to the spatial position conversion between the two-phase stationary coordinate system and the rotating coordinate system, the coordinate values of the voltage vector and the current vector on the rotating coordinate system are obtained;

The coordinate value of the voltage vector on the rotating coordinate system is:

In formula (18), γ is the initial angle of the xy coordinate system;

The coordinate value of the current vector on the rotating coordinate system is:

4) Use a low-pass filter to extract the coordinate value of the voltage vector on the rotating coordinate system, and obtain the coordinate values of the PCC point voltage and the positive sequence component of the fundamental wave of the load current on the rotating coordinate system:

In formula (20), is the magnitude of the fundamental positive sequence voltage and current, is the initial phase angle of the fundamental positive sequence voltage and current, and γ is the initial phase angle of the xy coordinate system;

5) According to the coordinate values of the fundamental positive sequence component of the voltage and current obtained in 3) and 4) on the rotating coordinate system in the same direction and at the same speed as the fundamental positive sequence voltage, the fundamental positive sequence component of the voltage and the current The angle between the positive sequence components of the fundamental wave is

Then according to the definition of active current, the expression of active current is obtained as follows:

In formula (21),

Then the coordinate value of the active current on the rotating coordinate system in the same direction and at the same speed as the fundamental positive sequence voltage is:

6) According to the deviation between the DC side voltage and the expected value, apply the PI controller to obtain the active current _ipdc required for voltage control, and then according to the coordinate value of the positive sequence component of the PCC point voltage fundamental wave obtained in step 3.4 on the rotating coordinate system, The i _pdc is also projected to the xy coordinate system, and its coordinate values are:

Add the component of i _pdc on the xy coordinate system to the component of the load active current on the xy axis coordinate respectively, then the coordinate value of the active current consumed by the system in the xy coordinate system is:

7) Perform matrix inverse transformation on the coordinate values of the active current on the rotating coordinate system in the same direction and at the same speed as the fundamental positive sequence voltage to obtain the three-phase instantaneous values of the active current as follows:

In formula (25), γ is the initial phase angle of the xy coordinate system;

8) Subtract the three-phase instantaneous value of the system active current obtained in 7) from the collected three-phase instantaneous value of the load current to obtain the command current signal of the active power filter,

The beneficial effects of the present invention are: the present invention is applicable to the direct current control method of the active power filter under the condition of weak power grid, can complete dynamic tracking compensation within one electric cycle, and has good dynamic response characteristics. It is not affected by the frequency deviation of the weak grid voltage. When the weak power grid system is in a steady state, APF can effectively and accurately compensate the reactive power and harmonic current of the load, without using a phase-locked loop during the entire control process, which effectively reduces the detection delay and ensures the dynamics of APF compensation .

Description of drawings

Fig. 1 is the topological structure diagram of APF main circuit in the active power filter direct current control method that the present invention is applicable to under the weak grid condition;

Fig. 2 is a two-phase stationary coordinate system to a two-phase xy rotating coordinate system in the step 3 of the direct current control method of an active power filter applicable to a weak grid condition of the present invention;

Fig. 3 is a block diagram of the APF control strategy in the direct current control method of the active power filter applicable to the weak grid condition of the present invention;

Figure 4 is the simulated waveform of the PCC point voltage of the weak grid system;

Fig. 5 is the simulation waveform of the load current of the weak grid system;

Fig. 6 is the simulation waveform of the PCC point voltage of phase A of the system and the current of the weak grid system before compensation;

Fig. 7 is the simulation waveform of the PCC point voltage of phase A of the system and the current of the weak grid system after compensation;

Figure 8 is the FFT analysis of the PCC point voltage of phase A of the system and the current of the weak grid system before compensation;

Figure 9 is the FFT analysis of the PCC point voltage of phase A of the system and the current of the weak grid system after compensation;

Fig. 10 is the simulation waveform of the load current when the load of the weak grid system changes suddenly;

Figure 11 is the simulation waveform of the inverter current tracking the command current when the load of the weak grid system changes suddenly;

Figure 12 is the simulated waveform of the PCC point voltage of phase A of the system and the current of the weak grid system after compensation when the load of the weak grid system changes suddenly;

Figure 13 is the simulation waveform of the PCC point voltage of phase A of the system and the current of the weak grid system after compensation when a +5Hz frequency deviation occurs in the weak grid system;

Figure 14 is the FFT analysis of the PCC point voltage of phase A of the system and the current of the weak grid system after compensation when a -5Hz frequency deviation occurs in the weak grid system;

Figure 15 is the simulation waveform of the PCC point voltage of phase A of the system and the current of the weak grid system after compensation when a +5Hz frequency deviation occurs in the weak grid system;

Figure 16 is the FFT analysis of the PCC point voltage of phase A of the system and the current of the weak grid system after compensation when a -5Hz frequency deviation occurs in the weak grid system.

detailed description

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

The present invention provides an active power filter direct current control method suitable for weak grid conditions, which is implemented according to the following steps:

Step 1, collect the instantaneous values of the voltages e _a , e _b and e _c at the PCC point of the weak grid system, the instantaneous values of the inverter DC side voltage v _dc , the instantaneous values of the load currents i _La , i _Lb and i _Lc , and Instantaneous values of currents i _ca , i _cb and i _cc sent by the inverter;

Step 2, the collected instantaneous values of e _a , e _b , e _c , v _dc , i _La , i _Lb and i _Lc , and the instantaneous values of current i _ca , i _cb and i _cc sent by the inverter are adjusted After the circuit is processed, it is input to the DSP processor and converted into digital signals e _a , e _b , e _c , v _dc , i _La , i _Lb , i _Lc , i _ca , i _cb and i _cc through the A/D module;

Step 3, the DSP processor processes the digital signals e _a , e _b , e _c , v _dc , i _La , i _Lb and i _Lc to obtain the command current signals i _refa , i _refb , i of the active power filter _refc ;

In step 3, the command current signal of the active power filter is obtained according to the following steps:

1) The instantaneous values of system PCC point voltage and load current are:

In formulas (1) and (2): m and n are harmonic times, + means positive sequence, - means negative sequence; ω is angular velocity, t is time, is the positive sequence m harmonic voltage amplitude, is the amplitude of the negative sequence mth harmonic voltage, is the initial phase angle of negative sequence m harmonic voltage, is the initial phase angle of the positive sequence mth harmonic voltage, is the positive sequence nth harmonic current amplitude, is the negative sequence nth harmonic current amplitude, is the initial phase angle of the negative sequence nth harmonic current, is the initial phase angle of positive sequence nth harmonic current;

2) Convert the instantaneous values of the voltage and load current at the PCC point into a two-phase stationary coordinate system;

The coordinate value of the voltage of PCC point on the two-phase stationary coordinate system is:

In formula (3), (4):

3) According to the spatial position conversion between the two-phase stationary coordinate system and the rotating coordinate system, the coordinate values of the voltage vector and the current vector on the rotating coordinate system are obtained;

The coordinate value of the voltage vector on the rotating coordinate system is:

In formula (5), γ is the initial phase angle of the xy coordinate system;

The coordinate value of the current vector on the rotating coordinate system is:

4) Use a low-pass filter to extract the coordinate value of the voltage vector on the rotating coordinate system, and obtain the coordinate values of the PCC point voltage and the positive sequence component of the fundamental wave of the load current on the rotating coordinate system:

In formula (7), is the magnitude of the fundamental positive sequence voltage and current, is the initial phase angle of the fundamental positive sequence voltage and current, and γ is the initial phase angle of the xy coordinate system;

5) According to the coordinate values of the fundamental positive sequence component of the voltage and current obtained in 3) and 4) on the rotating coordinate system in the same direction and at the same speed as the fundamental positive sequence voltage, the fundamental positive sequence component of the voltage and the current The angle between the positive sequence components of the fundamental wave is

Then according to the definition of active current, the active current is obtained, and the specific expression is as follows:

In formula (8),

Then the coordinate value of the active current on the rotating coordinate system in the same direction and at the same speed as the fundamental positive sequence voltage is:

6) According to the deviation between the DC side voltage and the expected value, apply the PI controller to obtain the active current i _pdc required for voltage control, and then according to the positive sequence component of the PCC point voltage fundamental wave obtained in 3) and 4) on the rotating coordinate system Coordinate values, i _pdc is also projected to the xy coordinate system, and its coordinate values are:

Add the component of i _pdc on the xy coordinate system to the component of the load active current on the xy axis coordinate respectively, then the coordinate value of the active current consumed by the system in the xy coordinate system is:

7) Perform matrix inverse transformation on the coordinate values of the active current on the rotating coordinate system in the same direction and at the same speed as the fundamental positive sequence voltage to obtain the three-phase instantaneous values of the active current as follows:

In formula (12), γ is the initial phase angle of the xy coordinate system;

8) Subtract the three-phase instantaneous value of the system active current obtained in 7) from the collected three-phase instantaneous value of the load current to obtain the command current signal of the active power filter,

When the PCC voltage frequency is shifted from ω to ω', the instruction current signal of the active power filter obtained in step 3 is implemented according to the following steps:

1) The instantaneous values of system PCC point voltage and load current are:

In formulas (14) and (15), m and n are harmonic times, + means positive sequence, - means negative sequence; ω ₀ is angular velocity, t is time, is the positive sequence m harmonic voltage amplitude, is the amplitude of the negative sequence mth harmonic voltage, is the initial phase angle of negative sequence m harmonic voltage, is the initial phase angle of the positive sequence mth harmonic voltage, is the positive sequence nth harmonic current amplitude, is the negative sequence nth harmonic current amplitude, is the initial phase angle of the negative sequence nth harmonic current, is the initial phase angle of positive sequence nth harmonic current;

2) Convert the instantaneous values of the voltage and load current at the PCC point into a two-phase stationary coordinate system;

The coordinate value of the voltage of PCC point on the two-phase stationary coordinate system is:

In formula (16), (17),

3) According to the spatial position conversion between the two-phase stationary coordinate system and the rotating coordinate system, the coordinate values of the voltage vector and the current vector on the rotating coordinate system are obtained;

The coordinate value of the voltage vector on the rotating coordinate system is:

In formula (18), γ is the initial angle of the xy coordinate system;

The coordinate value of the current vector on the rotating coordinate system is:

4) Use a low-pass filter to extract the coordinate value of the voltage vector on the rotating coordinate system, and obtain the coordinate values of the PCC point voltage and the positive sequence component of the fundamental wave of the load current on the rotating coordinate system:

In formula (20), is the magnitude of the fundamental positive sequence voltage and current, is the initial phase angle of the fundamental positive sequence voltage and current, and γ is the initial phase angle of the xy coordinate system;

5) According to the coordinate values of the fundamental positive sequence component of the voltage and current obtained in 3) and 4) on the rotating coordinate system in the same direction and at the same speed as the fundamental positive sequence voltage, the fundamental positive sequence component of the voltage and the current The angle between the positive sequence components of the fundamental wave is

Then according to the definition of active current, the expression of active current is obtained as follows:

In formula (21),

Then the coordinate value of the active current on the rotating coordinate system in the same direction and at the same speed as the fundamental positive sequence voltage is:

6) According to the deviation between the DC side voltage and the expected value, apply the PI controller to obtain the active current _ipdc required for voltage control, and then according to the coordinate value of the positive sequence component of the PCC point voltage fundamental wave obtained in step 3.4 on the rotating coordinate system, The i _pdc is also projected to the xy coordinate system, and its coordinate values are:

Add the component of i _pdc on the xy coordinate system to the component of the load active current on the xy axis coordinate respectively, then the coordinate value of the active current consumed by the system in the xy coordinate system is:

7) Perform matrix inverse transformation on the coordinate values of the active current on the rotating coordinate system in the same direction and at the same speed as the fundamental positive sequence voltage to obtain the three-phase instantaneous values of the active current as follows:

In formula (25), γ is the initial phase angle of the xy coordinate system;

8) Subtract the three-phase instantaneous value of the system active current obtained in 7) from the collected three-phase instantaneous value of the load current to obtain the command current signal of the active power filter,

Step 4, the DSP processor performs a hysteresis comparison of the command current signals i _refa , i _refb , i _refc and digital signals i _ca , i _cb and i _cc , and controls the PWM module of the DSP to send out PWM waves;

Step 5: Send the PWM wave sent by the DSP processor to the driving circuit of the IGBT module of the inverter, control the inverter to send current according to the command current signals i _refa , i _refb , and i _refc , and compensate the weak grid system according to the sent current Harmonics and reactive power.

The present invention is applicable to the direct current control method of the active power filter under the condition of weak grid. The active power filter, that is, APF, adopts a three-phase three-wire voltage source inverter, and the structure connected to the weak grid is shown in Figure 1 As shown, e _a , e _b , e _c are the voltages at the PCC point, _{isa , isb , isc} are the currents absorbed by the PCC point from the power grid, and i _La , i _Lb , i _Lc are the currents absorbed by the nonlinear load , i _ca , i _cb , i _cc are the currents generated by the inverter, R, L, and C are the connection impedance and DC side capacitance of the inverter, respectively. Z _ga , Z _gb , and Z _gc are grid impedances.

The invention is applicable to the direct current control method of the active power filter under the condition of weak power grid, and derives a rotating vector detection method based on the virtual synchronous coordinate system according to the vector characteristics of the voltage and current, and the coordinate transformation is shown in Fig. 2 . The dq coordinate system in the traditional method is replaced by the xy coordinate system that rotates at the same speed and in the same direction as the fundamental positive sequence voltage of the PCC point. Since the initial phase angle of the xy coordinate system can be any value, no PLL is required for phase angle detection. The matrix corresponding to the coordinate transformation of Figure 2 is:

In formula (27), γ is the angle between the positive sequence fundamental wave voltage and the x-axis.

Transform the voltage and load current of the PCC point to the virtual synchronous coordinate system xy, and its corresponding coordinate value is:

After a low-pass filter, the coordinate values of the positive sequence fundamental wave voltage and current vector on the xy coordinate system are obtained:

Therefore, the active component of the positive sequence fundamental wave current in the xy coordinate system is:

Perform inverse transformation on the detection results to obtain the active component of the positive sequence fundamental current as:

From the above test results, it can be found that the value of the angle of the virtual rotating coordinate system will not affect the test results.

The fluctuation of the capacitor voltage on the DC side of the APF will not only affect its compensation effect, but also affect the stability of the entire system. In dynamic processes such as APF startup, grid connection and load switching, it is necessary to control its DC side voltage. In the traditional control strategy, according to the deviation between the DC side voltage and the expected value, the PI controller is used to obtain the active current i _pdc required for voltage control, and adding it to the d-axis component of the load current to realize the closed-loop control of the DC side voltage.

Although the xy coordinate system and the dq coordinate system rotate at the same speed and in the same direction, there is an angle γ between it and the positive sequence fundamental wave voltage, and the value of γ is time-varying. The present invention also projects i _pdc to the xy coordinate system. The coordinate values are:

The components of the i _PDC on the xy coordinate system are respectively added to the components of the load active current on the xy axis coordinates to realize the DC side voltage closed-loop control equivalent to the traditional control.

As shown in Figure 3, under the condition of PCC voltage distortion and unbalance in the weak grid system, APF no longer needs to use PLL (that is, phase-locked loop) to detect the voltage phase, thus reducing the complexity of the control algorithm and reducing the power generated by The detection delay introduced by the PLL effectively improves the performance of the APF.

When a weak grid system containing a large number of distributed power sources operates in an island situation, power imbalance will cause grid voltage frequency deviation, and the present invention is also applicable to this situation. Assuming that the frequency of the fundamental voltage of the power grid is shifted from ω to ω', the corresponding current will also have a frequency deviation. After transforming to the virtual synchronous coordinate system, the positive sequence fundamental voltage and current vectors on the xy coordinate system are obtained through a low-pass filter The coordinate values are:

The active component of the positive sequence fundamental wave current in the xy coordinate system is:

Therefore, the active component of the three-phase positive sequence fundamental current is:

It can be seen from the formula (36) that the present invention can accurately detect the current when the voltage at the PCC point has a frequency deviation.

The system shown in Figure 1 is simulated in Matlab/Simulink software. The PCC point voltage is composed of positive sequence fundamental wave voltage superimposed negative sequence 5th and positive sequence 7th harmonic voltage. The load is a three-phase bridge uncontrollable rectifier circuit. The specific system The simulation parameters are shown in Table 1:

Table 1 System Simulation Parameters

Using Matlab/Simulink software, according to the system simulation parameters in Table 1, the simulation results shown in Figure 4-16 are obtained;

Figure 4 and Figure 5 are the PCC point voltage and load current waveforms before APF is put into operation. Among them, the per unit value of the negative sequence 5th harmonic voltage is 0.3, and the per unit value of the positive sequence 7th harmonic voltage is 0.15.

Figure 6, Figure 7, Figure 8, and Figure 9 are the waveforms of the A-phase voltage at the PCC point and the current flowing into the PCC point from the grid before and after the APF control method compensation, and the FFT analysis results of the current. Before the APF is put into operation, the total harmonic distortion rate of the incoming current is 25.66%, and there is a certain phase angle difference between the voltage and current, and the system power factor is 0.886; after the APF is put into operation, the total harmonic distortion of the current flowing into the PCC point The wave distortion rate is reduced to 1.71%, and the current is in the same phase as the positive sequence fundamental wave voltage, and the system power factor is increased to 1.0. When the weak power grid system is in a steady state, the APF can effectively and accurately compensate the reactive power of the load. wave current.

The weak grid system doubles the nonlinear load at 0.5s. Figure 10, Figure 11, and Figure 12 respectively show the load current waveform, the A-phase current output by the APF and its reference value waveform, and the weak-grid system PCC point A-phase voltage And the current waveform flowing into the grid. It shows that the APF adopts the invention, can complete the dynamic tracking compensation within one electrical cycle, and has good dynamic response characteristics.

Figure 13 and Figure 14 respectively show the waveforms of the voltage at the PCC point and the current flowing into the PCC point from the power grid when the voltage of the weak grid system has a frequency deviation of ±5Hz at 0.5s, and Figure 15 and Figure 16 respectively show the FFT analysis of the current , it can be seen from Figures 13, 14, 15 and 16 that when the frequency deviation of the system voltage occurs, the compensated grid inflow current can be kept in phase with the voltage after a period of adjustment, and the total harmonic distortion rate is 2.45% respectively , 2.04%. Therefore, the present invention is not affected by the frequency deviation of the weak grid voltage.

Claims (1)

1. The active power filter direct current control method applicable to weak grid conditions is characterized in that it is implemented according to the following steps: Step 1, collect the instantaneous values of the voltages e _a , e _b and e _c at the PCC point of the weak grid system, the instantaneous values of the inverter DC side voltage v _dc , the instantaneous values of the load currents i _La , i _Lb and i _Lc , and Instantaneous values of currents i _ca , i _cb and i _cc sent by the inverter; Step 2, the collected instantaneous values of e _a , e _b , e _c , v _dc , i _La , i _Lb and i _Lc , and the instantaneous values of current i _ca , i _cb and i _cc sent by the inverter are adjusted After the circuit is processed, it is input to the DSP processor and converted into digital signals e _a , e _b , e _c , v _dc , i _La , i _Lb , i _Lc , i _ca , i _cb and i _cc through the A/D module; Step 3, the DSP processor processes the digital signals e _a , e _b , e _c , v _dc , i _La , i _Lb and i _Lc to obtain the command current signals i _refa , i _refb , i of the active power filter _refc ; In step 3, the command current signal of the active power filter is obtained according to the following steps: 1) Suppose the instantaneous values of system PCC point voltage and load current are: $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\\ {\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\\ {\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ In formulas (1) and (2): m and n are harmonic times, + means positive sequence, - means negative sequence; ω is angular velocity, t is time, is the positive sequence m harmonic voltage amplitude, is the amplitude of the negative sequence mth harmonic voltage, is the initial phase angle of negative sequence m harmonic voltage, is the initial phase angle of the positive sequence mth harmonic voltage, is the positive sequence nth harmonic current amplitude, is the negative sequence nth harmonic current amplitude, is the initial phase angle of the negative sequence nth harmonic current, is the initial phase angle of positive sequence nth harmonic current; 2) Convert the instantaneous values of the voltage and load current at the PCC point into a two-phase stationary coordinate system; The coordinate value of the voltage of PCC point on the two-phase stationary coordinate system is: $\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}\\ {\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}\\ {\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\\ \sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$ In formula (3), (4): 3) According to the spatial position conversion between the two-phase stationary coordinate system and the rotating coordinate system, the coordinate values of the voltage vector and the current vector on the rotating coordinate system are obtained; The coordinate value of the voltage vector on the rotating coordinate system is: $\begin{array}{c}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}\\ {\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]\\ <span\; class="notranslate">\; =</span>\left[\begin{array}{c}\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span>\\ <span\; class="notranslate">\; -</span>\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span>\end{array}\right]\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$ In formula (5), γ is the initial phase angle of the xy coordinate system; The coordinate value of the current vector on the rotating coordinate system is: 4) Use a low-pass filter to extract the coordinate value of the voltage vector on the rotating coordinate system, and obtain the coordinate values of the PCC point voltage and the positive sequence component of the fundamental wave of the load current on the rotating coordinate system: In formula (7), is the magnitude of the fundamental positive sequence voltage and current, is the initial phase angle of the fundamental positive sequence voltage and current, and γ is the initial phase angle of the xy coordinate system; 5) According to the coordinate values of the fundamental positive sequence component of the voltage and current obtained in 3) and 4) on the rotating coordinate system in the same direction and at the same speed as the fundamental positive sequence voltage, the fundamental positive sequence component of the voltage and the current The angle between the positive sequence components of the fundamental wave is Then according to the definition of active current, the active current is obtained, and the specific expression is as follows: In formula (8), Then the coordinate value of the active current on the rotating coordinate system in the same direction and at the same speed as the fundamental positive sequence voltage is: $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; wxya</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; +</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; +</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; +</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; +</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; +</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; +</span>}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$ 6) According to the deviation between the DC side voltage and the expected value, apply the PI controller to obtain the active current i _pdc required for voltage control, and then according to the positive sequence component of the PCC point voltage fundamental wave obtained in 3) and 4) on the rotating coordinate system Coordinate values, i _pdc is also projected to the xy coordinate system, and its coordinate values are: $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; pdcx</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; pdc</span>}}<span\; class="notranslate">\; \&times;</span>\frac{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{\sqrt{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; pdcy</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; pdc</span>}}<span\; class="notranslate">\; \&times;</span>\frac{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}{\sqrt{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$ Add the component of i _pdc on the xy coordinate system to the component of the load active current on the xy axis coordinate respectively, then the coordinate value of the active current consumed by the system in the xy coordinate system is: $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; x</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$ 7) Perform matrix inverse transformation on the coordinate values of the active current on the rotating coordinate system in the same direction and at the same speed as the fundamental positive sequence voltage to obtain the three-phase instantaneous values of the active current as follows: In formula (12), γ is the initial phase angle of the xy coordinate system; 8) Subtract the three-phase instantaneous value of the system active current obtained in 7) from the collected three-phase instantaneous value of the load current to obtain the command current signal of the active power filter, $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; a</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; b</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$ When the PCC voltage frequency is shifted from ω to ω', the command current signal of the active power filter obtained in step 3 is implemented according to the following steps: 1) Suppose the instantaneous values of system PCC point voltage and load current are: $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m\&omega;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m\&omega;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\\ {\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m\&omega;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m\&omega;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\\ {\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m\&omega;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m\&omega;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 14</span>}<span\; class="notranslate">\; )</span>$ In formulas (14) and (15), m and n are harmonic times, + means positive sequence, - means negative sequence; ω ₀ is angular velocity, t is time, is the positive sequence m harmonic voltage amplitude, is the amplitude of the negative sequence mth harmonic voltage, is the initial phase angle of negative sequence m harmonic voltage, is the initial phase angle of the positive sequence mth harmonic voltage, is the positive sequence nth harmonic current amplitude, is the negative sequence nth harmonic current amplitude, is the initial phase angle of the negative sequence nth harmonic current, is the initial phase angle of positive sequence nth harmonic current; 2) Convert the instantaneous values of the voltage and load current at the PCC point into a two-phase stationary coordinate system; The coordinate value of the voltage of PCC point on the two-phase stationary coordinate system is: $\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}\\ {\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}\\ {\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m\&omega;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m\&omega;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\\ \sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m\&omega;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m\&omega;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$ In formula (16), (17), 3) According to the spatial position conversion between the two-phase stationary coordinate system and the rotating coordinate system, the coordinate values of the voltage vector and the current vector on the rotating coordinate system are obtained; The coordinate value of the voltage vector on the rotating coordinate system is: $\begin{array}{c}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}\\ {\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]\\ <span\; class="notranslate">\; =</span>\left[\begin{array}{c}\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m\&omega;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m\&omega;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span>\\ <span\; class="notranslate">\; -</span>\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m\&omega;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m\&omega;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span>\end{array}\right]\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; )</span>$ In formula (18), γ is the initial angle of the xy coordinate system; The coordinate value of the current vector on the rotating coordinate system is: 4) Use a low-pass filter to extract the coordinate value of the voltage vector on the rotating coordinate system, and obtain the coordinate values of the PCC point voltage and the positive sequence component of the fundamental wave of the load current on the rotating coordinate system: In formula (20), is the magnitude of the fundamental positive sequence voltage and current, is the initial phase angle of the fundamental positive sequence voltage and current, and γ is the initial phase angle of the xy coordinate system; 5) According to the coordinate values of the fundamental positive sequence component of the voltage and current obtained in 3) and 4) on the rotating coordinate system in the same direction and at the same speed as the fundamental positive sequence voltage, the fundamental positive sequence component of the voltage and the current The angle between the positive sequence components of the fundamental wave is Then according to the definition of active current, the expression of active current is obtained as follows: In formula (21), Then the coordinate value of the active current on the rotating coordinate system in the same direction and at the same speed as the fundamental positive sequence voltage is: 6) According to the deviation between the DC side voltage and the expected value, apply the PI controller to obtain the active current i _pdc required for voltage control, and then according to the coordinate value of the positive sequence component of the PCC point voltage fundamental wave obtained in step 3.4 on the rotating coordinate system, The i _pdc is also projected to the xy coordinate system, and its coordinate values are: $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; \&times;</span>\frac{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{\sqrt{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; \&times;</span>\frac{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}{\sqrt{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; three</span>}<span\; class="notranslate">\; )</span>$ Add the component of i _pdc on the xy coordinate system to the component of the load active current on the xy axis coordinate respectively, then the coordinate value of the active current consumed by the system in the xy coordinate system is: $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; x</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; four</span>}<span\; class="notranslate">\; )</span>$ 7) Perform matrix inverse transformation on the coordinate values of the active current on the rotating coordinate system in the same direction and at the same speed as the fundamental positive sequence voltage to obtain the three-phase instantaneous values of the active current as follows: In formula (25), γ is the initial phase angle of the xy coordinate system; 8) Subtract the three-phase instantaneous value of the system active current obtained in 7) from the collected three-phase instantaneous value of the load current to obtain the command current signal of the active power filter, $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; a</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; b</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 26</span>}<span\; class="notranslate">\; )</span>$ Step 4, the DSP processor performs a hysteresis comparison of the command current signals i _refa , i _refb , i _refc and digital signals i _ca , i _cb and i _cc , and controls the PWM module of the DSP to send out PWM waves; Step 5: Send the PWM wave sent by the DSP processor to the driving circuit of the IGBT module of the inverter, control the inverter to send current according to the command current signals i _refa , i _refb , and i _refc , and compensate the weak grid system according to the sent current Harmonics and reactive power.