A Reference Current Control Strategy Based on SOGI and FBD Method for Shunt Active Power Filter

In this paper, a reference current control strategy based on second-order generalized integrator and FBD method for shunt active power filter is proposed. The method uses the second-order generalized integrator and the symmetrical component method to obtain the fundamental sequence component of the grid voltage. And then the FBD method is used to decompose the load current under the fundamental positive-sequence voltage reference to obtain the reference value of the compensation current. This method does not need coordinate transformation, is simple to calculate, and has clear physical meaning. It can compensate harmonic current, reactive current and negative-sequence current at the same time even under complex grid voltage and load and frequency offset. The proposed method is compared with the existing method under a variety of experimental conditions. The experimental results prove the effectiveness and accuracy of the proposed method.


Introduction
The widespread use of power electronic devices such as non-linear loads, large quantities of harmonic current, reactive current and negative sequence current are injected into the power grid, which seriously threatens the safe and stable operation of power grids and electrical equipment.Shunt Active Power Filter (SAPF) is one of the most effective Power quality control devices, which can dynamically suppress harmonics, compensate reactive power and negative sequence current [1][2][3][4][5][6].
The reference current control is the key to determine the compensation performance of SAPF, which can be divided into two parts: one is to detect the reference value of SAPF injection current, the other is to ensure that SAPF injection current accurately tracks the reference value.For the first part, the existing detection methods are mainly divided into frequency-domain detection and time-domain detection.The frequency-domain detection methods mainly include discrete Fourier transform, fast Fourier transform and kalman filter, etc.Although they have high detection accuracy, they have the disadvantages of large computation and poor real-time performance, and KF method is not suitable for frequency offset cases [7][8][9][10][11][12][13]. FBD (fryze-buchholz-dpenbrock) method, p-q method and ip-iq method based on instantaneous reactive power theory are the main time-domain detection methods.P-q method and ip-iq method are more commonly used harmonic detection methods.Compared with the average power theory, using the p-q method based on instantaneous reactive power theory, SAPF has the advantages of fast response speed and simple control.However, it requires complex coordinate transformation, which not only increases the amount of calculation, but also limits its scope of application [14][15][16][17][18].However, FBD method has clear physical meaning and simple calculation, and is suitable for single-phase, three-phase three-wire system and three-phase four-wire system [19][20][21].In the second part, the control methods that have been widely used in current tracking include hysteresis control, non-differential control and proportional integral regulator control [22][23][24][25][26].
The main content discussed in this paper is the reference current detection link based on FBD method.The main principle of the FBD method is that the load in the actual circuit is equivalent to an ideal conductance element.It is considered that the power in the circuit is consumed by this equivalent conductance, and the current is decomposed according to the equivalent conductance.Since the calculation of equivalent conductance is based on the voltage as a reference, the final test result will be affected if the voltage contains harmonics or unbalance in the actual three-phase circuit.At present, the commonly used solution is to obtain the frequency and phase information of a certain phase voltage with PLL, so as to construct the reference voltage of the positive sequence of fundamental waves, which is not affected by harmonics or unbalance of the power grid [27][28][29][30][31]. Literature [32] used the voltage filter to extract the fundamental wave component of the power grid voltage, which could accurately detect the reference value of the compensation current in the case of non-sinusoidal power grid voltage.Meanwhile, the calculation method of moving average value was adopted to replace the original low-pass filter, thus reducing the system delay.However, this method is not applicable in the case of unbalanced voltage, where the voltage imbalance includes unequal amplitude or phase asymmetry.
References [13] and [32] do not consider phase asymmetry in voltage imbalance and load imbalances and frequency offset, among them, the reference [13] voltage fundamental wave extraction method does not adapt to the frequency offset situation, and the reference [32] not adapt to the phase asymmetry situation.
To solve these problems, this paper proposes a reference current control strategy based on second-order generalized integrator (SOGI) and FBD method for shunt active power filter.First, the shortcomings of the existing current reference current control method of the active power filter are analyzed.Then, consider complex grid voltage, load, and frequency offset.A method for extracting the active component of current fundamental positive sequence based on SOGI and symmetrical component method is given.Combined with the FBD method, a new reference current control strategy for SAPF is proposed.Finally, the proposed method is compared with the existing method under various experimental conditions to prove the effectiveness and accuracy of the method.
The content structure of this paper is as follows: Section 2 introduces the basic structure and the existing reference current calculation method of the shunt active power filter.Section 3 refers to the proposed reference current calculation method.The experimental results and various test cases are given in Section 4. Section 5 is the conclusion.

Structure of SAPF
The system structure of the three-phase shunt active power filter system is shown in Figure 1.SAPF is the basic working principle of detection of voltage and current compensation object, compensation current by instruction current arithmetic circuit calculation command signal, again through the PWM inverter control circuit according to the instruction signal current control PWM inverter output compensation, compensation current and load current to compensate harmonic and reactive current in offset, ultimately achieve the desired power supply current [3].
The basic working principle of SAPF is to detect the voltage and current of the compensation object, obtain the reference value of the compensation current through the reference current calculation algorithm, and then control the pulse width modulation (PWM) converter output compensation current according to the reference signal.It can compensate the harmonic component of the load current and make the incoming current sinusoidal.Due to the characteristics of the DC side capacitor, SAPF can also output reactive power and increase the power factor of the system.
The unbalance of nonlinear load will cause the unbalance of load current.The structure and parameters of the nonlinear load balancing circuit are shown in figure 2, and the structure and parameters of the nonlinear load unbalance circuit are shown in figure 3.
Fig. 2 Structure of balance load circuit Fig. 3 Structure of unbalance load circuit

Existing control strategy
The existing reference current control principle based on FBD method is consists mainly of two parts.One is voltage filtering, and the other is reference current calculation.

Voltage filtering
Voltage filtering is adopts a series resonance analog filter, and its differential equation is expressed as ( ) 1 ( ) ( ) ( ) Taking / du dt as input and / di dt as output, the state equation of the system can be obtained according to equation (1) as follows: Where, 2 0 1 / = LC  , and 1 R = .The discrete transfer function of the voltage filter can be calculated after the above equation is discretized, as shown in equation (3).The specific calculation process and filter parameter design can be referred to the literature [32].
Where, u is the input and y is the output.Both  and Γ as parameter matrix, The fundamental components fa u , fb u and fc u of each phase of the grid voltage can be obtained by using a voltage filter.

Reference current calculation
Reference current calculation using FBD method, and the FBD detection method was first proposed by the German scholar S.Freze.The basic idea is: the active current of a single-phase system is the minimum current required for active power transmission.Therefore, the load current L i of the single-phase system can be decomposed into the following two parts as shown in equation ( 4).
( ) ( ) ( ) Where, () p it is the active current, whose waveform is the same as the voltage waveform, and () it is orthogonal to the voltage waveform, which is the current component to be compensated in a single-phase system, that is, the current reference.F.Bouchholz and M.Dpenbrouck extended the definition to three-phase systems [33], where the active current can be calculated by the following equation Where, G is equivalent conductance, P is active power of the system, and s u is the instantaneous total voltage.
Where f u is the fundamental component of the grid voltage.
In discrete-time, the active power P and the voltage f u at an instant n can be expressed by ( 9) and (10).
Where N and s T are discrete signal period and sampling time respectively.After the active current of fundamental wave is obtained, the expression of reference current can be calculated as follows ii u (11) In the case of grid voltage balance, the above method can accurately obtain the three-phase symmetrical fundamental active current component.However, when the supply voltage is unbalanced, the instantaneous total voltage is composed of the DC component and the AC component whose frequency is twice the fundamental wave according to formula (10).The calculated fundamental active current pf i at this time will be asymmetric and contain large 3rd harmonic.Therefore, this method will fail under unbalanced grid voltage.The three-phase unbalance of grid voltage is characterized by unequal amplitudes or asymmetrical phases, as shown in Figure 4.In order to solve the problem that SAPF cannot effectively compensate harmonics when the frequency fluctuates or the voltage is unbalanced in the existing method.A new control method is proposed, and the control scheme of three-phase shunt active power filter is shown in figure 5.The basic working principle of SAPF is to calculate the reference current signal through the reference current calculation circuit according to the measured grid voltage and load current.Then, the PR controller controls the SAPF to output a reasonable compensation current according to the reference current signal.The compensation current is cancelled by the harmonic current, reactive current and negative sequence current in the load current, and finally the expected grid current close to the sine wave is obtained.

Positive sequence extraction based on SOGI
The extraction principle of the fundamental positive sequence component is shown in figure 6. SOGI can realize phase shift with a lag of 90° for input signals, and at the same time shows certain filtering characteristics, which has been widely used to extract the positive and negative sequence components of fundamental waves [34][35][36].The phase shift circuit based on SOGI is shown in figure 7.  12) and ( 13) are discretized by discretization of bilinear transformation and z-transformed [16] to obtain equation as follows: x y a x y Where, s T is the sampling time.According to the symmetric component method, the calculation formula of the fundamental positive-sequence component of the voltage under unbalanced complex grid voltage can be calculated by the following equation: Where, ,, Bring equation ( 19) into equation ( 18): In the above equation( 20

Proposed reference current calculation
In order to obtain the required reference current under unbalanced grid voltage, the fundamental positive sequence component must be taken as the reference voltage.The proposed reference current control schematic is shown in Figure 8.
The proposed method differs from the existing method in that: (1) In the Block-I, First, the phase shift and filtering of each phase voltage were performed by using SOGI, and then the fundamental positive sequence component were obtained by using the symmetric component method, thus replacing the voltage filter in the existing method.
(2) In the Block-II, the reference voltage changes from the fundamental component of the existing method to the fundamental positive sequence component.The calculation steps for detecting the reference current are as follows: firstly, the fundamental positive sequence voltage is obtained from the new module 1, According to equation ( 21), the fundamental positive sequence active current + p i can be obtained, and equation ( 22) is the corresponding equivalent conductance expression.Finally, the required reference current is obtained by subtracting + p i from the load current.
It can be seen that, the instantaneous total voltage is always DC after using the fundamental positive sequence voltage as the reference voltage, and the equivalent conductance G is also DC.According to equation (20), the fundamental positive sequence active current is three-phase symmetrical and in the same phase with the fundamental positive sequence grid voltage.

Experimental validation 4.1 Experiment setup
The experimental device is shown in Figure 9.We build an experimental platform to sample the grid voltage and load current, and then put the sampled data into the simulink model for simulation experiments.The grid voltage is provided by a 30kVA three-phase programmable AC power source, and the non-linear load is an uncontrollable rectifier circuit with an RL load, the load circuit structure is shown in figure 2 and figure 3. Detailed system parameters are shown in table 1.In order to verify the method proposed in this paper, we set up seven experimental cases and compared the method in this paper with existing method.The experimental cases are as follows: (1)Test case 1: Unbalanced grid voltage of unequal amplitude without harmonics.
(5)Test case 5: Unequal amplitude and asymmetric phases unbalanced grid voltage contains harmonics and load imbalance.
(6)Test case 6: Grid voltage balance without harmonics and frequency offset.
(7)Test case 7: Unequal amplitude and asymmetric phases unbalanced grid voltage contains harmonics and load imbalance and frequency offset.
(8)Test case 8: Grid frequency step and voltage amplitude step.
Among them, the existing method in Test case 6 is the experimental KF method in reference [13], and the existing methods in other Test cases are the methods in reference [32].
The effective values of three-phase voltage set to 240V, 220V and 200V respectively, as the state of unequal amplitude of grid voltage.The two phases of the grid voltage U and V are shifted by 20° respectively, as the state of asymmetric phases of grid voltage.The harmonic state of the grid voltage is set to include 3rd harmonics of 10%, 5rd harmonics of 8% and 7rd harmonics of 5%, and frequency offset state is set 52Hz.In order to verify the method proposed in this paper, seven test cases were set to compare the method of this paper with the method of reference [13] and reference [32].

TEST CASE 1: Unbalanced grid voltage of unequal amplitude without harmonics
Figure 10 shows the experimental waveforms under the condition of unbalanced grid voltage of unequal amplitude without harmonics.As can be seen from the figure, the load current waveform is unbalanced and contains a large number of harmonic, reactive and negative sequence currents.At this time, the THD value of the load current is 26.79%.The THD value of the grid current compensated by the existing method is 6.44%, and the THD value of the grid current compensated by proposed method is 3.24%.It can be seen that the grid current compensated by the existing method is unbalanced and the harmonic content is high.This shows that the existing method can't accurately extract the fundamental positive sequence current of the load current under the condition of unbalanced grid voltage of unequal amplitude, which does not meet the compensation requirements.The experimental results are consistent with the theoretical analysis.However, the use of proposed method can still meet the compensation requirements even under unbalanced grid voltage of unequal amplitude.

TEST CASE 2: Unbalanced grid voltage of unequal amplitude contains harmonics
Figure 11 shows the experimental waveforms under the condition of unbalanced grid voltage of unequal amplitude contains harmonics.As can be seen from the figure, the load current waveform is unbalanced and contains a large number of harmonic, reactive and negative sequence currents.At this time, the THD value of the load current is 27.44%.The THD value of the grid current compensated by the existing method is 7.35%, and the THD value of the grid current compensated by proposed method is 3.58%.It can be seen that the grid current compensated by the existing method is unbalanced and the harmonic content is high.This further shows that the existing method can't accurately extract the fundamental positive sequence current of the load current under the condition of unbalanced grid voltage of unequal amplitude, which does not meet the compensation requirements.The experimental results are consistent with the theoretical analysis.However, the use of proposed method can still meet the compensation requirements even under unbalanced grid voltage of unequal amplitude.

TEST CASE 3: Unbalanced grid voltage of asymmetric phases without harmonics
Figure 12 shows the experimental waveforms under the condition of unbalanced grid voltage of asymmetric phases without harmonics.As can be seen from the figure, the load current waveform is unbalanced and contains a large number of harmonic, reactive and negative sequence currents.At this time, the THD value of the load current is 34.4%.The THD value of the grid current compensated by the existing method is 23.87%, and the THD value of the grid current compensated by proposed method is 3.31%.It can be seen that the grid current compensated by the existing method is unbalanced and the harmonic content is high.This shows that the existing method can't accurately extract the fundamental positive sequence current of the load current under the condition of unbalanced grid voltage of asymmetric phases, which does not meet the compensation requirements.However, the use of proposed method can still meet the compensation requirements even under unbalanced grid voltage of asymmetric phases.

TEST CASE 4: Unequal amplitude and asymmetric phases unbalanced grid voltage contains harmonics
Figure 13 shows the experimental waveforms under the condition of unequal amplitude and asymmetric phases unbalanced grid voltage contains harmonics.As can be seen from the figure, the load current waveform is unbalanced and contains a large number of harmonic, reactive and negative sequence currents.At this time, the THD value of the load current is 36.07%.The THD value of the grid current compensated by the existing method is 29.71%, and the THD value of the grid current compensated by proposed method is 3.35%.It can be known that the grid current compensated by the existing method is unbalanced and the harmonic content is high.This shows that the existing method can't accurately extract the fundamental positive sequence current of the load current under the condition of unbalanced grid voltage which does not meet the compensation requirements.However, the use of proposed method can still meet the compensation requirements even under the condition of unequal amplitude and asymmetric phases unbalanced grid voltage contains harmonics.

TEST CASE 5: Unequal amplitude and asymmetric phases unbalanced grid voltage contains harmonics and load imbalance
Figure 14 shows the experimental waveforms under the condition of unequal amplitude and asymmetric phases unbalanced grid voltage contains harmonics and load imbalance.As can be seen from the figure, the experimental results are similar to Test Case 4 under load imbalance conditions.At this time, the THD value of the load current is 30.14%.The THD value of the grid current compensated by the existing method is 28.96%, and the THD value of the grid current compensated by proposed method is 2.96%.It can be known that the grid current compensated by the existing method is unbalanced and the harmonic content is high.This show that the use of proposed method can still meet the compensation requirements even under the condition of unequal amplitude and asymmetric phases unbalanced grid voltage contains harmonics and load imbalance.

TEST CASE 6: Voltage unbalance without harmonic and frequency offset
Figure 15 shows the experimental waveforms under the condition of unequal amplitude and asymmetric phases unbalanced grid voltage contains harmonics and load imbalance.As can be seen from the figure, the load current waveform is unbalanced and contains a large number of harmonic, reactive and negative sequence currents.At this time, the THD value of the load current is 28.74%.The THD value of the grid current compensated by the existing method is 4.46%, and the THD value of the grid current compensated by proposed method is 3.3%.Although both methods can meet the requirements of harmonic compensation, the grid current waveform gradually increases after compensation using existing methods.It can be known that the grid current compensated by the existing method is unbalanced.However, the use of proposed method can still meet the compensation requirements even under the condition of Voltage balance without harmonic and frequency offset.It can be known that the grid current compensated by the existing method is unbalanced and the harmonic content is high.This shows that the existing method isn't meet the compensation requirements.However, the use of proposed method can still meet the compensation requirements even under the condition of unequal amplitude and asymmetric phases unbalanced grid voltage contains harmonics and load imbalance and frequency offset.

TEST CASE 8: Grid frequency step and voltage amplitude step
Figure 17 shows the experimental waveforms under the condition of grid frequency step and voltage amplitude step.Among them, the grid frequency is stepped to 48Hz at 0.1s, and the voltage amplitude of the phase A and phase C is stepped to 240V and 200V at 0.1s respectively.The grid voltage does not contain harmonics and the load is balanced.Figures (a) and (b) are the experimental waveforms of the existing method and the proposed method respectively.Figure (c) is the analysis of THD value before and after current compensation.As can be seen from the figure, the load current waveform is unbalanced and contains a large number of harmonic, reactive and negative sequence currents.Before 0.1s, the grid frequency and voltage did not change, and SAPF compensated the load current within 0.05s to reach a stable state.A step occurs at 0.1s, the existing method cannot meet the compensation requirements, and the current waveform compensated by the method proposed in this paper is close to a sine wave and is in the same phase as the grid voltage.It shows that the power factor is 1.As can be seen from Figure (c), after the current is stable, the THD value of the load current is 31.42%.The THD value of the grid current compensated by the existing method is 29%, the THD value of the grid current after compensation by proposed method is 2.94%.It can be known that the grid current compensated by the existing method is high and the harmonic content is high.This shows that the existing methods do not meet the compensation requirements.However, even in the case of grid frequency step and voltage amplitude step, the proposed method can still meet the compensation requirements.2 shows the THD values before and after the grid current compensation under various experimental conditions.It can be seen from table 2 that under the condition of grid voltage balance with equal amplitude and symmetrical phase, The method in reference [32] and the method in this paper can meet the requirements of IEEE-519 [45] for grid current harmonic compensation, regardless of whether there are harmonics or not.However, in other cases, the existing methods of reference [32] cannot meet the compensation requirements, and the proposed method can still meet the compensation requirements.Similarly, in the case of frequency offset, the method in reference [13] cannot meet the compensation requirements, and the proposed method can still meet the compensation requirements.The experimental results show the effectiveness and accuracy of the proposed method, and it has better compensation effect than the two existing method even under the condition of complex grid voltage and load.

Conclusion
In this paper, a reference current control strategy based on SOGI and FBD method for shunt active power filter is proposed.Based on SOGI and symmetric component method, the strategy of extracting the positive sequence components of fundamental wave is constructed.With FBD method, the reference value of compensation current can be obtained accurately without coordinate transformation by taking the fundamental positive sequence component of the voltage as a reference.After compensation by the proposed method, the current THD value is greatly reduced to meet the compensation requirements.The experimental results show that the proposed method can compensate the load harmonic current, reactive current and negative sequence current at the same time under complex grid voltage and load, which has wider applicability than the existing methods.

Fig. 4
Fig.4 Structure of three-phase grid voltage imbalance

Fig. 7 From Figure 7
Fig. 7 Phase-shift circuit of SOGI From Figure 7: operator in 120 degrees, it can be expressed as follows:

Fig. 8
Fig. 8 Schematic of reference current calculation

Fig. 9
Fig. 9 Experimental setup waveforms of the supply voltage waveforms of the load current waveforms of the source current waveforms of the compensation current (b) Proposed method Fig.13 Unequal amplitude and asymmetric phases unbalanced grid voltage contains harmonics 0

Fig. 17 Figure 10 -
Fig.17 Grid frequency step and voltage amplitude step4.3Experiment summaryFigure10-17 compares the experimental results of the proposed method and the existing method under various conditions.Table2shows the THD values before and after the grid current compensation under various experimental conditions. )

Table 1
System parameters

TEST CASE 7: Unequal amplitude and asymmetric phases unbalanced grid voltage contains harmonics and load imbalance and frequency offset
Figure16shows the experimental waveforms under the condition of unequal amplitude and asymmetric phases unbalanced grid voltage contains harmonics and load imbalance and frequency offset.As can be seen from the figure, the load current waveform is unbalanced and contains a large number of harmonic, reactive and negative sequence currents.At this time, the THD value of the load current is 36.5%.The THD value of the grid current compensated by the existing method is 28.33%, and the THD value of the grid current compensated by proposed method is 3.17%.Figure(c) is the waveform of the DC voltage of the SAPF DC-link.It can be seen that the DC side voltage stabilizes within 0.05s and stabilizes around the voltage reference value of 750V.
16) Waveform of DC-link voltage Fig.16Unbalanced grid voltage contains harmonics and load imbalance and frequency offset

Table 2
THD% of phase-A source current