A New Method for Harmonic Current Detection in Square Wave Active Filter

1 Introduction

With the development of power electronics technology, the application of power electronic devices has become increasingly widespread, and the harmonic pollution caused by the power grid has become increasingly serious [1][2]. Therefore, it has become an important research direction to effectively suppress the harmonics of the power grid and dynamically compensate for the reactive power.

Using power filter devices to absorb the harmonic currents generated by harmonic sources nearby is an effective measure to suppress harmonic pollution. The traditional method is to use LC passive filters, which have the advantages of low cost and high efficiency, but their compensation characteristics are easily affected by the impedance of the grid and the operating state, and are prone to resonate with the system to cause harmonic amplification, and can only compensate for harmonics of fixed frequencies [2][3].

Active Power Filter (APF), which emerged based on the development of power electronics technology, has opened up a new way to eliminate harmonics in power systems and also solved the problem of reactive power compensation. The basic principle of APF is to detect harmonic current from the compensation object, and the compensation device generates a compensation current that is equal to the harmonic current but opposite in polarity, so that the grid current only contains the fundamental component. This filter has the incomparable advantages of LC filters: excellent dynamic and static compensation performance, and its compensation characteristics are not affected by the impedance of the grid, which can realize multi-functional integration and one machine for multiple uses.

From different perspectives, APF has different classification standards [3][4][5]. A single series or parallel APF has good compensation characteristics for small power systems, but is not suitable for large power systems [1] because this type of APF uses one inverter to generate all the harmonic signals to be compensated. This method has high requirements on the bandwidth of the inverter PWM modulation and can only be used in medium-capacity systems (500kW to 10MW). Using APF in series with a passive filter allows the APF to only bear harmonic voltages, thereby greatly reducing the capacity and can be used in systems with power above 10MW [1][6][7]. References [8][9] proposed a square wave active filter (Hybrid Parallel Active Power Filter-AP APF), which uses multiple small-capacity (about 1% to 2% of the nonlinear load capacity) inverters to compensate for the main harmonics separately, so that the inverter only bears a certain harmonic voltage, as shown in Figure 1.

Aiming at this new square wave APF, this paper proposes a method to detect current of specified harmonic order based on instantaneous reactive power theory. The effectiveness of this method is proved by theory and simulation.

2 Instantaneous reactive power theory

In 1983, the "instantaneous reactive power theory" proposed by Japanese scholar Yasufumi Akagi made the active power filter proposed in the 1970s

Figure 1 Square wave active filter system

Figure 2 Voltage and current vectors in the α-β coordinate system

Figure 3 Schematic diagram of the p-q operation method

After leaving the laboratory, this theory has been continuously improved[10].

Assume that the three-phase circuit is a three-phase three-wire system, and the instantaneous values ​​of the voltage and current of each phase are ea, eb, ec and ia, ib, ic respectively. Transform them into the two-phase orthogonal α-β coordinate system, as shown in Figure 2. (1) (2)

On the α-β plane shown in Figure 2, vectors eα , eβ and iα, iβ respectively synthesize the voltage vector e and the current vector i. The instantaneous reactive power q (instantaneous active power p) of the three-phase circuit is the product of the modulus of the voltage vector e and the instantaneous reactive current iq (instantaneous active current ip) of the three-phase circuit. (3)

From Figure 2 and coordinate transformation, we can get: (4) [page]

3. Detection method of harmonic current with specified harmonic order

3.1 P-Q method and IP-IQ method

Based on the above definitions of ip, iq and p, q, there are two methods for detecting harmonic current: the p-q method and the ip-iq method [11].

The principle diagram of the p-q method is shown in Figure 3. According to the above definition, p and q can be calculated, and the DC components p and q of p and q can be obtained through the low-pass filter LPF. When the power supply voltage is undistorted, p is generated by the action of the fundamental active current and voltage, and q is generated by the action of the fundamental reactive current and voltage. Therefore, the fundamental components iaf, ibf, and icf of the detected currents ia, ib, and ic can be calculated from p and q. (5)

Subtracting iaf, ibf, icf from ia, ib, ic will yield the harmonic components iah, ibh, ich of ia, ib, ic. The principle of the ip-iq method is shown in Figure 4. In the figure, C =. This method uses a phase-locked loop and a sine and cosine generating circuit to obtain a sine signal sinωt and a corresponding cosine signal cosωt in phase with the power supply voltage ea. These two signals together with ia, ib, ic are used to calculate ip and iq, and the DC components ip and iq of ip and iq are obtained by LPF filtering. Here, ip and iq are generated by iaf, ibf, icf, so iaf, ibf, icf can be calculated from ip and iq, and then iah, ibh, ich can be calculated.

3.2 Detection method of harmonic current with specified harmonic order

The above-mentioned p, q method and ip, iq method obtain iah, ibh, ich, that is, the source filter

Figure 4 Schematic diagram of IP-IQ operation method

Figure 5 Schematic diagram of the fifth harmonic detection method based on the p-q method

Figure 6 Schematic diagram of the fifth harmonic detection method based on the IP-IQ method

The sum of all harmonic components except the fundamental wave. On this basis, this paper proposes a detection method for harmonic current of specified harmonic order. The following takes the detection of the fifth harmonic as an example to study this method.

3.2.1 Detection principle

The principle of the fifth harmonic detection method based on pq is shown in Figure 5. This method first multiplies the voltage signal by five times, and then calculates p5 and q5 according to the definition. The DC components p5 and q5 of p5 and q5 are obtained by filtering with a low-pass filter LPF, and then the fifth harmonic components ia5, ib5, and ic5 of the detected current ia, ib, and ic are calculated from p5 and q5. (6)

The principle of the fifth harmonic detection method based on the ip and iq method is shown in Figure 6. This method first multiplies the power supply voltage ea by five times to obtain ea5, and uses a phase-locked loop and a sine and cosine generating circuit to obtain a sine signal sin5ωt and a corresponding cosine signal cos5ωt in phase with ea5. These two signals are used together with ia, ib, and ic to calculate ip5 and iq5, and the DC components ip5 and iq5 of ip5, iq5 are obtained by LPF filtering. Here, ip5 and iq5 are generated by ia5, ib5, and ic5. Therefore, ia5, ib5, and ic5 can be calculated from ip5 and iq5.

3.2.2 Detection theory analysis

Assume the current being detected is (7) [page]

Where: n=3k±1, k is an integer;

ω is the power frequency;

In and φn are the effective value and initial phase of each current.

(1) When the voltage is not distorted

Assume that the three-phase voltage is symmetrical (8)

A New Method for Harmonic Current Detection in Square Wave Active Filter

Then the fifth frequency of ea, eb, ec is (9)

Substituting equation (9) into equation (1), we get (10)

Substituting equation (7) into equation (2), we get (11)

In the formula: when n=3k+1, take the upper sign, when n=3k-1, take the lower sign, and the n appearing in the following formulas is the same.

According to the p-q-based calculation method, substitute equations (10) and (11) into equation (4), and replace Cpq in equation (4) with Cpq5 to obtain = 3E1 (12)

p5 and q5 are filtered by LPF to obtain (13)

At this time, e2=3E12, and substituting it into equation (6) together with equation (13) yields = (14)

In this way, ia5, ib5 and ic5 were calculated accurately.

According to the calculation method based on ipiq, the fifth frequency of ea is calculated first, and ea5=E1sin5ωt is obtained. From Figure 6, we can get = (15)

It can be seen that the detection method based on the IPIQ method also accurately calculated IA5, IB5, and IC5.

(2) When the power supply voltage is distorted

When the power supply voltage is distorted, in the fifth harmonic detection method based on the pq method, the harmonic components of the distorted voltage are involved in the calculation, and there is an error in the detection result. The principle of error is the same as the analysis in the literature [11]. However, in the fifth harmonic detection method based on the ipiq method, only the sin5ωt and -cos5ωt after ea is multiplied by five times are used for calculation, and the harmonic components of the distorted voltage do not appear in the calculation process. Therefore, the detection result is not affected by the voltage waveform distortion and the detection result is correct.

The following is a three-phase controlled bridge rectifier circuit. It is assumed that the power supply voltage is symmetrical and undistorted, the current contains the fifth and seventh harmonics, and the control angle is 30°, as shown in equation (16). The current ia is shown in Figure 7(a). The waveform of ia5 obtained by the fifth harmonic detection method based on the p-q operation method is shown in Figure 7(b).

In the formula: ω=2πf, f is the industrial frequency 50Hz.

Comparing the waveforms obtained by simulation with those of theoretical analysis, it can be seen that the detection results of the fifth harmonic detection method based on pq operation are accurate.

Figure 7 Simulation result waveform

(a) Current ia waveform (b) Fifth harmonic detection current ia5 waveform