Application of Instantaneous Reactive Power Theory in SVC Reactive Power Detection

1  引言
大功率电力电子器件和FACTS装置近年来被广泛应用于电力系统，相对于传统设备，其特点是快速动态的响应。其中应用较多的有静止无功功率补偿装置（SVC），在供电点安装SVC不仅可以提高供电点的功率因素，而且可以补偿三相符合不平衡造成的负序电流，其显著特点是能快速连续地对波动负荷进行动态补偿，通过分相调整补偿无功功率，有效地抑制系统的电压闪变和波动以及抵消不平衡负荷。

One of the focuses of SVC system research is the calculation and detection of reactive power. Reactive power can be defined or extended based on the relationship between apparent power and active power. In the reactive power calculation of SVC system, reactive power can be calculated based on the definition of reactive power in sinusoidal circuit. This traditional method first requires the analysis and estimation of line voltage, current and the phase between the two within a certain period, and then the calculation of reactive power on this basis, which is difficult to meet the requirements of dynamic and fast speed. Therefore, this paper adopts instantaneous reactive power theory to calculate the reactive power of SVC system. The instantaneous reactive power theory was proposed in the 1980s, breaking through the traditional power definition based on cycle, and can calculate the instantaneous value of the system to meet the requirements of fast and continuous action of reactive power compensation device.

2 Instantaneous Reactive Power Theory
There is no widely accepted scientific and authoritative definition of reactive power in non-sinusoidal circuits containing harmonics. According to the relationship between apparent power S, active power P and reactive power Q, S ² =P ² +Q ² , reactive power can be defined as:

(1)

The reactive power Q in the formula only reflects the flow and exchange of energy, but not the consumption of energy in the load, which is consistent with the most basic physical meaning of reactive power in a sinusoidal circuit. However, it does not distinguish between the reactive power generated between the fundamental voltage and current and the reactive power generated between the harmonic voltage and current of the same frequency, and the result has no clear meaning for the identification of harmonic sources and reactive power.

In a sinusoidal circuit, there is also a reactive power defined as (where is the phase difference between voltage and current). Thus, the total reactive power of a non-sinusoidal circuit can be similarly defined as the sum of the fundamental and harmonic reactive powers.

Where is the harmonic order, and are the effective values ​​of the fundamental and harmonic voltages and currents, is the phase difference between the fundamental and harmonic voltages and currents, is the reactive power of the fundamental and harmonics, and N is the highest harmonic order of interest.

The theory of instantaneous reactive power of three-phase circuit was first proposed by Yasufumi Akagi in 1983, and has been gradually improved through continuous research. The theory of instantaneous reactive power breaks through the definition of power based on average value, and systematically defines instantaneous power quantities such as instantaneous reactive power and instantaneous active power. Based on the theory of instantaneous reactive power, reactive power can be calculated. The principle of the theory of instantaneous reactive power of three-phase circuit is as follows.

[page] Assume that the instantaneous values ​​of the voltage and current of the three-phase circuit are and respectively. The instantaneous reactive power theory transforms the voltage and current in the three-phase circuit into a two-phase orthogonal coordinate system (Park transformation). The two-phase voltage and current are and respectively. The transformation is as follows

Where .
The voltage and current vector diagram on the plane is shown in Figure 1.

Figure 2.1 Voltage and current vector diagram

Where e and i are the voltage vector and current vector respectively, , , are the phase angles of the vectors respectively.
The instantaneous active power and reactive power of the three-phase circuit are the product of the modulus of the voltage vector and the active and reactive components of the instantaneous current of the three-phase circuit, written in matrix form:

Substituting the two-phase current expressions into the above formula, we can get the expressions of active power and reactive power:

3 SVC reactive power calculation

The three-phase voltage expression is

Where Em is the voltage amplitude and w is the angular frequency.
According to the instantaneous reactive matrix transformation, we can get

According to the expressions of active and reactive power, we can get

The line current is times the SVC current, the line voltage is , and the reactive power is

[page] In the actual system, the voltage and current are sampled data points one by one, and the instantaneous value of reactive power data points are calculated according to the above formula. These instantaneous reactive power data points contain some high-frequency interference in the actual system. When detecting the reactive power of SVC, it is hoped to filter out the results formed by these interferences, so as to have a reference significance for the SVC reactive monitoring and control system. Therefore, when performing interference filtering on the instantaneous value of reactive power, the sliding average window method is adopted. Assume that the sliding window length is M, and calculate the average value of reactive power at sampling point k. When k is between 1 and M/2, the average value of 1 to k+M/2 (k

The average reactive power expression is:

Where k is the sampling point, M is the sliding window length, is the average reactive power at the sampling point k, and is the instantaneous reactive power at the sampling point k.

4 Simulation results The
given input three-phase voltage is a sinusoidal signal with an effective value of 220V and a fundamental frequency of 50Hz; the three-phase current signal is a sinusoidal signal with an effective value of 20A and a phase lag of 30 degrees behind the voltage, which is a three-phase symmetrical system. The three-phase voltage and current waveforms are shown in Figure 2.

Figure 2 Three-phase voltage and current waveforms

According to the reactive power calculation formula of sinusoidal signal,

Where is the phase difference between the voltage and current signals.
According to the above three-phase instantaneous reactive power theory and derivation results, the three-phase reactive power is calculated, and the instantaneous reactive power waveform and the moving average reactive power waveform are shown in Figure 3.

Figure 3 Three-phase reactive power calculation
Assume that the three-phase voltage expression is the formula, then the three-phase current expression is

According to the expression of reactive power, we can get

The reactive power value thus calculated is approximately 6600 var, which is consistent with the result of the reactive power definition calculation of the sinusoidal signal.

Keeping the voltage and current signal parameter values ​​unchanged, the noise signal is mixed into the current signal, and the waveform is shown in Figure 4.

Figure 4 Three-phase voltage and disturbance current waveforms

[page] Due to the influence of noise signals, the reactive power should fluctuate around 6600 var. The instantaneous reactive power waveform and reactive power calculation waveform are shown in Figure 5.

Figure 5 Instantaneous reactive power and calculated waveform

The calculated reactive power value fluctuates around 6600 var, which is consistent with the analysis result.

Keeping the voltage and current of phase A and phase B unchanged, the voltage and current of phase C are reduced to 80% of the original. Under the condition of three-phase asymmetry, the three-phase voltage, current waveforms and reactive power calculation waveforms are shown in Figures 6 and 7 respectively.

Figure 6 Three-phase asymmetric voltage and current waveforms


Figure 7 Instantaneous reactive power and calculated waveforms

At this time, the reactive power is basically consistent with the waveform results.
[page] Keeping the three-phase asymmetric voltage and current signals unchanged, and mixing the noise signal into the current signal, the voltage, current waveform and reactive power calculation waveform are shown in Figure 8 and Figure 9 respectively. The obtained waveform is also basically consistent with the analysis results.

Figure 8 Three-phase asymmetric voltage and disturbance current waveforms

Figure 9 Instantaneous reactive power and calculated waveform

[page]5 Conclusion
This paper discusses the detection method of static VAR compensator (SVC) reactive power, and uses the instantaneous reactive theory to detect three-phase reactive power. The instantaneous reactive algorithm is implemented to calculate the SVC reactive power, and simulation experiments are carried out. The simulation results show that the instantaneous reactive theory can calculate the three-phase reactive power and realize the detection of reactive power. The experiment provides a theoretical basis for the monitoring and control of reactive power in the SVC monitoring system, which has good application value.

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