Reactive Power Compensation Design Under Harmonic Conditions

introduction

With the promotion and use of nonlinear loads such as frequency converters and power savers, the harmonic content of the power grid is increasing. Grid harmonics have a great impact on power reactive compensation equipment. In local power grids with serious harmonics, reactive compensation equipment of capacitors without reactance can hardly work. Many companies use the reactive compensation method of capacitors in series with reactors to avoid harmonics, but because they are not clear about the calculation method of reactance value, not only can they not achieve the ideal compensation effect, but they also cause harmonic amplification. Some companies have selected passive filters, but because they have not accurately measured the grid parameters, they cannot operate normally after being put into operation. In response to the harmonic control problem of reactive compensation in low-voltage systems, this article gives a detailed explanation of the design and calculation of compensation capacitors in series with reactors, clarifies the vague concept of passive filters in design, and proposes to use series reactors to solve the problem of passive filters being unable to be used under grid harmonics, and gives a practical calculation method.

1 Main components of harmonics

There are many reasons for the generation of harmonics, but the main composition of power grid harmonics is not complicated. Power grid harmonics refer to higher-order waves that are integer multiples of the fundamental wave, namely 2nd, 3rd, 4th, 5th, etc. harmonics. Among the harmonics, even harmonics are formed due to the asymmetry of the positive and negative half-cycles of the signal, and the asymmetry of the positive and negative half-cycles of the current in the power grid is not common, so the content of even harmonics is very small. In a three-phase system, 3, 6, 9, etc., the phases of 3 integer harmonics are the same, and they cannot flow in a three-phase three-wire system, nor can they flow in a three-phase compensation capacitor. As long as it is not split-phase compensation, there is no need to consider the influence of 3 integer harmonics.

In most cases, harmonics are generated by nonlinear loads, mainly rectification and filtering, which produce PN first harmonics in the power grid. P is the number of DC wave heads formed by rectification within a week, N is a natural number, and the lowest harmonic order of three-phase rectification is 5.

In inverter loads such as medium frequency furnaces and frequency converters, the inverter frequency is independent of the grid frequency, and harmonics with frequencies that are not integer multiples of the fundamental wave will be generated, which some people call fractional harmonics. However, these harmonics are isolated by the rectifier and filter circuit and will not be directly fed back to the grid.

In large-scale impact asymmetric loads such as arc furnaces, electrolytic aluminum, and chlor-alkali plants, although the harmonic components are very complex and the content is large, the harmonics generated due to the intermittent operation are mostly interharmonics, which are characterized by short duration, chaotic spectrum, and white noise after superposition. This type of harmonic can be treated by installing a low-pass filter before the harmonic load.

Electric locomotives are recognized as harmonic sources, but they mainly generate notch waves and unbalanced loads. After passing through the Y/Y connection transformer, the harmonics of multiples of 3 are isolated, and the harmonic components injected into the power grid are the same as those of inverter loads, so the main components of the power grid harmonics are 5th, 7th, 11th, 13th, 17th, 19th... harmonics.

2 Impact of harmonics on reactive power compensation

When the harmonic source is located in the local power grid where compensation is performed, it is called intranet harmonics. For intranet harmonics, the compensation capacitor and the system impedance (including the leakage reactance of the main transformer and the grid impedance) are in parallel. If the parallel resonance frequency is exactly equal to the harmonic source frequency, parallel resonance will occur, and harmonic current amplification will occur. At this time, even if the capacitor compensation capacity is greater than the harmonic source capacity, the capacitor may be overloaded. The capacity of the intranet harmonic source is usually smaller than the capacity of the local network main transformer, and a parallel filter should be used to absorb it.

When harmonics are introduced from the upper level power grid through the main transformer into the current level power grid, they are called external network harmonics. For external network harmonics, the compensation capacitor and the system impedance are in series. If the series resonance frequency is exactly equal to the frequency of the harmonic source in the system, series resonance will occur, resulting in harmonic voltage amplification, which may cause the compensation capacitor to overload. Since the system harmonic source is often large in capacity, it is usually impossible to absorb it using a parallel filter at this time, so the only way to prevent excessive harmonics from entering the capacitor is to use a series reactor filter. Therefore, it is very important to distinguish between internal network harmonics and external network harmonics in order to adopt the correct compensation filtering method.

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3 Reactive power compensation design under external grid harmonics

The characteristic curve of the series equivalent reactance of the external network harmonic compensation circuit is shown in Figure 1. The external network harmonic capacity is relatively large, which can be represented by the voltage source ESK, where k represents the harmonic order. Ignoring the resistance in the system impedance, the relationship between the system fundamental reactance XS, the capacitor fundamental reactance XC and the harmonic current IK can be simply written

In formula (1), part is the series equivalent reactance of the compensation capacitor circuit to the external harmonics, which is shown as curve 1 in Figure 1. For high-order harmonics, the series equivalent reactance of the external network harmonics often presents a low-resistance characteristic, and even presents a reactance of 0 at a certain frequency point, causing a large amount of external network harmonic current to flow into the compensation capacitor and cause overload.

Based on the fact that there are no 2nd, 3rd and 4th harmonics in the power grid, the project adopts the method of connecting a reactor in series with the compensation capacitor to suppress harmonics. At this time, the series equivalent reactance of the external network harmonic becomes: shown as curve 2 in Figure 1.

After the series reactance is added, the resonant frequency of the capacitor series circuit drops below the 5th harmonic. Since the harmonic content below the 5th is very small in the system, series resonance will not occur. The electrical characteristics presented are that the capacitor series circuit is inductive for harmonics greater than the resonant frequency, and capacitive for fundamental capacitor series circuits below the resonant frequency.

People tend to think that as long as the circuit is inductive to the system harmonics after the series reactor is connected, it can play a role in suppressing harmonics. In fact, if the resonance point of the circuit is selected too high, it will not only fail to suppress harmonics, but may amplify harmonics. From the characteristics of curve 2 in Figure 1, it can be seen that although the circuit characteristics become inductive at the 5th harmonic frequency after the series reactor is connected, the modulus of its reactance is smaller than the modulus of curve 1 before the series reactor is connected. In other words, the 5th harmonic current flowing into the capacitor after the series reactor is connected is larger. Therefore, when selecting the reactor reactance value, it should be ensured that the impedance modulus of the lowest harmonic after the series reactor is connected does not decrease. In actual design, the maximum possible harmonic current flowing into the compensation capacitor can be calculated based on the size of the system's voltage harmonic Esk, and the root mean square value of the main harmonic current and the fundamental current can be calculated. The root mean square value is used to verify the overload of the capacitor when there are harmonics. The calculation method of each harmonic current is

In the formula, the fundamental reactance equivalent reactance Xs of the power supply can be replaced by the transformer short-circuit reactance in simple calculations.

In the capacitor compensation system with group switching, the reactor should be connected in series with the group capacitor, and one group of reactors cannot be used with multiple groups of capacitors. In situations where the compensation capacity of the capacitor may become smaller (such as self-healing capacitors), a certain margin should be calculated to avoid the resonance point moving up and causing the wave blocking failure.

It does not mean that the larger the series reactance, the better. From Figure 1, it can be seen that the total fundamental impedance of the series circuit is also reduced after the series reactance is connected, while the capacitive reactance of the capacitor has not changed. Therefore, when the capacitor is connected in series with the reactor, the voltage at the power frequency fundamental terminal of the capacitor will increase. The value after the voltage increase is close to XC/(XC-XL) times the working voltage before the series reactance is connected. The larger the reactance is, the more the voltage increases. Therefore, when selecting the rated voltage of the capacitor, it must be higher than this voltage. In addition to considering the increase in fundamental voltage, the spike voltage that will appear when the harmonic voltage is superimposed on the fundamental voltage should also be considered. The spike voltage can be used to verify the short-term overvoltage capacity of the capacitor. Generally, power capacitors should reach a withstand voltage level of 170% overvoltage for 1 min without breakdown. If the withstand voltage of the product used does not meet the requirements, the rated voltage of the capacitor needs to be increased by 10-20%.

4 Reactive Power Compensation Design under Intranet Harmonics

Intranet harmonics are caused by the nonlinear load of the enterprise itself, so their capacity is limited. In principle, the series reactor should not be used when designing the compensator, because doing so will push the harmonics of the local grid to the upper grid.

The correct way should be to use harmonic filters to absorb the harmonics generated by the power grid itself, and then perform reactive compensation on the circuit. Figure 2 is the wiring schematic diagram of the most commonly used passive filter. In the design, the capacity of the filter capacitors of each harmonic branch must be greater than the capacity of the internal network harmonic source. In the case that the reactive compensation capacity does not exceed the limit, the capacitor capacity can be selected to be the same. Because the price of the capacitor is much smaller than the price of the reactor, the larger the capacitor capacity, the smaller the reactance required for the same resonant frequency, and the cheaper the overall cost. In the design of the filter reactor, the rated current of the reactor only needs to be greater than the harmonic current of the internal network harmonic source. The capacitive reactance value of the capacitor and the reactance value of the reactor are determined according to the series resonance condition of the filtered harmonic. For example, the capacitive reactance value of the 7th harmonic filter capacitor at the fundamental frequency is XC7, then the reactance value of the 7th harmonic reactor at the fundamental frequency is XL7=XC7/72=XC7-2%. Figure 2 lists the approximate values ​​of some filter reactances. Each branch of the harmonic filter presents the lowest impedance only to the harmonic of this time, and each branch presents capacitance to the fundamental wave, so each branch is performing reactive compensation. When calculating the compensation capacity, the reactive compensation capacity of the kth filter branch is [k2/(k2-1)]2 times the capacitor compensation capacity when the reactor is not connected in series. If the calculated reactive compensation capacity does not meet the overall design requirements, then additional reactive compensation equipment can be added. Of course, the capacity of each branch of the harmonic filter can also be increased, but this is not conducive to the adjustment of the compensation capacity.

When selecting the rated voltage of the capacitor, the filter resonant additional voltage should be added to the system power frequency voltage. The resonant additional voltage value is calculated according to the maximum possible harmonic current flowing through the filter capacitor. For example, the capacitive reactance of the 5th harmonic filter capacitor under the fundamental wave is XC5, and the maximum 5th harmonic current passing through is I5, then the 5th resonant additional voltage is

5. Design of reactive power compensation for internal network harmonics and external network harmonics

In actual systems, there are often not only internal network harmonics, but also external network harmonics. The capacity of the external network harmonic source is large, and it will pass through the transformer reactance into the filter, causing the filter to be severely overloaded and burned. An article proposes to adjust the resonant frequency of the filter so that the resonance point is changed to a frequency where harmonics do not exist, such as the 4th, 6th, 8th, and 10th harmonic frequencies. This is actually a way of avoidance, which will not only weaken the filtering effect of the filter on the internal network harmonics, but also be very dangerous. Since the resonant frequency of the filter branch is very close to the system harmonic frequency, once the grid operation mode changes or the capacitor parameters change, it is possible to resonate with the external network harmonics, causing the filter to be overloaded or even burned.

A more reasonable way is to connect a reactor in series between the filter and the power supply, as shown in Figure 3. For internal network harmonics, the resonance point of the filter in this way remains consistent with the harmonic frequency of the harmonic source, which will not affect the filtering effect. For external network harmonics, the filter always presents inductive properties and will not cause overload of the compensation and filter capacitors.

After the reactor XL is connected in series, there is still a certain amount of external network harmonic current entering the filter branch, so a certain amount of surplus capacity should be required when designing the branch filter capacitor. The external network harmonic current flowing into the filter branch is

Where:

k is the subharmonic order;

X S is the fundamental reactance of the power supply;

E sk is the amplitude of the external network harmonics.

Usually E sk is less than 5% of the rated voltage of the system, XL is approximately 1 to 2 times the fundamental value of the 5th harmonic reactance, and the calculated Ik will not exceed 10% to 20% of the maximum filter current of the intranet.

The reactance value XL cannot be too large, because adding reactance will increase the fundamental voltage at the filter inlet. If the filter has 4 filtering paths, 5th, 7th, 11th, 13th or more, then the voltage will increase by approximately 1/2 times after the series reactance is connected.

Where: XCK and XLK are the fundamental capacitive reactance of the capacitor and the fundamental inductive reactance of the reactor of the kth filter branch. After adding the reactance, the voltage increases by 1%~2%.

6 Conclusion

In a power grid with harmonics, reactive power compensation should be carried out by using a series reactor, which can not only solve the overcurrent and overvoltage problems of simple capacitor compensation, but also solve the overload problem of multi-branch passive filters. The calculation of reactor parameters in the design is very important. It is necessary not only to check the harmonic blocking effect of the lower limit of the reactor, but also to check the voltage increase caused by the upper limit of the reactor to the compensation filter circuit. According to the calculation formula given in this article, the required reactance value can be easily calculated.