Analysis of AC filter detuning characteristics and improvement measures in converter station

Shift of parameters of the double-tuned AC filter component and failure in prompt correction of detuning frequency may affect the filtering effect of the AC filter. Therefore, this paper studies impedance-frequency characteristics of the double-tuned AC filter according to detuned recording data of the A-typed double-tuned AC filter in the Congxi converter station. It analyzes the variation of the impedance-frequency characteristic curves and relative change rate of resonant frequency as there are deviations between actual values and rated values of each filter capacitance and inductance elements in different degrees, and concludes that variation of the parameter of each element in different degrees may cause different deviations of resonant points of the double-tuned AC filter. MATLAB simulation has proved it can reduce the detuning degree and improve the filtering performance of the filter by adjusting the parameters of the variable reactor to change in the opposite direction of the parameters of the resonant capacitor.


Introduction
The harmonic problem in the power system seriously affects people's daily lives and socio-economic development.Therefore, how to effectively filter out harmonics in the power system has become a focus issue in the field of the power industry.Passive filters are widely used for harmonic filtering and reactive power compensation in power systems due to their simple structure and low cost.Among them, double-tuned filters have more prominent filtering advantages compared to traditional single-tuned filters [1][2][3].However, during the operation of the filter, due to factors such as changes in environmental temperature, self-heating, and aging, the values of components such as capacitors and inductors will undergo certain changes, causing the actual resonance frequency of the filter to deviate from the original set value, leading to filter mismatch, and affecting the filtering effect of the filter.Therefore, it is important to delve into the detuning characteristics of dual-tuned filters and find corresponding solutions [4][5].
In [6], a method is proposed to calculate AC harmonic voltage by measuring the current of the AC filter in the HVDC transmission system and analyzing the influence of filter parameter mismatch on the accuracy of harmonic voltage calculation results.In [7], the setting principle of unbalanced current protection of H-type and ∏ type high-voltage filter capacitor banks is studied, and the advantages and disadvantages of the two are compared and analyzed.In [8][9], the detuning elements in series and parallel parts are judged by detecting the changes of high and low harmonic current of the detuning filter and the current changes of two parallel branches under specific harmonic frequencies respectively.In [10], various types of configurable protection and action logic of AC filters in HVDC 2 systems are introduced.It is mentioned that AC filter detuning monitoring can be realized by detecting zero sequence harmonic current on the ground side of the filter.In [11], the action logic of the detuning protection in detail is further introduced and explains that the detuning monitoring alarm can only send alarm signals, but cannot determine whether the harmonic zero-sequence current originates from the internal fault of the filter or the AC system.
In this paper, the detuning alarm event of the AC filter in the Congxi converter station is explored.According to the detuning fault record data of the type A DT11/24 AC filter, the setting value of the detuning alarm is calculated, and the causes of the detuning alarm in the Congxi converter station are analyzed.The basic impedance characteristics of double-tuned filter banks are analyzed deeply, and the influence of the parameter deviation of AC filter elements on the resonant frequency of the system is considered.

Background of AC filter detuning alarm event from Congxi converter station
The main AC harmonics in the converter station are characteristic harmonics produced by the converter station itself, and the components of the lower harmonics are relatively small.There are 22 groups of AC filters in the Congxi converter station, including 4 groups of A-type DT11/24 and B-type DT13/36 AC filters, and the remaining 14 groups are C-type high-voltage shunt capacitor filters.
For the Niu Congong DC station, 3A+4B+13C (that is, 3 type A, 4 type B, and 14 type C) or 4A+3B+13C AC filters can meet the filtering requirements of the full load level under the double-loop bipolar full voltage operation mode, and there will be no excessive harmonics causing the AC filter protection mismatch alarm.However, in actual operation, when A group of Type A or Type B AC filters are not available when the DC power rises to a certain level, a group of filters of the same type will appear as a mismatch alarm, and the signal is frequent.When A group of A-type AC filters is not available, the 11th harmonic is high.When a group of Type B AC filters is not available, the 13th harmonic is higher.

AC filter detuning protection configuration
The AC filter detuning protection device operates by detecting the zero-sequence current at the low-voltage end of the AC filter.This protection is sensitive to harmonic zero sequence current and can detect changes in impedance components in single-phase [12][13].If one of the three phases of the AC filter is detuned, the corresponding harmonics will not flow through this phase filter, and the current flowing through this large group of filters will change.
The detuning alarm detects small changes in the AC filter by detecting the phase current of the current transformer at the tail end of the filter and the self-generated zero sequence current and sends out a detuning alarm signal in case of abnormalities.The action conditions are: where k is the detuning braking coefficient, generally taken as 0.15; A is the fundamental amplitude of the tail phase current of the AC filter.A is the effective value of the 2nd to 36th harmonics in the self-generated zero sequence current at the tail end, namely: We take the mismatch alarm event that occurred at the Congxi converter station in 2018 as an example.We extract the recorded data labeled 592 and 562 for analysis, and the harmonic component monitoring interface of the 500 KV AC filter field at the Congxi converter station is shown in Figure 1.When the AC filter labeled 583 exits operation, the AC filter labeled 562 does not experience a detuning alarm, while the AC filter labeled 592 experiences a detuning alarm.From the fault recording analysis of AC filters 592 and 562, it can be seen that their 11th harmonic current is significantly higher.
Based on the recorded data of the detuning fault, we use Equations ( 1) and ( 2) to calculate the relevant parameters of the AC filters labeled 592 and 562 that trigger the detuning alarm.The fundamental phase current value Ilamp=0.103A of the double-tuned filter labeled 592, and the effective harmonic values of each order of the zero-sequence component Iharm=0.115A; The phase current fundamental value Ilamp=0.044A of the double-tuned filter labeled 562, and the effective value of each harmonic of the zero-sequence component Iharm=0.039 A. Both of them meet the setting value condition for detuning alarm with an Iharm greater than 0.15 Ilamp.However, due to the effective values of the zero sequence components of the double-tuned filter labeled 562 with Iharm lower than 0.060 A, the threshold condition for detuning alarm activation is not met.Therefore, the double-tuned filter labeled 562 does not trigger a detuning alarm, while the double-tuned filter labeled 592 triggers a detuning alarm.
Because labels 562 and 592 are both A-type filter banks, the voltage and current components flowing into each group of filters in the AC system should be consistent.However, the three-phase AC voltage and current measured at the end of the filter are inconsistent.After analysis, it was found that this is mainly due to the varying degrees of environmental impact during operation, resulting in inconsistent offsets in the capacitance and inductance parameters of these two sets of A-type AC filter banks.The deviation of the component parameters of the filter with Label 592 is greater than that of the filter with Label 562, resulting in a lower filtering effect of the 11th harmonic than that of the filter with Label 562, which does not meet the requirements for filtering the 11th harmonic.As a result, a detuning alarm occurs for the filter with Label 592, while no detuning alarm occurs for the filter with Label 562.

Basic filtering impedance characteristics
For the sake of simplicity, the influence of resistance in the dual-tuned AC filter circuit is omitted.The circuit structure of the dual-tuned filter is shown in Figure 2.  , which can simultaneously filter out the harmonics of these two frequencies.Its function is equivalent to two parallel single-tuned filters.From the analysis of circuit structure, a dual-tuned filter is composed of a series resonant circuit and a parallel resonant circuit connected in series.The resonant frequency of the series resonant circuit is 01  , and the resonant frequency of the parallel resonant circuit is 02  .
The relationship between resonant frequencies satisfies 1 By analyzing Figure 3, the impedance can be obtained.

( ) j ( j ) . jj
where ω is the filter frequency.
At the resonant point of the filter, the harmonic impedance of the double-tuned filter is almost zero, so that the corresponding harmonic current on the DC transmission line can be successfully filtered.Compared with the two single-tuned filters, the double-tuned filter can filter the harmonics of two different frequencies at the same time, and only one reactor can withstand all the impulse voltage, which has the advantages of high filtering efficiency, flexible operation, convenient backup, and maintenance.
According to the parameter configuration of A-type DT11/24 and B-type DT13/36 double-tuned filters from the Congxi converter station, the harmonic impedance characteristics of A-type double-tuned AC filters and B-type double-tuned AC filters are obtained by simulation, as shown in Figure 3.As can be seen from the simulation results in Figure 3, when A group of A-type double-tuned AC filters are put into operation, low impedance characteristics are presented at AC harmonic frequencies 11 and 24, that is, the 11th and 24th harmonics are allowed to pass through, to achieve the purpose of filtering harmonics.Similarly, according to the simulation results in Figure 5, when a group of B-type double-tuned AC filters is put into operation, low impedance characteristics are presented at AC harmonic frequencies 13 and 36, that is, the 13th and 36th harmonics are allowed to pass, thereby filtering out the frequency harmonics.
As described in Section 1, when A group of Type A double-tuned AC filters or a group of Type B double-tuned AC filters exit, the number of AC filter groups 3A+4B+13C or 4A+3B+13C input in the automatic reactive power control station should be able to meet the needs of filtering harmonics.Therefore, the simulation compares the impedance characteristics of all filters when they are put into operation with those of A group of Type A filters when they are withdrawn from operation, and the results are shown in Figure 4.  Compared with Figure 4, the impedance characteristic curves of one group of Type A filters when they are out of operation are the same as those of all filters when they are put into operation.Therefore, when only one group of Type A filters exits the operation, the filter effect of the whole system will not be greatly affected theoretically, and the AC filter bank can still meet the filtering requirements of the system.

Analysis of the detuning characteristics of the micro-variable parameters of double-tuned filters
It is assumed that the system frequency does not shift, the frequency shift caused by component parameter drift is analyzed.We set Equation (4) to be equal to 0, resulting in: We find the partial derivative of  with respect to 1 2 1 2 L L C C 、 、 、 on the above equation, respectively, and obtain: When the double-tuned filter works in practice, all four component parameters may drift, and the total offset of the tuning frequency is the sum of the offset of the four component parameters.Therefore, compared with the single-tuned filter, the double-tuned filter is more sensitive, and even if the component parameters are slightly shifted, the double-tuned filter is likely to be detuned and the filtering effect is significantly worse.From a single-tuned filter to a double-tuned filter, although the cost is reduced and economic benefits are brought, the robustness of the filter and the stability of the system are also reduced.

Control measures for a frequency change of double-tuned filter
When the double-tuned filter's parameter changes result in detuning, such as capacitor bank detuning, it is usually possible to replace the inductor in the filter with a variable reactor, which adjusts the impedance of the filter by changing its parameters in the opposite direction of the capacitor bank changing parameters, thereby improving the filtering ability of the filter in the case of detuning [15].It is assumed that the actual resonant frequency of the double-tuned filter is 12  、 .Based on Veda's theorem, Equation ( 5) can be transformed into: The relative change of     <<, it is known that the relative change in frequency is opposite to the relative change in the variable reactor, that is, the two changes in the opposite direction.It is assumed that the relative change of L1 is the same as that of L2, that is, .Then Equation ( 9) can be simplified as: 2.
As can be seen from Equation (10), if the resonant frequency of the system is shifted from 50 Hz to 49.5 Hz, that is, the downward shift is 1%, the parameters of the variable reactor will be increased by 2%.

ICEEPS-2023
) It is assumed that the relative change in C1 is the same as the relative change in C2, i.e., By combining Equations ( 10) and ( 12), the total relative variation of series and parallel resonant frequencies is obtained as: 22 When the capacitive component drifts, to maintain the normal operation of the dual-tuned filter, the relative offset of the series-parallel resonant frequency must be 0, that is, we set Equation ( 13) to be zero.The relationship between the relative change rate of the variable reactor and the relative change rate of the capacitor can be solved, that is: That is to say, the variable reactor and capacitor change in the opposite direction.If the capacitor increases by 1%, the variable reactor needs to decrease by 1% for the dual-tuned filter to work properly.

Example analysis
In this paper, taking the A-type double-tuned AC filter of the Congxi converter station as an example, the frequency offset and impedance characteristics of the inductance and capacitance parameters of the double-tuned filter in a series-parallel circuit are analyzed by MATLAB simulation software.At the same time, the influence of component parameter migration on the overall filter performance is investigated by mathematical method, and the change in the filter performance after parameter migration is further studied.

Influence of component parameter value deviation on the resonant frequency of the system
To analyze the 11th harmonic detuning of the A-type filter from the Congxi converter station, based on Equation (6), this section separately analyzes the change rate characteristics of the induced frequency relative to the parameters of the four impedance components of the A-type AC filter, and the results are shown in Figure 5.According to the analysis of Figure 5, it can be seen that at the 11th harmonic of the A-type double-tuned AC filter, the change rate of the resonant frequency relative to the parameters of the four impedance elements is less than 0, indicating that parameter offset will reduce the resonant frequency of the filter.The influence of capacitance parameter deviation on resonant frequency is greater than that of inductance parameter variation, and the influence of parallel element parameter deviation on resonant frequency is greater than that of series element parameter deviation.

Impedance-frequency characteristics after the offset of component parameter values
The parameter values of the four impedance elements of the A-type double-tuned AC filter were adjusted to make them offset to different degrees, and the impedance-frequency characteristic curves after parameter values offset were obtained by simulation and compared with the original impedance characteristic curves, as shown in Figure 6.According to the simulation results in Figure 6, the filter detuning degree in the above four cases is calculated, as shown in Table 1.6, when the parameters of any component of the double-tuned filter are offset, the entire impedance characteristics may change, affecting the filtering performance of the AC filter.Therefore, the double-tuned filter must be able to constantly adjust its parameters to adapt to the mismatch problem caused by internal or external factors, such as changing the inductance of the double-tuned wave detector to a variable reactor and adjusting the inductance value of the double-tuned filter by timing the harmonic parameters of the system.

The effect of variable reactor on improving system distuning
We adjust C1 and C2 so that they both have a 10% forward offset, and the impedance-frequency characteristic curves before and after the offset are obtained, as shown in Figure 7 (a).From the above analysis, it can be seen that the filtering ability of the filter in the case of detuning can be adjusted by adjusting the parameters of the variable reactor.Therefore, L1 and L2 are adjusted to reverse offset by 10%, and the impedance-frequency characteristic curves before and after the offset are obtained, as shown in Figure 7 7 (a) and 7 (b), when the variable reactor and the detuning capacitor adjust the parameters in the opposite direction, the detuning degree of the filter decreases, and the impedance offset near the resonant point becomes smaller, so the filtering performance of the filter is improved.

Conclusions
Based on the data recorded by the A-type AC filter of the Congxi converter station, this paper calculates the setting value of the alarm and analyzes the root cause of the alarm.At the same time, based on the impedance frequency characteristics of the double-tuned filter, the corresponding change of the tuning frequency when there is a deviation between the actual value and the rated value of the capacitor and inductor is analyzed, and the influence of the parameter deviation on the resonant frequency of the system is simulated.The results show that the double-tuned filter must be able to continuously adjust its parameters to adapt to the mismatch problem caused by internal or external factors.

Figure 1 .
AC filter detuning records for labels 592 and 562.

Figure 2 .
Figure 2. The circuit structure of the double-tuned filter.

Figure 4 .
Figure 4. Comparison of impedance characteristics when all filters are put into operation and a group of A-typed filters is quitted running.

Figure 5 .
Figure 5.The relative rate of change of resonant frequency when L1, L2, C1, and C2 change respectively.

Figure 7 .
Figure 7. Impedance-frequency characteristics after adjusting parameters of the variable reactor.

Table 1 .
Detuning characteristics after parameter values of impedance component shift.