4. Optimal Configuration Steps of DRPCE
4.1. Installation Location Configuration of DRPCE
According to the principle of local reactive power compensation, the compensation facilities are usually installed nearby. However, in MIDC, there is a strong electrical connection between DC and DC. The interaction between the installation site and the converter station of each subsystem should be considered comprehensively.
The CIGRE working group proposed the concept of multi-infeed interaction factor (MIIF) in 2008 [
17]. This revealed that the converter bus voltage can describe the interaction between converter stations of MIDC subsystems. The converter bus
m is connected with the three-phase symmetrical reactor. When the voltage of the converter bus decreases by 1%, MIIF refers to the change rate of voltage corresponding to the voltage at the other converter bus
j.
Inspired by the definition of MIIF, the voltage coupling factor MIADF (multi-infeed AC/DC factor) can be defined as Equation (11). It characterizes the interaction between AC bus and multi-inverter converter bus in the MIDC system.
where δ
d is the power weight coefficient of converter bus
d;
Pd is the power of the converter bus
d and
Zld and
Zll are the mutual-impedance and the self-impedance of AC bus
l, respectively.
The higher the MIADF value is, the greater the bus-to-bus interaction is. Stronger interaction means that the compensation at these buses can respond better than those with poor interaction [
18]. Therefore, the candidate area for DRPCE installation can be selected by sequencing the MIADF value in the receiving-side grid.
It is then necessary to make the installation nodes from the candidate installation area accurate. If the installed capacity of DRPCE is set as a fixed value △
q, and the index
Ri is defined, the response level can be evaluated as:
RMCCF (△
q) refers to the inhibitory effect of subsequent commutation failure under the configuration of DRPCE of capacity △
q, which can be obtained by Equation (7). The higher the value
Ri takes at node
i, the more sensitive the reactive compensation performed here is. All nodes in the candidate area are sorted according to the index value. The sorting process is carried out by the cycle selection method shown in
Figure 7.
4.2. Type and Capacity Configuration of DRPCE
SVC, synchronous condenser and STATCOM are the most commonly used DRPCEs. Among them, the synchronous condenser is a kind of synchronous motor that can generate a large amount of reactive power at the moment of fault, which provides short-circuit capacity and reactive power support for the system, but the response speed is slow and the loss is large. SVC is a kind of typical power electronic-reactive power compensation device, which uses a thyristor as a solid-state switch to control the capacity of the capacitor and reactor in the access system, so as to change the system admittance and control the reactive output power. The advantages of SVC are its fast response speed and continuous reactive power regulation. However, the reactive power compensation capacity of SVC is greatly affected by the system bus voltage. In case of serious fault, the reactive output current will decrease proportionally with the system voltage. The reactive power support capacity is limited. STATCOM is a new type of dynamic reactive power compensation equipment, which has faster response speed and reactive power support capability than SVC. It is insensitive to the external system operating conditions and structural changes. Moreover, it has a wider operation range and larger compensation capacity. Three kinds of common DRPCE have their advantages and disadvantages. In order to achieve comprehensive optimization, the most suitable type of dynamic reactive power compensation equipment should be selected according to the actual economic conditions while meeting the optimization objectives.
In this paper, the DRPCE is considered so as to maximize both the inhibitory effect and optimize economic performance. It is a typical multi-objective optimization problem.
The multi-objective optimization function F has two sub-objective functions, f1 and f2. Among them, f1 is the configuration cost function, and f2 uses the negative value of RMCCF to characterize the inhibitory effect of commutation failure; x is a control variable, representing the type of DRPCE and installation capacity; s is a 0–1 state variable; ci - x is the installation cost of the DRPCE, and the unit price of the DRPCE is pi - x. Qi - x is the reactive power compensation capacity.
Constraints
where:
, and
represent the conductance, admittance and phase difference between the branches
i-j, respectively.
,
,
,
,
,
,
and
are the lower and upper limits of active power, reactive power, voltage and reactive compensation capacity, respectively.
6. Example Analysis
Here we chose the East China Power Grid as an example to analyze and validate the DRPCE optimal configuration scheme for inhibiting subsequent HVDC commutation failures on the simulation platform MATLAB-BPA. The example considers eight DC feeds, as shown in
Appendix B. This paper only considers the reactive power compensation at major sites (≥ 500 kV). The DRPCEs used here are SVCs and synchronous condensers. Each device considers four candidate compensation nodes. The installation costs of SVCs and synchronous condensers are set to 38,675 USD and 46,410 USD, respectively. The reactive power compensation unit prices are 46,410 USD/Mvar and 77,350 USD/Mvar respectively [
21,
22].
The MIADF values of all nodes are calculated and sorted, and the top 20 nodes (marked in red) are selected as candidate installation areas, as shown in
Figure 9.
DRPCE is installed at the red nodes in the area, and the nodes are selected and sorted according to the compensation response evaluation index
Ri of each node. The results are shown in
Table 2.
Subsequently, the improved PSO algorithm is used to optimize the type and capacity of dynamic reactive power compensation equipment. Combined with this engineering practice, the capacity of SVC is continuously adjustable, and the single capacity of the synchronous condenser is fixed at 300 Mvar. Through the improved PSO, a group of optimal configuration non-inferior solutions on the Pareto front are obtained, which consider both the economic performance and the inhibitory effect of subsequent commutation failure, as shown in
Figure 10.
It can be seen from the figure that the inhibitory effect of DRPCE on subsequent commutation failure is positively related to the capacity configuration cost, which indicates that increasing the configuration capacity of DRPCE can effectively improve the inhibitory effect. However, the disadvantage is that it will greatly increase the cost. By observing the changing trend of the curve, it can be seen that the inhibitory effect of DC commutation failure and the increase in cost do not have a simple linear relationship, but a saturation. When the capacity is allocated to a certain extent, the improvement of the inhibitory effect on the subsequent commutation failure of DC is not obvious. At this time, increasing the allocated capacity will only bring a serious economic burden. Therefore, it is necessary to comprehensively evaluate the economic indicators and commutation failure inhibitory effect to select the most reasonable configuration scheme. The configuration scheme and evaluation are shown in
Table 3 and
Table 4, respectively.
According to the analysis in
Table 3 and
Table 4, the configuration capacity of the synchronous condenser is always higher than that of SVC in the configuration scheme optimized by PSO, proving the conclusion that the reactive power compensation effect of the synchronous condenser is better than that of SVC. However, if we want to pursue economic benefits, we should prioritize the installation of SVC.
As shown in
Table 4, the configuration cost of scheme six, which only installed SVC of 175 Mvar in the SJ node and does not install synchronous condensers, is the lowest. Although this configuration scheme achieves the optimal economic performance, the inhibitory effect on subsequent commutation failure is poor. Therefore, it is necessary to comprehensively consider the economic performance and the inhibitory effect of DC commutation failure. The results of AHP-TOPSIS are listed in
Table 4. Schemes one, two, three and four achieve good evaluation results. Scheme 3, with the highest score, is selected as the final configuration scheme. The configuration condition of Scheme 3 is shown in
Figure 11.
From the installation position, capacity and type of DRPCE, it can be seen that synchronous condensers with a large capacity are always installed in the DC infeed converter stations. Synchronous condensers installed in converter stations can quickly provide a lot of reactive power support in case of faults, maintain the voltage level of the converter bus and inhibit the risk of subsequent converter failure of an MIDC. SVC installed in some non-converter stations can reduce the indirect impact of a voltage drop in the non-converter buses on MIDC commutation failure. It not only ensures the inhibitory effect of subsequent commutation failure, but also takes the economic performance of the whole scheme into account.
Taking NQ station as an example, a three-phase short circuit fault at the midpoint of a 500 kV line is set at 0.1 s, and the fault is removed after 0.1 s. PSD-BPA is used to observe the voltage and DC power changes before and after the dynamic reactive power compensation equipment is installed in NQ station. The results are shown in
Figure 12.
From the curve comparison in the figures, it can be seen that without DRPCE, the sudden drop of voltage and DC power causes the failure of DC commutation in the NQ converter station. After the first commutation failure, the fault remains for 0.1 s, resulting in the subsequent commutation failures of the converter station, the voltage and DC power secondary drop and then oscillation, seriously threatening the system security. After the DRPCE is configured, it can support the voltage and power drop caused by the fault, stabilize the voltage fluctuation, maintain stable transmission power and effectively inhibit the risk of subsequent commutation failure.
To further verify the rationality of the proposed method, an N-1 scan of 500 kV and above lines under three-phase short circuit fault is carried out, and the average number of commutation failures is counted. The smaller the average number of commutation failures, the stronger the ability to resist the failure—that is to say, the better the inhibitory effect of subsequent commutation failure of DC after the configuration of DRPCE. The statistical results are shown in
Table 5.
It can be seen from
Table 5 that the installation of DRPCE can significantly improve the ability of the system to inhibit the subsequent commutation failure of DC. Compared with the scheme proposed in [
12], the joint configuration of SVC and synchronous condenser has a better effect. The average times of commutation failure are less, which verifies the rationality and effectiveness of the proposed method.