1. Introduction
With the progress of transmission technologies, the State Grid of China has been a large-scale AC/DC hybrid power grid [
1,
2]. In recent years, multiple types of flexible transmission system equipment have been put into operation in the State Grid of China, such as the unified power flow controller (UPFC) and the high-voltage direct current (HVDC) system based on a voltage source converter (VSC) [
3,
4]. With the operation of various power electronic devices, the operation characteristics of this AC/DC hybrid power grid are becoming more and more complex.
A large-scale AC/DC hybrid power grid usually has the following characteristics: a high proportion of DC power to total load, large installed capacity of generators, and deficiency of control means [
5]. These characteristics make a large-scale AC/DC hybrid power grid face some safety and stability problems [
6,
7]. In order to deal with these problems, a lot of technologies and devices can be used singly or in combination to form stability strengthening schemes. Considering the diversity of new technologies and the complexity of system operation characteristics, it is necessary to study the comprehensive stability strengthening schemes for AC/DC hybrid power grids, to help operators improve the power system stability on the premise of affordable economic investment.
At present, scholars have carried out a lot of research on AC/DC hybrid power grids, which mainly involves operation characteristics, simulation methods, control strategies, and stability evaluation methods. For example, the interaction between multiple VSC-HVDC systems and the receiving AC system under AC faults is studied in [
8]. Ref. [
9] presents an electromechanical–electromagnetic transient simulation system, in which the large AC/DC power grid is divided into small sub-networks. In [
10], a control scheme of LCC-VSCs interlinking converters is introduced, which can help the AC/DC network operate stably under various conditions. Ref. [
11] proposes an adaptive security risk assessment system for an electric power system, which is based on electricity regulation.
As for the evaluation methods and strengthening schemes for large-scale power grids, the existing research mainly focuses on certain equipment or one kind of stability problems. For example, some scholars proposed a method to calculate the AC short-circuit current near the converter station, considering the dynamic characteristics of the converter station [
12]. In [
13], the local load margin and some other indicators are applied to analyze the static voltage stability of power grids. Ref. [
14] introduces a new indicator, the hybrid multi-infeed effective short-circuit ratio (HMESCR), to evaluate the power stability of hybrid multi-infeed HVDC systems. In [
15], an analytical method based on multi-point linearization is applied to improve the accuracy of rotor angle stability analysis considering the influence of multi-terminal direct current (MTDC) systems. Ref. [
16] studies the rotor angle stability indicator from the perspective of time-domain simulation. Ref. [
17] discusses the rate of change of frequency (RoCoF) and its temporal and spatial aggregation. In [
18], a method for evaluating the inertia demand is presented, considering the constraints of RoCoF and the frequency nadir. In [
19], a method for evaluating the risk of commutation failure of the DC system after AC faults at the receiving end is proposed. However, an evaluation method considering only one single problem cannot measure a complex hybrid power grid in an all-around way. In addition, the existing research rarely takes the trade-off of technology and cost into account. Thus, how to comprehensively evaluate AC/DC hybrid power grids and their potential strengthening schemes integrating multi-dimensional technical evaluation and cost analysis needs to be further studied.
Obviously, the comprehensive evaluation of power systems can be regarded as a multi-criteria decision-making (MCDM) problem. In this regard, the research results obtained by mathematicians are worthy of reference. For example, the analytic hierarchy process (AHP) has been widely used to calculate subjective weights in MCDM problems since its birth [
20,
21,
22]. The best worst method (BWM) is another commonly used subjective weight calculation method, which requires less data and can produce reliable results [
23,
24]. In terms of objective weight calculation, the entropy weight method (EWM) [
25,
26], the technique for order preference by similarity to ideal solution (TOPSIS) [
27], and the critic method [
28] are some of the recognized methods. Actually, the work of this paper is based on BWM and EWM.
The contributions of this paper are summarized as follows:
An evaluation system including six indicators is established for AC/DC hybrid power grids, which covers various safety and stability issues.
For various safety and stability issues, measures that can be utilized to solve them are introduced.
A method for comprehensive evaluation of AC/DC hybrid power grids is proposed. Considering multiple dimensions to evaluate the safety and stability of the power system, this method can give technical scores for different schemes, and present curves reflecting the trade-off of the technical scores and the costs.
The remainder of this paper is organized as follows:
Section 2 introduces six evaluation indicators, which are the basis of the technical analysis of AC/DC hybrid power grids.
Section 3 summarizes some typical countermeasures for the problems faced by AC/DC hybrid power grids.
Section 4 introduces, in detail, the comprehensive evaluation method. Then, the case study of the Qujing Power Grid is implemented in
Section 5. Finally,
Section 6 concludes this paper.
2. Evaluation System and Indicators
The evaluation system proposed in this paper covers the evaluation of short-circuit current, voltage stability, power angle stability, frequency stability, thermal stability, and DC fault. Indicators used in the system are described below.
2.1. Short-Circuit Current Margin
Statistics show that the influence of the three-phase metallic short-circuit fault is the most serious. Thus, the short-circuit current margin,
Ksci, at bus
i can be defined as follows:
Here, Ibmaxi is the maximum allowable short-circuit current at bus i, which is usually the upper limit of the breaking capacity of the circuit breaker; Isci is the three-phase metallic short-circuit current at bus i. Obviously, the short-circuit current margin calculated according to (1) is a restrictive indicator. To ensure the safety of the power system, the short-circuit current margin of any bus should be positive. If Ksci < 0, it means that the short-circuit current at bus i exceeds the limit and the system has safety problems.
2.2. Local Load Margin
When analyzing the voltage stability of large-scale hybrid power grids, we usually focus on the impact of the load growth on bus voltage. Taking the power system shown in
Figure 1a as an example. When analyzing the local static voltage stability at bus
i, the original system can be simplified to an equivalent system using Thevenin’s theorem, with the power flow at bus
i remaining constant, as shown in
Figure 1b.
Then, some assumptions are made:
The system is large enough so that the equivalent voltage, U0, keeps unchanged during the load growth at bus i.
The power factor angle at bus i, φi, keeps unchanged.
The load at any other bus keeps unchanged, too.
Thus, the local load margin,
PLmgi, can be defined as (2):
Here, Pi is the active power of the load at bus i, and Pimax is the critical power value, at bus i, that make system unstable. Apparently, the local load margin, PLmgi, calculated by (2), is a restrictive indicator. To ensure the safety and stability of the power system, the local load margin should be greater than 0. The larger the margin is, the better the static voltage stability of the corresponding bus is. Based on engineering experience, the local load margin of every bus should be greater than 8% in normal conditions.
Based on the assumptions, we have [
29]:
Accordingly, the expression of
P-
U curve at bus
i,
Ui =
f (
Pi), can be obtained:
Here, A is an intermediate variable for ease of representation.
As shown in
Figure 2, the voltage and power at the rightmost end of the
P-
U curve at bus
i are named as
Ulmt1,i and
Plmt1,i.
Apparently, the active load,
Pi, is not allowed to exceed
Plmt1,i, otherwise voltage collapse will occur in the system. According to (5), the value of
Ulmt1,i can be obtained:
In addition, for the safety of the equipment, the operating voltage,
Ui, must be within a reasonable range. Actually, considering the trend of typical
P-
U curves, the lower limit of
Ui should be mainly concerned, which can be expressed as
Ulmt2,i. In real power systems,
Ulmt2,i is usually taken as 0.9. Then, the minimum allowed value of
Ui can be obtained as:
When Ui = Uimin, Pi in (5) will be the critical power value.
2.3. Critical Clear Time of Fault
The critical clear time of a fault, tcr, can be used to evaluate the large disturbance rotor angle stability of the system. For any fault in the system, if its duration exceeds its tcr, at least one generator will lose synchronization with the system, which means that rotor angle instability will occur. Considering the occurrence probability and the harm, the fault category analyzed in this paper is the three-phase metallic short-circuit fault at the end of a transmission line.
Take the two-area interconnected power system shown in
Figure 3 as an example. In this system, two lines constitute a transmission channel between bus
i and bus
j, and
PT is the active power transmitted through the channel. The rest of the power system is simplified, which is represented by two regional equivalent generators (G1/G2) and two equivalent transformers (T1/T2).
For the convenience of calculation, several assumptions are made:
For generators, the second-order model is used [
29]. In this model, the amplitude of the transient potential,
E′, remains unchanged for a short time after the fault.
The inertia time constants of the generators, TJG1/TJG2, are calculated using the base power of the system, while TJG2 is larger than TJG1.
The rotor angle of G2 is set as the reference angle.
For each line, the reactance is xLine, and its resistance is negligible compared with xLine.
For each transformer, the resistance is negligible.
As shown in
Figure 3, a three-phase metallic short-circuit fault occurs on Line2. According to the assumptions, it is easy to find that this fault has a greater impact on G1. In this case, the critical clear time of the fault can be estimated using the following formula (for details, see
Appendix A):
Here, the variables with subscript 0 are values before the fault; the variables with superscript * are per-unit values;
PG1 is the active power output by G1;
x with different subscripts is the reactances in the system, as shown in
Figure 3;
ωN is the rated electric angular velocity of the rotor;
δ1h is an intermediate variable for ease of derivation.
If the two areas in that system are also connected through a VSC-DC system, as shown in
Figure 4, the result will be different. On the one hand,
PT can be changed by adjusting the power transmitted by the DC system, so as to enlarge
tcr. On the other hand, the active power absorbed by VSC1 and VSC2 from the AC system can also be controlled after the fault, so as to change the “acceleration area” and “deceleration area” in the analysis of equal area criterion. In this way, the critical clear time of the fault can be estimated using the following formula (for details, see
Appendix A):
Here, the variables with subscript 0 are values before the fault; the variables with superscript * are per-unit values; ΔPVSC1* is the increase of the power absorbed by VSC1 from the AC system; δ1h’ and xΣ1* are intermediate variables.
For faults in other scenarios, tcr can be calculated similarly. Of course, in a complex power system, it is more convenient to get the value of tcr by time simulation.
Apparently, the critical clear time of a fault,
tcr, is a restrictive indicator. To ensure the safety and stability of the power system,
tcr should be strictly greater than the expected clear time for any fault, that is:
Here, tf is the expected clear time of the fault, that is, the sum of delay time and action time of the main protection mechanism. For three-phase metallic short-circuit faults, tf can be estimated as 0.1 s.
Since
tcr does not have a reasonable upper limit, it can also be expressed in the form of margin,
Ktime, as shown below:
Apparently, Ktime is a restrictive indicator, which should be strictly greater than zero.
2.4. Thermal Stability Margin
To limit the heating effect, there is a maximum allowable value of the apparent power that can be transmitted by a transmission line or a transformer. For line
i or transformer
i, this limit can be expressed as
Simax. Then, the thermal stability margin of line
i or transformer
i can be defined as
ξi [
29]:
Here, Si is the apparent power actually transmitted by line i or transformer i.
When the system operates in different conditions, Si will be different, resulting in a different value of ξi. Therefore, in order to avoid confusion, a unified method for calculating ξi is given in this paper.
Calculate Si successively in normal conditions and all the “single maintenance conditions”. Here, a “single maintenance condition” is a condition that there is only one transmission channel or one transformer in the system that is out of operation due to maintenance.
Substitute the maximum Si obtained in the previous step into (12) to calculate ξi.
If there are devices that can control the power flow in the system, the influence of them needs to be considered in the calculation of Si. Of course, when calculating the apparent power of different transformers or lines, it should be ensured that the influence of these power flow control devices stays consistent in the same operating condition.
Apparently, the thermal stability margin, ξi, calculated by (12), is a restrictive indicator. For the safety and stability of the power system, its value should be greater than a positive value given according to actual needs (usually 10%). The larger the value is, the better the thermal stability of the transmission channel or substation is.
2.5. Rate of Change of Frequency
To explain the definition of the rate of change of frequency, we can take a single generator with load as an example. For the generator, the rotor motion equation is [
29]:
Here, Pm* is the per unit value of the mechanical power; Pe* is the per unit value of the electromagnetic power; TJ is the inertia time constant calculated using the base power of the system; ω* is the per-unit value of the electric angular velocity.
In a steady state,
Pm* is equal to
Pe*. Thus, assuming that
Pm* keeps unchanged when a disturbance, Δ
Pe*, occurs, we have:
So, we can use the rate of change of frequency to evaluate the frequency stability of the system, which is defined as
μ [
17]:
Here, ΔPmax* is the maximum change of power that may occur when a single power supply or load is cut off after the fault, which is positive when a load is cut off and negative when a power supply is cut off. f and fN are the actual frequency and the rated frequency of the system, respectively. TJ is calculated after the cutting-off. In this way, μ can reflect the instantaneous rate of change of frequency at the moment of the cutting-off.
Considering the ability of some equipment to quickly control the active power, Equation (15) can be modified as:
Here, ΔPctrl* is the maximum change of active power that can be obtained immediately by the control of existing equipment, on the premise of safety and stability. More clearly, if ΔPctrl* is positive, it means that the control leads to the increase of power supplies or the decrease of load power. The rate of change of frequency, μ, is a restrictive indicator. For the safety and stability of the power system, it should be always within the specified range (usually the upper and lower limits are ±0.5 Hz/s). The closer it is to zero, the better the frequency stability of the system is.
2.6. Proportion of Buses Related to Commutation Failure
For an HVDC system based on a line commutated converter (LCC), the commutation failure is the most common fault of the inverter, which has a serious impact on the safety and stability of the receiving system.
If the three-phase metallic short-circuit fault of AC bus
i will cause the commutation failure of LCC-HVDC system
j, then bus
i can be named as a bus related to the commutation failure of the LCC-HVDC system
j. Thus, for LCC-HVDC system
j, the proportion of buses related to commutation failure of it,
Kfailj, can be defined as:
Here, nfailj is the number of buses related to commutation failure of DC system j, and Ntot is the total number of AC buses in the power grid.
Strictly speaking, in order to obtain the exact results of
nfailj and
Kfailj, it is necessary to perform fault analysis for all AC buses by time-domain simulation. However, when the accuracy requirement is not very high, a rough judgment can also be made according to the following formula [
14]:
Here, MIIFj,i is the multi-infeed interaction factor (MIIF) from bus i to the inverter station of DC system j; ΔUi is the voltage disturbance at bus i; and ΔUj is the corresponding AC bus voltage variation at the inverter station of DC system j.
If (18) is true, bus i can be roughly regarded as a bus related to commutation failure of DC system j. This is because the commutation failure usually occurs when the AC voltage at the inverter station suddenly drops below 0.85 p.u., and MIIF can be used to estimate the voltage variation at a bus due to the voltage disturbance at another bus.
The proportion of buses related to commutation failure of LCC-HVDC system j, Kfailj, is a comparative indicator; the larger it is, the higher the probability of commutation failure of LCC-HVDC system j is.
5. Case Study
To verify the comprehensive evaluation method proposed in this paper, a case study of the Qujing Power Grid, Yunnan Province, China, is implemented.
Yunnan Province is a province in Southwest China. Interconnected asynchronously with several other provincial power grids through HVDC systems, the Yunnan Power Grid is sending out a large amount of electricity power to other provinces. Meanwhile, due to the low level of local development, the internal transmission capacity of the Yunnan Power Grid is relatively weak. In this context, as one of the parts with the most concentrated load and export channels of the Yunnan Power Grid, the Qujing Power Grid may face some stability and security problems, which is worthy of analysis.
5.1. Current Situation of Qujing Power Grid
In flood season, part of the active power of Wudongde Hydropower Station needs to be fed into Longhai Substation and Baiyi Substation, as shown in
Figure 5. However, the load and the export channels are mainly concentrated in Qujing and nearby areas. As a result, a large amount of active power is transmitted on the transmission section (indicated by the red dotted line in
Figure 5), posing a threat to the power grid.
As shown in
Figure 6, there are electromagnetic ring networks in the Qujing Power Grid, composed of 500 kV lines, 220 kV lines, and several substations. Analysis shows that the electromagnetic ring networks are difficult to untie. However, if the situation remained, the Qujing Power Grid will have the problem of an insufficient thermal stability margin, which is common in regional power grids. The details of this problem are listed in
Table 2.
Other evaluation indicators are also applied, as shown in
Table 3,
Table 4,
Table 5 and
Table 6, and it should be noted that the original result of
Kfail is always zero since there is no inverter station in the Qujing Power Grid.
To sum up, it is necessary to apply a strengthening scheme to solve the problem of an insufficient thermal stability margin in the Qujing Power Grid.
5.2. Feasible Strengthening Schemes
Based on the local conditions, four feasible strengthening schemes are formulated.
5.2.1. Scheme 1–Scheme 3: Build New AC Lines
Building 500 kV AC lines is a measure considered in this case. According to the current and planning situation of the Qujing Power Grid, the following three feasible strengthening schemes are put forward, of which the conductor model can be selected from those types shown in
Table 7.
Scheme 1: Build 500 kV double circuit lines from Longhai to Duole, of which the length is 99 km, as shown in
Figure 7.
Scheme 2: Build 500 kV double circuit lines from Longhai to Xiping, of which the length is 82 km, as shown in
Figure 7.
Scheme 3: Build 500 kV double circuit lines from Longhai to Guishan, of which the length is 79 km, as shown in
Figure 7.
5.2.2. Scheme 4: Build a UPFC
As shown in
Figure 6, the lines that have problems of an insufficient thermal stability margin are connected in a series, while the problem of the 220 kV lines from Longhai to Jiaozishan is the most serious. Thus, we have proposed a scheme of building UPFC, which is a kind of equipment with a strong ability to control the power flow on the lines.
Scheme 4: Build a 220 kV UPFC, of which the series sides are installed on the two lines from Longhai to Jiaozishan, and the parallel side of it is connected to a Jiaozishan 220 kV Bus, as shown in
Figure 8. Based on the engineering experience, it is preliminarily determined that the capacity of the parallel end is 50 MVA, and the capacity range of each of the two series ends ranges from 50 MVA to 250 MVA. If built, the UPFC can directly control the power flow on the lines from Longhai to Jiaozishan, and then indirectly change the power flow on other problematic lines in
Table 2.
5.3. Calculation of the Weights of the Indicators
5.3.1. Subjective Weights
- (a)
The six evaluation indicators and the serial number of them are shown in
Table 1.
- (b)
According to the analysis of the current situation of the Qujing Power Grid, the thermal stability margin is selected as the best indicator, and the proportion of the bus related to commutation failure is selected as the worst indicator.
- (c)
By comparison, the resulting best-to-others vector and the resulting other-to-worst vector can be obtained:
- (d)
Then, the subjective weights of the indicators can be calculated using (23).
5.3.2. Objective Weights
The normalized values of the six evaluation indicators used to calculate the objective weights are shown in
Table 8. Then, the objective weights are calculated using (25).
5.3.3. Combined Weights
The combined weights are calculated using (27). The results are shown in
Table 9.
5.4. Comprehensive Evaluation of the Schemes
5.4.1. Evaluation of Scheme 1, Scheme 2, and Scheme 3
The estimated costs of Scheme 1, Scheme 2, and Scheme 3 are mainly related to the sectional area of the conductors. Meanwhile, based on the combined weights and the values of six indicators, the technical scores of the three schemes when selecting different conductors can be calculated. These results are all shown in
Table 10. Accordingly, the technology-cost curves of these schemes are drawn, as shown in
Figure 9.
Due to the consideration of practice, only a limited number of conductor choices are considered in these three schemes. Therefore, only a limited number of points on each curve in
Figure 9 correspond to the actual calculation results, while the whole dotted lines can only roughly fit the trends. Apparently, Scheme 2 is the best of the three schemes.
5.4.2. Comparison of Scheme 2 and Scheme 4
For Scheme 4, the estimated cost and the technical score are calculated repeatedly with the change of the series capacity of the UPFC, when the interval is 25 MVA. The results are shown in
Table 11. After that, the technology-cost curve of Scheme 4 is drawn, as shown in
Figure 10.
According to
Figure 10, it is obvious that the performance of Scheme 2 is better than that of Scheme 4. To sum up, for the strengthening of the Qujing Power Grid, Scheme 2 is the best of the schemes formulated in this paper. Moreover, considering the trend of the curve, the second type of conductor in
Table 7 is recommended for Scheme 2, which will bring a total cost of RMB 283 million.