Abstract
With the exacerbation of environmental issues and the ongoing energy crisis, the large-scale integration of renewable energy resources has significantly increased the demand for flexibility in distribution systems. Establishing a comprehensive flexibility evaluation index system is crucial for the development, promotion, and optimization of AC/DC distribution systems. This paper focuses on the flexibility evaluation of AC/DC distribution systems, proposing a detailed flexibility evaluation index system and a comprehensive evaluation method based on the ANP-Entropy weighting model. The proposed flexibility evaluation index system comprises 18 key indexes categorized into four essential dimensions: overall flexibility performance, flexible resources participation, operational performance, and economic performance. The ANP-Entropy weighting model is employed to perform a thorough evaluation of the flexibility of AC/DC distribution systems. To validate the effectiveness of the proposed evaluation method, a case study is conducted. Additionally, the study explores the impacts of controllable distributed generator (CDG) capacity, energy storage system (ESS) capacity, and voltage source converter (VSC) capacity on the flexibility of AC/DC distribution systems. The results provide valuable insights into optimizing the flexibility and performance of AC/DC distribution systems.
1 Introduction
To address the pressing concerns of the energy crisis and environmental degradation, the integration of large-scale renewable energy resources and electric vehicles into the distribution system has become imperative (). However, the inherent volatility and uncertainty associated with these resources have resulted in an increased demand for flexibility in the distribution system (; ). In this regard, the AC/DC hybrid distribution system is recognized as a pivotal development trend for future distribution systems (). To mitigate the negative impact of uncertainty from both the source and the load sides, it is essential for the AC/DC distribution system to enhance system flexibility through the comprehensively deployment of diverse flexible resources, including controllable distributed generator (CDG) (), energy storage systems (ESSs) (), demand resource (), electric vehicle (EV) (), microgrids (), voltage source converter (VSC) (), and more. Consequently, the evaluation of flexibility in AC/DC distribution systems and the quantitatively analysis of the improvement effects brought about by different dispatching schemes are critical considerations in the operation, planning, and design of such systems ().
Flexibility plays a crucial role in assessing the operational adaptability of distribution systems. Extensive research, both domestically and internationally, has been conducted to evaluate and quantify system flexibility. In , the concept of a “flexibility envelope” was introduced to analyze and assess the potential flexibility of power system. Additionally presented capacity, power, ramp rate, and duration as key parameters for evaluating power system flexibility. Furthermore proposed a comprehensive flexibility evaluation framework, encompassing evaluation time, scheduling measures, uncertainty, and operating costs as key aspects. Moreover introduced a robust optimization method to quantify the intra-hour flexibility region of a power system, offering valuable insights for evaluating power system flexibility.
In the realm of flexibility evaluation indexes, significant contributions have been made to assess the flexibility of power systems. Notably, the insufficient ramping resource expectation (IRRE) and periods of flexibility deficit (PFD) were proposed in , , respectively, as metrics to evaluate power system flexibility. In addition defined the lack of ramp probability (LORP) to guide the economic dispatching of the power grid. Furthermore developed the loss of flexibility probability (LOFP), loss of flexibility duration (LOFD), loss of flexibility expectation (LOFE), and flexibility demand short (FDS) to inform the planning and design of power grids. These indexes mentioned above are capable of reflecting the probability of flexibility shortage. However, they do not provide information regarding power curtailment. Therefore introduced two new measures, namely, Flexibility supply adequacy (FSA) and network transmission margin (NTM), to assess the system’s flexibility.
Based on the analysis above, it is evident that the majority of existing flexibility evaluation indexes adequately reflect the overall flexibility of a power system. However, they do not provide specific important regarding the caused of flexibility shortage, the extent of the contribution and participation of flexible resources, the performance of power system, and the economic benefit of flexible dispatching. To address these limitations, it is essential to establish a comprehensive flexibility evaluation index system. Such a system would assist grid operators in assessing the flexibility of AC/DC distribution systems from multiple perspectives. Moreover, it would guide the allocation of flexible resources and formulation of more effective, dispatching strategies that maximize system flexibility and economic benefits.
To address the aforementioned objectives, this paper focuses on evaluating the flexibility of AC/DC distribution systems and presents the following key contributions:
1. A comprehensive flexibility evaluation index system has been developed specifically for AC/DC distribution systems. This index system is constructed from four perspectives, namely, overall flexibility performance, flexible resource participation, operational performance, and economic performance.
2. A comprehensive evaluation method for assessing the flexibility of AC/DC distribution systems has been implemented, utilizing the ANP-Entropy weighting model. This method ensures that the evaluation results align with both practical experience and objective data.
The subsequent sections of the paper are structured as follows: In Section 2, the flexibility evaluation index system is presented. Section 3 proposes an evaluation method for assessing the flexibility of AC/DC distribution systems. In Section 4, a case study is presented along with the corresponding evaluation results. Finally, Section 5 gives the conclusions of this paper.
2 Flexibility evaluation index system of AC/DC distribution systems
The flexibility evaluation index system should not only reflect the overall flexibility of AC/DC distribution systems but also provide multidimensional information for grid operators. This information includes identifying reasons for flexibility shortage, assessing the participation and contribution of different flexible resources, evaluating system operational performance, and determining the economic benefits of flexible dispatching. Equipped with this information, grid operators can easily select optimal regulation strategies, develop more flexible dispatching schemes, and allocate different flexible resources effectively. Consequently, the flexibility evaluation index system for AC/DC distribution systems is constructed based on four aspects: overall flexibility performance, flexible resource participation, operational performance, and economic performance. The proposed evaluation index system encompasses a total of 18 indexes, as illustrated in Figure 1.
FIGURE 1
2.1 Overall flexibility performance indexes
The overall flexibility performance provides a comprehensively reflection of the AC/DC distribution systems’ ability to handle fluctuations arising from renewable energy resources and loads. This evaluation is primarily based on six key aspects: flexibility adequacy rate, flexibility supply adequacy rate, PV/WT abandonment rate, load shedding rate, average flexibility supply adequacy, and average network transmission margin.
1) Flexibility adequacy rate: The flexibility adequacy rate is a measure that reflects the overall flexibility of AC/DC distribution systems from a probabilistic standpoint. It is defined as the ratio of the total time when the system’s flexibility is deemed sufficient to the entire scheduling period T, which can be calculated by Eq. 1:
The larger the value
is, the more flexible the system is.
2) Flexibility supply adequacy rate: The flexibility supply adequacy rate reflects the degree of system flexibility supply from a probability perspective. It is defined as the proportion of the total time when system flexibility supply is sufficient to the entire scheduling period, which can be given by Eq. 2:
The higher the value
is, the more adequate the system flexibility supply is.
3) PV/WT abandonment rate: The PV/WT abandonment rate reflects the degree of downward flexibility insufficiency in AC/DC distribution systems. It is defined as the proportion of power abandonment of PV unit and WT to the overall power output of PV unit and WT, which can be given by Eq. 3:
Where,
and
are the power curtailment and total power output of the
ith WT at time
t, respectively.
and
are the power curtailment and total power output of the
ith PV unit at time
t, respectively.
The higher the value
is, the more insufficient the system downward flexibility is.
4) Load shedding rate: The load shedding rate demonstrates the degree of upward flexibility insufficiency in AC/DC distribution systems. It is defined as the proportion of power abandonment of load to the total system load, which can be calculated by Eq. 4:
where
and
are power abandonment of load i and the total system load at time t, respectively.
The higher the value
is, the more insufficient the system upward flexibility is.
5) Average flexibility supply adequacy: The average flexibility supply adequacy reflects the average adequacy of system flexibility supply. It is the average value of the flexibility supply adequacy during the whole dispatching period, which can be calculated by Eqs 5–7:
where
,
,
and
are the maximum upward and downward flexibility supply, the maximum upward and downward flexibility requirement of AC/DC distribution systems at time
t, respectively.
is system net load at time
t.
The higher the value
is, the more sufficient the system flexibility supply is.
6) Average network transmission margin: The average network transmission margin reflects the average adequacy of network transfer. It is defined as the average value of network transmission margin during the whole dispatching period, which can be calculated by Eqs 8, 9:
where
,
and
are the maximum transmission margin of line
i, transformer
i, and VSC
i, respectively.
The higher the value is, the more adequate the network transfer is.
2.2 Flexible resources participation indexes
The dimension of flexible resource participation showcases the contributions made by various flexible resources in enhancing system flexibility throughout the entire dispatching period. This dimension encompasses five key indexes: CDG participation, ESS participation, controllable load participation, EV participation, and average net load fluctuation rate.
1) CDG participation: The CDG participation is defined as the proportion of the total power output of CDGs to the total capacity of CDGs during the entire dispatching period, which is given by Eq. 10:
where
is the power output of CDG
iat time
t, and
is the capacity of CDG
i.
The larger the value
is, the more power output of CDGs is, indicating that CDGs are more important in improving system flexibility.
2) ESS participation: The ESS participation is defined as the proportion of the total charging and discharging power of ESSs to the total capacity of ESSs throughout the entire dispatching period, which can be determined by Eq. 11:
where
and
are the charging power and discharging power of the
ith ESS at time
t, respectively.
is the capacity of ESS
i.
and
are the charging state and discharging state of ESS
iat time
t, respectively.
The larger the value
is, the more power output of ESSs are, reflecting ESSs are more important in improving system flexibility.
3) Controllable load participation: The controllable load participation is defined as the proportion of the total load being translated or interrupted to the total system load during the entire dispatching period, which can be calculated by Eq. 12:
where
is the total power of controllable load
ibeing translated or interrupted at time
t.
The larger the value
is, the more important controllable loads in improving system flexibility is.
4) EV participation: The EV participation is defined as the ratio of the total power of EVs being shifted or discharged to the total charging power of EVs during the entire dispatching period, which can be determined by Eq. 13:
where
and
are the active power of the
ith EV in the
jth EV parking lot being shifted and discharged (
) at time
t, respectively.
is the total charging power of EVs in EV parking lot
jat time
t.
The larger the value
is, the more important EVs in improving system flexibility is.
5) Average net load fluctuation rate: The average net load fluctuation rate comprehensively reflects the contribution of ESSs, controllable loads and EVs in improving flexibility of AC/DC distribution systems, which can be calculated by Eq. 14:
The lower the value is, the smoother the fluctuation of system net load is, indicating that contributions of ESSs, controllable loads, and EVs in improving system flexibility are more higher.
2.3 Operational performance indexes
For AC/DC distribution systems, the operational performance is reflected in three indexes: voltage deviation margin, branch over-current margin, and branch balance rate.
1) Voltage deviation margin: The voltage deviation margin is the difference between the maximum allowable voltage deviation and the average voltage deviation, which can be determined by Eq. 15:
where
is the maximum allowable voltage deviation.
and
are voltage amplitude of bus
iat time
tand the rated voltage of bus
i, respectively.
The larger the value
is, the smaller the system voltage deviation is. When system operates near the rated voltage, the system has a good operation performance.
2) Branch over-current margin: The branch over-current margin is the average over-current margin of all branches in the AC/DC distribution system during the entire dispatching period, which can be given by Eq. 16:
where
and
are the actual current amplitude of branch
iat time
tand the rated current value of branch
i, respectively.
is the total number of branches in the AC/DC distribution systems.
The larger the value
is, the higher the over-current margin is, indicating that the AC/DC distribution system has better network transfer performance.
The smaller the value is, the branch current is more balance, indicating that the network transmission flexibility is better.
2.4 Economic performance indexes
Economic performance is an important aspect in the optimal dispatching of AC/DC distribution systems. It is reflected in four indexes, including electricity purchase rate, network loss cost rate, penalty cost rate, and total operation cost rate.
1) Power purchase rate: The power purchase rate is the proportion of the total cost of electricity purchased from higher-level grids to the total load cost during the entire dispatching period, which can be determined by Eq. 19:
where
is the active power purchased from outer grids at time
t.
is the unit price of electricity at time
t.
The larger the value
is, the more electricity is purchased from outer grids, reflecting that the power output of renewable energy resources is less consumed.
2) Network loss cost rate: The network loss cost rate is the ratio of network loss cost to the total load cost during the whole dispatching period, which can be calculated by Eq. 20:
where
is the power loss of sub-grid
iat time
t.
The larger the value
is, the higher the network loss cost is, indicating that the economic performance of AC/DC distribution systems is worse.
3) Penalty cost rate: The penalty cost rate is the ratio of the penalty cost of power abandonment from WT, PV unit, and load to the total load cost, which can be determined by Eq. 21:
where
,
and
are power abandonment of PV unit
i, WT
i, and load
iat time
t, respectively.
The larger the value
is, the higher the penalty cost is.
4) Total operation cost rate: The total operation cost rate is the ratio of the total operation cost to the total load cost during the whole dispatching period, which can be given by Eq. 22:
where
,
,
,
, and
are the total electricity purchase cost, network loss cost, operation cost, compensation cost, and penalty cost of AC/DC distribution systems, respectively. The calculation of
,
,
,
, and
can be referred to
.
The larger the value is, the worse the economic performance of the AC/DC distribution systems is.
3 Evaluation method on the flexibility of AC/DC distribution systems
3.1 ANP-entropy weighting method
3.1.1 ANP method
The analytic network progress (ANP) is a decision-making method that can be utilized for non-independent hierarchical structure (). The ANP method involves the following steps:
Step 1. Describe the decision-making problem and establish a hierarchal network structure.
Step 2. Construct a judgment matrix by comparing criteria. In the ANP, Assume there are m components represented by in the control layer, and n components represented by in the network layer. Each component Cj is composed of eij. Compare the elements in Ci based on their influence on eij and calculate the eigenvector [] using the eigenvalue method. If the consistency conditions are satisfied, the local weight vector matrices can be determined by Eq. 23:
Step 3. Construct a supermatrix. Comparing the internal and external relationships between the elements and other sets of elements. By comparing these relationships, we can obtain the weightless supermatrix W which is calculated by Eq. 24:
Step 4. Construct a weighted supermatrix. Compare the relative importance of Pi with Pj to obtain the normalized weight vector , then a weighted matrix can be calculated by Eq. 25:
Then the weighted supermatrix can be obtained by A multiplying W as in Eq. 26:
Step 5. Calculate the limit supermatrix to obtain the index weights.
Calculation results determined by (27) are the weights of each index.
3.1.2 Entropy method
The entropy weight method utilizes information entropy to calculate the entropy weight of each index. It is an objective weighting method that solely relies on data itself (). The steps to obtain index weights with the entropy weighting method are as in Eqs 28–35:
Step 1. Construct the flexibility evaluation index matrix R';
Step 2. Standardize evaluation index matrix to eliminate the influence of different criteria dimensions on the evaluation results. For the benefit attribute data:
For the cost attribute data:where and are the maximum value and minimum values of the jth criteria, respectively.
After that, a standardized evaluation matrix can be determined by:
Step 3. Normalize the standardized evaluation matrix:
Step 4. Determine the entropy ej for the jth criterion:where , satisfies and . Besides, when , .
Step 5. Calculate the divergence coefficient for the
jth criterion.
Step 6. Obtain the evaluation weight of the jth criteria according to:
3.1.3 Combination weighting method
The combination weighting method takes into account both subjective weights obtained through the ANP method and the objective weights determined by the entropy method. By combining these weights, it can effectively assess and objectively reflect the actual situation.
Assume that the subjective weights determined by the ANP method and the objective weights calculated by the entropy weight method are shown in Eqs 36, 37:where .
The final combined weights can be obtained by Eq. 38:where and satisfy and .
For the ith evaluation plan, the final evaluation result is determined by Eq. 39:
Evaluation results of each dispatching scheme are ranked according to the zi value. The larger the zi value is, the more flexible the distribution system is.
3.2 Flexibility evaluation process
The process of evaluating the flexibility of AC/DC distribution systems mainly incorporates dispatching scheme formulation, economic dispatching, flexibility indexes calculation, normalization of evaluation indexes, subjective weights, and objective weights calculation, et al. The steps to evaluate the flexibility of AC/DC distribution systems are given as follows:
Step 1. Input parameters of AC/DC distribution systems, including network topology, PV and WT power output, load demand forecasting, parameters of CDGs, ESSs, VSCs, et al.;
Step 2. Determine operation schemes of AC/DC distribution systems;
Step 3. Solve the economic dispatching model of the AC/DC distribution systems for each operation scheme. The objective function of optimal dispatching is given by Eq. 40:
Step 4. Calculate flexibility evaluation indexes based on optimal dispatching results for each operation scheme;
Step 5. Obtain the subjective weights with the ANP method and objective weights with the entropy weight method to get the combined weights of each index.
Step 6. Calculate the final evaluation results of each operation scheme and complete the flexibility assessment of the AC/DC distribution systems.
The flexibility evaluation process of the AC/DC distribution systems is shown in Figure 2.
FIGURE 2
4 Case study
4.1 Basic data
In order to validate the effectiveness of the proposed flexibility evaluation method, a 47-bus AC/DC distribution system as described in is utilized. The topology of this hybrid AC/DC distribution system is illustrated in Figure 3. For detailed information regarding the system parameters, please refer to the source mentioned in .
FIGURE 3
In this system, there are three asynchronous AC sub-grids that are connected to the DC sub-grid via four VSCs. Additionally, the system comprises eight WTs, seven PV units, and five EV parking lots. The specific locations of these components are as follows:
1. Wind Turbines (WTs): The WTs are situated at buses 9, 14, 15, 22, 32, 35, 45, and 46.
2. Photovoltaic (PV) Units: There are seven PV units connected to buses 13, 16, 19, 33, 34, 42, and 47.
3. Electric Vehicle (EV) Parking Lots: The five EV parking lots are connected to buses 5, 12, 20, 30, and 41.
Moreover, each PV unit is equipped with one ESS to enhance the flexibility and stability of the system.
4.2 Flexibility evaluation results of AC/DC distribution systems
In order to assess the effectiveness of the proposed evaluation method and investigate the impact of dispatching strategies on the flexibility of AC/DC distribution systems, the following five cases have been established:
Case 1:This case considers all flexible resources in the AC/DC distribution systems, including CDGs, ESSs, Controllable loads, EVs, and VSCs.
Case 2:This case considers flexible resources such as CDGs, ESSs, EVs, and VSCs.
Case 3:This case considers CDGs, ESSs, and flexible control of VSCs.
Case 4:This case considers ESS and flexible control of VSC in the AC/DC distribution systems.
Case 5:This case only considers the flexible control of VSC.The evaluation indexes of these five cases are calculated and presented in Tables 1–5. These tables provide insights into the overall flexibility performance, flexible resources participation, operational performance, and economic performance, respectively.From Tables 1–5, we can see that as less flexible resources are participated in dispatching, the flexibility adequacy rate , flexibility supply adequacy rate , and average flexibility supply adequacy decrease, whereas the PV/WT abandonment rate and load shedding rate increase. Moreover, the penalty cost and total operation cost increase. Among these five cases, system in Case 1 has the highest flexibility, and system in Case 5 has the lowest operation flexibility.Calculation results of flexibility evaluation indexes based on the combined weighting method are given in Table 5.The results presented in Table 5 indicate that the overall flexibility performance, flexible resource participation, operational performance, economic performance, and final score decrease gradually as fewer flexible resources participate in the dispatching process in cases 1–5. Among the five cases, Case 1, which comprehensively utilizes various flexible resources, demonstrates the highest overall flexibility performance, flexible resources participation, operational performance, economic performance, and the final score. This suggests that Case 1 exhibits the highest level of system flexibility.Conversely, Case 5, which only considers the optimization control of VSCs, shows the lowest overall flexibility performance, flexible resources participation, operational performance, economic performance, and the final score. These results indicate that Case 5 has the lowest system flexibility.When examining system operational performance, it is observed that the voltage deviation index and branch margin index in Case 2 are slightly higher compared to those in Case 3 and Case 4. Consequently, the system operational performance of Case 2 is lower than that of Case 3 and Case 4.Regarding economic performance, the network loss cost in Case 2 is relatively high, resulting in a lower score for economic performance compared to Case 3.The above analysis reveals that the flexibility evaluation results align with the optimal dispatching results, indicating that the proposed flexibility evaluation method accurately reflects the flexibility of AC/DC distribution systems.
TABLE 1
| Case 1 | 1 | 1 | 0 | 0 | 0.2514 | 0.3101 |
| Case 2 | 0.96 | 0.92 | 0.0040 | 0.0050 | 0.2166 | 0.2990 |
| Case 3 | 0.88 | 0.92 | 0.0071 | 0.0117 | 0.1932 | 0.2570 |
| Case 4 | 0.8 | 0.68 | 0.0057 | 0.0250 | 0.1688 | 0.2910 |
| Case 5 | 0.64 | 0.64 | 0.0177 | 0.0316 | 0.0498 | 0.2573 |
Values of overall flexibility performance indexes.
TABLE 2
| Case 1 | 1.1262 | 0.6964 | 0.3346 | 0.1655 | 0.1007 |
| Case 2 | 0.8686 | 0.5955 | 0 | 0.1940 | 0.1077 |
| Case 3 | 1.0247 | 0.7276 | 0 | 0 | 0.1070 |
| Case 4 | 0 | 0.6831 | 0 | 0 | 0.1098 |
| Case 5 | 0 | 0 | 0 | 0 | 0.1558 |
Values of flexible resource participation indexes.
TABLE 3
| Case 1 | 0.0242 | 0.1944 | 0.1881 |
| Case 2 | 0.0255 | 0.2029 | 0.1900 |
| Case 3 | 0.0244 | 0.1947 | 0.1889 |
| Case 4 | 0.0249 | 0.2002 | 0.1917 |
| Case 5 | 0.0253 | 0.2058 | 0.2000 |
Values of operational performance indexes.
TABLE 4
| Case 1 | 0.7459 | 0.0308 | 0 | 0.9005 |
| Case 2 | 0.7711 | 0.0363 | 0.0275 | 0.9377 |
| Case 3 | 0.7592 | 0.0325 | 0.0584 | 0.9498 |
| Case 4 | 0.8092 | 0.0356 | 0.0998 | 0.9663 |
| Case 5 | 0.8289 | 0.0390 | 0.1541 | 1.0204 |
Values of economic performance indexes.
TABLE 5
| Overall flexibility performance | Flexible resources participation | Operational performance | Economic performance | Final score | |
|---|---|---|---|---|---|
| Case 1 | 0.3800 | 0.1405 | 0.1279 | 0.1546 | 0.8030 |
| Case 2 | 0.3513 | 0.1277 | 0.1217 | 0.1226 | 0.7233 |
| Case 3 | 0.3099 | 0.1008 | 0.1271 | 0.1175 | 0.6554 |
| Case 4 | 0.2798 | 0.0505 | 0.1227 | 0.0926 | 0.5456 |
| Case 5 | 0.2163 | 0.0130 | 0.1157 | 0.0511 | 0.3961 |
Values of flexibility evaluation indexes.
4.3 Impact of flexible resource capacity on system flexibility
To analyze the impact of flexible resource capacity on system flexibility, studies are conducted by varying the capacity of CDG, ESS, and VSC on Case 1.
4.3.1 Impact of CDG capacity on system flexibility
By progressively increasing the capacity of CDG from 200 kW to 700 kW, the corresponding calculation results of system flexibility adequacy rate and load shedding rate are illustrated in Figures 4A, B, respectively. The outcomes presented in Figure 4 reveal a notable trend: as the CDG capacity increases, the load shedding rate decreases, indicating an improvement in system flexibility Moreover, the results clearly demonstrate that when the CDG capacity surpasses 500 kW, the system’s flexibility adequacy rate reaches 100%. Additionally, it is noteworthy that no power curtailment is observed for WT, PV units, and loads throughout the entire dispatching period.
FIGURE 4
The flexibility evaluation results of the AC/DC distribution systems under different CDG capacities are summarized in Table 6. The calculation results presented in Table 6 reveal a consistent pattern: as the CDG capacity increases, there is notable improvement in system flexibility, resulting in higher final evaluation scores. Notably, when the CDG capacity reaches 600 kW, the system achieves the highest level of flexibility, as evidenced by the highest final flexibility sore.
TABLE 6
| Capacity/kW | Overall flexibility performance | Flexible resources participation | Operational performance | Economic performance | Final score |
|---|---|---|---|---|---|
| 200 | 0.0694 | 0.1080 | 0.1215 | 0.1028 | 0.4018 |
| 300 | 0.2040 | 0.1103 | 0.1232 | 0.1218 | 0.5593 |
| 400 | 0.3373 | 0.1240 | 0.1256 | 0.1431 | 0.7300 |
| 500 | 0.3721 | 0.1368 | 0.1253 | 0.1555 | 0.7897 |
| 600 | 0.3789 | 0.1413 | 0.1275 | 0.1549 | 0.8026 |
| 700 | 0.3773 | 0.1367 | 0.1258 | 0.1562 | 0.7960 |
Values of flexibility evaluation indexes.
4.3.2 Impact of ESS capacity on system flexibility
By gradually increasing the ESS capacity from 500 kW to 1,200 kW, the calculation results of the system flexibility adequacy rate and load shedding rate are presented in Figures 5A, B, respectively. The test results depicted in Figure 5 demonstrates that as ESS capacity increases, the load shedding rate decreases and the system flexibility improves. Furthermore, when the ESS capacity exceeds 700 kW, the flexibility adequacy index reaches 100%. There is no power curtailment of WT, PV units, and loads throughout the entire dispatching period.
FIGURE 5
The flexibility evaluation results of the AC/DC distribution systems under different ESS capacities are listed in Table 7. Calculation results in Table 7 show that as the ESS capacity increases, system flexibility improves, and the final flexibility score increases too. When the ESS capacity reaches 1,200 kW, the final flexibility score is the highest.
TABLE 7
| Capacity/kW | Overall flexibility performance | Flexible resources participation | Operational performance | Economic performance | Final score |
|---|---|---|---|---|---|
| 500 | 0.2669 | 0.1373 | 0.1252 | 0.1353 | 0.6647 |
| 600 | 0.3219 | 0.1302 | 0.1262 | 0.1482 | 0.7266 |
| 700 | 0.3712 | 0.1321 | 0.1248 | 0.1499 | 0.7780 |
| 800 | 0.3721 | 0.13688 | 0.1253 | 0.1555 | 0.7897 |
| 900 | 0.3776 | 0.1397 | 0.1270 | 0.1553 | 0.7995 |
| 1,000 | 0.3761 | 0.1382 | 0.1258 | 0.1548 | 0.7949 |
| 1,200 | 0.3756 | 0.1459 | 0.1244 | 0.1550 | 0.8009 |
Values of flexibility evaluation indexes.
4.3.3 Impact of VSC capacity on system flexibility
Gradually increasing VSC capacity from 0.8 MW to 2.5 MW, the system flexibility adequacy rate and load shedding rate are illustrated in Figures 6A, B, respectively. The results in Figure 6 show that increasing the VSC capacity can reduce the load shedding rate and improve system flexibility. When the VSC capacity exceeds 1.7WM, the AC/DC distribution system has sufficient flexibility and there is no power curtailment of WT, PV units, and loads throughout the entire dispatching period.
FIGURE 6
The flexibility evaluation results of the AC/DC distribution systems under different VSC capacities are listed in Table 8. Results in Table 8 show that as the VSC capacity increases, system flexibility is improved and the final evaluation score increases too. When VSC capacity reaches 1.8 MW, the final flexibility score is the highest.
TABLE 8
| Capacity/MW | Overall flexibility performance | Flexible resources participation | Operational performance | Economic performance | Final score |
|---|---|---|---|---|---|
| 1.5 | 0.3395 | 0.1267 | 0.1182 | 0.1469 | 0.7313 |
| 1.7 | 0.3766 | 0.1382 | 0.1252 | 0.1504 | 0.7905 |
| 1.8 | 0.3737 | 0.1453 | 0.1269 | 0.1564 | 0.8023 |
| 2.0 | 0.3721 | 0.1368 | 0.1253 | 0.1555 | 0.7897 |
| 2.2 | 0.3743 | 0.1337 | 0.1262 | 0.1515 | 0.7857 |
| 2.5 | 0.3724 | 0.1323 | 0.1256 | 0.1497 | 0.7799 |
| 1.5 | 0.3395 | 0.1267 | 0.1182 | 0.1469 | 0.7313 |
Values of flexibility evaluation indexes.
Based on the above research, it is evident that increasing the capacity of flexible resources enhances system flexibility. However, beyond a certain threshold, this flexibility reaches saturation. Further increases in the capacity of flexible resources lead to resource redundancy and elevated costs.
5 Conclusion
This paper addresses the crucial topic of flexibility evaluation in AC/DC distribution systems. It introduces a comprehensive flexibility evaluation index system that covers key aspects such as overall flexibility performance, flexible resource participation, operational performance, and economic performance. The index system enables grid operators to assess the sufficiency of system flexibility and gain valuable insights into the underlying factors affecting flexibility, including resource participation and contribution, system operation, and economic benefits derived from flexible dispatching.
To determine the weights of the evaluation indexes, the paper adopts the ANP-entropy weight method, which combines subjective judgments and objective simulation results. This approach ensures the reliability and accuracy of the weight coefficients assigned to each index, thereby enhancing the overall evaluation process.
To demonstrate the effectiveness of the proposed evaluation method, a 47-bus AC/DC distribution system is used as a case study. The results obtained from the evaluation method confirm its ability to accurately reflect the flexibility of AC/DC distribution systems. Furthermore, by analyzing the impact of varying flexible resource parameters on system flexibility, the study reveals that increasing the capacities of VSCs, CDGs, and ESSs can significantly improve system flexibility. This paper did not consider the flexibility resources on the distribution network side in the evaluation. The next work is to study how to integrate the comprehensive flexibility evaluation system into the AC/DC distribution network planning.
Statements
Data availability statement
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.
Author contributions
LW: Conceptualization, Methodology, Writing–review and editing. QZ: Conceptualization, Project administration, Supervision, Writing–review and editing. SW: Conceptualization, Formal Analysis, Funding acquisition, Project administration, Resources, Supervision, Writing–review and editing. XJ: Data curation, Methodology, Software, Visualization, Writing–original draft.
Funding
The authors declare that financial support was received for the research, authorship, and/or publication of this article. This work was supported by the State Grid Corporation of China Science and Technology Project (No. 5108-202299256A-1-0-ZB).
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
The authors declare that this study received funding from the State Grid Corporation of China. The funder had the following involvement in the study: data collection and article publication.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
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Summary
Keywords
AC/DC distribution systems, flexibility, evaluation index, ANP-entropy weighting model, sustainable energy
Citation
Wang L, Zhao Q, Wang S and Jiang X (2024) Enhancing flexibility evaluation in AC/DC distribution systems for sustainable energy integration. Front. Energy Res. 12:1423189. doi: 10.3389/fenrg.2024.1423189
Received
25 April 2024
Accepted
24 May 2024
Published
12 June 2024
Volume
12 - 2024
Edited by
Kaiqi Sun, Shandong University, China
Reviewed by
Yang Lei, Anhui University, China
Lv Chaoxian, China University of Mining and Technology, China
Updates
Copyright
© 2024 Wang, Zhao, Wang and Jiang.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Shouxiang Wang, wly1393524105@163.com
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