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Abstract
The region-based method has been applied in transmission systems and traditional passive distribution systems without power sources. This paper proposes the model of total quadrant security region (TQSR) for active distribution networks (ADN) with high penetration of distributed generation (DG). Firstly, TQSR is defined as a closed set of all the N-1 secure operation points in the state space of ADN. Then, the TQSR is modeled considering the constraints of state space, normal operation and N-1 security criterion. Then, the characteristics of TQSR are observed and analyzed on the test systems with different DG penetrations. TQSR can be located in any quadrant of the state space. For different DG penetrations, the shape and security features of TQSR are also different. Finally, the region map is discovered, which summarizes the features of different types of distribution networks.
THE future distribution network, especially in the urban area, will develop as an active system, which is able to dynamically select economic and reliable operation mode according to the consecutive changes caused by external environment such as load fluctuations, intermittent distributed generation (DG) and demand response (DR) [
The most basic scientific problems for investigating a system include describing the maximum range of the system and determining the related maximum output. The research on transmission networks is mature. However, the security problem is not applicable to distribution networks. In a distribution network and under any single contingency, reliable power supplies should be maintained for the areas without a fault within operation limits. For ADN with DGs, the security and efficiency of distribution networks become more complicated. At present, with the help of advanced secondary equipment of ADN, real-time monitoring and security assessment for ADN can be realized. However, the existing security assessment is based on case-by-case simulation approach [
Distribution system security region (DSSR) is a new approach for the security analysis and assessment of distribution systems. DSSR is defined as a closed set of all the N-1 secure operation points [
The existing researches on DSSR are all related to traditional distribution systems, including the definition [
The contributions of this paper are as follows. It proposes the concept and model of TQSR for ADN. 2D projections of TQSR are observed in 2 scenarios with DG penetration. The characteristics of TQSR are summarized.
The rest of the papers is organized as follows. The studied scenarios are introduced in Section II. The TQSR model is formulated in Section III. Section IV presents the case study. And the region map is discovered in Section V. Finally, Section VI draws the conclusion.
For distribution systems, the region theory is mainly used in urban areas, where the ADN will be firstly developed. On one hand, the security-related problems in the urban distribution networks are usually more complicated than those in rural areas due to flexible switch operations [
The DG penetration will affect the security feature of the distribution systems. Two kinds of DG penetrations are usually used, which are capacity penetration (CP) and power penetration (PP). CP is used to define the percentage of annual maximum hourly distributed generation and maximum hourly consumption of the system. And PP is used to define the percentage of the power provided by distributed generators and the power consumption of the system at a specific moment [
According to different CPs, two typical scenarios for future ADN are studied in this paper, which are the high penetration supply network (HPSN) and very high penetration balanced network (VHPBN), respectively [
According to the concepts of HPSN and VHPBN as well as the effective planning schemes based on the definition in [
Some assumptions are made in this paper according to the aforementioned features of the scenarios.
1) The approach of DC power flow [
Firstly, the bus voltage profile is considered to be qualified. Both the system and the DGs are all able to regulate the bus voltage because the reactive power compensation equipment is sufficient and the voltage can be well controlled in the urban distribution networks. Even if the voltage profile has to be monitored, TQSR can be easily updated with the security voltage region (SVR) proposed in [
Secondly, the network loss can be included in the power flow of the feeder outlets [
Finally, it is shown in [
2) Three-phase imbalance is neglected [
3) The contingencies of DG are not considered.
The TQSR model is compactly formulated as:
| (1) |
where is the TQSR; is the n-dimension operation point, which is defined as the minimum set of the state variables that can determine the security state of ADN; is the state space, which is defined as the set of all the possible operation points; is the constraint of state space; is the capacity constraint of branches and substation under normal operation state; and is the N-1 security constraint. The state variables include the following:
1) Power flow data: the voltage amplitude and the angle of each bus, and the power and network loss of all the branches.
2) Operation data: the switch state and the tap position of transformers and capacitors.
Si is the total apparent power of bus i. Considering that one bus is connected to only one object (load or DG), Si can be expressed as:
| (2) |
where and are the apparent power of the load and DG on the bus i, respectively; L is the load set; and G is the DG set. The direction is positive when the power flows out of bus i (). Thus, and .
For some large-scale networks, the dimension of the operation point can be reduced by merging some buses [
TQSR is defined as a closed set of all the N-1 secure operation points in the state space of ADN. The physical meaning of TQSR is that all the operation status are secure within TQSR. And the status on the boundary is secure, while the status out of the region is insecure.
represents that the power of each bus should be kept in a reasonable range. For example, the load cannot exceed its capacity of distribution transformer and the DG output cannot exceed its generation capacity. is formulated as:
| (3) |
where and are the maximum and minimum apparent power of load i, respectively, and the default value of is 0; and is the capacity of DG i.
is formulated as:
| (4) |
where is the power of branch i and is the set of its downstream buses, and the term of downstream means the direction from a substation transformer towards its feeder terminal [
The absolute value symbol in (4) is necessary for the constraints formulated for bidirectional power flow.
If a distribution system is N-1 secure, it means that the load supply and DG absorption in the non-fault areas will not be interrupted without any overloading or off-limit voltages after any single contingency [
The contingency set is defined as the set of all the contingencies that the operator concerns. The contingency set of LSN contains only two kinds of serious contingencies, which are substation transformer contingency and feeder outlet contingency [
However, the premise of LSN is invalid when the bidirectional power flow is considered in ADN because the current could be large in the middle section of a feeder but very small in the feeder outlet. The contingency set in this case should include the failures of all the branches instead of the feeder outlets.
When a fault occurs at a substation transformer, the load of the faulty transformer will be transferred to adjacent transformers in the same substation with bus-tie switches. If the adjacent transformers are still overloading, some loads will be transferred to other substations by tie-switch operations among feeders.
When a fault occurs at a feeder branch, the breaker at the feeder outlet will be open. Then, the non-fault area on the same feeders has to go through a short outage. After the fault is isolated, the faulty feeder and connected feeders will be reconfigured to restore the service of the non-fault area as much as possible within the security constraints. There are usually more than one feasible restoration schemes [
The DG dispatch strategies after system contingencies will affect the security of ADN.
The main dispatch strategies of DG include 3 types: grid-connected DG, grid-disconnected DG and island DG [
The grid-connected DG is connected to the system after the system contingency. Thus, it can improve security because it enlarges the feeder capacity equivalently [
The grid-disconnected DG will be disconnected from the network when the fault occurs, then it could enlarge the outage area, which is negative for security. This type of DG can be regarded as the zero-output grid-connected DG after the contingency.
IEEE 1547 standard encourages the power utility and consumers to realize the islanded DG with advanced technologies. For multiple contingencies such as contingencies, some loads cannot be restored by the feeder power source with feeder switch operations. In this circumstance, the islanded DG is of great significance to improve the system reliability.
However, since only single contingency is considered in TQSR for the urban distribution networks with sufficient feeder links, a DG can always find a feeder as the power source after the system contingency by proper reconfiguration. Thus, the islanded DG is not adopted because the security is already guaranteed by system actions.
The security constraints are formulated as:
| (5) |
where is the contingency set; is the contingency k, which represents a single contingency of a branch or a substation transformer; and are the power of branch i and transformer i after contingency k, respectively; and are the sets of downstream buses of the branch i and transformer i after contingency k, respectively; and and denote that the calculations of the power flow of the faulty component are not needed.
After contingency k, the network will be reconfigured to restore the service of the non-fault area. The power flow of the branches and transformers could be changed.
In LSN, the constraints of the feeder outlet branch are modeled only because the feeder outlet always burdens larger currents than any other downstream sections. However, when the bidirectional power flow is considered in ADN, the constraints of each branch of DS must be modeled because it is uncertain which branch has the largest current.
The proposed TQSR model and traditional DSSR model [
Since the traditional DSSR only considers the loads only and the bus power is always a positive number, the state space is located in the quadrant I. However, the state space of ADN can cover all the quadrants because the bus power can be either positive or negative with the DG.
In the traditional DSSR model, the constraints in normal operation state are usually neglected because the constraints on an operation point are stronger under contingency than those in normal operation state. However, the constraints of TQSR model in normal operation state could be stronger than security and thus it must be formulated.
The contingency set of DSSR model contains only substation transformer contingency and feeder outlet contingency. However, the contingency set of TQSR model must include the contingencies of all the branches.
For TQSR model with bidirectional power flow, the constraints of each branch must be modeled and the absolute value symbols of the inequalities are necessary. For a traditional DSSR model with radial power flow, the constraints of the feeder outlet branch are modeled and the absolute value symbols are not needed.
The characteristics of TQSR are observed on a small 4- bus test system in 2 different scenarios including HPSN and VHPBN. In the case studies, the boundary equation is first calculated according to TQSR model (1)-(4). Then, it is projected onto the 2D subspace [
In this scenario, the security region of LSN and power collection distribution network (PCN) will be used as a comparison. The main function of PCN is to collect and deliver the generation of DGs to the upper-level transmission system [
The 4-bus test system of ADN is used, as is shown in
Fig. 1 4-bus test system of ADN.
The summit load of the ADN is 2 MVA. Thus, CP is 40%. It should be noted that each bus can be regarded as the sum of multiple DGs and loads. The security region characteristics can be clearly presented by a small case.
Considering the capacity constraints of the main transformer and the branch, the security boundary equations should be written and then simplified. The original equations of case grids are shown in Table SI of Supplementary Material A.
The physical meaning of all the security boundary equations is that the total actual power of the load and DGs carried by the branch shall be equal to the branch capacity.
According to the basic data of the grids for case study shown in
In
After observing the TQSR projections on 2D subspace, it can be concluded that TQSR can be located in any quadrant of the state space. The complete observation results are shown in Fig. S3-Fig. S15 of Supplementary Material A. The examples of quadrant IV are shown in
Fig. 2 Boundary figures using different power flow models. (a) DC power flow based model. (b) AC power flow based model.
In
In Figs. S16-S20 of Supplement Material A, the region for LSN is located in quadrant I [
According to the observation results of TQSR, the shape features of TQSR 2D projections can be included.
In general, 13 shapes can be observed in the 4-bus test system of HPSN according to the Figs. S3-S15 of Supplementary Material A. 2 shapes are the same as those of LSN and 11 shapes are newly added. Here, the same region figure in different quadrants will be counted as different shapes.
The 11 new shapes of TQSR can also be pentagon, ladder, rectangle or triangle, which is similar to those of traditional DSSR. The pentagon projection is shown in
However, the 11 new shapes of TQSR projections essentially differ from the traditional DSSR. They are not in quadrant I. Further, let be the angle between the inclined boundary and the coordinate axis towards the region, For the traditional DSSR, is always an acute angle (approximately 45), and it could be an obtuse angle (approximately 135) for TQSR.
Taking the pentagon in quadrant IV as an example, the comparison of traditional DSSR and TQSR as well as the angles between the inclined boundary and the coordinate axis is shown in
Fig. 3 Comparison of traditional DSSR and TQSR. (a) Triangle of traditional DSSR. (b) Pentagon of TQSR.
This shape feature will lead to the difference of security feature between DSSR and TQSR, which will be illustrated in the following subsection.
For the traditional DSSR, the most secure operation point is the original point (0, 0) [
Fig. 4 Most secure operation point of TQSR of HPSN.
In
Although the most secure point is changed, the general security principle of TQSR is the same as the traditional DSSR. In the traditional DSSR, the security degree decreases with the increasing load, which is called the monotone decreasing of the security [
Fig. 5 Cut-set of DG and load.
In
Note that the increase of |SG1|-SL2, which is the reverse power flow, is always less than the capacity of B3. Thus, for HPSN with 40% CP, it is always secure with the reverse power flow.
TQSR of VHPBN is studied in this subsection and compared with TQSR of HPSN. The network topology of the 4-bus test system for VHPBN is the same as that of HPSN, except that the capacity of each DG is increased to 1.5 MVA. The summit load is 3 MVA, and CP is 100%.
The boundary equations of VHPBN and HPSN are compared in
In
The complete results of TQSR of VHPBN are shown in Fig. S1-S10 of Supplementary Material B.
Firstly, the quadrant feature of VHPBN is the same as that of HPSN. TQSR of VHPBN can be located in any quadrant of the state space.
Secondly, as to the shape feature, 24 shapes can be observed in the 4-bus test system of VHPBN. 12 shapes are the same as those of HPSN and another 12 shapes are newly added. Here, the same region figure in different quadrants will be counted as different shapes.
12 TQSR shapes of VHPBN are the same as those of HPSN, which can be pentagon, rectangle and triangle in different quadrants. The shapes in quadrant IV are shown in Figs. S1-S3 of Supplementary Material B.
In these shapes, only the positive N-1 boundary exists because the level of the frozen loads is high and the frozen DG output is low. Thus, the branch overloading caused by the positive power flow occurs much more easily than that caused by the reverse power flow. Thus, the same shape region can be obtained.
12 TQSR shapes of VHPBN are different from those of HPSN, which can be divided into two types as follows.
Type 1: reverse shapes. There are 8 shapes in this type, which is similar to HPSN. The projections can also be pentagon and rectangle, as is shown in Figs. S4 and S5 of Supplementary Material B. However, the orientation of the projections is different from HPSN. The pentagon projections in quadrant IV of HPSN and VHPBN are compared in
Fig. 6 Comparison of positive pentagon of HPSN and reverse pentagon of VHPBN. (a) Positive pentagon of HPSN. (b) Reverse pentagon of VHPBN.
In
Type 2: shapes with double incline boundaries. 4 shapes of this type can be obtained. It is quite different from HPSN. The projections can be hexagon and new-type ladder. The hexagon projection in quadrant IV is shown in
Fig. 7 Hexagon projection of TQSR on 2D subspace in quadrant IV of VHPBN.
In
The security feature of VHPBN is different from that of HPSN.
1) The monotone decrease of the security holds for HPSN, which does not hold for VHPBN. For example, if VHPBN operates with the reverse power flow, the increase of bus power will reduce the reverse power flow and enlarge the security margin to the reverse boundary.
2) The most secure point for HPSN is corresponding to the maximum output of DGs and the zero loads, which should be original for VHPBN. It means that the load is zero or the DG output is zero. However, the requirement of original point is over-specific. If the operation point makes the cut-set power be zero, the point is also the most secure one. This is because the capacity of the branch adjacent to DGs is usually designed to be large enough to deliver the power generated by DGs. Thus, DG and its adjacent load can be regarded as a cut-set. For example, in
The security feature of TQSR for HPSN is based on an important premise. The total capacity of DGs on a feeder cannot exceed the feeder capacity (40% CP is consistent with the premise). However, in VHPBN, the capacity of total DGs with 100% CP could be larger than the feeder capacity and the security features will be different. The branch overloading could be caused by both positive and reverse power flows.
A modified IEEE RBTS test system [
Fig. 8 A modified IEEE RBTS test system with DGs.
The conclusion of the practical case is the same as the 4-bus test system. Due to the page limit, the complete results are shown in Supplementary Material C.
The region map is discovered based on the summary of the region characteristics of LSN, HPSN and VHPBN for the three grids with different DG penetrations, as shown in Fig. 9. Each symbol is marked with an ID below. In the ID, the first number means the quadrant. The alphabet represents the shape, in which T is triangle; L is ladder; P is pentagon; PL is parallelogram; and H is hexagon. “+” means the positive boundary exists in the shape and “” means the negative boundary exists. The rectangle region does not contain decline boundary so that it does not need “+” or “-”.
In Fig. 9, it can be seen that all the 4 shapes in LSN also exist in HPSN. Besides, 12 new shapes are added in HPSN, which are highlighted with yellow color. Each quadrant (II, III, IV) provides 4 new shapes of HPSN because the region is expanded to all of quadrants from single quadrant. Besides, all the 16 shapes in HPSN also exist in VHPBN. 24 new shapes are added in VHPBN, which are highlighted with yellow color. Each quadrant (I-IV) provides 6 new shapes because the reverse boundary exists in VHPBN.
1) The region map summarizes the features of DSSR and TQSR and shows the maximum possible region shapes that a distribution system could have. For instance, the region of LSN has at most 4 shapes according to the map. The pentagon will never be obtained in any LSN. The region of HPSN has at most 4 shapes according to the map. The hexagon will never be obtained in any HPSN.
In the 4-bus test system of HPSN, 13 shapes exist, all of which are included in the 16 shapes of HPSN in the region map. 3 shapes do not exist, whose ID are “1L+”, “1R” and “3L+”. In the 4-bus test system of VHPBN, 24 shapes exist, all of which are included in the 40 shapes of VHPBN in the region map. 16 shapes do not exist, whose ID are “1L+”, “1H+-”, “1L+-”, “1L-”, “1Pl+-”, “2L+”, “2L-”, “2Pl+-”, “3L+-”, “3L+”, “3H+-”, “3Pl+-”, “3L-”, “4L+”, “4L-”, “4Pl+-”.
2) The region map can be used to categorize the distribution networks. For example, if a hexagon region projection is observed in quadrant IV, it can be found in the map that the system is a VHPBN.
This paper proposes the concept and model of TQSR for ADN. The 2D projections of TQSR are observed in 2 DG penetration scenarios. The characteristics of TQSR are summarized as follows.
1) Compared with the traditional DSSR, it is most obvious that TQSR is transformed from a single-quadrant region to a total-quadrant region.
2) For HPSN, at most 12 new shapes will be obtained in quadrants II, III and IV compared with those in LSN, including the triangle, ladder, pentagon and rectangle. For VHPBN, at most 24 new shapes in all quadrants will be obtained compared with HPSN, including the reverse triangle, reverse ladder, reverse pentagon, hexagon, parallelogram and ladder with both positive and reverse boundaries.
3) For HPSN, the most secure operation point is the one in which the DG output reaches the peak value and the power of the load is zero. For VHPBN, the most secure point is the original point or the point that makes the cut-set power be zero.
The region map is discovered to summarize the characteristic of TQSR and provide the maximum possible shapes that a region could have, which can also be used to categorize the distribution networks.
TQSR will be useful for the optimization problem and probabilistic assessment of ADN with plenty of uncertainties. Future work includes complete security region considering energy storage, microgrid and active load. More serious contingencies will also be studied such as weather conditions, N-2 contingencies, and DG contingency.
References
D. A. Roberts and J. Scott, “Assessing future uncertainties on today’s distribution networks,” in Proceedings of IET Conference on Power in Unity: a Whole System Approach, London, UK, Oct. 2013, pp. 1-32. [百度学术]
Q. Shi, C. Chen, A. Mammoli et al., “Estimating the profile of incentive-based demand response (IBDR) considering technical models and social-psychological factors,” IEEE Transactions on Smart Grid, vol. 11, no. 1, pp. 171-183, Jan. 2020. [百度学术]
S. Chowdhury, S. P. Chowdhury, and P. Crossley, Microgrids and Active Distribution Networks. London: The Institution of Engineering and Technology, 2009, pp. 15-33. [百度学术]
K. Morison, L. Wang, and P. Kundur, “Power system security assessment,” IEEE Power & Energy Magazine, vol. 2, no. 5, pp. 30-39, Sept. 2004. [百度学术]
J. Xiao, W. Gu, C. Wang et al., “Distribution system security region: definition, model and security assessment,” IET Generation, Transmission & Distribution, vol. 6, no. 10, pp. 1029-1035, Oct. 2012. [百度学术]
F. Wu and S. Kumagai, “Steady-state security regions of power systems,” IEEE Transactions on Circuits & Systems, vol. 29, no. 11, pp. 703-711, Nov. 1982. [百度学术]
Y. Yu, H. Liu, and Y. Zeng, “Novel optimization method of transient stability emergency control based on practical dynamic security region (PDSR) of power systems,” Science in China, vol. 47, no. 3, pp. 376-382, Feb. 2004. [百度学术]
Y. Liu and Y. Yu, “Probabilistic steady-state and dynamic security assessment of power transmission system,” Science China Technological Sciences, vol. 56, no. 5, pp. 1198-1207, May 2013. [百度学术]
J. Xiao, L. Zuo, G. Zu et al., “Model of distribution system security region based on power flow,” Proceedings of the CSEE, vol. 37, no. 17, pp. 4941-4949, Sept. 2017. [百度学术]
J. Xiao, G. Zu, X. Gong et al., “Observation of security region boundary for smart distribution grid,” IEEE Transactions on Smart Grid, vol. 8, no. 4, pp. 1731-1738, Jul. 2017. [百度学术]
J. Xiao, G. Zu, X. Gong et al., “Model and topological characteristics of power distribution system security region,” Journal of Applied Mathematics, vol. 2014, pp. 1-13, Jul. 2014. [百度学术]
I. Genc, R. Diao, V. Vittal et al., “Decision tree-based preventive and corrective control applications for dynamic security enhancement in power systems,” IEEE Transactions on Power Systems, vol. 25, no. 3, pp. 1611-1619, Aug. 2010. [百度学术]
T. Jiang, H. Jia, Y. Jiang et al., “Cutset‐angle based wide area thermal security region and its application in china southern power grid,” International Transactions on Electrical Energy Systems, vol. 24, no. 11, pp. 1600-1617, Jan. 2015. [百度学术]
J. Xiao, G. Zu, Q. He et al., “A new DMS with real-time security analysis and control based on security region,” in Proceedings of PES General Meeting, Denver, USA, Jul. 2015, pp. 26-30. [百度学术]
J. Liu, H. Cheng, Q. Xu et al., “Stochastic planning of smart distribution network based on security distance methodology considering fault recovery,” Automation of Electric Power Systems, vol. 42, no. 5, pp. 64-71, Mar. 2018. [百度学术]
L. Yang, Y. Li, Z. Li et al., “Energy rebalance control and safe operation region analysis of MMC with sub-module fault,” Electric Power Automation Equipment, vol. 38, no. 4, pp. 52-59, Apr. 2018. [百度学术]
H. Xiao, Z. Ye, F. Ma et al., “Calculation and analysis of the safe operation boundary of shipboard DC zonal electric distribution system,” Transactions of China Electrotechnical Society, vol. 31, no. 20, pp. 202-208, Oct. 2016. [百度学术]
C. Wan, J. Lin, W. Guo et al., “Maximum uncertainty boundary of volatile distributed generation in active distribution network,” IEEE Transactions on Smart Grid, vol. 4, no. 9, pp. 2930-2942, Jul. 2018. [百度学术]
D. M. Staszesky, D. Craig, and C. Befus, “Advanced feeder automation is here,” Power and IEEE Energy Magazine, vol. 3, no. 5, pp. 56-63, Sept. 2005. [百度学术]
B. Zhao, X. Zhang, and B. Hong, “Energy penetration of large-scale distributed photovoltaic sources integrated into smart distribution network,” Electric Power Automation Equipment, vol. 32, no. 8, pp. 95-100, Aug. 2012. [百度学术]
J. Xiao, B. Zhang, J. Li et al., “Research idea on high penetration renewable energy generations distribution system planning based on security boundary,” Automation of Electric Power Systems, vol. 41, no. 9, pp. 1-9, May 2017. [百度学术]
D. V. Hertem, J. Verboomen, K. Purchala et al., “Usefulness of DC power flow for active power flow analysis with flow controlling devices,” in Proceedings of 8th IEE International Conference on AC and DC Power Transmission, London, UK, Mar. 2006, pp. 58-68. [百度学术]
J. Xiao, F. Li, W. Gu et al., “Total supply capability and its extended indices for distribution systems: definition, model calculation and applications,” IET Generation, Transmission & Distribution, vol. 5, no. 8, pp. 869-876, Aug. 2011. [百度学术]
S. Chen, Q. Chen, Q. Xia et al., “Steady-state security assessment method based on distance to security region boundaries,” IET Generation, Transmission & Distribution, vol. 7, no. 3, pp. 288-297, Mar. 2013. [百度学术]
W. Wei, F. Liu, and S. Mei, “Dispatchable region of the variable wind generation,” IEEE Transactions on Power Systems, vol. 30, no. 5, pp. 2755-2765, Sept. 2015. [百度学术]
T. Yang and Y. Yu, “Static voltage security region-based coordinated voltage control in smart distribution grids,” IEEE Transactions on Smart Grid, vol. 9, no. 6, pp. 5494-5502, Nov. 2018. [百度学术]
H. Liao, D. Liu, Y. Huang et al., “Load transfer capability analysis considering interconnection of distributed generation and energy storage system,” International Transactions on Electrical Energy Systems, vol. 24, no. 2, pp. 166-177, Feb. 2014. [百度学术]
L. Jia, X. Qian, H. Cheng et al., “Bi-level optimal renewable energy sources planning considering active distribution network power transfer capability,” Transactions of China Electrotechnical Society, vol. 32, no. 9, pp. 179-188, May 2017. [百度学术]
S. Adhikari, F. Li, Z. Wang et al., “Constructive back-feed algorithm for online power restoration in distribution systems,” in Proceedings of PES General Meeting, Calgary, Canada, Jul. 2009, pp. 4170-4174. [百度学术]
E. Lakervi and E. J. Holmes, Electricity Distribution Network Design, London： The Institution of Engineering and Technology, 2003. [百度学术]
J. Yang, J. E. Fletcher, and J. O’Reilly, “Multiterminal DC wind farm collection grid internal fault analysis and protection design,” IEEE Transactions on Power Delivery, vol. 25, no. 4, pp. 2308-2318, Oct. 2010. [百度学术]
J. Xiao, G. Zu, G. Bai et al., “Mathematical definition and existence proof of distribution system security region,” Proceedings of the CSEE, vol. 36, no. 18, pp. 4828-4836, Sept. 2016. [百度学术]
R. Billinton and S. A. Jonnavithula, “Test system for teaching overall power system reliability assessment,” IEEE Transactions on Power Systems, vol. 11, no. 4, pp. 1670-1676, Nov. 1996. [百度学术]
