【正文】 ork as shown in Fig. 4. The network includes three breakers and two transformers.Losing load at the bus load is used as the criterion of substation network failure.. Considering only open circuit failuresIn order to pare the network state technique with the minimum cut set method, it has been first assumed that only open circuit failures of transformers and breakers are considered and all short circuit faults are ignored. To obtain a relatively simple analytical expression of the result, it is assumed that the open circuit failure probability of all the breakers and transformers is identical and it is U. In the puter program, different failure probability values for different ponents can be easily specified in the data file. Using the cut set method, four minimum cut sets are identified.They are: S1 = (T1, T2}。 S2 = (B1, B2), S3 = (B1, B3, T2)。S4 = {B2, B3, T1). The probability of substation network failure is calculated by Fig. 4. A simple substation network.Pf = P(S1 ∪ S2 ∪ S3 ∪ S4) = 2U2 + 2U3 ? 5U4 + 2U5 (4)As usual, the four minimum cut sets are not mutually exclusive. The calculations from the left side of the second equality sign to its right side are associated with intersections among the minimum cut sets. For this simple case, it can be expressed asfollows:Pf = P(S1 ∪ S2 ∪ S3 ∪ S4)= P(S1) + P(S2) + P(S3) + P(S4) ? P(S1 ∩ S2)?P(S1 ∩ S3) ? P(S1 ∩ S4) ? P(S2 ∩ S3) ? P(S2 ∩ S4)?P(S3 ∩ S4) + P(S1 ∩ S2 ∩ S3) + P(S1 ∩ S2 ∩ S4)+P(S1 ∩ S3 ∩ S4) + P(S2 ∩ S3 ∩ S4)?P(S1 ∩ S2 ∩ S3 ∩ S4) (5)For a relatively large network, identifying all minimum cut sets and performing calculations of the union of nonmutually exclusive cut sets require considerable putational efforts. Using the presented network state enumeration with the labeling bus set approach, 16 network states are identified as failure states that lead to loss of load. Generally, although the number of network failure states is more than the number of minimum cut sets, it is much easier and faster to identify them using the labeling bus set approach in programming. Particularly, once the network failure states are identified, the total network failure probability is just the sum of probabilities of all network failure states without any calculation associated with the union and intersections. In this example, we can have the following analytical expression of substation network failure probability:Pf = 2U2(1 ? U)3 + 8U3(1 ? U)2 + 5U4(1 ? U) + U5 (6)It is interesting to note that Eqs. (4) and (6) look so different but they lead to the same result. This can be proven by assign Ua value. For instance, by letting U= , the substation network failure probability from both the equations is identical, which is.. Considering both open circuit failures and shortcircuit faultsIt is relatively difficult for the cut set method to incorporate dependent failure events, multiple failure modes and switching actions, which are associated with short circuit faults and need to be modeled in reliability evaluation of a substation configuration.It has been assumed in this example that the breakers can clear their own short circuit faults and only the short circuit faults on the two transformers are considered. When a short circuit fault happens on either transformer, the breakers B1 and B2 will be opened by a protection action. This results in a switching state. In this state, B1 and B2 are still healthy ponents. Their outages are not due to a failure and cannot be treated as ponents in a cut set. Then, the switches (not shown in the figure) at both sides of the failed transformer are manually opened to isolate it, and B1 and B2 are reclosed so that the load may be supplied through another transformer if the second transformer is not simultaneously down. This second state corresponds to a repairing state of the faulted transformer.3. ConclusionsThe network state enumeration technique bined with the labeling bus set approach proposed in the paper is suitable for reliability evaluation of a substation configuration or a looped distribution network that needs to model dependent failures, multiple failure modes and multiple states of ponents.Another advantage of the presented network state enumeration technique is that enumerated network states are mutually exclusive resulting in great simplification in calculating the total network failure probability pared to the minimum cut set method. The key in the presented technique is identification of whether a state is a failure one or not. The labeling bus set approach has been proposed for this purpose. A substation configuration is used to explain the procedure including a switching action associated with dependent outages and multiple states of network ponents. The presented method is easy to program and can be applied to any substation or looped distribution networks.The example of a substation network demonstrates that in the case of considering only open circuit failures, the same result is obtained using the proposed method and the minimum cut set method. The example also shows that the presented technique can handle the case of considering both open failures and short circuit faults which are associated with switching actions and protection logic.燕山大學(xué)本科生畢業(yè)設(shè)計(jì)（論文） 燕山大學(xué)畢業(yè)設(shè)計(jì)（論文）評審意見表指導(dǎo)教師評語：成績： 指導(dǎo)教師簽字： 年 月 日評閱人評語： 成績： 評閱人簽字： 年 月 日燕山大學(xué)畢業(yè)設(shè)計(jì)（論文）答辯委員會評語表答辯委員會評語：總成績： 答辯委員會成員簽字： 答辯委員會主席簽字： 年 月 日