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Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 2, 14 - 24, 2016 Reliability Evaluation of Distribution Network with Different Distributed Generators Binbin Fan, Limei Zhang*, Yongfu Liu, Jing Lv, Wenzhi Li College of Information Science and Technology, Agricultural University of Hebei, Baoding 071000, China Wei Tang College of Information and Electrical Engineering, China Agricultural University, Haidian District, Beijing 100083, China Abstract Different types of distributed generations(DG)have different impacts on the reliability of distribution network. In this paper, a new method of reliability evaluation for distribution network with multi-type of DG is proposed by analyzing the reliability models of different DG. Based on the analysis of the randomness of DG, the multi-state model for DG output power is established. The proposed evaluation method based on the breadth first search strategy can achieve a reasonable division of the island, and the network topology analysis is implemented to achieve the simplification of the distribution system network structure. The improved minimal path analysis is given to evaluate the reliability of distribution network with multi-type of DG. The RBTS Bus6 IEEE system is applied to demonstrate the feasibility and practicality of the proposed method. Numerical simulations results show that the proposed method is simple, practical and reliable, and can quickly and efficiently evaluate the reliability of distribution network with different DG. Key words: Distributed Generators, Distribution Network, Minimal Path Analysis, Reliability Evaluation. 1. INTRODUCTION Distributed generator (DG) which is distributed in the vicinity of the users is small size, economic, efficient and reliable power source (Liang and Hu, 2003). DGs not only can be used as a standby power source or integration of combined heat and power (CHP) units but also can regulate peak power and can realize independent power generation (Zhang and Tang, 2010). Because DG can make full use of abundant, clean and environmental local renewable resources, it has become a feasible measure to develop green power and achieve energy saving and emission reduction (KANG and GUO, 2010). In our country, it is one of the main application styles that DG connects to distribution network. However, a large number of DG connected, the distribution system transform from the original single power source network to multi-source power network. The power flow is no longer a one-way and two-way power flow will appear, which make the reliability evaluation models and methods of distribution network must be a big change (Liang and Hu, 2003; Li and Liu, 2012). At present, reliability evaluations of distribution network with different distributed generators mainly include analytical method (Wan and Ren, 2003) and simulation method (Wan and Ren, 2004). Reference (Qian and Yuan, 2008) considered the uncertainty of the components and original load parameters of distribution system, analyzed the influence of DG on distribution system reliability by using the method of interval calculation, and reduced the computation time through simplified network. In (Al-Muhaini and Heydt, 2013), authors make a comprehensive evaluation of the reliability index of distribution network with DG by establishing Markov model and state transfer matrix. In (Al-Muhaini and Heydt, 2013), the topology structure of distribution network was simplified, then minimal path and minimum cut sets were solved by prime coding and Peri network, finally reliability index were calculated. According to the influence of DG on distribution network reliability and the fault recovery method of distribution network partition, (Tian and Yuan, 2013) proposed the probability distribution model and algorithm of reliability with DG, effectively overcome the deficiency that the traditional expectation index is insufficient. In (Chowdhury and Agarwal, 2003; Mitra and Vallem, 2012), the sequential Monte Carlo simulation method was used to evaluate reliability on distributed network with DG or micro grid. This simulation method had included the uncertain impact of DG units, but the computation time would be longer than the other. At the moment, there have been considerable works with respect to reliability of distribution network under the certainty environment, but related research considering the randomness and uncertainty of renewable energy DG is lack. In addition, most of the researches have been carried out from single DG type, but they have a lack of adaptability to the reliability evaluation with various types of DG in distribution network. Therefore, this paper establishes the multi-state model for DG output power based on the analysis of the randomness of DG. The proposed evaluation method can achieve a reasonable division of the island based on the breadth first search strategy, and the network topology analysis is implemented to achieve the simplification of the distribution system network structure. The improved minimal path analysis is given to evaluate the reliability of distribution 14 Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 2, 14 - 24, 2016 network with multi-type of DG. The feasibility and practicability of the proposed method are verified by using the RBTS Bus6 IEEE system as an example. 2. MULTI-STATE MODEL OF DIFFERENT DG Wind power and photovoltaic power generation has been widely studied and applied because of its clean, environmental, renewable, and other characteristics. However, the randomness and uncertainty of the output power of the DG has an important influence on the reliability of distributed network (Wei and Wu, 2007; Chen and Wen, 2015). Therefore, based on the historical data of wind power generation and the probability distribution of photovoltaic power generation, the multi-state model of two kinds of DG output is established by using statistical analysis and Monte Carlo simulation method to analyze the influence of different DG on the reliability of distribution network. 2.1. Multi-State Model for DG Output of Wind Turbine At present, the researches of wind power generation in distributed network have accumulated a huge mass of data. Based on the Weibull distribution of wind speed and the existing wind speed data, the output of wind power is mainly calculated by following equation (1) (Guo and Xu, 2012; Karki and Hu, 2006). 0 0 ≤ π < π1 π + ππ + ππ 2 π1 ≤ π < π2 ππ€ = (1) ππ π2 ≤ π < π3 0 π ≥ π3 where, Pw is the output power of wind power generation.Pr isthe rated output power of wind power generator. π1 is cut-in wind speed, π2 israted wind speed, π3 is cut-out wind speed; a, b and c are parameters. In this paper, the wind speed data come from the historical measured data in a certain area, the data is measured every ten minutes. The multi-state model of DG output of wind power generation is obtained by statistical analysis, and the concrete steps are as follows: Step 1:When the wind speed is less than cut-in wind speed or greater than the cut-out wind speed, this part of the range is described a state, mean time the output power is 0; When the wind speed is greater than rated wind speed and less than the cut-out wind speed, this part of the range is described another state, meantime the output power is 1 MW; Finally, when the wind speed is greater than cut-in wind speed and less than the rated wind speed, this part of the range is divided into n states. So wind speed coordinate axis is in total divided into n+2 states. Step2: To statistical hours of wind speed of wind turbine belongs to each state within a year. Step 3:The average of the wind speed and power of each state is respectively calculated, they will be as output model of each state. Step 4:The calculated hours per state divide the total numbers of hours within one year (8760h), and the probability of each state will be obtained. It is assumed that the cut-in wind speed of wind turbine is 3m/s, the rated wind speed is 12 m/s, the cut-out wind speed is 25 m/s. The rated power of the wind turbine is 1MW. Let n be 3, the multi-state model of wind turbine DG output is shown in Table1. Table 1. Multi-state model of wind turbine wind speed(m/s) output power(MW) probability <3 or >25 0 0.3970 3~6 0.0277 0.1403 6~9 0.2399 0.0985 9~12 0.6753 0.0726 >12 and<25 1 0.2916 2.2. Multi-State Model for DG Output of Photovoltaic Generation The output of photovoltaic generation (PV) is closely related to the sun lighting, and the light intensity is generally subject to beta distribution (Guo and Xu, 2012), which can be simulated the light intensity of a certain region within a year (8760h) by Homer software. By the light intensity data, the output power of photovoltaic distributed generation (Park and Wu, 2009) can be expressed as ππ πΊbi 2 ππ = πΊπ π‘π π π ππ πΊbi πΊπ π‘π 0 ≤ πΊbi < π π π π ≤ πΊbi < πΊπ π‘π (2) ππ πΊbi ≥ πΊπ π‘π 15 Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 2, 14 - 24, 2016 where, Pp is the output power of the PV array;Pn is the rated output power of the PV array;Gbi is the light intensity coefficient of the i-th hours; Gstd is a given light intensity under the standard environment, usually take 1000W/m2; R c is a specific light intensity, usually take 150 W/m2. Fully considered the uncertainty of the sun lighting, the relationship between the multi-state model and the probability of photovoltaic generation system is established according to the size of output power of the PV generator. Specific steps are as follows: Step 1: To simulate and calculate power output of photovoltaic generation DG within a year (8760h), the output power per hour is sorted by descending order. Step 2: Take out of the maximum and minimum of the output power of the PV DG within a year, the output power is divided into n equal interval, each interval as a state of the DG output. Step 3: To statistical hours of output power of PV generation belongs to each state within a year. Step 4:To calculate the average of the output power of each state will be as output model of each state. Step 5: The calculated hours per state divide the total numbers of hours within one year (8760h), and the probability of each state will be obtained. Let n be 5, the multi-state model of photovoltaic power generation system is shown in Table 2. Table 2. Multi-state model of photovoltaic power generation system output power probability 0.01 0.5358 0.3016 0.041 0.4982 0.0341 0.7086 0.035 0.9902 0.3541 3.RELIABILITY INDEX OF DISTRIBUTION NETWORK WITH DG DG to connect to distribution network has important impacts on the reliability of load point and distribution system. Therefore, in this paper, authors make use of load point reliability index and system reliability index to study the effect of different DG on distribution system reliability through previously established multi-state model. 3.1.Reliability Index of Load Point Reliability index of load point includes (Guo, 2003): interruption frequencyλl , average interruption duration every fault, average interruption durationUl . Based on established multi-state model, probability formula with every DG is expressed as formula (3-5). λπ = π π=1(ππ ππ=1 ππ ) (3) πΎπ = ππ λπ π π =1 ππ ππ = (4) π π=1 ππ πΎπ (5) where, Pj is the probability of DG output power toπ; π is the model number of all output power states; λi is fault rate of componentπ; γi is average repair time of componentπ; πis the sum of all components. 3.2.Reliability Index of Distribution System The reliability index of the distribution system (Ghajar and Billinton, 2006; Balijepalli and Venkata, 2005)includes: the system average interruption frequency index (SAIFI), the system average interruption duration index(SAIDI), the average service availability index (ASAI), the energy not supplied index (ENSI), customer average interruption frequency index (CAIFI), customer average interruption duration index (CAIDI), calculated formulas are expressed as formula (6-10). SAIFI = π ππ ππ π ππ (6) SAIDI = ASAI = (8760 π ππ − π ππ CAIFI = π ππ ππ ππ ) 8760 π ππ (7) π ππ (8) ENSI = πΏπ(π) ππ (9) ππ ππ π ∈∅ ππ (10) π 16 Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 2, 14 - 24, 2016 CAIDI = π ππ ππ π ππ ππ (11) where, Nl is number of users of load point l; λl is fault rate of load point l; Ul is average interruption time of load point l; La(l) is average load of load pointl; ∅ is a set of load points affected by interruption power. 4.RELIABILITY EVALUATION METHODS OF DISTRIBUTION NETWORK WITH DG In this paper, the proposed evaluation method based on the breadth first search can achieve a reasonable the island division, and the network topology and position of the circuit breaker are judged to simplify the network structure of distribution system, finally reliability index is calculated. 4.1.Isolated Island Division Based on Breadth Search Isolated island is a new operation mode of the after DG is connected to distribution network, that is, DG can independently to supply power to a region. The isolated island can flexibly transform between grid-connected mode and islanded mode according to the actual situation. The operation mode can not only improve the comprehensive utilization of the energy efficiency, and ensure the power supply reliability of the system (Liu and Mu, 2015). Taking into account that the distributed generation is small scale, is located in the vicinity of the customer, so that the transmission distance should be considered in the view of reducing the network loss when isolated island is divided. At the same time, in this paper, in order to ensure the reliable supply of important power load, the weight coefficient is used to reflect the importance degree of load in the process of isolated island division. The high weight coefficient is given to the important loads, we give priority to consider that load of larger weight coefficient is divided into the isolated island. Isolated island formation process: firstly, breadth first search strategy is carried out from bus where DG lies in. The load is hierarchically put into the range of isolated island according to the transmission distance of DG. Secondly, the load of last layer of the same distance is successively divided into range of isolated island according to the size of load weight when the total load in the isolated islands close to the output power of the DG. At the same time, the rated power of the DG must meet the need of load in the isolated island, and the formed isolated island region is connected. A4 LP6 A3 A2 DG LP2 A1 LP1 Figure1. LP3 LP4 LP5 Isolated Island Division The process of isolated island division is shown in Figure 1. Load point LP1 connected to DG is divided into first layer of isolated island according to the connection relations among the load point. Then, the load LP2 and LP3 connected to LP1 are divided into second layer of isolated island; In turn, load LP4 is included into third layer of isolated island; If LP5 and LP6 were added into fourth layer of isolated island, total load would exceed the rated power of DG. In order to meet need of rated power of DG, LP5 is divided into the fourth layer of isolated island according to weight coefficient of the load point which is shown in Table 3. Load point Table 3. Load point data Weight coefficient Load/MW LP1 0.3 0.2 LP2 0.5 0.1 LP3 0.7 0.3 LP4 0.3 0.2 LP5 0.5 0.2 LP6 0.3 0.2 17 Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 2, 14 - 24, 2016 Table 4. Isolated Island division results Numbers of layer Node No. A1 DG,LP1 A2 LP2,LP3 A3 LP4 A4 LP5 4.2. Reliability Calculation Based on the Minimal Path Method The reliability evaluation of distribution system based on the minimal path method can not only take full account of the influence of the branch protection, section breaker, disconnecting switch and planned maintenance, but also can effectively deal with the situation of non-standby power supply and non-standby transformer (Guo, 2007). According to the actual configuration of the system, the algorithm can point out the weakest link in the system and can be applied to the distribution system with different connection modes. (1) Principle of minimum path method The graph is a set of nodes and arcs. A path between two nodes is a set that is composed of a lot of directed arcs or undirected arcs. If a path of removing any an arc is no longer a path, which is called the minimal path (Liu and Zhang, 2008). Start Input the connection relations of node in distribution network Stack initialization Input initial node, marked as "accessed" Push initial vertex into stack Pop up the current element of stack vertex Elements of stack vertex have the adjacent points not to access No Yes Output vertex W Vertex W be marked as "accessed" Push vertex W into stack No Vertex W is the goal vertex Yes Output minimum path of stack in sequence from starting vertex to the goal vertex End Figure 2. Flowchart of minimum path algorithm The basic principle of the minimum path method as follows: each load point is required to find the minimal path. The influence component fault of non-minimum path on the reliability of the load point will be converted into the corresponding node of minimal path according to the topological relation of distribution network, and the reliability calculation of the corresponding load point only consider component and node of the minimal path (Zhang and Chen, 1995; Bie and Wang, 1997). At present, the method of solving the minimal path has the incidence matrix method, the Boolean determinant method and the search method (Guo, 2003). Because the first 18 Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 2, 14 - 24, 2016 two methods are lack of adaptability to the programming of large scale nodes, this paper adopts the minimal path search method based on depth search. The minimal path search algorithm flow chart is shown in Figure 2. (2) Distribution network simplification based on topology structure According to calculating minimal path, the distribution network is simplified to reduce the calculation and improve the efficiency of the calculation. The paper assumes the circuit breaker is 100% reliable, and therefore, the distribution network is divided into 4 regions based on the circuit breaker position. The fault rate and fault time of the load will not be affected by the regions that are unrelated with minimal path of the load point to be calculated, so the unrelated regions can be ignored. In addition, the 100% reliable fuse is equipped at the forepart of the other load branches in the study area, so load malfunction can’t affect the reliability of the load point and the branch is removed from the distribution network. Taking IEEE RBTS Bus6 (Billinton and Jonnavithula, 1995) as an example, as shown in Figure 3, the reliability of load LP15 is calculated, and the distribution network is simplified as shown in figure 4. 1 LP2 LP1 2 3 LP3 4 LP4 5 7 LP6 6 9 8 DG 24 LP5 20 22 19 LP7 10 23 11 LP18 LP17 21 LP16 LP14 LP8 13 12 LP9 LP15 14 DG 26 28 30 LP23 25 15 29 LP22 27 LP21 LP19 LP10 16 LP11 17 LP12 LP20 18 LP13 Figure 3. Connection diagram of distribution network with DG 1 2 3 4 5 7 DG 24 6 9 8 20 22 19 10 23 11 21 13 12 LP15 14 25 15 Figure 4.Distribution network after simplification (3) Improved minimal path method The minimal path method can consider the issue of some components in solving the reliability of distribution system, but for relatively complex system composed of main feeder and branch line, it is complex 19 Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 2, 14 - 24, 2016 for solving and simplifying minimal path and time-consuming calculation (Guo, 2007). Therefore, the minimal path method is improved to calculate the reliability of distribution network with DG in this paper. Distribution network reliability assessment algorithm flow chart is shown in figure 5. According to the simplified distribution network, all the components in the system can be divided into the minimal path component and the non-minimal path component. Load point can be divided into two types of load points to calculate the reliability index based on whether in the area of the isolated island. Start Input the initial data Determine the scope of the isolated island Solve minimum path of the load points Simplify network Yes Load point is within the scope of the isolated island No All the equipment can be divided into: minimum path within or outside isolated island, non-minimum path All the equipment can be divided into: minimum path and non-minimum path Calculate reliability index of load points Calculate reliability index of load points No Load point search is completed Yes Calculate reliability index of system Output the result End Figure 5. Flow chart of reliability evaluation algorithm for distribution network The first category is the load point of the isolated island, the minimal path from bus to the load point is calculated, and then the minimal path from DG to the load point will be calculated. Because this kind of load point have two most paths which can switch the power supply lines, only when the components simultaneously fault in two minimal paths, the load point fault can be caused. The two second-order faults in minimal paths are converted, the conversion formula of interruption frequency ο¬l (times / year), average interruption duration in every fault ο¬l (hours/ times) and average interruption duration Ul (hours / year) are shown in (12), (13) and (14). ππ = ππ· ππ (πΎπ· + πΎπ ) (12) πΎπ = πΎπ· πΎπ (πΎπ· + πΎπ ) (13) ππ = ππ πΎπ (14) where,λD , γD is respectively fault rate and average interruption duration every fault of minimal of path from DG to load point;ο¬s, ο§s is respectively fault rate and average interruption duration every fault of minimal of path from bus to load point. Assuming that isolation switch or circuit breaker is equipped between components of non-minimum path and minimal path, the interruption time of load point is taken as the operation time of isolating devices. The second kind of load point is outside of isolated island, if the faults occurred in the components of minimal path, the faults of load point would be caused 20 Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 2, 14 - 24, 2016 5. ANALYSIS OF EXAMPLES 5.1. Simulation System Parameters In this section, simulation system adopts the RBTS Bus6 IEEE to verify the validity of purposed method. The RBTS Bus6 IEEE system have 23 load points, 21 isolated switches, 23 fuses, 23 power distribution transformers and 4 circuit breakers. It is assumed that operation of circuit breaker and fuse are 100% reliable, operation time of the isolating switch is 0.5H. The improved connected diagram of distribution network is shown in Figure 3. Other components data (Allan and Billinton, 1991) are shown in Table 5- Table 7. Table 5.Reliability indices of equipment Name Fault rate Average repair time/h feeder 0.05 time/ (km*year) 4 transformer 0.015 time /transformer 30 DG 5 time/year 50 Table 6. Line data Long/km Feeder type Line No. 1 0.60 7, 13 2 0.75 27 3 0.80 9, 21 4 0.90 4, 10 5 1.60 3, 5, 8, 15, 20, 28 6 2.50 2, 6, 18, 23, 26 7 2.80 1, 12, 16, 22, 25, 30 8 3.20 11, 17, 19, 24, 29 9 3.50 14 Table 7. Load Data Customer Load Type numbers of load node third 126 Number of Load node Load node No. 1 2 1 5 first 132 0.2070 2 1, 6 second 147 0.1659 2 15, 20 second 1 0.1861 2 4, 18 third 1 0.2431 2 7, 23 first 1 0.2101 2 9, 21 first 1 0.2831 3 3, 13, 17 third 1 0.2501 4 10, 12, 16, 22 second 76 0.1585 4 8, 11, 14, 19 Second 79 0.1554 Load Value/MW 0.1808 5.2. Parameters of DG In order to verify the influence of different types of DG on the reliability of distribution network, in this paper, the reliability simulation without DG is not only carried out, also reliability simulation under the other four kinds of DG scenarios are implemented. (1) Without DG 21 Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 2, 14 - 24, 2016 RBTS Bus6 IEEE system does not add any DG. (2) Constant power DG In the RBTS Bus6 system, the 23-node of the main feeders is connected with the constant power DG of 1MW, the output power is kept as 1MW; the 29-node is connected with the DG of the 1MW, and the output power is kept as 1MW. (3) Wind generation DG In the RBTS Bus6 IEEE system, the 23-node of the main feeders is connected with the wind generation DG, the rated power is 1MW; the 29-node is connected with the constant power DG of the 1MW and the output power is kept as 1MW. (4) Photovoltaic power generation DG In the RBTS Bus6 IEEE system, the 23-node of the main feeder is connected with the photovoltaic power generation DG, the rated power is 1MW; the 29-node is connected with the constant power DG of the 1MW and the output power is kept as 1MW. (5) Mixed DG In the RBTS Bus6 system, the 23-node of the main feeder is connected wind generation DG, the rated power is 1MW; 29-node is connected with photovoltaic power generation DG, the rated power is 1MW. 4.3 Simulation results and analysis The reliability indices of load point with different DG are shown in Tab. 8, Tab. 9 and Tab. 10. The changes of the system reliability indices in five cases are shown in Figure 6. Figure 6 has the two longitudinal coordinates to use MATLAB software to simulate, system reliability index such as SAIFI, SAIDI, CAIDI and ASAI may reference left vertical axis, ENSI system reliability index may reference right vertical axis. Table8.Load point reliability indices without DG / with constant power DG μ/(h*a-1) λ/(time*a-1) γ/(h*time-1) Load Constant Constant Constant point Without DG Without DG Without DG power DG power DG power DG 1 1.29 1.29 1.2229 1.2229 1.5775 1.5775 12 1.715 1.715 3.9723 3.9723 6.8125 3.8125 15 1.995 2.012 2.4762 1.2404 4.94 2.5022 17 1.955 1.9772 2.9194 1.6537 5.7075 3.2697 20 1.9725 2.0118 3.5234 1.3088 6.95 2.6330 22 1.935 1.9743 3.9483 1.6832 7.64 3.3230 Table 9.Load point reliability indices with wind DG / with PV DG λ/(time*a-1) γ/(h*ζ¬‘-1) Load Wind PV Wind PV point generation generation generation generation 1 1.29 1.29 1.2229 1.2229 μ/(h*a-1) Wind PV generation generation 1.5775 1.5775 12 1.715 1.715 3.9723 3.9723 6.8125 6.8125 15 2.0029 2.0046 2.0368 1.9427 4.0712 3.8849 17 1.9866 1.9864 1.1251 1.1398 2.347 2.2634 20 2.0118 2.0118 1.3088 1.3088 2.6330 2.6330 22 1.9743 1.9743 1.6832 1.6832 3.3230 3.3230 Table10.Load point reliability indices with mixed DG Load λ/(time*a-1) γ/(h*time-1) point 1 1.29 1.2229 μ/(h*a-1) 1.5775 12 1.715 3.9723 6.8125 15 2.0029 2.0368 4.0712 17 1.9866 1.1251 2.2347 20 1.9879 2.6550 5.2535 22 1.9825 1.2206 2.4194 22 Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 2, 14 - 24, 2016 4.3 23 SAIFI SAIDI CAIDI ASAI ENSI 3.8 22 3.3 21 2.8 20 2.3 19 1.8 18 1.3 17 0.8 Without DG Mixed DG PV DG Wind DG 16 Constant power DG Figure 6.Changes of system reliability index with DG 1) Comparison of reliability of load point index with DG and without DG, it can be seen that the reliability index of the load point within the isolated island is only affected by the connected to DG in distribution network. The fault rate of the load point in the isolated island is slightly increased, but the time of the load point in the isolated island is obviously reduced. 2) Compared with the load point index of different position, it can be seen that improvement of reliability index of the load point is more obvious within isolated island when the load point distance of connected to the DG is shorter. The improvement of reliability index of LP17 and LP22 in the simulation is best. 3) Compared with changes of system reliability index with different DG, it can be seen that, due to the uncertainty of wind generation and PV power generation, the fault time of load within isolated island with wind generation DG and PV DG is also significantly reduced, but it is worse than the reliability index of constant power DG. The improvement of constant power of DG on reliability of distribution network is the largest 6. CONCLUSIONS In this paper, a new method for reliability evaluation of distribution network with different types of DG is presented. Through the analysis of the randomness of the output power of DG, the multi-state model for output power DG is established. Finally, the reliability assessment of distribution network with different types of DG is calculated by using the minimal path method. 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