Reliability of Active Distribution Network Considering Uncertainty of Distribution Generation and Load

Abstract

An active distribution network is an important development trend of the power grid with widespread use of the distributed generation. The reliability of the active distribution network is not negligible due to the uninterruptible power supply. In the paper, the reliability evaluation method of the active distribution network is proposed in detail, based on combining the roulette wheel selection and the sequential Monte Carlo algorithm. The uncertainty of both the distribution generation and the load is taken into consideration based on the power probability distribution and the working state in the presented model. Furthermore, the IEEE-RBTS Bus 6 is used to verify the validity of the proposed method. The result shows that the new energy access improves the availability and the reliability of the active distribution network.

1. Introduction

In recent years, renewable energy sources have been vigorously developed to solve the energy shortage and environmental pollution problems. The penetration rate of photovoltaic and wind power sources have been increasing in the distribution network. The traditional distribution network is gradually transforming into the active distribution network [1]. The active distribution network is a complex distribution system composed of loads, various distribution generations (DGs), energy storage, energy conversion devices, and monitoring and protection devices.

However, renewable energy, including wind power and photovoltaic, has the random characteristic, which will cause a certain degree of voltage fluctuations and a complex power flow calculation [2]. Furthermore, the demand response is also taken into consideration due to the strong randomness of load [3,4]. The active distribution network is faced with many problems, such as the difficult control of the voltage and the complicated match between supply and demand. The common problems reduce the reliability of the distribution network.

In this context, active and fast progress has been made in the voltage control of the active distribution network. For instance, the plant wide control theory [5], the hybrid distribution transformer [6], and the control strategy with global sensitivities [7] have been studied in depth in order to maintain the stability of the distributed voltage. In addition, in [8], the multi-voltage level active distribution network model is presented based on real network data. However, the effect of the multi-voltage on the reliability of the active distribution network is not obviously involved. Meanwhile, through the active distribution network, communication technologies, including traffic control and differentiation [9], the wireless local area network based on IEEE 802.11s [10], and the coordinate embedding network [11], various applications for reliable and secure power delivery are enabled [12]. Based on the above literatures, the voltage control and communication technologies are relatively mature in the active distribution network. However, the uncertainty of the distribution generation and the load has a more significant impact on the reliability of the active distribution network.

Currently, some of the literature deals with the impact of the uncertainty on the active distributed network. For instance, the robust optimization framework is more tractable and practical for characterizing the uncertainties. An adaptive robust distribution expansion model is presented in order to determine the best distribution expansion planning of the active distribution network [13]. Furthermore, the uncertainty sources pertaining to loads, electricity prices, investment costs, and operation costs are taken into consideration [14,15]. However, the reliability of the active distribution network is ignored in the planning. The dynamic topology awareness approach is used to make judgments regarding operational states and to identify all possible topology changes with a full consideration of the DG uncertainties while the load uncertainty is not considered in the active distribution network [16]. In Ref. [17], the robust coordination expansion planning method, which considers non-network solutions is presented in a deregulated retail market, including the closed-loop demand response and other controllable strategies. However, the uncertainty model is built solely based on the micro-economic theory. In addition, an active distribution network reconfiguration strategy with uncertain factors is proposed for the maximum total supply capacity improvement [18]. Additionally, the bilevel integrated planning model accounting for multidimensional uncertainties from both cyberspace and physical space is proposed for the cyber-physical active distribution system [19]. However, the device state in the active distribution system is not addressed. In Ref. [20], the chance constrained mixed integer second-order cone model is used to address the uncertainty outputs of renewable energy for the day-ahead volt/var control; however, the mathematical model of the uncertainty is not clear.

For the moment, the reliability should be comprehensively considered in the process of the active distribution network operation. In Ref. [21], a multi-agent framework is proposed to address the expansion planning problem in a restructured active distribution network. The network reliability is also modeled while the reliability calculation is not covered. In order to achieve balance between being economic and being reliable, the modified non-dominated sorting genetic algorithm is employed, while the uncertainty of supply-demand is ignored [22]. Moreover, the reliability of cyber and physical subsystems is evaluated based on nonsequential and sequential Monte Carlo methods. The performance in distribution communication only analyzes the influences of cyber faults [23]. In Ref. [24], the genetic optimization algorithm approach is proposed. The reliability of distribution power systems is enhanced by optimizing the location and control of automatic and manual cross-section switches in the distribution power systems. Meanwhile, the impact of the cyber transmission performance on the reliability of an active distribution network is analyzed by the cyber link validity based on the frequency-time domain transformation [25]. The literature focuses on the cyber-physical systems in the active distribution network. In addition, a contingency-based analytical technique is adopted to conduct a reliability worth analysis [26]. Furthermore, by exploring the connections between network topology and reliability, a graph-based approach to enhance the reliability of the distribution systems by installing new tie-lines is proposed [27]. However, the uncertainty factors are not taken into consideration.

In this paper, the reliability evaluation method of the active distribution network is presented in detail, considering the uncertainty of the DGs and the load. With the increasing uncertainty of DGs and load in the active distribution network, the DGs power and the load demand need to be taken into account. In addition, the device state of the active distribution network should also be considered as it can affect the power of the DGs and the load. Furthermore, an improved algorithm is used to evaluate the network reliability. In general, the method proposed in this paper provides the following contributions:

(1)

The uncertainty model of the DGs and the load is established in detail. Both the power and the device state are considered simultaneously. Further, the network reliability is comprehensively calculated.

(2)

The combination of the roulette wheel selection algorithm and the sequential Monte Carlo algorithm is utilized to analyze the impact of the uncertainty on the active distribution network.

This paper mainly focuses on how to evaluate network reliability directly and fast. The rest of the paper is organized as follows. In Section 2, the uncertainty model of the DGs and the load is established. The roulette wheel selection algorithm and the sequential Monte Carlo algorithm are also used to solve the presented model. In Section 3, the results obtained by the simulating calculation are discussed in detail. Finally, the main conclusions from this research are drawn up in Section 4.

2. Materials and Methods

2.1. Reliability Model Considering Uncertainty Based on Probability Distribution

Thus far, DGs, including mainly wind (WG) and photovoltaic (PV) generation, are widely used. However, the output of the DGs has uncertainty due to the inherent intermittency and the randomness of the natural resources. The multi-state model of the DGs is comprehensively established to obtain the reliability of the active distribution network. Both the power and the working state of the DGs in the active distribution network are considered.

Generally, the working state of the DGs is in the fault or the normal. The power of the DGs follows a certain distribution. Hence, the uncertainty model of the DGs can be represented by:

$$H=\left[\begin{array}{c}{T}_n\\ T_f\end{array}\right]\times [\begin{array}{cccc}{\rho }_1& {\rho }_2& {\rho }_3& \begin{array}{cc}\dots & {\rho }_n\end{array}\end{array}]$$

(1)

where H represents the multi-state matrix of the DGs, T_n and T_f represent the working time under the normal and the fault, respectively. N is the working state number, and ρ is the power probability.

The issue to notice is that the actual power of the DGs must be zero under the fault. Further, the uncertainty model can be simplified into the following equation:

$$H_i=\left\{\begin{array}{cc}{T}_f+T_n\times {\rho }_i& i=1\\ T_n\times {\rho }_i& i>1\end{array}\right.$$

(2)

where H_i is the output in the i-th state.

2.1.1. Uncertainty Model of PV

Generally, the solar irradiance distribution is represented by the β distribution.

$$\left\{\begin{array}{l}f\left(S_t\right)=\frac{\mathsf{\Gamma }\left(a_t+b_t\right)}{\mathsf{\Gamma }\left(a_t\right)\mathsf{\Gamma }\left(b_t\right)}{\left(\frac{S_t}{S_{\max }}\right)}^{a_t-1}{\left(1-\frac{S_t}{S_{\max }}\right)}^{b_t-1}\hfill \\ a_t={\left(S_t^{\mathrm{ave}}\right)}^2\left(\frac{1-S_t^{\mathrm{ave}}}{{\sigma }_t^2}-\frac{1}{S_t}\right), b_t=a_t\left(\frac{1}{S_t^{\mathrm{ave}}}-1\right)\hfill \end{array}\right.$$

(3)

where Γ(z) is the Gamma function. a_t and b_t are the parameters which can be fitted by the historical light data in the Gamma function. S_t and S_max are the solar irradiance distribution at time t and the max value of the illumination intensity, respectively. $S_t^{\mathrm{ave}}$ and σ_t are the mean and the variance of the illumination intensity at time t, respectively.

Further, the output of the PV mainly depends on the illumination intensity. The relationship between the PV output and the illumination intensity can be approximated by the piecewise function [28].

$$P_{\mathrm{PV},t}\left(S_t\right)=\left\{\begin{array}{l}{P}_{\mathrm{SR}}\left(\frac{S_t^2}{S_{\max }·S_{\mathrm{C}}}\right), 0<S_t<S_{\mathrm{C}}\hfill \\ P_{\mathrm{SR}}\left(\frac{S_t}{S_{\max }}\right), S_{\mathrm{C}}\le S_t\hfill \end{array}\right.$$

(4)

where P represents the output of the PV, PSR is the rated power of the PV array, and S_c denotes a constant of the illumination intensity.

Based on Equations (3) and (4), the probability density function of the PV output can be written as follows:

$$f\left(P_{\mathrm{PV},t}\right)=\left\{\begin{array}{c}\frac{1}{S_{\max }}·\frac{\mathsf{\Gamma }\left(a_t+b_t\right)}{2·\mathsf{\Gamma }\left(a_t\right)\mathsf{\Gamma }\left(b_t\right)}{\left(\frac{P_{\mathrm{PV},t}{S}_{\mathrm{C}}}{P_{\mathrm{SR}}{S}_{\max }}\right)}^{\frac{a_t-1}{2}}·\\ \left[1-{\left(\frac{P_{\mathrm{PV},t}{S}_{\mathrm{C}}}{P_{\mathrm{SR}}{S}_{\max }}\right)}^{\frac{1}{2}{t}^{b_t-1}}\left(\frac{S_{\max }{S}_{\mathrm{C}}}{P_{\mathrm{PV},t}{P}_{\mathrm{SR}}}\right),0<P_{\mathrm{PV},t}<\frac{P_{\mathrm{SR}}{S}_{\mathrm{C}}}{S_{\max }}\right.\hfill \\ \frac{1}{S_{\max }}·\frac{\mathsf{\Gamma }\left(a_t+b_t\right)}{\mathsf{\Gamma }\left(a_t\right)\mathsf{\Gamma }\left(b_t\right)}{\left(\frac{P_{\mathrm{PV},t}}{P_{\mathrm{SR}}}\right)}^{a_t-1}{\left(1-\frac{P_{\mathrm{PV},t}}{P_{\mathrm{SR}}}\right)}^{b_t-1}\frac{S_{\max }}{P_{\mathrm{SR}}}\hfill \\ \hfill P_{\mathrm{PV},t}\ge \frac{P_{\mathrm{SR}}{S}_{\mathrm{C}}}{S_{\max }}\hfill \end{array}\right.$$

(5)

Hence, the probability of the PV output can be expressed as:

$${\rho }_i={\displaystyle {\int }_{P_{iX}}^{P_{iS}}f\left(P_{\mathrm{PV},t}\right)}d{P}_{\mathrm{PV},t}$$

(6)

where P_iS and P_iX are the upper and lower limits of the PV power in the i state.

It is noteworthy that the change in the illumination intensity is continuous. Hence, the output of the PV is also continuous. It is obvious that the PV output power cannot go from the very high value to zero directly. Therefore, the closed loop cannot be formed between the all-states of the PV output.

2.1.2. Uncertainty Model of WG

The WG output mainly depends on the wind speed. The probability models of wind speed mainly include the Weibull distribution, Chi-square distribution, and Gaussian distribution. The two-parameter Weibull distribution is widely utilized. In this paper, the two-parameter Weibull is used to describe the distribution of the wind speed. The probability density function f is written as:

$$f(v_t)=\frac{k}{\lambda }{\left(\frac{v_t}{\lambda }\right)}^{k-1}{e}^{-{(v_t/\lambda )}^k}$$

(7)

where v_t is the wind speed, k is the state parameter of the Weibull distribution, and λ is the scale parameter which reflects the average wind speed.

The expression between the WG output and the wind speed can be approximately expressed by:

$$P_{\mathrm{W}}\left(v_t\right)=\left\{\begin{array}{ll}0,\hfill & v_t<v_{\mathrm{in}}\\ P_{\mathrm{WR}}\frac{v_t-v_{\mathrm{in}}}{v_{\mathrm{R}}-v_{\mathrm{in}}}\hfill & v_{\mathrm{in}}\le v_t\le v_{\mathrm{R}}\\ P_{\mathrm{WR}}\hfill & v_{\mathrm{R}}\le v_t\le v_{\mathrm{off}}\end{array}\right.$$

(8)

where P_W is the WG output power, v_in represents the starting wind speed of the wind turbine, v_R represents the rated wind speed, v_off represents the excised wind speed, and P_WR represents the rated output power of the wind turbine.

Based on Equations (7) and (8), the probability density function of the WG output can be written as follows:

$$f\left(P_{\mathrm{W}}\right)=\left\{\begin{array}{l}\frac{k\left(v_{\mathrm{R}}-v_{\mathrm{in}}\right)}{{\lambda }^2·P_{\mathrm{WR}}}{\left[v_{\mathrm{in}}+\frac{P_{\mathrm{w}}}{P_{\mathrm{WR}}}\left(v_{\mathrm{R}}-v_{\mathrm{in}}\right)\right]}^k\ast \hfill \\ \exp \left\{-\left[\frac{v_{\mathrm{in}}+\left(P_{\mathrm{W}}/P_{\mathrm{WR}}\right)·\left(v_{\mathrm{R}}-v_{\mathrm{in}}\right)}{\lambda }\right]\right\}\begin{array}{cc}& \end{array}0\le P_{{\mathrm{W}}_1}\le P_{\mathrm{wR}}\hfill \\ 1-\exp \left[-{\left(\frac{v_{\mathrm{in}}}{\lambda }\right)}^k\right]+\exp \left[-{\left(\frac{v_{\mathrm{off}}}{\lambda }\right)}^k\right]\begin{array}{cc}& \end{array}{P}_{\mathrm{W}}=0\hfill \\ \exp \left[-{\left(\frac{v_{\mathrm{R}}}{\lambda }\right)}^k\right]-\exp \left[-{\left(\frac{v_{\mathrm{off}}}{\lambda }\right)}^k\right]\begin{array}{cc}& \end{array}{P}_{\mathrm{W}}=P_{\mathrm{WR}}\hfill \end{array}\right.$$

(9)

Hence, the probability of the WG output can be expressed as:

$${\rho }_i={\displaystyle {\int }_{P_{iX}}^{P_{iS}}f\left(P_W\right)}d{P}_W$$

(10)

where P_iS and P_iX are the upper and lower limits of the WG power in the i state.

2.1.3. Uncertainty Model of Load

The uncertainty of load can be described by the predicted value along with the probability distribution of the prediction error. The power of the load is expressed in the following form:

$$P_{load}(t)=P_{load}^f(t)+\mathsf{\Delta }{P}_{load}(t)$$

(11)

where P_load(t) is the load power in period t, $P_{load}^f\left(t\right)$ represents the predicted value of load, and ΔP_load(t) is the prediction error of the load.

Furthermore, it has been proved that the prediction error of load is highly consistent with the normal distribution. The probability density function of the prediction error can be written as:

$$f(x)=\frac{1}{\sqrt{2\pi }\sigma }\exp (-\frac{{(x-\mu )}^2}{2{\sigma }^2})$$

(12)

where µ is the mathematical expectation, and σ represents the standard deviation.

The probability density function of the prediction error is discretized to simplify the load model. The probability of the prediction error in each interval is α_i. The probability density of the load error discretized is shown in Figure 1.

Based on Equations (11) and (12), the power of the load can be described as follows:

$$P_{load}(t)=\left\{\begin{array}{ll}(1-3\sigma )P_{load}^f(t)\hfill & 0\le \alpha <{\alpha }_6\hfill \\ (1-2\sigma )P_{load}^f(t)\hfill & {\alpha }_6\le \alpha <{\alpha }_4\hfill \\ (1-\sigma )P_{load}^f(t)\hfill & {\alpha }_4\le \alpha <{\alpha }_2\hfill \\ P_{load}^f(t)\hfill & {\alpha }_2\le \alpha <{\alpha }_1\hfill \\ (1+\sigma )P_{load}^f(t)\hfill & {\alpha }_1\le \alpha <{\alpha }_3\hfill \\ (1+2\sigma )P_{load}^f(t)\hfill & {\alpha }_3\le \alpha <{\alpha }_5\hfill \\ (1+3\sigma )P_{load}^f(t)\hfill & {\alpha }_5\le \alpha <{\alpha }_7\hfill \end{array}\right.$$

(13)

where P_load(t) is the load power in period t, $P_{load}^f\left(t\right)$ represents the predicted value of load, and α is the probability value of the prediction error in period t.

2.2. Reliability Model Solving Algorithm

2.2.1. Roulette Wheel Selection (RWS) Algorithm

In order to characterize the uncertainty of the DG and the load, the roulette wheel selection algorithm [29], also called the proportional selection algorithm, is used in the paper. The data are divided into several fitness intervals based on the RWS algorithm to calculate the probability of elimination for each individual. It is worth noting that the elimination probability depends on the size of the divided interval. The individual fitness value is positively correlated with the probability of being selected by the roulette wheel.

The principle of the roulette algorithm is described in detail. The set N has n distinct elements, and u_m represents the fitness value of the individual m. Then, the probability q_m of the selected individual m can be calculated.

$$q_m=\frac{u_m}{{\displaystyle \sum u_m}},m=1,2,3,\dots ,n$$

(14)

Further, the cumulative probability of the individual is given by:

$$r_m={\displaystyle \sum _{j=1}^m{q}_m}$$

(15)

2.2.2. Sequential Monte Carlo (SMC) Method

For the reliability analysis of the active distribution network with the load and the renewable energy, the SMC method is adopted in order to simulate the working state sampling of the DGs and the load [20,30]. Meanwhile, the states of the devices are related in the active distribution network and the state transition of the devices has a certain sequence. The state of the distribution network components are not independent of each other. The state transitions have certain temporal relationships. When the device is the fault, it takes time for the device state to recover to a non-failure state. The repair time cannot be zero in practice. The SMC method can accurately sample each state according to the state transition relationship matrix, and the reliability evaluation results are more accurate and more practical than the classical Monte Carlo method.

The main parameter that needs to be set is only the simulation years in the SMC simulation. It is found that the reliability calculation results tend to converge if the simulation years exceed 500. It is worth mentioning that the simulation years means 500 times of simulation in the same year to ensure the accuracy of the reliability calculation results.

The specific evaluation process is as follows:

• Initialize all component states. It is generally assumed that each component is in the initially running state;
• Determine the number of simulation years, and set the initial time as 0;
• A random number between 0 and 1 is generated for the components in the system. The working time and the time which is used to resume running are fixed according to the random number;
• Other load points affected by the faulty component are found. Judge whether these load points are within the island. If the affected load point is inside the island, perform step 5, otherwise jump to step 6;
• Judge whether the renewable energy output power P can meet the total load L in the island. If P is greater than L, there will be no power outage at the load point. Otherwise, the load is optimized until that P can meet L. Then, calculate the uptime and the failure time of the load points;
• If the load point cannot meet its power supply demand, calculate the uptime and the failure time of the load points;
• Determine whether the set time is simulated. If so, go to step 8. Otherwise, skip to step 2;
• Calculating reliability index.

2.2.3. Reliability Index

The reliability of the distribution system is mainly assessed through reliability indexes. The reliability indexes of distribution network usually include the load point indexes and the system indexes [31]. Load point indexes are mainly used to evaluate the reliability degree of a single load point in the system, while system indexes are used to evaluate the reliability of the entire distribution system, which is calculated based on the load point indexes.

The reliability indexes of load point mainly include:

1.

Load point average failure rate λ;

The average failure rate of the load point refers to the expected number of power outages at the load point during the statistical time, and the unit is times/year.

2.

The annual average outage time of the load point U.

The annual average outage time of the load point refers to the expected duration of downtime of a load point due to faults during the statistical time, in hours/year.

The system reliability indexes mainly include:

3.

Energy not supplied (ENS);

In order to obtain the total power in the system, the energy not supplied is calculated.

$$ENS={\displaystyle \sum L_i{U}_i}$$

(16)

where L_i represents the average load at load point i.

4.

Average service availability index (ASAI);

ASAI is given by dividing the customer hours of the available service by the customer hours demanded.

$$ASAI=\frac{8760{\displaystyle \sum N_i}-{\displaystyle \sum U_i{N}_i}}{8760{\displaystyle \sum N_i}}$$

(17)

5.

System average interruption frequency index (SAIFI);

SAIFI is the frequency of the power outages in the system. It can be calculated by dividing the total power outages number of the customer by the customer number.

$$SAIFI=\frac{{\displaystyle \sum {\lambda }_i{N}_i}}{{\displaystyle \sum N_i}}$$

(18)

where λ_i represents the average failure rate at load point i, and N_i represents the number of users inside load point i. ∑λ_iN_i represents the total outage time of users, and ∑N_i is the total number of users.

6.

System average interruption duration index (SAIDI).

SAIDI is given by dividing the total power outages time of the customer by the customer number. In addition, it clearly shows how long the average power outage lasts.

$$SAIDI=\frac{{\displaystyle \sum U_i{N}_i}}{{\displaystyle \sum N_i}}$$

(19)

where U_i represents the average annual outage duration at load point i.

In the paper, the RWS algorithm is adopted in order to deal with the uncertainty of the DGs and the load. The typical scene is obtained based on the probability calculation. Further, the SMC method is used to calculate the reliability of the active distribution network system. A variety of the evaluation indexes of the system reliability is obtained in detail. Figure 2 shows the reliability calculation of the active distributed network based on the RWS and SMC algorithms.

2.3. Constrains of the Reliability Model

2.3.1. Power Flow Constraints

Assume that in normal operation, the node voltage is usually near the rated voltage, and the phase angle difference between the two ends of the branch is small. The active and reactive power on the branch can be expressed as:

$$\left\{\begin{array}{c}{P}_{ij}=(U_i^2-U_i{U}_j\cos {\theta }_{ij})G_{ij}-U_i{U}_j\sin {\theta }_{ij}{B}_{ij}\\ Q_{ij}=-(U_i^2-U_i{U}_j\cos {\theta }_{ij})B_{ij}-U_i{U}_j\sin {\theta }_{ij}{G}_{ij}\end{array}\right.$$

(20)

where, P_ij and Q_ij are the active and reactive power flowing through branch ij, U_i and U_j are the voltage amplitudes of nodes i and j, respectively. G_ij and B_ij are the conductance and reactance of branch ij, and θ_ij is the voltage phase angle difference between node i and node j.

2.3.2. Node Voltage Constraints

Node voltage constraints can be expressed as:

$$-7\%\le \frac{U_i-U_N}{U_N}\times 100\%\le 7\%$$

(21)

where U_N is the rated voltage value of the node.

2.3.3. Transmission Line Load Ratio

Transmission line load ratio expressed as:

$$S_{ij}^2=P_{ij}^2+Q_{ij}^2$$

(22)

$$\frac{S_{ij}}{S_{\max }}\le 50\%$$

(23)

where S_ij and S_max are the apparent power on branch ij and the upper limit of transmission line transmission power, respectively.

2.3.4. DG Power Output Constraints

The PV output and WG output are limited by the rated capacity of the planning equipment at the node, which can be expressed in the following formula:

$$0\le E_{i,t}^{PV}\le C_{PV,i}$$

(24)

$$0\le E_{i,t}^{WG}\le C_{WG,i}$$

(25)

where $E_{i,t}^{PV}$ and $E_{i,t}^{WG}$ are the PV and WG output of DG i at time t, and $C_{PV,i}$ and $C_{WG,i}$ are the installed capacity of PV and WG in DG I, respectively.

2.3.5. Energy Storage Device Constraints

The energy storage devices in DG should satisfy the following constraints:

$$0\le \left|E_{i,t}^{ESS}\right|\le E^{ESS,\max }$$

(26)

$$0\le Q_{i,t}\le C_{ESS,i}$$

(27)

$$S_{SO{C}_{i,t}}=\frac{Q_{i,t}}{C_{ESS,i}}$$

(28)

$$S_{SO{C}_{\min }}\le S_{SO{C}_{i,t}}\le S_{SO{C}_{\max }}$$

(29)

$$S_{SO{C}_{i,t}}=\left\{\begin{array}{c}{S}_{SO{C}_{i,t-1}}+{\eta }_0·E_{i,t}^{ESS},E_{i,t}^{ESS}>0\\ S_{SO{C}_{i,t-1}}+E_{i,t}^{ESS}/{\eta }_0,E_{i,t}^{ESS}\le 0\end{array}\right.$$

(30)

where E^ESS,max is the upper limit of the charging and discharging capacity of the energy storage device, $E_{i,t}^{ESS}$ is the amount of energy storage charge and discharge of DG i at time t, Q_i,t is the energy storage capacity of DG i at time t, C_ESS,I is the rated energy storage capacity of DG i, $S_{SO{C}_{i,t}}$ is the state of charge of the energy storage device of DG i at time t, $S_{SO{C}_{\min }}$ and $S_{SO{C}_{\max }}$ are the lower and upper limits of the SOC of the energy storage device, respectively, and η₀ is the charging and discharging efficiency of energy storage devices.

3. Results and Discussion

3.1. Case Introduction

In this section, the test system, namely, the IEEE-RBTS Bus 6, is used to verify the feasibility and the accuracy of the proposed method in the paper [32,33]. The modified structure of the active distributed network is shown in Figure 3. The studied system consists of 23 load branches. Meanwhile, the circuit breaker, the distribution transformer and the load are connected on the branches. In addition, there are 30 lines, 4 circuit breakers, and 1 segment switch in the system. In addition, four identical DGs are included in the system, connected to node 13, node 19, node 24, and node 28. Furthermore, the installed WT and PV capacity in each DG are 10 MW and 8 MW, respectively.

The load raw data are shown in

Table 1. Load data.

Load Level	Load Point Number	Number of Users
First class load	L5	132
First class load	L7, L23	1
First class load	L9, L21	1
Second class load	L1, L6	147
Second class load	L15, L20	1
Second class load	L10, L12, L16, L22	76
Third class load	L2	126
Third class load	L4, L18	1
Third class load	L3, L13, L17	1
Third class load	L8, L11, L14, L19	79

. The load can be classified into first class load, second class load, and third class load according to the importance. First class load is the safe load, and the third class load mainly includes the auxiliary load. Hence, the first class load is the most important load and it is shed last. The third class load is preferentially removed when the power is insufficient in the active distribution network. In addition, the failure rate of the feeder in the system is 0.048 times/(years*km). The failure rate of the switch is 0.006 times/year. The average repair time is 3 h for both.

Table 2. Length of feeder section.

Length/km	Feeder Number
0.5	7,13,30
0.75	1,4,6,9
0.8	2,3
0.85	5,8,10,15,18,20,23,24,28
1.0	11,12,16,22
1.3	14,17,19,27
1.5	21,25,26,29

shows the length of each feeder in the system. In addition, MATLAB is used as the simulation software.

3.2. Case Discussion

3.2.1. Scenario Generation

As shown in Figure 4, the four scenarios with the high probability are selected to characterize the typical daily load by the RWS algorithm. The probability decreases from scenario 1 to scenario 4. The renewable energy is not considered in scenario 0. In addition, the capacity of the DGs under each scenario is the same while the states of the DGs are different.

The results of scenario 1 require significant attention as scenario 1 has the highest probability of occurrence. The power of the electrical load under the typical scenarios is obtained during the day. The day is evenly divided into 24 h, and the load power is measured. Observing the load curves, the load power fluctuates considerably under the typical scenarios throughout the day. Meanwhile, there is an obvious peak-to-valley difference comparing the different scenarios. The electricity consumption is low between 4 a.m. and 6 a.m. while the peak of the load power is between 12 p.m. and 5 p.m., and one thing that is very noticeable is that many points of the load power overlap under different scenarios. It is clear that the typical scenarios are highly representative.

Similarly, the RWS algorithm is used to generate the typical scenarios of the WG and the PV during the day. The uncertainty of the DGs output is characterized in the typical scenarios. Different from the load, both the working state and the power state are considered in the output sampling of the DGs in order to simulate the uncertainty. The typical scenarios for the output of the WG and the PV are shown in Figure 5. As indicated in Figure 5a, the power generated by the WG from 0 to 4 o’clock is significantly higher than that at the other time due to the uneven distribution of the wind speed. In addition, the fluctuation of the WG output power under different scenarios is basically the same. As shown in Figure 5b, the light intensity is relatively high from 10 to 14 o’clock. Hence, the output of the PV is concentrated during this period. The light intensity is zero at night, so the PV output power is zero between 1 a.m. and 5 a.m. and between 7 p.m. and 12 a.m.

In order to comprehensively characterize the impact of the uncertainty on the reliability of the active distribution network, four typical scenarios are generated based on the combination of the load, the WG, and the PV. The typical scenarios are arranged in order of decreasing probability in Figure 6. The most likely outcome is scenario 1.

As shown in Figure 6, the power generated by the WG and the PV in the distribution network cannot meet the demands of the load under different scenarios. The electric power is purchased from the main grid to eliminate the energy deficit. The WG output is significantly high from 1 to 4 o’clock, and the PV output is relatively greater from 10 to 14 o’clock. The outputs of the WG and the PV have a significant complementary effect on the load. When the fault occurs in the distribution network during the two periods, there is relatively more renewable power generated in the island and fewer load points are disconnected. It has a greater positive impact on the reliability of the distribution network operation.

3.2.2. Analysis of Reliability Indicators

In the paper, the simulation time is set to 500 years to ensure the convergence and accuracy of the assessment results. The four typical scenarios of the active distribution network with the renewable energy and the typical scenario without renewable energy are both taken into consideration. The reliability indexes of the active distribution network are calculated to measure the reliability. In addition, the impact of distributed renewable energy access on the reliability of the distribution networks is obtained by comparing the reliability under different scenarios.

The average annual number of outages at each load point under different scenarios is shown in Figure 7a. Figure 7b shows the average annual outage time of each load point under different scenarios. It can be seen that the average number of annual outages and the average annual outage duration at the different load points under the typical scenario, without considering renewables, are overall higher than that under the four typical scenarios considering renewables. Comparing with the typical scenarios considering renewables, the average number of annual outages and the average annual outage duration at some load points under the typical scenario without considering renewables is approximately equal. The reason is that there is no distributed power in the vicinity of these load points which can form islands after the fault, resulting in no significant reduction in the load point number under the fault. Hence, the grid connection of distributed power can improve the network reliability by providing energy for the load and island reduction in an active distribution network.

The reliability indicators of the distribution system are shown in

Table 3. Comparison of distribution system reliability indexes.

Reliability Indexes	Scenario 0	Scenario 1	Scenario 2	Scenario 3	Scenario 4
SAIFI (times/household*year)	2.2980	1.9479	2.0927	2.0914	2.0881
SAIDI (h/household*year)	6.0743	5.7969	5.7096	5.7524	5.7367
First class load	1434.96	1346.19	1355.51	1281.65	1256.53
ENS (MW·h/year)	0.99930658	0.9993825	0.999348	0.9997612	0.999345117

. It should be noted that renewable energy is not connected to the system in only scenario 0. SAIFI is 2.298 times/household*year if there is no distributed power connection to the distribution system. Among the four typical scenarios considering the new energy access, scenario 1 has the lowest SAIFI value, while scenario 2 has the highest SAIFI value. Compared with scenario 0, the average frequency of system outages decreased in all scenarios where the distributed power access was considered. The most significant reduction in the average system outage frequency is seen in scenario 1. Compared with scenario 0, the 15.23% SAIFI reduction was obtained in the scenario 1, which has the high probability of occurring.

The SAIDI index is 6.0743 h/household*year in scenario 0, while the index is approximately 5.75 h/household*year in the remaining scenarios. The reduction is in the region of 5%. The average system outage time of the load has also been reduced. Meanwhile, the ENS index is 1434.96 MW*h/year if renewable power generation is not considered in scenario 0. Compared with the other scenarios, there is a significant increase in the ENS index under scenario 0. The ASAI index increases as the new energy is used in the active distribution network. Overall, the reliability index results under different scenarios have an obvious difference. Scenario 1 needs to be focused on the high probability. Compared with scenario 0, SAIFI and SAIDI under scenario 1 are obviously improved.

In general, some load points can form planned islands to meet part of the load demand if the renewable power generation is considered under the fault. The reliability of the load points within the islands increases significantly. The use of the new energy power improves the reliability indexes and has a positive impact on the reliability of the active distribution network.

3.2.3. Comparing Network Reliability Calculation among Three Algorithms

Further, the reliability indexes are calculated by using other common algorithms, including the minimum path (MP) algorithm [34] and the nonsequential Monte Carlo (NMC) algorithm [30] under scenario 1. The results and the calculation time obtained by three algorithms are compared in

Table 4. Comparison of calculation by three algorithms under scenario 1.

Indexes	MP	NMC	Proposed Method
SAIFI (times/household*year)	2.5134	2.0678	1.9479
SAIDI(h/household*year)	6.2348	6.0916	5.7969
ENS (MW·h/year)	0.9998719	0.9994171	0.9993825
Calculation time (s)	25.3	18.7	19.5

.

Comparing with the reliability indexes obtained by the MP algorithm and NMC algorithm, the indexes calculated by the proposed method in the paper are obviously smaller. In addition, the calculation time of the NMC algorithm is the shortest, while the NP algorithm needs the longest time in the process of network reliability. However, the state order of the DGs and the load needs to be taken into consideration. There are some errors between the results obtained by the NMC algorithm and the actual results. Hence, the proposed method is effective and advanced.

4. Conclusions

The reliability evaluation method of the active distribution network is comprehensively proposed considering the uncertainty of the DGs and the load in the paper. The uncertainty model of the DGs and the load is established in detail based on the probability statistics. Meanwhile, both the working state and the power output state of the DGs and the load are taken into consideration. Further, the RWS algorithm is used to deal with the uncertainty and generate the typical scenarios. In addition, the reliability indexes of the active distributed network under the typical scenes are calculated in detail. Finally, the IEEE-RBTS Bus 6 is used to verify the validity of the proposed method in the paper.

The reliability of the active distribution network is assessed using the proposed method. The reliability indexes, including the load point average failure rate, ENS, ASAI, are comprehensively calculated under the typical scenarios. The results show that the new energy access improves the availability and the reliability of the active distribution network by meeting the load demand. The study in the paper is helpful for renewable energy grid-connection and power quality improvement through the reliability evaluation of the active distributed network. In addition, the study can provide useful help for network topology reconstruction and network planning based on the reliability calculation.