Flexible Reconfiguration for Optimal Operation of Distribution Network Under Renewable Generation and Load Uncertainty

Abstract

The primary objective when operating a distribution network is to minimize operating costs while taking technical constraints into account. Minimizing the operational costs is difficult when there is a high penetration of renewable resources and variability of loads, which introduces uncertainty. In this paper, a flexible, dynamic reconfiguration model is developed that enables a distribution network to minimize operating costs on an hourly basis. The model fitness function is to minimize the system costs, including power loss, voltage deviation, purchased power from the upstream network, renewable generation, and switching costs. The uncertainty of the load and generation from renewable energies is planned to use their probability density functions via a scenario-based approach. The suggested optimization problem is solved using a metaheuristic approach based on the coati optimization algorithm (COA) due to the nonlinearity and non-convexity of the problem. To evaluate the performance of the presented approach, it is validated on the IEEE 33-bus radial system and TPC 83-bus real system. The simulation results show the impact of dynamic reconfiguration on reducing operation costs. It is found that dynamic reconfiguration is an efficient solution for reducing power losses and total energy drawn from the upstream network by increasing the number of switching operations.

1. Introduction

Modern distribution network (DN) operation is strongly impacted by the communication and automatic control infrastructures, high penetration of renewable resources, and installation of advanced metering and remote-controlled switches (RCSs) [1,2]. Renewable resources, such as solar and wind, depending on environmental conditions and their output power, are alternatives. These changes result in more dynamics and stochastic demeanors that happen in a DN, and the network structure needs to be modified from time to time so that the grid can react to fluctuations and improve the system operation. Hence, to answer the time-dependent loads and variable generation of renewable resources, network reconfiguration is proposed for system performance [3].

Reconfiguration is the process of altering the topology and some of its structural properties in the distribution network via deactivating the open/closed mechanism of sectionalizing and tie switches [4]. Commonly, reconfiguration in distribution networks is used for loss reduction, reliability, voltage profile improvement, and load balance [4]. In some cases, cyberattack issues can also result in reconfiguration [5]. Reconfiguration is divided into dynamic reconfiguration (DR) and static reconfiguration (SR), depending on the selected time period [6]. In SR, the optimal configuration is determined at a specific time with a fixed operation point for the studied network during the whole period, but DR considers the time-dependent essence of distribution networks, which makes it suitable for real-time applications. Both SR and DR problems are multi-objective and combinatorial optimization problems; also, they are nonlinear, with many electrical and topological constraints. The many components in a DN, along with their uncertainties, add to the complexity of the DR problem. Many algorithms are proposed for reconfiguration, subdivided into heuristic, meta-heuristic, and mathematical [3,6]. Meta-heuristic algorithms have been widely used in reconfiguration problems compared to the other two methods. These approaches involve intelligent search and iterative generation processes and are highly flexible. However, the investigation period is significant because the global optimum is not guaranteed [3,6].

DR formulates multi-period (or decomposition) problems [6,7,8] and complete dynamic problems [9,10,11,12,13,14,15,16]. The complete method considers all the periods, but the decomposition method selects certain multi-periods. The complete dynamic method has a large computational burden due to the number of variables and multiple periods; hence, decomposition models try to reduce the number of computations by classifying the periods of the complete model. Therefore, the response of this method depends on the number of the selected periods, which is an approximate model [17].

The multi-group flight slime mold algorithm (MFSMA) is used for multi-period DR [6]. In this paper, the daily load curve is divided into several categories based on the changes in the load amplitude; then, the optimal configuration of each period is determined. Decomposition DR is modeled based on load balance, power loss, and voltage stability, considering the time-varying load. In [7], the improved fuzzy C-means clustering (FCMC) algorithm divided the daily load curve into optimal reconfiguration time intervals. Decimal particle swarm optimization (PSO) is used to solve decomposition DR. A heuristic method based on switch opening and branch exchanging is introduced in [8], which is used for multi-hour stochastic reconfiguration under PV and load uncertainties. PV stochastic output was modeled via average irradiation. The proposed multi-hour method is a compromise between hourly and daily reconfiguration, which decreases the number of switches.

The valence of hourly reconfiguration with solar and wind energy resources is analyzed by [10]. This study develops a mathematical model to minimize total daily losses through hourly network reconfigurations. The model is implemented in GAMS and solved using MOSEK’s mixed-integer optimization method [10]. References [9,13] present multi-objective complete DR in automated distribution systems, which include the effect of reliability, switching operation, and power loss on the DR process. In [13], a mixed-integer linear programming (MILP) optimization model is developed for DR using the ‘‘path-switch-to-switch” modeling of distribution networks. The Lagrangian dual problem is developed to solve the determined MILP model. Reference [9] introduces a novel integrated optimization algorithm for the DR problem solution, using the grey wolf optimizer (GWO) and PSO. Time-varying load and electricity prices with the effect of dispatchable DG are considered for generalizing the proposed approach. Reference [11] introduces a hybrid algorithm to improve the exactitude and speed of dynamic reconfiguration. This algorithm employs parallel computation with variable population size. Reliability improvement and loss minimization are the objective functions of the proposed method.

Based on the deep learning algorithm, DR reduces the cost of switching operations and power loss of the distribution network [12]. The proposed method is based on the historical control data and the status of the real-time system. The main advantage of this method is determining the reconfiguration period according to the changes in operational costs, load demand, and DG output. In [14], a multi-objective sparrow search algorithm is presented for DR in an active distribution network, considering changes in load, electricity price, and DG output. This paper minimizes the power loss, voltage deviation, and cost. Reference [15] introduces a dynamic and static multi-objective reconfiguration scheme for a distribution system. A static plan is applied for a seasonal or yearly period, but for an hourly period, dynamic reconfiguration is performed. Although uncertainties are not involved, this paper considers a battery energy storage system and photovoltaic (PV) DG with optimum sizing during reconfiguration. The optimal radial structure is selected by maximization of loading and minimization of voltage deviation and losses. In [16], reconfiguration and consideration of three-phase load flow are used to improve three-phase balance in the presence of DG. This paper studies the time variation of load and DG without stochastic behaviors. A multi-objective molecular differential evolution algorithm is used to solve the problem. Reference [17] proposes a method for an automated distribution network (a network with remote and automated switches) for determining the best multi-period reconfiguration plan. Reconfiguration is represented as a weighted graph problem, and a backward dynamic programming algorithm is used to solve it. The graph nodes and arcs represent different static network configurations at different periods and costs of switching actions, respectively.

A risk-based DR method was proposed, which improves the hosting capacity of a distribution network under load and generation uncertainty [18]. In [19], DR, renewable energy sources, and energy storage systems were coordinated to reduce the operation cost of active distribution network. In [20], the impact of a mobile energy storage system and DR in a distribution system for active and reactive power coordination is studied. In this reference, a mixed-integer second-order cone programming (MISOCP) model is used for optimization. The proposed MISOCP model guarantees a globally optimal solution. In [21], dynamic network reconfiguration was used together with a traditional reactive power compensation device to improve the voltage quality. A novel graph reinforcement learning-based approach for the dynamic reconfiguration of active distribution networks with integrated renewable energy is proposed in [22]. An improved particle swarm optimization (IPSO) algorithm is presented to address the problem of dynamic distribution feeder reconfiguration in the presence of energy storage systems, distributed generation units, and solar photovoltaic arrays in [23]. The dynamic distribution network model with distributed power generation is established in [24], aiming to minimize active power loss and voltage deviation. The problem is solved using IMODBO combined with the K-means++ clustering algorithm.

Most of the reported works consider power loss and switching costs as the economic objective function for DR and neglect the uncertainty of renewable generation, upstream networks, and renewable resources’ power cost. Therefore, a more appropriate objective function is needed to investigate the optimal operation of the distribution network considering the time-varying generation and load. To solve this problem, this study proposes a method to select a set of open switches to consider the cost of total generation power (upstream network and renewable generation), power loss, voltage deviation, and switching.

Table 1. Comparing DR methods.

Ref.	DR Type *		Minimize Objective Function	Solution Method	DG	Uncertainty	Test Systems
	D	C
[6]	✓	🗴	Power loss, voltage stability, and load balance	MFSMA	Yes	No	33- and 118-bus
[7]	✓	🗴	Total energy losses	FCMC and PSO	Yes	Yes	70-bus
[8]	✓	🗴	Power loss	SOE	Yes	Yes	33-, 119-,84-, 136-, and 417-bus
[9]	🗴	✓	ENS, power loss, and operation cost	Integrated GWO and PSO	Yes	No	95-bus
[10]	🗴	✓	Total daily losses	MOSEK	Yes	Yes	33-bus
[11]	🗴	✓	Power loss, SAIFI, SAIDI, and AENS	Hybrid EMA and WGA	No	No	15-, 33-, 69- and, 85-bus
[12]	🗴	✓	Switching and power loss	Deep Learning Algorithm	Yes	No	33- and 84-bus
[13]	🗴	✓	Reliability, switching, and power loss	Lagrange Relaxation	Yes	No	15- and 1021-bus
[14]	🗴	✓	Losses, VDI, and economic cost	MOSSA	Yes	No	33-bus
[15]	🗴	✓	Losses, VDI, and load ability	Circular mechanism	Yes	No	69-bus
[16]	🗴	✓	Unbalance factor and switching factor	MOMDE	Yes	No	34-bus
[17]	🗴	✓	Cost of losses, wwitching, and ENS	MO Switching and ENS Programming	Yes	Yes	83-bus
[18]	🗴	✓	Hosting capacity, cost of losses, switching, and interruptions	MO MILP	Yes	Yes	33-bus
[19]	🗴	✓	Cost of emissions and switching	Stochastic MILP	Yes	Yes	119-bus
[20]	🗴	✓	Operation cost	MISOCP	Yes	No	33 bus
[21]	✓	🗴	Hosting capacity and CO2 emissions	MISOCP	Yes	No	33- and 84-bus
[22]	🗴	✓	Power loss and voltage deviations	graph reinforcement learning	Yes	No	33 bus
[23]	🗴	✓	Cost of losses, operation, and ENS	IPSO	Yes	Yes	95 bus
[24]	✓	🗴	Power loss and voltage deviations	IMODBO	Yes	Yes	33- and 69-bus
This work	🗴	✓	Cost (Cupn + Closs + CVD + CSW + CPV + CWind)	COA	Yes	Yes	33- and 84-bus

*—D: decomposition and C: complete.

compares the DR approaches for the current study. The main contributions are as follows:

(1)

Considering the effect of DR on the optimal operation of the distribution network.

(2)

Considering the hourly variations and stochastic characteristics of renewable generation (wind and solar) and load.

(3)

Improving the operating cost function of the distribution network by utilizing voltage deviation, renewable generation, and switching costs.

(4)

Using the coati optimization algorithm (COA) to solve the DR problem for optimal operation of the distribution network.

The rest of this research is as follows: Section 2 presents the proposed approach and Section 3 describes the solution methodology based on the Coati optimization algorithm. Section 4 provides the results of the simulation. Section 5 consists of the conclusions.

2. Proposed Approach

2.1. Scenario-Based Uncertainty Representation

Three uncertain quantities are considered as (1) wind-DG output power, (2) solar-DG output power, and (3) active and reactive power loads. The probabilistic models for the power generated by DG and the real and reactive power demand are described below.

2.1.1. Probabilistic Wind Power Modeling

Wind speed is not constant and has an intermittent nature. Hence, the power product of wind-DG is considered an indistinct variable. Thus, the Weibull probability distribution function is selected to explain the random movement of wind velocity during the predetermined period using historically recorded data. The Weibull distribution method regarding wind speed v_t (m/s) at time “t” is presented in the following [25,26,27,28].

$$f(v_t)={\displaystyle \frac{k_t}{{\lambda }_t}}{\left({\displaystyle \frac{v_t}{{\lambda }_t}}\right)}^{k_t-1}{{\displaystyle e}}^{{\left(-{\displaystyle \frac{v_t}{{\lambda }_t}}\right)}^{k_t}}$$

(1)

$$k_t={\left({\displaystyle \frac{{\sigma }_v^t}{{\mu }_v^t}}\right)}^{-1.086},$$

(2)

$${\lambda }_t={\displaystyle \frac{{\mu }_v^t}{\gamma (1+\frac{1}{k_t})}}.$$

(3)

where k_t and λ_t represent shape and scale variables at the time section “t”, correspondingly. γ describes the Gamma function and μ_v^t and σ_v^t represent the average and standard deviation (SD) of wind velocity at “t”.

Change in wind velocity is segregated into various distances called scenario distances to represent generated power from wind-DG in the role of the parameter with several states. The probability of every scenario and the average valence of wind velocity in the respective scenario is measured [27,29].

$${\pi }_{w,t}^{sc}={\displaystyle \underset{v_{s,t,sc}}{\overset{v_{e,t,sc}}{\int }}f(v_t)d{v}_t},$$

(4)

$$v_{w,t}^{sc}={\displaystyle \frac{1}{{\pi }_{w,t}^{sc}}}{\displaystyle \underset{v_{s,t,sc}}{\overset{v_{e,t,sc}}{\int }}{v}_t·f(v_t)d{v}_t},$$

(5)

where π_w,t^sc, v_w,t^sc, v_s,t^sc, and v_e,t^sc represent probability, the average of wind velocity, and the starting and ending point of the interval in the scth scenario at the tth time section, respectively. Finally, wind-DG power output (P_vw,t^sc) and mean wind velocity (v_w,t) in scenario sc at the time “t” is measured [27]:

$$P_{v_{w,t}}^{sc}=\left\{\begin{array}{ccc}0& v_{w,t}>v_{out}^{cut}& 0\le v_{w,t}<v_{in}^{cut}\\ {\displaystyle \frac{v_{w,t}-v_{in}^{cut}}{v_r-v_{in}^{cut}}}{P^r}_{WDG}& v_{in}^{cut}\le v_{w,t}<v_r& \\ {P^r}_{WDG}& v_r\le v_{w,t}<v_{out}^{cut}& \end{array}\right.,$$

(6)

where v_in^cut, v_out^cut, v_r, and P^r_WDG are the cut-in velocity, cut-off velocity, nominal velocity, and rated power of wind-DG on bus n, respectively.

2.1.2. Probabilistic Solar Power Modeling

Beta PDF models stochastic behavior for solar radiation. The distribution of radiation s_t (kW/m²) at time “t” is given by the following [25,30]:

$$f(s_t)={\displaystyle \frac{\gamma \left({\alpha }_t+{\beta }_t\right)}{\gamma \left({\alpha }_t\right)\gamma \left({\beta }_t\right)}}{s}^{{\alpha }_t-1}{(1-s_t)}^{{\beta }_t-1},$$

(7)

$${\beta }_t=(1-{\mu }_s^t)\left({\displaystyle \frac{{\mu }_s^t(1-{\mu }_s^t)}{{\left({\sigma }_s^t\right)}^2}}-1\right),$$

(8)

$${\alpha }_t={\displaystyle \frac{{\mu }_s^t\ast {\beta }_t}{(1-{\mu }_s^t)}}.$$

(9)

Beta PDF is a continuous parameter, which is segregated into several states to measure the resulting power in PV DG. The probability of solar radiation for each state is measured as follows:

$${\pi }_{s,t}^{sc}={\displaystyle \underset{s_{s,t,sc}}{\overset{s_{e,t,sc}}{\int }}f(s_t)d{s}_t},$$

(10)

$$s_{a,t}^{sc}={\displaystyle \frac{1}{{\pi }_{s,t}^{sc}}}{\displaystyle \underset{s_{s,t,sc}}{\overset{s_{e,t,sc}}{\int }}{s}_t.f(s_t)d{s}_t},$$

(11)

where π_s,t^sc, s_a,t^sc, s_s,t,sc, and s_e,t,sc represent probability, average solar irradiance, the starting and ending spot of the distance in the scth scenario at time “t”, respectively. Therefore, the resulting power of the PV array for scenario sc at the tth time segment (P_Sa, t_Sc), considering the ambient temperature, solar irradiance, and the characteristics of the module itself, are expressed as follows [30].

$$T_{C,t}^{sc}=T_{A,t}+s_{a,t}^{sc}({\displaystyle \frac{N_{OT}-20}{0.8}}),$$

(12)

$$I_t^{sc}=s_{a,t}^{sc}\left[I_{SC}+K_I(T_{C,t}^{sc}-25)\right],$$

(13)

$$V_t^{sc}=V_{OC}-K_V{T}_{C,t}^{sc},$$

(14)

$$P_{s_{a,t}}^{sc}=N_{PV}\ast FF\ast V_t^{sc}\ast I_t^{sc},$$

(15)

$$FF={\displaystyle \frac{V_{MPP}\ast I_{MPP}}{V_{OC}\ast I_{SC}}}.$$

(16)

In this representation, T_C,t^sc and T_A,t are cell and ambient temperatures (°C) at the tth time and scth states; K_I and K_V represent current and voltage temperature coefficients (A/°C and V/°C); N_OT represents the rated working temperature of the cell (°C); N_PV represents the total number of PV modules; FF represents the fill factor; V_OC and I_SC denote open-circuit voltage (V) and short-circuit current (A); and V_MPP and I_MPP denote voltage (V) and current (A) at the highest power point, correspondingly.

2.1.3. Probabilistic Load Modeling

The load uncertainty in the power system is represented with a normal (Gaussian) PDF [25]. The PDF of the load is separated into infinite intervals like wind velocity and solar irradiance within the scenario-based method. For each of them at time “t”, the probability (π_ln,t^sc) and mean demand (l_na,t^sc) in the bus “n” are calculated as follows [31]:

$${\pi }_{l_n,t}^{sc}={\displaystyle \underset{l_{n,t,sc}^{\min }}{\overset{l_{n,t,sc}^{\max }}{\int }}\frac{1}{{\sigma }_{l_n}^t\sqrt{2\pi }}}{e}^{\left(-{\displaystyle \frac{{(l_{n,t}-{\mu }_{l_n}^t)}^2}{2{({\sigma }_{l_n}^t)}^2}}\right)}d{l}_{n,t},$$

(17)

$$l_{na,t}^{sc}={\displaystyle \frac{1}{{\pi }_{l_n,t}^{sc}}}{\displaystyle \underset{l_{n,t,sc}^{\min }}{\overset{l_{n,t,sc}^{mac}}{\int }}\frac{l_{n,t}}{{\sigma }_{l_n}^t\sqrt{2\pi }}}{e}^{\left(-{\displaystyle \frac{{(l_{n,t}-{\mu }_{l_n}^t)}^2}{2{({\sigma }_{l_n}^t)}^2}}\right)}d{l}_{n,t},$$

(18)

where l_n,t is the real or reactive power load at the nth bus, while σ_ln^t and μ_ln^t are the standard deviations and mean of l_n,t, respectively; l_n,t,sc^min and l_n,t,sc^max are the starting and ending points of the interval in the scth load scenario. Moreover, index t shows the distinct time portion.

After probabilistic modeling and producing an appropriate amount of load, wind-DG, and PV output power uncertainty scenarios, the scenarios generate the combined load–wind–PV model, giving an independent relationship among them and multiplying probabilities in each scenario. The probability of the scth combination load–wind–PV scenario at time t (π_C,t^sc) is obtained as follows [30,32]:

$${\pi }_{C,t}^{sc}={\pi }_{l_n,t}^{sc}\times {\pi }_{w,t}^{sc}\times {\pi }_{s,t}^{sc}$$

(19)

2.2. Objective Function

This research focuses on stochastic dynamic reconfiguration to minimize the operation cost of the distribution network at a 24 h time horizon. This objective includes the cost of power losses (C^loss), voltage deviation (C^VD), switching operations (C^SW), energy absorbed from the upstream network (C^upn), generated energy by PV-DG (C^PV), and wind-DG (C^wind). The objective function is formulated as follows:

$$\mathrm{Cos}t(X)={\displaystyle \sum _{t=1}^{24}\left(C_t^{loss}+C_t^{VD}+C_t^{upn}+C_t^{PV}+C_t^{Wind}+C_t^{SW}\right)},$$

(20)

$$X=[\begin{array}{cccc}S{W}_1& S{W}_2& \dots & S{W}_{N_{SW}}\end{array}],$$

(21)

$$\begin{array}{cc}S{W}_j=[\begin{array}{cccc}S{W}_j^1& S{W}_j^2& \dots & S{W}_j^{24}\end{array}]& j\in \left\{1,2,\dots ,N_{Sw}\}\right.\end{array},$$

(22)

$$C_t^{loss}={\lambda }_t^{loss}{\displaystyle \sum _{sc=1}^{N_t^{sc}}{\pi }_{C,t}^{sc}{\displaystyle \sum _{j=1}^{N_b}{k}_j}}{r}_j{l}_{j,t,sc},$$

(23)

$$C_t^{VD}={\lambda }_t^{VD}{{\displaystyle \sum _{sc=1}^{N_t^{sc}}{\pi }_{C,t}^{sc}{\displaystyle \sum _{i=1}^{NB}\left|V_{rated}-V_{i,t,sc}\right|}}}^2,$$

(24)

$$C_t^{ups}={\lambda }_t^{ups}{\displaystyle \sum _{sc=1}^{N_t^{sc}}{\pi }_{C,t}^{sc}{\displaystyle \sum _{i=1}^{N_{ups}}{P}_{t,i,sc}^{ups}}},$$

(25)

$$C_t^{PV}={\lambda }_t^{PV}{\displaystyle \sum _{sc=1}^{N_t^{sc}}{\pi }_{C,t}^{sc}{\displaystyle \sum _{i=1}^{N_{PV}}{P}_{t,i,sc}^{PV}}},$$

(26)

$$C_t^{Wind}={\lambda }_t^{Wind}{\displaystyle \sum _{sc=1}^{N_t^{sc}}{\pi }_{C,t}^{sc}{\displaystyle \sum _{i=1}^{N_{Wind}}{P}_{t,i,sc}^{Wind}}},$$

(27)

$$C_t^{SW}={\lambda }_t^{SW}{\displaystyle \sum _{j=1}^{N_b}\left|S{W}_{j,(t-1)}^{ini}-S{W}_{j,t}^{rec}\right|}.$$

(28)

where $X$ represents the decision variable vector and SW_j is the jth set of open switches. λ^loss_t, λ^ups_t, λ^PV_t, and λ^Wind_t are the electricity loss price, upstream network, PV-DG, and wind-DG at time t, respectively. λ^VD_t is the penalty factor of voltage deviation and λ^SW_t is the switching operation cost at time t. In Equation (23), N^sc_t represents the general number of scenarios at time t; N_b denotes the number of branches; r_j and l_j,t,sc denote the resistance and squared current magnitude of branch j at time t in the scth scenario, correspondingly; and k_j is the topographical condition of the branches. k_j = 1 if branch j is close and k_j = 0 if branch j is open. In (24), NB represents the general number of buses, V_rated represents the rated voltage, and V_i,t,sc denotes the real voltage in bus i at time t in the scth scenario. In (25)–(27), P^ups_t,i,sc, P^PV_t,i,sc, and P^Wind_t,i,sc are the energy absorbed from ith upstream network, ith PV-DG, and ith wind-DG, respectively. N_ups, N_PV, and N_Wind are the upstream networks, PV-DG, and wind-DG, respectively.

In (28), SWⁱⁿⁱ_j,(t−1) and SW^rec_j,t are the statuses of the jth RCS in the initial and reconfiguration structure between t and (t − 1). In both cases, SW_j = 1 if RCS j is closed and k_j = 0 if RCS j is open.

2.3. Constraints

The objective functions (23)–(27) are restrained by the next constraints.

2.3.1. Power Balances

$$P_{t,i,sc}-V_{t,i,sc}{\displaystyle \sum _{j=1}^{NB}{V}_{t,j,sc}{Y}_{ij}\cos ({\delta }_{t,i,sc}-{\delta }_{t,j,sc}-{\theta }_{ij})=0},$$

(29)

$$Q_{t,isc}-V_{t,i,sc}{\displaystyle \sum _{j=1}^{NB}{V}_{t,j,sc}{Y}_{ij}\sin ({\delta }_{t,i,sc}-{\delta }_{t,j,sc}-{\theta }_{ij})=0},$$

(30)

where P_t,i,sc and Q_t,i,sc represent the active and reactive power constituents in the ith bus at time t in the scth scenario. δ_t,i,sc and V_t,i,sc represent the angle and magnitude for voltage in the ith bus at time t in the scth scenario, correspondingly. Y_ij and θ_ij denote the magnitude and angle for branch admittance between the ith and jth buses, correspondingly.

2.3.2. Bus Voltage

The voltage of the network should be in the permitted range at all times.

$$\begin{array}{cc}{V}_{i(\min )}\le V_{t,i}\le V_{i(\max )}& i=1,2,\dots ,NB\end{array}$$

(31)

V_i(min) and V_i(max) represent the minimum and maximum voltage ranges of the ith bus at time t, respectively.

2.3.3. Distribution Feeder VA Constraint

$$\begin{array}{cc}{L}_{MVA,t,j}\le L_{MVA,j}^{Max}& j=1,2,\dots ,N_b\end{array}$$

(32)

L_MVA,t,j and L_MVA,j^Max are the actual and maximum power flowing over the jth line at time t, respectively.

2.3.4. Output Power of DGs

$$0\le P_{DG,t,i}\le P_{DG,t,i}^{\max },$$

(33)

$$0\le Q_{DG,t,i}\le Q_{DG,t,i}^{\max },$$

(34)

P^max_DG,t,i and Q^max_DG,t,i denote the maximum active and reactive power in the ith DG at time t, respectively.

2.3.5. Radial Structure of the Distribution Network

The network topology should be radial when the reconfiguration is performed.

$$N_{b,t}=N{B}_t-N_{sub},$$

(35)

N_sub and NB_t are the number of substations and buses, respectively. Also, N_b,t is the number of branches with close switches at the tth time interval.

2.3.6. Number of Switching

The total number of switching operations (N^SW_RCSj) for each RCS must not violate the maximum number of possible switching operations (N^SW_max) in a 24 h time horizon.

$$N_{RC{S}_j}^{SW}={\displaystyle \sum _{t=1}^{24}\left|S{W}_{j,t}-S{W}_{j,t-1}\right|}$$

(36)

$$N_{RC{S}_j}^{SW}\le N_{\max }^{SW}$$

(37)

3. Solution Methodology

Evolutionary algorithms are commonly used for optimization problems; hence, in this paper, a new algorithm called coati optimization [33], was used for operation cost minimization based on stochastic DR.

3.1. Coati Optimization Algorithm (COA)

The COA tries to represent the natural habits of coatis [33]. These behaviors are a hunting strategy for iguanas and an escape strategy from predators, and are simulated as follows.

3.1.1. Initialization

Create a random position for every member of the population using the following equation:

$$\begin{array}{cc}{X}_i:x_{ij}=L{B}_j+r\ast (\mathrm{U}{B}_{\mathrm{j}}-L{B}_j)& \begin{array}{ccc}& i=1,2,\dots ,N& j=1,2,\dots ,m\end{array}\end{array}$$

(38)

where UB_j and LB_j are the upper band and lower band of the jth decision variable, respectively.

3.1.2. Hunting Strategy for Iguanas (Position Updating Phase 1)

Modeling the hunting behavior of the coati involves dividing the population (N) into two equal groups. The first group climbs to the top of the tree to move the iguana, and the second group waits on the ground to hunt the iguana. The mathematical model of the first category is expressed as follows [33]:

$$\begin{array}{cc}{X}_i^{P1}:x_{ij}^{P1}=x_{ij}+r\ast ({\mathrm{iguana}}_{\mathrm{j}}-I\ast x_{ij})& \begin{array}{ccc}& i=1,2,\dots ,⌊{\displaystyle \frac{N}{2}}⌋,j=1,2,\dots ,m& \end{array}\end{array}$$

(39)

When the iguana drops to the ground, its position is randomly determined. Then, the second group of coatis starts searching based on this position, as described in the following [33]:

$$Iguan{a}^{ground}:I{g}_j^{ground}=L{B}_j+r\ast (\mathrm{U}{B}_{\mathrm{j}}-L{B}_j)$$

(40)

$$\begin{array}{l}{X}_i^{P1}:x_{ij}^{P1}=\left\{\begin{array}{cc}{x}_{ij}+r\ast (I{g}_j^{ground}-I\ast x_{ij}),& f_{I{g}_j^{ground}}<f_i\\ x_{ij}+r\ast (x_{ij}-I{g}_j^{ground}),& else\end{array}\right.\\ i=\left[{\displaystyle \frac{N}{2}}\right]+1,\left[{\displaystyle \frac{N}{2}}\right]+2,\dots ,N-j=1,2,\dots ,m\end{array}$$

(41)

After the new positions are determined, the process of updating the positions is carried out as follows [33]:

$$X_i=\left\{\begin{array}{cc}{X}_i^{P1},& f_i^{P1}<f_i\\ X_i,& else\end{array}\right.$$

(42)

where X^P1_i, x^P1_i,j, and f^P1_i are the new locations for the ith coati, its jth dimension, and its objective function value, respectively. Iguana shows the situation of the finest member of the coati group. I is an integer and is randomly chosen between 1 and 2, and r is a random real digit in the interval [0, 1]. Ig^Ground, Ig^Ground_j, and F_Ig^Ground_j are the randomly generated positions for the on-the-ground iguana, its jth dimension, and its fitness function value, respectively [33].

3.1.3. Escape Strategy from Predators (Position Updating Phase 2)

This step simulates the behavior of the coati when encountering a predator. When a hunter assails a coati, the beast changes its place. With this movement, the coati is placed in a safe position and close to the previous position. This feature shows the ability of the algorithm to perform local searches. This step is expressed with the following mathematical relationship [33]:

$$L{B}_j^{local}={\displaystyle \frac{L{B}_j}{Iter}}\begin{array}{cc},& U{B}_j^{local}={\displaystyle \frac{U{B}_j}{Iter}}\end{array}\begin{array}{ccc}& Iter=1,2,\dots ,Ite{r}_{\max }& \end{array}$$

(43)

$$\begin{array}{l}{X}_i^{P2}:x_{ij}^{P2}=x_{ij}+(1-2r)\ast (L{B}_j^{local}+r\ast (\mathrm{U}{B}_j^{local}-L{B}_j^{local}))\\ \begin{array}{ccc}& i=1,2,\dots ,N& j=1,2,\dots ,m\end{array}\end{array}$$

(44)

$$X_i=\left\{\begin{array}{cc}{X}_i^{P2},& f_i^{P2}<f_i\\ X_i,& else\end{array}\right.$$

(45)

where X^P2_i, x^P2_i,j, and f^P2_i are the new positions for the ith coati, its jth dimension, and its objective function value in the second updating phase, respectively. Iter is the present iteration and Iter_max is the maximum number of iterations.

3.1.4. Repetition Process of COA

Following the completion of the first and second phases of updating the coati’s position in the search space, the process continues until the last iteration of the algorithm using Equations (39)–(45) [33].

Figure 1 shows the entire process of the COA as pseudo code.

3.2. Implementation of the COA for DR

The implementation of the COA for DR is shown in Figure 2. The proposed method is started by reading the network data and setting the COA parameters. Then, the probabilistic model of DG and load in a 24 h period are created using wind speed and solar irradiance data. Afterward, a random population of N solutions is generated for 24 h as decision variables. For each individual from N, the COA changes the network configuration according to SW_j and updates the system’s bus data using a probabilistic model of DG and load. In this paper, load flow is used and integrated into the solution process to calculate branch currents, bus voltage, and cost function evaluation. In the next step, the COA operators (hunting and escape from predators) are applied to all individuals, and their new position is determined. The fitness of individuals is evaluated, and constraints are verified; noncompliance results in penalties and exclusion. This iterative process continues until a predefined maximum iteration (iter_max) count is reached. The optimal solution, representing the lowest operational cost for the DR problem, is derived from the best-performing SW_j in the final time segment.

4. Case Study and Discussion

In this section, the DR for optimal operation in the IEEE 33-bus test system is simulated using the presented approach. Our approach is evaluated using an Intel Core i3 CPU with 1.9 GHz and 4 GB of RAM by MATLAB R2016b software.

4.1. Case Study Network Overview (IEEE 33-Bus)

The test network is a modified IEEE 33-bus system adopted from [10,34], and is shown in Figure 3. The system under consideration is a 12.66 kV hypothetical network with a total load capacity of 3.525 MW and 2.3 MVar. It comprises 33 buses and 37 branches, where branches S1–S32 represent sectional switches, and S33–S37 correspond to tie-line switches [35]. Power flow calculations are performed per unit, with S_base = 10 MVA and V_base = 12.66 kV.

The renewable generation size and location data are available in

Table 2. Renewable generation size and location (IEEE 33-bus).

DG Type	Location (No. Bus)	Size (kW)	Location (No. Bus)	Size (kW)
PV	7	350	14	450
Wind	10	400	33	500

[10]. Other data, such as wind-DG and PV module parameters, are taken from [25]. Also, the mean and standard deviation of wind speed and solar irradiance for modeling their uncertainties are shown in Figure 4 [36]. The network 24 h load profile used in this paper is illustrated in Figure 5.

The load is supposed to be normally dispersed about its average, with a coefficient of variance of 2%. At each time segment, the number of scenarios for load, wind-DG, and PV uncertainty are 3, 5, and 3, respectively. In this paper, distributed generations are administered within the state of a fixed power factor (pf) (with a lagging pf of 0.85 for wind-DG and unit pf for PV). Smaller and larger limits of the voltage intensity of the nodes are determined as follows: Vmin = 0.95 p.u. and Vmax = 1.05 p.u. The energy price of the upstream network, wind-DGs, and PVs is shown in Figure 6. It is assumed that the cost of each switching action (λ^SW) is USD 1 [2]. The maximum number of possible switching operations (N^SW_max) in a 24 h time horizon is four [2]. Also, the price of power losses (λ^loss) and voltage deviation (λ^VD) is 400 USD/MWh and 0.72 USD/p.u., respectively [37].

4.2. Discussion (IEEE 33-Bus)

The performance of the proposed COA for the reconfiguration problem was evaluated by comparing the results of the algorithm with other references, as shown in

Table 3. Loss reduction by the proposed COA and other references (IEEE 33-bus).

References	Optimization Method	Results
		Open Switches	Loss (kW)
[6]	MFSMA	S7, S9, S14, S32, S37	144.43
[8]	SOE	S7, S9, S14, S32, S37	139.55
[10]	GAMS Solver	S7, S9, S14, S32, S37	139.55
[11]	Hybrid EMA and WGA	S7, S9, S14, S32, S37	139.55
[38]	Convex Models	S7, S9, S14, S32, S37	139.55
[39]	Tabu Search algorithm	S7, S9, S14, S32, S37	139.55
[40]	Pareto algorithm	S7, S9, S14, S32, S37	139.55
This work	COA	S7, S9, S14, S32, S37	139.55

. In this table, reconfiguration is performed for power loss reduction in nominal loading conditions and without DG. The analysis in Table 3 indicates that the optimal configuration achieved by the COA is similar to the results attained in other references.

In order to analyze the DR effect on the optimal operation of the distribution network, four different cases are studied, as follows:

Case 1: The initial configuration; open switches include S33, S34, S35, S36 and S37.

Case 2: Optimal operation with static reconfiguration for maximum load and without renewable generation.

Case 3: Optimal operation with static reconfiguration for maximum load along with renewable generation with nominal power.

Case 4: Optimal operation with DR considering load and renewable generation variations under their uncertainty (proposed method).

Table 4. Comparison results for the studied cases.

Case	Time Period	Open Switches	Cost (USD)	Closs (USD)	CVD (USD)	CSW (USD)	Cupn (USD)	CPV (USD)	Cwind (USD)
1	24 h	S33, S34, S35, S36, S37	2799.20	633.49	0.581	0	1873.28	60.518	231.32
2	24 h	S7, S9, S14, S32, S37	2635.45	476.92	0.260	8	1858.42	60.518	231.32
3	24 h	S7, S10, S14, S30, S37	2649.57	489.54	0.431	8	1859.75	60.518	231.32
4	1–14 h	S6, S9, S34, S36, S37	2626.39	466.73	0.279	10	1857.53	60.518	231.32
	15–24 h	S7, S9, S14, S32, S37

shows the final operation scheme for all cases examined. This table shows the open switches, the total operating costs, and the partial terms of Equation (20) for all cases. Comparing all cases indicates that the total operation cost without reconfiguration is relatively high (USD 2799.20). In Case 2, the open switches are S7, S9, S14, S32, and S37, and the operating cost is USD 2635.45. In Case 3, the open switches are S7, S10, S14, S30, and S37, and the operating cost is USD 2649.57. In Case 4, the network has two optimal configurations. The first configuration corresponds to the period 1–14 h and is achieved by opening switches S7, S10, S14, S30, and S37. The second configuration corresponds to the period 15–24 h. In this period, switches S7, S9, S14, S32, and S37 are open. In Case 4, the total operating costs amount to USD 2626.39.

As expected, the total cost in Case 4 is better than in the static reconfiguration (Case 2 and Case 3). However, the total cost for the number of switches (USD 10) is higher than in the static reconfiguration (USD 8). The results show that the lowest costs for losses and energy from the upstream grid belong to Case 4. Furthermore, the costs for energy generation from renewable generation are the same in all four cases.

Table 5. Optimal power procured from the upstream network and renewable generation.

Time (h)	Pupst (kW)				PPVt,i (kW)		PWindt,i (kW)
	Case 1	Case 2	Case 3	Case 4	Bus 7	Bus 14	Bus 10	Bus 33
1	1799.61	1788.58	1787.19	1786.61	0	0	235.99	294.99
2	1827.26	1815.46	1814.32	1814.28	0	0	214.67	268.33
3	1873.89	1861.41	1860.39	1860.54	0	0	206.67	258.33
4	1860.19	1847.81	1846.88	1847.11	0	0	199.99	249.99
5	1823.11	1811.18	1810.40	1810.71	1.01	1.29	187.99	234.99
6	1704.40	1694.38	1693.49	1693.37	20.28	26.09	184.00	230.00
7	1459.67	1452.96	1451.68	1450.79	39.50	50.81	199.99	249.98
8	1494.89	1488.26	1486.76	1485.79	57.71	74.22	201.32	251.65
9	1432.54	1426.89	1425.05	1423.82	72.82	93.66	213.32	266.65
10	1488.07	1482.11	1480.07	1478.57	82.54	106.16	223.99	279.98
11	1647.52	1639.75	1637.31	1635.64	90.65	116.60	245.31	306.64
12	2059.78	2046.15	2043.67	2042.55	89.34	114.91	250.64	313.31
13	2352.92	2334.06	2334.53	2333.79	84.58	108.79	158.65	198.32
14	2381.40	2361.74	2362.26	2361.71	71.45	91.90	159.98	199.98
15	2420.55	2399.77	2400.43	2399.77	55.17	70.96	159.98	199.97
16	2326.42	2306.76	2307.52	2306.77	35.14	45.19	149.30	186.63
17	2396.16	2374.89	2376.79	2374.89	16.45	21.16	118.67	148.33
18	2470.62	2447.57	2451.04	2447.57	0	0	78.67	98.34
19	2680.77	2654.08	2660.39	2654.08	0	0	33.46	41.83
20	2753.97	2726.12	2733.57	2726.12	0	0	18.18	22.73
21	2718.13	2690.95	2698.29	2690.95	0	0	15.71	19.64
22	2596.53	2572.06	2579.08	2572.06	0	0	6.56	8.20
23	2538.06	2514.69	2521.44	2514.69	0	0	4.79	5.99
24	2501.18	2478.58	2485.21	2478.58	0	0	2.57	3.21

shows the optimal hourly electricity purchase from the upstream grid and renewable generation. The results for all study cases show that the maximum power purchase from the upstream network is reached at 20:00. The output power of the wind turbines reaches its peak at 12:00. This value is 63% of the nominal output. PVs reach the peak of output power in hour 11, which is 26% of the nominal output.

Table 6. Hourly optimal cost of power procured from the upstream network and renewable generation for studied cases.

Time (h)	Cupnt (USD)				CPVt (USD)		Cwindt (USD)
	Case 1	Case 2	Case 3	Case 4	Bus 7	Bus 14	Bus 10	Bus 33
1	50.38	50.08	50.04	50.02	0	0	4.72	5.89
2	43.85	43.57	43.54	43.54	0	0	4.29	5.36
3	41.22	40.95	40.92	40.93	0	0	4.13	5.16
4	42.78	42.49	42.47	42.48	0	0	3.99	4.99
5	43.75	43.46	43.44	43.45	0.025	0.032	3.76	4.69
6	42.61	42.35	42.33	42.33	0.51	0.65	3.68	4.60
7	39.41	39.23	39.19	39.17	1.38	1.78	3.99	4.99
8	47.83	47.62	47.57	47.54	2.02	2.59	4.02	5.03
9	53.00	52.79	52.72	52.68	2.55	3.27	7.46	9.33
10	65.47	65.21	65.12	65.05	2.89	3.71	7.83	9.79
11	69.19	68.86	68.76	68.69	3.17	4.08	8.58	10.73
12	82.39	81.84	81.74	81.70	3.12	4.02	8.77	10.96
13	98.82	98.03	98.05	98.02	2.96	3.80	5.55	6.94
14	102.40	101.55	101.57	101.55	2.50	3.21	5.59	6.99
15	111.34	110.38	110.42	110.38	2.76	3.54	7.19	8.99
16	109.34	108.41	108.45	108.41	1.75	2.26	6.71	8.39
17	116.21	115.18	115.27	115.18	0.82	1.05	5.34	6.67
18	119.82	118.71	118.87	118.71	0	0	3.54	4.42
19	134.04	132.70	133.02	132.70	0	0	1.50	1.88
20	123.92	122.67	123.01	122.67	0	0	0.81	1.02
21	103.28	102.25	102.53	102.25	0	0	0.70	0.88
22	93.47	92.59	92.84	92.59	0	0	0.29	0.36
23	76.14	75.44	75.64	75.44	0	0	0.17	0.21
24	62.53	61.96	62.13	61.96	0	0	0.09	0.11
∑	1873.28	1858.42	1859.75	1857.53	26.47	34.04	102.81	128.51

shows the costs for the purchased electricity. It can be seen that the minimum of C^upn is USD 1857.53 and is reached by DR in Case 4. Figure 7 presents the optimal power procured from the upstream network and renewable generation with load profile for Case 4.

The total power procured from the upstream network during 24 h is shown in Figure 8. Dynamic reconfiguration reduces the total power consumption.

The optimum value of the hourly cost of active power loss for the studied cases is given in

Table 7. Hourly cost of active power loss for studied cases.

Time (h)	Closst (USD)
	Case 1	Case 2	Case 3	Case 4
1	22.14	17.73	17.17	16.94
2	21.84	17.12	16.66	16.64
3	22.31	17.31	16.91	16.97
4	21.81	16.86	16.49	16.58
5	20.64	15.87	15.55	15.68
6	18.57	14.57	14.21	14.16
7	15.47	12.78	12.27	11.91
8	16.00	13.35	12.75	12.36
9	15.67	13.41	12.67	12.18
10	17.15	14.76	13.95	13.35
11	21.26	18.15	17.17	16.51
12	29.73	24.28	23.29	22.84
13	31.60	24.06	24.25	23.95
14	32.20	24.33	24.54	24.32
15	32.99	24.68	24.95	24.68
16	30.24	22.38	22.68	22.38
17	30.54	22.03	22.79	22.03
18	31.25	22.03	23.42	22.03
19	35.40	24.72	27.24	24.72
20	36.84	25.69	28.67	25.69
21	35.98	25.11	28.05	25.11
22	32.53	22.74	25.55	22.74
23	31.12	21.77	24.47	21.77
24	30.14	21.10	23.75	21.10
∑	633.39	476.92	489.54	466.73

. Figure 9 and Figure 10 compare the hourly and total active power loss. It is clear that dynamic reconfiguration (Case 4) reduces the C^loss by up to 26.31%, 2.14%, and 4.66% compared to Case 1, Case 2, and Case 3, respectively.

Figure 11 shows the hourly variation in the VD of all investigated configurations based on the predicted load profile. The results show that dynamic reconfiguration outperforms Case 1 and Case 2 and has characteristics similar to those of Case 2 in more hours. The minimum bus voltage profiles during the 24 h time horizon are displayed in Figure 12. It can be observed that Case 4 leads to better results for the minimum bus voltage.

4.2.1. Comparison Test of COA with PSO

The effectiveness of the COA for the dynamic reconfiguration of a distribution network was verified in this study by comparing the solution results for the IEEE 33-bus system using the PSO algorithm.

Table 8. Comparison of COA with PSO.

Method	Time Period	Open Switches	Cost (USD)	Closs (USD)	CVD (USD)	CSW (USD)	Cupn (USD)	CPV (USD)	Cwind (USD)
PSO	1–4 h	S7, S11, S28, S34, S36	2634.58	466.85	0.261	18	1857.63	60.518	231.32
	5–11 h	S7, S9, S28, S34, S36
	13–17 h	S7, S11, S28, S34, S36
	18–24 h	S7, S9, S14, S32, S37
COA	1–14 h	S6, S9, S34, S36, S37	2626.39	466.73	0.279	10	1857.53	60.518	231.32
	15–24 h	S7, S9, S14, S32, S37

shows a comparison between the COA and PSO. COA has the lowest total cost of the two algorithms for dynamic reconfiguration. PSO increases the switching cost during reconfiguration. The COA has good performance for C^loss. This validates the COA’s excellence in generating solutions for a variety of objectives. It has superior performance in comparison to PSO.

The minimum bus voltage profile comparison during the 24 h time horizon is displayed in Figure 13. It can be observed that COA and PSO lead to similar results for the minimum bus voltage.

4.2.2. Reliability Analysis

The expected amount of energy not being provided to the consumer load point due to unexpected outage occurrences is defined as Expected Energy Not Supplied (EENS). The EENS is an important parameter in the reliability determination of distribution systems, and it is calculated by using the failure rate in each branch and the number of interrupted loads due to failure. The following equations were used to compute the EENS:

$$EEN{S}_t={\displaystyle \sum _{sc=1}^{N_t^{sc}}{\pi }_{C,t}^{sc}{\displaystyle \sum _{i=1}^{NB}EEN{S}_{t,i}}}$$

(46)

$$EEN{S}_{t,i}={\displaystyle \sum _{j=1}^{n_b(i)}{\lambda }_j{r}_j{L}_{t,i}}$$

(47)

where n_b(i) is the number of branches, the outage of which can cause a failure at the ith bus; λ_j and r_j are the average failure rate and average failure duration of the jth element in set n_b(i), respectively; and L_t,i is the average load in bus i at time t [34].

Figure 14 shows the hourly variation in the EENS for all the studied configurations based on the forecasted load profile. The results show that dynamic reconfiguration has better efficiency than fixed configurations.

In

Table 9. Average and total values of EENS.

EENS	Case 1	Case 2	Case 3	Case 4
Average (MWh/year)	0.6192	0.5106	0.6245	0.5037
Total (MWh/year)	14.8602	12.2543	14.9887	12.0879

, the average and total values of the EENS are presented for the studied reconfigurations. It is clear that dynamic reconfiguration (Case 4) reduces the EENS compared to Case 1, Case 2, and Case 3.

4.3. Case Study Network Overview (TPC 83-Bus)

The second test system evaluated is the Taiwan Power Company (TPC) distribution network, represented in Figure 15. This system consists of 96 branches, incorporating 83 sectional switches and 13 tie-line switches. Detailed information about this system is available in [41]. In its initial configuration, switches numbered S84–S96 are initially open. The network operates at a nominal voltage of 11.4 kV and is designed to handle a load of 28.35 MW and 20.7 MVar. Power flow calculations are performed per unit, with S_base = 10 MVA and V_base = 11.4 kV.

The renewable generation size and location data are available in

Table 10. Renewable generation size and location (TPC 83-bus).

DG Type	Location (No. Bus)	Size (kW)	Location (No. Bus)	Size (kW)	Location (No. Bus)	Size (kW)	Location (No. Bus)	Size (kW)
PV	6	500	13	500	53	500	60	500
Wind	18	500	36	500	71	500	83	500

. Other factors such as load profile, wind speed, solar irradiance, etc., are similar to the IEEE 33-bus system.

4.4. Discussion (TPC 83-Bus)

The effectiveness of the COA in addressing the reconfiguration problem for power loss reduction under nominal loading conditions and without DG was assessed by comparing its results with other references, as shown in

Table 11. Loss reduction by the proposed COA and another reference (TPC 83-bus).

References	Optimization Method	Results
		Open Switches	Loss (kW)
[41]	MHBMO-SFLA	S7, S14, S34, S39, S42, S55, S62, S72, S83, S86, S88, S90, S92	463.28
[42]	PSO-EABCO	S7, S14, S34, S39, S42, S55, S62, S72, S83, S86, S88, S90, S92	463.28
[43]	ACO	S7, S34, S39, S41, S55, S62, S72, S83, S86, S88, S89, S90, S92	469.88
[44]	T-MSFLA	S7, S34, S39, S41, S55, S62, S72, S83, S86, S88, S89, S90, S92	469.88
This work	COA	S7, S14, S34, S39, S42, S55, S62, S72, S83, S86, S88, S90, S92	463.28

. The analysis of Table 11 indicates that the optimal configuration achieved by the COA is similar to the results attained in other references. The initial value of active power losses (without reconfiguration) is 531.99 kW.

The DR effect on the optimal operation of the TPC 83-bus are studied in four different cases, similar to IEEE 33-bus test system.

Table 12. Comparison results for the studied cases (TPC 83 bus).

Case	Time Period	Open Switches	Cost (USD)	Closs (USD)	CVD (USD)	CSW (USD)	Cupn (USD)	CPV (USD)	Cwind (USD)
1	24 h	S84, S85, S86, S87, S88, S89, S90, S91, S92, S93, S94, S95, S96	18,751.93	2223.8	0.813	0	15,861.9	151.32	514.05
2	24 h	S7, S14, S34, S39, S42, S55, S62, S72, S83, S86, S88, S90, S92	18,455.35	1936.6	0.364	18	15,835.1	151.32	514.05
3	24 h	S1, S6, S29, S86, S66, S88, S89, S90, S91, S92, S94, S95, S96	18,574.61	2054.5	0.603	8	15,846.1	151.32	514.05
4	1–19 h	S7, S34, S39, S41, S55, S62, S72, S83, S86, S88, S89, S90, S92	18,378.23	1866.1	0.368	18	15,825.3	151.32	514.05
	20–24 h	S7, S14, S34, S39, S42, S55, S62, S72, S83, S86, S88, S90, S92

shows the final operation scheme for all cases examined. Comparing all cases indicates that the total operation cost without reconfiguration is relatively high (USD 18,751.93). In Case 2, the operating cost is USD 18,455.35. In Case 3, the operating cost is USD 18,574.61. In Case 4, the network has two optimal configurations. The first configuration corresponds to the period 1–19 h and is achieved by opening switches S7, S34, S39, S41, S55, S62, S72, S83, S86, S88, S89, S90, and S92. The second configuration corresponds to the period 20–24 h. In this period, switches S7, S14, S34, S39, S42, S55, S62, S72, S83, S86, S88, S90, and S92 are open. In Case 4, the total operating costs amount to USD 18,378.23. As expected, the total cost in Case 4 is better than in the static reconfiguration (Case 2 and Case 3).

Figure 16 compares the total active power loss. It is clear that dynamic reconfiguration (Case 4) reduces the losses up to 16.08%, 3.64%, and 9.17% compared to Case 1, Case 2, and Case 3, respectively.

5. Conclusions

This paper introduces a method for the operation of a distribution network using flexible dynamic reconfiguration that takes into account renewable generation and load uncertainty. The uncertainty was modeled using a scenario-based method. The operation cost was optimized by minimizing the costs for power losses, voltage deviations, switching operations, energy taken from the upstream grid, and energy generated by PV-DG and wind-DG. The effectiveness of the proposed method was evaluated using the IEEE 33-bus test system and TPC 83-bus system in conjunction with the COA approach. Four different cases were examined to illustrate the impact of dynamic reconfiguration on the optimal operation of the distribution network. The simulation results revealed that the proposed dynamic reconfiguration could provide significant gains in total cost reduction compared to static reconfiguration. Dynamic reconfiguration proved to be an effective approach for reducing power losses and minimizing total energy purchases from the upstream network, achieved by increasing switching operations under similar conditions.