Keywords

1 Introduction

Electrical power system passes through different steps, production, transmission and distribution. Distribution has now become the most important part. It provides connection among transmission network and electricity consumers [1]. Researchers have given great importance to distribution networks in last years. This is due to introduction of distributed generation (DG) based on renewable sources of energy and non-renewable ones in those networks [2]. Distribution networks operate in lower voltages and present meshed structures, however, they must be operated in a radial structure [3]. A radial structure, i.e. each load bus is connected to the power bus (source station) by a single path [4]. The search of an optimal radial configuration (reconfiguration process) is the procedure on modifies distribution network topology by adjusting the switches stat to reduce the chosen objective [5]. The reconfiguration can be invariant on time (static reconfiguration case) or variant during the day according to the load and renewable generation power (dynamic reconfiguration case). Due to the Joule effect, the higher current causes the higher power losses. One of the Smart Grid characteristics is that it can help to minimize these losses [6]. The minimize power losses by dynamic reconfiguration task has a great importance in smart grid and in real time control. A Smart Grid is a modern distribution network, equipped by sensors, communications, control, automation and computer equipment to improve safety and flexibility [7]. Algeria is among the countries that are interested in the development and modernization of its electricity network (Transmission and Distribution network); it has effectively integrated various new technologies, such as programmable logic controllers, optical fiber links, digital protections, smart meters, SCADA system. In this context, a new contribution has been presented in this paper to propose a tool that helps the operator to determine the optimal distribution network configuration in each hour. Various techniques have been published are considered on static distribution network reconfiguration based conventional methods, artificial intelligence methods and metaheuristic methods [8]. But very few paper are published on Dynamic Distribution Network Reconfiguration (D-DNR) considering the photovoltaic production variation and/or load variation during day, for example: A method for solving the power system reconfiguration problem by introduction of distributed generation based objective of minimizing active losses and improving the voltage profile in the distribution network which has been presented in [9] considering different load levels, by application of Harmony Search algorithm. In paper [10] a method based on the genetic algorithm is presented to evaluate the reconfiguration problem of the distribution network taking into account the effect of load variation and stochastic production of renewable energy sources. According to reference [11], an optimal real-time reconfiguration algorithm is proposed, which uses a classical non-linear optimization technique and guarantees an optimal solution in the shortest possible time, and aims to minimize active losses in each interval time. A method has been proposed in [12] to solve the problem of dynamic reconfiguration of the electrical distribution network considering a variable load, application of the artificial immune network for combinatorial optimization, in order to minimize the losses energy cost in a given period. The study based the reference [13] proposes a method of dynamic reconfiguration that takes into account the initial topological variation in real time. The method combines dynamic topology analysis and network reconfiguration to solve the distribution network optimization problem in real time and in the presence of a fault. Depending on the network state, the optimal configuration is identified to reduce power losses and improve the distribution network voltage profile in real time. The dynamic reconfiguration of the distribution network focused on the Lagrange relaxation method has been proposed in [14]. The objective of this method is to determine the optimal topologies of the distribution network over a specified time interval, in order to minimize the active power losses. A recent research in [15] presents a multi-objective management based on the reconfiguration of the network in parallel by placement of renewable source and the dimensioning, to minimize the active power losses, the annual operating costs (installation costs, maintenance and active power loss) and pollutants gaseous emissions. The variation over time of the wind speed, the solar irradiation and the load is taken into account. The objective of this study is to find the optimal configuration of the network that has had conjunction with the placement and sizing of renewable sources considering multiple criteria. A dynamic reconfiguration approach for the three-phase asymmetric distribution network has been presented in [16]. The network topology is optimized for future periods of time and adapts to load and DG variation while minimizing the daily costs of active losses using mixed integer linear programming method. A recent review of reconfiguration techniques has been presented in [17] for the restoration of service in modern distribution networks based on various practical considerations. This paper present a Genetic Algorithm method based on graphs theory to design an optimal D-DNR taking account the photovoltaic production variation and load variation on real times. D-DNR determine by changing loops switches state to minimize the total real power losses. This study proposed to adapt the GA method to the strategy of balancing the load between medium voltage departures (branches permutation strategy). The proposed method is tested on IEEE distribution network 69 bus and validated on Algerian distribution network, 116 bus.

2 Problem Formulation

2.1 Objective Function

The first concern of the distribution system operator is to minimize active power losses as much as possible [18]. The objective of D-DNR problem is to find the best network configuration with minimal real losses subject to all exigency exploitation constraints. Since many switching combinations in a distribution network exist, the search for an optimal configuration is a NP-hard, non-linear, combinatory and a non-differentiable constraints optimization [19]. The goal is to minimize Eq. 2 in every hour of time. Figure 1 shows an equivalent circuit model of a distribution network in the presence of looping switchers.

$$ P_{loss}^{T} \left( t \right) = I_{pq}^{2} R_{pq} = \frac{{S_{pq}^{2} }}{{V_{p}^{2} }}R_{pq} = \frac{{P_{pq}^{2} + Q_{pq}^{2} }}{{V_{p}^{2} }}R_{pq} $$
(1)
$$ F = \mathop \sum \limits_{i = 1}^{{N_{B} }} P_{loss\left( i \right)} \left( t \right) $$
(2)

where \( \left| {V_{p} } \right|/\delta_{p} , \) is voltage/angle at bus \( p \), (\( r_{pq} \), \( x_{pq} \)) are resistance and reactance of branches joining bus \( p \) and bus \( q \), (\( P_{pq} \), \( Q_{pq} \)) are real and reactive power flow in branch between bus \( p \) and bus \( q \). This objective function is subject to equality and inequality constraints (See references [20, 21]).

Fig. 1.
figure 1

Two-bus distribution network with one line diagram

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3 Genetic Algorithm Method

The GA is an optimization technique inspired by natural selection and based on genetics laws (Mendel). The algorithm is based on a set of possible solutions randomly initialized in the search space. Individuals are represented by their design variables or by a coding of these chromosomes. Then evaluate their relative fitness in the base of their performance and create a new population of potential solutions using an evolutionary operations (the selection, crossover and mutation). Repeat this run until locating a solution, this algorithm have been proposed by Holland-John [22].

4 Simulations and Results

In this work, the optimization method chosen is the genetic algorithm; this method is applied to determine the optimal dynamic reconfiguration of distribution networks taking into account the dynamics of load and the dynamics of PV production during the day, under the distribution network constraints. To confirm the efficiency of the developed program, initially is tested on IEEE 69 bus, but with only one consumption (static configuration). After that, a validation on the 116 bus of Algerian network was carried out considering the variation of the load and the PV production during the day. For the case of dynamic reconfiguration, we consider that it is a set of static cases that last one hour of time, for this we necessity the values of the loads and the PV sources for each hour. IEEE 69 bus are generally defined in the literature [23], however the Algerian network consists: 116 bus, 124 branches containing 09 Tai-lines and 09 feeders. The nominal voltage of 116_busses network is 10 kV. The substation is connected to medium voltage network through a 30/10 kV transformer. The voltages limits considered in this paper between 0.95 pu and 1.05 pu. The total limit PV considered in this study is 09 MW, which distributed between the following busses (busses with low voltages): 62, 66, 106, 109, and 75, according to the operator obligation of the Algerian distribution power system \( \left( {\sum\nolimits_{{\varvec{i} = 1}}^{{\varvec{NPV}}} {\varvec{P}_{{\varvec{pvi}}} } } \right) \) ≤ 10 MW for distribution networks with a voltage level of 30 kV or 10 kV). The initial configuration of the 116 bus network is assured by opening the switches (116, 117, 118, 119, 121, 122, 123 and 124).

To determine the dynamic configuration of the Algerian network, it is necessary to have the daily values of the load and the PV production. For this reason, the measurements were made on 12/07/2017 to get the load and PV production profiles, the choice of this day is based on the highest consumption in the year. It should be mentioned that the PV source simulated in this study is located at the same location of the studied network (116 bus), called El-Hadjira source, which has been operational since 2017. The dynamics of the load laying the day (12/07/2017) is presented in Fig. 2. The Fig. 3 illustrates the dynamics of El-Hadjira PV production in the same day with a maximum total power output of 9986 kW.

Fig. 2.
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Dynamic curves of load profile

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Fig. 3.
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Dynamic curves of PV sources profile

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In the process of identifying an optimal configuration, the following steps must be followed: randomly select a network configuration by the GA method; a first test is performed for the feasibility of topological constraints by applying graph theory (see details in Ref [24]), if these constraints are satisfied, a power flow calculation (application of the Newton Raphson method) is used to determine the various electrical parameters, then the technical and security constraints (voltage and thermal limits of the lines) are verified. In the case of an unsatisfied constraint, the penalty of the objective function is necessary (see § 2.4) to exclude unfeasible solutions.

Following the different executions of the program under MATLAB software, the optimal parameters of GA used in this simulation are: population size is 100, maximum iteration is 200, crossover probability is 1, mutation probability is 0.01 and one point crossover.

The simulation results found by the GA method are displayed in the following Fig and tables. Table 1 shows the effectiveness of the proposed method comparable to the results found in previous work. Table 2 illustrates the simulation results of the reconfiguration of the 116 bus distribution network in the presence of PV installed over a 24-h period. Figures 4 and 5 shows respectively the hourly minimum voltages and the hourly active losses before and after the reconfiguration of the 116 bus network in the presence of PV sources in each hour. These curves illustrate the significant improvement in minimum voltages as well as the active losses caused by the reconfiguration of this network in the presence of PV source, particularly during the operation of PV in the day.

Table 1. The comparisons results with other works
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Table 2. D-DNR determined by GA method in presence PV sources
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Fig. 4.
figure 4

Hourly minimum voltage for 116_bus

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Fig. 5.
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Hourly total active loss for 116_bus

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The results given in Table 1 show the efficiency and robustness of the proposed method for minimizing active power losses, which encourages its use in practice. Table 2 shows that the configuration changes within each hour, this is because of the variation of the load and the PV production. During the interval of radiation presence between 07:00 and 19:00 (PV source operating period), the active power losses decrease significantly by up to 15% and therefore a significant enhancement in the voltage profile. In the same way, the more power injected by the PV source, the lower the active power losses and the better the voltage profile.

It should be noted that the qualities of smart grid (modern, automated and communicating) make it easy to vary the reconfiguration of its structure during the day. The optimization of the Algerian network configuration during the day is minimized the total losses from 5206.41 kW to 4675.63 kW which represents a reduction of 10.19%, this by no investment, it is only changing the state of the loop switches, which shows the importance of this task in modern distribution network (smart grid).

5 Conclusion

In this work, a hybrid genetic algorithm-graph theory is proposed in order to optimize D-DNR considering load and photovoltaic production variability during the day with objective to minimize of real power losses under technical, security and topological constraints. The effectiveness of this method is shown in the quality of the results comparable to the works of literature, by testing the algorithm proposed on IEEE distribution network (69 bus) and validating on real distribution network (116 bus). The usefulness of this management method stems from the fact that this reconfiguration does not require any heavy investment, it is only a way of exploiting equipment already existing in distribution network, especially since this task is becoming easier and easier in smart grid. As the future work is to propose to redo programming under industrial software like C++.