1. Introduction
The philosophies and techniques applied to the planning of medium-voltage (MV) and low-voltage (LV) distribution systems have evolved according to physical, economic, political, social, and environmental requirements. These requirements, which must be met by the distribution companies (DISCOs), relate to:
- The need to reduce the costs associated with distribution system planning, taking into account the different devices and equipment that can be integrated into the network during the planning and operation phases, such as distributed generation (DG);
- The reliability, continuity, and operational conditions of the system, imposed by the regulatory agencies;
- The need to reduce environmental impacts, especially those related to greenhouse gas emissions, considering renewable energy sources (RES) and losses and enabling the electrification of fossil fuel technology (e.g., transitioning to electric vehicles); and
- The growth of energy consumption globally, and so on.
In view of these requirements, RES need to be considered in the mathematical models of MV and LV distribution system planning. The connection of RES in distribution systems has a direct impact on planning decisions, reducing investment and operating costs, improving power quality and network reliability, and reducing environmental impacts [
1,
2,
3,
4,
5].
RES have become prominent in the modeling of distribution systems planning, due to a need for energy generation sources that meet the current environmental policies, competitiveness in energy commercialization, and the large volume of natural resources (sun and wind), available in certain regions [
1,
2,
3,
4,
5].
On the other hand, RES depend directly on climatic variables, which change constantly and, therefore, are difficult to determine accurately over a period of time [
4,
5]. Thus, considering RES in the planning phase can generate unreliable operation conditions of distribution systems. In this way, the mathematical models and solution techniques employed in distribution system planning have become even more complex. Hence, methodologies based on the generation of adequate scenarios are necessary to consider the variation of these climatic parameters in distribution system planning [
4,
5].
Therefore, variations in demand, wind speed, and solar irradiation parameters may lead to overcurrent in conductors, overvoltage and/or undervoltage in the system, and overpower in substations and distribution transformers. Therefore, it is necessary to propose distribution system planning methodologies that find solutions from an economic and robust point of view. In this paper, robust solutions are defined as solutions with a lower risk of exceeding the physical and operational limits of the distribution system. Thus, DISCOs can decide the most viable option in a technical and economical way among many possible solutions, taking into account the trade-off between these costs.
In the literature, there exist several works that have carried out distribution system planning with DG, considering them either as the property of DISCOs [
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26] or belonging to independent owners [
25,
26]. The different perspectives of distribution system planning with DG as operated by a DISCO include optimal allocation seeking power loss reduction [
6,
7,
8,
9], improvement of voltage and current levels [
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22], system reliability [
13,
21], maximum generation capacity [
23,
24], and analysis of the uncertainties related to RES [
4,
5]. In the case where DG belongs to independent producers, the objectives considered in the literature are mainly related to analyzing the impacts caused by them in distribution networks, aiming for a reduction of planning costs and system load growth, the maximum capacity of power injected by DG, implications in co-ordination, and control of distribution system protection, among other aspects [
25,
26].
Some works have addressed MV and LV distribution system planning including DG as two independent problems, considering DG owned by DISCO [
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26]. On the other hand, others works have carried out the planning of MV and LV systems together, without consideration of RES. Moreover, most of them have carried out MV/LV planning with many simplifications in the mathematical model, based on practical experience and the hierarchy of MV and LV planning problems [
27,
28,
29,
30,
31].
In the literature, there are some papers that have proposed methodologies to find more conservative planning solutions (due to the uncertainties related to demand and generation), which have used robust optimization, a totally different modeling methodology. In [
32], a robust planning methodology was proposed to identify the timing of feeder reinforcements. In [
33], a probability-weighted robust approach was proposed to optimize DG sizing and location under the worst uncertainty cases. In [
34], a robust chance-constrained approach was utilized to deal with the uncertainties of RES and loads. In [
35], a grey wolf optimization algorithm was applied to solve a robust design of microgrids with a reconfigurable topology under uncertainties.
In this paper, due to the uncertainties related to system demand and the power generated from RES, a robust planning index is proposed. This index is a new approach that seeks to find conservative solutions for distribution system planning. The advantages of this index, compared to other techniques in the literature, are:
(1) the mathematical formulation of this index is ease to solve;
(2) the robust planning index allows us to achieve solutions with a lower risk of overpower in substations and distribution transformers, overcurrent in conductors, and overvoltage and undervoltage at consumption points; and
(3) this index allows DISCOs to choose the level of robustness in the planning solutions.
The main objective of this paper is to present a methodology to carry out the MV and LV distribution system planning together, considering the existence of RES belonging to independent owners connected to the MV and LV networks. The proposed formulation seeks to obtain a single solution that contemplates MV/LV integrated planning. Furthermore, instead of proposing a robust optimization model, we propose an index that allows us to find robust and reliable planning solutions with lower risks of overcurrent, overpower, overvoltage, and undervoltage.
The main contributions of this paper, when compared with others in the literature, are:
- We propose a robust planning index, with the aim of finding robust planning solutions and reducing the risk of overpower, overvoltage, undervoltage, and overcurrent due to variations in system demand and power generation from RES, which occur during system operations;
- We propose a decomposition approach in the solution search process to solve the MV/LV distribution system planning problem;
- We consider RES in the MV/LV distribution system planning; namely, wind generators in the MV system and solar generators in the MV and LV systems owned by independent producers;
- We consider the costs of poles, support structures, and the installation of shared lines in the MV/LV distribution system planning (where shared lines are defined as lines in which there are MV and LV cables); and
- We obtain the relationship between investment and operation costs versus the robustness of each proposed solution in the MV/LV distribution system planning. In this way, DISCOs can choose the most viable and reliable system design.
MV/LV distribution system planning is a mixed-integer non-linear programming problem. The proposed planning framework in this paper aims to minimize the costs of investment (substations, distribution transformers, poles, support structures, and MV and LV cables) and operation (power losses from cables, substations, and distribution transformers) while maximizing the robustness of the solutions. The constraints in the mathematical formulation were derived from [
27,
28,
29,
30,
31], which include:
- Physical: the capacity of installed equipment, such as substations, distribution transformers, cables, support structures, and so on;
- Operational: voltage and current levels, load balancing among the distribution system phases, and maximum generation capacity of RES and connection ratios (voltage and current) in distribution transformer installation nodes; and
- Economical: the financial resources available to perform the MV/LV distribution system expansion planning.
The mathematical formulation used in this paper is not convex. Due to the great computational complexity of this formulation, with a large number of binary variables and constraints, it becomes extremely complicated to solve it using classical optimization techniques [
36]. Thus, in this paper, an MV/LV planning decomposition search with a general variable neighborhood search (GVNS) metaheuristic is used to solve this problem. Planning action encoding is performed using the node-depth representation, which allows us to store the network topologies obtained by the neighborhood structures from GVNS in a fast and efficient way [
37].
The paper is organized as follows.
Section 2 presents the scenario generation methodology.
Section 3 presents the robust planning indices.
Section 4 presents the mathematical formulation of the MV/LV distribution system planning.
Section 5 presents the proposed solution technique for solving the mathematical model.
Section 6 presents the numerical results obtained from an integrated test system, with 50 nodes connected in MV and 410 nodes in LV.
Section 6 also performs a detailed analysis of the numerical results obtained with the case studies, showing the main differences among them.
Section 7 presents the conclusions obtained.
3. Robust Planning Indices
RES allocation can generate several benefits for distribution systems. The scenario generation methodology used in this work considers that demand, wind speed, and solar irradiance parameters are selected when considering the mean values of each segment. As they are mean values, these parameters are below the maximum and above the minimum values, when compared with the historical data of each segment [
4,
5].
On the other hand, the variables related to demand and wind and photovoltaic energy generation may have variations throughout the operational scenarios, due to the uncertainties related to consumption profiles and power generation depending on solar irradiation and wind speed factors. In addition, a significant increase in system load may also occur. However, due to their physical capacity limits, the substations, transformers, and cables in the system may not be able to provide the necessary power for the distribution system. Similarly, a voltage drop or rise may occur in the distribution system. For very complex problems, such as MV/LV distribution system planning, which involves many integers and continuous and binary variables, a limited number of scenarios should be used due to the computational time required to evaluate them. Therefore, it is necessary to perform more investments in the distribution system to meet the system load. In this way, this paper presents a methodology that allows us to find conservative planning solutions through a robust planning index. This index allows us to estimate the robustness cost associated with each planning solution; that is, finding a solution that is more resistant to variations in system demand and power generation. Thus, with this index, the planning solution provides less risk to exceed the allowable voltage levels in the nodes, currents in the cables, and power limits in substations and distribution transformers.
Equations (
1) and (
2) are based on the robustness indices of substations (RS) and distribution transformers (RT), respectively. These indices calculate the power available at each equipment (i.e., substation or transformer) to reach the maximum capacity. By maximizing Equations (
1) and (
2), the risk of overpower in the distribution system is minimized.
The robustness indices of the cables installed in MV (RCM) and LV (RCL) systems are proposed by maximizing Equations (
3) and (
4), respectively. These equations ensure that the greater the difference between the current through the cable and its maximum capacity, the lower the risk of overcurrent.
Equations (
5) and (
6) are based on the voltage deviations of the MV (DMV) and LV (DLV) systems, respectively. These equations ensure that the closer the voltage is to the limits, the greater the risk of overvoltage and undervoltage in the distribution system. Therefore, by minimizing the voltage deviation from its nominal value, we improve the voltage regulation of the network.
Equation (
7) proposes an index based on the power injected into the network by RES (PIDG). This equation ensures that the higher the power injected from RES, the greater the risk associated with each planning solution. Therefore, this equation must be minimized.
The sum of Equations (
1)–(
7) determines the robust planning index (RPI), which is presented in Equation (
8). As
, Equations (
5)–(
7), which are minimizations, are transformed into maximizations to compose the RPI.
4. Problem Formulation
The mathematical model of the MV/LV distribution system planning considering RES can be written as a bi-objective formulation, with a weighting factor (
) between the investment and operation costs and the robustness of the solution in the objective function (Equation (
9)). As the mathematical model is bi-objective, the factors of costs and robustness do not need to be in the same units of measurement in the objective function.
The objective function in Equation (
9) consists of the fixed costs of substations (CS), distribution transformers (CT), and cables (CF); the variable costs of power losses in substations, distribution transformers, and cables (CL); and the robust planning index (RPI). As the RPI must be maximized, it is incorporated into the objective function (Equation (
9)) as a negative value. Variable costs are annualized in the mathematical formulation, due to the power loss costs of each year, while fixed costs are not annualized as they are realized only once (i.e., at the beginning of system planning). RPI is not annualized because it is an index that measures the robustness of system planning. The mathematical formulation of the MV/LV distribution system planning is:
where:
- CS: investment costs of construction or repowering substations, described in (
10);
- CT: investment costs of installation or exchange distribution transformers, described in (
11);
- CF: costs of MV and LV feeders, which include the installation and exchange of MV and LV cables (including isolated and shared cables, poles, and MV and LV supporting structures), as described in (
12);
- CL: costs of power losses (Equation (
13)), which include losses in MV cables (Equation (
14)) and LV cables (Equation (
15)), substations (Equation (
16)), and distribution transformers (Equation (
17));
- RPI: robust planning index of the MV/LV system planning, as described in Equation (
8);
subject to:
- Kirchhoff’s laws, represented by the static power flow equations (in each operation scenario of the planning horizon) described in Equations (
18)–(
21);
- Physical and electrical voltage and current constraints associated with the connection points of MV and LV systems (including the adjustment of tap transformers) described in Equations (
22)–(
24);
- The maximum operating capacity of substations and distribution transformers in each operation scenario of the planning horizon, represented in Equations (
25) and (
26), respectively;
- The maximum current limits in MV and LV cables (in each operation scenario of the planning horizon), described in Equations (
27) and (
28), respectively;
- The maximum financial resources available that can be allocated to carry out the MV/LV distribution system planning, described in (
29);
- The maximum and minimum voltage limits allowed at the MV and LV consumption points (in each operation scenario of the planning horizon), described in Equations (
30) and (
31), respectively;
- The uniqueness of the equipment installed in the distribution system for each planning action (e.g., transformers, conductors, and substations), in addition to the binary nature of some variables related to the planning, represented in Equations (
32)–(
36);
- Limits of active and reactive power from RES (in each scenario operating on the planning horizon), described in Equations (
37) and (
38), respectively;