Chance constrained simultaneous optimization of substations, feeders, renewable and non-renewable distributed generations in distribution network
Introduction
By annual increasing of electricity demand in power systems, distribution network should be properly upgraded in order to meet the load growth as well as providing the better service for customers. Distribution network expansion planning (DNEP) is one of the most important solution to upgrade the distribution network which aims to bring these targets who involves in installing new substations or increasing the capacity of existing ones, feeder reinforcement and other cases. In the deregulated environment and by privatization of utilities, these goals should be carried out in such a way that the asset management programs be satisfied as much as possible. Low cost investment subject to technical and operational constraints in the system and also risk management is the main goal of asset management policies. On the other hand, the role of distributed generation (DG) units has become much more important with the deregulation of power industry [1]. These units have become an interesting option in DNEP problem to meet the technical requirements of system and could considerably improve the environmental and technical as well as economic issues of system.
Generally, the DNEP can be categorized into two main phases [2] namely: (i) substation planning and (ii) feeder routing problem. Several references have studied these two phases from various perspectives. As one of the first studies, Crawford in Ref. [3] introduced a mathematical technique to find the optimal size and location of HV/MV substations as well as their service area. In Ref. [4], reference network models (RNMs) are implemented for planning of large scale MV/LV substations. Uncertainty in load demand is taken into account in Ref. [5] in which fuzzy mathematics method has been employed to solve the substation placement problem. A new model incorporating a non-discrete function is introduced in Ref. [6] to model the total planning cost of distribution substations and defining its service areas.
The DNEP problem is complex and, by its nature, mixed integer, nonlinear and nonconvex as well as non-smooth. There is no consensus on which optimization method is more capable than others in solving the problem. In Ref. [7] by using distribution functions for load changes and daily hour cycle, the locations of substations are founded by probabilistic methodologies. For the first time in Ref. [8], the free capacity of medium voltage feeders is considered in the substation expansion planning problem and the related cost function. An approximated technique to solve the DNEP problem for large scale system has been proposed in Ref. [9] corresponding to branch exchange of the radial network. Optimal sizing, siting and timing of substations and feeders in DNEP are obtained by pseudo dynamic planning model in Ref. [10]. Feeder routing problem is discussed in order to expand of distribution system in Ref. [11]. Ref. [12] investigated large scale distribution planning problem by applying clustering technique to allocate the HV/MV substations and also dividing the network to mini-zones in order to improve the load grouping. A novel approach is addressed in Ref. [13] which considered the urbanity uncertainties and its minus effect on the distribution expansion and specifically the feeder routing problem. An optimal multistage planning model is applied to expand the distribution network in Refs. [14] and [15] considering the dynamic behavior of system parameters and geographical constraints. Also, the minimum spanning tree (MST) approach is considered in Ref. [14] to have an optimal radial structure in feeder routing issue. In Ref. [16], a risk based method relies on conditional value at risk (CVaR) technique and is utilized for optimal planning of distribution network in which different risk strategies are implemented and tested to show the impacts of risk analysis on the DNEP problem.
The DNEP problem can be solved through various ways such as single-objective or multi-objective models, bi-level framework, and also multistage programming. Furthermore, the DNEP models presented in the literature are either static or dynamic. In the static planning models, all investment decisions are made at the beginning of the planning horizon, while in the dynamic models the investment decisions determine during planning horizon time. A multi-stage DNEP in the presence of distributed generators (DGs) is introduced in Ref. [17] based on pseudo dynamic procedure. In Refs. [18] and [19] new two stage optimization methods are proposed for multiyear expansion planning in distribution system to determine the optimal size and site of DG units as well as HV/MV substations and MV feeders. In Ref. [20], a dynamic multi-objective model is proposed for DG integrated expansion planning of distribution system. Reliability and security of energy is considered in DNEP problem in Ref. [21] where the feeders are integrated with the DG units. By incorporating the renewable resources in DNEP, the islanding capability in the presence of these units and their uncertainties are considered to get more accurate solution [22]. A stochastic multi-objective approach based on Monte Carlo simulation (MCS) is applied to solve the DNEP problem in Ref. [23] to create a tradeoff between the cost and reliability in determination of the size and location of distribution substations and DG units.
However, the DNEP problem is investigated in previous references, but integrated DNEP and various DG units planning problem considering cost-reliability based objective is not reported simultaneously in previous literature. Also, they have not considered various objective such as reliability, economic and technical issues coordinately. Moreover, the uncertainties of the problem must be taken into account and the risk of uncertainty should be analyzed. To fill out these gaps, this paper proposes a novel joint chance constraint programming (JCCP) approach to cope with uncertainty in solving the simultaneous substation and DG placement (SSDGP) problem. The various objectives are considered in the proposed model such as investment costs, reliability cost and energy purchasing cost which have been mathematically formulated as Mixed Integer Non-Linear Programming (MINLP) and converted into a single-objective function through weighted sum method. Finally, the obtained model has been minimized by adaptive genetic algorithm. Thus, by applying the proposed JCCP based model the optimal size and site of HV/MV substations, feeders and DG units are determined whereas the risks associated with uncertainties are managed. JCCP has the capability of deriving the deterministic equivalent of related constraints and handling the risks associated with uncertainties that are inherent with SSDGP. These uncertainties include renewable resources generation, energy price and load growth and will be fully discussed in the next section. The main contributions of this paper can be summarized as follows:
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Adapting an innovative JCCP method to cope with the technical and financial uncertainties.
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Simultaneous determination of the optimal size and site of sub-transmission substations and various DG units along with robust MV feeder routing.
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Considering distinct objectives in the planning process such as investment costs, energy not supplied (ENS) cost and energy purchasing cost from upstream network.
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Harnessing the risk of uncertain parameters on the proposed DNEP problem using integrated JCCP and CVaR method.
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Converting the multi-objective formulation based on MINLP model into a single-objective function through weighted sum method.
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Utilizing an adaptive genetic algorithm based on Taguchi test method to minimize the proposed objective function.
The remainder of this paper is organized as follows. The problem formulation is presented in Section 2. The proposed JCCP method is explained in Section 3; The applied optimization algorithm is presented in Section 4 and Section 5 shows the obtained results of numerical simulations applied on the 54-bus test network. Finally, the conclusion is given in Section 6.
Section snippets
Uncertainty modelling
Before discussing about the applied objective functions, the uncertainties existing in the SSDGP and their modeling process are defined as follow:
Chance constraint method
The main advantage of JCCP method which has been developed by Charnes and Cooper [33], is to solve the nonlinear problems with uncertainties by converting the stochastic constraints into the deterministic equivalent. The JCCP enforces with permission for the solutions to exceed the constraints to some range, while the probability to meet these constraints is above an appointed confidence level. If x be a decision vector and ξ be a stochastic vector in which and n is the total
Proposed optimization algorithm
In this paper, an adaptive genetic algorithm (AGA) is employed to solve the proposed stochastic chance constrained optimization model. Furthermore, the Taguchi test method [35] has been utilized for optimal tuning of genetic algorithm parameters in order to reach the best optimal solution. The Taguchi method contains an analysis that discloses which of the factors are most effective in reaching the goals and the directions in which these factors should be adjusted to improve the obtained
Simulation results
In this section, the SSDGP problem using JCCP method is studied on the 20 kV 54-bus test distribution network [30] represented in Fig. 3. It contains two existing substation which totally support 8 load points. This network must be expanded in a planning horizon of 5 years to service the new load points and also meet the load growth. In this context, two candidate substations are considered. Conductor types candidate to be installed in network are given in Table 1 with their characteristic. The
Conclusion
A stochastic joint chance constrained framework for optimal distribution network expansion planning was proposed in this paper which aimed to simultaneous siting and sizing of multiple DG units and HV/MV substations planning accompanied with MV feeder routing problem. Owing to high degree of uncertainties and constraints that must be satisfied in the planning process, the JCCP method was implemented to handle these uncertainties and derive the deterministic equivalent of constraints. The
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