A comparative analysis of generation and transmission expansion planning models for power loss minimization

Abstract

In modern power systems, renewable energy resources are becoming more relevant due to their eco-friendly nature and sustainable electrification. Therefore, it is important to consider the effects of the renewable energy resources (RERs) on the generation expansion planning and transmission expansion planning (GTEP) simultaneously. The proper assessment of power losses is essential in order to adequately evaluate the consequence of renewable energy resources in power systems. This paper presents multi-objective optimization problems that are solved using DC, modified DC and AC modelling methods in order to accurately and efficiently compute electrical losses and its impacts on the expansion planning procedure. This paper develops a Mixed Integer Non-linear Programming (MINLP) problem and was solved using CONOPT and CPLEX solvers embedded in Algebraic Modelling Language. The proposed methods are evaluated and validated on three case studies: IEEE Garver’s 6 bus system, IEEE 24 bus test system and a real-world Nigeria Power System. A comparative analysis of the three modelling approaches and a sensitivity analysis of the simulation results indicate that AC solution method provide an accurate computation of power losses and efficient optimal planning strategy as compared to the modified DC method.

Introduction

The integration of RERs in power systems can provide solutions to some of the challenges facing conventional power generation such as power quality, voltage instability, electrical losses and environmental pollution. Since the grid was not initially made for RERs, there is a need to give attention to the generation and transmission network expansion so as to effectively accommodate the RERs on the power grid [1], [2]. Generation expansion planning (GEP) problem is the determination of the type, capacity and location of prospective generating units to be built within a planning period to satisfy the growing load demand. Transmission expansion planning (TEP) problem is defined as aims of determining the best strategy for proper choice of new transmission lines that should be built so as to aid smooth power transfer between the generation and consumers as well as meet the growing energy demand whilst satisfying the technical and economic transmission network constraints.

The development of RERs has introduced some random and non-random uncertainties on the power grid. Therefore, it is important to consider the RERs impact on the system operating characteristics of the grid which are electrical losses, power dispatch and voltage magnitudes. Electrical loss is a main factor for power system expansion. Losses on the transmission line can hinder the power flow on the grid, thereby affecting the yearly load growth rates, inflation of power system investment and optimal power scheduling [3], [4], [5]. Hence, the proper assessment of power losses is essential in order to adequately evaluate the consequence of RERs in power grid. More importantly, the expansion of both generation and transmission networks should reflect the changes that is, uncertainties brought by RERs in the power system. In the past few decades, many studies have been done on GEP and TEP with most common objective function on minimizing the costs of building new power plants and new transmission lines respectively. Those objectives do not reflect the impacts of RERs in power system. Hence, this paper presents objective function that consider the investment cost, operating cost and power losses whilst satisfying the economic and technical constraints.

Generally, there are two widely used modelling system operation methods for both GEP and TEP problems which are DC model and AC model [6]. The DC model is a simple and fast model with easy of power flow computation and does not have convergence problem [7]. The AC model is most accurate, consisting of active and reactive power for calculating the electrical loss in the power system [8]. Both models have their drawbacks, DC model though simple and fast, but lack the ability to compute the power loss properly because the reactive power is always neglected. On the other hand, AC model leads to robust and complex NLP problem, giving rise to convergence problem and requiring large computation time. Many studies have applied DC model; Ref. [9] presents a DC model for TEP problem dealing with the uncertainties associated with generating capacity and demand using a two-stage optimization approach. Ref. [10] presents a scenario-based selection approach to achieve an optimal investment decision in a TEP problem. Ref. [11] presents a DC model for GEP problem with consideration to additional generating units in the power grid. In [12], a multi-objective DC model is proposed for GEP problem considering high percent of RERs. In Refs. [13] and [14], a method based on DC model for generation and transmission expansion planning considering the impacts of incorporating the RERs and demand response into the grid.

Similarly, an AC model have been applied to many researches. Ref. [15] presents a probabilistic TEP model with Distributed Generator (DG) and demand response in an AC based model. Ref. [6] proposes a non-linear AC model for TEP with emphasis on the evaluation of the system load flow. Ref. [8] presents an AC power flow model for a security constrained TEP problem. The optimization problem aims at reduce the number of solutions for the power flow. In [16], a methodology was developed for an AC based model for TEP problem. A linearization approach and NLP relaxation models were developed to solved the MINLP problems. Ref. [17] presents an AC based model for TEP problem in a deregulated electricity market with consideration to different level of uncertainties such as wind power generating units and load. Ref. [18] proposes a MINLP AC based model for generation and transmission expansion planning system. The model proposed minimizes the electrical losses, nodal marginal prices and harmonics contribution from RERs. In [19], a methodology is presented for minimizing costs and power outages in an AC based MINLP model for both expansion planning problems. The uncertainties associated with RERs and the transmitting medium were solved using multi-state Markov model. The non-linearity and complexity associated with AC model especially when considering classical optimization approach and the lack of consideration of power losses in DC model led to linearized approximation of power losses in DC model referred to as modified DC model. Therefore, in order to have less computation time and at the same time have accurate electrical loss assessment on the transmission line, most authors used modified DC model. Ref. [20] presents a modified DC model for TEP problem considering large-scale RERs with emphasis on linearization of power losses on the transmission line. Ref. [21] proposes a novel evolutionary algorithm for solving TEP problem. The optimization formulation considers a DC model with linearized transmission losses. In [22], a DC based TEP model with consideration to transmission losses and storage system was presented.

In order to solve the expansion planning problems, many optimization methods have been adopted such as mathematical and meta-heuristic optimization techniques. In mathematical optimization techniques, the optimality of GEP and TEP solutions are guaranteed but may not be able to solve a sophisticated optimization problem. This method includes linear programming (LP) [23], mixed integer linear programming (MILP) [24], mixed integer quadratic programming (MIQP) [13], NLP [25], MINLP [19], quadratic programming (QP) and bender’s decomposition (BD) [26], [27]. Meta-heuristic optimization methods are insensitive to the optimized model and most time do not guarantee an optimal GEP and TEP solutions, but they can render a better performance in terms of accurate computation time and better solutions [28]. Examples are non-dominated sorting genetic algorithm (NSGA) [29], particle swarm optimization (PSO) [30], evolutionary programming (EP) [31], Ant colony optimization (ACO) [28], artificial Immune systems (AIS) [32], simulated annealing (SA) [3], tree searching heuristic algorithm (TSHA) [33], gravitational search algorithm (GSA) [34] and imperialist competitive algorithm [35]. Both the mathematical and meta-heuristic based optimization techniques are widely employed for solving expansion planning problems.

A non-linear programming method was presented in [25] to solve TEP problem in an electricity market which is aimed at identifying the most effective prospective transmission lines to be constructed. In Ref. [22], a one stage TEP problem with transmission line losses and storage systems was investigated. MILP approach was used for solving the TEP problem. Ref. [29] presents a TEP upgrades considering the reliability assessment of wind farms and operational cost of the system. A NSGA optimization technique is proposed to achieve the Pareto front solution of the multi-objective problem. Ref. [35] presents a hybrid of sequential quadratic programming and ICA optimization techniques for a TEP problem containing RERs. The optimal power flow problem seeks to minimize the operation cost and system emissions. An Integer based PSO optimization approach was proposed in [36] for solving a TEP problem in Egyptian power system network. A combination of Fuzzy logic and Artificial neural network was used for load prediction for a long time whilst the optimization technique aimed at securing an optimal transmission path with minimum cost to meet the predicted load forecast. A gravitational search algorithm is applied to GEP model in [37], where an economic incentive associated with RES and its effects on the social welfare of the utilities and consumers. A reliability based GEP is presented in [38] and was solved using modified SFLA. A mapping process and encoding are adopted to enhance the proposed algorithm performance. Ref. [39] presents a SFLA for a multi-objective probabilistic TEP model considering wind power. In [40], a branch and bound algorithm was presented for solving an AC based TEP problem. A semidefinite relaxation of the OPF was employed for reduction of the computation time of the optimization process. Ref. [41] presents a novel constructive heuristic algorithm for solving a GTEP model with incorporation of distributed generation (DG).

Optimization models is an important factor in deciding the appropriate expansion planning decisions in a system operation through a DC model or AC model. Both DC and AC solution approaches has been widely used for formulating TEP models. The DC model gives a linear optimization formulation that assure the optimality of the solution approach when solving TEP problems, but often exhibit the inability to verify the voltage limit violations. However, the presence of power losses on the transmission lines may alter the operational dispatch of the power generation and thereby influence the transmission expansion planning procedure. Few literatures discussed the application of AC model in solving GTEP problems. The benefit of developing a TEP problem in an AC model is that the AC model presents a better approach for solving optimization problem with accurate representation of the power system network. The main drawback of AC model is that the approach does not guarantee an optimal solution owing to its nonlinearity and non-convex characteristics leading to large size and variables of the optimization problems that can lead to several expansion decisions. In order to ensure simplicity and render an efficient means of power loss calculation, a modified DC model is introduced. Therefore, this paper presents a comparative analysis of the three modelling methods for effective calculation of power losses and for achieving the best planning approach. Therefore, the key contributions of this paper are listed as follows:

• Providing analysis and comparison between the three modelling techniques as a means of solving the GTEP problems with presence of RERs in order to achieve the best planning approach.

• Developed a novel modified DC method to effectively compute the transmission line losses in a linearized approximation form.

• Developed multi-objective optimization function such as capital cost, operation cost, emissions and power losses and their impacts in the GTEP procedure.

• Considering the three modelling approaches such as DC, modified DC and AC modelling methods in solving the optimization problems for a real-world Nigeria Power System.

The remainder of the paper is structured as follows: Section 2 describes the mathematical modelling of GTEP problems considering different techniques such as DC, modified DC and AC modelling techniques. The simulation, case studies and the numerical results are presented in Section 3 to compare the three modelling approaches used in solving the optimization problems. The concluding remarks are given Section 4.