Transmission Expansion Planning Problem Research Articles

A MILP-based heuristic algorithm for transmission expansion planning problems

In the last years, a lot of effort was placed into approximated or relaxed models and heuristic and metaheuristic algorithms to solve complex problems, mainly with non-linear and non-convex natures, in a reasonable time. On one hand, approximated/relaxed mathematical models often provide convergence guarantees and allow the problem to be solved to global optimality. On the other hand, there is no guarantee that the optimal solution of the modified problem is even feasible in the original one. In contrast with that, the metaheuristic algorithms lack mathematical proof for optimality, but as the obtained solutions can be tested against the original problem, the feasibility can be ensured. In this sense, this work brings a new method combining exact solutions from a Mixed-Integer-Linear-Problem (MILP) Transmission Expansion Planning (TEP) model and stochastic solutions from metaheuristic algorithms to solve the non-linear and non-convex TEP problem. We identify the issues that came up with the linear approximations and metaheuristics procedures and we introduce a MILP-Based Heuristic (MBH) algorithm to overcome these issues. We demonstrate our method on a single-stage TEP with the RTS 24 nodes and on a multi-stage TEP with the IEEE 118 nodes test system. The AC TEP solution was obtained using Evolutionary Computation, while the DC TEP solution was obtained using a commercial solver. From the simulations results, the novel MBH method was able to reduce in 42% and in 85% the investment cost from an evolutionary computation solution for the single-stage and multi-stage TEP, respectively.

A New Global Solver for Transmission Expansion Planning With AC Network Model

To design a reliable and secure power system, it is necessary to have enough transmission capacity. The solution of transmission expansion planning (TEP) problem determines cost-optimal investment in future transmission equipment. In this paper, we propose a new global solver, named Global-TEP, for the TEP problem with an AC network representation (ACTEP), which is a mixed-integer nonlinear programming problem. The proposed solver is based on second-order cone relaxation, enhanced relaxation tightening constraints, and optimization-based/feasibility-based bound tightening techniques. Multiple enhanced relaxation tightening constraints are incorporated into the mixed-integer second-order cone relaxation of TEP in order to obtain a very strong relaxation as the lower bounding problem. In addition, a novel feasibility-based bound tightening technique is proposed to tighten the bounds of decision variables in a considerably short runtime. Finally, introducing a novel application of optimization-based bound tightening technique, Global-TEP is constructed that can solve the ACTEP problem efficiently with a guaranteed optimality gap. As illustrated by numerical case studies, Global-TEP is more scalable, more flexible, and much faster than the available global solvers.

Hybrid robust/stochastic transmission expansion planning considering uncertainties in generators’ offer prices: A second-order cone program approach

The aim of this paper is to propose a hybrid robust/stochastic model for transmission expansion planning (TEP) problem. The uncertainties related to demand and wind are modelled via stochastic programming (SP), while the uncertainties associated with the generators’ offer prices are modelled via robust optimization (RO). In this sense, an ellipsoidal uncertainty set is considered which the offer price values are known to lie in these given ellipsoids. The model presented is then divided into a master problem and several independent subproblems using a tailored implementation of Bender's decomposition (BD) method. Robust linear constraints of the lower level problems are then transformed into a convex second-order cone programming (SOCP) problem. We will apply the proposed model to IEEE-118 bus power system showing that generators’ offer price and their correlation can considerably affect the optimal plan of the transmission planning. It is observed that considering correlation among generators’ offer prices would not necessarily yield more expensive expansion plan in comparison with the case where correlation is ignored. Indeed, increase or decrease in investment cost depends on the entries of the variance-covariance matrix, network topology and the location of generators. Moreover, the results show the computational efficiency of the robust convex model.

Robust transmission expansion planning model considering multiple uncertainties and active load

Uncertainty must be well addressed in transmission expansion planning (TEP) problem, and it significantly affects the reliability and cost-effectiveness of power systems. Owing to the complex operating environment of power systems, it is crucial to consider different types of uncertainties during the planning stage. In this paper, a robust TEP model is proposed by considering multiple uncertainties and active load. Specifically, in this model, the uncertainties of wind power output and contingency probability are considered simultaneously. The uncertainties are described by scenario and interval, and the Benders decomposition technique is applied to solve the model. The feasibility and effectiveness of the proposed model are illustrated using the IEEE RTS and IEEE 118-node systems.

A coordinated scheme for transmission and distribution expansion planning: A Tri-level approach

In traditional power system planning problems, transmission and distribution networks are separated, which is not suitable for future power systems due to the rapid development of active distribution networks. This paper presents a hierarchy framework to optimize the transmission and distribution network expansion in a simultaneous manner. The proposed decentralized decision-making architecture forms a Tri-level structure where the first level is the transmission expansion planning (TEP) problem solved by the transmission system operator (TSO) as the leader, while the second level is the distribution expansion planning (DEP) problem solved by the distribution system operators (DSOs) as the second level followers. The third level problem is the optimal economic dispatch problem solved by the independent system operator (ISO) as the third level follower. The economic dispatch problem is replaced by its primal-dual (PD) formulation leading to a bilevel multi-follower mixed-integer linear programming (BMF-MILP) problem. Then, by using multi-parametric programming (MPP) method, the BMF-MILP problem is recast as several single level independent optimization problems. Numerical experiments are shown to corroborate the efficiency and tractability of the presented model. The results show the new coordinated transmission and distribution expansion planning (CTDEP) model provides additional flexibility and reduces the total cost.

Renewable Generation and Transmission Expansion Planning Coordination with Energy Storage System: A Flexibility Point of View

This paper presents a method for coordinated network expansion planning (CNEP) in which the difference between the total cost and the flexibility benefit is minimized. In the proposed method, the generation expansion planning (GEP) of wind farms is coordinated with the transmission expansion planning (TEP) problem by using energy storage systems (ESSs) to improve network flexibility. To consider the impact of the reactive power in the CNEP problem, the AC power flow model is used. The CNEP constraints include the AC power flow equations, planning constraints of the different equipment, and the system operating limits. Therefore, this model imposes hard nonlinearity onto the problem, which is linearized by the use of first-order Taylor’s series and the big-M method as well as the linearization of the circular plane. The uncertainty of loads, the energy price, and the wind farm generation are modeled by scenario-based stochastic programming (SBSP). To determine the effectiveness of the proposed solution approach, it is tested on the IEEE 6-bus and 24-bus test systems using GAMS software.

Transmission planning with security criteria via enhanced genetic algorithm

This paper proposes an enhanced genetic algorithm model, named EGA-TEP, to solve the transmission expansion planning (TEP) problem of electric power system networks. Heuristic information is integrated into the evolutionary process of metaheuristic to improve the expansion plans (solutions). This heuristic information is translated in the form of sensitivity indices, based on the circuit loading/overloading and observed load shedding, considering both the intact network and the “N-1” contingency operating conditions (security criteria). In addition, an iterative process of evolutionary runs (ERs) is adopted as the basis for designing the EGA-TEP. These contributions make the optimization tool more robust and ready to handle different types of systems. The efficiency of the proposed EGA-TEP tool is consistently evaluated through performance statistical indices. Results obtained with systems with different characteristics and dimensions are presented and widely discussed.

On the Improvement of representative demand curves via a hierarchical agglomerative clustering for power transmission network investment

This paper introduces an optimal clustering-based strategy to gain representative demand curves from hourly demand data that allow determining the power transmission network investment by solving the transmission expansion planning (TEP) problem. The proposed approach also provides a high-dimensionality data optimal reduction for the representative demand curves that feed the TEP problem. The key idea behind this strategy is to extract demand patterns from the electric power system demand data through the implementation of a hierarchical agglomerative clustering algorithm (HACA) based on the Elbow’s rule and a linkage criterion, such as Ward’s variance. Then, a 24-h demand pattern is provided by following three different grouping strategies: seasonal, monthly, and weekly. As a second stage, this strategy includes the TEP formulation together with the transmission losses’ linearised model aiming to test the representative demand curves achieved by HACA. To illustrate the efficiency, application, and superior functionality of the proposal, this is implemented over the IEEE 118-node network under several case studies. To determine the most appropriate approach, the results are compared with the well-known K-means method.

Transmission Expansion Planning Considering Power Losses, Expansion of Substations and Uncertainty in Fuel Price Using Discrete Artificial Bee Colony Algorithm

Transmission expansion planning (TEP) is an important part of power system expansion planning. In TEP, optimal number of new transmission lines and their installation time and place are determined in an economic way. Uncertainties in load demand, place of power plants, and fuel price as well as voltage level of substations influence TEP solutions effectively. Therefore, in this paper, a scenario based-model is proposed for evaluating the fuel price impact on TEP considering the expansion of substations from the voltage level point of view. The fuel price is an important factor in power system expansion planning that includes severe uncertainties. This factor indirectly affects the lines loading and subsequent network configuration through the change of optimal generation of power plants. The efficiency of the proposed model is tested on the real transmission network of Azerbaijan regional electric company using a discrete artificial bee colony (DABC) and quadratic programming (QP) based method. Moreover, discrete particle swarm optimization (DPSO) and decimal codification genetic algorithm (DCGA) methods are used to verify the results of the DABC algorithm. The results evaluation reveals that considering uncertainty in fuel price for solving TEP problem affects the network configuration and the total expansion cost of the network. In this way, the total cost is optimized more and therefore the TEP problem is solved more precisely. Also, by comparing the convergence curve of the DABC with that of DPSO and DCGA algorithms, it can be seen that the efficiency of the DABC is more than DPSO and DCGA for solving the desired TEP problem.

Bacterial Foraging Algorithm & Demand Response Programs for a Probabilistic Transmission Expansion Planning With the Consideration of Uncertainties and Voltage Stability Index

The rapid growth of the power system with respect to many uncertainties has made the transmission expansion planning (TEP) problem more tedious. This article proposes a novel holistic method to solve the TEP problem in the deregulated market environment considering uncertainties at the load side. A mixed-integer nonlinear programming model has been considered in solving the raised issue. A bacterial foraging algorithm has been employed to optimize the problem. Considering the nature of the power system, applying the ac power flow model is a necessity in optimizing the problem in order to obtain applicable results. Distributed generations (DGs) have been included at the load side to satisfy the variation in the demand. Demand response programs (DRPs) have been considered to reduce the cost and increase the closeness between customers and the utility side. Furthermore, this work uses the Monte Carlo simulation (MCS) to handle the uncertainties associated with DGs and DRPs at the load side. A voltage stability index study through PQVSI is carried out to ensure the applicability and stability of the considered plan. A comprehensive planning framework is obtained by testing the proposed method on the Colombian 93-bus test system. The use of DGs and DRPs has a significant impact on reducing the overall expansion plan of the network.

Long term transmission expansion planning to improve power system resilience against cascading outages

A Transmission Expansion Planning (TEP) problem is proposed to find the optimal configuration of the transmission network with considering security and resilience constraints. Due to the importance of blackouts and cascading failure, the proposed Resilient TEP (RTEP) minimizes the effects of cascading outages in term of load curtailment. In order to estimate the size of cascading outages, based on the total lost load, an iterative algorithm is proposed to analyze and simulate the steady state mechanism of cascading outages. A set of initiating events are defined as the triggering points of the cascading failure and the consequent chain of related outages are identified to determine the blackout size. In addition to the resilience constraints, the security constraints based on N-1 security criterion are also considered. Based on the Benders Decomposition (BD) algorithm, a multi-stage solution procedure is developed to handle the investment decisions, security constraints, and resilience requirements efficiently. In order to achieve the optimal resilient TEP configuration, all the master and sub-problems are formulated as Mixed Integer Programming optimization models. The proposed RTEP is implemented over the IEEE 24-bus test system.

Robust nonlinear mathematical transmission expansion planning based on German electricity market simulation

Requirements on electrical energy transmission and the work of system operators are changing due to the shift from centralized towards decentralized generation. This leads to an increased need of transport capacities in grids. In this paper, a robust method is presented to solve the resulting transmission expansion planning (TEP) problem using a nonlinear mathematical optimization. In terms of TEP optimization successive measures are considered in the used mathematical formulation such as grid optimization, grid enhancement and grid extension. The mathematical optimization is based on a DC power flow formulation using unreduced grid models. The concept of the TEP model design and the implementation of different measures are given in detail in the paper. The applicability of the developed approach is shown by the application to a model of the German transmission grid based on a German electricity market simulation for a yearly simulation calculating an expansion demand of 3047 GWkm.

Tight convex relaxation for TEP problem: a multiparametric disaggregation approach

In recent years, there has been an increasing interest in using AC power flow equations for the transmission expansion planning (TEP) studies. The AC power flow equations are quadratic and hence the TEP problem can be formulated as a mixed-integer quadratically constrained programme. Therefore, the complexity of the TEP problem lies in the non-convexity of AC power flow equations in which the global optimal solution is not guaranteed to be found. This study aims at proposing a tight convex relaxation for the TEP problem. In this context, first, the TEP problem is formulated as a mixed-integer bilinear problem by representing the complex bus voltage in its rectangular coordinates. Second, the multiparametric disaggregation technique (MDT) and piecewise McCormick relaxation are employed to generate a mixed-integer linear relaxation. MDT is based on the discretisation of the domain of one of the variables in every bilinear term. The method presented is much more precise compared with the DC or other linearisation approaches, while the optimal solution is of high quality. The results of the case studies show the tractability and exactness of the proposed model as well as its superiority over the state-of-the-art schemes.

A multi-period composite generation and transmission expansion planning model incorporating renewable energy sources and demand response

This study presents an evaluation of the potential impacts of Renewable Energy Sources (RES) and Demand Response (DR) on the Generation and Transmission Expansion Planning (GTEP) problem. This is highly essential in order to increase RES penetration in power systems thereby ensuring long term energy security and emissions reduction. GTEP with demand response is jointly considered so as to achieve an optimal expansion strategy for power systems by assisting the system planner make decisions about power system investments in order to meet the desired electricity demand. Therefore, the proposed model considers several levels of DR penetration in the planning system in order to assess its impact on the system performance. A multi-period multi-objective GTEP model was proposed and formulated as a Mixed Integer Quadratic Programming (MIQP) Problem. The developed MIQP was solved using the CPLEX 12.8.1 solver and is tested on two practical case studies: IEEE 24-bus and the real-world Nigerian Power system. Sensitivity analysis was performed on the system performance of the proposed model and the results indicate that an increase in penetration of DR resources in the planning procedure causes a decrease in the power generated, emissions and system costs whilst increasing RES utilization in power system.

Hybrid Binary PSO for Transmission Expansion Planning Considering N-1 Security Criterion

This paper presents an hybrid method based on the metaheuristic Particle Swarm Optimization (PSO) and quadratic programming (QP) for solving the multi-stage transmission expansion planning (TEP) problem. PSO solves the investment problem and QP solves the operational cost problem. Transmission losses and the N-1 security criterion are included in this model to give a more comprehensive approach. Undertaking a complete N-1 security analysis for any network topology is time consuming. To improve the convergence speed and to reduce computational effort, Line Outage Distribution Factors (LODF) are used to calculate the line's post-contingency power flows. The proposed approach is initially validated through numerical simulations of the classic Garver's system, and its performance is later tested and compared with other in the literature on the IEEE 24-bus system.

Optimal planning of renewable energy systems for power loss reduction in transmission expansion planning

Purpose The purpose of this study is to address the efficiency of power losses representation while still reducing the computational burden of an optimal power flow (OPF) model in transmission expansion planning (TEP) studies. Design/methodology/approach A modified TEP model is formulated with inclusions of linearized approximation of power losses for a large-scale power system with renewable energy sources. The multi-objectives function determines the effect of transmission line losses on the optimal power generation dispatch in the power system with and without inclusion of renewable energy sources with emphasis on minimizing the investment and operation costs, emission and the power losses. Findings This study investigates the impact of renewable energy sources on system operating characteristics such as transmission power losses and voltage profile. Sensitivity analysis of the performance for the developed deterministic quadratic programming models was analyzed based on optimal generated power and losses on the system. Research limitations/implications In the future, a comparison of the alternating current OPF and direct current (DC) OPF models based on the proposed mathematical formulations can be carried out to determine the efficiency and reduction of computation process of the two models. Practical implications This paper proposed an accurate way of computing transmission losses in DC OPF for a TEP context with a view of achieving a minimal computation time. Originality/value This paper addresses the following objectives: develop a modified DC OPF with a linearized approximation of power losses in TEP problem with large integration of RES. Investigate the impact of RES on system operating characteristics such as transmission power losses and voltage profile.

An efficient method for Contingency-Constrained Transmission Expansion Planning

This paper proposes an efficient method based on a mixed-integer linear programming (MILP) model to solve the multistage Contingency-Constrained Transmission Expansion Planning (CCTEP) problem. To account for security, an iterative algorithm based on Line Outage Distribution Factors (LODF) screens the worst-case contingency (either in existing or candidate lines) and dynamically adds constraints to the Transmission Expansion Planning (TEP) formulation to enforce the security criterion, reducing both the number of decision variables and simulation times with respect to alternative approaches. Transmission losses are included through the use of piecewise linear expressions. Furthermore, operational flexibility of generation resources is considered through the use of representative daily load curves (RDLC) to allow modeling of generator ramping constraints. The method is initially illustrated and validated through numerical simulations of the classic Garver’s system. Then, the IEEE 118-bus and 300-bus systems are used to test its performance. The proposed approach can avoid under-investment in network capacity caused by neglecting transmission losses, security, and flexibility constraints.

A Novel Salp Swarm Algorithm for Expansion Planning with Security Constraints

Transmission expansion planning (TEP) is one of the critical issues of the deregulated electricity market. In view of this, a salp swarm algorithm (SSA) is being considered in the present work for the solution of TEP problem with the added security constraint. The features of SSA algorithm are its foraging behavior of salps swarming in the oceans. Under the TEP problem, the work considered here is to determine the cost-effective expansion planning in the deregulated electricity market. For this act, some of the important constraints such as power flow of the lines, right-of-way’s validity and maximum line addition are taken into consideration. The studied power system networks are IEEE 25-bus system, Brazilian 46-bus system and Columbian 93-bus system for the study of TEP problem. The results are compared to those offered by some other state-of-the-art algorithms. It showed that SSA is effective algorithm for the TEP problem.

A Search Space Reduction Method for Transmission Expansion Planning Using an Iterative Refinement of the DC Load Flow Model

This paper provides a new methodology to compute a reduced but efficient set of candidate lines in a transmission expansion planning (TEP) context. Considering this reduced set of candidate lines should lead to similar investment decisions as if all the possible ac and dc candidate lines that could be installed in the network were considered. A first “hybrid” relaxed TEP problem is solved. Based on this initial solution, a new relaxed TEP problem is iteratively solved in which the dc load flow (DCLF) model is enforced to a certain extent in the partially expanded ac corridors. Once a convergence threshold has been reached, an upper bound of the number of candidate ac and dc lines to install in each corridor can be defined. This process results in a compact search space. Our algorithm has been implemented in General Algebraic Modeling Software (GAMS) and has been tested on a case study based on the European power system. The method produces very promising results and in the considered case study, leads to a very efficient investment.

Fault Current Constraint Transmission Expansion Planning Based on the Inverse Matrix Modification Lemma and a Valid Inequality

In the transmission expansion planning (TEP) problem, it is challenging to consider a fault current level constraint due to the time-consuming update process of the bus impedance matrix, which is required to calculate the fault currents during the search for the optimal solution. In the existing studies, either a nonlinear update equation or its linearized version is used to calculate the updated bus impedance matrix. In the former case, there is a problem in that the mathematical formulation is derived in the form of mixed-integer nonlinear programming. In the latter case, there is a problem in that an error due to the linearization may exist and the change of fault currents in other buses that are not connected to the new transmission lines cannot be detected. In this paper, we use a method to obtain the exact updated bus impedance matrix directly from the inversion of the bus admittance matrix. We propose a novel method based on the inverse matrix modification lemma (IMML) and a valid inequality is proposed to find a better solution to the TEP problem with fault current level constraint. The proposed method is applied to the IEEE two-area reliability test system with 96 buses to verify the performance and effectiveness of the proposed method and we compare the results with the existing methods. Simulation results show that the existing TEP method based on impedance matrix modification method violates the fault current level constraint in some buses, while the proposed method satisfies the constraint in all buses in a reasonable computation time.