Strategies to reduce the number of variables and the combinatorial search space of the multistage transmission expansion planning problem

This paper proposes strategies to reduce the number of variables and the combinatorial search space of the multistage transmission expansion planning problem (TEP). The concept of the binary numeral system (BNS) is used to reduce the number of binary and continuous variables related to the candidate transmission lines and network constraints that are connected with them. The construction phase of greedy randomized adaptive search procedure (GRASP-CP) and additional constraints, obtained from power flow equilibrium in an electric power system are employed for more reduction in search space. The multistage TEP problem is modeled like a mixed binary linear programming problem and solved using a commercial solver with a low computational time. The results of one test system and two real systems are presented in order to show the efficiency of the proposed solution technique. © 1969-2012 IEEE.

Implementation of an AC model for transmission expansion planning considering reliability constraints

In this paper, a hybrid heuristic methodology that employs fuzzy logic for solving the AC transmission network expansion planning (AC-TEP) problem is presented. An enhanced constructive heuristic algorithm aimed at obtaining a significant quality solution for such complicated problems considering contingency is proposed. In order to indicate the severity of the contingency, 2 performance indices, namely the line flow performance index and voltage performance index, are calculated. An interior point method is applied as a nonlinear programming solver to handle such nonconvex optimization problems, while the objective function includes the costs of the new transmission lines as well as the real power losses. The performance of the proposed method is examined by applying it to the well-known Garver system for different cases. The simulation studies and result analysis demonstrate that the proposed method provides a promising way to find an optimal plan. Obtaining the best quality solution shows the capability and the viability of the proposed algorithm in AC-TEP. © Tübi̇tak..

Risk/investment-driven transmission expansion planning with multiple scenarios

This study presents a new methodology based on risk/investment to solve transmission network expansion planning (TNEP) problem with multiple future scenarios. Three mathematical models related to TNEP problems considering multiple future generation and load scenarios are also presented. These models will provide planners with a meaningful risk assessment that enable them to determine the necessary funding for transmission lines at a permissible risk level. The results using test and real systems show that the proposed method presents better solutions compared with scenario analysis method. ©The Institution of Engineering and Technology 2013.

Multistage Transmission Expansion Planning Considering Fixed Series Compensation Allocation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A Modified Branch and Bound Algorithm to Solve the Transmission Expansion Planning Problem

In this paper a novel Branch and Bound (B&B) algorithm to solve the transmission expansion planning which is a non-convex mixed integer nonlinear programming problem (MINLP) is presented. Based on defining the options of the separating variables and makes a search in breadth, we call this algorithm a B&BML algorithm. The proposed algorithm is implemented in AMPL and an open source Ipopt solver is used to solve the nonlinear programming (NLP) problems of all candidates in the B&B tree. Strategies have been developed to address the problem of non-linearity and non-convexity of the search region. The proposed algorithm is applied to the problem of long-term transmission expansion planning modeled as an MINLP problem. The proposed algorithm has carried out on five commonly used test systems such as Garver 6-Bus, IEEE 24-Bus, 46-Bus South Brazilian test systems, Bolivian 57-Bus, and Colombian 93-Bus. Results show that the proposed methodology not only can find the best known solution but it also yields a large reduction between 24% to 77.6% in the number of NLP problems regarding to the size of the systems.

Transmission Expansion Planning Via a Constructive Heuristic Algorithm in Restructured Electricity Industry

The transmission expansion planning problem in modern power systems is a large-scale, mixed-integer, nonlinear and non-convex problem. this paper presents a new mathematical model and a constructive heuristic algorithm (CHA) for solving transmission expansion planning problem under new environment of electricity restructuring. CHA finds an acceptable solution in an iterative process, where in each step a circuit is chosen using a sensitivity index and added to the system. The proposed model consider multiple generation scenarios therefore the methodology finds high quality solution in which it allows the power system operate adequacy in an environment with multiple generators scenarios. Case studies and simulation results using test systems show possibility of using Constructive heuristic algorithm in an open access system.

Risk control in transmission system expansion planning with wind generators

With the advent of large-scale wind farms and their integration into electrical grids, more uncertainties, constraints and objectives must be considered in power system development. It is therefore necessary to introduce risk-control strategies into the planning of transmission systems connected with wind power generators. This paper presents a probability-based multi-objective model equipped with three risk-control strategies. The model is developed to evaluate and enhance the ability of the transmission system to protect against overload risks when wind power is integrated into the power system. The model involves: (i) defining the uncertainties associated with wind power generators with probability measures and calculating the probabilistic power flow with the combined use of cumulants and Gram-Charlier series; (ii) developing three risk-control strategies by specifying the smallest acceptable non-overload probability for each branch and the whole system, and specifying the non-overload margin for all branches in the whole system; (iii) formulating an overload risk index based on the non-overload probability and the non-overload margin defined; and (iv) developing a multi-objective transmission system expansion planning (TSEP) model with the objective functions composed of transmission investment and the overload risk index. The presented work represents a superior risk-control model for TSEP in terms of security, reliability and economy. The transmission expansion planning model with the three risk-control strategies demonstrates its feasibility in the case study using two typical power systems

Multistage and coordinated planning of the expansion of transmission systems

In this paper, an efficient genetic algorithm (GA) is presented to solve the problem of multistage and coordinated transmission expansion planning. This is a mixed integer nonlinear programming problem, difficult for systems of medium and large size and high complexity. The GA presented has a set of specialized genetic operators and an efficient form of generation of the initial population that finds high quality suboptimal topologies for large size and high complexity systems. In these systems, multistage and coordinated planning present a lower investment than static planning. Tests results are shown in one medium complexity system and one large size high complexity system.

Efficient method for AC transmission network expansion planning

A combinatorial mathematical model in tandem with a metaheuristic technique for solving transmission network expansion planning (TNEP) using an AC model associated with reactive power planning (RPP) is presented in this paper. AC-TNEP is handled through a prior DC model while additional lines as well as VAr-plants are used as reinforcements to cope with real network requirements. The solution of the reinforcement stage can be obtained by assuming all reactive demands are supplied locally to achieve a solution for AC-TNEP and by neglecting the local reactive sources, a reactive power planning (RPP) will be managed to find the minimum required reactive power sources. Binary GA as well as a real genetic algorithm (RCA) are employed as metaheuristic optimization techniques for solving this combinatorial TNEP as well as the RPP problem. High quality results related with lower investment costs through case studies on test systems show the usefulness of the proposal when working directly with the AC model in transmission network expansion planning, instead of relaxed models. (C) 2010 Elsevier B.V. All rights reserved.

Branch and bound algorithm for transmission system expansion planning using a transportation model

A method for optimal transmission network expansion planning is presented. The transmission network is modelled as a transportation network. The problem is solved using hierarchical Benders decomposition in which the problem is decomposed into master and slave subproblems. The master subproblem models the investment decisions and is solved using a branch-and-bound algorithm. The slave subproblem models the network operation and is solved using a specialised linear program. Several alternative implementations of the branch-and-bound algorithm have been rested. Special characteristics of the transmission expansion problem have been taken into consideration in these implementations. The methods have been tested on various test systems available in the literature.

Test systems and mathematical models for transmission network expansion planning

The data of four networks that can be used in carrying out comparative studies with methods for transmission network expansion planning are given. These networks are of various types and different levels of complexity. The main mathematical formulations used in transmission expansion studies-transportation models, hybrid models, DC power flow models, and disjunctive models are also summarised and compared. The main algorithm families are reviewed-both analytical, combinatorial and heuristic approaches. Optimal solutions are not yet known for some of the four networks when more accurate models (e.g. The DC model) are used to represent the power flow equations-the state of the art with regard to this is also summarised. This should serve as a challenge to authors searching for new, more efficient methods.

Transmission system expansion planning by a branch-and-bound algorithm

A branch and bound (B& B) algorithm using the DC model, to solve the power system transmission expansion planning by incorporating the electrical losses in network modelling problem is presented. This is a mixed integer nonlinear programming (MINLP) problem, and in this approach, the so-called fathoming tests in the B&B algorithm were redefined and a nonlinear programming (NLP) problem is solved in each node of the B& B tree, using an interior-point method. Pseudocosts were used to manage the development of the B&B tree and to decrease its size and the processing time. There is no guarantee of convergence towards global optimisation for the MINLP problem. However, preliminary tests show that the algorithm easily converges towards the best-known solutions or to the optimal solutions for all the tested systems neglecting the electrical losses. When the electrical losses are taken into account, the solution obtained using the Garver system is better than the best one known in the literature.

Specialized genetic algorithm for transmission network expansion planning considering reliability

This paper presents a methodology to solve the transmission network expansion planning problem (TNEP) considering reliability and uncertainty in the demand. The proposed methodology provides an optimal expansion plan that allows the power system to operate adequately with an acceptable level of reliability and in an enviroment with uncertainness. The reliability criterion limits the expected value of the reliability index (LOLE - Loss Of Load Expectation) of the expanded system. The reliability is evaluated for the transmission system using an analytical technique based in enumeration. The mathematical model is solved, in a efficient way, using a specialized genetic algorithm of Chu-Beasley modified. Detailed results from an illustrative example are presented and discussed. © 2009 IEEE.

Evolutionary multi-move path-relinking for transmission network expansion planning

This paper presents the application of a new metaheuristic algorithm to solve the transmission expansion planning problem. A simple heuristic, using a relaxed network model associated with cost perturbation, is applied to generate a set of high quality initial solutions with different topologies. The population is evolved using a multi-move path-relinking with the objective of finding minimum investment cost for the transmission expansion planning problem employing the DC representation. The algorithm is tested on the southern Brazilian system, obtaining the optimal solution for the system with better performance than similar metaheuristics algorithms applied to the same problem. ©2010 IEEE.