A data-mining-based methodology for transmission expansion planning

In recent decades, all over the world, competition in the electric power sector has deeply changed the way this sector’s agents play their roles. In most countries, electric process deregulation was conducted in stages, beginning with the clients of higher voltage levels and with larger electricity consumption, and later extended to all electrical consumers. The sector liberalization and the operation of competitive electricity markets were expected to lower prices and improve quality of service, leading to greater consumer satisfaction. Transmission and distribution remain noncompetitive business areas, due to the large infrastructure investments required. However, the industry has yet to clearly establish the best business model for transmission in a competitive environment. After generation, the electricity needs to be delivered to the electrical system nodes where demand requires it, taking into consideration transmission constraints and electrical losses. If the amount of power flowing through a certain line is close to or surpasses the safety limits, then cheap but distant generation might have to be replaced by more expensive closer generation to reduce the exceeded power flows. In a congested area, the optimal price of electricity rises to the marginal cost of the local generation or to the level needed to ration demand to the amount of available electricity. Even without congestion, some power will be lost in the transmission system through heat dissipation, so prices reflect that it is more expensive to supply electricity at the far end of a heavily loaded line than close to an electric power generation. Locational marginal pricing (LMP), resulting from bidding competition, represents electrical and economical values at nodes or in areas that may provide economical indicator signals to the market agents. This article proposes a data-mining-based methodology that helps characterize zonal prices in real power transmission networks. To test our methodology, we used an LMP database from the California Independent System Operator for 2009 to identify economical zones. (CAISO is a nonprofit public benefit corporation charged with operating the majority of California’s high-voltage wholesale power grid.) To group the buses into typical classes that represent a set of buses with the approximate LMP value, we used two-step and k-means clustering algorithms. By analyzing the various LMP components, our goal was to extract knowledge to support the ISO in investment and network-expansion planning.

Transmission system expansion planning by an extended genetic algorithm

The paper presents an extended genetic algorithm for solving the optimal transmission network expansion planning problem. Two main improvements have been introduced in the genetic algorithm: (a) initial population obtained by conventional optimisation based methods; (b) mutation approach inspired in the simulated annealing technique, the proposed method is general in the sense that it does not assume any particular property of the problem being solved, such as linearity or convexity. Excellent performance is reported in the test results section of the paper for a difficult large-scale real-life problem: a substantial reduction in investment costs has been obtained with regard to previous solutions obtained via conventional optimisation methods and simulated annealing algorithms; statistical comparison procedures have been employed in benchmarking different versions of the genetic algorithm and simulated annealing methods.

A Bilevel Approach to Transmission Expansion Planning Within a Market Environment

We present a bilevel model for transmission expansion planning within a market environment, where producers and consumers trade freely electric energy through a pool. The target of the transmission planner, modeled through the upper-level problem, is to minimize network investment cost while facilitating energy trading. This upper-level problem is constrained by a collection of lower-level market clearing problems representing pool trading, and whose individual objective functions correspond to social welfare. Using the duality theory the proposed bilevel model is recast as a mixed-integer linear programming problem, which is solvable using branch-and-cut solvers. Detailed results from an illustrative example and a case study are presented and discussed. Finally, some relevant conclusions are drawn.

Primary power distribution systems planning taking into account reliability, operation and expansion costs

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Transmission-expansion planning using the DC model and nonlinear-programming technique

The paper presents a constructive heuristic algorithm (CHA) for solving directly the long-term transmission-network-expansion-planning (LTTNEP) problem using the DC model. The LTTNEP is a very complex mixed-integer nonlinear-programming problem and presents a combinatorial growth in the search space. The CHA is used to find a solution for the LTTNEP problem of good quality. A sensitivity index is used in each step of the CHA to add circuits to the system. This sensitivity index is obtained by solving the relaxed problem of LTTNEP, i.e. considering the number of circuits to be added as a continuous variable. The relaxed problem is a large and complex nonlinear-programming problem and was solved through the interior-point method (IPM). Tests were performed using Garver's system, the modified IEEE 24-Bus system and the Southern Brazilian reduced system. The results presented show the good performance of IPM inside the CHA.

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.

Using traditional heuristic algorithms on an initial genetic algorithm population applied to the transmission expansion planning problem

This paper analyses the impact of choosing good initial populations for genetic algorithms regarding convergence speed and final solution quality. Test problems were taken from complex electricity distribution network expansion planning. Constructive heuristic algorithms were used to generate good initial populations, particularly those used in resolving transmission network expansion planning. The results were compared to those found by a genetic algorithm with random initial populations. The results showed that an efficiently generated initial population led to better solutions being found in less time when applied to low complexity electricity distribution networks and better quality solutions for highly complex networks when compared to a genetic algorithm using random initial populations.

An implementation of modified scatter search algorithm to transmission expansion planning

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

A combinatorial approach for transmission expansion & reactive power planning

A metaheuristic technique for solving the short-term transmission network expansion and reactive power planning problems, at the same time, in regulated power systems using the AC model is presented. The problem is solved using a real genetic algorithm (RGA). For each topology proposed by RGA an indicator is employed to identify the weak buses for new reactive power sources allocation. The fitness function is calculated using the cost of each configuration as well as constraints deviation of an AC optimal power flow (OPF) in which the minimum reactive generation of new reactive sources and the active power losses are objectives. With allocation of reactive power sources at load buses, the circuit capacity increases and the cost of installation could be decreased. The method is tested in a well known test system, presenting good results when compared with other approaches. © 2011 IEEE.

An application of a modified constructive heuristic algorithm to transmission expansion planning

Transmission expansion planning (TEP) is a non-convex optimization problem that can be solved via different heuristic algorithms. A variety of classical as well as heuristic algorithms in literature are addressed to solve TEP problem. In this paper a modified constructive heuristic algorithm (CHA) is proposed for solving such a crucial problem. Most of research papers handle TEP problem by linearization of the non-linear mathematical model while in this research TEP problem is solved via CHA using non-linear model. The proposed methodology is based upon Garver's algorithm capable of applying to a DC model. Simulation studies and tests results on the well known transmission network such as: Garver and IEEE 24-bus systems are carried out to show the significant performance as well as the effectiveness of the proposed algorithm. © 2011 IEEE.

An application of CHA to concurrent short-term transmission expansion & reactive power planning

In this paper a heuristic technique for solving simultaneous short-term transmission network expansion and reactive power planning problem (TEPRPP) via an AC model is presented. A constructive heuristic algorithm (CHA) aimed to obtaining a significant quality solution for such problem is employed. An interior point method (IPM) is applied to solve TEPRPP as a nonlinear programming (NLP) during the solution steps of the algorithm. For each proposed network topology, an indicator is deployed to identify the weak buses for reactive power sources placement. The objective function of NLP includes the costs of new transmission lines, real power losses as well as reactive power sources. By allocating reactive power sources at load buses, the circuit capacity may increase while the cost of new lines can be decreased. The proposed methodology is tested on Garver's system and the obtained results shows its capability and the viability of using AC model for solving such non-convex optimization problem. © 2011 IEEE.

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..

On the optimal capacity expansion of electric power systems

The analysis of investment in the electric power has been the subject of intensive research for many years. The efficient generation and distribution of electrical energy is a difficult task involving the operation of a complex network of facilities, often located over very large geographical regions. Electric power utilities have made use of an enormous range of mathematical models. Some models address time spans which last for a fraction of a second, such as those that deal with lightning strikes on transmission lines while at the other end of the scale there are models which address time horizons consisting of ten or twenty years; these usually involve long range planning issues. This thesis addresses the optimal long term capacity expansion of an interconnected power system. The aim of this study has been to derive a new, long term planning model which recognises the regional differences which exist for energy demand and which are present in the construction and operation of power plant and transmission line equipment. Perhaps the most innovative feature of the new model is the direct inclusion of regional energy demand curves in the nonlinear form. This results in a nonlinear capacity expansion model. After review of the relevant literature, the thesis first develops a model for the optimal operation of a power grid. This model directly incorporates regional demand curves. The model is a nonlinear programming problem containing both integer and continuous variables. A solution algorithm is developed which is based upon a resource decomposition scheme that separates the integer variables from the continuous ones. The decompostion of the operating problem leads to an interactive scheme which employs a mixed integer programming problem, known as the master, to generate trial operating configurations. The optimum operating conditions of each trial configuration is found using a smooth nonlinear programming model. The dual vector recovered from this model is subsequently used by the master to generate the next trial configuration. The solution algorithm progresses until lower and upper bounds converge. A range of numerical experiments are conducted and these experiments are included in the discussion. Using the operating model as a basis, a regional capacity expansion model is then developed. It determines the type, location and capacity of additional power plants and transmission lines, which are required to meet predicted electicity demands. A generalised resource decompostion scheme, similar to that used to solve the operating problem, is employed. The solution algorithm is used to solve a range of test problems and the results of these numerical experiments are reported. Finally, the expansion problem is applied to the Queensland electricity grid in Australia.