Marcos J. Rider

Imposing Radiality Constraints in Distribution System Optimization Problems

Distribution systems commonly operate with a radial topology, so all models of optimization problems in these distribution systems should consider radiality in their formulation. This work presents a literature review, a critical analysis, and a proposal for incorporating the radiality constraints in mathematical models of optimization problems for radial distribution systems. The objective is to show that the radiality constraints on such optimization problems can be considered in a simple and efficient way. The reconfiguration and expansion planning problems of distribution systems are used to test and verify the proposed radiality constraints. A generalization of radiality constraints is also examined.

Transmission Network Expansion Planning Considering Uncertainty in Demand

This paper presents two mathematical models and one methodology to solve a transmission network expansion planning problem considering uncertainty in demand. The first model analyzed the uncertainty in the system as a whole; then, this model considers the uncertainty in the total demand of the power system. The second one analyzed the uncertainty in each load bus individually. The methodology used to solve the problem, finds the optimal transmission network expansion plan that allows the power system to operate adequately in an environment with uncertainty. The models presented are solved using a specialized genetic algorithm. The results obtained for several known systems from literature show that cheaper plans can be found satisfying the uncertainty in demand

A Constructive Heuristic Algorithm for Distribution System Planning

A constructive heuristic algorithm (CHA) to solve distribution system planning (DSP) problem is presented. The DSP is a very complex mixed binary nonlinear programming problem. A CHA is aimed at obtaining an excellent quality solution for the DSP problem. However, a local improvement phase and a branching technique were implemented in the CHA to improve its solution. In each step of the CHA, a sensitivity index is used to add a circuit or a substation to the distribution system. This sensitivity index is obtained by solving the DSP problem considering the numbers of circuits and substations to be added as continuous variables (relaxed problem). The relaxed problem is a large and complex nonlinear programming and was solved through an efficient nonlinear optimization solver. Results of two tests systems and one real distribution system are presented in this paper in order to show the ability of the proposed algorithm.

A Metaheuristic to Solve the Transmission Expansion Planning

In this letter, a genetic algorithm (GA) is applied to solve the static and multistage transmission expansion planning (TEP) problem. The characteristics of the proposed GA to solve the TEP problem are presented. Results using some known systems show that the proposed GA solves a smaller number of linear programming problems in order to find the optimal solutions and obtains a better solution for the multistage TEP problem.

Optimal Operation of Distribution Networks Considering Energy Storage Devices

This paper presents a mixed-integer second-order cone programing (MISOCP) model to solve the optimal operation problem of radial distribution networks (DNs) with energy storage. The control variables are the active and reactive generated power of dispatchable distributed generators (DGs), the number of switchable capacitor bank units in operation, the tap position of the voltage regulators and on-load tap-changers, and the operation state of the energy storage devices. The objective is to minimize the total cost of energy purchased from the distribution substation and the dispatchable DGs. The steady-state operation of the DN is modeled using linear and second-order cone programing. The use of an MISOCP model guarantees convergence to optimality using existing optimization software. A mixed-integer linear programing (MILP) formulation for the original model is also presented in order to show the accuracy of the proposed MISOCP model. An 11-node test system and a 42-node real system were used to demonstrate the effectiveness of the proposed MISOCP and MILP models.

Artificial neural networks for solving the power flow problem in electric power systems

Abstract In this paper, the use of artificial neural networks (ANN) is proposed for solving the well known power flow (PF) problem of electric power systems (EPS). PF evaluates the steady state of EPS and is a fundamental tool for planning, operation and control of modern power systems. The mathematical model of the PF comprises a set of non-linear algebraic equations conventionally solved with the Newton-Raphson method or its decoupled versions. In order to take advantage of the superior speed of ANN over conventional PF methods, multilayer perceptrons neural networks trained with the second order Levenberg–Marquardt method have been used for computing voltages magnitudes and angles of the PF problem. The proposed ANN methodology has been successfully tested using the IEEE-30 bus system.

Reactive power pricing in deregulated electrical markets using a methodology based on the theory of marginal costs

In this paper, a flexible formulation about the pricing of active and reactive power is presented. This proposal is developed using a decoupled formulation identifying the active and reactive subproblems. A model for the price calculation of the reactive power which is intended to incentive the participation of agents of the electricity markets is analyzed. An optimal power flow (OPF) to solve the reactive power subproblem which considers the production costs of the reactive power and the active losses minimization in the objective function, has been implemented. In order to solve the OPF and consequently obtaining the active and reactive power marginal cost prices has been adopted a nonlinear programming methodology. Tests using a 9-bus system for several load conditions show the validity of the methodology.

Optimal Bidding Strategies for Thermal and Generic Programming Units in the Day-Ahead Electricity Market

This study has developed a stochastic programming model that integrates the day-ahead optimal bidding problem with the most recent regulation rules of the Iberian Electricity Market (MIBEL) for bilateral contracts (BC), with a special consideration for the new mechanism to balance the competition of the production market, namely virtual power plant (VPP) auctions. The model allows a price-taking generation company (GenCo) to decide on the unit commitment of the thermal units, the economic dispatch of the BCs between the thermal units and the generic programming unit (GPU), and the optimal sale/purchase bids for all units (thermal and generic), by observing the MIBEL regulation. The uncertainty of the spot prices has been represented through scenario sets built from the most recent real data using scenario reduction techniques. The model has been solved using real data from a Spanish generation company and spot prices, and the results have been reported and analyzed.

Optimal Conductor Size Selection and Reconductoring in Radial Distribution Systems Using a Mixed-Integer LP Approach

This paper presents a mixed-integer linear programming model to solve the conductor size selection and reconductoring problem in radial distribution systems. In the proposed model, the steady-state operation of the radial distribution system is modeled through linear expressions. The use of a mixed-integer linear model guarantees convergence to optimality using existing optimization software. The proposed model and a heuristic are used to obtain the Pareto front of the conductor size selection and reconductoring problem considering two different objective functions. The results of one test system and two real distribution systems are presented in order to show the accuracy as well as the efficiency of the proposed solution technique.

A Strategy to Solve the Multistage Transmission Expansion Planning Problem

In this letter, a heuristic to reduce the combinatorial search space (CSS) of the multistage transmission expansion planning (MTEP) problem is presented. The aim is to solve the MTEP modeled like a mixed binary linear programming (MBLP) problem using a commercial solver with a low computational time. The heuristic uses the solution of several static transmission expansion planning problems to obtain the reduced CSS. Results using some test and real systems show that the use of the reduced CSS solves the MTEP problem with better solutions compared to other strategies in the literature.