Bruno André Gomes

Modeling costs and load uncertainties in optimal power flow studies

Modeling uncertainties in power systems has long interested researchers. Nowadays, as in 70psilas, the volatility associated with generation or fuel prices, for one side, and the uncertainties related with load forecasting and generation capacity, for another, places a new emphasis on this kind of problems. As a result of this renewed interest, in this paper we are enlarging the original fuzzy optimal power flow, FOPF, model in order to consider not only load uncertainties, but also uncertainties in generation or fuel prices, specified using trapezoidal fuzzy numbers. This new approach is based on multiparametric linear programming techniques that lead to the identification of a number of critical regions covering all the uncertainty space. This contributes to build more accurate membership functions of all variables, namely generations, branch flows and power not supplied.

Impact of load and generation price uncertainties in spot prices

In this paper it is presented a formulation for the DC Optimal Power Flow problem considering load and generation cost uncertainties and the corresponding solution algorithms. The paper also details the algorithms implemented to allow the integration of losses on the results as well the algorithm developed to compute the nodal marginal price in the presence of such uncertainties. Since loads and generation costs are represented by fuzzy numbers, nodal marginal prices are no longer represented by deterministic values, but instead, by membership functions. To illustrate the application of the proposed algorithms, this paper also includes results based on a small 3 bus system and on the IEEE 24 bus/38 branch test system.

Calculation of Nodal Marginal Prices Considering Load and Generation Price Uncertainties

This paper presents the mathematical models and the solution algorithms of DC optimal power flow problems considering uncertainties represented by fuzzy numbers affecting loads as well as the elements of the cost function. The main purpose of this work corresponds to transfer the uncertainties affecting both the loads and the cost vector to the results that one usually obtain with such a DC optimal power flow model, that is, to characterize the uncertainties that affect the generations, the voltage phases, the branch flows. Apart from that, this paper also describes the algorithm to be used to calculate the uncertainties affecting the nodal marginal prices, since these prices are related with the dual variables of several constraints in the optimization problem. The developed algorithms are based in the solution of multiparametric problems in which one considers parameters both in the right hand side vector of the constraints (in order to represent load uncertainties) and in the cost function (to consider uncertainties in fuel costs, for instance). Finally, the paper includes a results of a case study designed to illustrate the application of the developed algorithms as well as results obtained for the IEEE 24 bus test system.

Computation of nodal marginal prices in the presence of load and generation cost Uncertainties

Marginal prices have been recognized as the core approach to the economic evaluation of generation and transmission services in an electricity market environment. In this context, this paper presents the New Fuzzy Optimal Power Flow algorithm as a model to addresses the impact of load and generation cost uncertainties in nodal marginal prices. Since loads and generation costs are represented by fuzzy numbers, nodal marginal prices will no longer be represented by deterministic values, but rather by fuzzy membership functions reflecting the specified uncertainties. The paper also presents the algorithm used for the integration of the transmission losses effect on the results. Since the proposed algorithm uses multiparametric programming techniques, it contributes to characterize in a better way the system behavior. Finally, it includes results based on the IEEE 24 bus/38 branch test system to illustrate the proposed approach.

Addressing the Impact of Demand and Generation Cost Uncertainties in the Operation of Power Systems

Abstract This paper describes a set of mathematical formulations designed to include uncertainties modeled by fuzzy numbers in DC OPF studies. These approaches enhance and generalize an initial formulation and solution algorithm described in several papers co-authored by the second author. The approaches described in this paper adopt multiparametric optimization techniques in order to translate to the results the uncertainties affecting loads, for one side, the generation costs, for another, and also both of them in a simultaneous way. These approaches can be very useful nowadays given the uncertainties and volatility affecting data required to run several studies. They can also be the basis for the computation of nodal short time marginal prices reflecting these uncertainties. This paper also includes results obtained from a Case Study based on the IEEE 24 bus test system.

Evaluation of transmission reinforcement strategies using risk indices in the presence of uncertainties

This paper describes a hybrid approach in which generation cost and demand uncertainties are represented by fuzzy numbers and the life cycle of system components is modeled by probabilistic models. The Monte Carlo simulation model is used to sample system states according to the failure rates of the system components and a Fuzzy DC OPF model is used to analyse each sampled state. This Fuzzy DC OPF model adopts multi-parametric optimization techniques and admits that loads, generation costs or both of them simultaneously are modeled using fuzzy numbers. At the end of this process, it is possible to compute estimates of the Power Not Supplied and also of the exposure and robustness indices that characterize the ability that the system has to accommodate the specified uncertainties. This information can then be used to characterize the ability each reinforcement has in increasing the robustness of the system. Finally, the paper includes results for two case studies. On of them is based on a 6 bus system and the second uses the IEEE 24 bus/38 branch test system to illustrate the developed approaches.

Dealing With Load and Generation Cost Uncertainties in Power System Operation Studies: A Fuzzy Approach

Power systems are currently facing a change of the paradigm that determined their operation and planning while being surrounded by multiple uncertainties sources. As a consequence, dealing with uncertainty is becoming a crucial issue in the sense that all agents should be able to internalize them in their models to guarantee that activities are profitable and that operation and investment strategies are selected according to an adequate level of risk. Taking into account the introduction of market mechanisms and the volatility of fuel prices, this paper presents the models and the algorithms developed to address load and generation cost uncertainties. These models correspond to an enhanced approach regarding the original fuzzy optimal power flow model developed by the end of the 1990s, which considered only load uncertainties. The paper also describes the algorithms developed to integrate an estimate of active transmission losses and to compute nodal marginal prices reflecting such uncertainties. The developed algorithms use multiparametric optimization techniques and are illustrated using a case study based on the IEEE 24 bus test system.