José A. Domínguez-Navarro

Statistical Analysis of Wind Power Forecast Error

Wind power forecast error usually has been assumed to have a near Gaussian distribution. With a simple statistical analysis, it can be shown that this is not valid. To obtain a more appropriate probability density function (pdf) of the wind power forecast error, an indirect algorithm based on the Beta pdf is proposed. Measured one-year time series from two different wind farms are used to generate the forecast data. Three different forecast scenarios are simulated based on the persistence approach. This makes the results comparable to other forecast methods. It is found that the forecast error pdf has a variable kurtosis ranging from 3 (like the Gaussian) to over 10, and therefore it can be categorized as fat-tailed. A new approximation function for the parameters of the Beta pdf is proposed because results from former publications could not be confirmed. Besides, a linear approximation is developed to describe the relationship between the persistence forecast and the related mean measured power. An energy storage system (ESS), which reduces the forecast error and smooths the wind power output, is considered. Results for this case show the usefulness of the proposed forecast error pdf for finding the optimum rated ESS power.

New multiobjective tabu search algorithm for fuzzy optimal planning of power distribution systems

This paper presents a new multiobjective Tabu search (NMTS) algorithm to solve a multiobjective fuzzy model for optimal planning of distribution systems. This algorithm obtains multiobjective nondominated solutions to three objective functions: fuzzy economic cost, level of fuzzy reliability, and exposure (maximization of robustness), also including optimal size and location of reserve feeders to be built for maximizing the level of reliability at the lowest economic cost (for a given level of robustness). The main characteristics of the NMTS algorithm are: search of planning solutions using several objective functions simultaneously; partition of the space of solutions to diversify the search; intensification of the search by ranking lists of the best network nodes of the distribution system; and an elaborated Tabu list that stores visited network nodes, avoiding unwanted movements. The NMTS algorithm has been intensively tested in real distribution systems, proving its practical application in large power distribution systems.

A Probabilistic Method for Energy Storage Sizing Based on Wind Power Forecast Uncertainty

A novel method is proposed for designing an energy storage system (ESS) which is dedicated to the reduction of the uncertainty of short-term wind power forecasts up to 48 h. The investigation focuses on the statistical behavior of the forecast error and the state of charge (SOC) of the ESS. This approach gives an insight into the influence of the forecast conditions (horizon, quality) on the distribution of SOC. With this knowledge, an optimized sizing of the ESS can be done with a well-defined uncertainty limit. For this study, one-year time series of power output measurements and forecasts were available for two wind farms. As a reference, different forecast quality degrees are simulated based on a persistence approach. With the forecast data, empirical probability density functions (pdfs) are generated which are the basis of the proposed method. This approach can lead to a considerable reduction of the ESS and provides important information about the unserved energy. This unserved energy represents the remaining forecast uncertainty. As a consequence, the proposed probabilistic method permits the sizing of energy storage systems as a function of the desired remaining forecast uncertainty, reducing simultaneously power and energy capacity.

Possibilistic model based on fuzzy sets for the multiobjective optimal planning of electric power distribution networks

This paper presents a new possibilistic (fuzzy) model for the multiobjective optimal planning of power distribution networks that finds out the nondominated multiobjective solutions corresponding to the simultaneous optimization of the fuzzy economic cost, level of fuzzy reliability, and exposure (optimization of robustness) of such networks, using an original and powerful meta-heuristic algorithm based on Tabu Search. This model determines the optimal location and size of the future feeders and substations in distribution networks with dimensions significantly larger than the ones usually presented in papers on the matter. The model also allows to determine the optimal reserve feeders (location and size) that provide the best distribution network reliability at the lowest cost for a given level of robustness (exposure). The model and the algorithm have been intensively tested in real distribution networks, which proves their practical application to large power distribution systems.

NSGA and SPEA Applied to Multiobjective Design of Power Distribution Systems

This paper presents, for the first time, an application of two well-know multiobjective optimization techniques, namely, nondominated sorting genetic algorithm (NSGA) and strength Pareto evolutionary algorithm (SPEA), to the multiobjective design of power distribution systems. These algorithms have been applied to a multiobjective optimization problem with some technical constraints, minimizing the total costs while maximizing the reliability of the power distribution system. The NSGA uses a fitness sharing scheme to achieve diversity among the obtained solutions. In SPEA, it is necessary to apply a reduction procedure because of the number of solutions. For this purpose, a fuzzy c-means (FCM) clustering algorithm has been applied, with this being the first time that an FCM algorithm in the SPEA has been used. The obtained results from both techniques have been compared, concluding that both offer similar efficiency in order to solve the stated multiobjective optimization problem. The developed methodology is applicable to practical cases of design, allowing for additional requirements that the designer imposes

Integral planning of primary-secondary distribution systems using mixed integer linear programming

Important research effort has been devoted to the topic of optimal planning of distribution systems. However, in general it has been mostly referred to the design of the primary network, with very modest considerations to the effect of the secondary network in the planning and future operation of the complete grid. Relatively little attention has been paid to the optimization of the secondary grid and to its effect on the optimality of the design of the complete electrical system, although the investment and operation costs of the secondary grid represent an important portion of the total costs. Appropriate design procedures have been proposed separately for both the primary and the secondary grid; however, in general, both planning problems have been presented and treated as different-almost isolated-problems, setting aside with this approximation some important factors that couple both problems, such as the fact that they may share the right of way, use the same poles, etc., among other factors that strongly affect the calculation of the investment costs. The main purpose of this work is the development and initial testing of a model for the optimal planning of a distribution system that includes both the primary and the secondary grids, so that a single optimization problem is stated for the design of the integral primary-secondary distribution system that overcomes these simplifications. The mathematical model incorporates the variables that define both the primary as well as the secondary planning problems and consists of a mixed integer-linear programming problem that may be solved by means of any suitable algorithm. Results are presented of the application of the proposed integral design procedure using conventional mixed integer-linear programming techniques to a real case of a residential primary-secondary distribution system consisting of 75 electrical nodes.

Optimal Conductor Size Selection in Radial Power Distribution Systems Using Evolutionary Strategies

This paper presents the application of a heuristic method, called evolutionary strategy (ES), to select optimal size of feeders in radial power distribution systems. ES incorporates biologically inspired structures and operators such as recombination, mutation and fitness based selection. ES prove to be successful when compared with other iterative methods on most problems. In this paper, the posed optimization problem consists in select a conductor type for each feeder of radial power distribution systems. The optimization procedure is subject to some technical constraints, which are the Kirchhoffs current law constraints for all the nodes, the capacity constraints for the feeders and substations, and the voltage drop constraints. As a case study, the proposed method is applied to radial power distribution systems with satisfactory results

Reactive power support pricing of Distributed Generators with primary energy source uncertainty

In this paper, a novel methodology to price the reactive power support ancillary service of Distributed Generators (DGs) with primary energy source uncertainty is shown. The proposed methodology provides the service pricing based on the Loss of Opportunity Costs (LOC) calculation. An algorithm is proposed to reduce the uncertainty present in these generators using Multiobjective Power Flows (MOPFs) implemented in multiple probabilistic scenarios through Monte Carlo Simulations (MCS), and modeling the time series associated with the generation of active power from DGs through Markov Chains (MC).

Multi-objective design optimization of hybrid renewable systems using UGF

Purpose – Renewable generation is a main component of most hybrid generation systems. However, randomness on its generation is a characteristic to be considered due to its direct impact on reliability and performance of these systems. For this reason, renewable generation usually is accompanied with other generation elements to improve their general performance. The purpose of this paper is to analyze the power generation system, composed of solar, wind and diesel generation and power outsourcing option from the grid as means of reserve source. A multi-objective optimization for the design of hybrid generation system is proposed, particularly using the cost of energy, two different reliability indexes and the percentage of renewable energy as objectives. Further, the uncertainty of renewable sources and demand is modeled with a new technique that permits to evaluate the reliability quickly. Design/methodology/approach – The multi-state model of the generators and the load is modeled with the Universal Gen...

Prosumers in the regulatory framework of two EU members: Italy and Spain

This paper focuses on a typical customer with a PV plant and a battery storage by the perspective of two EU members: Italy and Spain. The authors calculate the electricity bill of the considered customer in accordance with the respective legislative and regulatory frameworks. This calculation is a preparatory and preliminary activity for finding relevant differences, if any, that should not exist between EU members. Given the 15-min load profile of a 3kW–3700kWh/yr domestic user, numerical experiments return that the ratio, between the electricity bills in Italy and Spain, relevantly changes with respect the adoption of local generator and local storage.