Multinodal load forecasting for distribution systems using a fuzzy-artmap neural network
Introduction
Precisely knowing the electrical load is a prior condition for implementing strategies to provide consumers with quality, cost-effective electrical services (e.g., voltage, frequency, and waveform shape). Most of the proposals found in the literature are for global load forecasting, which is the sum of all demanded loads. In this case, the predicted global load is divided considering the several busses of the system using some heuristic method. This division generally leads to certain errors that can compromise the quality of the required studies for a power system's operation (load flow analysis, voltage, and angle stability, among other important studies). Thus, this work proposes to develop a multinodal load forecasting method considering the load at several points of the electrical network, such as substations, transformers, and feeders, based on an adaptive resonance theory (ART) [1] family neural network. It is a similar problem to global load forecasting, with the main difference corresponding to the use of a strategy to prepare the input and output data with several parallel neural modules aggregated to a global predictor. Therefore, historical consumption data provided by the electrical distribution systems are used. In this system, the load behavior is expected to repeat with some uncertainty. This uncertainty can be mitigated by utilizing exogenous information from historical sources in the prediction system. Generally, this was implemented as in the classical example known as the Box–Jenkins approach [2,3]. Today, researchers prefer the use of intelligent techniques, e.g., artificial neural networks (ANNs) [4], fuzzy logic [5], etc. However, multinodal prediction is complex in comparison to global prediction. The multinodal prediction method developed in this work employs two important resources: the use of the fuzzy-ARTMAP neural network (FANN) proposed by Grossberg [1] and the use of a global load participation factor (GLPF) [6,7]. The advantages of this approach are: (1) the low processing time in comparison to global forecasting and (2) using a FANN results in solutions orders of magnitude faster than backpropagation (BP) [8], which is a major benchmark of precision for ANNs. Full convergence is not even assured with BP neural networks when using diversified data. The preference for the ART family of ANNs [1] is due to the characteristic stability and plasticity that these architectures have to provide results quickly and precisely.
It is emphasized that the stability analysis of neural networks is an important matter considering the need to assure convergence in the training phase. Reference [9] provides a study in this sense.
To test the proposed prediction system, the results are presented considering substations of a power system centralized dataset (CDS) [10].
The load forecasting addressed in this paper is for 24 h in advance with 1 h (or ½ h) discretization. However, other resolutions can be achieved with little modification.
Section snippets
Related works
Global load forecasting accounts for the majority of the publications available in the literature based on techniques such as ANN [11], fuzzy logic [[12], [13], [14]], genetic algorithms [13], classical procedures [[15], [16], [17]], fuzzy-ART&ARTMAP ANN [18,19], ARIMA [2,3,16], ANN based on Levenberg–Marquardt [20] training method, ANN by gradient descent learning [21], and load forecasting based on multiregression–decomposition model [22]. There are few publications dealing with multinodal
Proposed methodology
The multinodal load forecasting method proposed in this work is based on ANN concepts [4] and the GLPF [6,7]. The ANN used is the Fuzzy-ARTMAP [1], the implementation of which is presented in Appendix A.
The prediction system is composed of two important parts: (1) global load forecasting (GLF) and (2) multinodal load forecasting (MLF) (composed by n local prediction modules). Executing the GLF, the MLF is realized using several parallel modules, each predicting the load of a considered bus
Results and discussion
It is necessary to normalize the results (Eq. (A.1)) in consideration of the definitions of the input and output vectors of module GLF (Eqs. (1) and (2)) of the FANN processing. This is necessary to maintain every component of vectors a and bpertaining to the interval [0,1]. As part of input vector a corresponds to the binary codification vector E, the normalization can only be done in relation to the data provided on the global load (vector L) and temperature (vector T). For convenience, the
Conclusion
This paper presents a new prediction model for load prediction up to 24 h in advance, based on the use of a FANN. The load forecasting is constituted by global prediction, i.e., considering the sum of all loads on the system, as well as in each node (busses of the electrical system). It is achieved without additional computational processing time costs, as the modules are processed in parallel. A reduced quantity of data is used to execute the local node training, thus reducing the time for
Acknowledgment
The authors thank CAPES (Brazilian Research Foundation) and CNPq (National Council for Scientific and Technological Development) for financial support.
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