Multifractional Brownian motion and quantum-behaved particle swarm optimization for short term power load forecasting: An integrated approach

Power load fluctuation is generally agreed to be a non-stationary stochastic process. The Fractional Brownian Motion (FBM) model is proposed to forecast a non-stationary time series with high accuracy. Computation of the Hurst exponent (H) for the power load data series using the Rescaled Range Analysis (RCS) in this study. This method is used to verify the Long-Range Dependent (LRD) characteristics of non-stationary power load data. For the real power load, however, H exponent takes on the self-similarity characteristics in a certain finite range of intervals, the global self-similarity is very rare to exist. The H exponent of the self-similarity usually has more than one value. We generalize multifractional H(t) to replace constant H. To improve the forecasting accuracy, the H(t) is optimized by the Quantum-Behaved Particle Swarm Optimization (QPSO). Once the optimal H(t) is obtained, then the optimal and parameters in the multi-Fractional Brownian Motion (mFBM) model can be deduced to forecast next power load data series with a higher accuracy. (C) 2020 Elsevier Ltd. All rights reserved.