Application of Signal Processing Methods in Energy and Water Sustainability Optimization.

Abstract

Solar irradiation is a non-stationary process with its mean and variance changing depending on time and day of the year. For solar irradiation prediction we remove both seasonal and time of day effects to make observations approximately stationary and then use prediction methods. We propose to use the zenith angle (the angle between sun beam and perpendicular line on horizontal surface) to remove both seasonal and time of day effects. Our simulations using least-squares (LS), time-varying least squares (TVLS), exponentially weighted recursive least squares (EWRLS) and one step estimation of second order statistics shows that using zenith angle normalization gives lower mean square error than traditional normalization by subtracting the mean and then dividing by deviation. In electric power grids, generation must equal load at all times. Since wind and solar power are intermittent, system operators must predict renewable generation and allocate operating reserves to mitigate imbalances. If they overestimate the renewable generation during scheduling, insufficient generation will be available during operation, which can be very costly. However, if they underestimate the renewable generation, usually they will only face the cost of keeping some generation capacity online and idle. Therefore overestimation of renewable generation resources usually presents a more serious problem than underestimation. Many researchers train their solar radiation forecast algorithms using symmetric criteria like RMSE or MAE, and then a bias is applied to the forecast later to reflect the asymmetric cost faced by the system operator - a technique we call indirectly biased forecasting. We investigate solar radiation forecasts using asymmetric cost functions (convex piecewise linear (CPWL) and LinEx) and optimize directly in the forecast training stage. We use linear programming and a gradient descent algorithm to find a directly biased solution and compare it with the best indirectly biased solution. We also modify the LMS algorithm according to the cost functions to create an online forecast method. Simulation results show substantial cost savings using these methods. We also propose two parametric probabilistic forecast methods by using beta and two sided power distribution for predicting solar irradiation and evaluate their performance. To improve their performance metrics a combining procedure based on the beta transformed linear opinion pool is utilized. Our simulations show that these methods -despite the simple structure- can accurately describe the stochastic characterization of solar irradiation and effectively reduce its uncertainty. The proposed approach is robust and algorithms can be modified for other point forecast methods. We also consider reliability of electric grid as a public good and we use an insurance policy to implement a benefit taxation mechanism that provides a framework to achieve optimal reliability levels. Finally, we examine energy efficient scheduling for pumping water in water supply networks. This is formulated as a nonconvex optimization problem and we find solutions and conduct simulations for small networks.