Researchers have proposed various probabilistic load forecasting models in the form of quantiles, densities, or intervals to describe the uncertainties of future energy demand. Density forecasts can provide more uncer...
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Researchers have proposed various probabilistic load forecasting models in the form of quantiles, densities, or intervals to describe the uncertainties of future energy demand. Density forecasts can provide more uncertainty information than can be expressed by just the quantile and interval. However, the combining method for density forecasts is seldom investigated. This paper proposes a novel and easily implemented approach to combine density probabilistic load forecasts to further improve the performance of the final probabilistic forecasts. The combination problem is formulated as an optimization problem to minimize the continuous ranked probability score of the combined model by searching the weights of different individual methods. Under the Gaussian mixture distribution assumption of the density forecasts, the problem is cast to a linearly constrained quadratic programming problem and can be solved efficiently. Case studies on the electric load datasets of eight areas verify the effectiveness of the proposed method.
This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one ca...
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This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrainedquadraticprogramming, the MM algorithm involves very simple updates.
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