Day-ahead Complementary Operation for a Wind-hydro-thermal System Considering Multi-dimensional Uncertainty

Along with the wide-ranging addition of wind power into power systems,multiple uncertainties are produced due to continuous changes of wind power,which in turn will affect the dispatching and operational process of the power grid.In this process,excessive pursuit of the lowest risk of wind energy may bring an apparent influence on the economic effect of the multi-energy complementary power generation system because a continuous imbalance between demand and supply may lead to wind curtailment.To solve these issues,a new model that couples the multi-dimensional uncertainty model with the day-ahead complementary operation model is developed for a wind-hydrothermal system.A multi-dimensional uncertainty model(MU)is used to deal with wind uncertainty because it can quantitatively describe the complex features of error distribution of hourly dayahead wind power forecasting.The multi-dimensional interval scenes attained by the MU model can reflect hour-to-hour uncertain interaction in the day-ahead complementary operation for the wind-hydro-thermal system.This new model can make up for the shortcomings of the day-ahead operation model by reducing wind power risk and optimizing the operational costs.A two-layer nested approach with the hierarchical structure is applied to handle the wind-hydro-thermal system’s complex equality and inequality constraints.The new model and algorithm’s effectiveness can be evaluated by applying them to the Shaanxi Electric Power Company in China.Results demonstrated that:compared with the conventional operation strategies,the proposed model can save the operational cost of the units by 7.92%and the hybrid system by 0.995%,respectively.This study can offer references for the impact of renewable energy on the power grid within the context of the day-ahead electricity market.

Two Concepts in Optics of Anisotropic Dispersive Media and Polariton Case in Coordinate-Invariant Way

Two concepts of phenomenological optics of homogeneous, anisotropic and dispersive media are compared, the younger and more general concept of media with spatial dispersion and the older concept of (bi)-anisotropic media with material tensors for electric and magnetic induction which only depend on the frequency. The general algebraic form of the polarization vectors for the electric field and their one-dimensional projection operators is discussed without the degenerate cases of optic axis for which they become two-dimensional projection operators. Group velocity and diffraction coefficients in an approximate equation for the slowly varying amplitudes of beam solutions are calculated. As special case a polariton permittivity for isotropic media with frequency dispersion but without losses is discussed for the usual passive case and for the active case (occupation inversion of two energy levels that goes in direction of laser theory) and the group velocity is calculated. For this active case, regions of frequency and wave vector with group velocities greater than that of light in vacuum were found. This is not fully understood and due to large diffraction is likely only to realize in guided resonator form. The notion of “negative refraction” is shortly discussed but we did not find agreement with its assessment in the original paper.

Tensor products of complementary series of rank one Lie groups

We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β)for small parameters α and β(in our parametrization). We prove further that for SO_0(n, 1) there are finitely many complementary series of the form π_(α+β+2j,)j = 0, 1,..., k, appearing in the tensor product π_α ? π_βof two complementary series π_α and π_β, where k = k(α, β, n) depends on α, β and n.