Mixed integer linear programming (MILP) based formulations and solution methods for short-term hydro generation scheduling (HGS) have been widely adopted by researchers, hydropower producers, and system operators in recent years. This approach calls for the nonlinear forebay level, tailrace level, penstock loss, and hydropower production functions to be replaced with their piecewise linear approximations. However, the effects of the linearization of the nonlinear functions and related constraints on solution feasibility have not been fully discussed in the literature. In this paper, the issues concerning solution feasibility are discussed in detail and a method is presented to ensure that the solution obtained based on the approximated MILP formulation remains feasible for the original nonlinear formulation. Furthermore, it is found that the real number water delay can be handled in the formulation without destroying the linear structure of the water balance constraints. Numerical testing results show that the method presented in this paper is effective.

An MILP Based Formulation for Short-Term Hydro Generation Scheduling With Analysis of the Linearization Effects on Solution Feasibility

Conventionally, power flow equations are used for distribution systems (DS) analysis to find the nodal voltages. For the particular form of the DS reconfiguration problem, however, a direct formulation in terms of branch flows allows a substantial increase in solution efficiency from an optimization point of view. In this paper, a set of linear current flow (LCF) equations are derived for DS. This formulation is then used within the network reconfiguration problem for loss minimization. A mixed-integer quadratically constrained programming (MIQCP) formulation, together with a mixed-integer linear programming (MILP) formulation, are proposed in this paper and assessed through simulations. In these comparisons, the MILP formulation shows computational advantages over the MIQCP version and the preceding literature. The proposed methods are evaluated on several test systems.

Linear Current Flow Equations With Application to Distribution Systems Reconfiguration

Research highlights? In genetic algorithms, selection based on the quality produce premature convergence. ? Crossover is sensitive to the gene position when the representation of the chromosome, is linear. ? The ends of this type of chromosome have very low probability of changing by mutation. ? A genetic algorithm is applied to the unit commitment problem using a deterministic selection operator and an annular crossover. One of the disadvantages of traditional genetic algorithms is premature convergence because the selection operator depends on the quality of the individual, with the result that the genetic information of the best individuals tends to dominate the characteristics of the population. Furthermore, when the representation of the chromosome is linear, the crossover is sensitive to the encoding or depends on the gene position. The ends of this type of chromosome have only a very low probability of changing by mutation. In this work a genetic algorithm is applied to the unit commitment problem using a deterministic selection operator, where all the individuals of the population are selected as parents according to an established strategy, and an annular crossover operator where the chromosome is in the shape of a ring. The results obtained show that, with the application of the proposed operators to the unit commitment problem, better convergences and solutions are obtained than with the application of traditional genetic operators.

A deterministic annular crossover genetic algorithm optimisation for the unit commitment problem

http://users.ntua.gr/pgeorgil/Files/J56.pdf

A new memetic algorithm approach for the price based unit commitment problem

Prices in electricity markets are given by the dual variables associated with the supply-demand constraint in the dispatch problem. However, in unit-commitment-based day-ahead markets, these variables are not easy to obtain. A common approach relies on re-solving the dispatch problem with the commitment decisions fixed, and utilizing the associated dual variables. This avenue may lead to inadequate revenues to generators, which has led to the introduction of uplift payments made by the market operator for further compensating the generators. An alternative pricing mechanism known as convex hull pricing has been proposed to reduce or eliminate uplift payments. Computation of these prices requires the global maximization of an associated Lagrangian dual problem. In this paper, we present an extreme-point-based procedure for obtaining a global maximizer. Unlike standard subgradient schemes where an arbitrary subgradient is used, we present an extreme-point subdifferential (EPSD) algorithm; this is a novel technique in which the steepest ascent direction is constructed by solving a continuous quadratic program. The EPSD algorithm initiates a move along this direction, employing an a priori constant steplength, with the intent of reaching the boundary of the face. A backtracking scheme selects a steplength that ensures descent with respect to a suitably defined merit function. As most electricity markets today co-optimize energy and reserves, an extension of the proposed convex hull pricing algorithm is provided for such integrated markets. Under suitable assumptions, we compare outcomes of energy-only and energy-reserve co-optimized markets under different pricing and uplift rules. In these examples, pricing rules have a major impact on the total payment while the uplift payment only accounts for a small portion of it. We also observe that it remains unclear whether marginal-cost pricing or convex-hull pricing leads to higher total payment.

http://www.meyn.ece.ufl.edu/assets/uploads/2014/12/EPSD_partI.pdf

An Extreme-Point Subdifferential Method for Convex Hull Pricing in Energy and Reserve Markets—Part I: Algorithm Structure

Fast unit commitment based on optimal linear approximation to nonlinear fuel cost: Error analysis and applications

: This paper explores the relay protection of the power grid with large-scale wind power access across the globe. First, the amplitude and attenuation characteristics of short circuit current in different types of wind turbines are analyzed, as well as the contributing factors to short-circuit current in wind farms. Second, the fault characteristics and corresponding protection strategies of the collector circuit in the wind power plant are discussed. Then, in view of the adaptability of HVDC protection to the grid power with wind power access, the performance of zero-sequence protection, reclosing and distance III section and the corresponding countermeasures are analyzed. Finally, suggestions for the directions of further research are proposed: strengthening research on fault characteristics of wind turbines; performing general electromagnetic transient modeling of wind turbines for protection; developing new principles and technologies of network protection applicable to protection of wind farm collector buses and networks; and strengthening collaborations between wind farms and power grids in protection and control to solve the problems in relay protection.

Jiping Yang

Papers

Fast unit commitment based on optimal linear approximation to nonlinear fuel cost: Error analysis and applications

Progress in research on relay protection of the power system with large-scale wind power access