Shaohua Zhang

Analysis of Probabilistic Optimal Power Flow Taking Account of the Variation of Load Power

This paper presents a probabilistic optimal power flow (POPF) algorithm taking account of the variation of load power. In the algorithm, system load is taken as a random vector, which allows us to consider the uncertainties and correlations of load. By introducing the nonlinear complementarity problem (NCP) function, the Karush-Kuhn-Tucker (KKT) conditions of POPF system are transformed equivalently into a set of nonsmooth nonlinear algebraic equations. Based on a first-order second-moment method (FOSMM), the POPF model which represents the probabilistic distributions of solution is determined. Using the subdifferential, the model which includes nonsmooth functions can be solved by an inexact Levenberg-Marquardt algorithm. The proposed algorithm is verified by three test systems. Results are compared with the two-point estimate method (2PEM) and Monte Carlo simulation (MCS). The proposed method requires less computational burden and shows good performance when no line current is at its limit.

Joint equilibrium analysis of electricity market with tradable green certificates

Renewable portfolio standard (RPS) and tradable green certificate (TGC) schemes are important mechanisms to promote the development of renewable energy. In order to investigate the impacts of RPS and TGC schemes on the electricity wholesale market competition, a joint equilibrium model considering the oligopolistic TGC market is proposed in the paper based on the oligopoly competition equilibrium theory. Therein all generation companies behave in accordance with cournot model in the wholesale market, while the renewable companies behave in accordance with supply function model in the TGC market. This model can be formulated as an equilibrium problem with equilibrium constraints (EPEC) and is solved by the nonlinear complementarity approach. The simulation results show that, when the RPS is relatively low, renewable companies tend to withhold some of TGCs to raise the TGC price. Nevertheless, when the RPS is relatively high, renewable companies have few TGCs to withhold, and they may choose to reduce their wholesale electricity output, so as to reduce the amount of TGCs and raise the TGC price. These strategic behaviors will raise the electricity market price, and have negative impacts on the market efficiency.

Two-stage joint equilibrium model of electricity market with tradable green certificates:

Renewable portfolio standard (RPS) with tradable green certificate (TGC) scheme has important influences on the market equilibrium outcomes and generation firms’ strategic behaviors. The main objective of this paper is to investigate that under the RPS with TGC scheme, who and how to exercise the market power, and to what extent market powers are exercised in the electricity wholesale and TGC markets. This is achieved by firstly proposing a two-stage joint equilibrium model based on the oligopolistic competition equilibrium theory. The model is then formulated as an equilibrium problem with equilibrium constraints (EPEC) by using the backward induction method, which is further solved by the nonlinear complementarity approach. Finally, simulation results show that renewable firms tend to withhold some of TGCs to raise the TGC prices when the RPS is relatively low, otherwise they choose to cut down their electricity output to reduce the volume of TGC and raise the TGC price. Moreover, facing the increasing TGC price, fossil fuel firms tend to withhold their electricity output to decrease the demand of TGCs and lower the TGC price. This study has meaningful implications for design of the electricity markets with TGC market.

Robust optimization of risk for power system based on information gap decision theory

Risk-control optimization has great significance for security of power system. Usually the probabilistic uncertainties of parameters are considered in the research of risk optimization of power system. However, the method of probabilistic uncertainty description will be insufficient in the case of lack of sample data. Thus non-probabilistic uncertainties of parameters should be considered, and will impose a significant influence on the results of optimization. To solve this problem, a robust optimization operation method of power system risk-control is presented in this paper, considering the non-probabilistic uncertainty of parameters based on information gap decision theory (IGDT). In the method, loads are modeled as the non-probabilistic uncertainty parameters, and the model of robust optimization operation of risk-control is presented. By solving the model, the maximum fluctuation of the pre-specified target can be obtained, and the strategy of this situation can be obtained at the same time. The proposed model is applied to the IEEE-30 system of risk-control by simulation. The results can provide the valuable information for operating department to risk management.

Allocation strategy based on prospect theory for power supplier

Power allocation into decision-making model plays a valuable role for the power supply company to mitigate price risks and improve their profitability in electricity market environment. In this paper, we develop a power allocation model based on the prospect theory, which considers the psychological factors of decision-making in reality, through calculating the value of electricity purchasing business function and weighting function retrieves the maximum number of prospects for the utility as the optimal allocation scheme. The results show that the risk preferences of the real decision makers will change along with the psychological expectations, the power allocation strategy is more conform to the actual decision model of decision-makers compared with the traditional power allocation model.

Solution of probabilistic load flow in power system based on non-intrusive arbitrary polynomial chaos theory

Non-intrusive arbitrary polynomial chaos theory (NIAPC) can overcome the defects of traditional methods which need abundant simulations and time. Meanwhile, NIAPC can deal with probabilistic load flow analysis with arbitrary distributed uncertainties precisely with a small quantity of simulations. The paper presents the probabilistic load flow based on non-intrusive arbitrary polynomial. Firstly, the probabilistic collocation points are chosen. Then, Hermite polynomial is solved, and the uncertain problems whose parameters obey to experienced probability distribution are solved. Finally, the paper simulated the process of probabilistic load flow (PLF) on the platform of Matlab. The results were compared between NIAPC and Monte Carlo (MC). Results indicate that the PLF calculation based on NIAPC is not only able to achieve a high accuracy compared to the MC, but also it does own high potential to relief the computation burden of traditional PLF calculation drastically.

Application of robust optimization theory to generation asset allocation

In the deregulated electricity market, the generation company (Genco) can sell energy through several trading choices such as the wholesale spot market, bilateral contracts and option contracts. These trading choices have different risk characteristics. To achieve a satisfactory risk-return target, the Genco should allocate the electricity among these trading choices reasonably. A robust optimization based risk management model is proposed for Gencos generation asset allocation under uncertain spot market prices. In this model, the robust profit (RP) and conditional robust profit (CRP) are used to describe Gencos profit under a certain confidence level. The objective of the Gencos generation asset allocation problem is to maximize Gencos CRP. With this method, different allocation strategies can be made for Gencos different attitudes toward risk. The Monte Carlo simulation-based numerical examples are presented to validate the reasonableness and effectiveness of proposed model.

Comparison of LOLE and EUE-Based Wind Power Capacity Credits by Probabilistic Production Simulation

To mitigate the global climate change and environmental issues, wind power generation is growing at a startling pace around the world. The wind power capacity credit can be used to measure the contribution of wind power resource to the capacity adequacy of a power system, thus plays an important role in development of wind power resources and expansion planning of power systems. Using the probabilistic production simulation technology, wind power capacity credits based on the capacity adequacy indexes LOLE and EUE are investigated and compared in this paper. The theoretical analysis and numerical simulation show that non-smoothness presents in variation of the LOLE index with load, while variation of the EUE index with load displays a good smoothness. This will lead to a difference in the EUE-based and the LOLE-based wind power capacity credits. In addition, the wind power capacity credits based on the LOLE index is non-monotonic for relatively small installed capacity of wind power.

Modeling and Simulation of Electricity Markets under Different Environmental Policies

Renewable energy quota obligation has been enforced in many countries to mitigate greenhouse gas emissions and promote renewable energy. To fulfill the quota obligations, many countries have adopted environmental policies such as carbon tax (CT) and feed-in tariff (FIT) in their electricity sectors. This paper aims to examine the impacts of different environmental policies on the electricity market competition and the social welfare. For this purpose, Cournot equilibrium models for electricity wholesale market competition are developed taking into account the CT and the FIT policies. The nonlinear complementarity approach is employed to solve these equilibrium problems. In addition, an environmental policy that combines the carbon tax and the feed-in tariff (CT&FIT) is also proposed in this paper. Numerical simulations are presented to assess the performances of different environmental policies. Some practically meaningful conclusions are derived.

The solution of optimal power flow based on a semismooth subdifferential method

A semismooth subdifferential method (SSM) for solving optimal power flow (OPF) is presented. The Karush-Kuhn-Tucker (KKT) conditions of OPF system, by introducing nonlinear complementarity problem (NCP) function, are transformed equivalently to a set of semismooth nonlinear algebraic equations. Then an inexact Levenberg-Marquardt (L-M) algorithm based on the subdifferential is improved and employed to solve the equations. The positive definitiveness of the iterative coefficient matrix is enhanced by using L-M parameter, while a reformed nonmonotone line search is used to enforce global convergence. Finally, the effectiveness of the SSM is shown by analyzing the computational performance and convergence characteristic of the proposed algorithm on test systems.