Robust Scheduling Model For Multi-area Power Systems With High-penetration Renewable Generation

Optimal power generation and transmission scheduling is a crucial process in the day-ahead operation of power systems.The scheduling process,if well performed,can help save a lot of operation costs either in vertically integrated or deregulated market schemes.Compared with that of single-area power systems,the scheduling problem in multi-area power systems is more challenging,as there are more decision variables,more constraints,and additional restriction on the pattern of decision making.Due to the ongoing reformation and liberalization of the power industry,the optimal interchange scheduling of multi-area power systems becomes even more important nowadays.On the other hand,the rapid increase of intermittent renewable generations(e.g.,wind power generation and photovoltaic generation)over the past decade has brought significant randomness and volatileness to the power system.Therefore,it is valuable to carry out researches on renewable generation integration and how to enhance the economic efficiency and reliability of the system while subject to inevitable uncertainties.In this thesis,we study the day-ahead optimal scheduling problem of multi-area power systems that have large share of renewable generations.The main work and results are summarized as follows:First,the multi-area robust security constrained unit commitment(SCUC)model with novel uncertainty sets is proposed according to the hierarchical decision-making scheme.The variance of system net load is used to construct the novel uncertainty set,which indicates the overall uncertainty requirement of the multi-area power system.We prove that such an uncertainty set can provide a more precise probabilistic guarantee than conventional budgeted sets.To solve the problem in decentralized manner,an upper-level robust convex optimization model is proposed to optimize the tie-line power flow and derive a generation interval for each area.Through the coordinated uncertainty requirement depicted by the generation interval,each regional system operator can solve a decoupled robust SCUC problem independently.Besides,a modified outer approximation algorithm is developed to obtain a higher-quality solution of the bilinear programming involved in the process.Simulation results on a two-area system demonstrate the effectiveness of the uncertainty set,and show the economic efficiencies of unit commitment solutions acquired from the hierarchical method.Next,in order to capture the spatiotemporal correlations of random wind power,and address the conservativeness issue of the robust optimization method,we investigate the SCUC problem through a data-based distributionally robust optimization approach.We assume that the first and second order moments of stochastic parameters can be inferred from historical data,and then employed to model the set of probability distributions.The resulting problem is a two-stage distributionally robust SCUC model with second order moment constraints,and we show that it can be recast as a mixed integer semidefinite programming(MISDP)with finite constraints.The solution algorithm of the problem comprises solving a series of relaxed MISDPs and a subroutine of feasibility checking and vertex generation.Based on the verification of strong duality of the semidefinite programming(SDP)problems,we propose a cutting plane algorithm for solving the MISDPs;we also introduce an SDP relaxation for the feasibility checking problem,which is an intractable biconvex optimization.Experimental results show that without any tunings of parameters,the real-time operation cost of distributionally robust SCUC method outperforms those of deterministic SCUC and two-stage robust SCUC methods in general,and our method also enjoys higher reliability of dispatch operations.Then,a value-function-based decomposition and coordination method is proposed in this thesis to address the issue that Lagrangian-dual-function-based algorithms cannot guarantee convergence and global optimality for decentralized multi-area SCUC problems.In our framework,first,each regional system operator sets the tie-line power injections as variational parameters in its regional SCUC model,and utilizes a finite algorithm to generate an MILP value function,which returns the optimal generation cost for any given interchange scheduling.Then,with the value functions available from all system operators,theoretically,a coordinator is able to devise a globally optimal interchange scheduling.Since power exchanges may alter the financial position of each area considerably from what it would have been via scheduling independently,we propose,further,a fair savings allocation method using the values functions derived above and the Shapley value in cooperative game theory.Numerical experiments on a two-area 12-bus system and a three-area 457-bus system were carried out.The validity of the value-functionbased method was verified for the decentralized multi-area SCUC problems.The outcome of savings allocation was compared with that of the locational-marginal-cost-based method.Finally,we study the day-ahead generation unit and tie-line scheduling problem,which is originated from the asynchronous interconnection of the southern China power system.To coordinate the generation of the sending-end and the demand of the receiving-end of the asynchronously interconnected system,we develop a two-stage mathematical optimization model.In the first-stage problem,the variance of the remaining load series of receiving-end is minimized to generate a near-optimal inter-area power transmission schedule.In the second-stage problem,the production level of generation units and power flow of HVDC tie-lines are determined with the objective of minimizing transmission losses.Moreover,in the second-stage problem,discrete characteristics of HVDC power profile are explicitly modeled,and a quadratic loss function derived from historical data is used to calculate the overall loss of each HVDC.Numerical experiments based on realistic data of China Southern Power Grid are carried out.The feasibility and effectiveness of the proposed method is verified through comparing the optimized generation and transmission schedules with original ones which are generated based on expert knowledge.