Demand response (DR) is considered to be an effective way to bring significant economic benefit to the commercial campus integrated energy system (CCIES) due to the large amount of flexible cooling and electric vehicle (EV) charging loads. To maximize DR’s benefits, this paper proposes an integrated DR framework that includes direct load control for cooling loads and time-of-use for EV charging station load in the CCIES. Moreover, multiple uncertainties threaten the secure and economic operation of the CCIES. To deal with these challenges, this paper establishes an interval optimization (IO) based economic dispatch (ED) model, considering the uncertain parameters, including ambient temperature, DR parameters, pipeline parameters, and maximum available PV power output. To improve the solution efficiency, the nonlinear constraints are linearized by applying multi-layer perceptron and affine arithmetic. The order relation and the possibility degrees of intervals are used to transform the interval ED model into a bi-level optimization model. The extreme value theorem of linear interval functions is used to obtain the analytical expressions of the optimal solutions of inner-level models, and the ED model is finally transformed into a solvable mix-integer linear programming model. Test results from actual CCIES demonstrate that the DR can improve the economy and reduce the uncertain fluctuation range of both the objective function and state variables. The ED result can maintain an economical and secure operation under multiple uncertain fluctuations.

An optimal preventive-corrective control model for static voltage stability under multiple $N-1$ contingencies considering the wind power uncertainty is established in this paper. The objective is to minimize the control variable adjustment cost including the load shedding cost of each contingency. The chance constraints of the static voltage stability margins (SVSMs) in the normal operation state and after each $N-1$ contingency are included. The approximate functions between the probability density functions (PDFs) of SVSMs and load shedding quantity with respect to preventive control variables are obtained to transform the expectation of load shedding quantity and the SVSM chance constraints into deterministic expressions. An approximate sequential convex quadratically constrained quadratic programming iteration method is proposed to solve the optimal control model. In each iteration, the approximate expressions and range are determined by the generated data samples. Moreover, a fast approximation calculation method of second-order matrices is proposed. By the naive Bayes classifier, the most severe $N-1$ contingencies are selected to replace all the contingencies to be added to the optimization model to improve the computational efficiency. Case studies on the IEEE-39 bus system and an actual provincial power grid demonstrate the effectiveness and efficiency of the proposed method.

Calculation of static voltage stability margin (SVSM) of AC/DC power systems with lots of renewable energy sources (RESs) integration requires consideration of uncertain load growth and renewable energy generation output. This paper presents a bi-level optimal power flow (BLOPF) model to identify the worst-case SVSM of an AC/DC power system with line commutation converter-based HVDC and multi-terminal voltage sourced converter-based HVDC transmission lines. Constraints of uncertain load growth's hypercone model and control mode switching of DC converter stations are considered in the BLOPF model. Moreover, uncertain RES output fluctuations are described as intervals, and two three-level optimal power flow (TLOPF) models are established to identify interval bounds of the system worst-case SVSM. The two TLOPF models are both transformed into max–min bi-level optimization models according to independent characteristics of different uncertain variables. Then, transforming the inner level model into its dual form, max–min BLOPF models are simplified to single-level optimization models for direct solution. Calculation results on the modified IEEE-39 bus AC/DC case and an actual large-scale AC/DC case in China indicate correctness and efficiency of the proposed identification method.

With more and more offshore wind power being increasingly connected to power grids, fluctuations in offshore wind speeds result in risks of high operation costs. To mitigate this problem, a risk-averse stochastic economic dispatch (ED) model of power system with multiple offshore wind farms (OWFs) is proposed in this paper. In this model, a novel GlueVaR method is used to measure the tail risk of the probability distribution of operation cost. The weighted sum of the expected operation cost and the GlueVaR is used to reflect the risk of operation cost, which can consider different risk requirements including risk aversion and risk neutrality flexibly by adjusting parameters. Then, a risk-averse approximate dynamic programming (ADP) algorithm is designed for solving the proposed model, in which multi-period ED problem is decoupled into a series of single-period ED problems. Besides, GlueVaR is introduced into the approximate value function training process for risk aversion. Finally, a distributed and risk-averse ADP algorithm is constructed based on the alternating direction method of multipliers, which can further decouple single-period ED between transmission system and multiple OWFs for ensuring information privacy. Case studies on the modified IEEE 39-bus system with an OWF and an actual provincial power system with four OWFs demonstrate correctness and efficiency of the proposed model and algorithm.

Multi-terminal voltage source converter-based high-voltage direct current (VSC-MTDC) transmission technology has become an important mode for connecting adjacent offshore wind farms (OWFs) to power systems. Optimal dispatch of an OWF cluster connected by the VSC-MTDC can improve economic operation under the uncertainty of wind speeds. A two-stage distributionally robust optimal dispatch (DROD) model for the OWF cluster connected by VSC-MTDC is established. The first stage in this model optimizes the unit commitment of wind turbines to minimize mechanical loss cost of units under the worst joint probability distribution (JPD) of wind speeds, while the second stage searches for the worst JPD of wind speeds in the ambiguity set (AS) and optimizes active power output of wind turbines to minimize the penalty cost of the generation deviation and active power loss cost of the system. Based on the Kullback-Leibler (KL) divergence distance, a data-driven AS is constructed to describe the uncertainty of wind speed, considering the correlation between wind speeds of adjacent OWFs in the cluster by their joint PD. The original solution of the two-stage DROD model is transformed into the alternating iterative solution of the master problem and the sub-problem by the column-and-constraint generation (C&CG) algorithm, and the master problem is decomposed into a mixed-integer linear programming and a continuous second-order cone programming by the generalized Benders decomposition method to improve calculation efficiency. Finally, case studies on an actual OWF cluster with three OWFs demonstrate the correctness and efficiency of the proposed model and algorithm.