The ever-increasing integration of variable wind energy requests for a power system with high flexibility. In this paper, we formulate the real-time economic dispatch problem as a multi-stage robust program to leverage flexible resources, especially energy storage systems, in a broader timescale, and also to avoid the risk of high costs in critical scenarios. The multi-stage robust program is decomposed to the dynamic programming form and the fast robust dual dynamic programming (FRDDP) algorithm is developed to solve it efficiently. To tackle the nonconvexities caused by the inter-temporal constraints of ESSs, an estimation-correction method is developed, and measures of the approximation accuracy are presented. Comprehensive case studies comprising units up to 1371 are carried out to verify the effectiveness of the proposed model. Numerical results show that compared with the existing ones, the proposed multi-stage robust model achieves lower cost under the worst-case scenario and shows better scalability in large-scale systems.

The modeling and multi-energy flow calculation of an integrated energy system (IES) are the bases of its operation and planning. This paper establishes the models of various energy sub-systems and the coupling equipment for an electricity-gas-thermal IES, and an integrated multi-energy flow calculation model of the IES is constructed. A simplified calculation method for the compressor model in a natural gas network, one which is not included in a loop and works in constant compression ratio mode, is also proposed based on the concept of model reduction. In addition, a numerical conversion method for dealing with the conflict between nominal value and per unit value in the multi-energy flow calculation of IES is described. A case study is given to verify the correctness and speed of the proposed method, and the electricity-gas-thermal coupling interaction characteristics among sub-systems are studied.

To coordinate the generation resources located in the integrated transmission and distribution systems considering renewable uncertainty, dynamic economic dispatch (DED) is essential. This article proposes a coordinated robust DED (CRDED) model to enhance the cost-effectiveness and reliability from a system perspective. Then, how to measure the operational risk in the robust model is discussed, if the probability function of the renewable output is obtained, with a risk-based CRDED model established correspondingly. A distributed framework is also presented to solve these two models in a decentralized way, as the transmission and distribution systems solve their regional problems autonomously. The alternating direction method of multipliers (ADMM), which is one of the most efficient dual decomposition methods, is utilized in this framework. Besides, to handle the problem that it is hard to predetermine the value of penalty factors, a varying penalty factor strategy is further applied to enhance the convergence property of ADMM, with the global optimal solution achieved within much fewer iteration numbers. Since the system operators only need to exchange the boundary power, the communication burden is light, and the regional information privacy is enhanced. Case studies on the 448-bus T118D10 system illustrate the effectiveness of the proposed model and approach.

To satisfy the robust and real-time requirements of power flow calculation for large-scale power systems, a globally convergent method is proposed with trust-region techniques, which shows satisfying robustness and convergence. Then, this method is combined with Newton's method to achieve a two-stage algorithm, benefiting from their different advantages. In the first stage, the proposed globally convergent method is used for searching power flow solution. When the values of state variables in a certain iteration are close enough to the real operational point, the algorithm enters the second stage to use Newton's method to achieve the solution. This two-stage algorithm can achieve an accurate solution for solvable cases, and can also achieve a least square solution, which is an approximate solution for unsolvable cases. Numerical experiments show that the proposed globally convergent method and two-stage algorithm have better robustness and efficiency than the existing methods in previous research. They have universality for well- and ill-conditioned systems as well as the cases under ill-conditioned operational modes, heavy loads and inappropriate initial values. They can also handle different limit violations, such as reactive power limit in PV buses and voltage limit with tap changers action, which could significantly benefit real practice.

Considering the separate management of transmission networks (TNs) and distribution networks (DNs), this paper proposes a chance-constrained optimal power flow (CCOPF) formulation for integrated transmission and distribution (I-T&D) networks and its solution algorithm with limited information interaction. The uncertainties of loads and renewable generations are considered in the formulation, which guarantees that generations, power flows, and voltage magnitudes in both TNs and DNs remain within their bounds with a predefined probability. A double-iterative solution algorithm is proposed to solve CCOPF, of which the inner-iteration is applied to solve a deterministic OPF of I-T&D networks while the outer-iteration is to repeatedly update uncertain margins around a forecasted solution to converge finally. Particularly, the heterogeneous decomposition algorithm is applied to solve the deterministic OPF, and an I-T&D-powerflow-based two-point estimation method is proposed to calculate uncertainty margins. The overall solution algorithm is realized based on boundary information exchange between TNs and DNs, where the data and model privacy of TNs and DNs are wellpreserved. Numerical experiments demonstrate the accuracy and efficiency of the proposed solution algorithm.

This paper introduces a novel successive-intersection-approximation-based power flow method for integrated transmission and distribution networks (I-T&D). In this method, the entire I-T&D is split into the transmission network part, distribution network part, and boundary part. Then, alternate iterations are processed between a transmission network (TN) and several distribution networks (DNs) by exchanging the voltage and power injection of boundary buses. Particularly, the voltage magnitude of the boundary buses will be modified every two iterations by obtaining an intersection with the results in the previous two iterations. The local quadratic convergence of the method is proved strictly. The numerical experiment demonstrates that the proposed method has the same accuracy as the method based on the global model. Also, better convergence and efficiency can be achieved under the proposed method compared with the master-slave-splitting method in several different circumstances, DNs with loops, DNs with distributed generations, DNs with on-load tap changers, large-scale systems, etc. Besides, the proposed method is applied in the contingency analysis, achieving satisfying convergence and efficiency.