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The stochastic economic dispatch problem of power system with multiple wind farms and pumped-storage hydro stations is formulated as a specific stochastic dynamic programming (DP) model, i.e. stochastic storage model, it is impossible to obtain an accurate solution due to the curse of dimensionality. Based on the approximate DP (ADP) method, the stochastic storage model can be transformed into a series of mixed-integer linear programming (MILP) models by describing the approximate value functions (AVFs) as convex piecewise linear functions in post-decision states. The AVFs are first initialised using the results of the deterministic model under a forecast scenario of wind farm output and then trained by scanning stochastic sampling scenarios consecutively with the successive projective approximation routine algorithm. To obtain a nearoptimal day-ahead dispatch scheme, the forecast scenario is substituted into the MILP models expressed by the trained AVFs and is solved forward through each time interval. The network constraints are incorporated by the while-loop detection of critical lines. Test results on an actual provincial power system and the modified IEEE 39-bus system, including the comparison among the ADP, DP, scenario-based and chance-constrained programming methods, demonstrate the feasibility and efficiency of the proposed model and algorithm.

For the controllability of the transmission power of DC transmission channels, the optimal power distribution (OPD) of AC-DC parallel transmission channels is an effective measure for improving the economic operation of an AC-DC interconnected power grid. A dynamic optimal power flow model for day-ahead OPD of AC-DC parallel transmission channels is established in this paper. The power flow equation constraints of an AC-DC interconnected power grid and the constraints of the discrete regulation requirement of the transmission power of DC channels are considered, which make the OPD model of the AC-DC parallel transmission channels a mixed-integer nonlinear non-convex programming (MINNP) model. Through a cone relaxation transformation and a big M method equivalent transformation, the non-convex terms in the objective function and constraints are executed with the convex relaxation, and the MINNP model is transformed into a mixed-integer second-order cone programming model that can be solved reliably and efficiently using the mature optimization solver GUROBI. Taking an actual large-scale AC-DC interconnected power grid as an example, the results show that the OPD scheme of the AC-DC parallel transmission channels obtained by the proposed algorithm can effectively improve the economical operation of an AC-DC interconnected power grid.

The secure operation of 110-kV networks should be considered in the optimal generation dispatch of regional power grids in large central cities. However, since 110-kV lines do not satisfy the premise of R << X in the direct current power flow (DCPF) model, the DCPF, which is mostly applied in the security-constrained unit commitment (SCUC) problem of high-voltage power grids, is no longer suitable for describing the active power flow of regional power grids in large central cities. Hence, the quadratic active power flow (QAPF) model considering the resistance of lines is proposed to describe the network security constraints, and an SCUC model for power system with 110-kV network and pumped-storage hydro (PSH) units is established. The analytical expressions of the spinning reserve (SR) capacity of PSH units are given considering different operational modes, and the SR capacity of PSH units is included in the constraint of the SR capacity requirement of the system. The QAPF is a set of quadratic equality constraints, making the SCUC model a mixed-integer nonlinear non-convex programming (MINNP) model. To reduce the computational complexity of solving the model when applied in actual large-scale regional networks, the QAPF model is relaxed by its convex hull, and the SCUC model is transformed into a mixed-integer convex programming (MICP) model, which can be solved to obtain the global optimal solution efficiently and reliably by the mature commercial solver GUROBI (24.3.3, GAMS Development Corporation, Guangzhou, China). Test results on the IEEE-9 bus system, the PEGASE 89 bus system and the Shenzhen city power grid including the 110-kV network demonstrate that the relaxed QAPF model has good calculation accuracy and efficiency, and it is suitable for solving the SCUC problem in large-scale regional networks.

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