A multi‐objective security‐constrained optimal generation dispatch (MOSCOGD) model for large‐scale power systems with wind farms and pumped‐storage hydroelectric (PSH) stations is proposed. In this model, fuel consumption, emission content of atmospheric pollutants, and power purchase costs are taken into account as objective functions, and network security under basic status and N − 1 criterion conditions, and the operational limits of PSH resources are included in the constraints. The difficulties associated with discrete variables for describing the operational characteristics of PSH resources are avoided by introducing two continuous variables, generation power and pumping power, which satisfy complementary constraints. The normalised normal constraint algorithm is used to transform the three‐objective optimal dispatch model into a series of single‐objective optimisation models, which are solved by the interior point method, resulting in a series of evenly distributed Pareto optimal solutions (POSs) and the complete Pareto frontier surface. The computational efficiency is greatly enhanced by employing a checking–adding–checking again‐adding again scheme to address network security constraints. Moreover, parallel computing is employed to improve the computation speed for solving the POSs of the MOSCOGD model. Test results on an actual large‐scale power system and the modified IEEE 39‐bus system demonstrate the effectiveness of the proposed method.

An optimal static voltage stability margin (SVSM) control model considering the uncertain wind farm output is proposed, in which the probability distribution of SVSM is required to satisfy the chance and variance constraints. A probabilistic distribution control method is proposed to solve the model. First, a linear weighted sum of B-spline basic functions is introduced to approximate the analytical function between the probability density function (PDF) of SVSM and control variables. Next, the analytical expression of the PDF of SVSM corresponding to a control variables’ sample is derived, and the sample of corresponding B-spline function weights is obtained, thus forming a series of ‘control variables-weights’ samples. Then, the analytic functions between weights and control variables are obtained using the generated samples to train a radial basis function neural-network, and the analytical function between the PDF of SVSM and control variables is obtained. After that, the chance and variance constraints are transformed into general nonlinear constraints with respect to control variables. Moreover, a method of selecting key control variables by calculating sensitivities is proposed to increase computational efficiency. Test results on the IEEE-39 bus system and an actual provincial power grid demonstrate the feasibility and effectiveness of the proposed method.

With lots of distributed renewable generators and storage devices integrated into distribution networks, the coordinate economic dispatch (ED) between transmission and distribution networks is needed. A stochastic ED algorithm based on distributed approximate dynamic programming for integrated transmission and distribution networks considering the uncertain renewable generator outputs is proposed. First, the convex power flow models of transmission and distribution networks are proposed. Then, the reservoir levels of pumped-storage hydro stations and the remaining stored electric energy of battery storage stations are deemed as the storage quantities, while the renewable generator outputs are deemed as the exogenous stochastic variables to establish the stochastic storage model for the stochastic ED problem of integrated transmission and distribution networks. The approximate value functions represented by the sum of the piecewise linear functions of the storage quantities are constructed to decouple the multiperiod ED problem into a series of single-period ED problems. Finally, by using the alternating direction method of multipliers, each single-period ED problem of integrated transmission and distribution networks is solved in a distributed manner among transmission and distribution networks. Test results on the modified T6D7 system and a practical Shenzhen city network demonstrate the correctness and efficiency of the proposed algorithm.

In the operation of microgrids (MGs), the stochastic production of solar/wind, the discrete variables of photovoltaic (PV) inverter's auxiliary service state and diesel generators’ (DGs’) off–on state generally need to be considered, and a stochastic mixed‐integer non‐linear non‐convex programming (MINNP) model is established for the optimal dispatch of MGs. In this model, the expected value of the sum of DGs’ operation as well as start‐up cost, the network‐loss cost and the PV inverter's auxiliary service cost, is considered as the objective function. The stochastic MINNP model is transformed into a stochastic mixed‐integer second‐order cone programming (MISOCP) model to reduce the computational complexity. The state‐space approximate dynamic programming algorithm is adopted to solve the stochastic MISOCP model. In the algorithm, based on the approximate value functions of typical states that are computed according to the Markov decision process, solving the optimisation model of multiple periods is executed by solving each period's optimisation model one by one to improve the computational efficiency. Meanwhile, parallel computing is executed to greatly improve the efficiency of the proposed algorithm. Test results on two modified IEEE‐33 bus and IEEE‐123 bus islanded MGs with PV/wind/diesel/battery demonstrate the correctness and efficiency of the proposed model and algorithm.

Calculation of the static voltage stability margin (SVSM) of a power system with high wind‐power penetration requires consideration of the uncertain fluctuation of wind farms' (WFs') output. Using interval numbers to describe the uncertain WF output fluctuation and based on the interval optimisation theory, a new SVSM interval calculation method is proposed. The method establishes two bi‐level optimal power flow (OPF) models to calculate the SVSM interval, including a min–min model for the upper bound and a max–min model for the lower bound. Through the dual theory of convex programming, the max–min model is transformed into a max–max model, which is solved by transforming it into a one‐layer optimisation model. Using correlation angles to describe the correlation of different WF output intervals and using linear transformation to decorrelate them into independent intervals, two bi‐level OPF models of calculating the SVSM interval considering different WFs' correlation are established. Take the IEEE‐39 bus system and an actual 964‐bus provincial power grid as examples, compared with the Monte‐Carlo method and the continuous power flow and affine interval integrated method, the results indicate the proposed method obtains more accurate SVSM interval and has better calculation efficiency.