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The efficient use of regenerative braking energy between trains can significantly reduce the net traction energy consumption in urban rail transit systems, and has attracted considerable attention in recent years. An effective way of using regenerative braking energy is to adjust the train's coasting or cruising phase to an acceleration phase to match the braking phase of a nearby train within the same substation. This paper formulates the train driving phase adjustment problem as a cooperative optimal control problem, where a novel energy constraint is introduced to ensure efficient use of regenerative braking energy during the adjusted phase with optimal traction effort. By applying the control parameterisation method and elaborate handling of the energy constraint and the non-smooth control bound constraint, we transform the formulated problem into a nonlinear programming problem. We then use the sequential quadratic programming algorithm to solve the resulting problem, with the gradients of the cost and constraint functions computed using the sensitivity method. Numerical examples based on real-world data for a subway line show the effectiveness of the proposed method and its advantages over a genetic algorithm in terms of energy savings and computational efficiency. • A novel energy constraint is proposed to sufficiently utilize the regenerative energy. • The control parameterisation method is employed to solve the cooperative optimal train operation problem. • The non-smooth control bound constraint is transformed equivalently into point constraints. • Performance of the proposed approach is demonstrated using data for a real subway line. [ABSTRACT FROM AUTHOR]

The parameter optimisation of designed controllers for power systems is always a big concern and needs a lot of effort of researchers especially when the electricity grid becomes larger and more complex. This study proposes a control parameterisation using genetic algorithms (GAs) for power oscillation damping (POD) incorporating synchronous condensers (SCs) via software-in-the-loop simulation to enhance the damping and frequency stability for low-inertia systems. A closed-loop interfaced setup among real-time digital simulator, MATLAB, and OLE for process communication running in real time is analysed and implemented to optimise the POD parameters of a SC. Furthermore, a Prony technique based on the system measurement is applied to find out the frequency and damping ratio of the dominant oscillation mode. The POD optimal parameters are determined by the GA objective function that maximises the damping ratio of the dominant oscillation mode. The effectiveness of the proposed method in damping power oscillations and frequency stability improvement is verified through simulation results of the future western Danish power system. Simulation results demonstrate that the proposed approach offers good performance for parameter optimisation of the POD.