Energy savings in electric rail transport are important in order to increase energy efficiency and reduce its carbon footprint. This can be achieved by storing and using the energy generated during regenerative braking. The system described in this paper consists of a supercapacitor energy storage system (SC ESS), a bidirectional DC/DC converter, and an algorithm to control the energy flow. The proper design of the algorithm is critical for maximizing energy savings and stabilizing the power grid, and it affects the lifetime of the SC ESS. This paper presents an energy flow control algorithm based on Pontryagin’s minimum principle that balances maximum energy savings with maximum SC ESS lifetime. The algorithm also performs SC ESS recharging while the rail vehicle stops on inclines to reduce the impact of its next acceleration on the power grid. To validate the algorithm, offline simulations are performed using real tram speed measurements. The results are then verified with a real-time laboratory emulation setup with HIL simulation. The tram and power grid are emulated with LiFePO4 batteries, while the SC ESS is emulated with a supercapacitor. The proposed algorithm controls a three-phase converter that enables energy exchange between the batteries and the supercapacitor. The results show that the proposed algorithm is feasible in real time and that it can be used under real operating conditions.

The paper presents a method for managing the energy storage and use of a mobile supercapacitor energy storage system (SC ESS) on a tram vehicle for the purpose of active voltage stabilization of the power grid. The method is based on an algorithm that identifies the need to utilize the energy of the SC ESS depending on changes in the voltage of the power grid caused by the driving of other nearby tram vehicles. The waveform of the current flowing into or out of the SC ESS during this control is determined based on Pontryagin’s minimum principle, which optimizes the minimum change in the voltage level at the pantograph and the minimum temperature of the supercapacitor. In this way, this approach aims to minimize the changes in the voltage of the power grid caused by other vehicles and to maximize the lifespan of the supercapacitor. The algorithm was tested within the MATLAB/Simulink R2022b programming environment and experimentally validated with an HIL simulation experiment in a laboratory setup to emulate the rail vehicle system, the supercapacitor, and the power supply network.

A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive control of a class of system of systems for which the overall objective function is the sum of convex quadratic cost functions of (locally) constrained linear subsystems that are coupled through a set of (global) linear constraints on the subsystems coordination parameters. The proposed control algorithm is based on parametrization and splitting of the underlying optimization problem into one global coordination problem and a set of local optimization problems pertaining to individual subsystems. The local optimization problems are solved off-line, via parametric optimization, while the coordination problem is solved on-line. The properties of the local parametric solutions are utilized to solve the coordination problem very efficiently. In particular, it is shown that, for a fixed number of coupling constraints, the coordination problem can be solved with a linear-time algorithm in a finite number of iterations if all subsystems have one-dimensional coordination parameters.

Dynamic Management of Electrical Power Distribution Networks