Regenerative energy management of electric drive based on Lyapunov stability theorem

J. Mod. Power Syst. Clean Energy (2019) 7(2):321–328 https://doi.org/10.1007/s40565-018-0497-y Regenerative energy management of electric drive based on Lyapunov stability theorem Shahab SABZI1, Mehdi ASADI1, Hassan MOGHBELI1 Abstract In recent years, urban rail systems have developed drastically. In these systems, when induction electrical machine suddenly brakes, a great package of energy is produced. This package of energy can be stored in energy storage devices such as battery, ultra-capacitor and flywheel. In this paper, an electrical topology is proposed to absorb regenerative braking energy and to store it in ultracapacitor and battery. Ultra-capacitor can to deliver the stored energy to DC grid and to charge the battery for auxiliary applications such as lighting and cooling systems. The proposed system is modeled based on large signal averaged modeling, which leads to the simplicity of calculations. The control system is based on Lyapunov stability theorem which guarantees system stability. Also, an energy management algorithm is proposed to control energy under braking and steady-state conditions. Finally, the simulation results validate the effectiveness of the proposed control and energy management system. Keywords DC/DC converter, Lyapunov stability, Bidirectional converter, Energy management system (EMS), Ultra-capacitor, Battery, Switching function CrossCheck date: 27 November 2018 Received: 10 March 2018 / Accepted: 27 November 2018 / Published online: 18 January 2019 Ó The Author(s) 2019 & Mehdi ASADI Shahab SABZI Hassan MOGHBELI 1 Department of Electrical Engineering, Arak University of Technology, Arak, Iran 1 Introduction Capacity, reliability and safety of urban rail systems make these devices suitable for public transportation in developed countries [1, 2]. Considering energy price and climate change, energy saving has become an important subject for research studies. Consumed energy in urban rail systems is divided into two parts, traction usage and nontraction usage. In such systems, about 50% of total consumed energy is related to the traction requirements and the rest is related to non-traction usage or auxiliary systems, such as cooling systems and lighting systems [3, 4], and therefore designing a power electronic topology capable of providing energy for these usages, apart from many benefits, can be useful to the economy. The topic of energy saving in urban rail systems has been investigated in different aspects. In [5], an energy management strategy for capacitor is proposed to adjust charging and discharging threshold voltage based on analysis of train operation states. The main parameter for energy calculations is state of charge (SOC) of energy storage device. In [6], capacitor is used for energy saving in train systems and a hierarchical control strategy is proposed based on energy management section and converter control section. The energy management system works based on an introduced machine and converter control mainly consist of a proportional-integral (PI) closed-loop strategy. Also an optimization algorithm is proposed to estimate the control parameter values at different operations. In [7], a train system considering renewable energy sources (photovoltage and wind power) and the capabilities of using regenerative braking energy is investigated. Apart from these aspects, uncertainties of renewable energies are considered through different scenarios and the whole problem is considered and solved as a large-scale nonlinear 123 322 optimization problem. Energy and economic energy saving of the proposed system under different strategies is also studied. In this paper, a topology for saving regenerative braking energy in storage devices is proposed and control system is designed. A bidirectional DC/DC converter and a unidirectional DC/DC converter are connected in series. Also, ultra-capacitor and battery are used as main energy storage devices. Regenerative energy generated by induction electrical machine (IEM) is a high power density package of energy which occurs during a very short period of time, so must be stored in a device with high power density such as ultra-capacitor [8–10]. To increase the reliability and system efficiency, ultra-capacitor is connected to DC link via a bidirectional DC/DC converter [11–14]. To control the proposed system, switching functions are extracted based on state-space equations [15]. Extraction of switching functions is a well-known method to control switching process of power electronic devices, in which, switching functions are obtained based on system’s requirements [16]. In this paper, switching functions are extracted using fundamentals of Lyapunov stability theorem. Fast and accurate tracking of reference values and maintaining system’s stability are main advantages of this method. Shahab SABZI et al. (a) (b) 2 Modeling and control of proposed system Schematic circuit diagram of the system is shown in Fig. 1a and power electronic model of the system is shown in Fig. 1b. As seen, the converter that is connected to the DC link and ultra-capacitor is bidirectional and the converter between ultra-capacitor and battery is unidirectional. Im is the current from IEM to DC link capacitor. IL1 is the current of bidirectional converter and is positive if the converter works in buck mode, or negative if the converter works in boost mode. IL2 that is either positive or zero, is the current of buck converter. Vdc and Cdc are the voltage and capacitor of DC link, respectively. Also, Cuc, Ruc and Vuc are capacity, resistance and voltage of ultra-capacitor, respectively. Vb is voltage of the battery. d1, d2, d3 are the duty cycles of switches S1, S2 and S3, respectively. L1 and L2 are the inductors of bidirectional and unidirectional converters, respectively. Moreover, there is a dynamic resistor Rdynamic that must dissipate surplus energy when DC link capacitor and ultra-capacitor are fully charged. Therefore, Sd and ud are the switch and its duty cycle of the circuit that connect the dynamic resistor to the DC link. A well-known method to model switching circuits is large signal averaged model, leading to simplicity of 123 Fig. 1 Complete proposed system for absorbing regenerative braking energy in battery and ultra-capacitor Fig. 2 Large signal averaged model of proposed system systems [17]. Averaged model of proposed system is shown in Fig. 2, where k is described as: ( 1 IL1 \0 (boostÞ k¼ ð1Þ 0 IL1 [ 0 (buckÞ Converters are controlled using switching functions, based on Lyapunov stability theorem. Switching functions are obtained separately for every state. In order to express the equations, first a new term named d12 combined of d1 and d2 is generated as [18]: d12 ¼ kð1  d2 Þ þ ð1  kÞd1 ð2Þ where d12 is the switching function of bidirectional converter. Regenerative energy management of electric drive based on Lyapunov stability theorem 2.1 Switching functions extraction us (...truncated)