Urban rail trains have undergone rapid development in recent years due to their punctuality, high capacity and energy efficiency. Urban trains require frequent start/stop operations and are, therefore, prone to high energy losses. As trains have high inertia, the energy that can be recovered from braking comes in short bursts of high power. To effectively recover such braking energy, an onboard supercapacitor system based on a radial basis function neural network-based sliding mode control system is proposed, which provides robust adaptive performance. The supercapacitor energy storage system is connected to a bidirectional DC/DC converter to provide traction energy or absorb regenerative braking energy. In the

Urban rail transit systems can effectively alleviate urban traffic congestion due to their ability to carry large loads at high speeds for long distances. More than 300 cities around the world have developed urban rail transit systems, and their passenger volumes have reached 50%–80% in many developed cities. As of 31 December 2018, there was a total of 5,139 km of urban rail transit in 34 cities of mainland China. It is clear that city rail transit has entered a period of vigorous development.

Due to the short distances between stations on urban lines and the high density of vehicles, considerable braking energy is generated during frequent starting/braking processes. Vehicle speeds have increased in recent years, such that greater braking energy is involved [

Automotive supercapacitor control systems are nonlinear and uncertain control systems that are susceptible to end-to-end disturbance [

However, in the design of practical control systems, chattering is prone to occur on both sides of the sliding mode surface when under sliding mode control. To alleviate the chattering problem effectively in traditional sliding mode control, the robustness of the neural network adaptive control system was improved to a certain extent. This study uses the advantages of RBF neural networks (excellent nonlinear function approximation, adaptiveness and self-learning abilities) to propose an onboard supercapacitor system with adaptive and robust sliding mode control. This can be used to recover regenerative braking energy and reduce the line losses of traction grids.

A structural diagram of an onboard ultracapacitor control system is shown in

With an on-board ultracapacitor control system, if the train starts or accelerates, the system will supply power to the train and the supercapacitor will be in a discharged state to avoid supplying power to the train and causing a drop in grid voltage. In this state, circuit modelling using the state-space averaging method can be used to model the discharge state [

where _{1} is the IGBT1 duty ratio.

If

Among them,

Then, the onboard ultracapacitor control system can be considered as a class of second-order nonlinear uncertain system:

Here,

If

Among them,

If

By substituting the control law into the above equation, it can be found that:

If

So, the control system designed in this paper can meet the stability requirements of Lyapunov theory. The RBF neural network is used for approximating

Through the above analysis, it can be seen that the on-board ultracapacitor control system satisfies the precise linearization condition of the nonlinear system, so it can be linearized [

If

In the above formula,

If

Similarly, it can be obtained that:

So,

Then, the feedback linearized state variable system equation is:

Due to the state discontinuity caused by frequent on-off events, the converter has nonlinear characteristics and is easily affected by disturbances, so the control effect is not ideal. A sliding mode variable structure control algorithm with independent parameter inputs and disturbances is used to design the controller [

According to the characteristics of the on-board supercapacitor system, a single, hidden-layer, three-layer, feed-forward, RBF neural network is adopted in this paper, which can approximate arbitrary nonlinear and linear functions. Its structure is shown in

In this paper, an RBF neural network is used to approximate the nonlinear mapping relationship between the sliding mode surface and the control quantity, with the switching function

The input and output algorithms of the RBF network are supposed as:

Among them,

The input of the neural network is

The control law is:

Substituting control law

Among them,

The Lyapunov function is designed as:

Among them,

From

The adaptation law can be derived as follows:

Then,

Because the RBF network’s approximation error

A simulation test was carried out on a certain track line with an operating interval of 1.98 km. The parameters of the supercapacitor are: capacitance = 30 F, rated voltage = 500 V and working current = −400–400 A. The parameters of the bidirectional DC/DC converter are: energy storage inductance = 7.5 mH and filter capacitance = 30,000 uF. The IGBT switching frequency = 10 kHz and the standard supply voltage of the DC traction network = 1500 V [

Simulink was used to establish a simulation model of a single train with an on-board ultracapacitor (

It can be seen from the simulation results (

It can be seen from

From the above analysis, it can be seen that the vehicle-mounted ultracapacitor energy storage system can effectively utilize regenerative braking energy, suppress fluctuations in grid voltage and reduce losses in the traction grid.

(1) With their high power density and long service life, ultracapacitors have unique advantages and development prospects in utilising regenerative energy in urban rail trains. They can improve the braking power of high-speed trains and allow operation without feeders, making trains more comfortable, safe and stable.

(2) An adaptive, neural network-based, sliding mode control system for supercapacitors was proposed in this paper. Through simulation, it was verified that the system can suppress fluctuations in network pressure, reduce losses in traction grids, and improve the utilization rate of regenerative braking energy.

We thank the team members for their hard work, the scientific research platform provided by the University, and the strong support from government funding.