The vanadium redox flow battery (VRB) is a nonlinear system with unknown dynamics and disturbances. The flowrate of the electrolyte is an important control mechanism in the operation of a VRB system. Too low or too high flowrate is unfavorable for the safety and performance of VRB. This paper presents a neural network predictive control scheme to enhance the overall performance of the battery. A radial basis function (RBF) network is employed to approximate the dynamics of the VRB system. The genetic algorithm (GA) is used to obtain the optimum initial values of the RBF network parameters. The gradient descent algorithm is used to optimize the objective function of the predictive controller. Compared with the constant flowrate, the simulation results show that the flowrate optimized by neural network predictive controller can increase the power delivered by the battery during the discharge and decrease the power consumed during the charge.
Because of the energy crisis, utilization of renewable energy sources such as wind and solar energy for electric power supply has received more and more attention in recent years. However, the intermittent nature of most renewable energy makes it highly dependent on reliable and economical energy storage systems. All-vanadium redox flow battery (VRB) is a promising candidate for the storage of renewable energy. Compared with other redox batteries such as zinc bromine battery and lead acid battery, VRB has many attractive features, including long cycle life, high energy conversion efficiency, flexible design, and low cost [
The flowrate of the electrolyte is an important control mechanism in the operation of a vanadium redox flow battery system. At low flowrates, the electrolyte is provided insufficiently for the chemical reaction and stagnant regions can form in the electrode. The higher electrolyte flowrate will increase the VRB performance. But on the other hand, if the flowrate is too high, there is a risk of leakage, and the pump consumption will increase, which will reduce the system efficiency [
Until recently, most researches are focused on the key materials of VRB, and there is little information available in the literature about the optimization of the electrolyte flowrate. An optimal strategy of electrolyte flowrate is proposed in [
Model predictive control (MPC) is an application of optimal control theory. In model predictive control, process model is utilized to predict the future response of a plant. An optimal control sequence is determined by solving a finite horizon optimization problem online at each sampling instant and the first control in this sequence is applied to the plant [
In this paper, a nonlinear model predictive control scheme is proposed to maximize the power delivered by the battery during the discharge and minimize the power consumed during the charge.
The VRB system consisted of two key elements: the cell stack, where electrochemical reaction occurred and the tanks of electrolytes, where energy is stored. The electrolytes were pumped from the tanks to the stack by a circulation system. A schematic diagram of a vanadium redox flow batter is given in Figure
A schematic diagram of a vanadium redox flow battery.
The main electrode reactions for the VRB are as follows:
A multiphysics model of a VRB system with 19 cells is introduced in [
The equilibrium potential of the individual cells can be approximated using the Nernst equation (assuming unit activity coefficients) as follows:
The
Assuming that each individual cell composing the stack has the same charging characteristics, the equilibrium voltage
The stack voltage
So stack voltage
Then the power of stack can be calculated as
The circulation system pumps the electrolytes from the tanks through the stack and back in the tanks. The power consumed by pumps is expressed as follows:
In practice,
The schematic of the neural network predictive control (NNPC) system developed in this research is shown in Figure Measure the input and output of the VRB system. Use the previous calculated control inputs and the neural network identifier to compute the cost function. Use the optimization algorithm to calculate a new control vector. Repeat steps Apply the first element of the control vector to the VRB system. Update the parameters of the NN with the new training set. Repeat steps
Schematics of the NNPC system.
According to previous section, the battery power can be expressed as follows
Suppose the stack current and temperature keep constant for a certain amount of time. So, there is only one control variable: the flowrate
The structure of the RBF network.
A Gaussian function is used as the activation function. So at the hidden layer, the output of RBF unit
The network output is calculated by
The
Consider the following:
The computational burden of the optimization problem showed in next subsection increases with the complexity of RBF network structure. In order to simplify the RBF network structure and simultaneously ensure the approximation accuracy, in this study, genetic algorithm (GA) is adopted to obtain the optimum initial values of the RBF network parameters before training the RBF network. These parameters include the output weights, the centers, and widths of the hidden unit.
There are different forms of the objective function under different control requirements. In this study, our purpose is to maximize the power delivered by the battery during the discharge and minimize the power consumed during the charge while ensuring the control signal is smooth. Noticing that the battery power is positive during the discharge and negative during the charge, the objective function is given as follows:
Since the function
Constraints on control sequence can be handled as follows: when any one of the
The derivative of the objective function at time
The partial derivative can be calculated by the chain rule:
where
To investigate the performance of the proposed controller, a 19 cells, 2.5 kW, 6 kWh VRB is simulated. Its main characteristics are listed in Table
The characteristics of the VRB stack.
Name | Value |
---|---|
Number of cells |
19 |
|
0.037 Ω |
|
0.039 Ω |
Electrolyte vanadium concentration | 2 mol/L |
Initial |
5 mol/L |
Tank size |
83 L |
Flow resistance |
14186843 Pa/m3 |
Cell temperature |
298 K |
Standard potential |
1.255 V |
In order to reduce the online computing time, the RBF network was trained offline before being applied to online control. The multiphysics model developed in Section
Physical model and RBF model outputs for battery power during the discharge at 100 A.
The RBF network trained offline works well when there are no disturbances. However, it can not accurately represent the VRB dynamics when VRB system is subjected to uncertainty. So, the RBF network requires to train online to adapt with the change in the process. Newest 100 samples were used for training.
Normally, in a charge-discharge cycle, the battery is charged at constant current, the battery SoC increases from 2.5% (discharged) to 97.5%, and then it is discharged at constant current until it reached its initial SoC [
Battery power during a charge-discharge cycle.
Optimal flowrate during a charge-discharge cycle.
Comparison of battery power at different flowrate.
The electrolyte flowrate of VRB system was optimized online using model predictive control based on artificial neural networks. An RBF network is built to predict the future battery power. In order to reduce the computational burden of the optimization problem, the hidden layer nodes were chosen as 5. The RBF network model was found to be valid for wide flowrate variation with random load disturbances. The gradient descent algorithm method is used to realize the optimization procedure. Simulation result at different flowrate indicates that the proposed controller can enhance the output power of battery during the discharge and reduce the operating cost during the charge. Future works will focus on control strategy for VRB and wind farm combined system.