Voltage equalizing method of energy storage system based on series connected supercapacitors

Abstract: This paper presents a novel voltage equalizer to equalize the voltage of series connected supercapacitors. The discrete time domain analysis is enhanced by applying diagonal matrix to accelerate the computation of circuit models. The simulation experiments were carried out for verification of the equalization effect and the algorithm efficiency. A voltage equalization prototype based on calculation parameters was created to validate the mathematics model and the simulation result. The new voltage equalizer named parallel capacitor equalizer with dynamic equalization characteristic is based on the net of switches, inductors, and capacitors. The unbalance charge is transferred from the supercapacitor to the balance capacitor through the switch. When the switch is in the off state, the unbalance energy is transferred between the balance capacitors. With the energy transfer process, the high voltage of the supercapacitor will decrease and the low voltage of the supercapacitor will increase. This energy transfer process will continue until the balanced state of series supercapacitors is achieved. One characteristic of this circuit is that the high precision A/D conversion is not necessary for the balancing process. The second characteristic of the circuit is that the balancing process is performed in parallel sequence. As a result, the balancing time will not increase linearly with the increase of the connected supercapacitor number. With the switch action, the unbalanced charges are transferred from the supercapacitor with high voltage to the supercapacitor with low voltage through balance capacitor. The discrete time domain analysis is used to establish the mathematics model of the equalization circuit. Because the iterated algorithm of typical discrete time domain analysis has large calculating quantity, the diagnose matrix was used to simplify the result of the difference equation. The compute step of enhanced discrete time domain analysis is shown below. First, the differential equations were built up to describe the circuit as the mathematics model. Second, the time domain result was achieved from the differential equations. Third, the continuous time domain result was transferred to the dispersion result. Fourth, a general expression was derived from the iterative result to reduce the computing amount. The curves of the supercapacitor voltage and voltage difference were drawn to analyze the characters of the balance circuit. The curves showed that the duty ratio affects the balance result. The scope of the duty ratio can be acquired through the feature of curves. As a result, the practicability and principle of this method were demonstrated through the analysis above. The simulation experiment was designed to verify the mathematics model and the dynamic performance of the method. The simulation results verified the derived result from the mathematics model. The typical states of static, charging and discharging, were used to study the dynamic performance of the equalizer. In the static state, the waveforms of supercapacitor voltage are trending to the same value with the equalization circuits while the waveforms of supercapacitors are trending to different values without the equalization circuits. In the discharge state, the trends to zero of the supercapacitor voltage is delayed with the equalization circuits compared to the trends of supercapacitor voltage without equalization circuits. In the charge state, the difference value between two supercapacitors decreased with the equalization circuit compared to the value without the equalization circuit. The result shows that the circuit has a dynamic effect in the triple state above. The simulation models of the supercapacitor module in the static state were experimented to verify the influence of supercapacitor amount on the effect of the equalizing process. The result indicates that the effect of equalization has weak ties with series connected supercapacitor amount. A voltage equalization prototype based on calculation parameters is created to validate the mathematics model. Isolate oscilloscope, load resistor, power source, and signals generator were used as experiment environment. NI-PXI5114 with labview9.0 was used to record the real time wave form of supercapacitor voltage. The experimental waveform supports the analysis result of mathematics model and simulation model. Experimental results demonstrate that the proposed method is effective with dynamic characteristics while no sampling device is used. The enhanced discrete time domain method reduces the computation burden of state equations solving process. This computation method can be applied to the analysis of the voltage equalization circuit.