A Control Method for Output Voltage Stability of Proton Exchange Membrane Fuel Cells

The widely used PEMFC (Proton Exchange Membrane Fuel Cell) analysis found that when the REMFC load is changed, its instantaneous output voltage fluctuates, and it causes voltage loss. The main reason is that it is activated by activation. The characteristics of the three-proton exchange membrane fuel battery characteristics of Ohm overvoltage and thickness cause voltage loss. By using the corresponding empirical formula in the Matlab / Simulink environment, the study designs the PID and the Fuzzy PID Controllers. After the established dynamic model of PEMFC, it controls the hydrogen supply module, changes the ratio of hydrogen and oxygen input, and indirectly controls the output voltage. Through experiments, it was found that Fuzzy PID Controller can achieve faster and smoother voltage stability than an ordinary PID Controller and less overshoot when load change, The controller can control the system voltage to reach a set point and to stabilize the supply voltage for the load.


Introduction
PEMFC is a common type of battery, which is widely used in some fields, such as automobiles, satellites, and submarines, due to its clean energy.The working principle of fuel cells is very simple.Oxygen and hydrogen are used as fuels, and electricity is generated through proton exchange membranes.Its exhaust gas only contains water vapor and a small amount of carbon dioxide [1] .Fuel cells have good development prospects.In order to improve the performance of PEMFC systems and reduce usage costs, studying the dynamic characteristics of PEMFC systems has high research value [2] .Through years of research, it has been found that there are many nonlinear factors inside fuel cells that affect the output voltage, such as pressure, temperature, and gas purity, all of which can cause voltage loss.In order to ensure the stable operation of the PEMFC system and reduce maintenance costs, it is necessary to adopt corresponding control methods.In the study of the dynamic characteristics of the system, the key lies in the study of control algorithms.When connecting multiple electrical devices to PEMFC, the degree of output voltage stability control is a standard for a mature battery system [3] .Therefore, in small systems with limited computing resources, it is necessary to establish a dynamic model to solve the nonlinear model and control algorithm problems of PEMFC systems.By adjusting the hydrogen flow rate through PID and Fuzzy PID, respectively, the output voltage of PEMFC can be controlled, achieving better control of the battery system.By comparing the control effect of Fuzzy PID control, the stable operation of the PEMFC system can be ensured.

Output voltage of PEMFC
The internal reaction process of fuel cells is complex, with many voltage losses.If the fuel gas is fully reacted, the voltage released by PEMFC is 1.229 V.Under the actual working condition, the potential will continue to drop.The voltage lost is called polarization overvoltage [4] , so the output voltage is expressed as: in the formula, E is the standard electromotive force; act v is the activation overvoltage; ohm v represents ohmic overvoltage, and con v represents concentration overvoltage.

Thermodynamic electromotive force
The electricity of PEMFC comes from the effective conversion of chemical energy [5] .The thermodynamic electromotive force E is affected by the current battery temperature and Ratio of reactants, expressed as:  is the change in free enthalpy; S  is the mutation of entropy; F is the Faraday constant; 2 O P is the partial pressure of oxygen; T is the battery temperature; 2 H P is the partial pressure of hydrogen gas; ref T is the reference temperature.

Activation overvoltage
Activation overvoltage refers to the loss of energy conversion during the reaction process, which is inevitable and hinders the reaction between electrons and electrodes, resulting in a slower conversion rate [6] , expressed as: in the formula, I is the load current; 1  , 2  , 3  , and 4  are empirical parameters; 2 O C is the anode oxygen concentration.

Ohmic overpotential
Ohmic overvoltage is caused by the impedance it carries, which affects the passage of electrons and causes voltage loss [7] , which can be expressed as: R is the internal electrical resistance.

Concentration overvoltage
Concentration overvoltage refers to the presence of certain resistance in the proton exchange membrane, resulting in differences in the concentration of reactants between the cathode and anode and voltage loss inside the battery [8] .The expression for concentration overvoltage of fuel cells is:

Flow rate of hydrogen
The hydrogen flow rate is controlled by the partial pressure of the hydrogen valve.This control method is to real-time control the hydrogen inlet pressure to ensure smooth operation of the system [9] , expressed as: in the formula, R is the gas constant; a K is the anode flow coefficient; is the discharge pressure for hydrogen gas; a V is the total volume of the anode flow field.

Design of PEMFC control method
There are many factors that interfere with the output of the PEMFC system, but the key factor is the gas flow rate, which changes the reaction speed of the proton exchange membrane and causes voltage fluctuations.The cathode oxygen is supplied by air and controlled by a fan, while hydrogen is the main reaction fuel controlled by a hydrogen valve, which has the greatest impact on the system.As the fan also has an impact on the heat, controlling the flow rate of anode hydrogen is the best choice [10] .
As shown in Figure 1, the controller has two input values, namely the set voltage value and the current system output voltage value.The difference between the two values is used as the input of the controller.The output voltage set in this project is 21 V, which is adjusted online through the Fuzzy PID control algorithm.Similarly, a PID controller is designed to compare the output to the partial voltage of hydrogen gas, ensuring voltage stability.
) 18~27 V is the voltage range that ensures the normal operation of 30 fuel cells, so the system voltage variation range of the Fuzzy PID control system is {-9, 9}.If {-10, 10}, {-1, 1}, and {-0.5, 0.5} are the actual universe of the three output quantities, {PB, PM, PS, Z, NS, NM, NB} are the language values of fuzzy language, {-8, 8} is the basic domain.The affinity function        The quantization coefficient of the system input is 6, and the quantization coefficients of the three output quantities are 0.183, 0.087, and 0.087, respectively.In a fuzzy reasoning process, up to four rules are enabled, namely: (1) (2) For any learning node (e, e c , d P, dK I , dK D ), it actually contains fuzzy information from the four rules mentioned above.Anti fuzziness adopts the weighted average method.The membership degree under the restriction of rules is:


is the membership degree of the input e in Rule j, and other variables are similar.Min refers to the decimation operation.The adjustment formula for PID parameters obtained through fuzzy reasoning is: is the domain value corresponding to the fuzzy subset of the output quantity of the jth rule, P K is the initial value, P dK is the coefficient adjusted by the control algorithm, and other variables are similar.

Analysis of dynamic model results
The overall dynamic modeling of the PEMFC system is shown in Figure 4, consisting of different subsystems.In order to better simulate the actual operation effect of the system, a capacitor is added after each loss voltage subsystem to smooth out the output voltage.The room temperature input is set to 25 degrees Celsius and load changes are simulated using step current.The controller is added on both sides of the hydrogen module to control the hydrogen flow rate through control algorithms so that the system output voltage reaches the set 21 V.This dynamic model meets the standard of simulating fuel cell operation.

Numbering
Through dynamic modeling of the PEMFC system, it is possible to visually observe the instantaneous changes in output voltage.The load was simulated using a step signal, and two load changes were set, at 100 s and 200 s, respectively.As the load of the simulated electrical equipment decreased and increased, the voltage decreased and increased accordingly.As shown in Figure 5, the voltage variation of the pink line without using control methods showed significant fluctuations.In actual work, sharp voltage fluctuations can easily damage electrical equipment.The ideal voltage value of 21 V for the PEMFC system is set and a PID control algorithm is added.The yellow and blue lines represent the voltage control curves of Fuzzy PID and traditional PID, respectively.It can be clearly seen that after adding the controller, the voltage fluctuation is significantly suppressed, and both can output the set 21 V voltage after stabilization.Through comparison between the two methods, the Fuzzy PID control effect is stronger, the effect of suppressing the peak voltage fluctuation is more obvious, and the time to reach stability is also shorter.The fluctuation error is controlled within 0.8 V, effectively ensuring the stable operation of the system.
After testing, the power of fuel cells increases with the increase of load.The power change curve at 200 s is shown in Figure 6.The output power undergoes a step increase in 200 s.The pink line represents the change in output power without a controller, the green line represents the change in the Fuzzy PID controller, and the yellow line represents the change in the PID controller.The power under all three conditions changes instantly, with a basic power fluctuation of 15 W, which can cause damage to the PEFMC system and increase the risk of damage.Compared with the two curves added to the controller, Fuzzy PID has a better control effect.

Conclusions
This article proposes a control method for the stability of fuel cell output voltage by studying the dynamic model of PEMFC, which can improve the stability and anti-interference characteristics of the system.This method establishes a dynamic model of the PEMFC system on Matlab/Simulink simulation tools.It analyzes the factors affecting the output voltage and adds a Fuzzy PID Controller to the hydrogen supply module.Compared to PID Control, the system has higher stability after control, which can effectively reduce system losses, The fluctuation of output voltage decreases when the load changes.

Figure 1 .
Figure 1.Hydrogen flow rate is under fuzzy PID control where e and ec are the error and error rate of output voltage, respectively, and are used as input quantities to adjust the three parameters of proportional, integral, and differential.The change values of the three PID parameters that need to be adjusted are the outputs, achieving dynamic adjustment of the PID through fuzzy control.The final output is the hydrogen flow rate.At time t, the output voltage error and the rate of change of the error of PEMFC are expressed as: the membership function output are shown in Figure 2. Through 7 fuzzy languages, there are a total of 49 fuzzy rules, and the output diagram of the fuzzy controller is shown in Figure 3.

Figure 2 .
Figure 2. Membership function output Figure 3. Fuzzy controller output diagram formula, e is the fuzzy subset value required by Rule (j) of the jth rule to satisfy e,   j e e

Figure 5 .Figure 6 .
Figure 5. Change curve of the voltage as the load current changes