KR101467901B1 - Method for optimization of operating conditions for high temperature pem fuel cells using design of experiments - Google Patents

Abstract

The present invention relates to a method for optimizing operating conditions for a high-temperature polymer electrolyte membrane fuel cell using a design of experiments. More particularly, the present invention provides a method for optimizing operating conditions for a high-temperature polymer electrolyte membrane fuel cell using a design of experiments, wherein a performance model is constructed using the result of experiments conducted according to the design of experiments and optimal operating conditions are deduced based on the constructed model in consideration of performance and durability.

Description

TECHNICAL FIELD [0001] The present invention relates to a method for optimizing operating conditions of a high temperature polyelectrolyte membrane fuel cell using an experimental design method,

The present invention relates to a method of optimizing operating conditions of a high temperature polyelectrolyte membrane fuel cell using an experimental design method. More specifically, the present invention relates to a method for constructing a performance model using experimental design results, The present invention relates to a method of optimizing operating conditions of a high temperature polyelectrolyte membrane fuel cell using an experimental design method that derives an optimal operating condition in consideration of durability.

Fossil fuels are inevitably depleted because their reserves are very limited. In particular, developed countries are focusing on the development of hydrogen energy using alternative energy or nuclear energy to reduce fossil fuels because the main source of greenhouse gases that cause global warming is fossil fuels. Energy sources that are emerging as alternative energy include solar energy, wind power generation, hydrogen energy, and biomes. Solar or wind power must be equipped with auxiliary facilities. Installation of heat collectors and windmills requires a large space, and other environmental problems such as ecosystem destruction and noise are also generated. Future energy requires requirements such as environmental acceptability, economic productability, and Eternal capability.

Fuel Cell is a new environmentally friendly future energy technology that generates electrical energy from substances that are abundant on the earth, such as hydrogen and oxygen, which convert chemical energy generated by oxidation directly into electrical energy.

In the fuel cell, oxygen is supplied to the cathode, hydrogen is supplied to the anode, and electrochemical reaction proceeds in the form of reverse electrolysis of water to generate electricity, heat, and water, It produces electrical energy.

Fuel cells that generate electricity and heat by using fuels such as city gas are a new growth engine industry that has a great effect of creating jobs as well as reducing GHG emissions. Commercialization is being promoted globally.

Fuel cells are considered to be the main reason for satisfying that both electricity and hot water can be created, saving energy and money for the home, and contributing to the prevention of global warming.

PEMFC (Proton-Exchange Membrane Fuel Cell) is an environmentally friendly energy technology for energy shortage due to high energy conversion efficiency, load followability and low pollutant emissions. However, residential power generators (RPGs) using conventional PEMFCs are vulnerable to CO poisoning, and water management is difficult, which leads to excessive use of auxiliary equipment (BOP, Balance Of Plant). This results in a large system and high initial costs. In addition, the utilization of the heat source is low due to the low temperature of hot water supplied from the system. High-temperature PEMFCs using phosphoric acid-loaded polybenzimidazole (PBI) membranes are attracting attention as a solution to these problems of existing systems. This technique uses phosphoric acid as a conduction medium for hydrogen ions, not water, and has an operating temperature range of 120-190 ° C. Therefore, no external humidification is required, and water is generated in a vapor phase at the cathode electrode layer, thereby solving a complicated water management problem. The high operating temperature dramatically increases the poisoning resistance of the catalyst layer to contaminants such as CO, thus simplifying the fuel reforming process. In addition, the temperature of the stack has a large temperature difference with the external environment, and it has an advantage that it can be effectively cooled and can recover heat source at a high temperature, and has a high heat utilization, and its performance and durability are greatly influenced by operating conditions. Nevertheless, the study period for the high-temperature PEMFC is shorter than that of the conventional PEMFC, so there are few cases of performance and durability according to the operating conditions, and it has been confirmed that the operating conditions greatly affect the performance and durability. But did not provide optimal operating conditions.

Therefore, it is necessary to study optimization of operating conditions to maximize performance and durability.

Korean Patent Laid-Open Publication No. 10-2011-0033490 discloses a method of operating a polymer electrolyte fuel cell.

Korean Published Patent [10-2011-0033490]

SUMMARY OF THE INVENTION Accordingly, the present invention has been made to solve the above-mentioned problems, and an object of the present invention is to provide a method and apparatus for preparing polyaniline-based polybenzimidazole (PBI) -based high temperature PEMFC The purpose of this study is to develop a model according to the operating conditions considering the performance and durability of the engine, and to derive the optimum operating condition using the developed model.

In order to accomplish the above object, there is provided a method for optimizing operating conditions of a high temperature polyelectrolyte membrane fuel cell using an experimental design method, (S10) for determining a factor affecting the characteristic value and a factor level of the factor and determining an experimental plan according to an experimental design method; An experimental step (S20) of experimenting by the experimental design method determined in the experimental planning step (S10); A performance model building step (S30) of constructing a performance model using the experimental result of the experimental step (S20); And a driving condition optimization step (S40) of finding an optimization point of the driving condition using the result of the performance model building step (S30).

In addition, the experiment planning step S10 is a long term test performed for a predetermined period of time under a specific experimental condition (operation condition).

In the experiment planning step (S10), the reaction surface method is used.

요인배치법, 2수준계의 일부실시법, 심플렉스 계획법 중 선택되는 어느 하나를 이용하는 것을 특징으로 한다.In addition, if it is determined that the estimation equation of the reaction surface method is appropriate as the first-order regression model,

Factor selection method, a partial arrangement method of a two-level system, and a simplex programming method.

요인배치법, 3수준계의 일부실시법, 중심합성계획법, 회전계획법, 회전중심합성계획법, Box-Behnken계획법 중 선택되는 어느 하나를 이용하는 것을 특징으로 한다.Also, in the experiment planning step (S10), if it is judged that the estimation equation of the reaction surface is appropriate as the quadratic regression model,

Factor selection method, factorial method, partial implementation of 3-level system, central composite programming method, rotation programming method, rotation center composite programming method and Box-Behnken programming method.

In addition, the experiment planning step S10 includes a variable determining step S11 for determining a characteristic value and a factor; And a factor level determination step (S12) of determining a factor level of the factor.

The characteristic value of the variable determining step S11 is a voltage and a voltage reduction rate per unit time.

The parameter of the variable determining step S11 is characterized by being a cell temperature, a fuel supercharging rate, and an air supercharging rate.

In addition, the factor level of the factor level determination step S12 is characterized by setting the cell temperature to 120-190 DEG C, the fuel supercharge rate to 1.2-3.0, and the air supercharge rate to 1.5-4.0.

The experimental step S20 is based on a Membrane Electrode Assembly (MEA) comprising a polybenzimidazole (PBI) membrane carrying phosphoric acid and a gas diffusion electrode (GDE) An experiment preparing step (S21) of adjusting a value corresponding to the factor and preparing the characteristic value to be measurable; An activation step (S22) of heating the cell from room temperature to a set temperature for a predetermined time; A fuel supply step (S23) for supplying dry hydrogen heated to the cell operating temperature by the line heater in the hydrogen and oxygen supply pipe and dry air to the anode and the cathode, respectively; And a fuel cell operation step (S24) of constantly applying a constant current density for a predetermined time.

The activation step (S22) is characterized in that the cell temperature is purged with nitrogen from a predetermined temperature to the set temperature.

In addition, the performance model building step S30 includes a variable input step S31 for inputting a value corresponding to each variable for constructing a performance model; A regression analysis step S32 for regression analysis using the value input in the variable input step S31; And a performance model determination step (S33) of determining a regression equation having the highest value of R ² (R-square) as a performance model using the regression coefficients calculated in the regression analysis step (S20) .

According to the method of optimizing the operating conditions of the high temperature polyelectrolyte membrane fuel cell using the experimental design according to the embodiment of the present invention, it is possible to reduce unnecessary experiments by using the experimental design method, and the performance of the high temperature polyelectrolyte membrane fuel cell It is possible to develop a model according to operating conditions considering durability and to derive optimal operating conditions using the developed model.

In addition, by performing long-term tests, it is possible to derive specific optimized operating conditions by using performance and durability results under unknown operating conditions as a severe condition test performed in a short period of time, It is effective.

In addition, according to the regression model suitable for the estimation formula of the reaction surface method and the reaction surface method, it is possible to construct a more accurate performance model by setting an experimental plan according to the regression model.

In addition, the accuracy and reliability can be ensured by determining the characteristic value, the factor and the factor level so as to ensure accuracy and reliability.

Also, by passing through the experimental preparation step, the activation step, the fuel supply step, and the fuel cell operation step, it is possible to minimize the external factors affecting the experimental results, thereby obtaining reliable experimental results.

In addition, a certain temperature range is purged with nitrogen, so that a higher actual test result can be obtained.

In addition, the regression equation having the highest R ² (R-square) value is determined as a performance model, so that the reliability model having the highest reliability can be obtained.

1 to 3 are flowcharts of a method for optimizing operating conditions of a high temperature polyelectrolyte membrane fuel cell using an experimental design method according to an embodiment of the present invention.
4 is a conceptual diagram of an experimental apparatus for an experiment.
5 is a flowchart of a method for optimizing operating conditions of a high temperature polyelectrolyte membrane fuel cell using an experimental design method according to an embodiment of the present invention.
6 is a graph showing voltage according to operating conditions;
7 is a graph showing regression coefficients of a voltage model;
8 is a graph showing the comparison result between the result of the voltage model and the experimental data.
9 is a graph showing the reaction surface of a voltage according to operating conditions;
10 is a graph showing durability according to operating conditions;
11 is a graph showing regression coefficients of the durability model;
12 is a graph showing the results of comparison between the results of the durability model and the experimental data.
13 is a graph showing the durability reaction surface according to the operating conditions;
FIG. 14 is a graph showing the performance and durability of the model considering the voltage model, the durability model, and the voltage and durability according to the target operating time.

Hereinafter, the present invention will be described in more detail with reference to the drawings. The following drawings are provided by way of example so that those skilled in the art can fully understand the spirit of the present invention. Therefore, the present invention is not limited to the following drawings, but may be embodied in other forms. In addition, like reference numerals designate like elements throughout the specification. It is to be noted that the same elements among the drawings are denoted by the same reference numerals whenever possible. Further, it is to be understood that, unless otherwise defined, technical terms and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Descriptions of known functions and configurations that may be unnecessarily blurred are omitted.

FIGS. 1 to 3 are flowcharts of a method for optimizing operating conditions of a high temperature polyelectrolyte membrane fuel cell using an experimental design method according to an embodiment of the present invention. FIG. 4 is a conceptual diagram of an experimental apparatus for an experiment, FIG. 6 is a graph showing a voltage according to an operating condition, FIG. 7 is a graph showing a regression coefficient of a voltage model, and FIG. 9 is a graph showing the reaction surface of a voltage according to operating conditions, FIG. 10 is a graph showing durability according to operating conditions, and FIG. Fig. 12 is a graph showing the regression coefficient of the durability model, and Fig. 12 is a graph showing the results of the durability model and the experimental data And, Figure 13 is a graph showing the durability of the response surface in accordance with the operating conditions, Figure 14 is a graph showing the performance and durability of the target run time of the model taking into account the voltage model and voltage model durability and durability.

As shown in FIG. 1, a method of optimizing operating conditions of a high temperature polyelectrolyte membrane fuel cell using an experimental design method according to an embodiment of the present invention includes steps of an experiment planning step (S10), an experimental step (S20) S30) and a driving condition optimization step (S40).

The experimental planning step (S10) determines the characteristic values required for predicting the performance and durability of the high temperature polyelectrolyte membrane fuel cell, the factors influencing the characteristic values and the factor levels of the factors, and determines the experimental plan according to the experimental design method. Here, the factor level refers to the range of selectable factors, and the factor to be used for the experiment can be selected in the range corresponding to the factor level.

Design of Experiments (DOEs) is based on mathematical statistics, which means planning experiments to obtain the greatest information through statistical analysis, reducing unnecessary experiments. The purpose of the experimental design method is to quantitatively determine which factors are significant to the reaction, to determine the influence of the insignificant factors and the measurement error, and to derive the optimum value for the response of the significant factors.

The experimental design method is performed in the following manner. First, we set the purpose of the experiment, select the characteristic value, and then determine the factors that affect the characteristic value. Thereafter, the level of the factor is determined, and the number of factors to be used in the experiment is determined at the level of the determined factor. Then, the experimental arrangement suitable for the purpose of the experiment is selected and the experiment is performed according to the experimental plan.

The experiment planning step S10 is a long term test performed for a predetermined period of time under a specific experimental condition (operating condition).

The durability test experiment can be divided into a severe condition test, which is performed in a short period of time, and a long term test, which is performed for a long period of time under specific experimental conditions.

Rigorous condition testing can observe the results over a relatively short period of time, but the performance and durability results under the specific operating conditions required to derive the optimized operating conditions are unknown, but the long term testing is based on performance and durability results under specified operating conditions Can be used to derive optimized specific operating conditions.

 However, there are many limitations in terms of time and economy to derive optimized operating conditions through long-term testing. In order to overcome this, experiments can be conducted by introducing experimental design method.

In the experiment planning step S10, a reaction surface method may be used.

The Response Surface Method (RSM) is a nonlinear regression equation for important variables that affect performance and refers to an experimental design method that optimizes the rectification point with minimal experimentation.

요인배치법, 2수준계의 일부실시법, 심플렉스 계획법 중 선택되는 어느 하나를 이용하는 것을 특징으로 할 수 잇으며, 상기 실험계획 단계(S10)는 반응표면의 추정식이 2차 회귀모형으로 적절하다고 판단되면,

요인배치법, 3수준계의 일부실시법, 중심합성계획법, 회전계획법, 회전중심합성계획법, Box-Behnken계획법 중 선택되는 어느 하나를 이용하는 것을 특징으로 할 수 있다. 이 중 중심합성계획법은 회귀계수를 추정, 곡면 추정하기 위해

요인실험에 중심점, 축점을 추가시킨 실험계획을 중심합성계획(CCD, Central Composite Design)이라고도 말한다. 중심점의 수를

으로 나타내면 중심합성계획의 실험횟수는 모두

가 된다.If it is determined that the estimation equation of the reaction surface method is appropriate as the first-order regression model,

Factor layout method, a part of the 2-level system, and the simplex programming method. In the experiment planning step (S10), it is determined that the estimation equation of the reaction surface is appropriate as the second-order regression model Then,

A factorial arrangement method, a partial implementation of a three-level system, a central synthetic programming method, a rotation programming method, a rotation center synthetic programming method, and a Box-Behnken programming method may be used. Among them, the central composite programming method estimates the regression coefficient,

The experimental plan that adds the center point and the axis point to the factor experiment is also referred to as the central composite design (CCD). The number of center points

The number of experiments in the center synthesis plan is all

.

For example, a total of 243 experiments are required to test five parameters with an argument level of 3. However, when the response surface method is introduced through the central synthesis plan, Relationships can be analyzed. In the present invention, the reaction surface method can be introduced to overcome the time limitation and perform statistical analysis between the characteristic values and the factors.

In other words, a more accurate performance model can be constructed by designing an experimental plan according to a regression model suitable for the estimation equation of the reaction surface method and the reaction surface method.

As shown in FIG. 2, the experiment planning step S10 may include a variable determining step S11 and an argument level determining step S12.

The variable determining step S11 determines a characteristic value and a factor.

In this case, the characteristic value of the variable determining step S11 may be a voltage and a voltage reduction rate per unit time, and the factor of the variable determining step S11 is a cell temperature, a fuel supercharging rate, and an air supercharging rate. can do.

The factor level determination step (S12) determines the factor level of the factor.

At this time, the factor level of the factor level determination step S12 may be characterized by setting the cell temperature to 120-190 DEG C, the fuel supercharge rate to 1.2-3.0, and the air supercharge rate to 1.5-4.0.

In other words, accuracy and reliability can be ensured by determining the characteristic value, the factor and the parameter level so as to secure accuracy and reliability.

The experimental step S20 is performed by the experimental design method determined in the experiment planning step S10.

As shown in FIG. 3, the experimental step S20 may include an experiment preparation step S21, an activation step S22, a fuel supply step S23, and a fuel cell operation step S24.

The experimental preparation step (S21) is based on the membrane electrode assembly (MEA: Membrane Electrode Assembly) containing a polybenzimidazole (PBI) membrane carrying phosphoric acid and a gas diffusion electrode (GDE) Is adjusted, and the characteristic value is prepared so as to be able to be measured.

The activation step S22 heats the cell from room temperature to the set temperature for a certain period of time.

Here, the activation step (S22) may be characterized in that the cell temperature is purged with nitrogen from a predetermined temperature to the set temperature.

It is better to go through the activation process to extract the normal performance of the first operating cell, and the higher temperature can be achieved by purging the nitrogen at a certain temperature interval.

The fuel supply step S23 supplies dry hydrogen and dry air heated to the cell operating temperature by the line heater in the hydrogen and oxygen supply lines to the anode and the cathode, respectively.

In the fuel cell operation step S24, constant current density is constantly applied for a predetermined time.

For example, if the cell is heated from room temperature to 160 ° C for about 1 hour, the cell temperature is purged from 80 ° C to 160 ° C with nitrogen, and when the cell temperature reaches 160 ° C, A dry hydrogen with a stoichiometric ratio of 1.6 and a dry air with a supercharging rate of 2.5 are supplied to the anode and the cathode respectively and the current density is constantly maintained at 0.2 A cm ^-2 for 100 hours can do.

In other words, by passing through the experimental preparation step S21, the activation step S22, the fuel supply step S23 and the fuel cell operation step S24, it is possible to obtain reliable experimental results by minimizing external factors on the experimental results have.

The Celtec-P 1000 Membrane Electrode Assembly (MEA) of Basf was used for the experiment of the optimization method of operating conditions of the high temperature polyelectrolyte membrane fuel cell using the experimental design according to one embodiment of the present invention. The MEA has an active area of 23.9 cm 2, and uses a phosphoric acid-supported PBI film and a carbon fiber gas diffusion electrode (GDE: Gas Defusion Electrode). Bipolar Plate (BP) is a carbon molded separator. Both the anode and the cathode have the same geometrical structure and have a 3-channel parallel pattern, a lip width of 1 mm, a lip depth of 1 mm, a land land width of 1 mm and channel length of 280 mm. A high heat resistant polymer hard type gasket made by Basf was used to make the thickness of the cell tight. The attached unit cell is made of gold to serve as a collecting plate. There is a hole at the top of the cell for connecting the cell, the load and the sensing wire. Insulation gaskets and Teflon were used to prevent shorting between the end plates through the bolts. The number of fastening bolts was 4, and a torque wrench was used for uniform tightening pressure. A graphite sheet was used to reduce the contact resistance and leakage between the separator plate and the end plate.

Figure 4 shows a schematic of a test station. The cell is externally controlled by the PID controller inside the furnace. Since the cell size is sufficiently small and the temperature gradient is not large, it is assumed that the temperature of the cell and EP (End Plate, the outermost supporting plate for cell joining) The temperature of the center of the EP was measured.

The reactants supplied to the cathode and the anode of the cell are heated to a cell temperature using a line heater. HCP-803 from Bio Logic was used as a load and data collection device. Minitab 16 was used for statistical analysis and regression.

For all experiments, a mixed gas with 80% H ₂ , 17% CO ₂ , CH 2 ₄ % and CO 1% was used for the anode and dry air was used as the oxide for the cathode.

In other words, in order to optimize the operating conditions of the high-temperature PEMFC using phosphoric acid-loaded PBI membrane in consideration of performance and durability, the characteristic values were determined by cell performance (voltage) and durability (voltage reduction rate per unit time). If the level of the factor is narrowed and it is set as an area outside the rectification point of the reaction surface, the optimal solution can not be obtained through the regression equation. If the factor level is too wide, a reliable rectification point can not be obtained. Therefore, a reliable regression equation Hard. Therefore, the level of the factor must be determined carefully. Factors and factors affecting the characteristics were determined by cell temperature (150-170 ℃), fuel supercharging rate (1.2-2.0), and air supercharging rate (2.0-3.0). In this case, the parameter level is set within the range that is generally applied in the PEMFC operation. In order to prevent the axial point from exceeding the level of the design variables, the experimentally arranged method uses a central composite face centered design (CCF) with α = 1 indicating the axial distance.

Table 1 shows the performance and durability test results and results according to each operating condition.

Run
Order Fuelλ Air? T
(° C) Voltage (V) 전압 drop
(μVh ^-1 ) One 1.6 2.5 160 0.6304 31.510 2 1.6 2.0 160 0.6243 44.950 3 1.6 2.5 160 0.6310 38,000 4 2.0 3.0 150 0.6108 2.690 5 2.0 2.0 150 0.6029 16.783 6 1.6 2.5 150 0.5974 4.604 7 1.2 2.0 150 0.5122 33.753 8 1.2 3.0 150 0.5182 22.253 9 1.6 2.5 160 0.6325 31.590 10 1.6 3.0 160 0.6370 27.706 11 1.2 2.5 160 0.6000 53.129 12 1.6 2.5 160 0.6339 41.066 13 1.6 2.5 170 0.6512 45.961 14 2.0 2.0 170 0.6486 103.802 15 1.2 3.0 170 0.6365 88.200 16 2.0 3.0 170 0.6566 50.201 17 1.2 2.0 170 0.6284 107.598 18 1.6 2.5 160 0.6337 31.510 19 2.0 2.5 160 0.6379 17.765 20 1.6 2.5 160 0.6337 41.066

A total of 20 experiments according to CCF were conducted at the factor test points; 8 times center point; 6 times, Axis; The experimental conditions are cell temperature (150, 160, 170 ℃), fuel supercharging rate (1.2, 1.6, 2.0) and air supercharging rate (2.0, 2.5, 3.0).

The performance and durability were within 0.5122-0.6566 V and 2.69-103.802 μV h ^-1 , respectively, when the current density was 0.2 A cm ^-2 within the experimental range.

Although the above-described experiment has been performed as an example of the verification of the present invention, the present invention is not limited thereto, and various applications are possible.

The performance model building step S30 constructs a performance model using the experimental result of the experimental step S20.

At this time, the performance model building step S30 may include a variable input step S31, a regression analysis step S32, and a performance model determination step S33.

The variable input step S31 inputs a value corresponding to each variable for constructing the performance model.

The regression analysis step S32 regression analysis is performed using the value input in the variable input step S31.

Regression analysis refers to a multivariate analysis technique that explains the variation of characteristics by a combination of control factors.

The regression analysis was performed to obtain the description of the population, the estimation of the prediction and the prediction, the extension analysis, the parameter estimation of the regression equation, the selection correlation of the control model, the correlation evaluation, the size and significance of the relationship, And the independent variable X1, X2, ... , And Xk, the multiple regression model is defined as follows.

는 추정되어야 할 회귀계수들이며,

는 서로 독립이고 동일한 분포

을 따르는 오차항을 나타낸다.

는

번째 독립변수

의 회귀계수를 의미하는데,

를 제외한 다른 모든 독립변수의 값이 고정된 상태에서

의 값이 한 단위 증가할 때의

값의 평균변화량을 나타낸다. 그리고

는 독립변수

의

번째 관측치를 의미한다.) (here

Are the regression coefficients to be estimated,

Are independent of each other and have the same distribution

Lt; / RTI >

The

Th independent variable

, Which is the regression coefficient,

All other variables are fixed

When the value of

Represents the average change amount of the value. And

Is independent variable

of

Means the second observation.)

The regression model above includes the first term for each independent variable. In some cases, the second term or higher term or interplay term may be included in the model as follows.

Higher order terms are used to fit when there is a nonlinear relationship with the independent variable. A model such as a formula with a higher order term is called a polynomial model.

Multiple regression models can be expressed in simple form by expressing Y, X, parameter and error as vectors and matrices, respectively.

In this case, the multiple regression model can be expressed in the following simple form.

은 정규분포를 따르는

개의 확률변수

들로 이루어졌기 때문에 다변량 정규분포를 따른다. Miscellaneous vector

Lt; RTI ID = 0.0 >

Random variables

And therefore follows a multivariate normal distribution.

는 다음과 같이 표현된다.Estimation of regression coefficients is based on least squares. Sum of squared errors

Is expressed as follows.

를 각

에 대하여 편미분하고 이를 0으로 하는 다음과 같은 연립방정식을 풀어

들을 구하는 것이다.The estimation of the regression coefficient by the least squares method

Respectively

And solves the following simultaneous equations to 0

.

를

라 하면 다음 관계가 성립하는데 이를 정규방정식이라 한다.Satisfy the simultaneous equations above

To

The following relation is established, which is called a normal equation.

The above normal equation is expressed as a vector-determinant.

는

의 전치행렬을 의미하며,

의 최소자승추정량은 다음과 같다.here

The

≪ / RTI >

The least squares estimate of

는

의 역행렬을 의미한다.here

The

≪ / RTI >

The performance model determination step S33 uses the regression coefficients calculated in the regression analysis step S20 to determine a regression equation having the highest R ² (R-square) as a performance model.

Table 2 shows the regression results for performance.

Factors uncoded coded Constant -4.35011 0.63356 H ₂ λ 1.10127 0.02616 O ₂ λ 0.08672 0.00426 T 0.04534 0.03798 H ₂ ? * H ₂ ? -0.10108 -0.01617 O ₂ ? * O ₂ ? -0.01771 -0.00443 T * T -0.00011 -0.01079 H ₂ ? * O ₂ ? 0.00105 0.00021 H ₂ ? * T -0.00447 -0.01788 O ₂ ? * T 0.00005 0.00027

6 shows the voltages according to the respective operating conditions. Performance increased by 13.6 mV, 37.9 mV, and 53.8 mV, respectively, with changes in air supercharging rate and fuel supercharging temperature. In the experimental conditions, the dependence of the temperature on the performance is the largest among the three operating conditions, and the change in performance due to the air is relatively small. The performance change by fuel increased significantly from 600.0 mV to 633.0 mV as the parameter level changed from -1 to 0, to 33 mV, while from 0 to 1 there was only 4.9 mV increase from 633.0 mV to 637.9 mV . It can be seen that the change in the parameter level from -1 to 0 is greater than that from 0 to 1 in all operating conditions. Therefore, it can be seen that the influence of each factor on performance is nonlinear.

Regression analysis The performance model was very significant, with R-square of 98.29% indicating how well the regression model explained and reflected the experimental data.

7 is a graph showing the regression coefficients of the voltage model. The uncoded coefficients in Table 2 represent the absolute values of each coefficient and represent the coefficients of the regression equation. The coded coefficient is a value for analyzing the influence of each coefficient. In Fig. 7, the influence of temperature and fuel supercharging rate is very large, while the influence of air supercharging rate is small. However, all three operating variables have a positive effect on performance.

The regression equation of performance (voltage)

to be.

Figure 8 compares the model results estimated by regression equations of performance with experimental data. The model predictive value estimates the experimental value well. Performance at very low temperature and fuel ratios of 8 and 7 is very low and the effect on other factors is very high when the temperature is 150 ℃ (4-8 experiments), whereas 170 ℃ (experiments 13-17) It can be observed that it is relatively small.

Fig. 9 shows the response surface of the voltage according to the two operating conditions. In (a), the influence by the fuel supercharging rate is very large, while the influence by the air supercharging rate is small. In (b) (C), the influence of the air supercharging rate is relatively small, and the influence of the temperature of the fuel is relatively small. On the other hand, when the temperature is high, the influence of the fuel supercharger is relatively large. .

In the three graphs of FIG. 9, the performance was high when all three operating variables were large. However, the air supercharging rate and the fuel supercharging rate showed the rectification point at the maximum point at the high factor level within the factor range, while the rectification point did not appear at the rectification point. Therefore, it is expected that there will be a rectification point at a temperature higher than the temperature of the experimental range. However, since the durability is also considered in this study, the range of the experiment is appropriate.

Table 3 shows the regression results for durability.

Factors uncoded coded Constant -670.289 31.764 H ₂ λ -139.084 -11.369 O ₂ λ -8.829 -11.584 T 7.794 31.568 H ₂ ? * H ₂ ? 60.772 9.724 O ₂ ? * O ₂ ? 42.416 10.604 T * T -0.004 -0.441 H ₂ ? * O ₂ ? -22.998 -4.600 H ₂ ? * T -0.164 -0.658 O ₂ ? * T -1.185 -5.926

FIG. 10 graphically shows the influence of air supercharging rate, fuel supercharging rate and temperature on durability. From the graph, it can be seen that the performance decrease rate varies with the change of the factor level in the order of temperature, air supercharging rate, and fuel supercharging rate.

However, as the temperature increases, the performance decrease rate increases, while the fuel increase rate and the air supercharge rate tend to decrease. In addition, the effect of temperature on the performance reduction rate is nonlinear, while the air and fuel supercharges are linear.

Regression analysis showed that the R-square value was 93.66%, which is somewhat lower than the performance regression model (98.29%), but it is considered to be significant.

11 is a graph showing regression coefficients of the durability model.

The regression equation of durability (voltage drop rate per unit time)

to be.

In Figure 11, the direct effect of temperature on the performance reduction rate is very large and appears to be a positive value. On the other hand, the direct effect of the fuel supercharger rate and the air supercharger rate on the performance reduction rate is relatively small compared to the influence on the temperature and appears as a negative value. Also, the correlation between the secondary fuel supercharger rate and the air supercharging rate for the performance reduction rate is large, while the temperature correlation is small.

Figure 12 compares the model results estimated from regression equations of durability with experimental data. It can be confirmed that the model predicted value matches the experimental value. Unlike the performance model, the durability model has a relatively low dependence of durability under different operating conditions when the temperature is low, and a greater dependency when the temperature is high. Figure 13 shows the durability response surface according to two operating conditions. In (a), as the air supercharging rate and the fuel supercharging rate increase, the performance reduction rate decreases and the convex reaction surface shows downward. In (b), as the fuel supercharging rate increases, the performance reduction rate decreases and increases as the temperature increases. In (c), as the air supercharging rate increases, the performance reduction rate decreases and increases as the temperature increases. it can be seen that the reaction surfaces of (b) and (c) have a saddle shape.

In addition, the regression equation having the highest R ² (R-square) value is determined as a performance model, so that the reliability model having the highest reliability can be obtained.

The optimization step S40 of the optimization of the driving condition is performed by using the result of the performance model building step S30.

In the method of optimizing the operation conditions of the high temperature polyelectrolyte membrane fuel cell using the experimental design according to the embodiment of the present invention, it is aimed to find an operation condition that maximizes the performance during the target operation time, It is defined as an objective function, and the operating temperature, oxygen supercharging rate, and hydrogen supercharging rate can be defined as determining variables.

The lifetime of a cell can be determined when the cell voltage drops below 0.55 V for the first time, and the range of each decision variable can be the same as the factor level.

Table 4 shows the optimization values according to the target driving time.

run time H2? O2? Temperature Voltage V Voltage drop rate
μV Average
Voltage V One 2000 1.70 2.76 170.0 0.663 53.67 0.609 2 2000 1.86 2.71 150.0 0.608 1.83 0.606 3 1000 1.79 2.85 167.6 0.660 44.31 0.637 4 2000 1.94 2.81 157.9 0.640 17.71 0.622 5 4000 1.99 2.74 150.0 0.613 0.05 0.613 6 6000 1.96 2.73 150.0 0.612 0.01 0.612

1 and 2 show the optimum operating conditions for 2000 hours when only initial performance and durability are considered. It can be seen that the optimized temperature is 170 ° C in order to increase the initial performance only at No. 1 and thus the voltage drop rate is large. In the case of No. 2, only the durability is considered, and the initial performance is very low instead of the operation temperature is 150 ° C. and the voltage drop rate is low.

3-6 shows the optimum operating conditions and average voltage of the model considering both performance and durability during the target operating time. 1, 2, and 4, it can be seen that the average voltage value of the developed model is significantly increased compared with the performance model and the durability model. The optimal point in the short-term operation No. 3 is low durability, but the initial performance is high. However, as the target operation time increases, the operating temperature decreases to 150 ° C for optimization and the air supercharge rate is slightly reduced.

While it is advantageous to focus on initial performance when the target operating time is short, it is more advantageous to focus on durability for long-term operation.

In order to optimize the operation of PEMFC based on PBT with phosphoric acid, we developed a statistical model according to the operating conditions considering performance and durability in the method of optimizing the operation condition of the high temperature polyelectrolyte membrane fuel cell using the experimental design method according to one embodiment of the present invention Respectively. From the economic viewpoint, we reduced the experiment time, introduced the response surface methodology for systematic statistical analysis, and applied the surface-centered synthesis plan. The performance and durability models were in good agreement with the experimental results. The effect of cell temperature and fuel supercharging rate on performance was 26.9 and 18.9 mV / level, respectively, while the effect of air supercharging rate was 6.8 mV / level , And all operating variables had a positive effect on performance. The effect of temperature on durability was large and negative, but the effects of fuel and air supercharges were relatively small and had a positive effect.

When the target operation time is 2000h, the optimized operation conditions considering initial performance and durability increased the average voltage by 13 mV and 16 mV, respectively, compared with the initial performance or durability alone. In conclusion, we developed an optimization model over time within the experimental range to derive optimal operating conditions. It has been found that focusing on initial performance at a short target operating time is advantageous and that a driving design focused on durability is required as the target operating time increases.

As a result, according to the method of optimizing the operation conditions of the high temperature polyelectrolyte membrane fuel cell using the experimental design according to the embodiment of the present invention, it is possible to reduce unnecessary experiments using the experimental design method and to improve the performance and durability of the high temperature polyelectrolyte membrane fuel cell It is possible to develop the model according to the operating condition and to derive the optimum operating condition by using the developed model.

It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

S10: experiment planning step S11: variable determination step
S12: Determination of the printing level Step S20: Experimental step
S21: Experimental preparation step S22: Activation step
S23: fuel supply step S24: fuel cell operation step
S30: Performance model building step S31: Variable input step
S32: regression analysis step S33: performance model determination step
S40: Optimization of driving conditions

Claims (12)

In order to find the operating conditions that maximize the performance during the target operating time of the high temperature polyelectrolyte membrane fuel cell, the characteristic values required for predicting the performance and durability, the factors affecting the characteristic values, and the factor levels of the factors are determined, An experimental planning step (SlO) for determining an experimental plan by the user;
An experimental step (S20) of experimenting by the experimental design method determined in the experimental planning step (S10);
A performance model building step (S30) of constructing a performance model using the experimental result of the experimental step (S20); And
A driving condition optimization step (S40) of finding an optimization point of the driving condition using the result of the performance model building step (S30);
/ RTI >
The experimental planning step (S10)
Determining a characteristic value and a parameter (S11); And
Determining a factor level of the factor (S12);
Lt; / RTI >
The characteristic value of the variable determining step (S11)
The cell average voltage and the voltage reduction rate per unit time during the target operating time,
The factor of the variable determining step S11 is
A cell temperature, a fuel supercharging rate, and an air supercharging rate,
The factor level of the factor level determination step (S12)
The cell temperature is 120-190 DEG C, the fuel supercharge rate is 1.2-3.0, and the air supercharge rate is 1.5-4.0,
The experimental step (S20)
A value corresponding to the factor is controlled based on a membrane electrode assembly (MEA) including a phosphoric acid-doped polybenzimidazole (PBI) membrane and a carbon fiber gas diffusion electrode (GDE: Gas Defusion Electrode) An experiment preparing step (S21) for preparing the characteristic value so as to be able to be measured;
An activation step (S22) of heating the cell from room temperature to a set temperature for a predetermined time;
A fuel supply step (S23) for supplying dry hydrogen heated to the cell operating temperature by the line heater in the hydrogen and oxygen supply pipe and dry air to the anode and the cathode, respectively; And
A fuel cell operating step (S24) for constantly applying a constant current density for a predetermined time;
Lt; / RTI >
The performance model of the performance model building step S30 is a model considering the voltage model, the durability model, and the performance and durability.
Estimating the performance of the cell based on the power supply voltage, estimating the durability of the cell based on the voltage reduction rate per unit time,
The operating condition optimization step (S40) defines the cell average voltage during the target operating time as an objective function, defines operating temperature, oxygen supercharge rate, and hydrogen supercharge rate as decision variables, and maximizes the performance during the target operating time Wherein the operating condition is found by finding an operating condition of the high temperature polyelectrolyte membrane fuel cell.
The method according to claim 1,
The experimental planning step (S10)
Wherein the long term test is performed for a predetermined period of time under a specific experimental condition (operating condition). The method for optimizing the operating condition of the high temperature polyelectrolyte membrane fuel cell using the experimental design method.
The method according to claim 1,
The experimental planning step (S10)
A method for optimizing operating conditions of a high temperature polyelectrolyte membrane fuel cell using an experimental design method using a reaction surface method.
The method of claim 3,
The experimental planning step (S10)
If the estimation equation of the response surface method is judged to be appropriate as the first-order regression model,

A method of optimizing the operating condition of the high temperature polyelectrolyte membrane fuel cell using the experimental design method, which is selected from among the factor selection method, the partial arrangement method of the level 2 system, and the simplex programming method.
The method of claim 3,
The experimental planning step (S10)
If it is judged that the estimation equation of the reaction surface is suitable as the second-order regression model,

The operation of the high-temperature polyelectrolyte membrane fuel cell using the experimental design method is characterized by using factor selection method, partial implementation of the 3-level system, central synthesis programming, rotation programming, rotation center synthesis programming and Box-Behnken programming. Condition optimization method.
delete delete delete delete delete The method according to claim 1,
The activation step (S22)
Wherein the cell temperature is purged with nitrogen from a predetermined temperature to the set temperature.
The method according to claim 1,
The performance model building step (S30)
A variable input step (S31) of inputting a value corresponding to each variable for constructing a performance model;
A regression analysis step S32 for regression analysis using the value input in the variable input step S31; And
A performance model determination step (S33) of determining a regression equation having the highest R ² (R-square) value as a performance model using the regression coefficients calculated in the regression analysis step (S20);
Optimization of Operating Conditions for High Temperature Polymer Electrolyte Membrane Fuel Cells Using Design of Experiments.

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