CN113314739B - Transient Modeling Method of Hydrogen Circulation Pump in Fuel Cell System - Google Patents
Transient Modeling Method of Hydrogen Circulation Pump in Fuel Cell System Download PDFInfo
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- 239000001257 hydrogen Substances 0.000 title claims abstract description 138
- 229910052739 hydrogen Inorganic materials 0.000 title claims abstract description 138
- UFHFLCQGNIYNRP-UHFFFAOYSA-N Hydrogen Chemical compound [H][H] UFHFLCQGNIYNRP-UHFFFAOYSA-N 0.000 title claims abstract description 129
- 239000000446 fuel Substances 0.000 title claims abstract description 27
- 238000000034 method Methods 0.000 title claims abstract description 19
- 230000001052 transient effect Effects 0.000 title claims abstract description 19
- 239000007789 gas Substances 0.000 claims abstract description 31
- 238000004364 calculation method Methods 0.000 claims abstract description 18
- 230000004044 response Effects 0.000 claims abstract description 8
- 238000011084 recovery Methods 0.000 claims abstract description 4
- IJGRMHOSHXDMSA-UHFFFAOYSA-N Atomic nitrogen Chemical compound N#N IJGRMHOSHXDMSA-UHFFFAOYSA-N 0.000 claims description 26
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Chemical compound O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims description 15
- 229910052757 nitrogen Inorganic materials 0.000 claims description 13
- 150000002431 hydrogen Chemical class 0.000 claims description 10
- 230000008859 change Effects 0.000 claims description 8
- 238000013459 approach Methods 0.000 claims description 4
- 238000010606 normalization Methods 0.000 claims description 3
- 238000011217 control strategy Methods 0.000 abstract description 5
- 238000004088 simulation Methods 0.000 abstract description 5
- 230000008878 coupling Effects 0.000 abstract description 2
- 238000010168 coupling process Methods 0.000 abstract description 2
- 238000005859 coupling reaction Methods 0.000 abstract description 2
- 230000008569 process Effects 0.000 description 6
- 230000000694 effects Effects 0.000 description 4
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- 238000011161 development Methods 0.000 description 1
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- 239000005431 greenhouse gas Substances 0.000 description 1
- 230000002427 irreversible effect Effects 0.000 description 1
- 239000007788 liquid Substances 0.000 description 1
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- H01M8/00—Fuel cells; Manufacture thereof
- H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
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Abstract
本发明公开了燃料电池系统中氢气循环泵瞬态建模方法，模型基于多项式回归的方法拟合得到氢气循环泵流量、转速和出口压强的关系函数，然后耦合驱动电机的惯性环节，构建出完整的瞬态离心式氢气循环泵模型，最后对驱动电机的控制电压进行PID控制，三种模型耦合计算得到氢气循环泵的瞬态响应，并控制氢气循环泵满足燃料电池堆的尾气回收需求，以此达到控制氢气循环泵的目的。该模型在保证了仿真准确性的前提下，显著提高了计算速率，其既可用于计算稳态下的燃料电池堆工况，又能仿真计算实际道路工况下，电堆变载时的实时瞬态响应，能够更好的与燃料电池系统进行联动仿真，对于优化燃料电池系统控制策略有着重要的意义。
The invention discloses a transient modeling method for a hydrogen circulating pump in a fuel cell system. The model is fitted with a polynomial regression method to obtain the relationship function of the hydrogen circulating pump flow, rotational speed and outlet pressure, and then coupling the inertial link of a driving motor to construct a complete The transient centrifugal hydrogen circulating pump model is based on the model, and finally the control voltage of the driving motor is controlled by PID. The three models are coupled to calculate the transient response of the hydrogen circulating pump, and the hydrogen circulating pump is controlled to meet the exhaust gas recovery requirements of the fuel cell stack. This achieves the purpose of controlling the hydrogen circulation pump. Under the premise of ensuring the accuracy of simulation, the model significantly improves the calculation rate. It can not only be used to calculate the fuel cell stack under steady-state conditions, but also to simulate the real-time calculation of the stack under load changes under actual road conditions. The transient response can be better simulated with the fuel cell system, which is of great significance for optimizing the control strategy of the fuel cell system.
Description
技术领域technical field
本发明属于燃料电池领域，具体涉及一种质子交换膜燃料电池中的氢气循环泵瞬态建模方法。The invention belongs to the field of fuel cells, and in particular relates to a transient modeling method for a hydrogen circulation pump in a proton exchange membrane fuel cell.
背景技术Background technique
近几十年来，空气质量的负面影响一直是国际急需解决的问题，其中机动车排气污染占有很大比例。为改善城市的空气质量，质子交换膜燃料电池吸引了许多国家的关注，其显著特点是温室气体排放量为零、负载响应快、能量转换效率高、静音和工作温度低等，因此燃料电池汽车成为了新能源汽车发展的重要方向。In recent decades, the negative impact of air quality has been an urgent problem to be solved internationally, among which motor vehicle exhaust pollution accounts for a large proportion. In order to improve the air quality of cities, proton exchange membrane fuel cells have attracted the attention of many countries, and their notable features are zero greenhouse gas emissions, fast load response, high energy conversion efficiency, quietness and low operating temperature, so fuel cell vehicles It has become an important direction for the development of new energy vehicles.
燃料电池汽车使用的燃料是来自于高压氢气罐内存储的氢气。如果车用燃料电池提供的氢气量减小、甚至短缺都会对电池堆造成不可逆的损伤和性能下降。因此，必须保证一定存量的氢气来维持电池堆的运行，但是如果没有设置氢气回收子系统，未反应的氢气会直接排放到环境中。燃料的浪费除了会提高使用成本、缩减续航里程外，关键是会出现安全问题。此外，为了得到更好的性能，电池堆阳极入口的氢气往往需要加湿，而加湿器会增加系统的体积和成本，并且加湿器内残留的液态水会在零度以下冻结，影响燃料电池的冷启动速度。若在燃料电池系统内使用氢气循环泵，便能有效的解决上述两个问题。氢气循环泵会将阳极出口未反应的氢气和水蒸气送回供应系统的歧管，与氢气罐供应的氢气混合，再次进入电池堆，既提高了燃料的利用率，又起到对氢气加湿的作用。Fuel cell vehicles use hydrogen stored in high-pressure hydrogen tanks. If the amount of hydrogen provided by the vehicle fuel cell is reduced, or even a shortage, it will cause irreversible damage and performance degradation to the battery stack. Therefore, a certain amount of hydrogen must be guaranteed to maintain the operation of the stack, but if the hydrogen recovery subsystem is not set up, the unreacted hydrogen will be directly discharged into the environment. In addition to increasing the cost of use and reducing the cruising range, the waste of fuel is the key to safety issues. In addition, in order to obtain better performance, the hydrogen gas at the anode inlet of the stack often needs to be humidified, and the humidifier will increase the volume and cost of the system, and the residual liquid water in the humidifier will freeze below zero, affecting the cold start of the fuel cell. speed. If the hydrogen circulation pump is used in the fuel cell system, the above two problems can be effectively solved. The hydrogen circulation pump will return the unreacted hydrogen and water vapor at the anode outlet to the manifold of the supply system, mix with the hydrogen supplied by the hydrogen tank, and enter the cell stack again, which not only improves the fuel utilization rate, but also plays a role in humidifying the hydrogen. effect.
使用氢气循环泵必然会提高燃料电池的性能和使用寿命，但在具体的使用过程中将出现多种复杂的问题，如果采用数学建模的方法来获得实验研究的成果，无疑是本行业之所求，它能够大幅降低研发成本，也能够对出现的实际问题进行预判。The use of a hydrogen circulating pump will inevitably improve the performance and service life of the fuel cell, but there will be a variety of complex problems in the specific use process. If the mathematical modeling method is used to obtain the results of experimental research, it is undoubtedly the industry's It can greatly reduce the cost of research and development, and can also predict the actual problems that arise.
发明内容SUMMARY OF THE INVENTION
本发明的目的是，提出一种质子交换膜燃料电池系统中离心式氢气循环泵的瞬态建模方法。通过采用多项式回归的方法拟合离心式氢气循环泵的流量、转速和出口压强的关系，然后耦合驱动电机的惯性环节，构建瞬态的离心式氢气循环泵模型，最后对驱动电机的控制电压进行比例积分微分控制(PID)控制，以此达到控制氢气循环泵的目的。The purpose of the present invention is to propose a transient modeling method for a centrifugal hydrogen circulating pump in a proton exchange membrane fuel cell system. By using the polynomial regression method to fit the relationship between the flow rate, rotational speed and outlet pressure of the centrifugal hydrogen circulating pump, and then coupling the inertial link of the drive motor to construct a transient centrifugal hydrogen circulating pump model, and finally the control voltage of the drive motor is calculated. Proportional-integral-derivative control (PID) control, so as to achieve the purpose of controlling the hydrogen circulating pump.
本发明方法的技术方案是：建立包括氢气循环泵体积流量、转速和出口压强的关系模型、驱动电机的惯性环节模型、以及驱动电机控制电压的PID控制模型，三种模型耦合计算得到氢气循环泵的瞬态响应，并控制氢气循环泵满足燃料电池堆的尾气回收需求。每个模型建立的具体步骤如下：The technical scheme of the method of the invention is as follows: establish a relationship model including the volume flow rate, rotational speed and outlet pressure of the hydrogen circulating pump, an inertial link model of the driving motor, and a PID control model of the driving motor control voltage, and the three models are coupled and calculated to obtain the hydrogen circulating pump. The transient response of the fuel cell stack is controlled, and the hydrogen circulation pump is controlled to meet the exhaust gas recovery needs of the fuel cell stack. The specific steps for building each model are as follows:
(1)构建氢气循环泵体积流量、转速和出口压强的关系模型(1) Construct the relationship model of the volume flow rate, rotational speed and outlet pressure of the hydrogen circulating pump
首先拟合氢气循环泵的特性曲线，对氢气循环泵入口气体的体积流量和转子的角速度与转速，进行温度和压强的修正如下：First, the characteristic curve of the hydrogen circulating pump is fitted, and the temperature and pressure are corrected for the volume flow of the gas at the inlet of the hydrogen circulating pump and the angular velocity and rotational speed of the rotor as follows:
其中，Wbc、ωbc和Nbc分别表示修正后的体积流量、角速度和转速，Wbl、ωbl和Nbl表示实际的体积流量、角速度和转速，Tin和Pin表示入口气体的温度和压强，Tref和Pref表示参考温度和压强。where W bc , ω bc and N bc represent the corrected volume flow, angular velocity and rotational speed, respectively, W bl , ω bl and N bl represent the actual volume flow, angular velocity and rotational speed, and T in and P in represent the temperature of the inlet gas and pressure, T ref and P ref represent the reference temperature and pressure.
为了提高数据拟合的精度，对已公开的(文献)氢气循环泵特性曲线中的样本点进行数据标准化处理，如下：In order to improve the accuracy of data fitting, the data standardization process is carried out on the sample points in the published (document) hydrogen circulating pump characteristic curve, as follows:
其中，x和y表示经过数据标准化处理后的转速和体积流量，μN和μW表示样本点的转速和体积流量的平均值，σN和σW表示样本点的转速和体积流量的标准差。Among them, x and y represent the rotational speed and volume flow after data normalization, μ N and μ W represent the average value of the rotational speed and volume flow at the sample point, σ N and σ W represent the standard deviation of the rotational speed and volume flow at the sample point .
基于氢气循环泵特性曲线中的样本点，利用二元二次多项式对氢气循环泵体积流量、转速和出口压强的关系进行拟合，关系式如下：Based on the sample points in the characteristic curve of the hydrogen circulating pump, a binary quadratic polynomial is used to fit the relationship between the volume flow rate, rotational speed and outlet pressure of the hydrogen circulating pump. The relationship is as follows:
Pout＝a0+a1x+a2y+a3x2+a4xy+a5y2 (1-3)P out = a 0 +a 1 x+a 2 y+a 3 x 2 +a 4 xy+a 5 y 2 (1-3)
其中，Pout表示氢气循环泵的出口压强，a0,a1,a2,a3,a4,a5分别表示多项式拟合系数。Among them, P out represents the outlet pressure of the hydrogen circulating pump, and a 0 , a 1 , a 2 , a 3 , a 4 , and a 5 represent the polynomial fitting coefficients, respectively.
(2)构建驱动电机的惯性环节模型(2) Build the inertial link model of the drive motor
氢气循环泵的惯性环节计算表达式如下：The calculation expression of the inertia link of the hydrogen circulating pump is as follows:
其中，ωbl表示转子的角速度，t表示时间，Jbl表示氢气循环泵转子部分的转动惯量，τbm表示驱动电机的驱动力矩，τbl表示氢气循环泵的负载力矩。Among them, ω bl represents the angular velocity of the rotor, t represents the time, J bl represents the moment of inertia of the rotor part of the hydrogen circulating pump, τ bm represents the driving torque of the driving motor, and τ bl represents the load torque of the hydrogen circulating pump.
驱动电机的驱动力矩计算表达式如下：The calculation expression of the driving torque of the driving motor is as follows:
其中，ηbm表示驱动电机效率，Rbm表示驱动电机电阻，κt表示驱动电机的力矩常数，κv表示驱动电机的电压常数，vbm表示驱动电机的控制电压，ωbl表示转子的角速度。Among them, η bm is the drive motor efficiency, R bm is the drive motor resistance, κ t is the torque constant of the drive motor, κ v is the voltage constant of the drive motor, v bm is the control voltage of the drive motor, and ω bl is the angular velocity of the rotor.
氢气循环泵的负载力矩计算表达式如下：The calculation expression of the load torque of the hydrogen circulating pump is as follows:
其中，pbl表示氢气循环泵的功率，cp,in表示入口气体的定压比热容，Tin表示进气的温度，ηbl表示氢气循环泵的效率，Pout、Pin分别表示氢气循环泵出口与入口的压强，γg,in表示入口气体的比热比系数，min表示入口气体的质量流量。Among them, p bl represents the power of the hydrogen circulating pump, c p,in represents the constant pressure specific heat capacity of the inlet gas, T in represents the temperature of the intake air, η bl represents the efficiency of the hydrogen circulating pump, P out and P in represent the hydrogen circulating pump respectively The pressure between the outlet and the inlet, γ g,in represents the specific heat ratio coefficient of the inlet gas, and min represents the mass flow rate of the inlet gas.
入口气体的定压比热容和比热比系数计算表达式如下：The constant pressure specific heat capacity and specific heat ratio coefficient of the inlet gas are calculated as follows:
其中，
经过氢气循环泵压缩后的出口气体温度计算表达式如下：The calculation expression of the outlet gas temperature after being compressed by the hydrogen circulating pump is as follows:
其中，Tout表示出口气体的温度。where T out represents the temperature of the outlet gas.
(3)构建驱动电机控制电压的PID控制模型(3) Build the PID control model of the drive motor control voltage
当氢气循环泵的转速达到稳定后，驱动力矩等于氢气循环泵的负载力矩，然后求解驱动电机的稳定控制电压，计算表达式如下：When the rotational speed of the hydrogen circulating pump is stable, the driving torque is equal to the load torque of the hydrogen circulating pump, and then the stable control voltage of the driving motor is solved. The calculation expression is as follows:
将计算得到的实际出口压强和目标出口压强进行对比，然后两者的差值作为PID控制的偏差量，从而计算出控制电压的变化量：The calculated actual outlet pressure is compared with the target outlet pressure, and then the difference between the two is used as the deviation of the PID control, so as to calculate the change of the control voltage:
e(t)＝Ptar-Pout (3-2)e(t)=P tar -P out (3-2)
vbm,new＝vbm+u(t) (3-4)v bm,new =v bm +u(t) (3-4)
其中，Ptar和Pout分别表示目标出口压强和实际出口压强，e(t)表示偏差量，Kp、KI、KD分别表示比例、积分、微分系数，u(t)表示控制电压的变化量，vbm,new表示经过PID控制后的驱动电机控制电压。Among them, P tar and P out represent the target outlet pressure and actual outlet pressure, respectively, e(t) represents the deviation, K p , K I , K D represent the proportional, integral, and differential coefficients, respectively, and u(t) represents the control voltage The amount of change, v bm, new represents the control voltage of the drive motor after PID control.
将氢气循环泵入口的体积流量和当前时刻的转速进行修正后，配合氢气循环泵特性曲线，得到当前的出口压强，与目标出口压强进行对比，两者的差值作为PID控制的偏差量，从而计算出控制电压的变化量，再根据惯性环节模型，得到新的转速，最后结合入口的体积流量重新计算，如此往复循环，使实际的出口压强逐渐逼近乃至等于目标出口压强。After correcting the volume flow at the inlet of the hydrogen circulating pump and the rotational speed at the current moment, and matching the characteristic curve of the hydrogen circulating pump, the current outlet pressure is obtained, which is compared with the target outlet pressure. The difference between the two is used as the deviation of the PID control. Calculate the change of the control voltage, and then obtain the new speed according to the inertial link model, and finally recalculate it in combination with the volume flow of the inlet. This reciprocating cycle makes the actual outlet pressure gradually approach or even equal to the target outlet pressure.
氢气循环泵的出口压强由氢气循环泵入口的体积流量和转子的转速决定，而氢气循环泵的转子是由驱动电机带动的，驱动电机的转速是由控制电压决定的。因此，氢气循环泵瞬态模型需要构建上述三种模型。The outlet pressure of the hydrogen circulating pump is determined by the volume flow of the hydrogen circulating pump inlet and the rotational speed of the rotor, while the rotor of the hydrogen circulating pump is driven by the drive motor, and the rotational speed of the driving motor is determined by the control voltage. Therefore, the transient model of the hydrogen circulating pump needs to construct the above three models.
结合模型(1)和模型(2)，便可以构建出完整的离心式氢气循环泵的稳态模型，然后再结合模型(3)，可以构建出能自动调节转速，控制出口压强的离心式氢气循环泵的瞬态模型。前者可以在给定转速和体积流量的情景下，计算出氢气循环泵实际的稳定出口压强，后者可以在给定目标出口压强的情境下，通过PID控制，自动更新驱动电机的控制电压，进而调节转子转速，使实际的出口压强逐渐逼近乃至等于目标出口压强。Combining model (1) and model (2), a complete steady-state model of the centrifugal hydrogen circulating pump can be constructed, and then combined with model (3), a centrifugal hydrogen pump that can automatically adjust the speed and control the outlet pressure can be constructed Transient model of a circulating pump. The former can calculate the actual stable outlet pressure of the hydrogen circulating pump under the situation of a given speed and volume flow, and the latter can automatically update the control voltage of the driving motor through PID control under the situation of a given target outlet pressure, and then Adjust the rotor speed so that the actual outlet pressure gradually approaches or even equals to the target outlet pressure.
本发明的特点及产生的有益效果是：构建的离心式氢气循环泵瞬态模型相较与传统的三维复杂流体力学分析模型而言，在保证了仿真准确性的前提下，计算速率有着显著的优势，其克服了三维模型参数过多且无法耦合入电堆系统进行多部件多子系统联合仿真和实时仿真的缺点。构建的模型不仅可用于计算稳态下的燃料电池堆工况，而且能仿真计算实际道路工况下，电堆变载时的实时瞬态响应，提高了系统层次仿真的真实性，有着广泛的可适用性。该模型还能响应不同的电堆控制策略，进而优化燃料供给子系统的控制策略，有效缩减了电堆研发过程中的台架试验成本，具有重要的科学意义和经济价值。The characteristics and the beneficial effects of the present invention are: compared with the traditional three-dimensional complex fluid mechanics analysis model, the constructed transient model of the centrifugal hydrogen circulating pump has a significant calculation speed under the premise of ensuring the accuracy of the simulation. Advantages, it overcomes the shortcomings of too many 3D model parameters and cannot be coupled into the stack system for multi-component multi-subsystem co-simulation and real-time simulation. The constructed model can not only be used to calculate the fuel cell stack operating conditions in steady state, but also can simulate the real-time transient response of the stack when the load changes under actual road conditions, which improves the authenticity of the system-level simulation and has a wide range of applications. applicability. The model can also respond to different stack control strategies, thereby optimizing the control strategy of the fuel supply subsystem, effectively reducing the cost of bench testing in the process of stack research and development, and has important scientific and economic value.
附图说明Description of drawings
图1是文献中公开的离心式氢气循环泵特性曲线图。Fig. 1 is a characteristic curve diagram of a centrifugal hydrogen circulating pump disclosed in the literature.
图2是本发明离心式氢气循环泵控制流程图。Fig. 2 is the control flow chart of the centrifugal hydrogen circulating pump of the present invention.
图3是本发明二元二次多项式拟合结果。Fig. 3 is the fitting result of the binary quadratic polynomial of the present invention.
图4是本发明氢气循环泵模型在PID控制策略下的性能表现。Fig. 4 is the performance performance of the hydrogen circulating pump model of the present invention under the PID control strategy.
图5是本发明氢气循环泵模型在优化后的PID控制策略下的性能表现。FIG. 5 shows the performance of the hydrogen circulating pump model of the present invention under the optimized PID control strategy.
具体实施方式Detailed ways
以下通过具体实施例对本发明的建模过程作进一步的说明，需要说明的是本计算实施例是叙述性的，而不是限定性的，不以此限定本发明的保护范围。The modeling process of the present invention will be further described below through specific embodiments. It should be noted that this calculation embodiment is descriptive, not restrictive, and does not limit the protection scope of the present invention.
燃料电池系统中氢气循环泵瞬态建模方法，首先将氢气循环泵入口的体积流量和当前时刻的转速进行修正，配合氢气循环泵特性曲线，得到当前的出口压强，与目标出口压强进行对比，两者的差值作为PID控制的偏差量，从而计算出控制电压的变化量，再根据惯性环节模型，得到新的转速，最后结合入口的体积流量重新计算，如此往复循环，使实际的出口压强逐渐逼近乃至等于目标出口压强。The transient modeling method of the hydrogen circulating pump in the fuel cell system firstly corrects the volume flow of the hydrogen circulating pump inlet and the rotational speed at the current moment, and cooperates with the characteristic curve of the hydrogen circulating pump to obtain the current outlet pressure, which is compared with the target outlet pressure. The difference between the two is used as the deviation of the PID control, so as to calculate the change of the control voltage, and then according to the inertia link model, the new speed is obtained, and finally combined with the volume flow of the inlet to recalculate, so that the reciprocating cycle makes the actual outlet pressure Gradually approach or even equal to the target outlet pressure.
氢气循环泵为离心式氢气循环泵。PID控制是指比例积分微分控制。The hydrogen circulating pump is a centrifugal hydrogen circulating pump. PID control refers to proportional integral derivative control.
实施算例涉及到的主要参数如下：The main parameters involved in the implementation example are as follows:
离心式氢气循环泵参数：转动惯量为2.6×10-3kg m2，驱动电机常数κt、κv分别为0.15N/mA、0.15V/(rad/s)，驱动电机效率ηbm为0.9，氢气循环泵效率ηbl为0.8，电机电枢电阻Rbm为0.82Ω。The parameters of the centrifugal hydrogen circulating pump: the moment of inertia is 2.6×10-3kg m 2 , the driving motor constants κ t and κ v are 0.15N/mA and 0.15V/(rad/s) respectively, the driving motor efficiency η bm is 0.9, The hydrogen circulation pump efficiency η bl is 0.8, and the motor armature resistance R bm is 0.82Ω.
氢气循环泵的进气温度为343.15K，进气压强为0.9bar，进气流量为7.59m3/h，进气的氢气浓度、水蒸气浓度和氮气浓度分别为44.26mol/m3、9.00mol/m3和0，进气的氢气质量分数、水蒸气质量分数和氮气质量分数分别为0.3551、0.6449和0。The inlet temperature of the hydrogen circulating pump is 343.15K, the inlet pressure is 0.9bar, the inlet flow is 7.59m 3 /h, and the hydrogen, water vapor and nitrogen concentrations of the inlet are 44.26mol/m 3 and 9.00mol respectively. /m 3 and 0, the hydrogen mass fraction, water vapor mass fraction and nitrogen mass fraction of the intake air are 0.3551, 0.6449 and 0, respectively.
氢气的定压比热容为14283J/kg/K，水蒸气的定压比热容为1867J/kg/K，氮气的定压比热容为1038J/kg/K。The constant pressure specific heat capacity of hydrogen is 14283J/kg/K, the constant pressure specific heat capacity of water vapor is 1867J/kg/K, and the constant pressure specific heat capacity of nitrogen is 1038J/kg/K.
氢气的比热比系数为1.4378，水蒸气的比热比系数为1.3519，氮气的比热比系数为1.4008。The specific heat ratio coefficient of hydrogen is 1.4378, that of water vapor is 1.3519, and that of nitrogen is 1.4008.
驱动电机当前转速为4000RPM。The current speed of the drive motor is 4000RPM.
以下选取氢气循环泵的目标出口压强由1bar变到1.5bar时，氢气循环泵稳态模型在一个时间步长的响应过程作为算例。In the following, when the target outlet pressure of the hydrogen circulating pump changes from 1 bar to 1.5 bar, the response process of the steady state model of the hydrogen circulating pump in one time step is taken as an example.
首先需要对氢气循环泵入口气体的体积流量和转子的角速度与转速进行温度和压强的修正：First of all, it is necessary to correct the temperature and pressure of the volume flow of the gas at the inlet of the hydrogen circulating pump and the angular velocity and speed of the rotor:
Wbc(m3 h-1)和Wbl(m3 h-1)表示修正后和实际的体积流量，ωbc(rad s-1)和ωbl(rads-1)表示修正后和实际的角速度，Nbc(RPM)和Nbl(RPM)表示修正后和实际的体积流量转速，Tin(K)和Pin(bar)表示入口气体的温度和压强，参考温度Tref＝288K，参考压力Pref＝1bar。W bc (m 3 h -1 ) and W bl (m 3 h -1 ) represent the corrected and actual volume flow, ω bc (rad s -1 ) and ω bl (rads -1 ) represent the corrected and actual volume flow Angular velocity, N bc (RPM) and N bl (RPM) represent corrected and actual volume flow speed, T in (K) and P in (bar) represent inlet gas temperature and pressure, reference temperature T ref = 288K, reference Pressure Pref = 1 bar.
然后计算当前时刻的氢气循环泵出口压强，在此之前需要拟合出氢气循环泵的特性曲线图，提取图1中的样本点，模型的构建是在Python 3.7.9编程环境中实现的，使用scikit-learn库进行拟合，拟合结果如图3所示。首先对样本点进行了数据标准化处理，如下：Then calculate the outlet pressure of the hydrogen circulating pump at the current moment. Before that, it is necessary to fit the characteristic curve of the hydrogen circulating pump and extract the sample points in Figure 1. The model construction is implemented in the Python 3.7.9 programming environment, using The scikit-learn library performs fitting, and the fitting result is shown in Figure 3. First, the data standardization process is carried out on the sample points, as follows:
氢气循环泵的特性曲线图可以从公开的论文中获取，如图1所示。x和y表示经过数据标准化处理后的转速和体积流量，样本点转速的平均值μN＝3714.285PRM，样本点体积流量的平均值μW＝7.032m3/h，样本点转速的标准差σN＝1030.158，样本点体积流量的标准差σW＝4.394。The characteristic curve of the hydrogen circulating pump can be obtained from the published paper, as shown in Fig. 1. x and y represent the rotational speed and volume flow after data normalization, the average value of the rotational speed at the sample point μ N =3714.285PRM, the average value of the volume flow at the sample point μ W =7.032m 3 /h, the standard deviation of the rotational speed at the sample point σ N = 1030.158, the standard deviation of the volume flow at the sample point σ W = 4.394.
利用二元二次多项式对氢气循环泵体积流量、转速和出口压强的关系进行拟合，关系式如下：A binary quadratic polynomial is used to fit the relationship between the volume flow rate, rotational speed and outlet pressure of the hydrogen circulating pump. The relationship is as follows:
Pout＝a0+a1x+a2y+a3x2+a4xy+a5y2 P out =a 0 +a 1 x+a 2 y+a 3 x 2 +a 4 xy+a 5 y 2
其中，Pout(bar)表示氢气循环泵的出口压强，a0,a1,a2,a3,a4,a5分别表示多项式拟合系数，系数取值如下表。拟合结果的决定系数为0.9923，这表明拟合结果和样本点之间的拟合效果较好(如图3所示)。Among them, P out (bar) represents the outlet pressure of the hydrogen circulating pump, a 0 , a 1 , a 2 , a 3 , a 4 , a 5 represent the polynomial fitting coefficients, respectively, and the coefficients are as follows. The coefficient of determination of the fitting result is 0.9923, which indicates that the fitting effect between the fitting result and the sample points is good (as shown in Figure 3).
(2)驱动电机的惯性环节(2) Inertia link of drive motor
通过修正公式计算得到，修正后的体积流量Wbc＝9.21m3/h，修正后的角速度ωbc＝383.74rad/s，修正后的转速Nbc＝3664.50RPM。然后，将其代入多项拟合式中，得到当前时刻的氢气循环泵出口压强为1.215bar。Calculated by the correction formula, the corrected volume flow rate W bc =9.21m 3 /h, the corrected angular velocity ω bc =383.74rad/s, and the corrected rotational speed N bc =3664.50RPM. Then, it is substituted into the polynomial fitting formula, and the outlet pressure of the hydrogen circulation pump at the current moment is obtained as 1.215 bar.
入口气体的定压比热容和比热比系数计算表达式如下：The constant pressure specific heat capacity and specific heat ratio coefficient of the inlet gas are calculated as follows:
其中，
通过已知条件可计算得到，入口气体的定压比热容cp,in＝6275.93J/kg/K，入口气体的比热比系数γg,in＝1.3824。According to the known conditions, it can be calculated that the constant pressure specific heat capacity of the inlet gas c p,in =6275.93J/kg/K, and the specific heat ratio coefficient of the inlet gas γ g,in =1.3824.
氢气循环泵功率的计算表达式如下：The formula for calculating the power of the hydrogen circulating pump is as follows:
pbl(W)表示氢气循环泵的功率，cp,in(J kg-1K-1)表示入口气体的定压比热容，Tin(K)表示进气的温度，ηbl表示氢气循环泵的效率，Pout(bar)、Pin(bar)分别表示氢气循环泵出口与入口的压强，γg,in表示入口气体的比热比系数，min(kg s-1)表示入口气体的质量流量。p bl (W) represents the power of the hydrogen circulating pump, c p,in (J kg -1 K -1 ) represents the constant pressure specific heat capacity of the inlet gas, T in (K) represents the temperature of the intake air, η bl represents the hydrogen circulating pump The efficiency of , P out (bar), P in (bar) represent the pressure at the outlet and inlet of the hydrogen circulation pump, respectively, γ g,in represents the specific heat ratio coefficient of the inlet gas, and min (kg s-1) represents the inlet gas. Mass Flow.
当氢气循环泵的转速达到稳定后，驱动力矩就等于氢气循环泵的负载力矩，然后求解驱动电机的稳定控制电压，计算表达式如下：When the rotational speed of the hydrogen circulation pump is stable, the driving torque is equal to the load torque of the hydrogen circulation pump, and then the stable control voltage of the driving motor is solved. The calculation expression is as follows:
通过已知条件可计算得到，入口气体的质量流量min＝5.30×10-4kg/s，氢气循环泵的功率pbl＝123.57W，驱动电机的控制电压vbm＝64.62V。According to the known conditions, it can be calculated that the mass flow of the inlet gas is min =5.30×10 -4 kg/s, the power of the hydrogen circulation pump p bl = 123.57W , and the control voltage of the driving motor v bm =64.62V.
(3)PID控制以及瞬态响应(3) PID control and transient response
氢气循环泵控制流程的简要示意图如图2所示。将计算得到的实际出口压强和目标出口压强进行对比，然后两者的差值作为PID控制的偏差量，从而计算出控制电压的变化量：A brief schematic diagram of the control flow of the hydrogen circulating pump is shown in Figure 2. The calculated actual outlet pressure is compared with the target outlet pressure, and then the difference between the two is used as the deviation of the PID control, so as to calculate the change of the control voltage:
e(t)＝Ptar-Pout e(t)=P tar -P out
vbm,new＝vbm+u(t)v bm,new =v bm +u(t)
Ptar(bar)和Pout(bar)分别表示目标出口压强和实际出口压强，e(t)(bar)表示偏差量，u(t)(V)表示控制电压的变化量，vbm,new(V)表示经过PID控制后的驱动电机控制电压。在本例中，比例系数Kp＝2.842，积分系数KI＝232.770，微分系数KD＝1.854。P tar (bar) and P out (bar) represent the target outlet pressure and actual outlet pressure respectively, e(t)(bar) represents the deviation, u(t)(V) represents the change of the control voltage, v bm,new (V) represents the drive motor control voltage after PID control. In this example, the proportional coefficient K p =2.842, the integral coefficient K I =232.770, and the differential coefficient K D =1.854.
该组系数经过优化后得到的。如果使用默认值，例如Kp＝KI＝KD＝1，控制效果如图4所示。可见在使用该组系数的条件下，氢气循环泵出口压强达到目标压强的时间较长，且波动较大，不利于氢气循环泵的使用。使用经过优化后的系数对氢气循环泵的控制效果见图5，与图4相比，氢气循环泵出口压强达到目标压强的时间大大缩短，而且几乎没有抖动，实现了高效控制氢气循环泵的目的。This set of coefficients is obtained after optimization. If the default value is used, eg K p =K I =K D =1, the control effect is shown in Figure 4 . It can be seen that under the condition of using this set of coefficients, the time for the outlet pressure of the hydrogen circulating pump to reach the target pressure is long, and the fluctuation is large, which is not conducive to the use of the hydrogen circulating pump. The control effect of the hydrogen circulating pump using the optimized coefficient is shown in Figure 5. Compared with Figure 4, the time for the outlet pressure of the hydrogen circulating pump to reach the target pressure is greatly shortened, and there is almost no jitter, realizing the purpose of efficiently controlling the hydrogen circulating pump. .
通过已知条件可计算得到，偏差量e(t)＝0.285V，控制电压的变化量u(t)＝+12.72V，PID控制后的驱动电机控制电压vbm,new＝77.34V。According to the known conditions, it can be calculated that the deviation e(t)=0.285V, the variation of the control voltage u(t)=+12.72V, and the drive motor control voltage after PID control v bm,new =77.34V.
驱动电机的驱动力矩计算表达式如下：The calculation expression of the driving torque of the driving motor is as follows:
τbm(N m)表示驱动电机的驱动力矩，ηbm表示驱动电机效率，Rbm(Ω)表示驱动电机电阻，κt表示驱动电机的力矩常数，κv表示驱动电机的电压常数，vbm(V)表示驱动电机的控制电压，ωbl(rad s-1)表示转子的角速度。τ bm (N m) represents the driving torque of the driving motor, η bm represents the driving motor efficiency, R bm (Ω) represents the driving motor resistance, κ t represents the torque constant of the driving motor, κ v represents the voltage constant of the driving motor, v bm (V) represents the control voltage of the drive motor, and ω bl (rad s −1 ) represents the angular velocity of the rotor.
氢气循环泵的负载力矩计算表达式如下：The calculation expression of the load torque of the hydrogen circulating pump is as follows:
τbl(N m)表示氢气循环泵的负载力矩，pbl(W)表示氢气循环泵的功率，ωbl(rad s-1)表示实际的角速度。τ bl (N m) represents the load torque of the hydrogen circulating pump, p bl (W) represents the power of the hydrogen circulating pump, and ω bl (rad s-1) represents the actual angular velocity.
通过已知条件可计算得到，PID控制后的驱动电机驱动力矩τbm＝2.388N m，当前时刻的氢气循环泵负载力矩τbl＝0.295N m。According to the known conditions, it can be calculated that the driving torque of the drive motor after PID control is τ bm =2.388N m, and the load torque of the hydrogen circulating pump at the current moment is τ bl =0.295N m.
氢气循环泵的惯性环节计算表达式如下：The calculation expression of the inertia link of the hydrogen circulating pump is as follows:
ωbl(rad s-1)表示转子的角速度，t(s)表示时间，Jbl(kg m2)表示氢气循环泵转子部分的转动惯量。ω bl (rad s −1 ) represents the angular velocity of the rotor, t(s) represents the time, and J bl (kg m 2 ) represents the moment of inertia of the rotor part of the hydrogen circulation pump.
通过上式和已知条件，可算出经过PID控制后的新转子角速度ωbl,new＝499.38rad/s，新的转子转速Nbl＝4768.71RPM。Through the above formula and known conditions, the new rotor angular velocity ω bl,new =499.38rad/s and the new rotor speed N bl =4768.71RPM after PID control can be calculated.
最后将当前时刻的转子转速和进气流量代入修正式以及体积流量、转速和出口压强的关系式中，可求出当前时刻氢气循环泵的出口压强为1.447bar，与目标压强1.5bar的差距为0.053bar，而上一个时刻的出口压强为1.215bar，与目标压强的差距为0.285bar。可见，经过PID的优化控制后，氢气循环泵的出口压强与目标压强之间的差距快速地缩小了。Finally, by substituting the rotor speed and intake air flow at the current moment into the correction formula and the relationship between volume flow, speed and outlet pressure, it can be found that the outlet pressure of the hydrogen circulating pump at the current moment is 1.447 bar, and the gap with the target pressure of 1.5 bar is 0.053bar, while the outlet pressure at the last moment was 1.215bar, and the gap with the target pressure was 0.285bar. It can be seen that after the optimized control of PID, the gap between the outlet pressure of the hydrogen circulating pump and the target pressure is rapidly reduced.
此后，继续循环上述步骤，便能使得氢气循环泵的出口压强逐渐逼近乃至等于目标压强。After that, by continuing to cycle the above steps, the outlet pressure of the hydrogen circulating pump can be gradually approached or even equal to the target pressure.
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