PEMFC frequency modulation control method based on adaptive power tracking control

Abstract

The invention discloses a PEMFC frequency modulation control method based on adaptive power tracking control, and provides an active power-frequency droop control method for droop coefficient self-adjustment by considering the relationship between frequency and power and considering the characteristics of a PEMFC. Secondly, a self-adaptive power tracking control algorithm is provided based on the basic principle of a perturbation observation method, so that the PEMFC has the capability of dynamically adjusting the output power so as to support the system frequency; and finally, considering the maximum power point characteristic of the PEMFC, limiting the operating point of the PEMFC, and avoiding the situation that the service life of the PEMFC is shortened due to the fact that a large amount of energy is wasted and electrode carbon corrosion is caused by insufficient reactant supply caused by high current density when the PEMFC operates in a concentration polarization region. When the system is disturbed, the reference power required to be output by the PEMFC is calculated according to droop control, and then the actual output power of the PEMFC is dynamically adjusted according to the adjustment requirement by using a self-adaptive power tracking control algorithm, so that power compensation is performed on the system, and the frequency stability of the system is improved.

Description

Technical Background

[0001] This technology belongs to the PEMFC frequency modulation control technology of proton exchange membrane fuel cells, and specifically relates to a PEMFC frequency modulation control method based on adaptive power tracking control. Background Art

[0003] Due to its own volatility, it is difficult for a high proportion of clean energy to continuously and stably provide electricity, which puts higher requirements on the flexible regulation ability of the power system. Under the dual pressures of the "dual carbon" goal and the construction of a new power system, it is urgent to efficiently realize the mutual conversion of multiple energy forms and give full play to the supporting role of various types of regulating resources. As an emerging, clean and pollution-free new energy storage system, hydrogen energy storage has good development prospects. During the operation of the hydrogen energy storage system, the proton exchange membrane fuel cell (PEMFC) has the advantages of fast response, high efficiency, good stability, and low working temperature, and is the best energy conversion device for hydrogen-electricity. The coupling and complementarity of hydrogen energy and electric energy can provide flexible, efficient and adaptable energy for the power grid. On the one hand, it can promote the wide utilization of renewable energy, and on the other hand, it can ensure the safe and stable operation of the system.

[0004] In the hydrogen energy storage system, as the core device, the stability of the operating state of the PEMFC directly affects the reliability and efficiency of the power grid. In order to achieve the efficient coordinated operation of the PEMFC and the power grid, researchers have proposed a variety of grid-connected control methods to improve the response ability and stability of the system. The two most common methods are Constant Power Control (CPC) and Maximum Power Point Tracking (MPPT).

[0005] When the PEMFC adopts constant power control, the output power remains fixed, unaffected by load fluctuations, and the control method is simple, suitable for occasions with high requirements for power stability. The existing technologies include the use of a current-fed dual-active full-bridge DC / DC converter to achieve efficient and constant power output of the PEMFC; a numerical study on a residential combined heat and power system based on the PEMFC to explore the system operation characteristics under different operating modes of the PEMFC, and it is verified that the combined heat and power efficiency is higher in the constant power mode. However, the constant power control has certain limitations. Especially in the case of large load fluctuations, the output power of the PEMFC may not be able to fully adapt to the changes in grid demand, resulting in a decrease in efficiency or system instability. At the same time, the existing technologies ignore the dynamic characteristics of the PEMFC, reducing the flexibility of overall regulation. The maximum power point tracking control can adjust the relevant operating parameters of the PEMFC in real time through certain control algorithms, such as the commonly used perturbation observation method, conductance increment method, fixed voltage method, etc., and is applicable to various load conditions, enabling it to always output at the maximum power, which can, to a certain extent, address the deficiencies of constant power control. With the application of intelligent algorithms, the response speed and power tracking accuracy of the system have been further improved. However, in the new power system, the diverse loads have heterogeneity and randomness, and neither of the above two methods can cope with the challenges brought by the dynamic demands of fluctuating loads, so they do not have the ability to provide frequency support for the new power system.

[0006] To solve the above problems, according to the electrochemical reaction principle of the PEMFC itself, its power characteristic curve can be divided into an activation polarization region, an ohmic polarization region, and a concentration polarization region. When the PEMFC operates in the concentration polarization region, under high current density conditions, the reactant supply in the catalyst layer is insufficient, which will lead to the degradation of the catalyst layer, a decrease in the active surface area of the catalyst, and the excessive oxidation of the electrode surface at too high current density, causing electrode corrosion and reducing the battery performance and life. However, the above studies have all been carried out within the full operating range of the PEMFC device without restricting the PEMFC to operate in the concentration polarization region.

[0007] Based on the above analysis, when the PEMFC adopts maximum power point tracking control or constant power control, it lacks the ability to adjust the output power in the face of load fluctuations, thus unable to perform power compensation on the system to improve the system frequency stability, and the existing primary frequency modulation model of the PEMFC cannot limit its operation in the concentration polarization region, which may lead to damage to battery materials and affect the service life. Summary of the Invention

[0008] Object of the Invention: Aiming at the problem of insufficient frequency modulation control of the PEMFC mentioned in the above existing technologies, the present invention aims to provide a PEMFC frequency modulation control method based on adaptive power tracking control.

[0009] Technical solution: A PEMFC frequency modulation control method based on adaptive power tracking control, including: considering the relationship between frequency and power, taking into account the characteristics of PEMFC itself, calculating the reference power required for PEMFC output during load fluctuations through droop control, and using it as the input signal of the adaptive power tracking control algorithm;

[0010] Operating on the input reference power signal, PEMFC actual output power signal, and current signal through the adaptive power tracking algorithm to obtain the reference current for PEMFC operation, then outputting a PWM control signal, and finally enabling the PEMFC output power to dynamically follow the change of the reference power, so as to achieve power compensation for the system during load fluctuations and thus suppress system frequency fluctuations.

[0011] Furthermore, the method includes obtaining the reference output current of FEMFC during load fluctuations through the adaptive power tracking control algorithm, using PI control to adjust the actual output current of PEMFC, and further controlling the output power of PEMFC;

[0012] The implementation steps of this method include:

[0013] S1. Define the difference between the actual output power of PEMFC and the required reference power as:

[0014] P diff =P ref -P

[0015] In the formula, P ref represents the reference active power; P represents the actual active power, and P diff represents the power demand error between the reference power and the actual power;

[0016] When P diff satisfies -ε ≤ P diff ≤ ε, it is considered that the actual output power of PEMFC is equal to the reference power at this time, and ε in the formula represents the allowable error threshold;

[0017] S2. Since the frequency of the system changes with time, if the output power of PEMFC is to dynamically follow the change of the system frequency and make corresponding adjustments, there is:

[0018]

[0019] In the formula, represents the reference power that PEMFC should output at time k; P k represents the actual output power of PEMFC at time k; represents the power demand error at time k;

[0020] S3. Based on the basic principle of the perturbation observation method, considering the changes in the actual output power and output current of the PEMFC, the following expressions exist:

[0021] ΔP k =P k -P k-1

[0022] ΔI k =I k -I k-1

[0023] In the formula, P k 、P k-1 represent the output power of the PEMFC at time k and time k - 1 respectively; ΔP k represents the power change of the PEMFC at time k; I k 、I k-1 represent the output current of the PEMFC at time k and time k - 1 respectively, A; ΔI k represents the current change of the PEMFC at time k;

[0024] S4. According to the positive and negative of ΔP k 、ΔI k and combined with the sign function, including determining the operating state of the PEMFC on the power characteristic curve at time k according to the adaptive power tracking control algorithm.

[0025] Furthermore, the specific adaptive power tracking control algorithm described in step S4 is as follows:

[0026] First, measure and calculate the input signal, and use the judgment condition to determine which algorithm step should be executed during this period; the judgment conditions are as follows:

[0027] 1) When , at this time, the actual output power of the PEMFC is equal to the reference power, and the reference current should remain unchanged, that is, I ref =I k ;

[0028] 2) When and sign(ΔP k )×sign(ΔI k )>0, at this time, the PEMFC is operating on the uphill section of the power characteristic curve and the actual output power is less than the reference power. In order to track the reference power, the actual output power should increase, so the reference current at the next moment should increase, that is, I ref =I k +μ(μ>0);

[0029] 3) When and sign(ΔP k)×sign(ΔI k ) > 0, at this time the PEMFC operates on the uphill section of the power characteristic curve and the actual output power is greater than the reference power. The actual output power should be reduced, so the reference current should be reduced, that is, I ref = I k - μ;

[0030] 4) When I k > I m , the PEMFC operates in the concentration polarization region. At this time, the reference current should be adjusted to avoid it operating in this region, satisfying I ref = I m - μ.

[0031] Furthermore, the method models the output characteristics of the PEMFC as follows:

[0032] (1) PEMFC output voltage

[0033] According to the electrochemical reaction principle of the PEMFC, its output voltage V out is affected by the open-circuit voltage E n , activation polarization overpotential V act , ohmic polarization overpotential V ohm and concentration polarization overpotential V conc . The output voltage of a single cell is V out = E n - V act - V ohm - V conc ;

[0034] (2) Open-circuit voltage

[0035] According to the simplified Nernst electromotive force equation, the open-circuit voltage of a single cell is obtained as:

[0036]

[0037] where T represents the operating temperature of the PEMFC, K; and represent the hydrogen partial pressure and oxygen partial pressure respectively;

[0038] (3) Activation polarization overpotential

[0039] The activation polarization overpotential includes the activation electromotive force of the cathode and the activation electromotive force of the anode. The activation electromotive force is caused by the slow reaction on the electrode surface and is affected by the operating temperature T, hydrogen partial pressure oxygen partial pressure and the output current i of the PEMFC. Its calculation formula is:

[0040]

[0041] (4) Ohmic polarization overpotential

[0042] The calculation formula for the ohmic polarization overpotential is as follows:

[0043] V ohm = iR ohm

[0044] R ohm = R M + R C

[0045]

[0046] In the formula, R ohm represents the ohmic resistance; R M represents the equivalent resistance of the proton flow channel; R C represents the equivalent resistance of the electron flow channel; p M is the conductivity of the proton exchange membrane; l is the membrane thickness; λ represents the membrane water content;

[0047] (5) Concentration polarization overpotential

[0048] The concentration polarization overpotential is caused by the decrease in the concentration of reactants on the electrode surface. Its magnitude is related to the structure and operating state of the PEMFC. Its calculation formula is as follows:

[0049]

[0050] In the formula, n is a constant;

[0051] (6) Current limit at the maximum power point of the fuel cell

[0052] For power regulation requirements below the maximum power point, there are two operating points P 1 and P 2 on the fuel cell power characteristic curve with equal power but unequal currents. When the PEMFC operates at P 2 , the PEMFC is operating in the concentration polarization region at this time; due to the excessive current density in the concentration polarization region and the influence of local polarization, it will corrode the electrode material and reduce the battery service life. Therefore, it is necessary to limit its working current, which is expressed as:

[0053] 0 ≤ i ≤ I m

[0054] In the formula, I m represents the working current corresponding to the maximum power point of the PEMFC; after limiting the working current of the PEMFC, the PEMFC will only operate on the uphill section of the power characteristic curve, avoiding operating in the concentration polarization region.

[0055] Furthermore, the frequency modulation control process in the method includes the following frequency modulation control steps considering the maximum power point of PEMFC:

[0056] Establish an equation between active power and frequency, and use active-frequency droop control to enable PEMFC to dynamically adjust its output power according to system load changes to suppress system frequency fluctuations;

[0057] The mathematical expression between active power and frequency is as follows:

[0058] P ref -P = K f (f n -f s )

[0059] In the formula, P ref represents the reference active power; P represents the actual active power; f n , f s represent the system rated frequency and the actual frequency respectively; K f represents the frequency droop coefficient;

[0060] For different frequency change situations, the output of PEMFC is based on the following mathematical expression:

[0061]

[0062] In the formula, P max represents the output power corresponding to the maximum power point of PEMFC; Δf DB represents the frequency modulation dead zone; Δf max represents the maximum allowable frequency fluctuation range during system operation;

[0063] Considering that its output power is related to the hydrogen flow rate, the droop coefficient is set to be adjusted accordingly with the change of the hydrogen flow rate. For example, when the hydrogen flow rate decreases, K f is increased accordingly, which is expressed as:

[0064]

[0065] In the formula, v flow , v flow_max represent the actual hydrogen flow rate and the hydrogen flow rate at the maximum power output of PEMFC respectively; γ represents the relative flow rate; represents the droop coefficient affected by the hydrogen flow rate.

[0066] Furthermore, the adaptive power tracking control algorithm enables the output power of PEMFC to be dynamically adjusted according to the change of load, achieving the effect of suppressing frequency fluctuations.

[0067] A PEMFC frequency modulation control method based on adaptive power tracking control according to the present invention has the following substantial features and remarkable progress:

[0068] (1) Aiming at the problem that when the PEMFC adopts constant power control or maximum power point tracking control, it cannot dynamically adjust the output power to support the system frequency in the face of load fluctuations, an adaptive power tracking control algorithm is proposed based on the principle of the perturbation observation method, which enables the PEMFC to dynamically adjust its output power according to the adjustment requirements to support the system frequency.

[0069] (2) Aiming at the problem that the primary frequency modulation models of PEMFCs in existing research do not consider the harm when they operate in the concentration polarization region, considering its maximum power point characteristics, the operating state of the PEMFC is restricted to prevent it from operating in the concentration polarization region.

[0070] (3) According to the characteristics of the PEMFC itself, considering the influence of the hydrogen gas flow rate on the output power of the PEMFC, a droop control method with variable droop coefficients is proposed, which is more flexible than the droop control with fixed coefficients. Description of the Drawings

[0071] Figure 1 is the comprehensive control block diagram of the PEMFC grid-connected to participate in system frequency modulation;

[0072] Figure 2 is the fuel cell stack modeling diagram;

[0073] Figure 3 is the PEMFC power characteristic curve;

[0074] Figure 4 is the flow chart of the adaptive power tracking control algorithm;

[0075] Figure 5 shows the output power of the PEMFC and the system frequency in the simulation example (system parameters at steady state), where Figure 5(a) is the output power of the PEMFC and Figure 5(b) is the system frequency;

[0076] Figure 6 shows the PEMFC output power tracking under different power demand conditions, where Figure 6(a) is the power tracking when the reference power changes stably, and Figure 6(b) is the power tracking when the reference power changes dynamically.

[0077] Figure 7 is the current waveform considering the maximum power point characteristics of the PEMFC;

[0078] Figure 8 shows the PEMFC output power under different control methods, where Figure 8(a) is the constant power control, Figure 8(b) is the fixed droop coefficient, and Figure 8(c) is the variable droop coefficient;

[0079] Figure 9 shows the system frequency under different control methods. Figure 9(a) is the constant power control, Figure 9(b) is the fixed droop coefficient, and Figure 9(c) is the variable droop coefficient. Detailed implementation method

[0080] To describe in detail the technical solution disclosed by the present invention, a model is built on the MATLAB / Simulink simulation platform in this embodiment to verify the effectiveness of the proposed control strategy.

[0081] 1. PEMFC grid-connected system topology and control framework

[0082] Figure 1 The shown is the comprehensive control block diagram of the PEMFC grid-connected system participating in system frequency regulation. The droop control is used to calculate the reference power required for the PEMFC output during load fluctuations, and it is used as the input signal of the adaptive power tracking control algorithm. The input reference power signal, the actual output power signal of the PEMFC, and the current signal are operated through the adaptive power tracking algorithm to obtain the reference current for the PEMFC to work, and then the PWM control signal is output. Finally, the PEMFC output power dynamically follows the reference power change, achieving the purpose of power compensation for the system during load fluctuations to suppress the system frequency fluctuation.

[0083] 2. PEMFC output characteristic modeling

[0084] (1) PEMFC output voltage

[0085] According to the electrochemical reaction principle of the PEMFC, its output voltage V out is affected by the open-circuit voltage E n , the activation polarization overpotential V act , the ohmic polarization overpotential V ohm and the concentration polarization overpotential V conc . The PEMFC stack modeling is as shown in Figure 2 . Its single-cell output voltage is:

[0086] V out = E n - V act - V ohm - V conc (1)

[0087] The PEMFC stack is composed of N series-connected single cells. The PEMFC stack output voltage V fc can be expressed as:

[0088] V fc = N · V out (2)

[0089] (2) Open-circuit voltage

[0090] Generally, according to the simplified Nernst electromotive force equation, the open-circuit voltage of a single cell can be obtained as follows:

[0091]

[0092] In the formula: T represents the operating temperature of the PEMFC, K; and represent the partial pressures of hydrogen and oxygen, respectively, in atm.

[0093] (3) Activation polarization overpotential

[0094] The activation polarization overpotential includes the activation electromotive force of the cathode and the activation electromotive force of the anode. The activation electromotive force is caused by the slow reaction on the electrode surface and is affected by the operating temperature T, the partial pressure of hydrogen the partial pressure of oxygen and the output current i of the PEMFC. Its calculation formula is:

[0095]

[0096] In the formula: ε 1 ~ε 4 are empirical coefficients. Among them, the values of ε 1 , ε 3 , ε 4 are -0.9514, 7.4×10 -5 , -1.87×10 -4 , represents the dissolved concentration of O 2 , in mol / cm 3 , and the calculation formulas of ε 2 , are respectively:

[0097]

[0098] In the formula, A represents the activation area of the PEMFC, in cm 2 ; represents the dissolved concentration of H 2 , in mol / cm 3 , and its calculation formula is:

[0099]

[0100] (4) Ohmic polarization overpotential

[0101] The calculation formula of the ohmic polarization overpotential is:

[0102] V ohm =iR ohm (8)

[0103] Rohm = R M + R C (9)

[0104]

[0105] Wherein, R ohm represents the ohmic resistance, Ω; R M represents the equivalent resistance of the proton flow channel, Ω; R C represents the equivalent resistance of the electron flow channel, Ω, where the value of R C is generally a constant, and the value range is 0.0001 - 0.0008 Ω; p M is the conductivity of the proton exchange membrane, Ω·cm; l is the membrane thickness, cm; λ represents the membrane water content, and the value range is usually 0 - 23.

[0106] (5) Concentration polarization overpotential

[0107] The concentration polarization overpotential is caused by the decrease in the concentration of reactants on the electrode surface. Its magnitude is related to the structure and operating state of the PEMFC. The calculation formula is:

[0108]

[0109] Wherein, n is a constant, and generally takes a value of 8×10 -3 cm 2 / mA.

[0110] (6) Current limit at the maximum power point of the fuel cell

[0111] For the power regulation requirements below the maximum power point, there are two operating points P1 and P2 on the fuel cell power characteristic curve with equal power but unequal currents, as Figure 3 shown. When the PEMFC operates at P2, the PEMFC is operating in the concentration polarization region at this time. Due to the excessive current density in the concentration polarization region and the influence of local polarization, it will corrode the electrode material and reduce the battery service life. Therefore, it is necessary to limit its working current, which can be expressed as:

[0112] 0 ≤ i ≤ I m (13)

[0113] Wherein, I m represents the working current corresponding to the maximum power point of the PEMFC, A. As Figure 3 can be seen, after limiting the working current of the PEMFC, the PEMFC will only operate on the uphill section of the power characteristic curve, avoiding operating in the concentration polarization region.

[0114] 3. Frequency modulation control strategy considering the maximum power point of PEMFC

[0115] (1) Active - frequency droop control with variable droop coefficient

[0116] In order to enable the PEMFC to dynamically adjust its output power according to the system load changes and thus suppress the system frequency fluctuations, it is first necessary to determine the changing trend of the active power when the frequency changes. To obtain the reference power that the PEMFC should output when the system frequency changes, an equation between the active power and the frequency should be established. Using the traditional active - frequency droop control, we have:

[0117] P ref -P = K f (f n -f s ) (14)

[0118] In the formula, P ref represents the reference active power, kW; P represents the actual active power, kW; f n , f s represent the system rated frequency and the actual frequency respectively, Hz; K f represents the frequency droop coefficient.

[0119] Rewrite the above formula (14) as:

[0120] P ref = P 0 + ΔP = P 0 + K f Δf (15)

[0121] Δf = f n -f s (16)

[0122] In the formula, P 0 represents the output power of the PEMFC at the initial moment before the system frequency changes, kW. Formula (15) represents the reference power that the PEMFC should output when the system frequency changes. In practical applications, relying solely on formula (15) is not sufficient to fully describe the relationship between the output power of the PEMFC and the frequency. The output situation of the PEMFC under different frequency change conditions should also be considered, that is:

[0123]

[0124] In the formula, P max represents the output power corresponding to the maximum power point of the PEMFC, kW; Δf DB represents the dead - band of frequency regulation, Hz; Δf max represents the maximum allowable frequency fluctuation range during system operation, Hz.

[0125] As can be seen from Equation (17), the output power of the PEMFC is different when the frequency change range is different. When the system frequency change Δf is within the dead zone, that is, Δf ≤ |Δf DB |, at this time the frequency change is very small, it is considered that the system frequency is stable, and the output power of the PEMFC remains the initial value P 0 unchanged; when the frequency change exceeds the frequency modulation dead zone, that is, Δf DB <|Δf| ≤ Δf max at this time, the output power of the PEMFC increases or decreases correspondingly based on the initial value P 0 according to the frequency change trend; when the system frequency change exceeds the allowable maximum frequency change range, that is, Δf > |Δf max |, the PEMFC should output according to the maximum power or minimum power. For example, when Δf > Δf max , it means that the system frequency is too low at this time, and the PEMFC needs to output at the maximum power P max to make up for the power shortage and prevent the system frequency from continuing to drop; when Δf < -Δf max , it means that the frequency is too high at this time and the system power is excessive, and the PEMFC needs to stop delivering power to the system, that is, the output power is 0.

[0126] In order to enable the PEMFC to better adjust the control parameters according to the load change and system state, considering that its output power is related to the hydrogen flow rate, the droop coefficient is set to be adjusted accordingly with the change of the hydrogen flow rate. For example, when the hydrogen flow rate decreases, K f is increased accordingly, which can be expressed as:

[0127]

[0128] where v flow and v flow_max represent the actual hydrogen flow rate and the hydrogen flow rate at the maximum power output of the PEMFC, respectively, L / min; γ represents the relative flow rate; represents the droop coefficient considering the influence of the hydrogen flow rate in Equation (17).

[0129] (2) Adaptive power tracking control algorithm

[0130] When the PEMFC is connected to the grid with maximum power point tracking control or constant power control, it does not have the ability to regulate frequency. Based on the basic principle of the perturbation observation method, an adaptive power tracking control algorithm is proposed. Through the adaptive power tracking control algorithm, the reference output current of the FEMFC is obtained under load fluctuations. Using PI control, the actual output current of the PEMFC is adjusted, and then the output power of the PEMFC is controlled. The adaptive power tracking control algorithm enables the output power of the PEMFC to be dynamically adjusted according to the change of the load, achieving the effect of suppressing frequency fluctuations.

[0131] Define the difference between the actual output power of the PEMFC and the required reference power as:

[0132] P diff =P ref -P (20)

[0133] In the formula, P diff represents the power demand error between the reference power and the actual power, kW.

[0134] When P diff meets the condition shown in Equation (21), it is considered that the actual output power of the PEMFC is equal to the reference power at this time, that is:

[0135] -ε≤P diff ≤ε (21)

[0136] In the formula, ε represents the allowable error threshold.

[0137] Since the frequency of the system changes with time, if the output power of the PEMFC is to dynamically follow the change of the system frequency and make corresponding adjustments, there should be:

[0138]

[0139] In the formula, represents the reference power that the PEMFC should output at time k, kW; P k represents the actual output power of the PEMFC at time k, kW; represents the power demand error at time k.

[0140] Based on the basic principle of the perturbation observation method, considering the change of the actual output power of the PEMFC and the change of the output current, as shown in Equations (24)-(25):

[0141] ΔP k =P k -P k-1 (24)

[0142] ΔI k =Ik -I k-1 (25)

[0143] Wherein, P k 、P k-1 represent the output power of the PEMFC at time k and time k-1 respectively, in kW; ΔP k represents the power change of the PEMFC at time k, in kW; I k 、I k-1 represent the output current of the PEMFC at time k and time k-1 respectively, in A; ΔI k represents the current change of the PEMFC at time k. According to the positive and negative of ΔP k 、ΔI k and combined with the sign function, the operating state of the PEMFC on the power characteristic curve at time k can be determined. The algorithm flow chart is as shown in Figure 4 shown.

[0144] The specific process can be briefly described as follows:

[0145] When the algorithm starts, the input signal is first measured and calculated, and during this period, the decision condition is used to determine which step of the algorithm should be executed. The decision conditions are as follows:

[0146] (1) When , at this time, the actual output power of the PEMFC is equal to the reference power, and the reference current should remain unchanged, that is, I ref =I k .

[0147] (2) When and sign(ΔP k )×sign(ΔI k )>0, at this time, the PEMFC is operating on the uphill section of the power characteristic curve and the actual output power is less than the reference power. In order to track the reference power, the actual output power should increase, so the reference current at the next moment should increase, that is, I ref =I k +μ(μ>0).

[0148] (3) When and sign(ΔP k )×sign(ΔI k )>0, at this time, the PEMFC is operating on the uphill section of the power characteristic curve and the actual output power is greater than the reference power. The actual output power should decrease, so the reference current should decrease, that is, I ref =I k -μ.

[0149] (4) When I k >I mWhen the PEMFC operates in the concentration polarization region, the reference current should be adjusted to avoid its operation in this region. Then, I ref = I m - μ.

[0150] 4 Case Analysis

[0151] To verify the effectiveness of the control strategy proposed in the present invention, a model was built on the MATLAB / Simulink simulation platform for simulation experiment analysis. The original parameters in the circuit are set as follows: C 1 = 100 uF, C 2 = 0.05 F, C 3 = 1 uF, L 1 = L 2 = 0.001 H, R 1 = R 2 = 0.001 Ω, and the rated frequency is 50 Hz. When the system operates stably, the output power of the PEMFC and the system frequency are shown in Figure 5.

[0152] As shown in Figure 5, at steady state, the PEMFC operates at a power of 50 kW. Due to startup, the system frequency has a small fluctuation and then gradually returns to stability and remains near the rated frequency of 50 Hz.

[0153] Simulation Parameter Table 1

[0154]

[0155] 4.1 Verification of the Effectiveness of the Adaptive Power Tracking Algorithm

[0156] To verify whether the proposed adaptive power tracking algorithm can dynamically adjust the output power of the PEMFC according to the power regulation requirements, a step signal and a sine signal are respectively used as the reference power signals to simulate the cases when the reference power is stable at a certain value or continuously changing, as shown in Figure 6.

[0157] As shown in Fig. 6(a), at t = 0.2 s, 0.4 s, 0.6 s, and 0.8 s, the power demand changes from the initial 50 kW to 40 kW, 60 kW, 80 kW, and 70 kW respectively. After a slight time delay, the actual output power of the PEMFC strictly tracks the change of the reference power and stably outputs at the corresponding reference value. Fig. 6(a) represents the power tracking situation of the PEMFC when the power demand does not change continuously in a short time. In Fig. 6(b), when the power demand changes continuously, after a slight time delay, the actual output power of the PEMFC dynamically follows the change of the reference power and makes corresponding adjustments. Through experiments, it is found that the tracking effect of the PEMFC output power is affected by the sampling frequency and the power demand error threshold. When the sampling frequency increases, the smoothness of the PEMFC output power curve becomes better; when the error threshold ε decreases, the magnitude of the PEMFC output power is closer to the magnitude of the reference power.

[0158] As Figure 7 shown is the current change waveform considering the maximum power point characteristic of the PEMFC, which is used to verify whether the proposed control strategy can limit the PEMFC to operate in the concentration polarization region. Before t = 0.3 s, after a slight delay, the PEMFC operates stably on the uphill section of the power characteristic curve and the current magnitude remains unchanged. After 0.3 s, the operating point position of the PEMFC is changed to exceed the maximum power point, and the output current of the PEMFC will exceed the set threshold I m , and at this time the reference current magnitude is the current I m at the maximum power point minus μ. Since the input signal is constant after 0.3 s and the current magnitude always has a tendency to exceed I m , the current waveform presents a rectangular wave with periodic changes.

[0159] 4.2 Support Effects of Different Control Strategies on System Frequency

[0160] To verify the support effect of the proposed control strategy on the system frequency, constant power control, adaptive power tracking control with a fixed droop coefficient, and adaptive power tracking control with a variable droop coefficient are respectively adopted for the PEMFC. When the load fluctuates, the output of the PEMFC and the system frequency waveform are shown in Figs. 8 and 9.

[0161] At t = 0.3 s and t = 0.6 s, the load is disconnected and reconnected respectively. In Fig. 8(a), the PEMFC adopts constant power control to maintain a constant output of 50 kW active power, and the system frequency waveform is shown in Fig. 9(a). It can be seen that at t = 0.3 s and t = 0.6 s, due to the sudden disconnection and reconnection of the load, the system frequency fluctuates, and the peak values of the fluctuations reach 50.22 Hz and 49.79 Hz respectively, exceeding the limit of ±0.2 Hz. Figs. 8(b), (c) and Figs. 9(b), (c) correspond to the output power curves and system frequency waveforms when the PEMFC adopts fixed droop coefficient and variable droop coefficient adaptive power tracking control respectively. When adopting fixed droop coefficient control, the peak values of the frequency fluctuations occurring at 0.3 s and 0.6 s are reduced, to 50.19 Hz and 49.81 Hz respectively. When adopting variable droop coefficient control, the peak values of the frequency fluctuations occurring at 0.3 s and 0.6 s are reduced to 50.17 Hz and 49.84 Hz respectively. The comparison results of the peak values of the frequency fluctuations under the three control strategies are shown in Table 2.

[0162] Table 2 Peak values of system frequency fluctuations under different control methods

[0163]

[0164]

[0165] It can be seen that when the PEMFC adopts constant power control, since the output power remains unchanged, the PEMFC cannot perform power compensation during load fluctuations, resulting in large fluctuations in the system frequency, exceeding the allowable maximum frequency deviation range. When adopting adaptive power tracking control, the output power of the PEMFC can automatically adjust its output according to the load change to perform power compensation, thereby suppressing the frequency fluctuation. Comparing the PEMFC output curves in Figs. 8(b), (c) and the system frequency waveforms in Figs. 9(b), (c), it can be seen that at the corresponding peak values of the frequency fluctuations, the maximum output of the PEMFC when adopting fixed droop coefficient control is 80.16 kW, and the minimum output is 4.01 kW; when adopting variable droop coefficient control, the maximum output of the PEMFC is 85.69 kW, and the minimum output is 0. It can be seen that when adopting variable droop coefficient control, the output depth of the PEMFC is higher than that of fixed droop coefficient control, and it can perform better power compensation.

[0166] In summary, the present invention adopts adaptive power tracking control based on variable droop coefficient, which can dynamically adjust the output power of the PEMFC when the system load changes, limit the operating position of the PEMFC on the power characteristic curve, support the system frequency, and maintain the stability of the system.

[0167] Aiming at the frequency modulation problem during the grid connection of PEMFC, the present invention constructs a corresponding model. Through comparative analysis, the effectiveness of the proposed control strategy is verified, and the following conclusions are obtained:

[0168] (1) By adopting the frequency modulation control strategy proposed by the present invention for PEMFC, it can dynamically adjust the output power according to the regulation requirements, better compensate the power of the system, and suppress the frequency fluctuation of the system.

[0169] (2) By restricting the current at the maximum power point on the power characteristic curve of PEMFC, PEMFC is prevented from operating in the concentration polarization region.

[0170] (3) Considering the characteristics of PEMFC itself, variable droop coefficient control is adopted. Compared with the fixed droop coefficient control, the output depth of PEMFC is greater, and the peak values of frequency fluctuation are further reduced by 0.02 Hz and 0.03 Hz.

[0171] (4) The PEMFC frequency modulation control strategy proposed by the present invention can provide an idea for PEMFC to participate in frequency modulation during grid connection. A more refined active-frequency droop control model and an adaptive power tracking control algorithm model can be designed to make the output of PEMFC respond more quickly, accurately, and stably according to the regulation requirements, and further improve its frequency support ability.

Claims

1. A PEMFC frequency modulation control method based on adaptive power tracking control, characterized in that: include: This method considers the relationship between frequency and power, and takes into account the characteristics of PEMFC itself. It calculates the reference power required to be output by PEMFC when the load fluctuates through droop control, and uses it as the input signal of the adaptive power tracking control algorithm. The input reference power signal, the actual output power signal of PEMFC and the current signal are calculated through the adaptive power tracking algorithm to obtain the reference current of PEMFC operation, and then the PWM control signal is output. Finally, the output power of PEMFC dynamically follows the reference power change, so as to realize power compensation for the system when the load fluctuates, thereby suppressing the system frequency fluctuation.

2. The PEMFC frequency modulation control method based on adaptive power tracking control according to claim 1 is characterized in that: The method includes obtaining a reference output current of the FEMFC when the load fluctuates by using an adaptive power tracking control algorithm, adjusting the actual output current of the PEMFC by using PI control, and then controlling the output power of the PEMFC; The implementation steps of the method include: S1. The difference between the actual output power of PEMFC and the required output reference power is defined as: P diff =P ref -P Where P ref represents the reference active power; P represents the actual active power, P diff Represents the power demand error between the reference power and the actual power; When P diff Satisfy -ε≤P diff ≤ε, the actual output power of PEMFC is equal to the reference power, and ε represents the allowable error threshold; S2. Since the frequency of the system changes with time, if the output power of PEMFC is to be adjusted dynamically to follow the change of the system frequency, we get: In the formula, represents the reference power that PEMFC should output at time k; P k represents the actual output power of PEMFC at time k; represents the power demand error at time k; S3. Based on the basic principle of the perturbation observation method, considering the changes in the actual output power and output current of PEMFC, the following expression exists: ΔP k =P k -P k-1 ΔI k =I k -I k-1 Where P k , P k-1 represents the PEMFC output power at time k and time k-1 respectively; ΔP k Represents the power change of PEMFC at time k; I k ,I k-1 represents the PEMFC output current at time k and time k-1 respectively; ΔI k represents the current change of PEMFC at time k; S4, according to ΔP k , ΔI k The positive and negative of and combined with the sign function, including determining the operating state of the PEMFC on the power characteristic curve at time k according to the adaptive power tracking control algorithm; The adaptive power tracking control algorithm is as follows: First, the input signal is measured and calculated, and during this period, the judgment conditions are used to determine which step of the algorithm should be executed; the judgment conditions are as follows: 1) When When the actual output power of PEMFC is equal to the reference power, the reference current should remain unchanged, that is, I ref =I k ; 2) When And sign(ΔP k )×sign(ΔI k )>0, at this time, PEMFC operates in the upslope section of the power characteristic curve and the actual output power is less than the reference power. In order to track the reference power, the actual output power should increase, so the reference current should increase at the next moment, that is, I ref =I k +μ(μ>0); 3) When And sign(ΔP k )×sign(ΔI k )>0, at this time, PEMFC operates in the upslope section of the power characteristic curve and the actual output power is greater than the reference power. The actual output power should be reduced, and the reference current should be reduced, that is, I ref =I k -μ; 4) When I k >I m When PEMFC operates in the concentration polarization region, the reference current should be adjusted to avoid operating in this region and satisfy I ref =I m -μ.

3. The PEMFC frequency modulation control method based on adaptive power tracking control according to claim 1 or 2, characterized in that: This method models the PEMFC output characteristics as follows: (1) PEMFC output voltage According to the electrochemical reaction principle of PEMFC, its output voltage V out The open circuit voltage E n , activation polarization overpotential V act 、Ohmic polarization overpotential V ohm and concentration polarization overpotential V conc The output voltage of a single battery is V out =E n -V act -V ohm -V conc ; (2) Open circuit voltage According to the simplified Nernst electromotive force equation, the open circuit voltage of a single cell is obtained as: Where T represents the operating temperature of PEMFC, K; P H2 and P O2 represent the partial pressure of hydrogen and oxygen respectively; (3) Activation polarization overpotential The activation polarization overpotential includes the activation electromotive force of the cathode and the activation electromotive force of the anode. The activation electromotive force is caused by the slow reaction on the electrode surface and is affected by the working temperature T, the hydrogen partial pressure Oxygen partial pressure The influence of PEMFC output current i is calculated as follows: V act =-[ε1+ε2T+ε3Tln(C O2 )+ε4Tln(i)] (4) Ohmic polarization overpotential The calculation formula of Ohm polarization overpotential is: V ohm =iR ohm R ohm =R M +R C In the formula, R ohm Represents ohmic resistance; R M Represents the equivalent resistance of the proton flow channel; R C Represents the equivalent resistance of the electron flow channel; p M is the conductivity of the proton exchange membrane; l is the membrane thickness; λ represents the water content of the membrane; (5) Concentration polarization overpotential The concentration polarization overpotential is caused by the decrease in the concentration of the reactants on the electrode surface. Its size is related to the structure and working state of the PEMFC. Its calculation formula is: Where n is a constant; (6) Current limitation at the maximum power point of the fuel cell For the power regulation requirement below the maximum power point, there are two operating points P1 and P2 with equal power but unequal current on the fuel cell power characteristic curve. When PEMFC operates at P2, it works in the concentration polarization region. Due to the excessive current density in the concentration polarization region and the influence of local polarization, the electrode material will be corroded and the battery life will be reduced. Therefore, it is necessary to limit its working current, which is expressed as: 0≤i≤I m In the formula, I m Represents the operating current corresponding to the maximum power point of PEMFC; after limiting the operating current of PEMFC, PEMFC will only operate in the upslope section of the power characteristic curve, avoiding operation in the concentration polarization region.

4. The PEMFC frequency modulation control method based on adaptive power tracking control according to claim 2 is characterized in that: The frequency modulation control process in the method includes the following frequency modulation control steps taking into account the maximum power point of the PEMFC: Establish an equation between active power and frequency, and use active power-frequency droop control to achieve dynamic adjustment of PEMFC output power according to system load changes to suppress system frequency fluctuations; The mathematical expression between active power and frequency is as follows: P ref -P=K f (f n -f s ) Where P ref represents the reference active power; P represents actual active power; f n 、f s Represent the system rated frequency and actual frequency respectively; K f represents the frequency droop coefficient; For different frequency changes, the output of PEMFC is based on the following mathematical expression: Where P max Represents the output power corresponding to the maximum power point of PEMFC; Δf DB Represents the frequency modulation dead zone; Δf max Represents the maximum frequency fluctuation range allowed when the system is running; Considering that its output power is related to the hydrogen flow rate, the droop coefficient is set to be adjusted accordingly with the change of hydrogen flow rate. For example, when the hydrogen flow rate decreases, K is increased accordingly. f , expressed as: In the formula, v flow 、v flow_max They represent the actual hydrogen flow rate and the hydrogen flow rate at the maximum power output of PEMFC respectively; γ represents the relative flow rate; Representative expression for the droop coefficient affected by hydrogen flow rate.

5. The PEMFC frequency modulation control method based on adaptive power tracking control according to claim 2 or 3, characterized in that: The adaptive power tracking control algorithm enables the output power of PEMFC to be dynamically adjusted according to load changes, thereby achieving the effect of suppressing frequency fluctuations.

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