Fuel cell system
By using a converter with an n-phase magnetic coupling reactor and an n-phase switch in the fuel cell system, the on-off and duty cycle of the switch are controlled, and the AC impedance measurement accuracy problem caused by the degradation of the converter's response performance is solved, and the optimal control of the operating state of the fuel cell is achieved.
Patent Information
- Application Number
- CN202210616228.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Priority Date
- 2021-06-07
- Filing Date
- 2022-06-01
- Publication Date
- 2025-05-27
- Estimated Expiration
- 2042-06-01
AI Technical Summary
In a fuel cell system, the area of the responsive performance of the converter results in a reduced AC impedance measurement accuracy, and the AC impedance of the fuel cell cannot be properly measured, affecting the optimal control of the operating state of the fuel cell.
Using a converter with an n-phase magnetic coupling reactor and an n-phase switch, the current value of the coil is monitored by controlling the on-off of the switch and the periodic increase or decrease of the duty cycle, ensuring that when specific conditions are met, the amplitude of the duty cycle increases significantly, so as to appropriately measure the AC impedance of the fuel cell.
It effectively solves the problem of AC impedance measurement accuracy in the area of reduced response performance, ensuring that AC impedance can be measured properly under dead-range conditions, and thus the operation status of the fuel cell can be optimally controlled.
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Figure CN115513488B_ABST
Abstract
Description
Technical Field
[0001] The present disclosure relates to a fuel cell system. Background Art
[0002] Various studies have been conducted on converters included in systems mounted on vehicles such as fuel cell vehicles. In DC / DC converters used for various electronic devices and the like, a circuit including a reactor, a switch, a diode, a capacitor, and the like is often used. The DC / DC converter controls an increase and a decrease in current flowing through the reactor based on an on / off signal of the switch.
[0003] For example, Patent Document 1 discloses a fuel cell system that measures the AC impedance of a fuel cell stack with high precision.
[0004] In addition, Patent Document 2 discloses a vehicle-mounted fuel cell system that can measure the impedance of a fuel cell with high precision without being affected by load fluctuations of auxiliary machines.
[0005] In addition, Patent Document 3 discloses an impedance measurement method that calculates impedance with high precision in a short time with a simple device and structure.
[0006] In addition, Patent Document 4 discloses a fuel cell system that applies an alternating current for measuring the impedance of a fuel cell to the fuel cell with high precision using a bidirectional buck-boost converter provided with a dead time.
[0007] In addition, Patent Document 5 discloses a power supply device that can detect the state of a power supply while maintaining the control stability of a conversion unit that converts the voltage of the power supplied to the power supply.
[0008] Patent Document 1: Japanese Patent Application Laid-Open No. 2008-098134
[0009] Patent Document 2: Japanese Patent Application Laid-Open No. 2014-232681
[0010] Patent Document 3: Japanese Patent Application Laid-Open No. 2013-145692
[0011] Patent Document 4: Japanese Patent Application Laid-Open No. 2014-235781
[0012] Patent Document 5: Japanese Patent Application Laid-Open No. 2017-153242
[0013] As one of the indicators for controlling the operating state of a fuel cell to be optimal, the AC impedance of the fuel cell is used. A converter performs step-up and step-down control of the output voltage of the fuel cell based on the switching operation by a switching element (switch). It is well known that there is a region where the response performance deteriorates with respect to the duty ratio variation in the converter. If the AC impedance of the fuel cell is measured in such a response performance deterioration region, the overlapping accuracy of the high-frequency signal of the converter with respect to the fuel cell decreases, and thus an adverse condition occurs in which the AC impedance measurement accuracy significantly decreases.
[0014] Aiming at miniaturizing the converter, as an option, it is possible to consider introducing a magnetic coupling converter that includes a magnetic coupling reactor formed by magnetically coupling a plurality of coils on the same iron core. In the magnetic coupling converter, in order to mitigate the magnetic saturation of the iron core of the reactor and reduce the output current ripple, the magnetically coupled coils are generally switched alternately so that the phase difference becomes equally spaced at the same duty ratio. The magnetic coupling reactor operates in a discontinuous mode including the time when the current flowing in the coil becomes zero at low output of the fuel cell.
[0015] The researchers of the present case newly discovered the existence of a "dead zone". For this dead zone, during operation in the discontinuous mode with current interruption, due to the negative current from other coils caused by mutual inductance, which is a phenomenon peculiar to the magnetic coupling reactor, it becomes a suspected switch-on state, and the control of switching from off to on of the switch cannot be smoothly performed, resulting in a state where even if the duty ratio is changed, the output current value of the fuel cell does not change. In the dead zone, even if an AC signal for measuring the AC impedance is applied by changing the duty ratio, as described above, the output current value of the fuel cell hardly changes, and thus the AC impedance of the fuel cell cannot be properly measured. This corresponds to the response performance deterioration region of the above-mentioned Patent Document 1, but there are frequently time periods when the AC impedance is not measured or time periods when the AC impedance cannot be measured, which may lead to the inability to optimally control the operating state of the fuel cell. Summary of the Invention
[0016] The present disclosure has been made in view of the above actual situation, and its main object is to provide a fuel cell system capable of appropriately measuring the AC impedance of a fuel cell.
[0017] The fuel cell system of the present disclosure is characterized in that the fuel cell system includes: a fuel cell, and a converter that performs at least one of boosting and bucking on the output voltage of the fuel cell. The converter includes: a reactor in which n-phase coils are magnetically coupled to each other, n-phase switches respectively connected to the coils, and a control unit, where n is an integer of 2 or more. The control unit performs on-off control of the n-phase switches, the control unit monitors the current values of the coils, the control unit operates the n-phase switches at different phases respectively, the control unit operates while periodically increasing and decreasing the duty ratios of the n-phase switches, measures the AC impedance of the fuel cell based on the current waveform and voltage waveform of the fuel cell, and when the control unit determines that the following condition 1 is satisfied, sets the amplitude of increasing and decreasing the duty ratio to be larger than that in other operating conditions. Condition 1 is an operating condition in which when the n-phase switches are respectively operated at different phases, when the current flowing in the coils is in a discontinuous mode and the current value flowing in one-phase coil is maintained at zero, the switch connected to at least one other-phase coil is switched from on to off.
[0018] In the fuel cell system of the present disclosure, it may also be configured such that the control unit operates the n-phase switches at a phase difference of (360 / n)°.
[0019] In the fuel cell system of the present disclosure, it may also be configured such that the control unit determines whether condition 1 is satisfied based on the current waveforms flowing in the respective coils immediately before measuring the AC impedance of the fuel cell.
[0020] In the fuel cell system of the present disclosure, it may also be configured such that when the control unit increases and decreases the duty ratios of the n-phase switches in such a way that the amplitude of the current value of the coils becomes a normal amplitude, and when the amplitude of the measured current value of the coils is less than the expected value, it is determined that condition 1 is satisfied.
[0021] In the fuel cell system of the present disclosure, it may also be configured such that when n = 2 and the two-phase switches that are magnetically coupled to each other are respectively operated at a phase difference of 180°, when the current flowing in the coils is in a discontinuous mode, and the duty ratios of the two-phase switches are less than 50% (D < 0.5), and when either equation (A) or equation (B) is satisfied, the control unit determines that condition 1 is satisfied.
[0022] Equation (A): D < {(1 / 2)(L - M)(V H -V L )} / (LV L +MV L -MV H )
[0023] Formula (B): D < (1 / 2){1 - (V L / V H )}
[0024] In Formula (A) and Formula (B), L is the self - inductance of the above - mentioned reactor, M is the mutual inductance of the above - mentioned reactor, V H is the output voltage of the above - mentioned converter, V L is the input voltage of the above - mentioned converter, and D is the duty ratio.
[0025] In the fuel cell system of the present disclosure, it can also be configured that the above - mentioned control unit pre - stores a data set representing the relationship between the input voltage and output voltage of the converter, the duty ratio of the above - mentioned switch, and the current value of the above - mentioned coil.
[0026] When the above - mentioned control unit determines that the above - mentioned Condition 1 is satisfied, with reference to the above - mentioned data set, the amplitude of increasing or decreasing the duty ratio of the above - mentioned n - phase switch is set to be larger than that in other operating conditions.
[0027] In the fuel cell system of the present disclosure, it can also be configured that the above - mentioned control unit confirms the presence or absence of the AC impedance measurement request of the above - mentioned fuel cell. When the above - mentioned control unit confirms that there is an AC impedance measurement request of the above - mentioned fuel cell, it determines whether the above - mentioned Condition 1 is satisfied. When the above - mentioned control unit determines that the above - mentioned Condition 1 is satisfied, the amplitude of increasing or decreasing the duty ratio of the above - mentioned n - phase switch is set to be larger than that in other operating conditions, and the AC impedance of the above - mentioned fuel cell is measured.
[0028] According to the fuel cell system of the present disclosure, the AC impedance of the fuel cell can be appropriately measured. Brief Description of the Drawings
[0029] Figure 1 is a diagram showing an example of the circuit structure of a fuel cell system having a boost converter and peripheral components.
[0030] Figure 2 is a diagram showing the current change of the average current value (single - phase average current value) flowing through each coil of the reactor when the input voltage Vfc is 200V, the output voltage Vh is 350V, the boost ratio is kept constant, and two mutually magnetically - coupled coils are driven and the duty ratio is slowly increased.
[0031] Figure 3 is a diagram showing the current waveforms of the two magnetically - coupled coils in the region where dead zones occur.
[0032] Figure 4This is a diagram showing the current waveform when driving coils of two magnetically coupled phases, overlapping sine waves of 270 Hz with amplitudes of ±3A in each phase, and scanning the DC load current in the range of 5 to 25A.
[0033] Figure 5 This is a diagram showing an example of a two-phase magnetically coupled boost circuit of the U-phase and V-phase.
[0034] Figure 6 This is a diagram showing an example of a two-phase magnetically coupled buck circuit of the U-phase and V-phase.
[0035] Figure 7 This is a diagram showing an example of a two-phase magnetically coupled buck-boost circuit of the U-phase and V-phase.
[0036] Figure 8 This is a diagram showing an example of the current waveform when the current flowing through the coil of the reactor of the boost converter is in the continuous mode.
[0037] Figure 9 This is a diagram showing an example of the current waveform when the current flowing through the coil of the reactor of the boost converter is in the discontinuous mode.
[0038] Figure 10 This is a diagram showing an example of the relationship between the duty ratio of the switch in the magnetically coupled converter and the single-phase average current value flowing through the coil of the reactor.
[0039] Figure 11 This is a diagram showing the dead zone generation area in the discontinuous mode.
[0040] Figure 12 This is a flowchart showing an example of the control when measuring the AC impedance of a fuel cell in a fuel cell system including a converter having an n-phase magnetically coupled reactor.
[0041] Figure 13 This is a flowchart showing an example of the control when measuring the AC impedance of a fuel cell in a fuel cell system including a converter having a two-phase magnetically coupled reactor.
[0042] Figure 14 This is a flowchart showing another example of the control when measuring the AC impedance of a fuel cell in a fuel cell system including a converter having an n-phase magnetically coupled reactor.
[0043] Figure 15 This is a flowchart showing another example of the control when measuring the AC impedance of a fuel cell in a fuel cell system including a converter having an n-phase magnetically coupled reactor.
[0044] Description of reference numerals
[0045] 10...Fuel cell; 20...Boost converter; 21...Reactor; 22...Current sensor; 23...Switch; 24...Diode; 25...Capacitor; 50...External load. Detailed implementation mode
[0046] The fuel cell system of the present disclosure is characterized in that the fuel cell system includes: a fuel cell, and a converter that performs at least one selected from the group consisting of boosting and bucking on the output voltage of the fuel cell. The converter includes: a reactor formed by magnetically coupling n-phase coils to each other, n-phase switches respectively connected to the coils, and a control unit, where n is an integer of 2 or more. The control unit performs on-off control of the n-phase switches, the control unit monitors the current value of the coils, the control unit causes the n-phase switches to operate with different phases respectively, the control unit operates while periodically increasing and decreasing the duty ratio of the n-phase switches, measures the AC impedance of the fuel cell according to the current waveform and voltage waveform of the fuel cell, and when the control unit determines that the following condition 1 is satisfied, sets the amplitude of increasing and decreasing the duty ratio to be larger than that in other operating conditions. Condition 1 is an operating condition in which when the n-phase switches operate with different phases respectively, when the current flowing in the coils is in the discontinuous mode and the current value flowing in one-phase coil is maintained at zero, the switch connected to at least one other-phase coil switches from on to off.
[0047] In the present disclosure, under the operating conditions that generate a dead zone, which is a phenomenon peculiar to the magnetically coupled reactor, the duty ratio is increased and decreased in such a way that the target current amplitude value becomes larger than that in other operating conditions, so that an amplitude can also be given to the actual current, and the AC impedance measurement can be appropriately performed.
[0048] The relationship between the duty ratio of the switch of the converter and the reactor current is not linear, but has different slopes according to the operating conditions. In the case of meeting <Condition 1>, considering the difference in slopes, the switching is performed in such a way that the amplitude of the current in the relational expression becomes larger. Specifically, for the magnetically coupled n-phase, it is also possible to increase and decrease the duty ratio based on Figure 10 , Figure 2 and other duty ratio-current characteristic curves, so that the current of each phase increases and decreases across the dead zone, and the current increases and decreases with an amplitude larger than the dead zone current interval shown in Figure 2 .
[0049] By controlling the duty ratio in such a way that the current oscillates beyond the current interval generating the dead zone as described above, even in the region where the dead zone is generated, the current can be reliably increased and decreased to overlap the sine wave, and the AC impedance can be appropriately measured.
[0050] Generally, when increasing or decreasing the current, the output of the fuel cell is excessive or insufficient with respect to the requirements from the fuel cell system, and the battery compensates for the excess or deficiency. However, due to the charge and discharge of the battery, the battery deteriorates and its life becomes shorter. Therefore, it is desirable to minimize the increase and decrease of the current. Thus, by setting the amplitude of the duty ratio given for AC impedance measurement to be larger only when the operating condition is <Condition 1> than in other operating conditions, it is possible to both suppress battery deterioration and appropriately perform impedance measurement.
[0051] Figure 1 FIG. is an example of the circuit configuration of a fuel cell system having a boost converter and peripheral components.
[0052] Figure 1 The fuel cell system shown is mounted on a vehicle, for example, and a drive motor of the vehicle is connected as an external load 50 via an inverter. Although not shown, a battery may also be provided in parallel with the fuel cell 10 and the boost converter 20. The output power of the fuel cell 10 is boosted by the boost converter 20 and then further converted from DC to AC by the inverter and supplied to the motor.
[0053] The boost converter 20 includes a six-phase boost circuit connected in parallel with each other. In Figure 1 FIG., a structure having a six-phase boost circuit is shown, but the number of phases is not particularly limited.
[0054] The boost circuit includes a reactor 21, a current sensor 22, a switch 23, a diode 24, and a capacitor 25. The boost circuit may also include an input voltage sensor and an output voltage sensor.
[0055] In the six-phase boost circuit, every two phases can share the core of one reactor 21 and be magnetically coupled to each other. In each boost circuit, when the switch 23 is turned on, the current flowing in the reactor 21 increases, and when the switch 23 is turned off, the current flowing in the reactor 21 decreases. When the current reaches zero, it is maintained at zero. The current sensor 22 obtains the current value flowing in the reactor 21.
[0056] The control unit controls the boost ratio in the converter 20 and the output current value from the fuel cell 10 by controlling the on / off of the switch 23.
[0057] The output power of the fuel cell 10 varies significantly according to the requirements of the vehicle (such as speed, acceleration, load, and road gradient), and correspondingly, the output current also varies significantly. When the output current of the fuel cell 10 is large, if this current is made to flow through a single boost circuit, the heat generation increases, resulting in a decrease in power conversion efficiency. Additionally, even when only a small current flows through a boost circuit that can withstand a large current, the losses increase, and the power conversion efficiency also decreases. Therefore, the boost converter 20 is equipped with a multi-phase boost circuit (6 phases in the example shown in Figure 1 ), and the boost converter 20 switches the number of phases to be driven according to the output current value of the fuel cell 10. For example, when the output current value of the fuel cell 10 is 0 to 150 A, it is driven in two phases; when it is 150 to 300 A, it is driven in 4 phases; and when it is 300 to 600 A, it is driven in 6 phases. Since the efficiency of the boost circuit varies according to the flowing current, by changing the number of driving phases, it is possible to operate with the optimal efficiency in each current region.
[0058] The fuel cell system includes a fuel cell and a converter.
[0059] The fuel cell can have only a single cell or can be a fuel cell stack formed by laminating multiple single cells.
[0060] The converter performs at least one selected from the group consisting of boosting and bucking on the output voltage of the fuel cell. The converter can be a boost converter, a buck converter, or a buck-boost converter.
[0061] The converter can also be a DC / DC converter.
[0062] The converter includes a reactor in which coils of n (n is an integer of 2 or more) phases are magnetically coupled to each other, n-phase switches respectively connected to the coils, and a control unit. The converter can also include components such as diodes, current sensors, optocouplers, and capacitors.
[0063] The reactor has a coil and an iron core.
[0064] Coils of n (n is an integer of 2 or more) phases can be wound around the iron core. It is sufficient that n is 2 or more, and there is no particular limitation on the upper limit, which can be 10 or less, 5 or less, 4 or less, or 3 or less.
[0065] The iron core and coil of the reactor can be the iron core and coil used in conventional converters.
[0066] In the present disclosure, a reactor having an iron core around which an independent coil is wound is referred to as a non-magnetically coupled reactor. In the present disclosure, a converter equipped with a non-magnetically coupled reactor is referred to as a non-magnetically coupled converter. In the present disclosure, a reactor having an iron core around which two or more independent coils are wound is referred to as a magnetically coupled reactor. In the present disclosure, a converter equipped with a magnetically coupled reactor is referred to as a magnetically coupled converter.
[0067] The independent coil in the present disclosure refers to a coil having one or more windings and two terminal portions.
[0068] As the switch (switching element), it can be an IGBT, MOSFET, etc.
[0069] The diode can be the diode used in a conventionally known converter.
[0070] The current sensor is not particularly limited as long as it can obtain the current value flowing in the coil of the reactor (sometimes referred to as the reactor current value), and a conventionally known ammeter, etc. can be used.
[0071] The control unit can be an electronic control unit (ECU: Electronic Control Unit), etc. The ECU is configured to include a CPU (Central Processing Unit), a memory, and an input / output buffer.
[0072] The control unit can detect the current value flowing in the coil of the reactor based on the signal from the current sensor, thereby monitoring the current value of the coil.
[0073] The control unit performs on / off control of the switches of n phases. The control unit can cause the magnetically coupled switches of n phases to operate at a constant frequency.
[0074] The control unit performs on / off control of the switches by periodically switching the on command and off command for the switches. Thereby, the output current value from the fuel cell can be controlled.
[0075] In the present disclosure, the period of the switch (switching period) refers to the period from the moment when the switch is switched from off to on until the moment when the switch is switched from off to on again.
[0076] The control unit causes the switches of n phases to operate at different phases respectively. The control unit can cause the switches of n phases to operate with the same duty ratio respectively. The control unit can also cause the switches of n phases to operate with slightly different duty ratios.
[0077] The control unit can also cause the switches of n phases to operate with a phase difference of (360 / n)°.
[0078] When the control unit determines that the following Condition 1 is satisfied, the amplitude for increasing or decreasing the duty ratio is set to be larger than other operating conditions.
[0079] Condition 1: This is an operating condition where when the above-mentioned switches of n phases operate with different phases, and when the current flowing in the above-mentioned coil is in the discontinuous mode and the current value flowing in the above-mentioned coil of one phase is maintained at zero, the above-mentioned switch connected to the coils of at least one other phase is switched from on to off.
[0080] [Explanation of dead zone]
[0081] "Dead zone" refers to a region where even if the PWM duty ratio of the converter is increased or decreased, the average current value flowing along the coil of the reactor remains almost unchanged. In a two-phase magnetically coupled unidirectional boost (buck) circuit, due to the negative current caused by the mutual inductance of magnetic coupling, the dead zone appears in a part of the discontinuous mode region where the duty ratio is 50% or less (D ≤ 0.5).
[0082] Figure 2 This is a graph showing the current change of the average current value (single-phase average current value) flowing along each coil of the reactor when the input voltage Vfc is 200V, the output voltage Vh is 350V, and the duty ratio is slowly increased by driving the coils of two magnetically coupled phases while keeping the boost ratio constant. In Figure 2 the self-inductance of the coil is 96.4 μH, the mutual inductance of the coil is 62.7 μH, and the driving frequency of the switch is 20 kHz.
[0083] According to the state equation (described later) for calculating the average current value flowing along the coil of the reactor, as shown by the dotted line in Figure 2 as the duty ratio increases, the average current value flowing along the coil of the reactor should also monotonically increase. However, in reality, as shown by the solid line, the current shows a stepped increase characteristic. In the part surrounded by the dotted line, there is a "dead zone" where even if the duty ratio is increased, the average current value flowing along the coil of the reactor does not increase. When the average current value flowing along the coil of the reactor is in the above-mentioned dead zone, even if the duty ratio changes, the average current value flowing along the coil of the reactor, that is, the output current value of the fuel cell, does not change, and the AC impedance of the fuel cell cannot be properly measured.
[0084] Figure 3 This is a graph showing the current waveforms of the two magnetically coupled coils in the region where the dead zone is generated. In Figure 3 the current of phase U is marked as L1, and the current of phase V is marked as L2.
[0085] During the period from time t0 to t1, the switch of the V phase is turned on, and the current of L2 gradually increases. On the other hand, the switch of the U phase is in the off state, and the current of L1 is maintained at 0. At time t1, the switch of the V phase is switched from on to off, and thus the current of L2 in the V phase starts to decrease. Here, the switch of the U phase remains off, but after time t1, due to the interaction of the V phase, the current of L1 flowing along the U phase alternately decreases and increases.
[0086] Here, for example, at time t2, even if the switch of the U phase is turned on when the current of L1 in the U phase is increasing, since the current has already increased, the signal of the switch being turned on is not recognized. After that, at time t3 when it comes to the timing of the current of L1 in the U phase decreasing, the switch of the U phase is first recognized as being turned on, and then the current of L1 increases until the switch of the U phase is turned off. Since the timing when the signal of the switch being turned on is not recognized and the timing when the signal of the switch being turned on is recognized alternate, as Figure 2 shown, the dead zone recurs.
[0087] In addition, as described above, when the current value of the coil of one phase of the magnetic coupling is 0, if the switch of the other phase is switched from on to off, a current increase and decrease will be generated in the coil of one phase, and as a result, a dead zone appears.
[0088] Therefore, as in Condition 1, when driving the switches of the n phases with different phases respectively, when the current flowing in the above-mentioned coil is in the discontinuous mode and the current value of the coil of one phase of the magnetic coupling is maintained at 0, and when the switch of the other phase is switched from on to off under such operating conditions, it can be said that a dead zone is generated.
[0089] Figure 4 is a diagram showing the current waveforms when driving the coils of two magnetically coupled phases, overlapping sine waves of 270 Hz with an amplitude of ±3A respectively in each phase, and scanning the DC load current in the range of 5 - 25A. In Figure 4 it is the same as Figure 2 where the input voltage Vfc is 200V, the output voltage Vh is 350V, the boost ratio is kept constant, the self-inductance of the coil is 96.4 μH, the mutual inductance of the coil is 62.7 μH, and the driving frequency of the switch is 20 kHz. In Figure 4 in the case of, it can be considered that the relationship between the duty ratio and the average current value flowing along the coil of the reactor follows the Figure 2 dotted line shown, so the duty ratio is oscillated following the dotted line. However, as described above, actually the change of the current value is stepped as shown by the solid line in Figure 2 , so even if the duty ratio is increased or decreased in the dead zone represented by the dotted line in Figure 2 , the current does not change, as shown in Figure 4As shown by the dashed line, there is a region in the current where sine waves cannot overlap, and it is impossible to measure the AC impedance of the fuel cell in this region. In addition, when a sharp change in the DC load occurs in the specific region represented by Figure 4 the dashed line, there is also a case where the output response of the fuel cell is delayed and the load of the battery or the like increases.
[0090] Considering Figure 4 , when the control unit increases or decreases the duty ratio of the n-phase switch so that the amplitude of the current value of the coil becomes the normal amplitude, it can be determined that Condition 1 is satisfied when the amplitude of the measured current value of the coil is less than the expected value. When the amplitude of the current value of the coil is less than the expected value, it is equivalent to a state where sine waves do not overlap, and it can be determined that the dead zone has been entered.
[0091] Figure 5 FIG. is a diagram showing an example of a two-phase magnetic coupling boost circuit of the U-phase and the V-phase. In Figure 5 , V L represents the input voltage (voltage before boosting), I L represents the input current, V H represents the output voltage (voltage after boosting), I H represents the output current, D represents a diode, S represents a switch, M represents a mutual inductor, L represents a self-inductor, and r represents an internal resistance.
[0092] Equation (1) is the state equation of the current I vector. By solving this state equation, the current curve represented by the dashed line in Figure 2 can be obtained. The voltage V vector in Equation (1) is represented as shown in Table 1. Table 1 shows the voltage V vector in Equation (1) and the dead zone generation conditions (hatched part).
[0093] Due to the negative current caused by the mutual inductance of the magnetic coupling represented by Figure 5 and M in Equation (1), in a two-phase magnetic coupling unidirectional boost (buck) circuit, as shown in the hatched part of Table 1, a dead zone appears in a part of the discontinuous mode region where the duty ratio is less than 50% (D < 0.5) under the condition that the two-phase switches are in the off state, that is, under 180° phase difference driving. For the mechanism, as obtained by solving Equation (1) over time under the conditions of Table 1, when the current flowing through one coil is 0 A and the current flowing through the other coil is positive in the state where the two-phase switches are off, an electromotive force caused by the mutual inductance is generated in the 0 A side coil, resulting in a negative current. After that, as the negative current increases, the electromotive force of the coil disappears and immediately starts to decrease. However, during the period until it returns to 0 A, as shown in the hatched part of Table 1, the switch becomes a suspected on state. Therefore, regardless of whether the negative current side switch is on or off, it cannot affect the current waveform and becomes a control dead zone.
[0094] In addition, for example, in the case of a three-phase magnetic coupling boost circuit of the U-phase, V-phase, and W-phase, the dead zone generation conditions are assumed to be: all three-phase switches are off and I U > 0, I V ≤ 0, I W ≤ 0, or all three-phase switches are off and I U > 0, I V > 0, I W ≤ 0, etc.
[0095]
Formula 1
[0096]
[0097] Table 1
[0098]
[0099] Figure 6 is a diagram showing an example of a two-phase magnetic coupling buck circuit of the U-phase and V-phase.
[0100] Figure 7 is a diagram showing an example of a two-phase magnetic coupling buck-boost circuit of the U-phase and V-phase.
[0101] Not only in the boost circuit, but also in the buck circuit and the buck-boost circuit, there is a problem of current control dead zone in the same way as in the boost circuit. By making the amplitude of increasing and decreasing the duty ratio under the operating conditions of condition 1 where the dead zone is generated larger compared to other operating conditions, the AC impedance of the fuel cell can be appropriately measured. In addition, for a bidirectional circuit without a discontinuous mode, it can be considered that there is no dead zone.
[0102] [Explanation of continuous mode and discontinuous mode]
[0103] Figure 8 is a diagram showing an example of a current waveform in the case where the current flowing through the coil of the reactor of the boost converter is in the continuous mode.
[0104] Figure 9 is a diagram showing an example of a current waveform in the case where the current flowing through the coil of the reactor of the boost converter is in the discontinuous mode.
[0105] As Figure 8 shown, the current flowing through the coil of the reactor of the boost converter (reactor current) becomes a triangular wave along with the switching operation, and the central value of the triangular wave is the average reactor current (hereinafter, referred to as the average current). Here, if the duty ratio is reduced to lower the average current, the lowest point of the triangular wave reaches 0 A. If the average current is further reduced after that, since the boost converter is a unidirectional circuit, as Figure 9As shown, a period starts when the reactor current becomes zero. In this way, the operation with a period during which the current flowing through the coil of the reactor in the converter is zero is called the discontinuous mode, and the operation without a period during which the current flowing through the coil of the reactor is zero is called the continuous mode.
[0106] Conceiving different situations according to conditions, the control unit can pre-store a data set representing the relationship between the input voltage and output voltage of the converter, the duty ratio of the switch, and the current value of the coil.
[0107] When the control unit determines that condition 1 is satisfied, it sets the amplitude for increasing or decreasing the duty ratio of the n-phase switch to be larger than that in other operating conditions with reference to the above data set.
[0108] Figure 10 It is a diagram showing an example of the relationship between the duty ratio of the switch in the magnetic coupling converter and the single-phase average current value flowing through the coil of the reactor.
[0109] When keeping the output voltage (V H ) of the converter constant, the average current value flowing through the coil of the reactor is determined according to the input voltage (V L ) to the converter and the duty ratio. Generally, if the duty ratio increases, the average current value flowing through the coil of the reactor also increases.
[0110] The control unit may also have a map (data set) storing the characteristics shown in Figure 10 . When measuring the AC impedance of the fuel cell, the duty ratio is increased or decreased so that the average current value of the coil flowing through the reactor increases or decreases with a specified amplitude. The slope of the diagram shown in Figure 10 can be considered to determine the amplitude of the duty ratio. In the present disclosure, the duty ratio may also be increased or decreased with a larger amplitude in such a way that the amplitude of the current is larger under the operating condition of condition 1 where a dead zone is generated than in other operating conditions. For example, if it is determined that condition 1 is not met when the input voltage (V L ) to the converter is 20V and the average current value of the coil flowing through the reactor is 9A, then when measuring the AC impedance of the fuel cell, the duty ratio is increased or decreased within a range such that the amplitude of the current becomes about ±3A, that is, the current value of the coil oscillates between 6A and 12A. On the other hand, under the operating condition of condition 1 where a dead zone is generated, the duty ratio may also be increased or decreased within a range such that the amplitude of the current becomes about ±5A, that is, the current value of the coil oscillates between 4A and 14A. As shown in Figure 10 , the slope of the duty ratio and the current value of the coil varies according to the operating conditions. Therefore, with reference to Figure 10While selecting an amplitude with an appropriate duty ratio, a sine wave is superimposed on the current flowing in the coil.
[0111] Figure 11 It is a diagram showing the dead-time generation region in the discontinuous mode.
[0112] The present researcher has recognized the following: In a boost converter in which (each) two phases are magnetically coupled with L > M, the region surrounded by the slanted lines as the dead-time generation region is the one that satisfies Condition 1 and generates dead time.
[0113] Furthermore, L is the self-inductance of the reactor, M is the mutual inductance, and they are inherent values determined by the physical property values of the reactor. V L is the input voltage (voltage before boosting) of the boost converter, and V H is the output voltage (voltage after boosting) of the boost converter.
[0114] In the case of two-phase magnetic coupling (n = 2), it is sufficient that the phases of the two phases being driven are different, and the phase difference can also be 180°. In the case where the phases of the two phases being driven are different, if it is in the discontinuous mode and the duty ratio is less than 50% (D < 0.5), then when the average current value of the coil of one of the magnetically coupled phases is maintained at 0, the switch of the other phase is switched from on to off.
[0115] From the viewpoint of accurately determining the operating conditions for generating dead time, the control unit may also be configured such that, in the case of two-phase magnetic coupling (n = 2), when it is determined that Figure 11 the conditions for the dead-time generation region shown, that is, "when the switches of the two magnetically coupled phases are operated with a phase difference of 180°, the current flowing in the coil is in the discontinuous mode, and the duty ratios (D) of the switches of the two phases are less than 50% (D < 0.5), and either of the following equations (A) and (B) is satisfied", it is determined that Condition 1 is satisfied.
[0116] Equation (A): D < {(1 / 2)(L - M)(V H - V L )} / (LV L + MV L - MV H )
[0117] Equation (B): D < (1 / 2){1 - (V L / V H )}
[0118] [In Equations (A) and (B), L is the self-inductance of the reactor, M is the mutual inductance of the reactor, V H is the output voltage of the converter, V L is the input voltage of the converter, and D is the duty ratio.]
[0119] In the case where (each) two phases are magnetically coupled, one of the conditions in Condition 1 is the case where "when the switches of the two magnetically coupled phases operate with a phase difference of 180°, the current flowing in the coil is in a discontinuous mode and the duty ratios of the switches of the two phases are less than 50% (D < 0.5)".
[0120] On the other hand, for Condition 1 when driving (each) n magnetically coupled phases with a phase difference of (360 / n)° between the n magnetically coupled phases, instead of the condition "when the switches of the two magnetically coupled phases operate with a phase difference of 180°, the current flowing in the coil is in a discontinuous mode and the duty ratios of the switches of the two phases are less than 50% (D < 0.5)", it becomes "when the switches of the n magnetically coupled phases operate with a phase difference of (360 / n)°, the current flowing in the coil is in a discontinuous mode and the duty ratios of the switches of the n phases are less than (100 - 100 / n)%.
[0121] [Measurement of AC impedance]
[0122] The control unit operates while periodically increasing and decreasing the duty ratios of the switches of the n phases, and measures the AC impedance of the fuel cell based on the current waveform and voltage waveform of the fuel cell.
[0123] The control unit can also confirm the presence or absence of a request for measuring the AC impedance of the fuel cell. Moreover, the control unit can determine whether Condition 1 is satisfied when it is confirmed that there is a request for measuring the AC impedance of the fuel cell. By determining whether Condition 1 is satisfied only when there is a request for measuring the AC impedance of the fuel cell, the control can be simplified.
[0124] On the other hand, the control unit can also confirm the presence or absence of a request for measuring the AC impedance of the fuel cell when it is determined that Condition 1 is satisfied. Moreover, the control unit can also set the amplitude of increasing and decreasing the duty ratios of the above-mentioned switches of the n phases to be larger than that in other operating conditions when it is confirmed that there is a request for measuring the AC impedance of the fuel cell, thereby measuring the AC impedance of the fuel cell. By determining whether there is a request for measuring the AC impedance of the fuel cell only when Condition 1 is satisfied, the control can be simplified.
[0125] For the control unit, in order to grasp the state of the electrolyte membrane of the fuel cell and the state of gas supply, the AC impedance of the fuel cell is measured at a specified frequency during the operation of the fuel cell.
[0126] The control unit switches while periodically increasing and decreasing the PWM duty ratio of the converter, and obtains the output voltage and output current value of the fuel cell when a load current including a certain frequency component is applied as time-series waveform data for one wavelength or more. The discrete Fourier transform is performed on this waveform data, and the discrete Fourier transform result of the voltage signal is divided by the discrete Fourier transform result of the current signal, thereby calculating the AC impedance of the fuel cell.
[0127] In the low-load region called the discontinuous mode, when the duty ratio is increased, the average current value flowing through the coil of the reactor also increases.
[0128] In order to obtain the AC impedance of the above fuel cell, for example, the duty ratio can be controlled in such a way that it becomes a sine wave with an amplitude of the output current value of about ±3A.
[0129] In addition, for the output voltage value of the fuel cell, the voltage of the entire fuel cell stack can be obtained, or the voltage of each single cell can be obtained. If the voltage value of the entire fuel cell stack is used, the AC impedance of the entire fuel cell stack can be obtained, and if the voltage value of each single cell is used, the AC impedance of each single cell can be obtained.
[0130] In addition, if the voltage is obtained for every multiple single cells (for example, every 2 single cells, every 4 single cells, etc.), the AC impedance of any arbitrary single cell block can be obtained.
[0131] When the single cell area is about several hundred cm 2 or so, the components of the AC impedance obtained during power generation above 200 Hz mainly represent the proton transfer resistance and contact resistance of the electrolyte membrane, and the components of several 10 Hz represent the gas diffusion resistance.
[0132] In addition, the method for measuring the AC impedance of the fuel cell of the present disclosure is not particularly limited, and a known method can be applied. For example, it can also be the same method as the method described in Japanese Patent Laid-Open No. 2008-098134.
[0133] (Typical example)
[0134] Figure 12 It is a flowchart showing an example of control when measuring the AC impedance of a fuel cell in a fuel cell system including a converter having an n-phase magnetic coupling reactor.
[0135] The control unit determines whether there is a request for measuring the AC impedance of the fuel cell. When the control unit determines that there is no request for measuring the AC impedance of the fuel cell, it may end the control or maintain the amplitude that increases or decreases the current duty ratio. On the other hand, when the control unit determines that there is a request for measuring the AC impedance of the fuel cell, it monitors the current value of the coil and determines whether Condition 1 is satisfied, that is, "when the switches of the n phases operate with different phases respectively, the current flowing in the coil is in the discontinuous mode and when the current value flowing in one phase of the coil is maintained at zero, the switch connected to at least one other phase of the coil is switched from on to off operating condition". When the control unit determines that Condition 1 is not satisfied, it measures the AC impedance of the fuel cell while maintaining the amplitude that increases or decreases the current duty ratio. On the other hand, when the control unit determines that Condition 1 is satisfied, it sets the amplitude that increases or decreases the duty ratio of the switches of the n phases to be larger than the current operating condition and measures the AC impedance of the fuel cell. For example, when increasing or decreasing the duty ratio in such a way that the target current amplitude value that constitutes the current operating condition becomes A, the control unit may, when determining that Condition 1 is satisfied, set the amplitude that increases or decreases the duty ratio to be larger than the current operating condition in such a way that the target current amplitude value becomes B (B > A) which is larger than A. In addition, the target current amplitude to be changed may be set according to the duty ratio D, the inlet voltage V L , the outlet voltage V H .
[0136] (Specific example)
[0137] In the case of two-phase magnetic coupling (n = 2), the control unit may also determine that Condition 1 is satisfied when it determines that the above "when the switches of the two magnetically coupled phases operate with a 180° phase difference respectively, the current flowing in the coil is in the discontinuous mode, and the duty ratios of the switches of the two phases are less than 50% (D < 0.5), and either Equation (A) or Equation (B) is satisfied".
[0138] Figure 13 It is a flowchart showing an example of the control when measuring the AC impedance of a fuel cell in a fuel cell system including a converter having a two-phase magnetic coupling reactor.
[0139] The control unit determines whether there is a request for measuring the AC impedance of the fuel cell. When the control unit determines that there is no request for measuring the AC impedance of the fuel cell, it may end the control or maintain the amplitude that increases or decreases the current duty ratio. On the other hand, when the control unit determines that there is a request for measuring the AC impedance of the fuel cell, it monitors the current value of the coil and determines whether, as condition 1, "when the switches of two magnetically coupled phases are each operated with a 180° phase difference, the current (driven phase) flowing in the coil is in the discontinuous mode, and the duty ratios of the switches of the two phases are less than 50% (D < 0.5), and either equation (A) or equation (B) is satisfied". When the control unit determines that condition 1 is not satisfied, it measures the AC impedance of the fuel cell while maintaining the amplitude that increases or decreases the current duty ratio in such a way that the target current amplitude value becomes A. On the other hand, when the control unit determines that condition 1 is satisfied, it sets the amplitude that increases or decreases the duty ratios of the switches of the two phases to be larger than the current operating conditions in such a way that the target current amplitude value becomes B (B > A), thereby measuring the AC impedance of the fuel cell.
[0140] In Figure 13 the example shown, during the operation of the fuel cell system, when measuring the AC impedance of the fuel cell in a state of entering the above-mentioned dead zone generation area, compared with when measuring the AC impedance under other conditions, Figure 10 the duty ratio is oscillated in such a way that the amplitude of the current value becomes larger on the map of Figure 2 . The amplitude width of the current value is set to be greater than or equal to the step difference of the current in
[0141] As Figure 11 shown, the "dead zone generation area" may also be "when the switches of two magnetically coupled phases are each operated with a 180° phase difference, the current flowing in the coil is in the discontinuous mode, and the duty ratios of the switches of the two phases are less than 50% (D < 0.5), and either equation (A) or equation (B) is satisfied". Therefore, for example, when the operating conditions transfer to Figure 11 the timing of the dead zone generation area shown, it transfers from an operating mode with a smaller target current amplitude to an operating mode with a larger target current amplitude.
[0142] In addition, when the conditions of "when the switches of two magnetically coupled phases are each operated with a 180° phase difference, the current flowing in the coil is in the discontinuous mode, and the duty ratios of the switches of the two phases are less than 50% (D < 0.5)" are not satisfied, a state with a smaller target current amplitude is achieved, thereby reducing the degree of charge and discharge of the storage battery and suppressing the shortening of the life of the storage battery.
[0143] The means for determining whether the condition 1 for generating the dead zone is satisfied is not limited to the above cases. For example, the range equivalent to the dead zone can also be defined based on the input voltage and the duty ratio. When the input voltage and the duty ratio show an entry into or approach the range equivalent to the dead zone, it is determined that the condition 1 is satisfied.
[0144] As described above, by pre - defining the range equivalent to the dead zone and switching the amplitude of the duty ratio when entering this range, the AC impedance of the fuel cell can be quickly obtained when the AC impedance of the fuel cell is desired to be obtained.
[0145] In Figure 13 as the condition 1 for increasing the target current amplitude, it is set to "when the switches of two magnetically - coupled phases are operated with a phase difference of 180°, the current flowing in the coil is in the discontinuous mode, and the duty ratios of the switches of the two phases are less than 50% (D < 0.5), and either Equation (A) or Equation (B) is satisfied", but the condition of "when either Equation (A) or Equation (B) is satisfied" can also be removed.
[0146] That is, as the condition 1, it can also be set to "when the switches of two magnetically - coupled phases are operated with a phase difference of 180°, the current flowing in the coil is in the discontinuous mode, and the duty ratios of the switches of the two phases are less than 50% (D < 0.5)". In this case, for example, it can be configured such that when the required output to the fuel cell decreases and the transition is made from the state where the current flowing in the coil is in the discontinuous mode and the duty ratios of the switches of the two phases are 50% or more (D ≥ 0.5) to the state where the current flowing in the coil is in the discontinuous mode and the duty ratios of the switches of the two phases are less than 50% (D < 0.5), the amplitude of the duty ratios of the switches of the two phases is switched.
[0147] As Figure 11 shown, the area removed from the range of increasing the current amplitude according to Equation (A) and Equation (B) is not large. Therefore, it can be considered that even if the condition of "when either Equation (A) or Equation (B) is satisfied" is removed, the impact on increasing the battery life is limited. On the other hand, by removing the condition of "when either Equation (A) or Equation (B) is satisfied", the control can be simplified and the measurement of the AC impedance of the fuel cell can be appropriately performed.
[0148] In addition, as a modification example, as Condition 1, it may also be set to "when the switches of two magnetically coupled phases operate with a phase difference of 180°, the current flowing in the coil is in a discontinuous mode, the duty ratios of the switches of the two phases are less than 50% (D < 0.5), and the formula (A) is satisfied", or "when the switches of two magnetically coupled phases operate with a phase difference of 180°, the current flowing in the coil is in a discontinuous mode, the duty ratios of the switches of the two phases are less than 50% (D < 0.5), and the formula (B) is satisfied".
[0149] (Modification Example 1)
[0150] As described above, when the control unit increases or decreases the duty ratio of the n-phase switches so that the amplitude of the current value of the coil becomes the normal amplitude, when the measured amplitude of the current value of the above coil is less than the expected value, it is determined that Condition 1 is satisfied.
[0151] Figure 14 It is a flowchart showing another example of the control when measuring the AC impedance of a fuel cell in a fuel cell system including a converter having an n-phase magnetically coupled reactor.
[0152] In Figure 14 , the control unit determines whether there is a request for measuring the AC impedance of the fuel cell. When the control unit determines that there is no request for measuring the AC impedance of the fuel cell, it may end the control or maintain the amplitude of increasing or decreasing the current duty ratio. On the other hand, when the control unit determines that there is a request for measuring the AC impedance of the fuel cell, it increases or decreases the duty ratio so that the amplitude of the current value becomes the normal amplitude (the target current amplitude value becomes A). Moreover, the control unit determines whether the condition of "when increasing or decreasing the duty ratio of the n-phase switches so that the amplitude of the current value of the coil becomes the normal amplitude of the current value, the measured (actual) amplitude of the current value of the coil is less than the expected value" is satisfied as Condition 1. When the measured amplitude of the current value of the coil is less than the expected value, the control unit sets the amplitude of increasing or decreasing the duty ratio to be larger than the current operating condition so that the amplitude of the current value of the coil becomes the target current amplitude value B (B > A), and measures the AC impedance of the fuel cell. On the other hand, when the measured amplitude of the current value of the coil is the expected value, the control unit measures the AC impedance of the fuel cell while maintaining the amplitude of increasing or decreasing the current duty ratio.
[0153] In this case, the duty ratio can be increased or decreased so that the amplitude of the current value becomes the normal amplitude, and when the amplitude of the actual current value is less than the expected value, it is determined that the dead zone has been entered.
[0154] As described above, it is determined whether or not the dead zone has been entered based on the amplitude of the actual current value. Thus, for example, even when the region of the dead zone deviates from normal due to product differences or the like, the duty ratio can be appropriately switched to obtain the AC impedance of the fuel cell.
[0155] (Modification Example 2)
[0156] The control unit may also determine whether or not Condition 1 is satisfied based on the current waveforms flowing in the respective coils immediately before measuring the AC impedance of the fuel cell.
[0157] Figure 15 FIG. is a flowchart showing another example of control when measuring the AC impedance of a fuel cell in a fuel cell system including a converter having an n-phase magnetic coupling reactor.
[0158] In Figure 15 , the control unit determines whether there is a request for measuring the AC impedance of the fuel cell. The control unit may also end the control or maintain the amplitude for increasing or decreasing the current duty ratio when it is determined that there is no request for measuring the AC impedance of the fuel cell. On the other hand, when it is determined that there is a request for measuring the AC impedance of the fuel cell, the control unit acquires the current waveforms flowing in the respective coils immediately before measuring the AC impedance of the fuel cell. Then, based on the acquired current waveforms, the control unit determines whether, as Condition 1, "when the above-described switches of the n phases are operated with different phases, the current flowing in the above-described coils is in a discontinuous mode and the switch connected to at least one other phase coil is switched from on to off when the current value flowing in one phase of the above-described coils is maintained at zero". Further, when it is determined that Condition 1 is satisfied, the control unit sets the amplitude for increasing or decreasing the duty ratio to be larger than that in other operating conditions so that the target current amplitude value becomes B (B > A). On the other hand, when it is determined that Condition 1 is not satisfied, while maintaining the amplitude for increasing or decreasing the current duty ratio so that the target current amplitude value becomes A, the control unit measures the AC impedance of the fuel cell.
[0159] The current waveforms flowing in the respective coils immediately before measuring the AC impedance of the fuel cell may also be, for example, the current waveforms of the previous one of the switching periods. The switching period is, for example, about 30 kHz. Even if it is the previous one of the periods, the operating conditions are substantially the same, and it can be considered that Figure 11 the dead zone generation region in is also the same, and it is possible to accurately determine whether or not Condition 1 is satisfied.
Claims
1. A fuel cell system, characterized in that, the fuel cell system includes: a fuel cell, and a converter that performs at least one of boosting and bucking on the output voltage of the fuel cell, the converter includes: a reactor formed by magnetically coupling n-phase coils, n-phase switches respectively connected to the coils, and a control unit, where n is an integer of 2 or more, the control unit performs on-off control of the n-phase switches, the control unit monitors the current values of the coils, the control unit operates the n-phase switches at different phases respectively, the control unit operates while periodically increasing and decreasing the duty ratios of the n-phase switches, measures the AC impedance of the fuel cell based on the current waveform and voltage waveform of the fuel cell, and when the control unit determines that the following Condition 1 is satisfied, sets the amplitude of increasing and decreasing the duty ratio to be larger than other operating conditions, Condition 1 is an operating condition in which when the n-phase switches are operated at different phases respectively, when the current flowing in the coils is in the discontinuous mode and the current value flowing in one-phase coil is maintained at zero, the switch connected to at least one other-phase coil is switched from on to off, when n = 2 and the two-phase switches that are magnetically coupled are operated with a phase difference of 180°, when the current flowing in the coils is in the discontinuous mode, and the duty ratios of the two-phase switches are less than 50%, that is, D < 0.5, and when either Equation A or Equation B is satisfied, the control unit determines that Condition 1 is satisfied, Formula A: D < {(1 / 2)(L - M)(V H - V L )} / (LV L + MV L - MV H ) Formula B: D < (1 / 2){1 - (V L / V H )} In Formula A and Formula B, L is the self-inductance of the reactor, M is the mutual inductance of the reactor, V H is the output voltage of the converter, V L is the input voltage of the converter, and D is the duty cycle.
2. The fuel cell system according to claim 1, characterized in that, the control unit prestores a data set representing the relationship between the input voltage and output voltage of the converter, the duty ratio of the switches, and the current values of the coils, when the control unit determines that Condition 1 is satisfied, refers to the data set and sets the amplitude of increasing and decreasing the duty ratios of the n-phase switches to be larger than other operating conditions.
3. The fuel cell system according to claim 1 or 2, characterized in that, the control unit confirms the presence or absence of a request for measuring the AC impedance of the fuel cell, when the control unit confirms that there is a request for measuring the AC impedance of the fuel cell, determines whether Condition 1 is satisfied, when the control unit determines that Condition 1 is satisfied, sets the amplitude of increasing and decreasing the duty ratios of the n-phase switches to be larger than other operating conditions, and measures the AC impedance of the fuel cell.
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