State estimation device, fault detection device, and state estimation / fault detection device

Abstract

To provide a state estimation device, a failure determination device, and a state estimation / failure determination device that can estimate the performance and / or determine failure of polymer electrolyte fuel cells that have deteriorated over time.SOLUTION: A state estimation device includes first means for updating a parameter Pm[i] and a parameter Qn[i] included in a voltage estimation model of a polymer electrolyte fuel cell, second means for sequentially acquiring the current I[i] and the voltage measurement value Vmes[i], third means for calculating an estimated voltage value Vest[i] using the voltage estimation model including the updated Pm[i] and Qn[i], and fourth means for correcting a correction coefficient CF[i] used for updating the Pm[i] and / or the Qn[i] such that |Vmes[i]-Vest[i]| becomes small. A failure determination device includes failure determination means for determining failure of a polymer electrolyte fuel cell using the Vest[i], Pm_est[i], and / or Qn_est[i]. A state estimation / failure determination device includes such a state estimation device and a failure determination device.SELECTED DRAWING: Figure 3

Description

Technical Field

[0001] The present invention relates to a state estimation device, a fault determination device, and a state estimation and fault determination device. More specifically, the present invention relates to a state estimation device, a fault determination device, and a state estimation and fault determination device capable of estimating the state of a solid polymer fuel cell deteriorated over time and / or determining the presence or absence of a fault in a solid polymer fuel cell deteriorated over time.

Background Art

[0002] A solid polymer fuel cell includes a membrane electrode assembly (MEA) in which catalyst layers containing a catalyst are joined to both surfaces of an electrolyte membrane. The catalyst layer is a portion that serves as a reaction field for electrode reactions and generally consists of a composite of carbon supporting catalyst particles such as platinum and a solid polymer electrolyte (catalyst layer ionomer). In a solid polymer fuel cell, a gas diffusion layer is usually disposed outside the catalyst layer. Outside the gas diffusion layer, a current collector (separator) having a gas flow path is further disposed. A solid polymer fuel cell usually has a structure (fuel cell stack) in which a plurality of single cells each composed of such an MEA, a gas diffusion layer, and a current collector are stacked.

[0003] When a solid polymer fuel cell is used as an in-vehicle power source, the voltage of the solid polymer fuel cell varies greatly depending on the driving conditions of the vehicle. When the solid polymer fuel cell is in a low load state, the power generation efficiency is high, but the cathode catalyst is exposed to a high potential state, so that the catalyst component is likely to elute from the cathode catalyst. On the other hand, when the solid polymer fuel cell is in a high load state, the power generation efficiency is low, but the cathode catalyst is exposed to a low potential state, so that the eluted catalyst component is likely to redeposit on the surface of the cathode catalyst. Therefore, there is a problem that the cathode catalyst gradually deteriorates when the cathode catalyst is repeatedly exposed to high and low potential states.

[0004] On the other hand, the performance of polymer electrolyte fuel cells is affected not only by steady-state voltage drops due to catalyst degradation, but also by temporary voltage fluctuations caused by changes in power generation conditions (i.e., voltage fluctuations caused by the formation and reduction of oxide films on the catalyst surface). Therefore, simply monitoring the voltage of a polymer electrolyte fuel cell, which changes moment by moment, makes it difficult to accurately estimate the true performance of the polymer electrolyte fuel cell at present.

[0005] Therefore, various proposals have been made to solve this problem. For example, Patent Document 1 contains: (a) Measure the fuel cell stack voltage of the fuel cell power generation system, (b) Change the effective electrode area of ​​the fuel cell cell in the simulation model so that the stack voltage of the simulation model follows the stack voltage of the fuel cell stack, (c) If the effective electrode area of ​​the fuel cell cell in the simulation model falls outside the normal range, it is considered an abnormality. A fuel cell power generation monitoring system has been disclosed. The document states: (A) This method allows for accurate monitoring of the deterioration status inside the fuel cell power generation system, and (B) Using such a simulation model, it is possible to obtain a future prediction of the effective electrode area of ​​the fuel cell cell if operation continues under current conditions. It is stated.

[0006] The method described in Patent Document 1 determines an abnormality when the effective electrode area of ​​a fuel cell cell falls outside the normal range, and does not take into account temporary fluctuations in cell voltage. Therefore, temporary fluctuations in cell voltage may be treated as changes in the effective electrode area of ​​the fuel cell cell, and the simulation model may be corrected accordingly. As a result, there is a risk of detecting an abnormality even when the system is functioning normally. Furthermore, the method described in Patent Document 1 uses only the effective electrode area of ​​the fuel cell cell for anomaly detection, which is considered to result in low anomaly detection accuracy. In addition, Patent Document 1 does not disclose a simulation model and therefore lacks specificity.

[0007] Furthermore, the performance of a fuel cell is affected not only by steady-state voltage drops due to catalyst degradation and temporary voltage fluctuations due to the formation and reduction of oxide films on the catalyst surface, but also by voltage drops due to malfunctions (irreversible voltage drops that occur accidentally due to causes other than catalyst degradation). However, there have been no previous examples of fuel cell fault detection devices that can accurately determine voltage drops due to malfunctions without being affected by steady-state voltage drops or temporary voltage fluctuations. [Prior art documents] [Patent Documents]

[0008] [Patent Document 1] Japanese Patent Publication No. 2007-305327 [Overview of the Initiative] [Problems that the invention aims to solve]

[0009] The problem that this invention aims to solve is to provide a state estimation device capable of estimating the net performance of a polymer electrolyte fuel cell that has deteriorated over time. Another problem that the present invention aims to solve is to provide a fault detection device capable of accurately determining whether or not a polymer electrolyte fuel cell is malfunctioning. Furthermore, another problem that the present invention aims to solve is to provide a state estimation and fault detection device capable of both state estimation and fault detection for a polymer electrolyte fuel cell. [Means for solving the problem]

[0010] To solve the above problems, the state estimation device according to the present invention is (A) A voltage estimation model is stored in memory, which is used to calculate an estimated value Vest[i] of the voltage of a polymer electrolyte fuel cell at time[i], and which includes at least one parameter Pm[i] and / or at least one internal state Qn[i] at time[i]. Using the estimated voltage Vest[i-1] of the polymer electrolyte fuel cell at time [i-1], the measured voltage Vmes[i-1], and the correction coefficient CF[i-1], at least one selected from the group consisting of the estimated parameter Pm_est[i](m≧1) at time [i] and the estimated internal state Qn_est[i](n≧1) at time [i] is calculated. A first means updates Pm[i] and Qn[i] based on the calculated Pm_est[i] and Qn_est[i], and stores the updated Pm[i] and Qn[i] in the memory, respectively. (B) A second means that, before or after executing the first means, sequentially acquires the current I[i] and the measured voltage Vmes[i] of the polymer electrolyte fuel cell at the time[i] and stores them in the memory, (C) A third means for calculating Vest[i] using the voltage estimation model which includes I[i], Vmes[i], and the updated Pm[i] and Qn[i], and storing the calculated Vest[i] in the memory, (D) In ​​place of CF[i-1], an arbitrary provisional correction coefficient CF in the range of -δ1 to +δ2 * [i-1] is used to correct the parameter Pm * [i] and / or corrected internal states Qn * [i] Calculate, Said Pm * [i] and the Qn * [i] Using the voltage estimation model including the above, the corrected voltage estimate Vest * [i] is calculated, The aforementioned Vest *[i] is the judgment formula: |Vmes[i] - Vest * [i]| ≤ |Vmes[i - 1] - Vest[i - 1]| is judged, and the CF * [i - 1] that satisfies the judgment formula is stored in the memory as the correction coefficient CF[i] at the time [i] as the fourth means, and is provided. However, the "parameter Pm[i]" is a constant included in the voltage estimation model, and is a variable constant that may change its value according to Vmes[i]. The "internal state Qn[i]" is a state quantity included in the voltage estimation model that may change every time [i], and refers to those other than I[i] and Vmes[i].

[0011] The failure determination device according to the present invention uses at least one selected from the group consisting of (a) the estimated value Vest[i] of the voltage of the solid polymer fuel cell at the time [i], (b) the estimated value Pm_est[i] (m ≥ 1) of the parameter at the time [i], and (c) the estimated value Qn_est[i] (n ≥ 1) of the internal state at the time [i] to perform failure determination of the solid polymer fuel cell, and is provided with failure determination means.

[0012] Furthermore, the state estimation / failure determination device according to the present invention includes the state estimation device according to the present invention, and the failure determination device according to the present invention and is provided with them.

Effect of the Invention

[0013] Using a voltage estimation model, it is possible to calculate Vest[i], an estimated value of the voltage of a polymer electrolyte fuel cell at time[i]. Furthermore, by using a voltage estimation model that takes into account steady-state voltage drops due to catalyst degradation and transient voltage fluctuations due to oxide film formation and reduction, a Vest[i] that takes into account the effects of steady-state voltage drops and transient voltage fluctuations can be obtained. However, even when Vest[i] is calculated using such a voltage estimation model, it may not be possible to perfectly reproduce Vmes[i]. This is thought to be due to machine-specific variations, modeling errors, and unknown factors that cannot be modeled. In contrast, when Vest[i] is calculated using a voltage estimation model, if at least one of the parameters Pm[i] and internal state Qn[i] included in the voltage estimation model is corrected so that Vest[i] approaches Vmes[i], and Vest[i] is calculated using the corrected Pm[i] and Qn[i], it is possible to suppress Vest[i] from deviating significantly from Vmes[i].

[0014] In a polymer electrolyte fuel cell, if only steady-state voltage drops due to catalyst degradation and / or temporary voltage fluctuations due to oxide film formation and reduction occur, the values ​​and changes in Pm[i] and Qn[i] can be known or estimated in advance. On the other hand, if a voltage drop occurs due to a fault, Vest[i] is not directly affected by the fault, so Vest[i] calculated by the voltage estimation model deviates significantly from Vmes[i]. Therefore, when a failure occurs, if Pm[i] and / or Qn[i] are corrected so that Vest[i] approaches Vmes[i], the values ​​and changes in Pm[i] and Qn[i] will change significantly before and after the failure. As a result, the presence or absence of a failure can be accurately estimated based on the changes in Vest[i], Pm[i] before correction (i.e., Pm_est[i]), and / or Qn[i] before correction (i.e., Qn_est[i]). [Brief explanation of the drawing]

[0015] [Figure 1]This is a schematic cross-sectional view of Pt particles with an oxide film formed on them. [Figure 2] This is a block diagram of the voltage estimation model. [Figure 3] This is a block diagram of a state estimation device that includes a voltage estimation model and means for correcting the parameter Pm[i] and the internal state Qn[i]. [Figure 4] This is a flowchart for performing state estimation and fault determination according to the first embodiment of the present invention. [Figure 5] This is a flowchart for performing state estimation and fault determination according to a second embodiment of the present invention. [Modes for carrying out the invention]

[0016] One embodiment of the present invention will be described in detail below. [1. State Estimation Device] The state estimation device according to the present invention comprises a first means, a second means, a third means, and a fourth means.

[0017] [1.1. First means] The first method is, The memory stores a voltage estimation model used to calculate the estimated voltage Vest[i] of the polymer electrolyte fuel cell at time[i], which includes at least one parameter Pm[i] and / or at least one internal state Qn[i] at time[i]. Using the estimated voltage Vest[i-1] of the polymer electrolyte fuel cell at time [i-1], the measured voltage Vmes[i-1], and the correction coefficient CF[i-1], at least one selected from the group consisting of the estimated parameter Pm_est[i](m≧1) at time [i] and the estimated internal state Qn_est[i](n≧1) at time [i] is calculated. This means updates Pm[i] and Qn[i], respectively, based on the calculated Pm_est[i] and Qn_est[i], and stores the updated Pm[i] and Qn[i] in the memory, respectively.

[0018] [1.1.1. Voltage Estimation Model] A "voltage estimation model" is a physical model capable of calculating an estimated value Vest[i] of the voltage of a polymer electrolyte fuel cell at time[i], wherein the model comprises at least one parameter Pm[i](m≧1) and / or at least one internal state. Qn[i](n≧1) This refers to things that include The voltage estimation model may be a simplified model that can calculate Vest[i] using only the measured current I[i] and voltage Vmes[i] of the polymer electrolyte fuel cell at time[i], or it may be a more rigorous model that can calculate Vest(i) using I[i] and Vmes[i], as well as the measured temperature Tmes[i] and ohm resistance Rion[i] of the polymer electrolyte fuel cell at time[i]. Specific examples of voltage estimation models will be described later.

[0019] If we know Vmes[i], and Tmes[i] and Rion[i] as needed, we can use these to obtain a voltage estimation model (i.e., an estimated current-voltage characteristic IVest[i]) that represents the relationship between the current I[i] at time[i] and Vest(i). By substituting I[i] into the obtained voltage estimation model, we can calculate Vest[i]. The Vest[i] calculated using the voltage estimation model is stored directly in memory. Vest[i] may be used for fault detection, as described later.

[0020] [1.1.2. Parameter Pm[i]] "Parameter Pm[i]" refers to a constant included in the voltage estimation model that may change its value depending on Vmes[i] (a variable constant). The voltage estimation model includes variables and constants. The constants are: (a) Invariant constants (e.g., Faraday constant, gas constant, etc.) (b) Variables (variable constants) that should ideally be constants, but whose values ​​may be changed to match experimental results (measured values) and These can be broadly classified into two categories. In this invention, Pm[i] refers to the latter, the "variable constant".

[0021] In other words, Pm[i] is a constant that, in the voltage estimation model, is treated as a constant on the surface, but whose value may be adjusted according to Vmes[i]. For example, state variables that should be treated as variables in a rigorous model may be treated as constants in a simplified model. In this invention, such constants may be treated as "variable constants" and their values ​​may be adjusted.

[0022] In this invention, the type of Pm[i] is not particularly limited, and the most suitable type can be selected depending on the purpose. The voltage estimation model is preferably one in which Pm[i] includes at least one variable constant that correlates with the steady-state voltage drop caused by the degradation of the noble metal catalyst particles contained in the polymer electrolyte fuel cell. When the voltage estimation model includes such a Pm[i], it is possible to calculate Vest[i] that takes into account the effect of the steady-state voltage drop caused by catalyst degradation.

[0023] Examples of Pm[i] that correlate with the steady-state voltage drop include A1 and C, which are included in equations (1) to (13) described later. O2 Rgas, Rion, α i Examples include (i=1~4). Details of these will be discussed later.

[0024] [1.1.3. Internal State Qn[i]] "Internal state Qn[i]" refers to a state variable included in the voltage estimation model that may change at each time [i], other than I[i] and Vmes[i]. As a polymer electrolyte fuel cell (MSF) continues to operate, the internal environment of the MSF changes moment by moment. If the state variables related to these internal environmental changes are treated as constants, the estimation accuracy of Vest[i] may decrease. In contrast, adjusting Qn[i] in accordance with the changes in the internal environment of the MSF improves the estimation accuracy of Vest[i].

[0025] In this invention, the type of Qn[i] is not particularly limited, and the most suitable one can be selected depending on the purpose. The voltage estimation model is preferably one in which Qn[i] includes at least one state variable that correlates with the transient voltage fluctuations caused by the formation and reduction of oxide films on the surface of noble metal catalyst particles contained in the polymer electrolyte fuel cell. When the voltage estimation model includes such a Qn[i], it is possible to calculate Vest[i] that takes into account the effects of transient voltage fluctuations caused by the formation and reduction of oxide films.

[0026] Examples of Qn[i] that correlate with temporary voltage fluctuations include the coverage θoxj[i] (j=1, 2, or 3) included in equations (18) to (20) described later, and the catalyst surface utilization rate θact[i] calculated using θoxj[i]. Details of these will be described later.

[0027] [1.1.4. Correction coefficient CF[i-1]] The "correction coefficient CF[i-1]" refers to the correction coefficient used when calculating the estimated parameter Pm_est[i] and the estimated internal state Qn_est[i] at time[i]. CF[i-1] is a set of various physical quantities obtained at time[i-1] (e.g., Vest[i-1], Vmes[i-1], etc.). (do) This is a value that has already been calculated and stored in memory. On the other hand, the correction coefficient CF[i] at time[i] is calculated in the fourth means described later, based on various physical quantities obtained at time[i]. The method for calculating CF[i] will be described later. Furthermore, the calculated CF[i] is stored in memory and used when calculating Pm_est[i+1] and Qn_est[i+1] at time[i+1].

[0028] CF[i-1] is used to correct for the deviation of Vest[i-1] from Vmes[i-1] caused by factors other than failure of the polymer electrolyte fuel cell, such as modeling errors, steady-state voltage drops, and temporary voltage fluctuations. Therefore, if the difference between Vest[i-1] and Vmes[i-1] is judged to be within an acceptable range, zero may be adopted as CF[i-1]. On the other hand, if the difference between Vest[i-1] and Vmes[i-1] is judged to exceed an acceptable range, a positive or negative value may be adopted as CF[i-1].

[0029] [1.1.5. Updates to Pm[i] and Qn[i]] The first means includes an update means for updating Pm[i] and / or Qn[i]. Here, "update means" refers to a means of determining the value of Pm[i] or Qn[i] using various data stored in memory at time[i-1], regardless of whether a failure or deterioration has occurred in the polymer electrolyte fuel cell (in other words, regardless of whether Vest[i] matches Vmes[i] or not), and based on predetermined update rules.

[0030] More specifically, "means of updating" means: Using the estimated voltage Vest[i-1] of the polymer electrolyte fuel cell at time [i-1], the measured voltage Vmes[i-1], and the correction coefficient CF[i-1], at least one selected from the group consisting of the estimated parameter Pm_est[i](m≧1) at time [i] and the estimated internal state Qn_est[i](n≧1) at time [i] is calculated. This refers to a means for updating Pm_est[i] and Qn_est[i], respectively, based on the calculated Pm_est[i] and Qn_est[i], and storing the updated Pm[i] and Qn[i] in the memory, respectively.

[0031] Pm_est[i] is a relational expression containing Vest[i-1], Vmes[i-1], and CF[i-1], and is calculated based on a predetermined expression (for example, equation (16) described later). Then, Pm[i] is updated based on Pm_est[i]. "Updating Pm[i] based on Pm_est[i]" means: (a) Use the calculated Pm_est[i] as is, or (b) Apply a predetermined determination formula (for example, formula (17) described later) to the calculated Pm_est[i] and select either Pm_est[i] or another value as Pm[i] based on that determination formula. It refers to. The Pm_est[i] calculated by the first method is stored directly in memory. Pm_est[i] may be used in the fault determination process described later.

[0032] Similarly, Qn_est[i] is a relational expression containing Vest[i-1], Vmes[i-1], and CF[i-1], and is calculated based on a predetermined expression (for example, equations (18) to (20) described later). Then, Qn[i] is updated based on Qn_est[i]. "Update Qn[i] based on Qn_est[i]" means: (a) Use the calculated Qn_est[i] as is, or (b) Apply a predetermined determination formula (for example, formula (21) described later) to the calculated Qn_est[i] and select either Qn_est[i] or another value as Qn[i] based on that determination formula. It refers to. The Qn_est[i] calculated by the first method is stored directly in memory. Qn_est[i] may be used in the fault determination described later.

[0033] [1.2. Second means] The second means is a means of sequentially acquiring the current I[i] and the measured voltage Vmes[i] of the polymer electrolyte fuel cell at time[i] before or after executing the first means, and storing them in the memory. The second means is for obtaining the state quantities necessary for calculating Vest[i] and does not directly affect the updating of Pm[i] and Qn[i]. Therefore, the second means may be performed before the first means is performed, or after the first means is performed.

[0034] The relationship P = I × V holds for the power P, current I, and voltage V of a polymer electrolyte fuel cell. When a required power Pref is requested from a polymer electrolyte fuel cell, I and V are usually selected to maximize efficiency. Let Iref[i] be the commanded value of the current selected when Pref[i] is requested at time[i]. The current value I[i] obtained in the second means may be either the commanded value of the current at time[i], Iref[i], or the measured value of the current at time[i], Imes[i]. The same result can be obtained using either.

[0035] The second means may further include means for acquiring, in addition to I[i] and Vmes[i], a measured value Tmes[i] of the temperature of the polymer electrolyte fuel cell at time[i] and a measured value Rion[i] of the ohm resistance of the polymer electrolyte fuel cell at time[i], and storing these in memory. As described above, in this invention, the estimated voltage Vest[i] of the polymer electrolyte fuel cell at time[i] is calculated using a voltage estimation model. Various voltage estimation models exist, ranging from simplified models to rigorous models. Tmes[i] and Rion[i] are used when calculating the estimated voltage Vest[i] of the polymer electrolyte fuel cell at time[i] using a voltage estimation model (rigorous model) that includes these values. Therefore, when calculating Vest[i] using a simplified model, it is not necessarily required to obtain Tmes[i] and Rion[i].

[0036] [1.3. Third means] The third method is, This means calculates Vest[i] using the voltage estimation model which includes I[i], Vmes[i], and the updated Pm[i] and Qn[i], and stores the calculated Vest[i] in the memory.

[0037] If the second means includes means for further acquiring the measured temperature of the polymer electrolyte fuel cell at time [i], Tmes[i], and the measured ohm resistance of the polymer electrolyte fuel cell at time [i], and storing these in memory, The third means preferably includes means for calculating Vest[i] using a voltage estimation model that includes I[i], Vmes[i], Tmes[i], Rion[i], and updated Pm[i] and Qn[i], and storing the calculated Vest[i] in memory.

[0038] [1.4. Fourth means] The fourth method is, Instead of the aforementioned CF[i-1], use any provisional correction coefficient CF in the range of -δ1 to +δ2 * [i-1] is used to correct the parameter Pm * [i] and / or corrected internal states Qn * Calculate [i] death, Said Pm * [i] and the Qn* [i] Using the voltage estimation model including the above, the corrected voltage estimate Vest * [i] is calculated, The aforementioned Vest * [i] is the condition: |Vmes[i]-Vest * Determine whether [i]|≦|Vmes[i-1]-Vest[i-1]| is satisfied, The CF that satisfies the above determination formula * This refers to a means of storing [i-1] in the memory as the correction coefficient CF[i] at the aforementioned time [i].

[0039] As mentioned above, there are various physical models for voltage estimation, ranging from simplified models to rigorous models. When a simplified model is used as the voltage estimation model, Vest[i] tends to deviate from Vmes[i] over time. On the other hand, when an exact model is used as the voltage estimation model, the discrepancy between Vest[i] and Vmes[i] is smaller compared to when a simplified model is used. However, even when an exact model is used, the discrepancy between Vest[i] and Vmes[i] may increase over time due to variations caused by individual differences (machine-specific variations), modeling errors, and unknown factors that cannot be modeled.

[0040] In this invention, to solve this problem, at least one of Pm[i] (m≧1) and / or Qn[i] included in the voltage estimation model is corrected so that the absolute value of the difference between Vmes[i] and Vest[i] decreases with each calculation step. Qn[i] Specifically, this correction is performed by correcting the correction coefficient CF[i].

[0041] As mentioned above, CF[i-1] is used to correct errors in Vest[i] caused by reasons other than failure. Therefore, if the absolute difference between Vmes[i] and Vest[i] calculated using CF[i-1], |ΔV[i]|=|Vmes[i]-Vest[i]|, is less than or equal to |ΔV[i-1]|, it indicates that the value of CF[i-1] is reasonable and there is little need to change CF[i-1]. However, even when no malfunction occurs, Vest[i] gradually deviates from Vmes[i] due to various factors. Therefore, in this invention, CF[i] is corrected so that |ΔV[i]| decreases with each calculation step, bringing Vest[i] closer to Vmes[i].

[0042] The correction of CF[i] is, specifically, (a) Replace CF[i-1] with any "provisional correction coefficient CF" in the range of -δ1 to +δ2 (where δ1 and δ2 are arbitrary values). * Except for using [i-1], the "corrected parameter Pm*[i]" and / or "corrected internal state Qn*[i]" are calculated in the same manner as the first method, (b) Pm * [i] and Qn * [i] Except for using a voltage estimation model that includes the following, the method is the same as the third method, and the "corrected voltage estimate Vest * [i]" is calculated, (c)Vest * [i] is the condition: |Vmes[i]-Vest * Determine whether [i]|≦|Vmes[i-1]-Vest[i-1]| is satisfied, (d) CF that satisfies the decision formula * [i-1] is stored in memory as the correction coefficient CF[i] at time [i]. This is done by [means].

[0043] In this case, CF applies to all values ​​within the range of -δ1 to +δ2. * Search for [i-1] and find a CF that satisfies the decision. *In [i-1], |ΔV * [i]|=|Vmes[i]-Vest * [i]| When CF is minimized * [i-1] may also be selected as CF[i]. Alternatively, CF can be performed in a predetermined order (e.g., ascending power order, descending power order, etc.) * Search for [i-1] and find a CF that satisfies the decision. * The search is terminated when [i-1] is found, and the CF at this time * You may also select [i-1] as CF[i].

[0044] [1.5. Voltage Estimation Model] Various models have been proposed for voltage estimation. In this invention, the type of voltage estimation model is not particularly limited, and various models can be used depending on the purpose. In order to calculate Vest[i] using the voltage estimation model described later, it is first necessary to know the catalytic potential Vcat[i] of the cathode catalyst and the catalyst surface utilization rate θact[i].

[0045] [1.5.1. Catalyst potential Vcat[i]] "Vmes[i]" refers to the measured value of the potential difference across the fuel cell stack at time [i] (i.e., the total voltage of the polymer electrolyte fuel cell). On the other hand, the "catalytic potential Vcat[i] of the cathode catalyst" is, strictly speaking, the value obtained by adding the potential drop due to internal resistance to the cathode potential of each single cell at time [i]. Strictly speaking, Vcat[i] is calculated based on Vmes[i], I[i], and Rion[i], but if Rion[i] cannot be obtained, it may be calculated by an approximate calculation using only Vmes[i]. Rion[i] can be identified by high-frequency impedance measurement.

[0046] Specifically, Vcat[i] is represented by the following equation (14) or equation (15). In the present invention, either can be used. The calculated Vcat[i] is stored in memory. The Vcat[i] expressed by equation (14) is an approximation of Vcat[i] that ignores the potential drop due to internal resistance. Equation (14) is less accurate in calculation than equation (15). However, using equation (14) allows Vcat[i] to be calculated without using I[i] and Rion[i], thus simplifying the calculation of Vcat[i].

[0047] Vcat[i] is strictly expressed by equation (15). In equation (15), the first term on the right-hand side represents the potential difference (cell voltage) across the single cell. In the first term on the right-hand side, Vmes[i] is expressed as N cell The potential per cell is calculated by dividing by . The second term on the right-hand side represents the potential drop per cell due to internal resistance. In the second term on the right-hand side, I[i] and Rion[i] are converted to values ​​per area or per cell, respectively. Using equation (15), Vcat[i] can be calculated accurately. In order to calculate Vest[i] accurately, it is preferable to use equation (15) to calculate Vcat[i].

[0048]

number

[0049] however, N cell The number of stacked cells in the aforementioned polymer electrolyte fuel cell, A cell This is the area of ​​the aforementioned cell.

[0050] [1.5.2. Catalyst surface utilization θact[i]] "Catalyst surface utilization rate θact[i]" refers to the ratio of the surface area used for the oxygen reduction reaction (ORR) (i.e., the surface not covered by an oxide film) to the surface area of ​​the noble metal catalyst particles contained in a polymer electrolyte fuel cell.

[0051] [A. Precious metal catalyst particles] In the present invention, "precious metal catalyst particles (hereinafter also simply referred to as "catalyst particles")" refers to particles made of a metal or alloy containing a precious metal element that are active in oxygen reduction reactions (ORR). In the present invention, the material of the catalyst particles is not particularly limited as long as it exhibits ORR activity. As for the material of the catalyst particles, (a) Precious metals (Au, Ag, Pt, Pd, Rh, Ir, Ru, Os), (b) Alloys containing two or more precious metal elements, (c) Alloys containing one or more noble metal elements and one or more base metal elements (e.g., Fe, Co, Ni, Cr, V, Ti, etc.) These are some examples.

[0052] [B. Types of Oxides] When catalyst particles on the cathode side are exposed to a high potential, catalyst components are more likely to leach out of the catalyst particles. On the other hand, when catalyst particles are exposed to a high potential, an oxide film (containing hydroxides) forms on the surface of the catalyst particles, suppressing the leaching of catalyst components from the catalyst particles. However, since the rate of oxide film formation is slow, if the cathode potential fluctuates rapidly, the formation of the oxide film is delayed, making it easier for catalyst components to leach out of the catalyst particles. In other words, if a fuel cell is used continuously in an environment where rapid potential fluctuations are repeated, the catalyst particles will eventually deteriorate. In other words, the durability of the noble metal catalyst particles on the cathode side depends on the total amount of noble metal oxides and noble metal hydroxides present on the surface of the noble metal catalyst particles. On the other hand, among the surfaces of noble metal catalyst particles, those covered with an oxide film have lower ORR activity compared to surfaces not covered with an oxide film. Therefore, the IV characteristics of a polymer electrolyte fuel cell depend on the θact[i] of the catalyst particles.

[0053] The noble metal oxides present on the surface of noble metal catalyst particles are (a) Noble metal hydroxide adsorbed on the surface of noble metal catalyst particles, (b) Noble metal oxide A adsorbed on the surface of noble metal catalyst particles, (c) Oxygen diffuses into the interior of the noble metal catalyst particles, forming noble metal oxide B just below the surface of the particles. They can be broadly categorized into these two groups.

[0054] Figure 1 shows a schematic cross-sectional view of Pt particles with an oxide film formed on them. When Pt particles are exposed to a high potential, oxides (including hydroxides) are formed on the surface of the Pt particles. In this case, the oxide on the surface of the Pt particles is (a) Pt hydroxide (PtOH) adsorbed on the surface of Pt particles ad ), (b) Pt oxide (PtO) adsorbed on the surface of Pt particles ad ), and, (c) Oxygen diffuses into the interior of the Pt particles, forming Pt oxide (PtO) just below the surface of the Pt particles. sub ) It consists of.

[0055] Here, PtOH ad Let θox1[i] be the coverage of the noble metal hydroxide adsorbed on the surface of the noble metal catalyst particles at time [i]. θox1[i] is expressed as the ratio (=S1 / S0) of the area (S1) of the noble metal hydroxide adsorbed on the surface of the noble metal catalyst particles to the surface area (S0) of the noble metal catalyst particles. Similarly, PtO ad Let θox2[i] be the coverage of the noble metal oxide A adsorbed on the surface of the noble metal catalyst particles at time [i]. θox2[i] is expressed as the ratio (=S2 / S0) of the area (S2) of the noble metal oxide A adsorbed on the surface of the noble metal catalyst particles to S0. Similarly, PtO sub Let θox3[i] be the coverage of the noble metal oxide B present inside the noble metal catalyst particles at time [i]. θox3[i] is expressed as the ratio (=S3 / S0) of the area (S3) of the noble metal oxide B present inside the noble metal catalyst particles to S0.

[0056] Furthermore, as shown in Figure 1, PtOH is present on the surface of the Pt particles. ad or PtOad PtO sub This can sometimes be formed. Therefore, the overall coverage of the Pt particles does not necessarily coincide with the sum of θox1[i]~θox3[i]. θox1[i] to θox3[i] can each be determined by sequentially calculating them using a reaction model based on the reaction rate equation. Furthermore, once θox1[i] to θox3[i] are known, θact(i) can be calculated using these values.

[0057] [C. Reaction Model] There are various methods for calculating θact[i]. In this invention, the method for calculating θact[i] is not particularly limited, and the most suitable method can be used depending on the purpose. The calculated θact[i] is stored in memory. In particular, θact[i] is preferably calculated using the following equation (3) or equation (4). In the present invention, either can be used to calculate θact[i].

[0058]

number

[0059] however, θox1[i] is the coverage of noble metal hydroxide adsorbed on the surface of the noble metal catalyst particles contained in the polymer electrolyte fuel cell at time [i], and is represented by formula (5). θox2[i] is the coverage of the noble metal oxide A adsorbed on the surface of the noble metal catalyst particles at time [i], and is represented by formula (6). θox3[i] is the coverage of the noble metal oxide B present inside the noble metal catalyst particles at time [i], and is represented by formula (7). Γ is the maximum surface coverage oxygen amount per unit surface area (constant). v1[i] to v3[i] are the reaction rates of the formation and disappearance of the noble metal hydroxide, the noble metal oxide A, and the noble metal oxide B at time [i], respectively, and are represented by formulas (8) to (10). G1[i] to G3[i] are the free energies of the reactions v1[i] to v3[i] at time [i], respectively, and are represented by equations (11) to (13). Ts is the calculation step width. α1~α4, α 11 ~α 17 , α 21 ~α 27 , α 31 ~α 37 These are the fitting coefficients, Vcat[i] is the catalytic potential of the cathode of the polymer electrolyte fuel cell at time[i].

[0060] Specifically, Ts represents the time from time [i-1] to time [i]. The value of Ts is not particularly limited, and it is preferable to set an optimal value according to the purpose. α1~α 37 It is preferable that each of these be determined to correspond to the actual IV characteristics and test results obtained by cyclic voltammetry (CV). In the present invention, α1 to α 37 It is sometimes treated as a "variable constant." As shown in equations (5) to (13), v1[i] to v3[i] and G1[i] to G3[i] are used to calculate θox1[i], θox2[i], and θox3[i]. In this invention, θox1[i], θox2[i], and θox3[i] may be treated as "state variables" that may change at each time [i].

[0061] θox1[i-1], θox2[i-1], and θox3[i-1] are the coverage rates at time [i-1], respectively, and are already stored in memory. θox1[i-1], θox2[i-1], and θox3[i-1] can be calculated sequentially if their initial values ​​are known. Alternatively, the initial values ​​may be the values ​​from the previous shutdown and used as the initial values. Generally, when a fuel cell is shut down, it is often kept at a low potential, in which case all oxides are reduced. Therefore, the initial values ​​after shutdown may be θox1=θox2=θox3=0. Therefore, once Vcat[i] is obtained, θact[i] can be calculated using equation (3) or equation (4).

[0062] Equation (4) calculates θact[i] by subtracting the product of each coverage rate and coefficient (α2~α4) from the total surface area (α1). θox1[i] represents the coverage rate of hydroxide due to a one-electron reaction. θox2[i] and θox3[i] represent the coverage rates of oxides due to two-electron reactions, respectively. Assuming that one platinum surface site is destroyed per one-electron reaction, α1=1, α2=1, α3=2, and α4=2. In actual use, since the platinum surface is not uniform, α1~α4 are determined to fit the test results.

[0063] However, equation (4) does not take into account that surface oxide species (coverage θox1[i], θox2[i]) and internal oxide species (coverage θox3[i]) occur at the same platinum site, and in such cases there is a concern that θact[i] may be underestimated. For example, when Vcat[i] remains high for a continuous period, θox1[i], θox2[i], and θox3[i] each become large, which exacerbates the above problem and raises concerns about a decrease in accuracy. In contrast, equation (3) has the advantage of being able to estimate accurately even in the above case by taking the ratio of surface oxidation species to internal oxidation species. On the other hand, in other cases, there is concern that equation (3) will be less accurate than equation (4).

[0064] [1.5.3. Specific Examples of Voltage Estimation Models] Various models have been proposed for voltage estimation. Among the voltage estimation models, the one expressed by the following equation (1) is particularly preferred.

[0065]

number

[0066] however, Vocv is the open-circuit voltage of the polymer electrolyte fuel cell. R is the gas constant. α is the motion constant in the Butler-Bolmer equation. F is the Faraday constant. Cref is the cell reference oxygen concentration. C O2 This is the average oxygen concentration within the cell. Rgas is the gas diffusion resistance. Rion is an ohm resistor, I0[i] is the exchange current density, which is expressed by equation (2). A1 is the fitting coefficient, ract[i] is the catalytic activity maintenance rate, θact[i] is the catalyst surface utilization rate.

[0067] In equation (1), the first term on the right-hand side represents the open-circuit electromotive force, the second term on the right-hand side represents the activation overpotential, the third term on the right-hand side represents the concentration overpotential, and the fourth term on the right-hand side represents the resistance overpotential. In equation (1), "intra-cell reference oxygen concentration Cref" refers to the reference value of the intra-cell oxygen concentration, which is the oxygen concentration of the oxygen partial pressure. In this embodiment, Cref is treated as an "invariant constant," but it may also be treated as a "variable constant." In equation (1), "Cell average oxygen concentration C" O2 " refers to the average value of the oxygen concentration inside the cell. In this embodiment, C O2 While it is generally treated as an "invariant constant," it is sometimes treated as a "variable constant."

[0068] In equation (1), "gas diffusion resistance Rgas" represents the transport resistance of oxygen [s / m], and the concentration gradient [mol·m] -3 ] is the flow velocity [J / mol·m -2 ·s -1 This refers to the coefficient when expressed as ]. Rgas is correlated with the electrochemical surface area (ECSA) of the catalyst particles. In this embodiment, Rgas is treated as a "variable constant," but it may also be treated as an "invariant constant." In equation (1), Rion represents the ohm resistance. Unlike in equation (15), Rion in equation (1) is treated as a constant. In this embodiment, Rion is treated as an "invariant constant," but it may also be treated as a "variable constant."

[0069] In equation (1), "exchange current density I0[i]" refers to the current when the electrode reaction is in a state of dynamic equilibrium. In this embodiment, I0[i] itself is not treated as a "variable constant" or "state variable," but A1 and θact[i] included in I0[i] may be treated as a "variable constant" and a "state variable," respectively. In equation (1), the "catalyst activity maintenance rate ract[i]" can be calculated from the ECSA maintenance rate. In this embodiment, ract[i] may be treated as a "variable constant".

[0070] [1.5.4. Block Diagram] Figure 2 shows a block diagram of the voltage estimation model. In Figure 2, the voltage estimation model 10 includes an oxide model 12, a catalyst surface utilization rate model 14, an exchange current density model 16, an ECSA degradation model 18, a catalyst activity maintenance rate model 20, and an FC voltage model 22. Equation (1) is a mathematical expression of this voltage estimation model 10.

[0071] In Figure 2, first, Vmes[i] is input to the oxide model 12. In the oxide model 12, θox1[i] to θox3[i] are calculated using Vmes(i). The calculated θox1[i] to θox3[i] are input into the catalyst surface utilization model 14. In the catalyst surface utilization model 14, θact[i] is calculated using θox1[i] to θox3[i]. The calculated θact[i] is input into the exchange current density model 16.

[0072] Furthermore, Vmes[i] and Tmes[i] are also input to the ECSA degradation model 18. The ECSA degradation model 18 calculates the ECSA maintenance rate. Specifically, the ECSA maintenance rate can be calculated based on Vmes[i], Tmes[i], and humidity. The calculated ECSA maintenance rate is input to the catalyst activity maintenance rate model 20. In the catalyst activity maintenance rate model 20, ract[i] is calculated. Specifically, ract[i] can be calculated as the product of the ECSA maintenance rate and the specific activity (SA) maintenance rate. The calculated ract[i] is input into the exchange current density model 16. Furthermore, in the exchange current density model 16, I0[i] is calculated based on θact[i] and ract[i].

[0073] The acquired Tmes[i] and calculated Io[i] are input to the FC voltage model 22. Equation (1) is stored in the FC voltage model 22, and Tmes[i] and I0[i] are input to equation (1). When Iref[i] or Imes[i] is substituted for I[i] in the resulting equation (1), Vest[i] is output from the FC voltage model 22.

[0074] [1.5.5. Specific Examples of Updating and Correcting Pm[i]] [A. Updating Pm[i]: First method] When calculating Vest[i] using the voltage estimation model represented by equation (1), consider the case where Pm[i] updated in the first means includes A1, α1, α2, α3, α4, and / or Rgas.

[0075] In this case, the first means is, (a) As the CF[i - 1], use the first correction coefficient km[i - 1] included in the following formula (16), and calculate the Pm_est[i] using the formula (16). (b) Based on the calculated Pm_est[i], update the Pm[i] according to the following formula (17), and store the updated Pm[i] in the memory. Preferably, it includes the means.

[0076]

Number

[0077] However, Pm_est[i] is an estimated value of the Pm[i] calculated based on the difference between the Vmes[i - 1] and the Vest[i - 1]. Pm_est[i - 1] is an estimated value of the parameter Pm[i - 1] at the time [i - 1]. km[i - 1] is the first correction coefficient. Pm_upper is the upper limit value allowed for the Pm[i]. Pm_lower is the lower limit value allowed for the Pm[i].

[0078] In formula (16), Pm_est[i - 1], km[i - 1], Vest[i - 1], and Vmes[i - 1] are already stored in the memory. Therefore, by substituting these values stored in the memory into formula (16), Pm_est[i] can be calculated immediately. The Pm_est[i] calculated based on formula (16) is stored in the memory.

[0079] Formula (17) is (a) When Pm_lower ≤ Pm_est[i] ≤ Pm_upper, select Pm_est[i] as Pm[i]. (b) When Pm_est[i] < Pm_lower, select Pm_lower as Pm[i]. (c) When Pupper < Pm_est[i], select Pm_upper as Pm[i]. To express something. Equation (17) is not strictly necessary, but using it allows us to correct Pm[i] within the range of acceptable upper and lower limits for Pm[i]. Furthermore, using equation (17) allows us to expect that Pm[i] will converge to its true value. The updated Pm[i] using equation (17) is used to calculate Vest[i].

[0080] [B. Correction of Pm[i]: Fourth method] After calculating Vest[i] using the updated Pm[i], in the fourth step, at least one of the Pm[i] (m≧1) included in the voltage estimation model is corrected so that the absolute value of the difference between Vmes[i] and Vest[i] decreases with each calculation step. As described above, the correction of Pm[i] is performed by correcting CF[i]. If Pm[i] includes A1, α1, α2, α3, α4, and / or Rgas, the fourth means is CF * [i-1] is a temporary First correction coefficient km * Using [i-1], km satisfy the criteria according to the procedure described above. * Search for [i-1] and find km that satisfy the criteria. * Preferably, the system includes means for storing [i-1] in the memory as the first correction coefficient km[i] at the time [i]. * The details of the search procedure for [i-1] are as described above, so we will omit further explanation.

[0081] A1 is a matching coefficient included in the exchange current density I0[i] and can be used to adjust for the influence of catalyst degradation on Vest[i]. When correcting A1, k * The sign of [i-1] is |ΔV * [i]| is selected in such a way that it becomes smaller.

[0082] α1 to α4 are fitting coefficients used to adjust for the effect of the platinum oxide coating ratio on the catalyst surface utilization rate, and affect the accuracy of estimating reversible voltage fluctuations. Reversible voltage fluctuations are known to occur significantly in the low current density range. Therefore, when correcting α1 to α4, k * It is preferable to select the absolute value of [i-1] such that it increases in the low current density region. Also, k * The sign of [i-1] is |ΔV * [i]| is selected in such a way that it becomes smaller.

[0083] Rgas is the gas diffusion resistance used in equation (1). This effect is particularly noticeable in the high current density region. Therefore, when correcting Rgas, k * It is preferable to select the absolute value of [i-1] such that it increases in the high current density region. Also, k * The sign of [i-1] is |ΔV * [i]| is selected in such a way that it becomes smaller.

[0084] The same applies when correcting Pm[i] other than A1, α1, α2, α3, α4, and Rgas; it is preferable to correct Pm[i] using the method described above.

[0085] [1.5.6. Specific Examples of Correction and Update of Qn[i]] [A. Updating Qn[i]: First method] When calculating Vest[i] using the voltage estimation model represented by equation (1), the Qn[i] updated in the first means is at least one of θoxj[i] (j=1, 2, or 3). Tsuga Let's consider the cases where it is included.

[0086] In this case, the first means is, (a) Using the second correction coefficient hj[i-1] (j=1, 2, or 3) included in the following equations (18) to (20) as CF[i-1], at least one of θoxj_est[i] (j=1, 2, or 3) is calculated using the above equations (18) to (20), (b) Based on the calculated θoxj_est[i], update θoxj[i] using the following equation (21), and store the updated θoxj[i] in the memory. It is preferable that the means be included.

[0087]

number

[0088] however, θox1_est[i], θox2_est[i], and θox3_est[i] are estimated values ​​of θox1[i], θox2[i], and θox3[i] respectively, calculated based on the difference between Vmes[i-1] and Vest[i-1]. θox1[i-1], θox2[i-1], and θox3[i-1] are the coverage rates of the noble metal hydroxide, noble metal oxide A, and noble metal oxide B at time [i-1], respectively. θox1_upper, θox2_upper, and θox3_upper are the upper limits allowed for θox1[i], θox2[i], and θox3[i], respectively. θox1_lower, θox2_lower, and θox3_lower are the lower limits allowed for θox1[i], θox2[i], and θox3[i], respectively. h1[i-1], h2[i-1], and h3[i-1] are the second correction coefficients, respectively. j = 1, 2, or 3.

[0089] In equations (18) to (20), θoxj[i-1], Ts, v j [i], Γ, hj[i-1], Vmes[i-1], and Vest[i-1] are already stored in memory. Therefore, by substituting these values ​​stored in memory into equations (18) to (20), θoxj_est[i] can be calculated immediately. θoxj_est[i] calculated based on equations (18) to (20) is stored in memory.

[0090] Equation (21) is, (a) When θoxj_lower≦θoxj_est[i]≦θox1_upper, select θoxj_est[i] as θoxj[i], (b) When θoxj_est[i] < θoxj_lower, select θoxj_lower as θoxj[i], (c) When θoxj_upper < θoxj_est[i], select θoxj_upper as θoxj[i]. To express something. Equation (21) is not strictly necessary, but using it allows us to correct θoxj[i] within the range of the upper and lower limits that are permissible for θoxj[i]. Furthermore, using equation (21) allows us to expect that θoxj[i] will converge to its true value. The updated θoxj[i] using equation (21) is used to calculate Vest[i].

[0091] [B. Correction of Qn[i]: Fourth method] After calculating Vest[i] using the updated Qn[i], in the fourth step, at least one of the Qn[i](m≧1) included in the voltage estimation model is corrected so that the absolute value of the difference between Vmes[i] and Vest[i] decreases with each calculation step. As described above, the correction of Qn[i] is performed by correcting CF[i]. If Qn[i] includes at least one of θoxj[i] (j=1, 2, or 3), the fourth means is the CF * [i-1] is a provisional second correction coefficient hj * Using [i-1], hj satisfies the determination formula according to the procedure described above. * [i-1] is searched for and the hj that satisfies the above determination formula * Preferably, the configuration includes means for storing [i-1] in the memory as the second correction coefficient hj[i] at the time [i]. hj * [i-1] The details of the search procedure are as described above, so we will omit further explanation.

[0092] θoxj[i] is correlated with transient voltage fluctuations caused by the internal state of the polymer electrolyte fuel cell. When correcting θoxj[i], hj * The sign of [i-1] is |ΔV * [i]| is selected in such a way that it becomes smaller. By correcting θox1[i]~θox3[i] using the method described above, the deviation of Vest[i] from Vmes[i] affected by the oxide film is automatically corrected. As a result, the estimation accuracy of Vest[i] is improved even when reversible voltage fluctuations caused by the oxide film occur.

[0093] [1.6. Specific Examples of State Estimation Devices] Figure 3 shows a block diagram of a state estimation device that includes a voltage estimation model and correction means for parameters Pm[i] and internal state Qn[i]. In Figure 3, the state estimation device 30 includes a voltage estimation model 10 and correction means 40. The voltage estimation model 10 includes an oxide model 12, a catalyst surface utilization rate model 14, an exchange current density model 16, an ECSA degradation model 18, a catalyst activity maintenance rate model 20, and an FC voltage model 22. Details of the voltage estimation model 10 are the same as those shown in Figure 2, so their explanation is omitted.

[0094] The correction means 40 includes a first correction means 42 connected to the FC voltage model 22, a second correction means 44 connected to the exchange current density model 16, a third correction means 46 connected to the catalyst surface utilization rate model 14, and a fourth correction means 48 connected to the oxide model 12. Although not shown in the figures, the correction means 40 may further include a fifth correction means connected to the ECSA degradation model 18 and / or a sixth correction means connected to the catalyst activity maintenance rate model 20.

[0095] The first correction means 42 is a means for correcting the parameter Pm[i] (e.g., Rgas included in equation (1)) and / or the internal state Qn[i] related to the FC voltage model 22. Similarly, the second correction means 44 is a means for correcting the parameter Pm[i] (e.g., the matching coefficient A1 included in equation (2)) and / or the internal state Qn[i] related to the exchange current density model 16.

[0096] Similarly, the third correction means 46 is a means for correcting the parameters Pm[i] (e.g., the fitting coefficients α1 to α4 included in equations (3) and (4)) and / or Qn[i] related to the catalyst surface utilization rate model 14. Similarly, the fourth correction means 48 is a means for correcting the internal state Qn[i] (e.g., θox1[i]~θox3[i] included in equations (3) and (4)) and / or the parameter Pm[i] related to the oxide model 12.

[0097] At time i, when the actual fuel cell 50 is operated such that the current equals Iref[i], Vmes[i] and Tmes[i] are output from the fuel cell 50. When Iref[i], Vmes[i] and Tmes[i] are input to the voltage estimation model 10, Vest[i] is output from the voltage estimation model 10.

[0098] Next, the difference between Vest[i] output from the voltage estimation model 10 and Vmes[i] output from the fuel cell 50 is input to the correction means 40. The first correction means 42 to the fourth correction means 48 each use the determination formula |ΔV * CF that satisfies |<|ΔV[i-1]| * [i-1] is searched, and CF that satisfies the decision is found. * [i-1] is stored in memory as CF[i]. CF[i] is used at the next time [i+1] to calculate Pm_est[i+1] and / or Qn_est[i+1].

[0099] Using the state estimation device 30 shown in Figure 3, it is possible to automatically prevent the estimated voltage Vest[i] calculated by the physical model from deviating from the measured voltage Vmes[i], which is affected by machine variation, catalyst degradation, and voltage fluctuations due to oxide films. In other words, the state estimation device 30 can automatically eliminate the above factors that cause Vest[i] to deviate from Vmes[i].

[0100] [2. Failure determination device] The fault determination device according to the present invention outputs from the state estimation device according to the present invention. (a) Estimated value of the voltage of the polymer electrolyte fuel cell at the aforementioned time [i], Vest[i], (b) Estimated parameter values ​​Pm_est[i](m≧1) at time[i], and (c) Estimated value of the internal state at time [i] Qn_est[i] (n≧1) The system includes a failure determination means for determining a failure in a polymer electrolyte fuel cell, using at least one selected from the group consisting of the following.

[0101] In a polymer electrolyte fuel cell, if only steady-state voltage drops due to catalyst degradation and / or temporary voltage fluctuations due to oxide film formation and reduction occur, the values ​​and changes in Pm[i] and Qn[i] can be known or estimated in advance. On the other hand, if a voltage drop occurs due to a fault, Vest[i] is not directly affected by the fault, so Vest[i] calculated by the voltage estimation model deviates significantly from Vmes[i]. Therefore, when a failure occurs, if Pm[i] and / or Qn[i] are corrected so that Vest[i] approaches Vmes[i], the values ​​and changes in Pm[i] and Qn[i] will change significantly before and after the failure. As a result, the presence or absence of a failure can be accurately estimated based on the changes in Vest[i], Pm[i] before correction (i.e., Pm_est[i]), and / or Qn[i] before correction (i.e., Qn_est[i]).

[0102] [2.1. Fault detection using Vest[i]] The fault detection method is, (A) A first determination means that determines a failure when the absolute value of the difference between the measured voltage Vmes[i] of the polymer electrolyte fuel cell at time[i] and Vest[i] |Vmes[i]-Vest[i]| is greater than or equal to a first threshold ε1 or greater than ε1, and / or (B) A second determination means that determines a failure when the sum of the absolute values ​​of the differences between Vmes[i] and Vest[i], Σ|Vmes[i]-Vest[i]|, is equal to or greater than a second threshold ε2 or greater than ε2. It's also acceptable if it includes [something].

[0103] [2.1.1. First determination means] As mentioned above, when a failure occurs, Vest[i] may deviate significantly from Vmes[i]. On the other hand, in this invention, Pm[i] and / or Qn[i] are corrected so that Vest[i] matches Vmes[i], but Vest[i] itself, calculated at time[i], is stored in memory as is without correction. Therefore, when |Vmes[i]-Vest[i]| is greater than or equal to the first threshold ε1, it can be determined that there is a high probability that a failure has occurred. In this case, the magnitude of ε1 is not particularly limited, and the optimal value can be selected according to the purpose. Furthermore, ε1 may belong to the "true" side or the "false" side of the proposition. These points are also true for other thresholds.

[0104] [2.1.2. Second determination means] When a failure occurs, Vmes[i] may decrease rapidly or gradually. In the latter case, if the calculation step width Ts is narrow, it may be difficult to determine the failure using |Vmes[i]-Vest[i]|. In such cases, it is preferable to determine the failure using the integrated value of |Vmes[i]-Vest[i]|. If a voltage drop due to a fault occurs continuously, Σ|Vmes[i] - Vest[i]| gradually increases. Therefore, when Σ|Vmes[i] - Vest[i]| is equal to or greater than the second threshold value ε2 or exceeds ε2, it can be determined that there is a high possibility of a fault occurrence.

[0105] [2.2. Fault determination using Pm_est[i]] The fault determination means (A) A third determination means for determining a fault when the Pm_est[i] exceeds the upper limit value Pm_upper allowed for the Pm[i] (Pm_upper < Pm_est[i]), or when the Pm_est[i] is equal to or greater than the Pm_upper (Pm_upper ≤ Pm_est[i]); (B) The integrated value Σ of the difference between the Pm_est[i] and the Pm_upper with respect to the time [i] i (Pm_est[i] - Pm_upper) is a fourth determination means for determining a fault when it is equal to or greater than the third threshold value ε3 or exceeds the ε3; (C) A fifth determination means for determining a fault when the Pm_est[i] is less than the lower limit value Pm_lower allowed for the Pm[i] (Pm_est[i] < Pm_lower), or when the Pm_est[i] is equal to or less than the Pm_lower (Pm_est[i] ≤ Pm_lower), and / or (D) The integrated value Σ of the difference between the Pm_est[i] and the Pm_lower with respect to the time [i] i (Pm_lower - Pm_est[i]) is a sixth determination means for determining a fault when it is equal to or greater than the fourth threshold value ε4 or exceeds the ε4 may include.

[0106] [2.2.1. Third determination means] Pm_est[i] is calculated using Equation (16) as described above. Therefore, when Vmes[i - 1] shows an abnormal value due to a fault, Pm_est[i] may exceed the upper limit value Pm_upper allowed for Pm[i]. Therefore, when Pm_upper < Pm_est[i] or Pm_upper ≤ Pm_est[i], it can be determined that there is a high possibility that a fault has occurred.

[0107] [2.2.2. Fourth determination means] Even when no fault has occurred, Pm_est[i] may temporarily exceed Pm_upper due to reasons other than a fault. In such a case, if the third means is used to determine a fault, there may be a misjudgment. On the contrary, when a fault occurs, the frequency of Pm_est[i] exceeding Pm_upper may increase. Therefore, when the integrated value Σ i (Pm_est[i] - Pm_upper) is equal to or greater than the third threshold value ε3 or exceeds ε3, it can be determined that there is a high possibility that a fault has occurred.

[0108] [2.2.3. Fifth determination means] Contrary to the third means, when Vmes[i - 1] shows an abnormal value due to a fault, Pm_est[i] may fall below the lower limit value Pm_lower allowed for Pm[i]. Therefore, when Pm_est[i] < Pm_lower or Pm_est[i] ≤ Pm_lower, it can be determined that there is a high possibility that a fault has occurred.

[0109] [2.2.4. Sixth determination means] Even when no fault has occurred, Pm_est[i] may temporarily fall below Pm_lower due to reasons other than a fault. In such a case, if the fifth means is used to determine a fault, there may be a misjudgment. On the contrary, when a fault occurs, the frequency of Pm_est[i] falling below Pm_lower may increase. Therefore, when the integrated value Σ iWhen (Pm_lower - Pm_est[i]) is equal to or greater than the fourth threshold value ε4, it can be determined that there is a high possibility of a failure.

[0110] [2.3. Fault determination using Qn_est[i]] When Qn_est[i] includes at least one of θoxj_est[i] (j = 1, 2, or 3), The fault determination means (A) The seventh determination means for determining a fault when the θoxj_est[i] (j = 1, 2, or 3) exceeds the upper limit value θoxj_upper allowed for the θoxj[i] (θoxj_upper < θoxj_est[i]), or when the θoxj_est[i] is equal to or greater than the θoxj_upper (θoxj_upper ≤ θoxj_est[i]); (B) The integrated value Σ of the difference between the θoxj_est[i] and the θoxj_upper with respect to the time [i] i The eighth determination means for determining a fault when Σ(θoxj_est[i] - θoxj_upper) is equal to or greater than the fifth threshold value ε5 or exceeds the ε5; (C) The ninth determination means for determining a fault when the θoxj_est[i] is less than the lower limit value θoxj_lower allowed for the θoxj[i] (θoxj_est[i] < θoxj_lower), or when the θoxj_est[i] is equal to or less than the θoxj_lower (θoxj_est[i] ≤ θoxj_lower), and / or (D) The integrated value Σ of the difference between the θoxj_est[i] and the θoxj_lower with respect to the time [i] i The tenth determination means for determining a fault when Σ(θoxj_lower - θoxj_est[i]) is equal to or greater than the sixth threshold value ε6 or exceeds the ε6 may include.

[0111] In this invention, θoxj[i] may be corrected to prevent Vest[i] from deviating from Vmes[i] due to causes other than failure. In this case, if Vest[i] deviates significantly from Vmes[i] due to failure, θoxj_est[i] may exceed the upper limit θoxj_upper allowed for θojx[i], or fall below the lower limit θoxj_lower allowed for θoxj[i]. Therefore, by monitoring the relative magnitudes of θoxj_est[i] and θoxj_upper or θoxj_lower, or the cumulative value of the difference at time[i], it is possible to determine whether or not a fault has occurred. Other aspects of the seventh to tenth determination means are the same as those of the third to sixth determination means, so the explanation is omitted.

[0112] [3. State Estimation and Fault Detection Device] The state estimation and fault determination device according to the present invention is A state estimation device according to the present invention, The fault detection device according to the present invention It is equipped with. Details of the state estimation device and fault detection device are as described above, so we will omit further explanation.

[0113] [4. Flowchart] [4.1. First Embodiment] Figure 4 shows a flowchart for performing state estimation and fault determination according to the first embodiment of the present invention. Figure 4 shows an example in which only the correction of Pm[i] is performed.

[0114] First, in step 1 (hereinafter simply referred to as "S1"), Pm[i] is updated (first means). Specifically, a voltage estimation model is first stored in memory, which is used to calculate the estimated voltage Vest[i] of the polymer electrolyte fuel cell at time[i] and includes at least one parameter Pm[i] at time[i], and / or at least one internal state Qn[i] at time[i].

[0115] Next, at least one estimated parameter value Pm_est[i] (m≧1) at time [i] is calculated using the estimated voltage Vest[i-1] of the polymer electrolyte fuel cell at time [i-1], the measured voltage Vmes[i-1], and the correction coefficient CF[i-1]. Furthermore, Pm[i] is updated based on the calculated Pm_est[i], and the updated Pm[i] is stored in memory. It is preferable to use equations (16) and (17) described above to update Pm[i].

[0116] Next, in S2, the measured values ​​of the current I[i] and voltage Vmes[i] of the polymer electrolyte fuel cell at time[i] are successively acquired and stored in memory (second means). S2 may also acquire the measured value of the temperature Tmes[i] of the polymer electrolyte fuel cell at time[i] and the measured value of the ohm resistance Rion[i] of the polymer electrolyte fuel cell at time[i] and store these in memory. Note that S2 may be performed before S1.

[0117] Next, in S3, Vest[i] is calculated using a voltage estimation model that includes I[i], Vmes[i], and the updated Pm[i], and the calculated Vest[i] is stored in memory (third means). Next, in S4, km[i] is corrected (fourth means). The details of the method for correcting km[i] are as described above, so the explanation will be omitted.

[0118] Next, the process proceeds to S5. In S5, it is determined whether |ΔV[i]| is greater than the first threshold ε1 (first determination means). If |ΔV[i]| is not greater than ε1 (S5: NO), it is highly likely that no fault has occurred. In this case, the process proceeds to S6, and 1 is added to time[i]. After that, the process returns to S1. Then, when the next calculation time arrives, each step from S1 to S6 described above is repeated. On the other hand, if |ΔV[i]|>ε1 (S5:YES), there is a high probability that a failure has not occurred. In this case, proceed to S7 and announce that a failure has occurred.

[0119] In the example shown in FIG. 4, the presence or absence of a fault is determined based on whether |ΔV[i]| > ε1. Instead of this, (a) Whether Σ|ΔV[i]| > ε2 (second determination means), (b) Whether Pm_upper < Pm_est[i] (third determination means), (c) Σ i (Whether (Pm_est[i] - Pm_upper) > ε3 (fourth determination means), (d) Whether Pm_est[i] < Pm_lower (fifth determination means), and / or, (e) Σ i (Whether (Pm_lower - Pm_est[i]) > ε4 (sixth determination means) may be used to determine the presence or absence of a fault.

[0120] [4.2. Second Embodiment] FIG. 5 shows a flowchart for performing state estimation and fault determination according to a second embodiment of the present invention. FIG. 5 shows an example in which Pm[i] and Qn[i] are corrected.

[0121] First, in S11, Pm[i] is updated (first means). It is preferable to use the above-described equations (16) and (17) for updating Pm[i]. Next, in S12, Qn[i] is updated (first means). It is preferable to use the above-described equations (18) to (21) for updating Qn[i].

[0122] Next, in S13, I[i] and Vmes[i] are sequentially acquired and stored in the memory (second means). S13 may further acquire Tmes[i] and Rion[i] and store them in the memory. Note that S13 may be performed before S11. Next, in S14, Vest[i] is calculated using a voltage estimation model including I[i], Vmes[i], and the updated Pm[i] and Qn[i], and the calculated Vest[i] is stored in the memory (third means).

[0123] Next, in S15, km[i] is corrected (fourth means). The details of the method for correcting km[i] are as described above, so the explanation will be omitted. Furthermore, in S16, hj[i] is corrected (fourth means). The details of the method for correcting hj[i] are as described above, so the explanation is omitted.

[0124] Next, the process proceeds to S17. In S17, it is determined whether |ΔV[i]| is greater than ε1 (first determination means). If |ΔV[i]| is not greater than ε1 (S17: NO), it is highly likely that no fault has occurred. In this case, the process proceeds to S18, and 1 is added to time[i]. After that, the process returns to S11. Then, when the next calculation time arrives, each step from S11 to S18 described above is repeated. On the other hand, if |ΔV[i]|>ε1 (S17:YES), a fault occurs. Is it possible? This is highly probable. In this case, proceed to S19 and report the occurrence of a malfunction.

[0125] Note that in the example shown in Figure 5, the presence or absence of a fault is determined by whether |ΔV[i]|>ε1 or not, but instead, (a) Whether Σ|ΔV[i]|>ε2 or not (second determination means), (b) Whether θoxj_upper < θoxj_est[i] or not (7th determination means), (c)Σ i (θoxj_est[i]-θoxj_upper)>ε5 or not (8th determination means), (d) Whether θoxj_est[i] < θoxj_lower or not (9th determination means), and / or (e)Σ i (θoxj_lower-θoxj_est[i])>ε6 or not (10th determination means) Then, you can determine whether or not there is a malfunction. Alternatively, steps S11 and S15 may be omitted, and only the updating and correction of θoxj[i] may be performed.

[0126] [5. Effect] [5.1. State Estimation] Numerous voltage estimation models exist for estimating the voltage of polymer electrolyte fuel cells. Using such voltage estimation models, it is possible to calculate the estimated voltage Vest[i] of the polymer electrolyte fuel cell at time i. Furthermore, by using a voltage estimation model that takes into account steady-state voltage drops due to catalyst degradation and transient voltage fluctuations due to oxide film formation and reduction, a Vest[i] that takes into account the effects of steady-state voltage drops and transient voltage fluctuations can be obtained.

[0127] Voltage estimation models include model parameters necessary for estimating voltage. To accurately estimate the voltage of a fuel cell, these model parameters must be defined to correspond to those of the actual device. Therefore, parameter fitting using the least squares method is generally performed to ensure that the model estimation results match the experimental results as closely as possible.

[0128] However, the values ​​of these parameters obtained from a specific experimental subject may differ from those of a different subject (machine variability). Furthermore, after parameter fitting, the discrepancy between the estimated voltage Vest[i] calculated from the voltage estimation model and the measured voltage Vmes[i] may increase over time, and it may become impossible to perfectly reproduce Vmes[i]. This is thought to be due to modeling errors or unknown factors that cannot be modeled. Therefore, in order to improve the estimation accuracy of Vest[i], it is necessary to recalculate the parameters for each subject or periodically. Otherwise, Vest[i] is expected to deviate from Vmes[i].

[0129] In contrast, when Vest[i] is calculated using a voltage estimation model, if at least one of the parameters Pm[i] and internal state Qn[i] included in the voltage estimation model is corrected so that Vest[i] approaches Vmes[i], and Vest[i] is calculated using the corrected Pm[i] and Qn[i], it is possible to suppress Vest[i] from deviating significantly from Vmes[i].

[0130] [5.2. Failure determination] When calculating Vmes[i] using a voltage estimation model, a failure may cause Vest[i] to deviate from Vmes[i]. On the other hand, deviations of Vest[i] from Vmes[i] can also occur due to factors other than failure, such as machine variation and catalyst particle degradation. Therefore, when calculating Vest[i] using a voltage estimation model, if Vest[i] deviates significantly from Vmes[i] due to causes other than failure, it becomes difficult to determine whether there is a failure or not. In this case, frequent parameter fitting can improve the accuracy of voltage estimation. However, even in such cases, simply comparing the instantaneous values ​​of Vest[i] and Vmes[i] may not accurately determine whether a fault or not exists.

[0131] In contrast, in a polymer electrolyte fuel cell, if only a steady voltage drop due to catalyst degradation and / or a temporary voltage fluctuation due to the formation and reduction of an oxide film occur, the values ​​and changes of Pm[i] and Qn[i] can be known or estimated in advance. On the other hand, if a voltage drop occurs due to a fault, Vest[i] is not directly affected by the fault, so Vest[i] calculated by the voltage estimation model deviates significantly from Vmes[i]. Therefore, when a failure occurs, if Pm[i] and / or Qn[i] are corrected so that Vest[i] approaches Vmes[i], the values ​​and changes in Pm[i] and Qn[i] will change significantly before and after the failure. As a result, the presence or absence of a failure can be accurately estimated based on the changes in Vest[i], Pm[i] before correction (i.e., Pm_est[i]), and / or Qn[i] before correction (i.e., Qn_est[i]).

[0132] Although embodiments of the present invention have been described in detail above, the present invention is not limited in any way to the above embodiments, and various modifications are possible without departing from the spirit of the present invention. [Industrial applicability]

[0133] The state estimation device, fault determination device, and state estimation / fault determination device according to the present invention can be used for estimating the internal state of a polymer electrolyte fuel cell mounted in a fuel cell vehicle, and / or for fault determination.

Claims

1. (A) The memory contains, used to calculate the estimated voltage Vest[i] of the polymer electrolyte fuel cell at time [i], at least one parameter Pm[i] at time [i], and / or at least one internal state Qn at time [i]. Store the voltage estimation model that includes [i], Using the estimated voltage Vest[i-1] of the polymer electrolyte fuel cell at time [i-1], the measured voltage Vmes[i-1], and the correction coefficient CF[i-1], at least one selected from the group consisting of the estimated parameter Pm_est[i] (m≧1) at time [i] and the estimated internal state Qn_est[i] (n≧1) at time [i] is calculated. A first means updates Pm[i] and Qn[i] based on the calculated Pm_est[i] and Qn_est[i], and stores the updated Pm[i] and Qn[i] in the memory, respectively. (B) Before or after performing the first means, the measured values ​​Vmes of the current I[i] and voltage of the polymer electrolyte fuel cell at time [i]. A second means for sequentially acquiring [i] and storing them in the memory, (C) Said I A third means for calculating Vest[i] using the voltage estimation model which includes [i], Vmes[i], and the updated Pm[i] and Qn[i], and storing the calculated Vest[i] in the memory, (D) Instead of the above CF[i-1], -δ 1 ~ + δ 2 Any hypothetical correction factor CF within the range * [i-1] is used to correct the parameter Pm * [i] and / or the corrected internal state Qn * [i] are calculated, Said Pm * Using the voltage estimation model including [i] and the above Qn * [i], the corrected voltage estimate Vest * [i] is calculated, The aforementioned Vest * [i] is the determination formula: | Vmes[i] - Vest * Determine whether [i]| ≤ |Vmes[i-1] - Vest[i-1]| is satisfied, The CF that satisfies the determination formula * Fourth means for storing [i - 1] in the memory as the correction coefficient CF[i] at the time [i], and A state estimation device equipped with the following features. However, the "parameter Pm[i]" refers to a constant included in the voltage estimation model, which is a variable constant whose value may change depending on the Vmes[i]. The "internal state Qn[i]" refers to a state quantity included in the voltage estimation model that may change at each time [i], other than I[i] and Vmes[i].

2. The I[i] is the command value Iref of the current at the time [i]. The state estimation device according to claim 1, wherein [i] is the measured value of the current at time i, Imes[i].

3. The state estimation device according to claim 1 or 2, wherein the voltage estimation model includes, as Qn[i], at least one state quantity that correlates with a temporary voltage fluctuation caused by the formation and reduction of an oxide film on the surface of the noble metal catalyst particles contained in the polymer electrolyte fuel cell.

4. The state estimation device according to any one of claims 1 to 3, wherein the voltage estimation model includes, as Pm[i], at least one variable constant that correlates with a steady-state voltage drop caused by the degradation of the noble metal catalyst particles contained in the polymer electrolyte fuel cell.

5. The second means includes means for further acquiring the measured temperature Tmes[i] of the polymer electrolyte fuel cell at time [i] and the measured ohm resistance Rion[i] of the polymer electrolyte fuel cell at time [i], and storing these in the memory. The third means includes means for calculating Vest[i] using the voltage estimation model which includes I[i], Vmes[i], Tmes[i], Rion[i], and the updated Pm[i] and Qn[i], and storing the calculated Vest[i] in the memory. A state estimation device according to any one of claims 1 to 4.

6. The state estimation device according to claim 5, wherein the voltage estimation model is represented by the following formula (1). [Math 1] however, Vocv is the open-circuit voltage of the polymer electrolyte fuel cell. R is the gas constant. α is the motion constant in the Butler-Bolmer equation. F is the Faraday constant. Cref is the cell reference oxygen concentration. C O2 This is the average oxygen concentration within the cell. Rgas is the gas diffusion resistance. Rion is an ohm resistor, I 0 [i] is the exchange current density, which is expressed by equation (2). A 1 is the coefficient of fit, ract[i] is the catalytic activity maintenance rate. θact[i] is the catalyst surface utilization rate, which is expressed by the following formula (3) or formula (4). [Math 2] however, θox1[i] is the coverage rate of noble metal hydroxide adsorbed on the surface of the noble metal catalyst particles contained in the polymer electrolyte fuel cell at time [i], and is represented by formula (5). θox2 [i] is the coverage of the noble metal oxide A adsorbed on the surface of the noble metal catalyst particles at time [i], and is represented by formula (6). θox3 [i] is the coverage of the noble metal oxide B present inside the noble metal catalyst particles at time [i], and is represented by formula (7). Γ is the maximum surface coverage oxygen per unit surface area (constant). v 1 [i]~v 3 [i] is the reaction rate of the formation and disappearance of the noble metal hydroxide, the noble metal oxide A, and the noble metal oxide B at time [i], represented by formulas (8) to (10), G 1 [i]~G 3 [i] is v at the aforementioned time [i], respectively. 1 [i]~v 3 The free energy of the reaction in [i], which is represented by equations (11) to (13), Ts is the calculation step width. α 1 ~α 4 , α 11 ~α 17 , α 21 ~α 27 , α 31 ~α 37 These are the fitting coefficients, Vcat[i] is the catalytic potential of the cathode of the polymer electrolyte fuel cell at time [i], and is represented by the following formula (14) or formula (15). [Math 3] however, N cell The number of stacked cells in the aforementioned polymer electrolyte fuel cell, A cell This is the area of ​​the aforementioned cell.

7. The voltage estimation model is defined as follows: Pm[i] = A 1 , the aforementioned α 1 , the aforementioned α 2 , the aforementioned α 3 , the aforementioned α 4 , and / or including the RGas, The first means is, As CF[i-1], the first correction coefficient km[i-1] included in the following equation (16) is used, and Pm_est[i] is calculated using equation (16). Based on the calculated Pm_est[i], Pm[i] is updated by the following formula (17), and the updated Pm The means includes storing [i] in the memory, The fourth means is the CF * [i-1] is a provisional first correction coefficient km * Using [i-1], the km that satisfies the above determination formula * The means includes storing [i-1] in the memory as the first correction coefficient km[i] at the time [i]. The state estimation device according to claim 6. [Math 4] however, Pm_est[i] is an estimated value of Pm[i] calculated based on the difference between Vmes[i-1] and Vest[i-1]. Pm_est[i-1] is the estimated value of the parameter Pm[i-1] at the aforementioned time [i-1]. km[i-1] is the first correction coefficient. Pm_upper is the upper limit value allowed for Pm[i]. Pm_lower is the lower limit value allowed for Pm[i].

8. The voltage estimation model includes at least one of θoxj[i] (j = 1, 2, or 3) as Qn[i], The first means is, As the CF[i-1], use the second correction coefficient hj[i-1] (j=1, 2, or 3) included in the following equations (18) to (20), and calculate at least one of θoxj_est[i] (j=1, 2, or 3) using the above equations (18) to (20). The system includes means for updating θoxj[i] based on the calculated θoxj_est[i] using the following formula (21), and storing the updated θoxj[i] in the memory, The fourth means is the CF * Let [i-1] be a provisional second correction coefficient hj * Using [i-1], the hj that satisfies the above determination formula. * The means includes storing [i-1] in the memory as the second correction coefficient hj[i] at the time [i]. The state estimation device according to claim 6 or 7. [Math 5] however, θox1_est[i], θox2_est[i], and θox3_est[i] are calculated based on the difference between Vmes[i-1] and Vest[i-1], respectively. [i], and θox3 [i] Estimated value, θox1[i-1], θox2[i-1], and θox3[i-1] are the coverage rates of the noble metal hydroxide, noble metal oxide A, and noble metal oxide B at time [i-1], respectively. θox1_upper, θox2_upper, and θox3_upper are, respectively, θox1[i] and θox2 [i], and the θox3 [i] The upper limit that is allowed, θox1_lower, θox2_lower, and θox3_lower are, respectively, θox1[i] and θox2 [i], and the θox3 [i] The lower limit that is allowed, h 1 [i-1], h 2 [i-1], and h 3 [i-1] are the second correction coefficients, j = 1, 2, or 3.

9. Output from the state estimation device according to any one of claims 1 to 8: (a) Estimated value of the voltage of the polymer electrolyte fuel cell at the above time [i], Vest[i] (b) Estimated parameter values ​​Pm_est[i] (m≧1) at time [i], and (c) Estimated value of the internal state at the above time [i] Qn_est[i] (n≧1) A failure determination device comprising a failure determination means for determining a failure in a polymer electrolyte fuel cell using at least one selected from the group consisting of the following.

10. The fault determination means is (A) The measured voltage Vmes of the polymer electrolyte fuel cell at the aforementioned time [i] The absolute value of the difference between [i] and Vest[i] |Vmes[i] - Vest[i]| is the first threshold ε 1 The above or the above ε 1 A first determination means that determines a malfunction when it exceeds a certain value, and / or (B) The sum of the absolute values ​​of the differences between Vmes[i] and Vest[i], Σ|Vmes[i]-Vest[i]|, is the second threshold ε 2 The above or the above ε 2 A second determination means that determines a malfunction when the value is excessive. A fault determination device according to claim 9, including the following:

11. The fault determination means is (A) A third determination means that determines a failure when Pm_est[i] exceeds the upper limit Pm_upper allowed for Pm[i] (Pm_upper < Pm_est[i]), or when Pm_est[i] is greater than or equal to Pm_upper (Pm_upper ≤ Pm_est[i]), (B) The cumulative value Σ of the time [i] of the difference between Pm_est[i] and Pm_upper i (Pm_est[i] - Pm_upper) is the third threshold ε 3 The above or the above ε 3 A fourth determination means that determines a malfunction when it exceeds a certain value. (C) A fifth determination means that determines a failure when Pm_est[i] is less than the lower limit Pm_lower that is permissible for Pm[i] (Pm_est[i] < Pm_lower), or when Pm_est[i] is less than or equal to Pm_lower (Pm_est[i] ≤ Pm_lower), and / or (D) The cumulative value Σ of the time [i] of the difference between Pm_est[i] and Pm_lower i (Pm_lower - Pm_est[i]) is the fourth threshold ε 4 The above or the above ε 4 A sixth determination means that determines a malfunction when the value is excessive. A fault determination device according to claim 9 or 10, including the following:

12. The Qn_est[i] includes at least one of the θoxj_est[i] (j=1, 2, or 3) output from the state estimation device described in claim 8, The fault determination means is (A) When the θoxj_est[i] (j = 1, 2, or 3) exceeds the upper limit θoxj_upper allowed for the θoxj[i] (θoxj_upper < θoxj_est A seventh determination means that determines a failure when [i]) or when θoxj_est[i] is greater than or equal to θoxj_upper (θoxj_upper≦θoxj_est[i]), (B) The integrated value Σ of the difference between θoxj_est[i] and θoxj_upper at time [i] i (θoxj_est[i] - θoxj_upper) is the fifth threshold ε 5 The above or the above ε 5 An eighth determination means that determines a malfunction when it exceeds a certain value. (C) A ninth determination means that determines a failure when θoxj_est[i] is less than the lower limit value θoxj_lower that is allowed for θoxj[i] (θoxj_est[i] < θoxj_lower), or when θoxj_est[i] is less than or equal to θoxj_lower (θoxj_est[i] ≤ θoxj_lower), and / or (D) The cumulative value Σ of the difference between θoxj_est[i] and θoxj_lower at time [i] i (θoxj_lower - θoxj_est[i]) is the sixth threshold ε 6 The above or the above ε 6 A tenth determination means that determines a malfunction when the value is greater than the limit. A fault determination device according to any one of claims 9 to 11, including the following:

13. A state estimation device according to any one of claims 1 to 8, A fault determination device according to any one of claims 9 to 12 and A state estimation and fault detection device equipped with the following features.

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