Method for estimating state of charge of all-vanadium redox flow battery based on adaptive observer

Abstract

The application discloses a kind of based on adaptive observer's all-vanadium redox battery state of charge estimation method, comprising: for all-vanadium redox battery system, establish the equivalent circuit model of all-vanadium redox battery based on 1 order RC network;The equivalent circuit model of all-vanadium redox battery based on 1 order RC network is rewritten as state space equation form, obtain the changed equivalent circuit model of all-vanadium redox battery;For the changed equivalent circuit model of all-vanadium redox battery, introduce high gain and auxiliary variable, establish the second adaptive observer, and then according to the second adaptive observer designed to realize the estimation of the voltage to be observed in system and model parameter;According to the voltage value estimated, realize the estimation of all-vanadium redox battery state of charge.The application provides a new idea for the online, accurate estimation of all-vanadium redox battery state of charge, and compared with traditional estimation method, can significantly improve estimation accuracy.

Description

TECHNICAL FIELD

[0001] The application relates to a method for estimating the state of charge of a full vanadium flow battery based on an adaptive observer and belongs to the technical field of full vanadium flow batteries. BACKGROUND

[0002] With the development of clean and low-carbon energy, large-scale energy storage systems have become an important part of new power systems to match the needs of power grids and avoid the impact on power grids when renewable energy is directly connected to power grids. Among the many large-scale energy storage systems, full vanadium flow batteries are widely concerned due to their high efficiency, fast response, strong deep discharge capability, long cycle life, high safety, economy and no cross-contamination of electrolytes. Therefore, research on full vanadium flow battery systems is of great significance to further improve the overall strength of the renewable energy power generation industry. Among the many performance indicators of the battery, the state of charge (SOC) is one of the most important performance indicators of the battery, which can reflect the amount of available power in the battery and provide guidance for subsequent control and optimization strategies. Therefore, designing a suitable estimation method to accurately estimate the SOC of the full vanadium flow battery online is of great significance in the practical application of the full vanadium flow battery.

[0003] The SOC of the full vanadium flow battery is related to the concentration of the four different valence states of vanadium ions inside the battery, but the internal vanadium ion concentration is difficult to measure in real time. The traditional method for measuring the SOC of the battery in engineering applications is to directly integrate the battery current to obtain the SOC estimation of the coulomb counting method, but this method does not take into account the loss of electric quantity caused by battery polarization, battery ohmic resistance and other factors during battery operation, and the error will gradually increase with time, so there is obvious error in practical application.

[0004] Therefore, the application is proposed. SUMMARY

[0005] The application provides a method for estimating the state of charge of a full vanadium flow battery based on an adaptive observer to realize online and accurate estimation of the SOC of the full vanadium flow battery.

[0006] The technical scheme of the application is as follows:

[0007] The application discloses a method for estimating the state of charge of a vanadium redox flow battery based on an adaptive observer, which comprises the following steps: Step 1, establishing an equivalent circuit model of the vanadium redox flow battery based on a first-order RC network for a vanadium redox flow battery system; rewriting the equivalent circuit model of the vanadium redox flow battery based on the first-order RC network into a state space equation form to obtain a changed equivalent circuit model of the vanadium redox flow battery; Step 2, introducing a high gain and an auxiliary variable for the changed equivalent circuit model of the vanadium redox flow battery to establish a second adaptive observer, and then realizing the estimation of the voltage to be observed in the system and the model parameters according to the designed second adaptive observer; and Step 3, realizing the estimation of the state of charge of the vanadium redox flow battery according to the estimated voltage value.

[0008] The establishment of the equivalent circuit model of the vanadium redox flow battery based on the first-order RC network comprises the following steps:

[0009] According to the operation principle of the vanadium redox flow battery, the equivalent circuit model of the vanadium redox flow battery based on the first-order RC network is established by utilizing the series-parallel connection property and Ohm's law, and the equation of the established equivalent circuit model is as follows:

[0010]

[0011] Wherein, C bat , C pol ∈R are capacitors affecting the open-circuit voltage OCV and polarization loss of the battery; R sd , R pol , R ohm ∈R are resistors affecting the self-discharge, polarization loss and ohmic loss of the battery; E OCV , E POL , E∈R represent the open-circuit voltage OCV, polarization voltage and terminal voltage of the battery; I b ∈R is the battery current; and R is a real number set.

[0012] The rewriting of the equivalent circuit model of the vanadium redox flow battery based on the first-order RC network into the state space equation form to obtain the changed equivalent circuit model of the vanadium redox flow battery is specifically as follows: the open-circuit voltage E OCV and the polarization voltage E POL of the battery are selected as state variables, the measurable terminal voltage of the battery is used to obtain the system output y, the battery current is used as the system input u, the equivalent circuit model of the vanadium redox flow battery based on the first-order RC network is rewritten into the state space equation form to obtain the changed equivalent circuit model of the vanadium redox flow battery:

[0013]

[0014] Wherein, x=[E OCV E POL ] T ∈R2×1 represents the state variable, i.e. the voltage value to be observed in the system, T is the transpose, R 2×1 represents the dimension of the matrix is 2x1; u=I b is the battery current; Φ(x, u) ∈ R 2×3 is a regression vector matrix related to the internal voltage state and the battery current, R 2×3 represents the dimension of the matrix is 2x3; θ ∈ R 3×1 is the model parameter to be estimated, R 3×1 represents the dimension of the matrix is 3x1; y is the battery voltage without ohmic loss as the system output, y ∈ R, R is the real set; C = [1 1] ∈ R 1×2 , R 1×2 represents the dimension of the matrix is 1x2.

[0015] The Step2 comprises:

[0016] Step2.1, for the changed equivalent circuit model of the all-vanadium redox flow battery, an output feedback item with high gain is added and a compensation item ρ to compensate the influence of parameter estimation error on the observation of the state variable to preliminarily construct an adaptive observer, and a first adaptive observer is obtained:

[0017]

[0018] wherein, are the estimated values of the state variable x and the model parameter θ respectively; a ≥ 1 ∈ R is the high gain parameter of the first adaptive observer, R is the real set; is a diagonal matrix, R 2×2 represents the dimension of the matrix is 2x2; K ∈ R 2×1 is the feedback gain, R 2×1 represents the dimension of the matrix is 2x1; y is the battery voltage without ohmic loss as the system output, y ∈ R, R is the real set; C = [1 1] ∈ R 1×2 , R 1×2 represents the dimension of the matrix is 1x2; ρ ∈ R 2×1 is a compensation to compensate the influence of parameter estimation error on the observation of the state variable; is a regression vector matrix related to the estimated value of the internal voltage state and the battery current; is the derivative of time t;

[0019] Step2.2, in order to calculate the compensation item ρ, the auxiliary variable is constructed to obtain:

[0020]

[0021] wherein, is an auxiliary variable, R 2×3 denotes the dimension of the matrix is 2x3;

[0022] Step2.3, using auxiliary variable designing compensation term p:

[0023]

[0024] wherein, is derivative of time t;

[0025] Step2.4, according to the first adaptive observer and compensation term, the second adaptive observer is obtained as:

[0026]

[0027] The second adaptive observer is based on the output feedback error design parameter adaptive law to update the model parameters, the expression is:

[0028]

[0029] wherein, Γ∈R 3×3 is a symmetric positive definite gain matrix.

[0030] The Step3, comprising:

[0031] Step3.1, according to the Nernst equation, the open circuit voltage E of the all-vanadium redox flow battery is obtained OCV The expression is as follows:

[0032]

[0033] wherein, N is the number of batteries; E θ is the standard voltage of the battery; R1 is the atmospheric constant; T is the temperature of the stack; F is the Faraday constant; based on the open circuit voltage expression of all-vanadium redox flow battery, the state of charge of the battery is calculated, and the calculation expression of the state of charge SOC is:

[0034]

[0035] In the formula, e is the natural constant;

[0036] Step3.2, using the second adaptive observer to obtain the observed value of the open circuit voltage OCV of the battery And substituting the calculation expression of the state of charge SOC, the estimated value of the state of charge SOC is obtained

[0037]

[0038] The beneficial effects of the present application are: the present application converts the estimation problem of vanadium ion concentration inside the all-vanadium redox flow battery into the estimation problem of battery OCV by establishing the equivalent circuit model based on the first-order resistance-capacitance (RC) network, uses the output feedback error to construct the adaptive law to realize the model parameter identification, and introduces it into the adaptive observer design, and finally obtains the relationship between the battery state of charge and the open circuit voltage (OCV) through the Nernst equation, so that the estimation of the battery state of charge can be realized by using the OCV observation value, and the estimation process of the battery state of charge is greatly simplified without complex and accurate electrochemical model modeling and without estimating the internal vanadium ion concentration; the online estimation of the state of charge of the all-vanadium redox flow battery can be realized only by the current and voltage signals which are easy to measure online, so that the present application is easy to realize in engineering application. The simulation experiment further shows that the estimation accuracy can be significantly improved compared with the traditional SOC estimation method. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 The adaptive observer diagram of the present application is shown in the figure;

[0040] Figure 2 The structure schematic diagram of the all-vanadium redox flow battery is shown in the figure;

[0041] Figure 3 The equivalent circuit model diagram of the all-vanadium redox flow battery is shown in the figure;

[0042] Figure 4 The input current and terminal voltage signal diagram in the simulation experiment is shown in the figure;

[0043] Figure 5 The equivalent circuit model parameter identification result diagram is shown in the figure;

[0044] Figure 6 The open circuit voltage and polarization voltage estimation performance comparison diagram is shown in the figure;

[0045] Figure 7 The state of charge SOC estimation performance comparison diagram is shown in the figure. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical scheme and advantages of the embodiments of the present application more clear, the technical scheme in the embodiments of the present application will be described clearly and completely below with reference to the drawings. All other embodiments obtained by those skilled in the art based on the embodiments in the present application without creative labor are within the scope of protection of the present application. It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other in any way without conflict.

[0047] Example 1: Figures 1-7 As shown, a method for estimating the state of charge of an all-vanadium liquid flow battery based on an adaptive observer includes: Step 1, establishing an all-vanadium liquid flow battery equivalent circuit model based on a first-order RC network for the all-vanadium liquid flow battery system to avoid a complex and accurate electrochemical modeling process; rewriting the all-vanadium liquid flow battery equivalent circuit model based on the first-order RC network into a state space equation form to obtain a changed all-vanadium liquid flow battery equivalent circuit model; Step 2, introducing high gain and auxiliary variables for the changed all-vanadium liquid flow battery equivalent circuit model to establish a second adaptive observer, and then accurately estimating the voltage to be observed and the model parameters in the system based on the designed second adaptive observer; Step 3, estimating the state of charge of the all-vanadium liquid flow battery based on the estimated voltage value.

[0048] According to the above steps of the present invention, a typical all-vanadium redox flow battery cell (such as Figure 2 As shown in FIG, the battery state of charge estimation based on the designed adaptive observer was performed, and a simulation verification was performed in Matlab to further illustrate the present invention.

[0049] Furthermore, the establishment of the equivalent circuit model of the all-vanadium redox flow battery based on the first-order RC network includes:

[0050] In order to avoid the complex and accurate electrochemical modeling process for all-vanadium redox flow batteries, according to the operating principle of all-vanadium redox flow batteries, using the series-parallel properties of circuits and Ohm's law, an equivalent circuit model of all-vanadium redox flow batteries based on a first-order RC network is established. The equation of the established equivalent circuit model is as follows:

[0051]

[0052] Among them, C bat , C pol ∈R are the capacitances that affect the battery open circuit voltage OCV and polarization loss, R is a real number set; R sd , R pol , R ohm ∈R are the resistances that affect battery self-discharge, polarization loss, and ohmic loss respectively; E OCV , E POL , E∈R represent the battery open circuit voltage OCV, polarization voltage and terminal voltage respectively; I b ∈R is the battery current. In this simulation, set C bat =500F, C pol =250F, R sd =2Ω, R ohm =0.02Ω, R pol =0.01Ω.

[0053] Further, the equivalent circuit model of the all-vanadium redox flow battery based on the first-order RC network is rewritten into a state space equation form to obtain a changed equivalent circuit model of the all-vanadium redox flow battery, including: selecting the open-circuit voltage E OCV and the polarization voltage E POL as state variables, obtaining the system output y by using the measurable terminal voltage of the battery, and taking the battery current as the system input u, rewriting the equivalent circuit model of the all-vanadium redox flow battery based on the first-order RC network into a state space equation form to obtain a changed equivalent circuit model of the all-vanadium redox flow battery:

[0054]

[0055] wherein x = [E OCV E POL ] T ∈R 2×1 represents the voltage value to be observed in the system, T is a transpose, R 2×1 represents the dimension of the matrix is 2x1; u = I b is the battery current; is a regression vector matrix related to the internal voltage state and the battery current, x1 and x2 represent the open-circuit voltage E OCV and the polarization voltage E POL respectively, R 2×3 represents the dimension of the matrix is 2x3; is a model parameter to be estimated, R 3×1 represents the dimension of the matrix is 3x1; y = E-R ohm I b is the battery voltage without ohmic loss, y ∈ R; C = [1 1] ∈ R 1×2 , R 1×2 represents the dimension of the matrix is 1x2. In the simulation experiment, the theoretical parameter to be estimated θ = [0.001 0.004 0.002] T .

[0056] Further, the Step2 includes:

[0057] Step2.1, for the changed equivalent circuit model (1.2) of the all-vanadium redox flow battery, adding an output feedback term with high gain and a compensation term ρ used to compensate the influence of the parameter estimation error on the observation of the state variable to preliminarily construct an adaptive observer, obtaining a first adaptive observer:

[0058]

[0059] wherein, are the estimates of state x and model parameters θ, respectively; a ≥ 1 ∈ R is the first adaptive observer high-gain parameter; is a diagonal matrix; K ∈ R 2×1 is the feedback gain; p ∈ R 2×1 is the compensation used to compensate the effect of parameter estimation error on state variable observation; is the internal voltage state estimation value and the battery current. In this simulation experiment, the feedback gain K = [1 2] T , and the high gain a = 20.

[0060] Step 2.2, in order to calculate the compensation term p, the auxiliary variable is constructed , and the following is obtained:

[0061]

[0062] wherein, is the auxiliary variable.

[0063] Step 2.3, the auxiliary variable is used to design the compensation term p:

[0064]

[0065] wherein, is the derivative of with respect to time t.

[0066] Step 2.4, according to the first adaptive observer (1.3) and the compensation term (1.5), the second adaptive observer is obtained as:

[0067]

[0068] Further, the second adaptive observer designs a parameter adaptive law based on the output feedback error to update the model parameters, and the expression is:

[0069]

[0070] wherein, Γ ∈ R 3×3 is a symmetric positive definite gain matrix; T is the transpose. In this simulation experiment, the adaptive law constant gain is set as Γ = diag([200 2.1 1]).

[0071] Further, in order to avoid the complexity of the estimation of vanadium ion concentration, the relationship between the battery open circuit voltage OCV and the state of charge SOC is obtained through the Nernst equation, and the battery SOC value is calculated by using the observation results of the designed second adaptive observer, which specifically includes:

[0072] Step3.1, according to Nernst equation, the open circuit voltage of the all-vanadium redox flow battery is as follows:

[0073]

[0074] Wherein, N is the number of batteries; E θ is the standard voltage of the battery; R1 is the atmospheric constant; T is the temperature of the battery; F is the Faraday constant. In the simulation experiment, the number of batteries is set to N = 1, the standard voltage of the battery is E θ = 1.35V, the atmospheric constant R1 is 8.314J / (mol·K), the Faraday constant is 96485C / mol, and the battery temperature is considered to be consistent with the room temperature, which is set to 28℃.

[0075] Based on the formula, the state of charge SOC of the battery can be calculated, and the expression is:

[0076]

[0077] In the formula, e is the natural constant;

[0078] Step3.2, the observed value of the open circuit voltage OCV of the battery is obtained by using the second adaptive observer And substitute into (1.9) to get the estimated value of the state of charge SOC

[0079]

[0080] Repeat Step2-Step3, only use measurable terminal voltage and battery current signal, introduce high gain and auxiliary variable design a kind of adaptive observer based on equivalent circuit model and adaptive law based on output feedback error, through Nernst equation, the observed value of OCV is used to realize the online and accurate estimation of the state of charge of the all-vanadium redox flow battery. At the same time, according to the above technical scheme, the adaptive observer based on equivalent circuit model of the application can avoid the complex electrochemical modeling process, the estimation process of vanadium ion concentration and the accumulation of integral current error, reduce the calculation amount, and improve the estimation accuracy.

[0081] Figure 2 The principle diagram of the all-vanadium redox flow battery system can be seen, which mainly consists of four parts: storage tank for storing positive and negative electrolyte, pump and pipeline for realizing the circulation of electrolyte, electrode and proton exchange membrane. The charging and discharging of the battery is realized by the oxidation-reduction reaction of different valence vanadium ions on the electrode, and the positive and negative electrolytes are separated by the proton exchange membrane. The battery is connected with the power supply or load through the current collecting plate.

[0082] In order to verify the effectiveness of the estimation of the proposed adaptive observer method, the present application carries out simulation on the adaptive observer based on output feedback shown in formula (1.6) and (1.7), and the SOC estimation formula shown in formula (1.10). The input battery current is a synthetic sweep signal, and the initial state of the voltage value to be observed is x(0) = [0 0] T .

[0083] Figures 4-7 It is a simulation verification diagram of the SOC estimation method based on the adaptive observer designed by the present application for the single cell system of the all-vanadium redox flow battery. Figure 4 It is a schematic diagram of the input battery current and the terminal voltage. Figure 5 It is a comparison diagram of the estimation parameter effect, and it can be seen that the estimation parameters can quickly converge to the true value. Among them, C bat can converge to the true value within 20s; C pol Although it does not directly converge to the true value, it also quickly converges to the true value within 10s, and finally converges to the true value; R sd The convergence is relatively slow, but from the experiment itself, it also indicates that it quickly converges to the true value. Figure 6 It is a comparison diagram of the estimation effect of the battery OCV and the polarization voltage, and from the diagram, it can be seen that the estimated value can quickly converge to the true value and remain within a very small error range. Figure 7 It is a comparison of the estimation results of the battery state of charge SOC, and it can be seen that the estimated value of SOC also converges to the true value within a very short time, and the error is very small. Therefore, it can be seen that the SOC estimation method based on the adaptive observer can ensure accurate estimation of the model parameters, the voltage state and the state of charge SOC.

[0084] The specific embodiments of the present application are described in detail above in combination with the drawings, but the present application is not limited to the above-mentioned embodiments, and various changes can be made within the knowledge possessed by those skilled in the art without departing from the purpose of the present application.

Claims

1. A method for state of charge estimation of a vanadium redox flow battery based on an adaptive observer, characterized in that, The application relates to a method for estimating the state of charge of a full vanadium redox flow battery, and belongs to the technical field of battery management. Step 1, an equivalent circuit model of a full vanadium redox flow battery based on a first-order RC network is established for a full vanadium redox flow battery system; the equivalent circuit model of the full vanadium redox flow battery based on the first-order RC network is rewritten into a state space equation form, and a changed equivalent circuit model of the full vanadium redox flow battery is obtained; Step 2, a second adaptive observer is established by introducing high gain and auxiliary variables for the changed equivalent circuit model of the full vanadium redox flow battery, and then the second adaptive observer is designed to realize the estimation of the observed voltage and model parameters in the system; Step 3, the state of charge of the full vanadium redox flow battery is estimated according to the estimated voltage value; The Step 2 comprises: Step 2.1, for the changed equivalent circuit model of all-vanadium redox flow battery, increase the output feedback term containing high gain and a compensation term p used to compensate the influence of parameter estimation error on state variable observation to preliminarily construct an adaptive observer, and a first adaptive observer is obtained: wherein, are the estimates of the state variable x and the model parameters θ, respectively; a > 1 e R is the first adaptive observer high-gain parameter, and R is the set of real numbers; is a diagonal matrix, R 2×2 denotes the dimension of the matrix as 2 x 2; K e R 2×1 is the feedback gain, R 2×1 denotes the dimension of the matrix as 2 x 1 ; y is the battery voltage without ohmic losses as the system output, y e R, and R is the set of real numbers; C = [1 1] e R 1×2 , R 1×2 denotes the dimension of the matrix as 1 x 2; p e R 2×1 is the compensation used to compensate the effect of the parameter estimation error on the state variable observation; is the internal voltage state estimate and the regression vector matrix related to the battery current; is the derivative with respect to time t; Step 2.

2. To compute the compensation term p, one has to solve the equation Constructing auxiliary variables one obtains: wherein R is an auxiliary variable 2×3 denotes that the dimensions of the matrix are 2 x 3; Step 2.3, using auxiliary variables Designing the compensation term p: wherein is derivative with respect to time t; Step 2.4, the second adaptive observer is obtained according to the first adaptive observer and a compensation term, and is as follows:

2. The adaptive observer based state of charge estimation method for a vanadium redox flow battery according to claim 1, wherein, The establishment of the equivalent circuit model of the full vanadium redox flow battery based on the first-order RC network comprises: According to the operation principle of the full vanadium redox flow battery, the equivalent circuit model of the full vanadium redox flow battery based on the first-order RC network is established by using the series-parallel connection property of a circuit and Ohm's law, and the equation of the established equivalent circuit model is as follows: where C bat , C pol ∈ R are capacitances affecting the open-circuit voltage OCV and polarization loss of the battery, respectively; sd , R pol , R ohm ∈ R are resistances affecting the self-discharge, polarization loss, and ohmic loss of the battery, respectively; OCV , E POL , E∈ R represent the open-circuit voltage OCV, polarization voltage, and terminal voltage of the battery, respectively; b ∈ R is the battery current; and R is the set of real numbers.

3. The adaptive observer based state of charge estimation method for all vanadium redox flow battery of claim 1, wherein, The first-order RC network-based equivalent circuit model of the all-vanadium redox flow battery is rewritten into a state space equation form to obtain a changed equivalent circuit model of the all-vanadium redox flow battery, specifically: selecting the open-circuit voltage E OCV and the polarization voltage E POL As state variables, the system output y is obtained by using the measurable terminal voltage of the battery, and the battery current is used as the system input u. The first-order RC network-based equivalent circuit model of the all-vanadium redox flow battery is rewritten into a state space equation form to obtain a changed equivalent circuit model of the all-vanadium redox flow battery: where x = [E OCV E POL ] T ∈R 2×1 represents the voltage value to be observed in the system, i.e., the state variable, T is the transpose, R 2×1 represents the dimension of the matrix as 2x1; u = I b is the battery current; Φ(x, u) ∈ R 2×3 is a regression vector matrix related to the internal voltage state and the battery current, R 2×3 represents the dimension of the matrix as 2x3; θ ∈ R 3×1 is a model parameter to be estimated, R 3×1 represents the dimension of the matrix as 3x1; y is the battery voltage without ohmic loss as the system output, y ∈ R, R is the real number set; C = [11] ∈ R 1×2 , R 1×2 represents the dimension of the matrix as 1x2.

4. The adaptive observer based state of charge estimation method for a vanadium redox flow battery of claim 1, wherein, The second adaptive observer is designed based on the output feedback error parameter adaptive law to update the model parameters, and the expression is as follows: where Γ∈R 3×3 is a symmetric positive definite gain matrix.

5. The adaptive observer based state of charge estimation method for a vanadium redox flow battery of claim 1, wherein, The Step 3 comprises: Step 3.1, According to Nernst equation, the open circuit voltage E of the vanadium redox flow battery is obtained OCV The expression is as follows: Where N is the number of batteries; E θ is the standard voltage of the battery; R1 is the atmospheric constant; T is the stack temperature; F is the Faraday constant; based on the open-circuit voltage expression of the all-vanadium redox flow battery, the calculation expression of the battery state of charge SOC is: In the formula, e is a natural constant; Step 3.2, obtaining the observed value of the open circuit voltage OCV of the battery by using the second adaptive observer and substituting the calculation expression of the state of charge SOC, obtaining the estimated value of the state of charge SOC

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