阅读说明：本技术 一种基于滚动时域算法的全钒液流电池峰值功率估计方法 (Rolling time domain algorithm-based all-vanadium redox flow battery peak power estimation method ) 是由 熊斌宇 董思迪 李旸 苏义鑫 张清勇 唐金锐 于 2021-01-19 设计创作，主要内容包括：本发明涉及一种基于滚动时域算法的全钒液流电池峰值功率估计方法,基于一阶等效电路模型估计电池未来一段时间内峰值功率,在已知模型参数和电池荷电状态的基础上,采用滚动时域方法对电池未来一段时间内的峰值功率进行估计,滚动时域方法的原理通过未来的时刻的预测控制量,补偿未来时刻的期望输出与未来时刻的预测输出之间的误差。在本发明中,假设峰值电流在估计周期内是变化的,根据目标函数,优化变量为电池电流,期望则为电池尽可能的充电或放电,优化峰值电流。(The invention relates to a peak power estimation method of an all-vanadium redox flow battery based on a rolling time domain algorithm, which is used for estimating the peak power of the battery in a period of time in the future based on a first-order equivalent circuit model, and on the basis of known model parameters and the state of charge of the battery, the peak power of the battery in the period of time in the future is estimated by adopting the rolling time domain method, and the error between the expected output of the future time and the predicted output of the future time is compensated by the principle of the rolling time domain method through the predicted control quantity of the future time. In the present invention, assuming that the peak current varies within the estimation period, the optimization variable is the battery current according to the objective function, and it is expected that the peak current is optimized for charging or discharging the battery as much as possible.)

1. A peak power estimation method of an all-vanadium redox flow battery based on a rolling time domain algorithm is characterized by comprising the following steps:

step 1: establishing a first-order equivalent circuit model according to the characteristics of the all-vanadium redox flow battery, wherein the model comprises a voltage source, an RC first-order parallel network and a series resistor, the RC first-order network describes the polarization characteristics of the all-vanadium redox flow battery, and R is₀，R₁Respectively showing ohmic internal resistance and polarization resistance, C₁Polarization capacitance:

U_t＝E_ocv-U₁-U₀ (1)

U₀＝IR₀ (3)

E_ocv(SOC)＝f(SOC)＝a₀+a₁SOC+a₂SOC²+a₃SOC³+a₄SOC⁴+a₅SOC⁵

(4)

in the formula (1), E_ocvIs the open circuit voltage of the equivalent circuit as a function of the state of charge, SOC; u shape₁For terminal voltage of RC parallel network, U₀Is ohmic internal resistance R₀The voltage across; in the formula (2), I is working current, and when electricity is used, I is positive; during charging, I is negative; formula (4) represents SOC and E_ocvWherein SOC is the state of charge, a_i(i ═ 0,1,2,3,4,5) is a coefficient to be determined, and is obtained by fitting experimental data, and f () is a function expression; in the formula (5), SOC₀Is the initial state of charge, η is the coulombic efficiency, C_NThe rated capacity of the battery;

step 2: the columns write the state space equation and the output equation, which are expressed as equation (10):

wherein x is each state quantity in the system; k is an estimation time; u is the input quantity of the system; a is a state matrix; b is an input matrix; c is an output matrix; d is a direct transfer matrix; the matrix is as follows:

and step 3: the battery state and the terminal voltage with the time domain length of n steps are listed, and the battery state with the time domain length of n steps is shown as the formula (13):

the terminal voltage of the battery with the time domain length of n steps is shown as the formula (14):

wherein the content of the first and second substances,predicting a matrix for the state variables;predicting a matrix for terminal voltage; x (k) is a state variable matrix at time k;is an input variable matrix; p is a prediction state matrix; q is a prediction input matrix; f is a prediction output matrix; g is a prediction direct transfer matrix;

and 4, step 4: according to the desired output, column-write the objective function, which is:

wherein H isdiag is a function for constructing a diagonal matrix, e₁＝[1 0 0](ii) a Const is a constant; t is a transposition function; w and U are simplification matrixes;to optimize the reference value.

And 5: power is defined as the product of current and voltage. The peak power expression at each predicted time in the estimation period is as follows:

wherein the content of the first and second substances,optimizing the working current for the quadprog function;optimizing the terminal voltage corresponding to the current;estimating the peak power of each time in the period;

step 6: peak power is defined as the maximum power that the battery can continue to emit or absorb over a future period of time. Thus, the expression for the future specified time period peak power calculation is as follows:

wherein min and max are minimum and maximum functions, respectively; SOP_disAnd SOP_chgRespectively, a discharge peak power and a charge peak power.

2. The method for estimating the peak power of the all-vanadium redox flow battery based on the rolling time domain algorithm according to claim 1, characterized in that: the state space equation is obtained by the following steps:

step 201: discretizing the formulas (2) and (5) in the step 1; the dispersion results are shown in formula (6) and formula (7);

where Δ t is the discretized time period.

Step 202: carrying out Taylor formula expansion on the formula (4), and approximately calculating open-circuit voltages at adjacent moments at the moment k, wherein the result is shown as a formula (8);

E_ocv(k+1)＝f(SOC(k+1))≈E_ocv(k)+f′(SOC(k))[SOC(k+1)-SOC(k)]

(8)

step 203: the formula (6) is brought into the formula (8), and the simplified result is shown as the formula (9):

step 204: equation (6), equation (7), and equation (9) are jointly written as the predicted state equation (10).

3. The method for estimating the peak power of the all-vanadium redox flow battery based on the rolling time domain algorithm according to claim 1, characterized in that: the obtaining step of the objective function in the step 4 is as follows: establishing an objective function as shown in formula (15);

wherein the content of the first and second substances,to estimate the state of charge of the battery during the cycle.Is a reference value, and when the battery is discharged, the value is 0; when charging, the value is 1; the optimization objective function is shown in equation (16):

wherein the content of the first and second substances,

the constraint conditions are satisfied as follows:

wherein, I_maxAnd I_minThe maximum value of the discharge current and the maximum value of the charge current are respectively; u shape_t,maxAnd U_t,minMaximum and minimum values of terminal voltage respectively; SOC_maxAnd SOC_minMaximum and minimum values of SOC, respectively; diag is a function for constructing a diagonal matrix; e.g. of the type₁＝[1 0 0](ii) a Equation (16) is converted to a quadratic programming problem: equation (16) is converted to a quadratic programming problem:

wherein, W and V are coefficient matrixes in the quadratic programming problem respectively, and are shown as a formula (18); u is an optimization vector, which is the working current in this patent; l is a constraint condition coefficient matrix; b is a constraint augmentation matrix.

Technical Field

The invention relates to the technical field of power system energy storage, in particular to a rolling time domain algorithm-based peak power estimation method for an all-vanadium redox flow battery.

Background

The large-scale energy storage technology can effectively improve the power supply characteristics of renewable energy power generation, can be used for stabilizing power generation output fluctuation, tracking and predicting errors, participating in frequency modulation and voltage regulation of a power system and the like, and improves the friendliness of new energy power generation grid connection. The all-vanadium redox flow battery has the advantages of high safety, mutually independent output power and capacity, strong overload capacity, strong deep discharge capacity, long cycle life and the like, and is successfully applied to a large-scale energy storage system. The real-time monitoring and estimation of the battery state of the battery management system have important significance for improving the overall safety, reliability and efficiency of the battery. Estimating the peak battery power is one of the key tasks of the battery management system. The peak power of the battery is defined as the maximum power that the battery can continuously emit or absorb in a certain period of time in the future under the constraint of the operation conditions (such as cut-off voltage, current, state of charge, temperature and the like).

The peak power can provide a basis for power scheduling of the energy storage system, and the battery can be guaranteed to operate in a safe range, so that accurate peak power estimation has important significance. At present, common methods for estimating the peak power of the all-vanadium redox flow battery comprise a feature mapping method and a model prediction method. The signature mapping method estimates the battery peak power using the established correlations between peak power, battery state of charge and parameters (temperature and estimation period). The main advantages of this method are simplicity and immediacy. However, the method has poor adaptability and low precision, and is not suitable for peak power estimation under the complex condition of actual dynamic of the battery. Compared to the feature mapping method, the battery model-based method can consider the peak power limit of current, voltage, state of charge, etc., and consider the dynamic characteristics of the battery. The method has good adaptability and robustness. In existing model-based estimation of battery peak power methods; the peak current in the estimation period is considered constant, while the actual peak current is varied. Peak power estimation errors are caused by inaccuracies in the peak current estimation.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a peak power estimation method of an all-vanadium redox flow battery based on a rolling time domain algorithm.

In order to achieve the purpose, the invention designs an all-vanadium redox flow battery peak power estimation method based on a rolling time domain algorithm, which is characterized by comprising the following steps:

the method comprises the following steps:

step 1: establishing a first-order equivalent circuit model according to the characteristics of the all-vanadium redox flow battery, wherein the model comprises a voltage source, an RC first-order parallel network and a series resistor, the RC first-order network describes the polarization characteristics of the all-vanadium redox flow battery, and R is₀，R₁Respectively showing ohmic internal resistance and polarization resistance, C₁Polarization capacitance:

U_t＝E_ocv-U₁-U₀ (1)

U₀＝IR₀ (3)

E_ocv(SOC)＝f(SOC)＝a₀+a₁SOC+a₂SOC²+a₃SOC³+a₄SOC⁴+a₅SOC⁵

(4)

in the formula (1), E_ocvIs the open circuit voltage of the equivalent circuit as a function of the state of charge, SOC; u shape₁Terminal voltage for an RC parallel network; u shape₀Is ohmic internal resistance R₀The voltage across; in the formula (2), I is working current, and is positive during discharging; charging of electricityWhen, I is negative; formula (4) represents SOC and E_ocvWherein SOC is the state of charge, a_i(i ═ 0,1,2,3,4,5) is a coefficient to be determined, and is obtained by fitting experimental data, and f () is a function expression; in the formula (5), SOC₀Is the initial state of charge, η is the coulombic efficiency, C_NThe rated capacity of the battery;

step 2: the columns write the state space equation and the output equation, which are expressed as equation (10):

wherein x is each state quantity in the system; k is the estimated time; u is the input quantity of the system; a is a state matrix; b is an input matrix; c is an output matrix; d is a direct transfer matrix; the matrix is as follows:

and step 3: the battery state and the terminal voltage with the time domain length of n steps are listed, and the battery state with the time domain length of n steps is shown as the formula (13):

the terminal voltage of the battery with the time domain length of n steps is shown as the formula (14):

wherein the content of the first and second substances,predicting a matrix for the state variables;predicting a matrix for terminal voltage; x (k) is a state variable matrix at time k;is an input variable matrix; p is a prediction state matrix; q is a prediction input matrix; f is a prediction output matrix; g is a prediction direct transfer matrix;

and 4, step 4: according to the desired output, column-write the objective function, which is:

wherein H isdiag is a function for constructing a diagonal matrix, e₁＝[1 0 0](ii) a Const is a constant; t is a transposition function; w and U are simplification matrixes;to optimize the reference value;

and 5: power is defined as the product of current and voltage. The peak power expression at each predicted time in the estimation period is as follows:

wherein the content of the first and second substances,optimizing the working current for the quadprog function;optimizing the terminal voltage corresponding to the current;estimating the peak power of each time in the period;

step 6: peak power is defined as the maximum power that the battery can continue to emit or absorb over a future period of time. Thus, the expression for the future specified time period peak power calculation is as follows:

wherein min and max are minimum and maximum functions, respectively; SOP_disAnd SOP_chgRespectively, a discharge peak power and a charge peak power.

Preferably, the state space equation is obtained by the following steps:

step 201: discretizing the formulas (2) and (5) in the step 1; the dispersion results are shown in formula (6) and formula (7);

where Δ t is the discretized time period.

Step 202: carrying out Taylor formula expansion on the formula (4), and approximately calculating open-circuit voltages at adjacent moments at the moment k, wherein the result is shown as a formula (8);

E_ocv(k+1)＝f(SOC(k+1))≈E_ocv(k)+f′(SOC(k))[SOC(k+1)-SOC(k)]

(8)

step 203: the formula (6) is brought into the formula (8), and the simplified result is shown as the formula (9):

step 204: equation (6), equation (7), and equation (9) are jointly written as the predicted state equation (10).

Preferably, the obtaining step of the objective function in step 4 is as follows: establishing an objective function as shown in formula (15);

wherein the content of the first and second substances,estimating the state of charge of the battery in the period;is a reference value, and when the battery is discharged, the value is 0; when charging, the value is 1; the optimization objective function is shown in equation (16):

wherein the content of the first and second substances,

the constraint conditions which are optimized and met are as follows:

wherein, I_maxAnd I_minThe maximum value of the discharge current and the maximum value of the charge current are respectively; u shape_t,maxAnd U_t,minMaximum and minimum values of terminal voltage respectively; SOC_maxAnd SOC_minMaximum and minimum values of SOC, respectively; diag is a construction of a diagonal matrixA function; e.g. of the type₁＝[1 0 0](ii) a Equation (16) is converted to a quadratic programming problem:

wherein, W and V are coefficient matrixes in the quadratic programming problem respectively, and are shown as a formula (18); u is an optimization vector, which is a working current in the present invention; l is a constraint condition coefficient matrix; b is a constraint augmentation matrix.

The method estimates the peak power of the battery in a period of time in the future based on a first-order equivalent circuit model, estimates the peak power of the battery in the period of time in the future by adopting a rolling time domain method on the basis of known model parameters and the state of charge of the battery, and compensates the error between the expected output of the future time and the predicted output of the future time according to the principle of the rolling time domain method through the predicted control quantity of the future time. The traditional method assumes that the peak current remains unchanged in the estimation period, which not only causes inaccuracy of peak power estimation, but also limits the estimation period; in the present invention, the peak current is optimized by assuming that the peak current varies within the estimation period and optimizing the variable to be the battery current according to the objective function, expecting to charge or discharge the battery as much as possible.

Drawings

Fig. 1 is an equivalent circuit diagram of an all-vanadium redox flow battery.

FIG. 2 is a flowchart of an estimation method of peak power of an all-vanadium redox flow battery based on a rolling time domain algorithm.

Detailed Description

The invention is described in further detail below with reference to the figures and specific embodiments.

The invention provides a technology of an estimation method of peak power of an all-vanadium redox flow battery based on a rolling time domain algorithm, which comprises the steps of establishing an equivalent circuit model of the all-vanadium redox flow battery; and estimating the peak power of the battery in a future period of time by adopting a model control prediction method based on the known SOC and equivalent model parameters.

An equivalent circuit diagram of the all-vanadium flow battery is shown in FIG. 1, and the parameters of the all-vanadium flow battery are shown in Table 1, wherein the all-vanadium flow battery with 5kW/3.3kWh is taken as an example for description.

TABLE 1 parameters of all vanadium flow batteries

Parameter name/Unit	Numerical value
		Power/kW	5
Capacity/kWh	3.3
		Ampere hour capacity/Ah	62
Maximum current/A of discharge	100
		Maximum current/A of charge	100
Discharge voltage limiting/V	40
		Charging voltage limiting/V	60
Lower limit of SOC	0
		Upper limit of SOC	1

As shown in fig. 2, the operation optimization method of the all-vanadium redox flow battery provided by the invention is carried out according to the following steps,

step 1: establishing a first-order equivalent circuit model according to the characteristics of the all-vanadium redox flow battery, and expressing the mathematical model by using an equation shown in the formula (1) to the equation (5):

U_t＝E_ocv-U₁-U₀ (1)

U₀＝IR₀ (3)

E_ocv(SOC)＝f(SOC)＝a₀+a₁SOC+a₂SOC²+a₃SOC³+a₄SOC⁴+a₅SOC⁵

(4)

in the formula (1), E_ocvIs the Open Circuit Voltage (OCV) of the equivalent circuit, which is a function of the state of charge (SOC). U shape₁For terminal voltage of RC parallel network, U₀The voltage across the ohmic internal resistance. In the formula (2), I is the working current. In this patent, I is positive during discharging and negative during charging. In the formula (4), SOC and E_ocvIn a functional relationship of (a), wherein₀＝41.91，a₁＝137，a₂＝-1193，a₃＝5858，a₄＝-16540，a₅27610. In formula (5), η is coulombic efficiency and has a value of 1; c_NThe value is 62Ah for the rated capacity of the battery.

Step 2: column write stateThe method comprises the following steps of: in this example, SOC is 0.4 and the corresponding parameter value is R₀＝0.0485Ω，R₁0.0127 Ω and C₁＝1274.6F，n＝60；

Step 201: discretizing the formulas (2) and (5) as follows; the dispersion results are shown in formula (6) and formula (7);

where Δ t is the discretization interval and has a value of 1 s.

Step 202: carrying out Taylor formula expansion on the formula (4), namely, approximately calculating the open-circuit voltage at the adjacent moment at the k moment; the result is shown in formula (8);

E_ocv(k+1)＝f(SOC(k+1))≈E_ocv(k)+f′(SOC(k))[SOC(k+1)-SOC(k)]

(8)

step 203: the formula (6) is brought into the formula (8), and the simplified result is shown as the formula (9):

step 204: equation (6), equation (7) and equation (9) are written as the predicted state equation, as shown in equation (10):

wherein x is each state quantity in the system; k is the estimated time; u is the input quantity of the system; a is a state matrix; b is an input matrix; c is an output matrix; d is a direct transfer matrix; the output equation is as follows:

and step 3: the method comprises the following specific steps of:

step 301: according to equation (10), the battery state with time domain length of n steps is shown as equation (13):

step 302: according to equation (10), the battery terminal voltage with time domain length of n steps is shown as equation (14):

wherein the content of the first and second substances,predicting a matrix for the state variables;predicting a matrix for terminal voltage; x (k) is a state variable matrix at time k;is an input variable matrix; p is a prediction state matrix; q is a prediction input matrix; f is a prediction output matrix; g is a prediction direct transfer matrix;

and 4, step 4: the column writes the objective function according to the desired output. In the present invention, the desired output is that in a safe operating range, the battery is charged or discharged as much as possible in an estimated period, and the objective function is as shown in equation (15);

wherein the content of the first and second substances,estimating the SOC of the battery in the period;to optimize the reference value, the battery has a value of 0 when discharged and a value of 1 when charged. The optimization objective function is as follows:

wherein the content of the first and second substances,

the constraint conditions are satisfied as follows:

wherein, I_maxAnd I_minThe maximum value of the discharge current and the maximum value of the charge current are respectively; u shape_t,maxAnd U_t,minMaximum and minimum values of terminal voltage respectively; SOC_maxAnd SOC_minMaximum and minimum values of SOC, respectively; diag is a function for constructing a diagonal matrix; e.g. of the type₁＝[1 0 0](ii) a Equation (16) is converted to a quadratic programming problem:

wherein, W and V are coefficient matrixes in the quadratic programming problem respectively, and are shown as a formula (18); u is an optimization vector, which is a working current in the present invention; l is a constraint condition coefficient matrix; b is a constraint augmentation matrix. Equation (13) is the estimated in-cycle system state value, which includes the predicted state of charge. Therefore, substituting the predicted SOC into equation (16) results in the following simplification:

wherein H isdiag is a function for constructing a diagonal matrix, e₁＝[1 0 0](ii) a Const is a constant; t is a transposition function; w and U are simplification matrixes;to optimize the reference value.

And 5: power is defined as the product of current and voltage. Is optimizedAccording to the formula (14), the corresponding terminal voltage can be calculatedThe peak power expression at each predicted time in the estimation period is as follows:

wherein the content of the first and second substances,optimizing the working current for the quadprog function;optimizing the terminal voltage corresponding to the current;estimating the peak power of each time in the period;

step 6: the SOP is defined as the maximum power that the battery can continue to emit or absorb over a future period of time. Therefore, the peak power calculation expression is as follows:

wherein min and max are minimum and maximum functions, respectively; SOP_disAnd SOP_chgRespectively, a discharge peak power and a charge peak power.

It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.