Alkaline electrolytic cell model for frequency analysis of power system

Abstract

The invention discloses an alkaline electrolytic cell model for power system frequency analysis, and belongs to the field of power system modeling. The model is firstly based on an electrochemical semi-empirical formula of the electrolytic cell, and a first-order equivalent circuit model containing ohm voltage, inverse voltage and activation voltage is established; secondly, according to an equivalent circuit model, deriving an analytic relation between activation voltage and current of the electrolysis cell, and converting the analytic relation into a transfer function of a Laplacian domain; and finally, a PI control link is adopted to replace an inverter control link, the initial power, the power change value and the operation electrolysis power are used as input, the cell voltage is used as output, and a complete electrolytic cell frequency analysis model is constructed. According to the method, by simplifying the electrochemical process and performing frequency domain linearization processing, the application limitation of a traditional nonlinear model in frequency response analysis is overcome while the key dynamic characteristics of the electrolytic cell are reserved, and a practical and reliable tool is provided for frequency analysis and operation management of a power system.

Description

Technical Field

[0001] The invention belongs to the field of power system modeling, and in particular relates to an alkaline electrolyzer model for power system frequency analysis. Background Art

[0002] As the world's reliance on renewable energy continues to increase, power systems are facing new challenges, especially in maintaining frequency stability. Traditional power systems mainly rely on synchronous generators to provide inertia and frequency response capabilities. However, with the widespread application of renewable energy sources such as solar and wind power, these inverter-based energy sources lack the inherent inertia of synchronous machines, making the system more susceptible to frequency disturbances, and the system's frequency stability faces severe tests.

[0003] Alkaline electrolyzer (AWE) is seen as a potential solution for enhancing the frequency stability of power systems due to its fast dynamic response capability. By converting excess renewable energy into hydrogen energy, the electrolyzer can not only improve energy efficiency, but also provide flexible load regulation when there is an imbalance between electricity demand and supply. This dual function makes the alkaline electrolyzer unique in the application value of new power systems.

[0004] However, alkaline electrolyzers have the characteristics of strong model nonlinearity and complex parameter coupling. The electrochemical reaction process inside involves multiple mutually influencing physical and chemical parameters, including temperature, pressure, etc. The interaction between these parameters makes it difficult to accurately apply its traditional nonlinear model in the power system frequency response analysis. In addition, the dynamic characteristics of the electrolyzer are closely related to its operating conditions, which further increases the complexity of modeling.

[0005] To this end, the present invention proposes a simplified and practical alkaline electrolytic cell model based on the existing electrochemical semi-empirical formula. The model not only retains the key dynamic characteristics of the electrolytic cell, but also has the characteristics of frequency domain linearization, and is suitable for frequency response analysis of power systems. Summary of the invention

[0006] In view of the shortcomings of the prior art, the purpose of the present invention is to provide an electrolytic cell model for power system frequency analysis, which can effectively describe the dynamic response characteristics of the electrolytic cell under different operating conditions while also having the characteristics of frequency domain linearization, thereby providing a reliable model basis for the electrolytic cell to participate in power system frequency regulation.

[0007] The purpose of the present invention can be achieved through the following technical solutions: an alkaline electrolytic cell model for power system frequency analysis, which is first based on the electrochemical semi-empirical formula of the electrolytic cell, by establishing a first-order equivalent circuit model including ohmic voltage, reverse voltage and activation voltage; secondly, according to the equivalent circuit model, the analytical relationship between the activation voltage and current of the electrolytic chamber is derived, and it is converted into a transfer function in the Laplace domain; finally, the PI control link is used to replace the inverter control link, and the initial power, power change value and operating electrolysis power are used as inputs, and the chamber voltage is used as output to construct a complete electrolytic cell frequency analysis model. The model has the following core features:

[0008] For a single electrolytic cell, its UI relationship is expressed by a first-order equivalent circuit; the voltage in the first-order equivalent circuit is represented by the ohmic voltage U Ω , reverse voltage U rev And the activation voltage U act The three parts are connected in series; the relationship between ohmic voltage and current is represented by a constant resistance R Ω The reverse voltage is represented by a voltage source, and the activation voltage is represented by an equivalent resistor R act,eq With equivalent capacitance C act,eq After being connected in parallel, it is connected to the equivalent voltage source U act,eq0 Series connection;

[0009] According to the equivalent circuit model, the activation voltage U of a single electrolysis chamber can be derived: act With the chamber current I cell The analytical relationship between them can be converted into the Laplace domain to obtain the transfer function between the activation voltage and current;

[0010] The inverter control link is replaced by the PI control link. The input of the control loop is the initial power, the power change value and the operating electrolysis power. The output is the cell voltage U cell ;

[0011] Furthermore, according to the semi-empirical electrochemical formula commonly used in alkaline electrolytic cells, the relationship between the ohmic voltage and current of the alkaline electrolytic cell can be expressed as:

[0012]

[0013] In the formula, r 1 and r 2 is the empirical fitting coefficient, T is the electrolytic cell temperature, and A is the plate area.

[0014] Since the frequency response lasts only tens of seconds, which is much shorter than the time for the electrolytic cell temperature to change, the present invention assumes that the temperature remains unchanged during the response process. Therefore, in the equivalent circuit, the ohmic resistance can be calculated as follows:

[0015]

[0016] Further, the reverse voltage of the alkaline electrolyzer can be expressed as follows:

[0017]

[0018] Where U rev0 To fix the reverse voltage, R 0 is the gas constant, T is the temperature, F is the Faraday constant, p is the alkaline electrolytic cell pressure, p 0 is standard atmospheric pressure.

[0019] Since the gas pressure and temperature will not fluctuate significantly during the operation of the electrolytic cell, they are assumed to be constant. Therefore, in the equivalent circuit, the reverse voltage can be calculated using the above formula.

[0020] Furthermore, the equivalent resistance in the activation voltage equivalent circuit can be expressed as follows:

[0021] According to the semi-empirical electrochemical formula commonly used in alkaline electrolyzers, the activation voltage can be modeled as follows:

[0022]

[0023] Where s, t 1 , t 2 and t 3 All are empirical fitting parameters.

[0024] Since the electrolytic cell can only work at the working current [I min ,I max ] range, the equivalent activation resistance R act,eq It can be calculated as:

[0025]

[0026] Furthermore, the equivalent voltage source in the activation voltage equivalent circuit can be expressed as follows:

[0027] U act,eq0 =-I min R act,eq +U act (I min )

[0028] Furthermore, the equivalent capacitance in the activation voltage equivalent circuit can be expressed as follows:

[0029] The time constant of the electrochemical reaction in the electrolytic cell can be predicted by the following formula:

[0030] C=0.0467A anode +0.00225A cathode

[0031]

[0032] In the subscripts, anode and cathode represent the anode and cathode, respectively.

[0033] Therefore, following the principle of time constant conservation, the equivalent capacitance can be expressed as follows:

[0034] C act,eq =τ / R act,eq

[0035] Furthermore, the UI relationship of the equivalent circuit can be expressed as follows:

[0036] U cell =I cell R Ω +U act,eq +U rev

[0037]

[0038] Furthermore, the electrolytic cell frequency response model can be obtained:

[0039] P awe =NU cell I cell

[0040]

[0041] I cell =(U cell -U rev -U act,eq0 )G U

[0042]

[0043] Where N represents the number of electrolytic cells in the electrolytic cell, K p is the proportional coefficient of PI control, K i is the integral coefficient of PI control, ΔP ref is the power required by the electrolyzer to change under frequency response, P initial is the initial power of the electrolysis system, P awe is the actual power of the electrolysis system.

[0044] Beneficial effects of the present invention:

[0045] The method of the present invention simplifies the electrochemical process and realizes frequency domain linearization, which not only retains the important dynamic characteristics of the electrolytic cell, but also overcomes the application limitations of traditional nonlinear models in frequency response analysis, reduces the coupling problems of complex parameters, makes the characteristics of the electrolytic cell easier to analyze and apply, and provides reliable tools and methods for actual power system frequency analysis and operation management, which significantly improves the application value of alkaline electrolytic cells in new power systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0047] Figure 1 is an equivalent circuit diagram of the electrochemical model of the alkaline electrolytic cell in the present invention;

[0048] Figure 2 It is a frequency analysis model diagram of the alkaline electrolytic cell in the present invention. DETAILED DESCRIPTION

[0049] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0050] The present invention relates to an electrolytic cell model for power system frequency analysis. The model is first based on the electrochemical semi-empirical formula of the electrolytic cell, by establishing a first-order equivalent circuit model including ohmic voltage, reverse voltage and activation voltage; secondly, according to the equivalent circuit model, the analytical relationship between the activation voltage and current of the electrolytic chamber is derived, and it is converted into a transfer function in the Laplace domain; finally, the PI control link is used to replace the inverter control link, and the initial power, power change value and operating electrolysis power are used as inputs, and the chamber voltage is used as output to construct a complete electrolytic cell frequency analysis model. The model has the following core features:

[0051] For a single electrolytic cell, its UI relationship is expressed by a first-order equivalent circuit; the voltage in the first-order equivalent circuit is represented by the ohmic voltage U Ω , reverse voltage U rev And the activation voltage U act The three parts are connected in series; the relationship between ohmic voltage and current is represented by a constant resistance R ΩThe reverse voltage is represented by a voltage source, and the activation voltage is represented by an equivalent resistor R act,eq With equivalent capacitance C act,eq After being connected in parallel, it is connected to the equivalent voltage source U act,eq0 Series connection;

[0052] According to the equivalent circuit model, the activation voltage U of a single electrolysis chamber can be derived: act With the chamber current I cell The analytical relationship between them can be converted into the Laplace domain to obtain the transfer function between the activation voltage and current;

[0053] The inverter control link is replaced by the PI control link. The input of the control loop is the initial power, the power change value and the operating electrolysis power. The output is the cell voltage U cell ;

[0054] This embodiment models an electrolytic cell, and its parameters are shown in the following table.

[0055] Temperature T(℃) 90 Number of electrolytic chambers N 535 <![CDATA[The plate area A (m 2 )]]> 0.75 s 0.12 <![CDATA[t 1 ]]> 1.002 <![CDATA[t 2 ]]> 8.424 <![CDATA[t 3 ]]> 8.424 <![CDATA[r 1 ]]> <![CDATA[8.05*10 -5 ]]> <![CDATA[r 2 ]]> <![CDATA[-0.25*10 -7 ]]> <![CDATA[R 0 ]]> 8.314 F 96485 p 1.6e06 <![CDATA[K p ]]> 300 <![CDATA[K i ]]> 1 <![CDATA[p 0 ]]> 101.325e03 Current operating range (A) [2024,10530]

[0056] According to the semi-empirical electrochemical formula commonly used in alkaline electrolytic cells, the relationship between the ohmic voltage and current of alkaline electrolytic cells can be expressed as follows:

[0057]

[0058] Since the frequency response lasts only tens of seconds, which is much shorter than the time for the electrolytic cell temperature to change, the present invention assumes that the temperature remains unchanged during the response process. Therefore, in the equivalent circuit, the ohmic resistance can be calculated as follows:

[0059]

[0060] Further, the reverse voltage of the alkaline electrolyzer can be expressed as follows:

[0061]

[0062] The equivalent resistance in the activation voltage equivalent circuit can be expressed as follows:

[0063] According to the semi-empirical electrochemical formula commonly used in alkaline electrolyzers, the activation voltage can be modeled as follows:

[0064]

[0065] Since the electrolytic cell can only work at the working current [I min ,I max ] range, the equivalent activation resistance R act,eq It can be calculated as:

[0066]

[0067] Furthermore, the equivalent voltage source in the activation voltage equivalent circuit can be expressed as follows:

[0068] U act,eq0 =-I min R act,eq +U act (I min )=-2530*9.4480e-06+0.4294=0.4065

[0069] Furthermore, the equivalent capacitance in the activation voltage equivalent circuit can be expressed as follows:

[0070] The time constant of the electrochemical reaction in the electrolytic cell can be predicted by the following formula:

[0071] C=0.0467A anode +0.00225A cathode =0.0367

[0072]

[0073] In the subscripts, anode and cathode represent the anode and cathode, respectively.

[0074] Therefore, following the principle of time constant conservation, the equivalent capacitance can be expressed as follows:

[0075] C act,eq =τ / R act,eq =0.4381

[0076] Furthermore, the UI relationship of the equivalent circuit can be expressed as follows:

[0077] U cell =I cell R Ω +U act,eq +U rev

[0078]

[0079] Furthermore, we can obtain Figure 2 The electrolyser frequency response model is shown:

[0080] P awe =NU cell I cell

[0081] =535U cell I cell

[0082]

[0083] Icell =(U cell -U rev -U act,eq0 )G U

[0084] =(U cell -1.2367-0.4065)G U

[0085]

[0086] Where N represents the number of electrolytic cells in the electrolytic cell, K p is the proportional coefficient of PI control, K i is the integral coefficient of PI control, ΔP ref is the power required by the electrolyzer to change under frequency response, P initial is the initial power of the electrolysis system, P awe is the actual power of the electrolysis system.

[0087] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0088] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. An alkaline electrolyzer model for power system frequency analysis, characterized in that: The model is first based on the semi-empirical formula of electrochemical electrolysis of the electrolytic cell, by establishing a first-order equivalent circuit model including ohmic voltage, reverse voltage and activation voltage; secondly, according to the equivalent circuit model, the analytical relationship between the activation voltage and current of the electrolytic chamber is derived, and it is converted into a transfer function in the Laplace domain; finally, the PI control link is used to replace the inverter control link, with the initial power, power change value and operating electrolysis power as input and the chamber voltage as output to construct a complete electrolytic cell frequency analysis model.

2. The alkaline electrolyzer model for power system frequency analysis according to claim 1, characterized in that: The first-order equivalent circuit of the alkaline electrolytic cell is composed of an ohmic voltage, a reverse voltage and an activation voltage in series, wherein the UI relationship of the ohmic voltage is represented by an ohmic resistor, the reverse voltage is represented by a voltage source, and the activation voltage is composed of an activation resistor connected in parallel with an activation electric heater and then connected in series with an activation voltage source.

3. The alkaline electrolyzer model for power system frequency analysis according to claim 1, characterized in that: According to the semi-empirical electrochemical formula commonly used in alkaline electrolytic cells, the relationship between the ohmic voltage and current of alkaline electrolytic cells is expressed as follows: In the formula, r1 and r2 are empirical fitting coefficients, T is the electrolytic cell temperature, A is the plate area, In the equivalent circuit, the ohmic resistance is calculated as follows:

4. The alkaline electrolyzer model for power system frequency analysis according to claim 3, characterized in that: The reverse voltage of an alkaline electrolyzer is expressed as follows: Where U rev0 is a fixed reverse voltage, R0 is the gas constant, T is the temperature, F is the Faraday constant, p is the alkaline electrolytic cell pressure, and p0 is the standard atmospheric pressure.

5. The alkaline electrolyzer model for power system frequency analysis according to claim 4, characterized in that: The equivalent resistance in the activation voltage equivalent circuit is expressed as follows: According to the semi-empirical electrochemical formula commonly used in alkaline electrolyzers, the activation voltage is modeled as follows: Where s, t1, t2 and t3 are empirical fitting parameters. Since the electrolytic cell can only work at the working current [I min ,I max ] range, the equivalent activation resistance R act,eq Calculated as:

6. The alkaline electrolyzer model for power system frequency analysis according to claim 5, characterized in that: The equivalent voltage source in the activation voltage equivalent circuit is expressed as follows: U act,eq0 =-I min R act,eq +U act (I min )。 7. The alkaline electrolyzer model for power system frequency analysis according to claim 6, characterized in that: The equivalent capacitance in the activation voltage equivalent circuit is expressed as follows: The time constant of the electrochemical reaction in the electrolytic cell is predicted by the following formula: C=0.0467A anode +0.00225A cathode In the subscripts, anode and cathode represent the anode and cathode respectively. Therefore, following the principle of conservation of time constant, the equivalent capacitance is expressed as follows: C act,eq =τ / R act,eq 。 8. The alkaline electrolyzer model for power system frequency analysis according to claim 7, characterized in that: The UI relationship of the equivalent circuit is expressed as follows:

9. The alkaline electrolyzer model for power system frequency analysis according to claim 8, characterized in that: The frequency response model of the electrolyzer is obtained: P awe =NO cell and cell AND cell =(U cell -IN rev -IN act,eq0 )MR U Where N represents the number of electrolytic cells in the electrolytic cell, K p is the proportional coefficient of PI control, K i is the integral coefficient of PI control, ΔP ref is the power required by the electrolyzer to change under frequency response, P initial is the initial power of the electrolysis system, P awe is the actual power of the electrolysis system.

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