Random frequency unit combination method and system based on state space model

Abstract

The invention discloses a random frequency unit combination method and system based on a state space model, and relates to the technical field of power system frequency safety, and the method comprises the steps: building a state space model of a system based on a single-machine equivalent model; calculating a mean value and a covariance of the state space model to obtain a confidence interval of state variables including frequency of the system; and taking the lower limit of the confidence interval as a frequency security constraint, embedding the frequency security constraint into a unit combination and solving the frequency security constraint. According to the method, the influence of random disturbance on frequency dynamic response is considered, a state space model of a system is listed and written based on a single-machine equivalent model, a confidence interval of state variables including frequency of the system is obtained, and finally, the lower limit of the obtained confidence interval is used as a frequency security constraint, embedded into a unit combination and solved, so that the frequency security constraint is obtained. The problem of unit combination of random frequency safety of the electric power system under the combined action of random disturbance and high-power disturbance is solved, and the development requirement of a novel electric power system is met.

Description

Technical Field

[0001] The present invention relates to the technical field of power system frequency safety, in particular to a random frequency unit combination method and system based on a state space model. Background Art

[0002] Frequency is an important operating indicator of the power system. With the construction and development of new power systems, frequency safety issues urgently need to be fully considered in the unit combination of the power system. Existing literature has formed frequency safety constraints and embedded them into the unit combination model, but it only considers the frequency safety of large power step disturbances. As the fluctuations between sources and loads become larger and larger, the dynamic impact of random disturbances on frequency cannot be ignored. Therefore, this application proposes a unit combination method based on a state space model that considers random frequency safety. Summary of the invention

[0003] In view of the above-mentioned problems, the present invention is proposed.

[0004] Therefore, the technical problem solved by the present invention is: how to make a random frequency safe unit combination of the power system under the combined effects of random disturbance and high-power disturbance.

[0005] To solve the above technical problems, the present invention provides the following technical solutions: a random frequency unit combination method based on a state space model, comprising: constructing a state space model of the system based on a single machine equivalent model; calculating the mean and covariance of the state space model to obtain the confidence interval of the system's state variables including frequency; using the lower limit of the confidence interval as a frequency safety constraint, embedding it into the unit combination and solving it.

[0006] As a preferred solution of the random frequency unit combination method based on the state space model described in the present invention, the construction of the state space model includes introducing an intermediate state variable ΔP into the system disturbance of non-zero bias Gaussian white noise. m1 , the frequency dynamic response model is equivalently converted into the model with Δf, ΔP n1 , ΔP n is the state space model of the state variable, and the system disturbance of the non-zero bias Gaussian white noise is expressed as:

[0007] ΔP d =μ+∑σ i w i (t)

[0008] The state space model is expressed as:

[0009]

[0010] Among them, μ represents the determined high-power extreme disturbance of the system, and its value does not change with time, ∑σ i w i (t) represents the uncertain random disturbance of system source, load, measurement and communication, Δf is the frequency, ΔP n is the frequency modulation power of the system, and s is a complex variable.

[0011] As a preferred solution of the random frequency unit combination method based on the state space model described in the present invention, wherein: the random disturbances of the state space model are aggregated and considered to be independent of each other, then the aggregated random disturbances are expressed as:

[0012]

[0013] Among them, w i (t) and w(t) are both standard Gaussian white noise, is the disturbance intensity after aggregation, σ i is the intensity of each random perturbation.

[0014] As a preferred solution of the random frequency unit combination method based on the state space model described in the present invention, the state space model is converted into a matrix form:

[0015] dX(t)=AX(t)dt+D(μ+σw(t))dt

[0016] =AX(t)dt+D(μdt+σdB(t))

[0017] Based on the theory of random linear systems, the analytical solution is:

[0018]

[0019] Where B(t) is the standard Wiener process, It is the Ito integral of a simple process. At a fixed moment, it is a random variable that obeys a Gaussian distribution. Therefore, the system state X(t) at a certain moment is also from a Gaussian distribution.

[0020] As a preferred solution of the random frequency unit combination method based on the state space model described in the present invention, based on the theory of stochastic calculus, the system state mean is expressed as:

[0021]

[0022] The system state covariance is expressed as:

[0023]

[0024] Using matrix similarity transformation, we can obtain the analytical expression of the system state covariance and perform eigenvalue decomposition on A, A=PAP -1 , Λ=diag[λ1,λ2,λ3] is the eigenvalue matrix, the column vector of P is the eigenvector, and the analyzed system state covariance is expressed as:

[0025]

[0026] Where E is the symbol for finding the mean, s is the integration variable,

[0027] As a preferred solution of the random frequency unit combination method based on the state space model described in the present invention, wherein: F = P -1 DD T (P -1 ) T ,G=ΓP -1 DD T (P -1 ) T Γ T , we can get:

[0028]

[0029] make but

[0030]

[0031] Let the matrix J be the element whose i-th row and j-th column is

[0032]

[0033] Combining the above formulas, we get:

[0034] As a preferred solution of the random frequency unit combination method based on the state space model described in the present invention, wherein: the confidence interval of Δf under a certain confidence level is drawn

[0035]

[0036] The objective function of the unit combination considering random frequency safety is to minimize the operating cost of each type of power supply, which can be expressed as:

[0037]

[0038] Among them, T is the time set, tp is the thermal power set, n is the nuclear power set, h is the hydropower set, w is the wind power set, p is the photovoltaic set, e is the energy storage set, C g is the operating cost coefficient, Cg,s is the startup cost, C g,p The cost of abandoning energy is the enemy;

[0039] The obtained frequency confidence interval is used as the frequency safety constraint, which is expressed as:

[0040] Δf =μ f (t)-Φ -1 (α)σ f (t)≥Δf min

[0042] Where Δf min is the frequency drop limit.

[0043] In the second aspect, another object of the present invention is to provide a mixed environmentally friendly gas proportioning system, including: a model building module, a calculation module and a data processing module; the data acquisition module is used to build a state space model of the system based on a single machine equivalent model; the calculation module is used to calculate the mean and covariance of the state space model to obtain the confidence interval of the system's state variables including frequency; the data processing module is used to use the lower limit of the calculated confidence interval as a frequency safety constraint, embed it into the unit combination and solve it.

[0044] In a third aspect, a computer device includes a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the random frequency unit combination method based on the state space model as described above when executing the computer program.

[0045] In a fourth aspect, a computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the random frequency unit combination method based on the state-space model as described above.

[0046] Beneficial effects of the present invention: The random frequency unit combination method and system based on the state space model provided by the present invention take into account the influence of random disturbances on the frequency dynamic response, write out the state space model of the system based on the single-machine equivalent model, obtain the confidence interval of the system's state variables including the frequency, and finally use the lower limit of the obtained confidence interval as the frequency safety constraint, embed it into the unit combination and solve it, so as to solve the problem of unit combination of random frequency safety of the power system under the combined effect of random disturbances and high-power disturbances, and adapt to the development needs of new power systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0048] Figure 1 An overall flow chart of a random frequency unit combination method based on a state space model provided by one embodiment of the present invention;

[0049] Figure 2 A wind-solar load power curve diagram of a random frequency unit combination method based on a state space model provided by an embodiment of the present invention;

[0050] Figure 3 A schematic diagram of upper and lower limits of a random frequency response confidence interval of a random frequency unit commitment method based on a state space model provided by an embodiment of the present invention;

[0051] Figure 4 A schematic diagram of the start-stop state of a random frequency unit commitment method based on a state space model provided by an embodiment of the present invention;

[0052] Figure 5 A schematic diagram of the lowest frequency values ​​at different times of a random frequency unit combination method based on a state space model provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0053] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0054] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0055] Example 1

[0056] Reference Figure 1 , is an embodiment of the present invention, and provides a random frequency unit combination method based on a state space model, comprising:

[0057] S1: Construct the state space model of the system based on the single machine equivalent model;

[0058] Furthermore, the system disturbance is in the form of non-zero biased Gaussian white noise, expressed as Equation 17.

[0059] ΔP d =μ+∑σ i w i (t) (1)

[0060] Where μ represents the determined high-power extreme disturbance of the system, and its value does not change with time, ∑σ i w i (t) represents the uncertain random disturbance of system source, load, measurement and communication, Δf is the frequency, ΔP m is the frequency modulation power of the system, and s is a complex variable. The multi-machine model is equivalent to a single-machine model by using the equivalent method based on capacity ratio. If the frequency dynamic response model of the random process is based on Δf, ΔP m is the system state variable. Writing the corresponding equation will produce the second-order derivative. For this purpose, the intermediate state variable ΔP is introduced. m1 The frequency dynamic response model is equivalent to the model with Δf and ΔP m1 , ΔP m The state space model of the state variables is:

[0061]

[0062] Expand the last term in equation (18):

[0063]

[0064] σ is the random disturbance intensity, w is Gaussian white noise, and the number of columns of the matrix obtained by multiplying the first two matrices in the second term on the right side of formula (19) is the same as the number of random disturbances, which will greatly increase the matrix dimension and is not conducive to subsequent analysis and calculation. Therefore, each random disturbance is aggregated here and is considered to be independent of each other. The aggregated random disturbance is

[0065]

[0066] w in formula 20 i (t) and w(t) are both standard Gaussian white noise, is the disturbance intensity after aggregation, σ i is the intensity of each random perturbation.

[0067] Record system state variables

[0068]

[0069] System state matrix

[0070]

[0071] System Input Matrix

[0072]

[0073] Convert equation (18) into matrix form

[0074]

[0075] B(t) in formula (24) is a standard Wiener process. Based on the theory of random linear systems, the analytical solution of formula (24) is:

[0076]

[0077] In formula (25), It is the Ito integral of a simple process. At a fixed moment, it is a random variable that obeys a Gaussian distribution. Therefore, the system state X(t) at a certain moment is also from a Gaussian distribution.

[0078] S2: Calculate the mean and covariance of the state space model to obtain the confidence interval of the state variables of the system including the frequency;

[0079] Furthermore, based on the theory of stochastic calculus, the mean of the system state

[0080]

[0081] X(t) is the matrix X, which is a quantity that changes with time. The matrices A and D are constant matrices that do not change with time. t0 is the initial moment, E is the symbol for finding the mean, and s is the integral variable. A mechanism analysis of equation (26) shows that the mean of the system state, including the system frequency, is only related to the system parameters (corresponding to the state matrices A and D), the duration t of the disturbance, the initial value of the system (corresponding to X(t0)), and the mean μ of the disturbance, but has nothing to do with the intensity of the disturbance (i.e., the variance σ).

[0082] Covariance of the system

[0083]

[0084] Since there are integrals that cannot be solved directly analytically, the similarity transformation of the matrix is ​​used to obtain the analytical expression of the system state covariance. Perform eigenvalue decomposition on A, A = PAP -1 , Λ=diag[λ1,λ2,λ3] is the eigenvalue matrix, and the column vector of P is the eigenvector. Substituting into equation (27) we get

[0085]

[0086] In formula (28)

[0087] Let F = P -1 DD T (P -1 ) T ,G=ΓP -1 DD T (P -1 ) T Γ T , we can get

[0088]

[0089] G(i,j) is the i-row and j-column of matrix G. Let but

[0090]

[0091] Let the matrix J be the element whose i-th row and j-th column is

[0092]

[0093] Combining equations (30) and (31), we can obtain

[0094] H=FoJ (16)

[0095] Substituting equation (32) into equation (28), we get

[0096]

[0097] The mechanism analysis of equation (33) shows that the covariance of the system state is related to the system parameters A and D, duration t (contained in matrix J), and σ, and has nothing to do with X(t0). When a random disturbance occurs in the system, the covariance matrix is ​​proportional to the square of the random disturbance intensity, which indicates that when a forced oscillation is caused by a random disturbance in the power system, reducing the intensity of this random disturbance can effectively reduce the variance of the system frequency fluctuation.

[0098] Since the system state variables obey the Gaussian distribution at a fixed time, and the mean and variance of the system state variables have been obtained, the confidence interval of Δf under a certain confidence level can be drawn

[0099]

[0100] Where Φ -1 (α) represents the two-sided quantile with a confidence level of 1-α, is the upper limit of the confidence interval, Δf is the lower limit of the confidence interval, μ fis the mean of the random frequency response, Mean[X(t)], first row, first column, σ f is the variance, Var[X(t)], the first row and the first column.

[0101] S3: The lower limit of the confidence interval is used as the frequency safety constraint, embedded into the unit combination and solved.

[0102] Furthermore, the objective function of the unit combination considering random frequency safety is to minimize the operating cost of each type of power supply, that is,

[0103]

[0104] Where T is the time set, tp is the thermal power set, n is the nuclear power set, h is the hydropower set, w is the wind power set, p is the photovoltaic set, e is the energy storage set, and C g is the operating cost coefficient, C g,s is the startup cost, C g,p is the energy abandonment cost coefficient.

[0105] The constraints of unit combination include conventional unit combination constraints, such as system inertia constraints, power balance constraints, output upper and lower limit constraints, climbing and descending constraints, energy storage power constraints, etc. The lower limit of the frequency confidence interval obtained in Section 2.2 is used as the frequency safety constraint, that is,

[0106] Δf =μ f (t)-Φ -1 (α)σ f (t)≥Δf min (20)

[0107] Where Δf min is the frequency drop limit.

[0108] The model is decomposed into a main problem and a sub-problem, which are connected by a frequency safety cut constraint. The main problem is the unit combination considering the linear minimum inertia constraint, and the sub-problem is the transient assessment problem of the lowest point of dynamic frequency.

[0109] When the frequency safety constraint is not met, it means that the system's inertia or primary frequency regulation capability is insufficient. Increasing the system's inertia constraint, i.e., the frequency safety constraint, can improve the system's inertia and primary frequency regulation capability.

[0110] Example 2

[0111] In one embodiment of the present invention, a mixed environmentally friendly gas proportioning system is provided, comprising:

[0112] Model building module, calculation module and data processing module;

[0113] The data acquisition module is used to construct a state space model of the system based on the single machine equivalent model;

[0114] The calculation module is used to calculate the mean and covariance of the state space model to obtain the confidence interval of the state variables of the system including the frequency;

[0115] The data processing module is used to use the lower limit of the calculated confidence interval as a frequency safety constraint, embed it into the unit combination and solve it.

[0116] Example 3

[0117] An embodiment of the present invention is different from the first two embodiments in that:

[0118] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program code.

[0119] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, which can be embodied in any computer-readable medium for use by an instruction execution system, apparatus or device (such as a computer-based system, a system including a processor or other system that can fetch instructions from an instruction execution system, apparatus or device and execute instructions), or used in conjunction with these instruction execution systems, apparatuses or devices. For the purpose of this specification,

[0120] A "computer-readable medium" can be any apparatus that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.

[0121] More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic device), a portable computer disk case (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be a paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering or, if necessary, processing in another suitable manner, and then stored in a computer memory.

[0122] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, a plurality of steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0123] Example 4

[0124] See also Figure 2 to Figure 5 , which is an embodiment of the present invention, provides a random frequency unit combination method based on a state space model. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation experiments.

[0125] like Figure 2 As shown in the figure, the volatility of wind power and photovoltaic power and the dynamic change trend of load are clearly displayed, which provides input basis for subsequent random disturbances and power response and helps analyze the dynamic characteristics of the system. Figure 3 As shown in Figure 1, the upper and lower limits of the confidence interval show the possible impact range of random disturbances on the frequency, providing a safety margin for the dynamic changes in system frequency. In the design of unit combination, the lower limit is used as a frequency safety constraint to ensure that the frequency is always within an acceptable range, thereby enhancing the safety and robustness of the system.

[0126] like Figure 4 As shown in the figure, the start and stop status of the units in the chart indicates the optimized operation arrangement of the system, which reflects the optimal unit combination strategy under random frequency safety. Figure 5As shown, the dynamic response effect of the system frequency is better under the combined action of multiple random disturbances and high-power disturbances. By analyzing whether the lowest frequency value is within the safe confidence interval, the frequency stability and response capability of the system under the new scheme are verified, thereby reflecting the adaptability and improvement effect of the scheme to random disturbances and high-power disturbances.

[0127] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A random frequency unit commitment method based on a state space model, characterized in that: include: Construct the state space model of the system based on the single machine equivalent model; Calculating the mean and covariance of the state space model to obtain the confidence interval of the state variables of the system including the frequency; The lower limit of the confidence interval is used as the frequency safety constraint, embedded into the unit commitment and solved.

2. The random frequency unit commitment method based on the state space model as claimed in claim 1, characterized in that: The construction of the state space model includes introducing an intermediate state variable ΔP into the system disturbance of non-zero bias Gaussian white noise m1 , the frequency dynamic response model is equivalently converted into the model with Δf, ΔP m1 , ΔP m is the state space model of the state variable, and the system disturbance of the non-zero bias Gaussian white noise is expressed as: ΔP d =μ+∑σ i w i (t) The state space model is expressed as: Among them, μ represents the determined high-power extreme disturbance of the system, and its value does not change with time, ∑σ i w i (t) represents the uncertain random disturbance of system source, load, measurement and communication, Δf is the frequency, ΔP m is the frequency modulation power of the system, and s is a complex variable.

3. The random frequency unit commitment method based on the state space model as claimed in claim 2, characterized in that: The random disturbances of the state space model are aggregated and considered to be independent of each other. The aggregated random disturbances are expressed as: Among them, w i (t) and w(t) are both standard Gaussian white noise, is the disturbance intensity after aggregation, σ i is the intensity of each random perturbation.

4. The random frequency unit commitment method based on the state space model as claimed in claim 3, characterized in that: Convert the state-space model into matrix form: dX(t)=AX(t)dt+D(μ+σw(t))dt=AX(t)dt+D(μdt+σdB(t)) Based on the theory of random linear systems, the analytical solution is: Where B(t) is the standard Wiener process, It is the Ito integral of a simple process. At a fixed moment, it is a random variable that obeys the Gaussian distribution. Therefore, the system state X(t) is Gaussian distributed at a certain moment. The matrices A and D are constant matrices that do not change with time. t0 is the initial moment.

5. The random frequency unit commitment method based on the state space model as claimed in claim 4, characterized in that: Based on the theory of stochastic calculus, the mean value of the system state is expressed as: The system state covariance is expressed as: Using matrix similarity transformation, we can obtain the analytical expression of the system state covariance and perform eigenvalue decomposition on A, A=PAP -1 , Λ=diag[λ1,λ2,λ3] is the eigenvalue matrix, the column vector of P is the eigenvector, and the analyzed system state covariance is expressed as: Where E is the symbol for finding the mean, s is the integration variable, 6. The random frequency unit commitment method based on the state space model as claimed in claim 5, characterized in that: Let F = P -1 DD T (P -1 ) T ,G=ΓP -1 DD T (P -1 ) T Γ T , we can get: make but Let the matrix J be the element whose i-th row and j-th column is Combining the above formulas, we get:

7. The random frequency unit commitment method based on the state space model as claimed in claim 6, characterized in that: Plot a confidence interval for Δf at a certain confidence level Δf =μ f (t)-Φ -1 (a)s f (t) The objective function of the unit combination considering random frequency safety is to minimize the operating cost of each type of power supply, which can be expressed as: Among them, T is the time set, tp is the thermal power set, n is the nuclear power set, h is the hydropower set, w is the wind power set, p is the photovoltaic set, e is the energy storage set, C g is the operating cost coefficient, C g,s is the startup cost, C g,p The cost of abandoned energy is the enemy, Φ -1 (α) represents the two-sided quantile with a confidence level of 1-α; The obtained frequency confidence interval is used as the frequency safety constraint, which is expressed as: Δf =μ f (t)-Φ -1 (a)s f (t)≥Δf min Where Δf min It is the frequency drop limit.

8. A system using the random frequency unit commitment method based on the state space model as claimed in any one of claims 1 to 7, characterized in that: include: Model building module, calculation module and data processing module; The data acquisition module is used to construct a state space model of the system based on a single machine equivalent model; The calculation module is used to calculate the mean and covariance of the state space model to obtain the confidence interval of the state variables of the system including the frequency; The data processing module is used to use the calculated lower limit of the confidence interval as a frequency safety constraint, embed it into the unit combination and solve it.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the random frequency unit combination method based on the state space model according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the random frequency unit combination method based on the state space model according to any one of claims 1 to 7 are implemented.

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