Method and system for constructing frequency response model of large power grid considering voltage characteristics

Abstract

The application provides a method and system for constructing a large power grid frequency response model considering voltage characteristics. On the basis of a classical system frequency response model, the influence of load voltage characteristics on power system frequency is considered, and a frequency response model capable of reflecting the joint influence of prime movers and governors and loads is constructed. Through model analysis, the calculable part of the model parameters is determined, and the number of parameters to be identified is reduced. Finally, according to the measured large power grid data, all the remaining parameters of the frequency response model considering voltage characteristics are identified based on a particle swarm algorithm. The application can solve the problem that the classical system frequency response model does not work well when voltage drops, accurately simulate the frequency drop process of a large power grid, and improve the accuracy and applicability of the classical frequency response model. The model can quickly and accurately calculate the dynamic response process of the system frequency of a power system under different power disturbances, which is helpful for frequency safety analysis and control of a large power grid.

Description

Technical Field

[0001] This invention relates to the field of smart grid technology, and in particular to frequency security and stability analysis and control technology for modern large power grids. Specifically, it relates to a method and system for constructing a frequency response model for a large power grid that takes into account the influence of load voltage characteristics on frequency. Background Technology

[0002] Frequency is one of the key indicators for the safe and stable operation of a power grid. Traditional power system stability studies generally consider frequency stability and voltage stability separately, assuming that active power determines frequency and reactive power determines voltage. Frequency fluctuations are primarily affected by active power imbalances. However, frequency drops are often accompanied by voltage drops, resulting in an interaction between voltage and frequency. In high-voltage and high-efficiency power systems, the coupling effect between frequency and voltage becomes increasingly pronounced, and the two stability issues often occur intertwined. This reduces the practicality and reliability of analysis methods and control measures that independently consider voltage and frequency.

[0003] Currently, methods for determining system frequency response mainly include full-state time-domain simulation, linearized model analysis, artificial intelligence methods, and equivalent model methods. The Average System Frequency Response (ASF) and System Frequency Response (SFR) models are the main equivalent model methods. These models have simple structures and are widely used in areas such as low-frequency load shedding tuning and system frequency safety assessment. Even though the ASF can reflect more nonlinear characteristics of the prime mover-governor compared to the SFR, the universality of these classic system frequency response models is still relatively poor, often only applicable to simple constant power load models.

[0004] Current research on the interaction between voltage and frequency mainly focuses on islanded power grids, because the coupling between voltage and frequency is more pronounced in islanded grids due to their smaller scale. For large power grids, research on the interaction between voltage and frequency mainly focuses on low-frequency load shedding, such as optimizing the load shedding amount by considering the static voltage characteristics of the load; some studies equate the effect of load voltage drop on frequency to inertia, but none of these methods comprehensively consider the combined effect of voltage characteristics on frequency response. Summary of the Invention

[0005] To address the technical problems of existing frequency response models failing to reflect the impact of voltage characteristics on frequency and having a narrow range of applicability, the present invention aims to propose a method and system for constructing a large power grid frequency response model that takes voltage characteristics into account. This model can reflect the impact of voltage on frequency dynamics, which is helpful for frequency safety and stability analysis. It can also quickly and accurately calculate the dynamic frequency response process of the power system under different power disturbances, thereby facilitating more accurate frequency control during voltage fluctuations.

[0006] To achieve the above objectives, the first aspect of the present invention proposes a method for constructing a frequency response model for a large power grid that takes into account load voltage characteristics, comprising the following steps:

[0007] Step 1: Based on the classical system frequency response model, construct a frequency response model that takes into account the load voltage characteristics;

[0008] Step 2: Analyze the model structure, determine the computable parameters in the model, and reduce the number of parameters to be identified;

[0009] Step 3: Identify all remaining unknown parameters of the frequency response model using the measured frequency response data and the particle swarm optimization algorithm.

[0010] Based on the first aspect of this invention, a system for constructing a frequency response model for a large power grid that takes into account load voltage characteristics is also proposed, comprising:

[0011] The first module is used to construct a frequency response model that takes into account load voltage characteristics based on the classical system frequency response model.

[0012] The second module is used to obtain the computable parameters in the model based on the model structure, thereby reducing the number of parameters to be identified.

[0013] The third module is used to identify all remaining unknown parameters based on measured geogrid data using a particle swarm optimization algorithm.

[0014] Compared with the prior art, the technical solution of the present invention can achieve the following beneficial effects:

[0015] (1) The frequency response model construction method that takes into account voltage characteristics proposed in this invention can more accurately characterize the dynamic change process of frequency because the traditional method for studying the SFR model does not consider the influence of load node voltage change on power deficit: on the one hand, compared with the original simplified second-order frequency response model, it is more accurate because the influence of voltage characteristics is considered; on the other hand, compared with the traditional method of obtaining frequency response based on detailed model, it has fewer parameters, simpler model structure, and faster calculation speed.

[0016] (2) The method for constructing a frequency response model that takes into account voltage characteristics proposed in this invention can be used for frequency simulation calculation of power systems after identifying some unknown parameters. It can quickly simulate the frequency dynamic response process of the system when power disturbances of different magnitudes occur. Therefore, this method is highly practical and has broad application prospects.

[0017] It should be understood that all combinations of the foregoing concepts and the additional concepts described in more detail below may be considered part of the inventive subject matter of this disclosure, provided that such concepts do not contradict each other. Furthermore, all combinations of the claimed subject matter are considered part of the inventive subject matter of this disclosure.

[0018] The foregoing and other aspects, embodiments, and features of the teachings of the present invention will be more fully understood from the following description in conjunction with the accompanying drawings. Other additional aspects of the invention, such as features and / or beneficial effects of exemplary embodiments, will become apparent from the following description or may be learned through practice of specific embodiments according to the teachings of the present invention. Attached Figure Description

[0019] The accompanying drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component shown in the various figures may be denoted by the same reference numeral. For clarity, not every component is labeled in each figure. Embodiments of various aspects of the invention will now be described by way of example and with reference to the accompanying drawings.

[0020] Figure 1 A flowchart illustrating the implementation of a method for constructing a large power grid frequency response model considering voltage characteristics, as an exemplary embodiment of the present invention.

[0021] Figure 2 This is a schematic diagram of the load characteristics incorporated into the system frequency response model in this invention.

[0022] Figure 3 This is a structural diagram of the system frequency response model considering voltage characteristics in this invention.

[0023] Figure 4 This is a structural diagram of an IEEE 10-machine 39-node example system according to an embodiment of the present invention. The generator sets corresponding to buses 31, 32, 33, and 37 are hydroelectric generator sets, the generator sets corresponding to buses 30 and 34 are doubly-fed wind turbine generator sets that cannot provide frequency support, and the generator sets corresponding to buses 35, 36, 38, and 39 are thermal power generator sets.

[0024] Figure 5 This is a comparison chart of the frequency response curve of the detailed BPA model and the output result of the frequency response model considering voltage characteristics described in this invention when the load adopts a constant impedance model in the example and the system experiences a 1% power deficit.

[0025] Figure 6 This is a comparison chart of the frequency response curve of the detailed BPA model and the output result of the frequency response model considering voltage characteristics described in this invention when the load adopts a constant impedance model in the example and the system experiences a 2.5% power deficit.

[0026] Figure 7This is a comparison chart of the frequency response curve of the detailed BPA model and the output result of the frequency response model considering voltage characteristics described in this invention when the load adopts a constant impedance model in the example and the system experiences a 5% power deficit.

[0027] Figure 8 In the example, the load adopts a constant impedance model. When the system experiences a 2.5% power deficit, the frequency response curve of the detailed BPA model is compared with the output results of the identification parameters of the frequency response model considering voltage characteristics described in this invention when using a 1% power deficit. Detailed Implementation

[0028] To better understand the technical content of the present invention, specific embodiments are described below in conjunction with the accompanying drawings.

[0029] Various aspects of the invention are described in this disclosure with reference to the accompanying drawings, which illustrate numerous illustrative embodiments. The embodiments of this disclosure are not necessarily intended to encompass all aspects of the invention. It should be understood that the various concepts and embodiments described above, as well as those described in more detail below, can be implemented in any of many ways, because the concepts and embodiments disclosed herein are not limited to any particular implementation. Furthermore, some aspects of the invention disclosed may be used alone or in any suitable combination with other aspects of the invention disclosed.

[0030] Referring to the illustrations, the method for constructing a frequency response model for a large power grid considering voltage characteristics according to the embodiments disclosed in this invention is applicable to modern large power grids that include thermal power, hydropower, and new energy power generation. The implementation process includes the following steps: Step 1: Construct a frequency response model considering load voltage characteristics based on the classical system frequency response model; Step 2: Analyze the model structure, determine the computable parameters in the model, and reduce the number of parameters to be identified; Step 3: Identify all remaining unknown parameters of the frequency response model based on the particle swarm optimization algorithm using measured frequency response data.

[0031] The implementation process of the aforementioned method will now be described in more detail with reference to the accompanying drawings.

[0032] In an optional embodiment, step 1, based on the classical system frequency response model, constructs a frequency response model that takes into account the load voltage characteristics, including:

[0033] Step 11: Based on a simple single-machine, single-load power system, obtain the relationship between power disturbance and voltage sag:

[0034] In a simple power system with a single machine and a single load, the active power transmitted by the power source (hereinafter referred to as power) can be expressed as:

[0035] P = EUBsinδ

[0036] In the formula, E is the generator internal potential, U is the node voltage, B is the line susceptance, and δ is the phase angle difference between the node voltage and the generator internal potential.

[0037] Assuming the internal electromotive force E of the generator is constant is equivalent to assuming the power source is an infinitely large system;

[0038] If a small disturbance occurs in the power supply, let P = P0 + ΔP, U = U0 + ΔU, δ = δ0 + Δδ, then the approximate linearization can be obtained as follows:

[0039] △P=EBsinδ0△U+EBUcosδ0△δ

[0040] Since the phase angle deviation is the integral of the frequency deviation, the Laplace transform expression for voltage drop with respect to power loss is obtained as follows:

[0041] △U=K1△P+K0△δ

[0042]

[0043] In the formula, K1 and K0 are the parameters to be identified, Δf is the power grid frequency response, and s is the Laplace operator;

[0044] Step 12: Obtain the expressions for the effects of voltage and frequency on disturbance power:

[0045] Under small disturbances, the load can be described using a transfer function model.

[0046] △P L (s)=G L1 (s)△f(s)+G L2 (s)△U(s)

[0047] In the formula, △P L G represents the change in active power of the load. L1 (s) and G L2 (s) is the transfer function describing the relationship between power, frequency, and voltage;

[0048] Based on this transfer function model, the effects of voltage and frequency changes on the disturbance power can be obtained:

[0049]

[0050] In the formula, G Lf (s) is used to describe the change of disturbance power with frequency, G LP (s) describes the effect of the initial disturbance power on the disturbance power; it can be seen that when a power disturbance occurs in the system, taking into account voltage and frequency changes, the load power change is determined by both the disturbance power and the frequency deviation.

[0051] Step 13: Based on the classical system frequency response model (SFR), obtain the frequency response model considering voltage characteristics:

[0052] The original frequency response model consists of an inertial element (including the equivalent damping coefficient) and an equivalent governor-motor model. The equivalent model of the prime mover and governor in the classical system frequency response model SFR can be represented by a standard second-order transfer function G. m (s) represents the standard second-order transfer function, which is expressed as follows:

[0053]

[0054] In the formula, a0, a1, b0, and b1 are the coefficients of the standard second-order transfer function, and ΔP m This is the power deficit in the power grid.

[0055] Compared to the system frequency response model SFR, the average system frequency response model (ASF) retains every prime mover-governor model and preserves more nonlinear characteristics.

[0056] By incorporating load power variation into the frequency response model, we can obtain Figure 2 The model G shown m (s) Schematic diagram. For example... Figure 2 As shown in the figure, △P d For power disturbance, T J G is the equivalent inertial time constant, D is the equivalent damping coefficient, and G is the equivalent inertial time constant. m (s) is the equivalent governor-prime mover model.

[0057] right Figure 2 By merging the relevant steps, an overall equivalent model can be obtained, such as... Figure 3 As shown.

[0058] Taking voltage characteristics into account, the transfer function G of the original prime mover and governor model can be fed back. m (s) changed to G f (s)=G m (s)+G Lf (s).

[0059] Additionally, a transfer function G is added before the feedback path. P (s)=1-G LP (s).

[0060] G P (s) includes the influence of voltage characteristics, G f (s) includes the combined effects of the governor, prime mover, and load.

[0061] Since both are equivalent components, they are described using the standard transfer function:

[0062]

[0063] In the formula, a i b is the coefficient in the denominator of the transfer function. j The coefficients are those of the numerator of the transfer function.

[0064] In an optional embodiment, step 2 involves analyzing the model structure, determining the computable parameters in the model, and reducing the number of parameters to be identified, including:

[0065] Step 21: Obtain the detailed expression for the frequency deviation:

[0066] The frequency response model considering voltage characteristics is expressed in the form of a transfer function:

[0067]

[0068] In the formula, H is the equivalent inertial time constant of the system, D is the equivalent damping coefficient, and G is the equivalent damping coefficient. m (s) is the equivalent model of prime mover-governor, and the transfer function G Lf (s) and G P (s) are all standard transfer functions with unknown coefficients;

[0069] Based on this, the Laplace transform of the frequency deviation under unit perturbation is:

[0070]

[0071] In the formula, 1 / s is the Laplace transform of the step function u(t);

[0072] Step 22: Based on the measured steady-state data of the large power grid, specifically the steady-state power disturbance ΔP... d∞ and steady-state frequency deviation Δf ∞ This reduces the number of unidentifiable coefficients in the frequency response model that takes voltage characteristics into account.

[0073] According to the final value theorem, by letting s→0, the steady-state frequency difference can be obtained; let K be the reciprocal of the equivalent droop coefficient including damping. G We can obtain:

[0074]

[0075] In the formula, K G K represents the equivalent droop coefficient of the classical frequency response model. G 'd' is the actual equivalent droop coefficient calculated based on the actual steady-state power disturbance and steady-state frequency. f For the transfer function G Lf The constant term of the molecule of (s), d pFor the transfer function G P The constant term of the molecule of (s);

[0076] Therefore, we can conclude that:

[0077] d f =K G 'd p -K G

[0078] Transfer function G P (s) and G Lf For the constant term of the molecule (s), only one of these two parameters needs to be identified;

[0079] Step 23: Based on the measured dynamic data of the large power grid, reduce the number of unidentified coefficients in the frequency response model that takes into account voltage characteristics:

[0080] The Laplace change of the rate of change of frequency is,

[0081]

[0082] According to the initial value theorem, the formula for calculating the initial rate of change of frequency RoCoF can be obtained:

[0083]

[0084] A detailed analysis of the model structure reveals that G m The numerator order of (s) is less than the denominator order, and it becomes zero as s approaches infinity; if G P If the order of the numerator of (s) is less than the order of the denominator by more than one, then sG P (s) The limit at this point must be zero; if G P The order of the molecule of (s) is one order less than that of the denominator, sG P The limit of (s) is a constant, namely the quotient of the coefficients of the highest order of the numerator and denominator. However, due to the presence of 2Hs in the denominator, the limit of the entire fraction is still 0. Since the order of the numerator of the transfer function must be less than or equal to the denominator, G... P The numerator and denominator of (s) must have the same order; then the transfer function can be reduced to "a constant term plus a rigorous rational fraction whose numerator polynomial power is less than the denominator polynomial power";

[0085] If G Lf If the order of the numerator of (s) is less than the order of the denominator, its limit is 0; if the order of the numerator is equal to the order of the denominator, its limit is a constant, but it has no effect on the limit of the whole.

[0086] If we let G P (s) The quotient of the coefficients of the highest-order terms in the numerator and denominator is K. P Therefore, the initial slope value can be obtained as K.P / 2H;

[0087] Transfer function G P (s) The coefficient of the highest order term in the numerator and denominator. Only one of these two parameters needs to be identified.

[0088] As an optional implementation, in step 3 above, all remaining unknown parameters of the frequency response model are identified using measured frequency response data and a particle swarm optimization algorithm, including:

[0089] Step 31: Select the standard transfer function G Lf (s) and G P The order of (s) is in the following form:

[0090]

[0091]

[0092] In the formula, a i b i c i d i It is a unit step function;

[0093] Step 32: Obtain known parameters and identify unknown parameters:

[0094] Based on the aforementioned steps, the transfer function G Lf (s) and G P Simplify some coefficients of (s).

[0095] d1 = K G 'b1-K G

[0096]

[0097] In the formula, K G 'K' is the reciprocal of the actual equivalent adjustment factor of the measurement. G RoCoF is the reciprocal of the equivalent descent coefficient of the classic SFR model, and RoCoF is the measured maximum rate of change of frequency.

[0098] Inertial time constant H and the reciprocal of the equivalent droop coefficient K G All of these can be obtained through the equivalent aggregation of model parameters.

[0099] After simplification, there are five parameters to be identified: b1, a0, d0, c0, and c1.

[0100] Using the particle swarm optimization algorithm, the model input is the actual power perturbation, and the output is the measured frequency deviation, which can yield these five unknown parameters to be identified.

[0101] The invention will now be illustrated with specific examples.

[0102] The system used in the following examples is such as Figure 4 The figure shows an IEEE 10-machine 39-node example system. The generators corresponding to buses 31, 32, 33, and 37 are hydroelectric generators, the generators corresponding to buses 30 and 34 are doubly-fed wind turbines that cannot provide frequency support, and the generators corresponding to buses 35, 36, 38, and 39 are thermal power generators.

[0103] The example system has a total load power of 1104MW and a steady-state frequency of 50Hz.

[0104] In the example system, the load is set as a constant impedance model, so that the load power changes with voltage and frequency. At the same time, load power disturbances of 1%, 2.5%, and 5% are set to simulate scenarios when the system experiences power deficits of different magnitudes. The 1% and 5% power disturbances are each identified twice.

[0105] The frequency response model used here is the average system frequency response model (ASF).

[0106] Based on steps 1, 2, and 3 of the method, identify the transfer function G in the frequency response model of the meter and voltage characteristics. Lf (s) and G P The parameters of (s) and the identification results are shown in Table 1:

[0107] Table 1. Frequency response model parameters of the IEEE 39-bus system considering voltage characteristics.

[0108]

[0109] As can be seen from the table, the identification results of most parameters are quite similar. The fluctuations and changes of some parameters indicate that the parameters are less sensitive to frequency changes, which also shows that the identification results are not unique.

[0110] When a 1% power disturbance occurs, the parameters in groups ① and ② are the identified model parameters. The frequency response of the detailed BPA model of the example system is compared with the calculated results of the frequency response model considering voltage characteristics based on the identified parameters. Figure 5 As shown.

[0111] When a 2.5% power disturbance occurs, the parameters in group ③ are the identified model parameters. The frequency response of the detailed BPA model of the example system is compared with the calculated results of the frequency response model considering voltage characteristics of the identified parameters. Figure 6 As shown.

[0112] When a 5% power disturbance occurs, the parameters in groups ④ and ⑤ are the identified model parameters. The frequency response of the detailed BPA model of the example system is compared with the calculated results of the frequency response model considering voltage characteristics based on the identified parameters. Figure 7 As shown.

[0113] Therefore, it can be seen that the model can well reflect the influence of voltage characteristics on frequency response and can adapt to disturbances of different magnitudes.

[0114] To verify the adaptability of the model described in this invention under different identification parameters, when a 2.5% power disturbance occurs, the parameters of group ① are used in the frequency response model that takes into account the voltage characteristics. The output of the model at this time is compared with the frequency response of the detailed BPA model. Figure 8 As shown in the figure, even if the identification results are not unique, the identified model parameters can still reflect the dynamic changes of the system under different magnitudes of disturbance.

[0115] According to another embodiment of the present invention, in combination Figure 1 The example shown also proposes a system for constructing a large power grid frequency response model that takes into account voltage characteristics, including:

[0116] The first module is used to construct a frequency response model that takes into account load voltage characteristics based on the classical system frequency response model.

[0117] The second module is used to analyze the model structure, determine the computable parameters in the model, and reduce the number of parameters to be identified.

[0118] The third module is used to identify all remaining unknown parameters of the frequency response model based on measured frequency response data of the power grid and the particle swarm optimization algorithm, so as to obtain a complete frequency response model of the large power grid that takes into account voltage characteristics.

[0119] The first module for constructing a frequency response model considering load voltage characteristics based on the classical system frequency response model is configured to construct the frequency response model considering load voltage characteristics in the following manner:

[0120] Step 11: Based on a simple single-machine-single-load power system, obtain the relationship between power disturbance and voltage drop: Assuming the power source is an infinite system, if a small disturbance occurs in the power source, let P = P0 + ΔP, U = U0 + ΔU, δ = δ0 + Δδ, and approximate linearize to obtain:

[0121] △P=EBsinδ0△U+EBUcosδ0△δ

[0122] In the formula, E is the generator internal potential, U is the node voltage, B is the line susceptance, and δ is the phase angle difference between the node voltage and the generator internal potential.

[0123] Since the phase angle deviation is the integral of the frequency deviation, the Laplace transform expression for voltage drop with respect to power loss is obtained as follows:

[0124] △U=K1△P+K0△δ

[0125]

[0126] In the formula, K1 and K0 are the parameters to be identified, Δf is the power grid frequency response, and s is the Laplace operator;

[0127] Step 12: Obtain the expressions for the effects of voltage and frequency on disturbance power: Under small disturbances, the load is described using a transfer function model:

[0128] △P L (s)=G L1 (s)△f(s)+G L2 (s)△U(s)

[0129] In the formula, △P L G represents the change in active power of the load. L1 (s) and G L2 (s) is the transfer function describing the relationship between power, frequency, and voltage;

[0130] Based on this transfer function model, the effects of voltage and frequency changes on the disturbance power are obtained:

[0131]

[0132] In the formula, G Lf (s) is used to describe the change of disturbance power with frequency, G LP (s) describes the effect of the initial disturbance power on the disturbance power;

[0133] Step 13: Based on the classical system frequency response model (SFR), obtain the frequency response model considering voltage characteristics:

[0134] The original frequency response model consisted of an inertial element with equivalent damping coefficients and an equivalent governor-motor model. The equivalent model of the prime mover and governor in the classical system frequency response model SFR is represented by a standard second-order transfer function G. m (s) represents the standard second-order transfer function, which is expressed as follows:

[0135]

[0136] In the formula, a0, a1, b0, and b1 are the coefficients of the standard second-order transfer function, and ΔP m This is due to the power deficit in the power grid;

[0137] Taking voltage characteristics into account, the transfer function G of the original prime mover and governor model is fed back. m (s) changed to G f (s)=G m (s)+G Lf (s);

[0138] At the same time, a transfer function G is added before the feedback path. P (s)=1-G LP (s);

[0139] G P (s) includes the influence of voltage characteristics, G f (s) includes the combined effects of the governor, prime mover, and load;

[0140] Since both are equivalent components, they are described using the standard transfer function, expressed as:

[0141]

[0142] In the formula, a i b is the coefficient in the denominator of the transfer function. j The coefficients are those of the numerator of the transfer function.

[0143] The second module, used to analyze the model structure, determine the computable parameters therein, and reduce the number of parameters to be identified, is configured to determine the computable parameters therein in the following manner:

[0144] Step 21: Obtain the detailed expression for the frequency deviation: Express the frequency response model considering voltage characteristics as a transfer function:

[0145]

[0146] In the formula, H is the equivalent inertial time constant of the system, D is the equivalent damping coefficient, and G is the equivalent damping coefficient. m (s) is the equivalent model of the prime mover-governor, with transfer function G. Lf (s) and G P (s) are all standard transfer functions with unknown coefficients;

[0147] Based on this, the Laplace transform of the frequency deviation under unit perturbation is:

[0148]

[0149] In the formula, 1 / s is the Laplace transform of the step function u(t);

[0150] Step 22: Based on the measured steady-state data of the large power grid, specifically the steady-state power disturbance ΔP... d∞ and steady-state frequency deviation Δf∞ This reduces the number of unidentifiable coefficients in the frequency response model that takes voltage characteristics into account.

[0151] According to the final value theorem, by letting s→0, the steady-state frequency difference can be obtained. Let K be the reciprocal of the equivalent droop coefficient, which includes damping. G Therefore, we can conclude that:

[0152]

[0153] In the formula, K G K represents the equivalent droop coefficient of the classical frequency response model. G 'd' is the actual equivalent droop coefficient calculated based on the actual steady-state power disturbance and steady-state frequency. f For the transfer function G Lf The constant term of the molecule of (s), d p For the transfer function G P The constant term of the molecule of (s) is then obtained as follows:

[0154] d f =K G 'd p -K G

[0155] Transfer function G P (s) and G Lf For the constant term of the molecule (s), only one of these two parameters needs to be identified;

[0156] Step 23: Based on the measured dynamic data of the large power grid, reduce the number of coefficients to be identified in the frequency response model that takes into account voltage characteristics: the Laplace change of the rate of frequency change is:

[0157]

[0158] According to the initial value theorem, the formula for calculating the initial rate of change of frequency RoCoF is obtained, which is expressed as:

[0159]

[0160] A detailed analysis of the model structure yields G. m The numerator order of (s) is less than the denominator order, and it becomes zero as s approaches infinity; if G P If the order of the numerator of (s) is less than the order of the denominator by more than one, then sG P (s) The limit at this point must be zero; if G P The order of the molecule of (s) is one order less than that of the denominator, sG PThe limit of (s) is a constant, namely the quotient of the coefficients of the highest order of the numerator and denominator. However, due to the presence of 2Hs in the denominator, the limit of the entire fraction is still 0. Since the order of the numerator of the transfer function must be less than or equal to the denominator, G... P The numerator and denominator of (s) must have the same order; then the transfer function can be reduced to "a constant term plus a rigorous rational fraction whose numerator polynomial power is less than the denominator polynomial power";

[0161] If G Lf If the order of the numerator of (s) is less than the order of the denominator, its limit is 0; if the order of the numerator is equal to the order of the denominator, its limit is a constant, but it has no effect on the limit of the whole.

[0162] If we let G P (s) The quotient of the coefficients of the highest-order terms in the numerator and denominator is K. P Then the initial slope value is K. P / 2H;

[0163] Transfer function G P (s) The coefficient of the highest order term in the numerator and denominator. Only one of these two parameters needs to be identified.

[0164] The third module, which identifies all remaining unknown parameters of the frequency response model based on measured grid frequency response data and uses the particle swarm optimization algorithm to obtain a complete grid frequency response model considering voltage characteristics, is configured to obtain the complete grid frequency response model considering voltage characteristics in the following manner:

[0165] Step 31: Select the standard transfer function G Lf (s) and G P The order of (s) is expressed in the following form:

[0166]

[0167]

[0168] In the formula, a i b i c i d i It is a unit step function;

[0169] Step 32: Obtain known parameters and identify unknown parameters: Based on the previous steps, analyze the transfer function G. Lf (s) and G P Simplify some coefficients of (s):

[0170] d1 = K G 'b1-K G

[0171]

[0172] In the formula, K G 'K' is the reciprocal of the actual equivalent adjustment factor of the measurement. G RoCoF is the reciprocal of the equivalent droop coefficient of the classical SFR model, and RoCoF is the measured maximum rate of change of frequency; the inertial time constant H and the reciprocal of the equivalent droop coefficient K are also mentioned. G All were obtained through the equivalent aggregation of model parameters;

[0173] After simplification, there are five parameters to be identified: b1, b0, d0, c0, and c1. Using the particle swarm optimization algorithm, the model input is the actual power perturbation, and the output is the measured frequency deviation, thus obtaining these five parameters.

[0174] It should be understood that the specific implementations of the first module, the second module, and the third module described above can be implemented based on the exemplary implementation process of the above embodiments, and will not be repeated here.

[0175] While the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Those skilled in the art can make various modifications and refinements without departing from the spirit and scope of the invention. Therefore, the scope of protection of the present invention shall be determined by the claims.

Claims

1. A method for constructing a frequency response model for a large power grid that takes into account voltage characteristics, characterized in that, Includes the following steps: Step 1: Based on the classical system frequency response model, construct a frequency response model that takes into account the load voltage characteristics; Step 2: Analyze the model structure, determine the computable parameters in the model, and reduce the number of parameters to be identified; Step 3: Based on the measured frequency response data of the power grid, identify all remaining unknown parameters of the frequency response model using the particle swarm optimization algorithm to obtain a complete frequency response model of the large power grid that takes into account voltage characteristics. In step 3, based on the measured frequency response data of the power grid, all remaining unknown parameters of the frequency response model are identified using the particle swarm optimization algorithm to obtain a complete large power grid frequency response model considering voltage characteristics, including: Step 31: Select the standard transfer function and The order is expressed in the following form: ； In the formula, , , , It is a unit step function; Step 32: Obtain known parameters and identify unknown parameters: Based on the previous steps, analyze the transfer function. and Simplify some coefficients: ； In the formula, The actual equivalent adjustment factor of the measurement is the reciprocal. RoCoF is the reciprocal of the equivalent droop coefficient of the classical SFR model, and RoCoF is the measured maximum rate of change of frequency; inertial time constant. and the reciprocal of the equivalent adjustment coefficient All were obtained through the equivalent aggregation of model parameters; After simplification, there are five parameters to be identified: , , , , Using the particle swarm optimization algorithm, the model input is the actual power perturbation, and the output is the measured frequency deviation, thus obtaining these five parameters.

2. The method for constructing a large power grid frequency response model considering voltage characteristics according to claim 1, characterized in that, Based on the classical system frequency response model, a frequency response model considering load voltage characteristics is established, including: Step 11: Based on a simple single-machine, single-load power system, obtain the relationship between power disturbance and voltage sag: Assuming the power source is an infinite system, if a small power disturbance occurs on the power source side, let... , , Approximate linearization yields: ； In the formula, E is the generator internal electromotive force, U is the node voltage, and B is the line susceptance. The phase angle difference between the node voltage and the generator internal potential; Since the phase angle deviation is the integral of the frequency deviation, the Laplace transform expression for voltage drop with respect to power loss is obtained as follows: ； ； In the formula, and For the parameters to be identified, Let be the power grid frequency response, and s be the Laplace operator; Step 12: Obtain the expressions for the effects of voltage and frequency on disturbance power: Under small disturbances, the load is described using a transfer function model: ； In the formula, This represents the change in active power of the load. and The transfer function describes the relationship between power, frequency, and voltage; Based on this transfer function model, the effects of voltage and frequency changes on the disturbance power are obtained: ； In the formula, Used to describe the change of disturbance power with frequency. Describe the effect of the initial disturbance power on the total disturbance power; Step 13: Based on the classical system frequency response model (SFR), obtain the frequency response model considering voltage characteristics: The original frequency response model consisted of an inertial element with equivalent damping coefficients and an equivalent governor-motor model. The equivalent model of the prime mover and governor in the classical system frequency response model (SFR) is represented by a standard second-order transfer function. The standard second-order transfer function is expressed as follows: ； In the formula, The coefficients are those of a standard second-order transfer function. This is due to the power deficit in the power grid; Taking voltage characteristics into account, the transfer function of the original prime mover and governor model is fed back. Modified to ; At the same time, add a transfer function before the feedback path. ; This includes the influence of voltage characteristics. It includes the combined effects of the governor, prime mover, and load; Since both are equivalent components, they are described using the standard transfer function, expressed as: ； In the formula, The coefficients in the denominator of the transfer function are... The coefficients are those of the numerator of the transfer function.

3. The method for constructing a large power grid frequency response model considering voltage characteristics according to claim 1, characterized in that, Analyze the model structure to determine the computable parameters and reduce the number of parameters to be identified, including: Step 21: Obtain the detailed expression for the frequency deviation: Express the frequency response model considering voltage characteristics as a transfer function: ； In the formula, H is the equivalent inertial time constant of the system, and D is the equivalent damping coefficient. For the equivalent model of prime mover-governor, the transfer function and All are standard transfer functions with unknown coefficients; Based on this, the Laplace transform of the frequency deviation under unit perturbation is: ； In the formula, Step function The Laplace transform of; Step 22: Based on the measured steady-state data of the large power grid, specifically the steady-state power disturbance... and steady-state frequency deviation This reduces the number of unidentifiable coefficients in the frequency response model that takes voltage characteristics into account. According to the final value theorem, let The steady-state frequency difference can then be obtained. Let the reciprocal of the equivalent droop coefficient, which includes damping, be... Therefore, we can conclude that: ； In the formula, The equivalent droop coefficient for the classical frequency response model. This is the actual equivalent droop coefficient calculated based on the actual steady-state power disturbance and steady-state frequency. For transfer function The constant term of the molecule, For transfer function The constant term of the molecule, at this point, yields: ； transfer function and For the constant term of the molecule, only one of these two parameters needs to be identified; Step 23: Based on the measured dynamic data of the large power grid, reduce the number of coefficients to be identified in the frequency response model that takes into account voltage characteristics: the Laplace change of the rate of frequency change is: ； According to the initial value theorem, the formula for calculating the initial rate of change of frequency RoCoF is obtained, which is expressed as: ； A detailed analysis of the model structure yields the following results: The numerator order is less than the denominator order, and it becomes zero as s approaches infinity; if If the order of the numerator is less than the order of the denominator by more than one, then... The limit at this point must be zero; if The molecule's order is one order smaller than the denominator's. The limit is a constant, which is the quotient of the coefficients of the highest order of the numerator and denominator. Since the denominator contains... The existence of , the limit of the overall fraction is still 0; and the order of the numerator of the transfer function must be less than or equal to the denominator, therefore The orders of the numerator and denominator must be the same; therefore, the transfer function can be reduced to "a constant term plus a rigorous rational fraction whose numerator polynomial power is less than the denominator polynomial power"; like If the order of the numerator is less than the order of the denominator, its limit is 0; if the order of the numerator is equal to the order of the denominator, its limit is a constant, but it has no effect on the limit of the whole. If we assume The quotient of the coefficients of the highest-order terms in the numerator and denominator is Then the value of its initial slope is obtained. ; transfer function Only one of the two parameters, the coefficient of the highest-order term in the numerator and denominator, needs to be identified.

4. A system for constructing a large power grid frequency response model considering voltage characteristics, which implements the method for constructing a large power grid frequency response model considering voltage characteristics as described in claim 1, characterized in that, include: The first module is used to construct a frequency response model that takes into account load voltage characteristics based on the classical system frequency response model. The second module is used to analyze the model structure, determine the computable parameters in the model, and reduce the number of parameters to be identified. The third module is used to identify all remaining unknown parameters of the frequency response model based on measured frequency response data of the power grid and the particle swarm optimization algorithm, so as to obtain a complete frequency response model of the large power grid that takes into account voltage characteristics.

5. The system for constructing a large power grid frequency response model considering voltage characteristics according to claim 4, characterized in that, The first module, used to construct a frequency response model considering load voltage characteristics based on a classical system frequency response model, is configured to construct the frequency response model considering load voltage characteristics in the following manner: Step 11: Based on a simple single-machine, single-load power system, obtain the relationship between power disturbance and voltage sag: Assuming the power source is an infinite system, if a small power disturbance occurs on the power source side, let... , , Approximate linearization yields: ； In the formula, E is the generator internal electromotive force, U is the node voltage, and B is the line susceptance. The phase angle difference between the node voltage and the generator internal potential; Since the phase angle deviation is the integral of the frequency deviation, the Laplace transform expression for voltage drop with respect to power loss is obtained as follows: ； ； In the formula, and For the parameters to be identified, Let be the power grid frequency response, and s be the Laplace operator; Step 12: Obtain the expressions for the effects of voltage and frequency on disturbance power: Under small disturbances, the load is described using a transfer function model: ； In the formula, This represents the change in active power of the load. and The transfer function describes the relationship between power, frequency, and voltage; Based on this transfer function model, the effects of voltage and frequency changes on the disturbance power are obtained: ； In the formula, Used to describe the change of disturbance power with frequency. Describe the effect of the initial disturbance power on the total disturbance power; Step 13: Based on the classical system frequency response model (SFR), obtain the frequency response model considering voltage characteristics: The original frequency response model consisted of an inertial element with equivalent damping coefficients and an equivalent governor-motor model. The equivalent model of the prime mover and governor in the classical system frequency response model (SFR) is represented by a standard second-order transfer function. The standard second-order transfer function is expressed as follows: ； In the formula, The coefficients are those of a standard second-order transfer function. This is due to the power deficit in the power grid; Taking voltage characteristics into account, the transfer function of the original prime mover and governor model is fed back. Modified to ; At the same time, add a transfer function before the feedback path. ; This includes the influence of voltage characteristics. It includes the combined effects of the governor, prime mover, and load; Since both are equivalent components, they are described using the standard transfer function, expressed as: ； In the formula, The coefficients in the denominator of the transfer function are... The coefficients are those of the numerator of the transfer function.

6. The system for constructing a large power grid frequency response model considering voltage characteristics according to claim 4, characterized in that, The second module, used for analyzing the model structure, determining the computable parameters therein, and reducing the number of parameters to be identified, is configured to determine the computable parameters therein in the following manner: Step 21: Obtain the detailed expression for the frequency deviation: Express the frequency response model considering voltage characteristics as a transfer function: ； In the formula, H is the equivalent inertial time constant of the system, and D is the equivalent damping coefficient. For the equivalent model of prime mover-governor, the transfer function and All are standard transfer functions with unknown coefficients; Based on this, the Laplace transform of the frequency deviation under unit perturbation is: ； In the formula, Step function The Laplace transform of; Step 22: Based on the measured steady-state data of the large power grid, specifically the steady-state power disturbance... and steady-state frequency deviation This reduces the number of unidentifiable coefficients in the frequency response model that takes voltage characteristics into account. According to the final value theorem, let The steady-state frequency difference can then be obtained. Let the reciprocal of the equivalent droop coefficient, which includes damping, be... Therefore, we can conclude that: ； In the formula, The equivalent droop coefficient for the classical frequency response model. This is the actual equivalent droop coefficient calculated based on the actual steady-state power disturbance and steady-state frequency. For transfer function The constant term of the molecule, For transfer function The constant term of the molecule, at this point, yields: ； transfer function and For the constant term of the molecule, only one of these two parameters needs to be identified; Step 23: Based on the measured dynamic data of the large power grid, reduce the number of coefficients to be identified in the frequency response model that takes into account voltage characteristics: the Laplace change of the rate of frequency change is: ； According to the initial value theorem, the formula for calculating the initial rate of change of frequency RoCoF is obtained, which is expressed as: ； A detailed analysis of the model structure yields the following results: The numerator order is less than the denominator order, and it becomes zero as s approaches infinity; if If the order of the numerator is less than the order of the denominator by more than one, then... The limit at this point must be zero; if The molecule's order is one order smaller than the denominator's. The limit is a constant, which is the quotient of the coefficients of the highest order of the numerator and denominator. Since the denominator contains... The existence of , the limit of the overall fraction is still 0; and the order of the numerator of the transfer function must be less than or equal to the denominator, therefore The orders of the numerator and denominator must be the same; therefore, the transfer function can be reduced to "a constant term plus a rigorous rational fraction whose numerator polynomial power is less than the denominator polynomial power"; like If the order of the numerator is less than the order of the denominator, its limit is 0; if the order of the numerator is equal to the order of the denominator, its limit is a constant, but it has no effect on the limit of the whole. If we assume The quotient of the coefficients of the highest-order terms in the numerator and denominator is Then the value of its initial slope is obtained. ; transfer function Only one of the two parameters, the coefficient of the highest-order term in the numerator and denominator, needs to be identified.

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