New energy station frequency security planning method and device based on same-frequency modal correlation

Abstract

The present application relates to the technical field of power system, disclose a new energy station frequency safety planning method based on the correlation of the same frequency mode, including: for the planning candidate composed of candidate access node and candidate installed capacity, the finite dimension linear time invariant frequency response model of each active power disturbance position to each protected node is established;The modal decomposition is carried out to the frequency response model, and the explicit modal response set and the remaining response not decomposed are obtained, and the direct feedthrough response is extracted;The non-negative frequency range is divided into several continuous frequency intervals that cover all non-negative frequencies, based on the amplitude and phase correlation characteristics of the same frequency modal response, the modal response in the explicit modal response set is paired and screened, and the actual modal response pair and the unpaired modal response are obtained.The present application makes the obtained boundary cover the full frequency response of the checked reference frequency response model, and reduces the excessive conservatism of independent boundary calculation of each mode.

Description

Technical Field

[0001] This invention relates to the field of power system planning technology, specifically to a method and apparatus for frequency security planning of new energy power plants based on co-frequency mode correlation. Background Technology

[0002] With the large-scale integration of new energy power generation into the power system, the connection nodes and installed capacity of power plants will change the system's inertia distribution, damping characteristics, and the transmission relationship of active power disturbances to the frequency deviation of each node. Frequency security constraints must be incorporated into the planning stage of new energy power plants to ensure the safe operation of the power grid under different disturbance scenarios. Existing frequency security planning technologies for new energy power plants typically employ mode decomposition to break down the frequency response of active power disturbances to protected nodes. By obtaining the amplitude boundaries of each mode response, an upper bound of the frequency response gain is synthesized. Based on this, frequency security constraints are constructed, and then the connection node and installed capacity scheme of the power plant is solved.

[0003] However, existing frequency security planning methods based on mode decomposition generally obtain the overall gain upper bound by directly superimposing the independent amplitude upper bounds of each modal response, without utilizing the amplitude and phase correlation characteristics between modal responses at the same frequency for pairing and joint upper bound calculation. This results in an overly conservative frequency response gain boundary, which unnecessarily compresses the planning feasible region, excludes actual site access candidates that can meet frequency security requirements, and affects the rationality of the new energy site planning results. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a frequency safety planning method and device for new energy power stations based on co-frequency mode correlation, which is used to solve the aforementioned technical problems.

[0005] Firstly, a frequency security planning method for new energy power plants based on co-frequency mode correlation is provided, including:

[0006] For the planning candidates consisting of candidate access nodes and candidate installed capacity, a finite-dimensional linear time-invariant frequency response model is established from each active power disturbance location to each protected node.

[0007] Modal decomposition is performed on the frequency response model to obtain the explicit modal response set and the residual response without explicit decomposition, and the direct feedthrough response is extracted.

[0008] The non-negative frequency range is divided into several continuous frequency intervals that together cover all non-negative frequencies. Based on the amplitude and phase correlation characteristics of the same-frequency modal response, the modal responses in the explicit modal response set are paired and screened to obtain actual modal response pairs and unpaired modal responses.

[0009] The joint amplitude upper bound is calculated for the actual modal response pair. The sum of the independent amplitude upper bounds of the corresponding two modal responses is replaced by the joint amplitude upper bound. Then, it is synthesized non-repeatingly with the amplitude upper bounds of the unpaired modal response, the direct feedthrough response, and the undecomposed residual response to obtain the gain upper bound of each continuous frequency interval. The maximum value of the gain upper bound of all intervals is taken to obtain the full-frequency response gain upper bound.

[0010] Frequency safety constraints are constructed based on the preset upper limit of disturbance power amplitude, the limit of node frequency response amplitude, and the upper limit of the full-frequency response gain, and the site access nodes and installed capacity are obtained by solving.

[0011] Furthermore, for the planning candidates consisting of candidate access nodes and candidate installed capacity, a finite-dimensional linear time-invariant frequency response model is established from each active power disturbance location to each protected node, including:

[0012] The equivalent dynamic parameters and nodal injection power of the planned candidate new energy power stations are updated, and power flow calculations are performed on the power grid to obtain the steady-state operating point.

[0013] Linearize the system components and active power equations at the steady-state operating point, fix the reference node phase angle or eliminate the invariant mode corresponding to the uniform phase angle translation, and obtain the dynamic matrix, disturbance input matrix, frequency response output matrix and direct feedthrough matrix;

[0014] Port truncation is performed on the disturbance input matrix and frequency response output matrix. The frequency response transfer relationship is constructed by combining the dynamic matrix and the direct feedthrough matrix to obtain a finite-dimensional linear time-invariant frequency response model.

[0015] Furthermore, modal decomposition is performed on the frequency response model to obtain the explicit modal response set and the residual response without explicit decomposition, and the direct feedthrough response is extracted, including:

[0016] The spectrum of the dynamic matrix is ​​divided into groups to obtain multiple modes that are separate from each other and closed under complex conjugate operations.

[0017] Explicitly filter the multiple modal groups to obtain explicit modal groups;

[0018] Calculate the projection matrix for the invariant subspace corresponding to each explicit mode group to obtain the projection matrix corresponding to each explicit mode group;

[0019] The projection matrices of all explicit mode groups are integrated and calculated to obtain the residual spectrum projection matrix;

[0020] The dynamic response components of the frequency response model are projected based on the projection matrix of each explicit mode group to obtain the set of explicit modal responses determined by the same frequency variable.

[0021] Based on the residual spectrum projection matrix, the dynamic response components of the frequency response model are projected and calculated to obtain the residual response that is not explicitly decomposed.

[0022] The corresponding terms of the direct feedthrough matrix are extracted to obtain the direct feedthrough response.

[0023] Furthermore, the non-negative frequency range is divided into several continuous frequency intervals that collectively cover all non-negative frequencies. Based on the amplitude and phase correlation characteristics of the same-frequency modal responses, the modal responses in the explicit modal response set are paired and screened to obtain actual modal response pairs and unpaired modal responses, including:

[0024] Within the frequency response channel corresponding to the same planning candidate, the same disturbance location, and the same protected node, the real cross term is calculated for the two modal responses in each continuous frequency interval to obtain the corresponding real cross term.

[0025] The pairing condition is checked on the real cross term. When the real cross term is not positive and its absolute value is not less than the product of the cancellation coefficient and the amplitude of the two modal responses, the two modal responses are determined as candidate modal response pairs.

[0026] All candidate modal response pairs are deduplicated so that the same modal response belongs to at most one modal response pair, resulting in actual modal response pairs and unpaired modal responses.

[0027] Furthermore, a pairing condition check is performed on the real cross-terms. When a real cross-term is non-positive and its absolute value is not less than the product of the cancellation coefficient and the amplitudes of the two modal responses, the two modal responses are determined as candidate modal response pairs, including:

[0028] The upper and lower bounds of the amplitude of the modal response within each continuous frequency range are determined to obtain the upper and lower bounds of the amplitude of each modal response;

[0029] The upper and lower bounds of the amplitude are used to perform interval operations on the real cross term to obtain the value range of the real cross term;

[0030] Based on the value interval of the real cross term and the judgment interval of the square difference, the pairing condition is initially judged, and the closed subintervals where the pairing condition cannot be determined are obtained.

[0031] If the closed sub-interval is divided into binary iterative sections and the maximum number of binary sections or the minimum interval width is still not reached, then the modal response pairs in the corresponding sub-intervals will not be determined as candidate modal response pairs.

[0032] Verification and summarization were completed for all frequency ranges to obtain candidate modal response pairs.

[0033] Furthermore, a joint amplitude upper bound is calculated for the actual modal response pairs. This joint amplitude upper bound is then used to replace the sum of the independent amplitude upper bounds of the corresponding two modal responses. This sum is then combined non-repeatingly with the amplitude upper bounds of the unpaired modal response, the direct feedthrough response, and the undecomposed residual response to obtain the gain upper bound for each continuous frequency range. The maximum value of the gain upper bound for all ranges is taken to obtain the full-frequency response gain upper bound, including:

[0034] Determine the upper bounds of the amplitudes of various types of responses within each continuous frequency range, including the upper bounds of the amplitudes of explicit modal responses, residual responses, and direct feedthrough responses;

[0035] Based on the upper and lower bounds of the amplitude of the two modal responses, calculate the joint upper bound of the amplitude for each actual modal response pair;

[0036] The sum of the independent amplitude upper bounds of the corresponding two modal responses is replaced by the joint amplitude upper bound, and non-repeating interval synthesis is performed with the amplitude upper bounds of the unpaired modal response, the direct feedthrough response, and the residual response.

[0037] When the frequency response model used has an approximate error relative to the reference frequency response model, the upper bound of the independently calculated model error amplitude is simultaneously included to obtain the upper bound of the gain for each continuous frequency range.

[0038] The upper bound of the gain is obtained by selecting the maximum value of the upper bound of the gain for all continuous frequency ranges, wherein the continuous frequency ranges include the unbounded high frequency range.

[0039] Furthermore, determining the upper bound of the amplitude for each type of response includes:

[0040] The Riesz projection method is used to calculate the projection matrix of the corresponding invariant subspace of the explicit mode group to obtain the corresponding projection matrix.

[0041] Based on the projection matrix, the finite frequency range is divided into sub-intervals for coverage. The complex interval linear equations are solved by rounding outwards to obtain the complex rectangular inclusion result of the modal response.

[0042] The unbounded high-frequency interval is transformed into a bounded interval by inverse frequency variable transformation, and the same complex interval solution method is used to calculate the upper bound of the amplitude of the bounded interval.

[0043] Using the same complex interval solution method, the upper bounds of the magnitudes of the residual response and model error are calculated respectively.

[0044] Furthermore, based on the preset upper limit of disturbance power amplitude, the limit of node frequency response amplitude, and the upper limit of the full-frequency response gain, frequency security constraints are constructed, and the site access nodes and installed capacity are obtained by solving, including:

[0045] The upper limit of the disturbance power amplitude and the limit of the nodal frequency response amplitude are determined to obtain the constraint boundary parameters;

[0046] Frequency security constraints are constructed for each disturbance location and the corresponding protected node to obtain all frequency security constraints; wherein, the frequency security constraints are frequency domain response amplitude constraints.

[0047] The planning objective function is solved within the set of engineering constraints to obtain the access nodes and installed capacity of the power station;

[0048] When planning candidates, power grid operation mode, network topology, or equipment parameters change, the frequency response model, the upper bound of the full-frequency response gain, and the frequency security constraints are recalculated and verified.

[0049] Secondly, a frequency security planning device for new energy power stations based on co-frequency mode correlation is provided, which is based on the frequency security planning method for new energy power stations based on co-frequency mode correlation described in any of the preceding items, including:

[0050] The frequency response model module is configured to establish a finite-dimensional linear time-invariant frequency response model from each active power disturbance location to each protected node for a planning candidate consisting of candidate access nodes and candidate installed capacity.

[0051] The modal response module is configured to perform modal decomposition on the frequency response model to obtain an explicit modal response set and a residual response that is not explicitly decomposed, and to extract the direct feedthrough response.

[0052] The pairing and filtering module is configured to divide the non-negative frequency range into several continuous frequency intervals that jointly cover all non-negative frequencies, and based on the amplitude and phase correlation characteristics of the same-frequency modal responses, to perform pairing and filtering on the modal responses in the explicit modal response set to obtain actual modal response pairs and unpaired modal responses.

[0053] The full-frequency response gain upper bound module is configured to calculate the joint amplitude upper bound for the actual modal response pairs, replace the sum of the independent amplitude upper bounds of the corresponding two modal responses with the joint amplitude upper bound, and then perform non-repetitive synthesis with the amplitude upper bounds of the unpaired modal response, the direct feedthrough response, and the undecomposed residual response to obtain the gain upper bound of each continuous frequency interval; take the maximum value of the gain upper bound of all intervals to obtain the full-frequency response gain upper bound;

[0054] The solution module is configured to construct frequency security constraints based on the preset upper limit of disturbance power amplitude, the limit of node frequency response amplitude, and the upper limit of the full-frequency response gain, and to solve for the site access nodes and installed capacity.

[0055] Thirdly, a terminal is provided, including a processor, an input device, an output device, and a memory, wherein the processor, input device, output device, and memory are interconnected, wherein the memory is used to store a computer program, the computer program including program instructions, and the processor is configured to call the program instructions to execute the new energy power station frequency security planning method based on co-frequency mode correlation as described in any of the preceding claims.

[0056] Fourthly, a computer-readable storage medium is provided, characterized in that the computer-readable storage medium stores a computer program, the computer program including program instructions, which, when executed by a processor, cause the processor to execute the frequency security planning method for new energy power stations based on co-frequency mode correlation as described in any of the preceding claims.

[0057] The invention employing the above technical solution has the following advantages:

[0058] 1. This invention utilizes the amplitude and phase correlation characteristics of each modal response at the same frequency to pair and screen modal responses. By replacing the direct superposition of the traditional independent amplitude upper bounds for each mode with a joint upper bound, the destructive characteristics between modes are fully utilized, resulting in a more compact upper bound for the full-frequency response gain. This alleviates the problem of conservative results caused by the traditional independent superposition method.

[0059] 2. Based on the upper bound of the gain, this invention constructs frequency security constraints and solves the planning scheme. Under the premise of meeting the node frequency security limit, a more reasonable access node and installed capacity of new energy power stations can be obtained, thereby improving the economy of the planning scheme and the ability of new energy to absorb new energy.

[0060] 3. This invention adopts an analysis method that divides the non-negative frequency range into continuous intervals, replacing the frequency-point-by-frequency traversal calculation mode. It can obtain the upper bound of the gain of a single continuous interval at once, effectively reducing the amount of computation in the entire frequency domain. Combined with the standardized analysis framework of mode decomposition, the calculation process is regular and can be adapted to iterative calculation scenarios with multiple candidate schemes and multiple operating modes in the planning stage, thereby improving the overall planning solution efficiency. Attached Figure Description

[0061] To more clearly illustrate the specific embodiments of the present invention, the accompanying drawings used in the specific embodiments will be briefly described below. In all the drawings, the elements or parts are not necessarily drawn to scale.

[0062] Figure 1 This is a flowchart of the frequency security planning method for new energy power stations based on co-frequency mode correlation according to the present invention;

[0063] Figure 2 This is an architectural diagram of the new energy power station frequency safety planning device based on co-frequency mode correlation of the present invention. Detailed Implementation

[0064] The embodiments of the technical solution of the present invention will now be described in detail with reference to the accompanying drawings. These embodiments are merely illustrative of the technical solution of the present invention and are therefore intended to limit the scope of protection of the present invention.

[0065] like Figures 1-2 As shown, the frequency security planning method for new energy power stations based on co-frequency mode correlation of the present invention has the following planning candidates denoted as... It consists of candidate access nodes and candidate installed capacity; the grid operation mode includes the power generation unit start-up mode, load level, and network operation status; the network topology includes nodes, branches, and their connection relationships; the equipment parameters include dynamic parameters of synchronous power generation units, new energy power generation units, load, and frequency regulation links. This method does not require pre-fixing a unique disturbance location, but achieves coverage by traversing all active power disturbance locations one by one, activating only the input channel corresponding to one disturbance location at a time, specifically including:

[0066] For the planning candidates consisting of candidate access nodes and candidate installed capacity, a finite-dimensional linear time-invariant frequency response model is established from each active power disturbance location to each protected node.

[0067] In this embodiment, for the planning candidates consisting of candidate access nodes and candidate installed capacity, a finite-dimensional linear time-invariant frequency response model from each active power disturbance location to each protected node is established, including:

[0068] The equivalent dynamic parameters and nodal injection power of the planned candidate new energy power stations are updated, and power flow calculations are performed on the power grid to obtain the steady-state operating point.

[0069] Linearize the active power equations of system components and network at the steady-state operating point, fix the phase angle of the reference node or eliminate the invariant mode corresponding to the uniform phase angle translation, and obtain the dynamic matrix, disturbance input matrix, frequency response output matrix and direct feedthrough matrix.

[0070] Port truncation is performed on the disturbance input matrix and the frequency response output matrix. The frequency response transfer relationship is constructed by combining the dynamic matrix and the direct feedthrough matrix, resulting in a finite-dimensional linear time-invariant frequency response model.

[0071] Specifically, for each planning candidate Based on the candidate access nodes and candidate installed capacity, the equivalent dynamic parameters and node injection power of the new energy power station are updated, power flow calculations are performed, and the corresponding steady-state operating point is determined. At the steady-state operating point, the equations of synchronous generation units, new energy generation units, load frequency characteristics, frequency regulation links, and network active power are linearized. After fixing the phase angle of the reference node or eliminating the invariant mode corresponding to the uniform phase angle translation, a finite-dimensional linear time-invariant model is formed.

[0072]

[0073] in, For state vectors, This is the active power disturbance vector. This is the node frequency response vector. It is a dynamic matrix. The perturbation input matrix, The frequency response output matrix, This is a direct feedthrough matrix. When a planning candidate changes its access nodes or installed capacity, the equivalent dynamic parameters, node injection power, and steady-state operating point change accordingly, thus forming a matrix corresponding to that planning candidate. , , and .

[0074] Select the column of the input matrix corresponding to the perturbation position k The output matrix row corresponding to the protected node i A frequency response model is established with active power disturbance as input and nodal frequency response as output, according to the following formula:

[0075]

[0076] in, For complex frequencies, It is the identity matrix. Perturbation location The corresponding input matrix columns, Protected node The corresponding output matrix rows, This is a direct feedthrough term; after fixing the reference node phase angle or eliminating invariant modes, the poles of the frequency response model are all located in the left half of the complex plane, and The value is finite to ensure that the frequency response model is stable and has finite high-frequency gain.

[0077] Repeat the above operation for all disturbance locations and all protected nodes to obtain the planning candidate. The corresponding set of location-based frequency response models. Only one input channel corresponding to a disturbance position is activated at a time, and each disturbance position is covered by traversing it one by one, without needing to pre-fix the disturbance position as a unique node.

[0078] Modal decomposition is performed on the frequency response model to obtain the explicit modal response set and the residual response without explicit decomposition, and the direct feedthrough response is extracted.

[0079] In this embodiment, modal decomposition is performed on the frequency response model to obtain the explicit modal response set and the residual response without explicit decomposition, and the direct feedthrough response is extracted, including:

[0080] The spectrum of the dynamic matrix is ​​divided into groups to obtain multiple modes that are separate from each other and closed under complex conjugate operations.

[0081] Explicitly filter multiple modal groups to obtain explicit modal groups;

[0082] Calculate the projection matrix for the invariant subspace corresponding to each explicit mode group to obtain the projection matrix corresponding to each explicit mode group;

[0083] The projection matrices of all explicit mode groups are integrated and calculated to obtain the residual spectrum projection matrix;

[0084] The dynamic response components of the frequency response model are projected based on the projection matrix of each explicit mode group to obtain the set of explicit modal responses determined by the same frequency variable.

[0085] The dynamic response components of the frequency response model are projected onto the residual spectrum projection matrix to obtain the undecomposed residual response.

[0086] The corresponding terms of the direct feedthrough matrix are extracted to obtain the direct feedthrough response.

[0087] Specifically, the dynamic matrix The spectrum is divided into mutually separate mode groups, each closed under complex conjugate operations. Each mode group may contain a real eigenvalue or at least a pair of complex conjugate eigenvalues. From these, m explicit mode groups that require explicit computation are selected, and the projection matrix of the corresponding invariant subspace is determined for the p-th explicit mode group. The p-th modal response, determined by the same frequency variable w, is obtained according to the following formula:

[0088]

[0089] in, The imaginary unit is used, and all explicit modal responses use the same frequency variable. .

[0090] The residual spectral projection matrix and residual response without explicit decomposition are determined according to the following formula:

[0091]

[0092]

[0093] in, The residual spectral projection matrix is ​​contributed to the spectrum that was not selected into the explicit mode group.

[0094] The complete frequency response is expressed as:

[0095]

[0096] in, This represents the number of explicit mode groups. For direct feedthrough response, This represents the remaining response that was not explicitly decomposed.

[0097] The residual response includes only the spectral contributions of the frequency response model that were not selected for the explicit mode group. If the frequency response model has an approximation error relative to the reference frequency response model, the model error will be determined separately and will not be included. .

[0098] In this embodiment, the non-negative frequency range is divided into several continuous frequency intervals that together cover all non-negative frequencies. Based on the amplitude and phase correlation characteristics of the same-frequency modal response, the modal responses in the explicit modal response set are paired and screened to obtain actual modal response pairs and unpaired modal responses.

[0099] In this embodiment, the non-negative frequency range is divided into several continuous frequency intervals that collectively cover all non-negative frequencies. Based on the amplitude and phase correlation characteristics of the same-frequency modal responses, the modal responses in the explicit modal response set are paired and screened to obtain actual modal response pairs and unpaired modal responses, including:

[0100] Within the frequency response channel corresponding to the same planning candidate, the same disturbance location, and the same protected node, the real cross term is calculated for the two modal responses in each continuous frequency interval to obtain the corresponding real cross term.

[0101] Pairing condition verification is performed on real cross terms. When a real cross term is not positive and its absolute value is not less than the product of the cancellation coefficient and the amplitude of the two modal responses, the two modal responses are determined as candidate modal response pairs.

[0102] All candidate modal response pairs are deduplicated so that the same modal response belongs to at most one modal response pair, resulting in actual modal response pairs and unpaired modal responses.

[0103] Specifically, the non-negative frequency range is divided into a union of... Several consecutive frequency ranges The endpoints of adjacent intervals are assigned according to predetermined rules to ensure coverage of all frequencies without omissions; the last interval can be taken as... ,in, This is the preset starting point of the high-frequency range.

[0104] For fixed , , and Select two modal responses and ,calculate:

[0105]

[0106] And in Determine the frequency range across all frequencies:

[0107]

[0108] in, The cancellation coefficient is used to represent the degree of quantization of the real cross term relative to the product of the two response amplitudes; when the amplitude of either modal response is zero, the above relationship is not divided by the modulus length and is treated as a continuous relationship.

[0109] Can be within [0,1] Perform a binary search and select the results that pass the above criteria. The lower bound is used as the cancellation coefficient corresponding to this frequency range.

[0110] Two modal responses that satisfy the above relationship are identified as candidate modal response pairs. From these candidate pairs, actual modal response pairs are selected such that the same modal response belongs to at most one modal response pair. Selection can be done sequentially according to a predetermined order, or, without repeating the use of the same modal response, by selecting combinations that result in smaller upper bounds of the interval. Modal responses not selected into actual modal response pairs are included in the unpaired modal response set based on their independent amplitude upper bounds. .

[0111] In this embodiment, a pairing condition check is performed on the real cross term. When the real cross term is non-positive and its absolute value is not less than the product of the cancellation coefficient and the amplitudes of the two modal responses, the two modal responses are determined as a candidate modal response pair, including:

[0112] The upper and lower bounds of the amplitude of the modal response within each continuous frequency range are determined to obtain the upper and lower bounds of the amplitude of each modal response;

[0113] The upper and lower bounds of the amplitude are used to perform interval operations on the real cross terms to obtain the value range of the real cross terms;

[0114] Based on the value interval of the real cross term and the judgment interval of the square difference, the pairing condition is initially judged, and the closed subintervals where the pairing condition cannot be determined are obtained.

[0115] If the closed subinterval is divided into binary iterative partitions and the maximum number of binary partitions or the minimum interval width is still not reached, the modal response pairs in the corresponding subintervals will not be identified as candidate modal response pairs.

[0116] Verification and summarization were completed for all frequency ranges to obtain candidate modal response pairs.

[0117] Specifically, using rational endpoint closed subintervals Construct a complex interval matrix covering each finite frequency range. The interval vector is obtained by solving the complex interval linear equation by rounding out. ,make:

[0118]

[0119] This results in a complex rectangle containing all modal response values:

[0120]

[0121] Determine the lower and upper bounds of the amplitude based on the complex rectangle:

[0122]

[0123] in, Represents the interval from zero to the real region The distance. For coverage Taking the corresponding minimum lower bound and maximum upper bound of all closed subintervals, we obtain and .

[0124] In the same closed subinterval Above, according to and The rounding interval for real cross terms is formed according to the following formula:

[0125]

[0126] The following formula is used to form the judgment interval for the difference of squares without modulus division:

[0127]

[0128] when and When determining the relationship between the real cross term (which is non-positive and whose absolute value is not less than the cancellation coefficient) and the product of the amplitudes of the two modal responses within the closed subinterval, It can be established within. Internal Perform a binary search and select the result that passes the initial judgment. The lower bound is used as the cancellation coefficient.

[0129] If the current interval is too wide to determine the relationship, then... The rational midpoint is bisected and recalculated; if the maximum number of bisections or the minimum interval width given by the calculation accuracy requirements still cannot determine the modal response pair, the two modal responses are not listed as candidate modal response pairs. After the actual modal response pairs are selected, the modal responses that were not selected are counted according to their respective upper bounds of amplitude.

[0130] Therefore, a response amplitude of zero or an indeterminate relationship will not lead to the omission of the corresponding modal response.

[0131] When selecting actual modal response pairs from candidate modal response pairs, the same modal response will be included in at most one modal response pair. Selection can be made sequentially according to a predetermined order, or by selecting combinations that minimize the upper bound of the interval, provided that the same modal response is used repeatedly. Unselected modal responses will be included in the unpaired modal response set. .

[0132] For the actual modal response pairs, calculate the joint amplitude upper bound, replace the sum of the independent amplitude upper bounds of the corresponding two modal responses with the joint amplitude upper bound, and then perform non-repeating synthesis with the amplitude upper bounds of the unpaired modal response, the direct feedthrough response, and the undecomposed residual response to obtain the gain upper bound of each continuous frequency interval; take the maximum value of the gain upper bound of all intervals to obtain the full-frequency response gain upper bound.

[0133] In this embodiment, the joint amplitude upper bound is calculated for the actual modal response pairs. This joint amplitude upper bound is then used to replace the sum of the independent amplitude upper bounds of the corresponding two modal responses. This sum is then synthesized non-repeatingly with the amplitude upper bounds of the unpaired modal response, the direct feedthrough response, and the undecomposed residual response to obtain the gain upper bound for each continuous frequency range. The maximum value of the gain upper bound for all ranges is taken to obtain the full-frequency response gain upper bound, including:

[0134] Determine the upper bounds of the amplitudes of various types of responses within each continuous frequency range, including the upper bounds of the amplitudes of explicit modal responses, residual responses, and direct feedthrough responses;

[0135] Based on the upper and lower bounds of the amplitude of the two modal responses, calculate the joint upper bound of the amplitude for each actual modal response pair;

[0136] The sum of the independent amplitude upper bounds of the corresponding two modal responses is replaced by the joint amplitude upper bound, and non-repeating interval synthesis is performed with the amplitude upper bounds of the unpaired modal response, the direct feedthrough response, and the residual response.

[0137] When the frequency response model used has an approximate error relative to the reference frequency response model, the upper bound of the independently calculated model error amplitude is simultaneously included to obtain the upper bound of the gain for each continuous frequency range.

[0138] The upper bound of the gain is obtained by selecting the maximum value for the upper bound of the gain across all continuous frequency ranges, where the continuous frequency ranges include the unbounded high-frequency range.

[0139] Specifically, for each actual modal response pair, the upper bound of the joint amplitude is calculated:

[0140]

[0141] Calculate the maximum value among the four endpoints of the amplitude range. Alternative .

[0142] The combination of four endpoints is only one recalcible way to calculate the upper bound of the joint amplitude. The premise of the modal response pair calculation is still that the real cross-quantization relationship is satisfied at all frequencies in the continuous frequency range of the same positional frequency response channel.

[0143]

[0144] And determine the upper bound of the full-frequency response gain:

[0145]

[0146] in, For the set of actual modal response pairs, For the set of unpaired modal responses, This represents the upper bound of the residual response amplitude before explicit decomposition; when the frequency response model has an approximation error relative to the reference frequency response model, This is the upper bound of the magnitude of the approximation error; otherwise... Continuous frequency ranges include unbounded high-frequency ranges, therefore It covers all non-negative frequencies.

[0147] The following is a computable finite mathematical example based on the joint upper bound calculation principle. We take a stable model with finite high-frequency gain:

[0148]

[0149] The eigenvalues ​​of this model are and equations The conjugate roots of , whose real parts are all less than zero. Take and We obtain two modal responses determined by the same frequency variable:

[0150]

[0151] The direct feedthrough response and the undecomposed residual response are both zero. The complete response is:

[0152]

[0153] The sum of squared amplitudes and real cross terms of the two modal responses are as follows:

[0154]

[0155]

[0156] Divide non-negative frequencies into and ,calculate Use its closure when it is at the upper bound. .exist Inside, , It is acceptable ;exist Within the closure, , ,and:

[0157]

[0158] Therefore, it is acceptable. .exist Place This ensures that the cross-quantization relationship holds true as a continuous relationship. The calculation yields:

[0159]

[0160] on the other hand, The accurate full-frequency gain of this model is ,satisfy If we take the upper bounds of the two modes separately and then add them together, the resulting upper bound is: The frequency response model in this example is an exact finite-dimensional representation of the reference frequency response model, therefore... , and Take the upper limit of the frequency domain amplitude of the disturbance power. ,Right now And take the node frequency response amplitude limit. When the candidate satisfies other engineering constraints, ,thus It holds true for all non-negative frequencies, and provides an independent upper bound for each mode. .

[0161] This finite mathematical example is used to illustrate that the frequency domain joint upper bound calculation chain is recalculated and maintains upper bound coverage. It does not imply that the real power grid or all planning candidates have the same difference, nor does it imply that the frequency domain gain is the upper bound of the lowest point of the time domain frequency or the maximum instantaneous frequency deviation.

[0162] In this embodiment, determining the upper bound of the amplitude for various responses includes:

[0163] The Riesz projection method is used to calculate the projection matrix of the corresponding invariant subspace of the explicit mode group to obtain the corresponding projection matrix.

[0164] The finite frequency range is divided into sub-intervals based on the projection matrix, and the complex interval linear equations are solved by rounding outwards to obtain the complex rectangular inclusion result of the modal response.

[0165] The unbounded high-frequency interval is transformed into a bounded interval by inverse frequency variable transformation, and the same complex interval solution method is used to calculate the upper bound of the amplitude in the bounded interval.

[0166] Using the same complex interval solution method, the upper bounds of the magnitudes of the residual response and model error are calculated respectively.

[0167] Specifically, select only the area surrounding the first... A closed contour consisting of a modal group and not enclosing other eigenvalues. Calculate the Riesz projection matrix:

[0168]

[0169] in, For complex integral variables.

[0170] For a finite frequency range, the rational endpoint closed sub-interval J is used for coverage. The complex rectangular coverage result of the modal response is obtained by solving the complex interval linear equation with outward rounding, thereby determining the corresponding upper bound of the amplitude.

[0171] For the unbounded high-frequency interval, let ,make Mapped to .

[0172] for , will the The dynamic modal response is written as:

[0173]

[0174] and define The remaining response is subjected to the same inverse frequency transformation and then... Replace with When model errors exist, they are also included in the corresponding error response on the closed-loop frequency sub-interval; the direct feedthrough response is still counted as an independent response component. The unbounded high-frequency interval is one of the continuous frequency intervals, and its upper bound of gain, together with the upper bounds of gain of other intervals, participates in the calculation of the maximum value.

[0175] For the remaining response that is not explicitly decomposed, in each rational endpoint closed subinterval The interval vector is obtained by solving the complex interval linear equation by rounding out. ,make:

[0176]

[0177] Forming a complex rectangle of residual response The upper bound formula for the complex rectangular amplitude is obtained using the same formula as that for the explicit modal response. And order:

[0178]

[0179] in, Traverse the coverage frequency range All closed subintervals. Therefore, the explicit modal response and the spectral contributions of the non-explicitly decomposed modal responses are respectively... and Projection, without double counting.

[0180] When the frequency response model has an approximate error relative to the reference frequency response model, the model error response is defined as follows:

[0181]

[0182] in, The frequency response is the reference frequency response model. The frequency response interval is calculated by rounding outwards. When the reference frequency response model has a finite-dimensional state-space representation, the complex interval responses of the two models are included and the interval difference is calculated to obtain the coverage. The error response complex rectangle is then used to determine:

[0183]

[0184] Depend on The decomposition relationship between explicit modal response and residual response, and the definition of the upper bound of model error magnitude; the upper bound of interval gain covers the frequency response of the reference frequency response model within the corresponding interval; when the frequency response model is an exact finite-dimensional representation of the reference frequency response model, let and .

[0185] Frequency safety constraints are constructed based on the preset upper limit of disturbance power amplitude, the limit of node frequency response amplitude, and the upper limit of full-frequency response gain, and the access nodes and installed capacity of the site are obtained by solving.

[0186] The frequency safety constraint referred to in this invention refers to the limitation of the amplitude of the frequency response components of each protected node at all non-negative frequencies within the spectrum envelope of the active power disturbance under consideration; the frequency safety constraint does not directly characterize the lowest point of time-domain frequency, the maximum instantaneous frequency deviation, or the rate of frequency change.

[0187] In this embodiment, frequency security constraints are constructed based on preset upper limits for disturbance power amplitude, node frequency response amplitude, and full-frequency response gain. These constraints are then used to solve for the site access nodes and installed capacity, including:

[0188] The upper limit of the disturbance power amplitude and the limit of the nodal frequency response amplitude are determined to obtain the constraint boundary parameters;

[0189] Frequency security constraints are constructed for each disturbance location and the corresponding protected node to obtain all frequency security constraints; among them, the frequency security constraints are frequency domain response amplitude constraints.

[0190] The planning objective function is solved within the set of engineering constraints to obtain the access nodes and installed capacity of the power station;

[0191] When planning candidates, power grid operation mode, network topology, or equipment parameters change, the frequency response model, the upper bound of the full-frequency response gain, and the frequency security constraints are recalculated and verified.

[0192] Specifically, the following provides an example of the planning and implementation process for new energy power plants. Assume a multi-node power system includes synchronous generation units and several candidate nodes for new energy power plants, with the set of candidate access nodes being... Select the set of access nodes from it. Configure the installed capacity for each selected node. This forms the planning candidates Let the set of possible active power disturbance locations be . The set of protected nodes is .

[0193] For a planning candidate First, based on the candidate access nodes and installed capacity, the equivalent dynamic parameters and node injection power of the new energy power station are updated. Power flow calculations are then performed to determine the steady-state operating point. After fixing the phase angle of the reference node or eliminating the invariant modes corresponding to the uniform phase angle translation, linearization is completed and a system is formed. , , and Then for each and each Establish Perform mode decomposition and continuous frequency range calculation to obtain the desired result. The upper bound of the full-frequency response gain; then according to Determine the upper limit of the frequency domain amplitude of the disturbance power at each disturbance location, and compare it with the nodal frequency response amplitude limit of each protected node. Frequency security constraints are also incorporated. After verifying all locations and nodes of the current candidates, the planning and solution process changes the set of access nodes or the installed capacity to form new planning candidates. The above model establishment, full-frequency response gain upper bound calculation, and frequency security constraint verification are then re-executed on the new candidates.

[0194] Let the objective function of the program be... The set of engineering constraints is Engineering constraints may include access node availability, single-site capacity upper and lower limits, total installed capacity, power flow balance, branch capacity, and equipment operating range. The planning model is represented as:

[0195] For each planning candidate Each protected node and each perturbation location Construct frequency safety constraints according to the following formula:

[0196] ;

[0197] ;

[0198] ;

[0199]

[0200] ;

[0201] Based on this, the planning optimization model is expressed as:

[0202]

[0203]

[0204]

[0205] ;

[0206] Solving the planning model yields the access nodes and installed capacity of new energy power stations. The planning objective function can be selected based on specific planning tasks, including construction costs, operating costs, network losses, or other predefined planning indicators, but without altering the frequency domain response amplitude safety constraint formed by the upper bound of the full-frequency response gain.

[0207] When candidate access nodes, candidate installed capacity, grid operation mode, network topology, or equipment parameters change, the original frequency response model is not directly used for the new candidate; instead, a new model is built based on the changed parameters. Recalculate And recalibrate the frequency security constraints.

[0208] In other embodiments, a frequency security planning device for new energy power stations based on co-frequency mode correlation is provided, and a frequency security planning method for new energy power stations based on co-frequency mode correlation based on any of the preceding embodiments is provided, including:

[0209] The frequency response model module is configured to establish a finite-dimensional linear time-invariant frequency response model from each active power disturbance location to each protected node for a planning candidate consisting of candidate access nodes and candidate installed capacity.

[0210] The modal response module is configured to perform modal decomposition on the frequency response model to obtain the explicit modal response set and the residual response without explicit decomposition, and to extract the direct feedthrough response;

[0211] The pairing and filtering module is configured to divide the non-negative frequency range into several continuous frequency intervals that jointly cover all non-negative frequencies. Based on the amplitude and phase correlation characteristics of the same-frequency modal response, it performs pairing and filtering on the modal responses in the explicit modal response set to obtain actual modal response pairs and unpaired modal responses.

[0212] The full-frequency response gain upper bound module is configured to calculate the joint amplitude upper bound for the actual modal response pairs, replace the sum of the independent amplitude upper bounds of the corresponding two modal responses with the joint amplitude upper bound, and then perform non-repeating synthesis with the amplitude upper bounds of the unpaired modal response, the direct feedthrough response, and the undecomposed residual response to obtain the gain upper bound of each continuous frequency interval; take the maximum value of the gain upper bound of all intervals to obtain the full-frequency response gain upper bound;

[0213] The solution module is configured to construct frequency safety constraints based on preset upper limits of disturbance power amplitude, node frequency response amplitude, and upper limits of full-frequency response gain, and then solve for the access nodes and installed capacity of the site.

[0214] Specifically, the frequency response model module corresponds to the step of establishing a frequency response model; the modal response component module corresponds to the step of modal decomposition and response extraction; the pairing and screening module corresponds to the step of modal response pairing and screening; the full-frequency response gain upper bound module corresponds to the step of calculating the full-frequency response gain upper bound; and the solution module corresponds to the step of constructing and planning the solution of frequency safety constraints.

[0215] In other embodiments, a terminal is provided, including a processor, an input device, an output device, and a memory, which are interconnected. The memory is used to store a computer program, which includes program instructions. The processor is configured to invoke the program instructions to execute the frequency security planning method for new energy power stations based on co-frequency mode correlation as described above.

[0216] In other embodiments, a computer-readable storage medium is characterized in that it stores a computer program, the computer program including program instructions that, when executed by a processor, cause the processor to perform the frequency security planning method for new energy power stations based on co-frequency mode correlation as described in any of the preceding embodiments.

[0217] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A frequency security planning method for new energy power stations based on co-frequency mode correlation, characterized in that, include: For the planning candidates consisting of candidate access nodes and candidate installed capacity, a finite-dimensional linear time-invariant frequency response model is established from each active power disturbance location to each protected node. Modal decomposition is performed on the frequency response model to obtain the explicit modal response set and the residual response without explicit decomposition, and the direct feedthrough response is extracted. The non-negative frequency range is divided into several continuous frequency intervals that together cover all non-negative frequencies. Based on the amplitude and phase correlation characteristics of the same-frequency modal response, the modal responses in the explicit modal response set are paired and screened to obtain actual modal response pairs and unpaired modal responses. The joint amplitude upper bound is calculated for the actual modal response pair. The sum of the independent amplitude upper bounds of the corresponding two modal responses is replaced by the joint amplitude upper bound. Then, it is synthesized non-repeatingly with the amplitude upper bounds of the unpaired modal response, the direct feedthrough response, and the undecomposed residual response to obtain the gain upper bound of each continuous frequency interval. The maximum value of the gain upper bound of all intervals is taken to obtain the full-frequency response gain upper bound. Frequency safety constraints are constructed based on the preset upper limit of disturbance power amplitude, the limit of node frequency response amplitude, and the upper limit of the full-frequency response gain, and the site access nodes and installed capacity are obtained by solving.

2. The frequency security planning method for new energy power stations based on co-frequency mode correlation according to claim 1, characterized in that, For the planning candidates consisting of candidate access nodes and candidate installed capacity, a finite-dimensional linear time-invariant frequency response model is established from each active power disturbance location to each protected node, including: The equivalent dynamic parameters and nodal injection power of the planned candidate new energy power stations are updated, and power flow calculations are performed on the power grid to obtain the steady-state operating point. Linearize the system components and active power equations at the steady-state operating point, fix the reference node phase angle or eliminate the invariant mode corresponding to the uniform phase angle translation, and obtain the dynamic matrix, disturbance input matrix, frequency response output matrix and direct feedthrough matrix; Port truncation is performed on the disturbance input matrix and frequency response output matrix. The frequency response transfer relationship is constructed by combining the dynamic matrix and the direct feedthrough matrix to obtain a finite-dimensional linear time-invariant frequency response model.

3. The frequency security planning method for new energy power stations based on co-frequency mode correlation according to claim 1, characterized in that, Modal decomposition is performed on the frequency response model to obtain the explicit modal response set and the residual response without explicit decomposition, and the direct feedthrough response is extracted, including: The spectrum of the dynamic matrix is ​​divided into groups to obtain multiple modes that are separate from each other and closed under complex conjugate operations. Explicitly filter the multiple modal groups to obtain explicit modal groups; Calculate the projection matrix for the invariant subspace corresponding to each explicit mode group to obtain the projection matrix corresponding to each explicit mode group; The projection matrices of all explicit mode groups are integrated and calculated to obtain the residual spectrum projection matrix; The dynamic response components of the frequency response model are projected based on the projection matrix of each explicit mode group to obtain the set of explicit modal responses determined by the same frequency variable. Based on the residual spectrum projection matrix, the dynamic response components of the frequency response model are projected and calculated to obtain the residual response that is not explicitly decomposed. The corresponding terms of the direct feedthrough matrix are extracted to obtain the direct feedthrough response.

4. The frequency security planning method for new energy power stations based on co-frequency mode correlation according to claim 1, characterized in that, The non-negative frequency range is divided into several continuous frequency intervals that collectively cover all non-negative frequencies. Based on the amplitude and phase correlation characteristics of the same-frequency modal responses, the modal responses in the explicit modal response set are paired and screened to obtain actual modal response pairs and unpaired modal responses, including: Within the frequency response channel corresponding to the same planning candidate, the same disturbance location, and the same protected node, the real cross term is calculated for the two modal responses in each continuous frequency interval to obtain the corresponding real cross term. The pairing condition is checked on the real cross term. When the real cross term is not positive and its absolute value is not less than the product of the cancellation coefficient and the amplitude of the two modal responses, the two modal responses are determined as candidate modal response pairs. All candidate modal response pairs are deduplicated so that the same modal response belongs to at most one modal response pair, resulting in actual modal response pairs and unpaired modal responses.

5. The frequency security planning method for new energy power stations based on co-frequency mode correlation according to claim 4, characterized in that, The pairing condition is checked on the real cross terms. When the real cross term is non-positive and its absolute value is not less than the product of the cancellation coefficient and the amplitudes of the two modal responses, the two modal responses are determined as candidate modal response pairs, including: The upper and lower bounds of the amplitude of the modal response within each continuous frequency range are determined to obtain the upper and lower bounds of the amplitude of each modal response; The upper and lower bounds of the amplitude are used to perform interval operations on the real cross term to obtain the value range of the real cross term; Based on the value interval of the real cross term and the judgment interval of the square difference, the pairing condition is initially judged, and the closed subintervals where the pairing condition cannot be determined are obtained. If the closed sub-interval is divided into binary iterative sections and the maximum number of binary sections or the minimum interval width is still not reached, then the modal response pairs in the corresponding sub-intervals will not be determined as candidate modal response pairs. Verification and summarization were completed for all frequency ranges to obtain candidate modal response pairs.

6. The frequency security planning method for new energy power stations based on co-frequency mode correlation according to claim 1, characterized in that, The joint amplitude upper bound is calculated for the actual modal response pair. The sum of the independent amplitude upper bounds of the corresponding two modal responses is replaced by the joint amplitude upper bound. Then, it is synthesized non-repeatingly with the amplitude upper bounds of the unpaired modal response, the direct feedthrough response, and the undecomposed residual response to obtain the gain upper bound of each continuous frequency range. The upper bound of the full-frequency response gain is obtained by taking the maximum value of the upper bound of the gain across all intervals, including: Determine the upper bounds of the amplitudes of various types of responses within each continuous frequency range, including the upper bounds of the amplitudes of explicit modal responses, residual responses, and direct feedthrough responses; Based on the upper and lower bounds of the amplitude of the two modal responses, calculate the joint upper bound of the amplitude for each actual modal response pair; The sum of the independent amplitude upper bounds of the corresponding two modal responses is replaced by the joint amplitude upper bound, and non-repeating interval synthesis is performed with the amplitude upper bounds of the unpaired modal response, the direct feedthrough response, and the residual response. When the frequency response model used has an approximate error relative to the reference frequency response model, the upper bound of the independently calculated model error amplitude is simultaneously included to obtain the upper bound of the gain for each continuous frequency range. The upper bound of the gain is obtained by selecting the maximum value of the upper bound of the gain for all continuous frequency ranges, wherein the continuous frequency ranges include the unbounded high frequency range.

7. The frequency security planning method for new energy power stations based on co-frequency mode correlation according to claim 6, characterized in that, The determination of the upper bound of the amplitude for various responses includes: The Riesz projection method is used to calculate the projection matrix of the corresponding invariant subspace of the explicit mode group to obtain the corresponding projection matrix. Based on the projection matrix, the finite frequency range is divided into sub-intervals for coverage. The complex interval linear equations are solved by rounding outwards to obtain the complex rectangular inclusion result of the modal response. The unbounded high-frequency interval is transformed into a bounded interval by inverse frequency variable transformation, and the same complex interval solution method is used to calculate the upper bound of the amplitude of the bounded interval. Using the same complex interval solution method, the upper bounds of the magnitudes of the residual response and model error are calculated respectively.

8. The frequency security planning method for new energy power stations based on co-frequency mode correlation according to claim 1, characterized in that, Frequency security constraints are constructed based on the preset upper limit of disturbance power amplitude, the limit of node frequency response amplitude, and the upper limit of the full-frequency response gain. The resulting data on the access nodes and installed capacity of the power station are then obtained, including: The upper limit of the disturbance power amplitude and the limit of the nodal frequency response amplitude are determined to obtain the constraint boundary parameters; Frequency security constraints are constructed for each disturbance location and the corresponding protected node to obtain all frequency security constraints; wherein, the frequency security constraints are frequency domain response amplitude constraints. The planning objective function is solved within the set of engineering constraints to obtain the access nodes and installed capacity of the power station; When planning candidates, power grid operation mode, network topology, or equipment parameters change, the frequency response model, the upper bound of the full-frequency response gain, and the frequency security constraints are recalculated and verified.

9. A frequency safety planning device for new energy power stations based on co-frequency mode correlation, characterized in that, The frequency security planning method for new energy power stations based on co-frequency mode correlation as described in any one of claims 1 to 8 includes: The frequency response model module is configured to establish a finite-dimensional linear time-invariant frequency response model from each active power disturbance location to each protected node for a planning candidate consisting of candidate access nodes and candidate installed capacity. The modal response module is configured to perform modal decomposition on the frequency response model to obtain an explicit modal response set and a residual response that is not explicitly decomposed, and to extract the direct feedthrough response. The pairing and filtering module is configured to divide the non-negative frequency range into several continuous frequency intervals that jointly cover all non-negative frequencies, and based on the amplitude and phase correlation characteristics of the same-frequency modal responses, to perform pairing and filtering on the modal responses in the explicit modal response set to obtain actual modal response pairs and unpaired modal responses. The full-frequency response gain upper bound module is configured to calculate the joint amplitude upper bound for the actual modal response pairs, replace the sum of the independent amplitude upper bounds of the corresponding two modal responses with the joint amplitude upper bound, and then perform non-repeating synthesis with the amplitude upper bounds of the unpaired modal response, the direct feedthrough response, and the undecomposed residual response to obtain the gain upper bound of each continuous frequency interval; take the maximum value of the gain upper bound of all intervals to obtain the full-frequency response gain upper bound; The solution module is configured to construct frequency security constraints based on the preset upper limit of disturbance power amplitude, the limit of node frequency response amplitude, and the upper limit of the full-frequency response gain, and to solve for the site access nodes and installed capacity.

10. A terminal, characterized in that, The system includes a processor, an input device, an output device, and a memory, which are interconnected. The memory stores a computer program, which includes program instructions. The processor is configured to invoke the program instructions to execute the frequency security planning method for new energy power stations based on co-frequency mode correlation as described in any one of claims 1 to 8.

11. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, the computer program including program instructions, which, when executed by a processor, cause the processor to perform the frequency security planning method for new energy power stations based on co-frequency mode correlation as described in any one of claims 1 to 8.

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