Online calculation method of main and distribution coordination comprehensive stability boundary considering source load uncertainty

Abstract

The application discloses an online calculation method of a main-distribution coordination comprehensive stability boundary considering source-load uncertainty, and belongs to the technical field of power system safety stability analysis and main-distribution coordination operation control. According to the historical prediction error and real-time operation data of new energy output and load, the method adopts a rolling time window to construct a source-load joint uncertainty set; the safety margin under different source-load uncertain operation states is calculated, and the most unfavorable source-load operation state and the limiting safety stability constraint are determined; the accompanying sensitivity is calculated, and the comprehensive stability boundary is tracked in combination with the power consistency relationship of the main-distribution network connection boundary; the boundary point is iteratively determined by combining pseudo-arc length prediction with alternating current power flow and safety stability checking, and the comprehensive stability boundary is updated in rolling according to the real-time source-load state. The method can reduce repeated boundary search and stability calculation under the change of source-load state, and improve the online calculation efficiency and operation state adaptability of the main-distribution coordination comprehensive stability boundary.

Description

Technical Field

[0001] This invention belongs to the field of power system stability control technology, specifically involving an online calculation method for the integrated stability boundary of the main distribution system considering the uncertainty of source load. Background Technology

[0002] Coordination between primary and secondary power sources is becoming an inevitable trend in the development of new power systems. Considering the significant intermittency, volatility, and low reactive power support characteristics of new energy sources (wind and solar power), and their technical characteristics differing greatly from traditional power generation methods, the reactive power regulation capability of the entire power system is limited. Increased uncertainty in the bidirectional interaction between power sources and loads leads to a decrease in static voltage stability, making frequency-voltage coordinated control more difficult, and the identification of stable region boundaries more challenging.

[0003] Existing research has proposed methods for online assessment of static voltage stability in high-proportion renewable energy power systems. However, the critical stability state of a high-proportion renewable energy main-distribution power system is not always determined by a single static voltage stability constraint. Under different renewable energy output, load levels, and main-distribution boundary exchange states, the constraint closest to the system's safety limit may manifest as a static voltage stability constraint, a frequency stability constraint, or a transient voltage recovery constraint. Furthermore, the dominant relationship between different safety and stability constraints may shift as the operating state changes. Therefore, relying solely on a single stability index or a single type of stability margin is insufficient to uniformly describe the comprehensive stability boundary of main-distribution coordination under the combined effect of multiple types of safety and stability constraints, and it is also difficult to accurately identify the safety and stability constraints that truly limit the system's safe operating range under the current operating state.

[0004] On the other hand, existing methods for coordinating transmission and distribution networks typically achieve coordination between the operating states of the main grid and distribution network sides through active and reactive power exchange at the main grid-distribution network interconnection boundary, and meet the power consistency requirements of the main grid-distribution network boundary through power flow calculation, decomposition coordination, or optimization methods. These methods primarily focus on coordinating operating variables and solving operating objectives in the main grid and distribution network. However, for continuous online tracking of the comprehensive stability boundary under the combined effects of multiple security and stability constraints, repeated stability calculations and boundary searches are still required for different boundary operating states. When source load uncertainties continuously change, performing a large-scale boundary scan from the initial operating point for each new source load operating state and executing AC power flow and dynamic stability calculations separately will generate a significant amount of online computation. Furthermore, as the stability boundary operating point changes, the security and stability constraints limiting the safe operating range of the system may switch. If a pre-fixed stability constraint or a fixed boundary search direction is always used, it is difficult to accurately reflect the local variation characteristics of the actual comprehensive stability boundary in the active-reactive power exchange space at the main grid-distribution network interconnection boundary.

[0005] Furthermore, the integrated stability boundary of the main and distribution system is usually a continuously changing nonlinear boundary. There is a certain degree of local continuity and directional correlation between adjacent stability boundary operating points. If the local change information near the obtained stability boundary operating points cannot be effectively utilized, it is necessary to repeatedly search within a large power space of the main and distribution boundary. When the output of new energy sources and the load state change in a rolling manner, if the stability boundary information obtained in the previous calculation period cannot be further utilized, it will also lead to repeated boundary searches and repeated stability calculations, thereby affecting the efficiency of online calculation of the integrated stability boundary.

[0006] Therefore, there is an urgent need for an online calculation method for the integrated stability boundary of the main distribution network that considers the uncertainty of source and load. This method should be able to uniformly evaluate various safety and stability constraints, such as static voltage stability, frequency stability, and transient voltage recovery, under the condition of uncertain changes in renewable energy output and load. It should identify the most unfavorable source and load operating state and restrictive safety and stability constraints, and continuously track the integrated stability boundary of the main distribution network based on the local change information corresponding to the current restrictive safety and stability constraints. While ensuring that the boundary operating point meets the requirements of power consistency, AC power flow, and safety and stability of the main distribution network connection boundary, it should also realize the rolling online update of the integrated stability boundary as the source and load state changes in real time. Summary of the Invention

[0007] This invention addresses the shortcomings of existing integrated stability analysis methods that cannot simultaneously consider source load uncertainty, multiple types of safety and stability constraints, and the characteristics of coordinated operation of the main and distribution networks. It provides an online calculation method for the integrated stability boundary of the main and distribution networks that considers source load uncertainty, so as to achieve the identification of the most unfavorable operating state under uncertain source load conditions, the determination of restrictive safety and stability constraints, and the continuous online tracking of the integrated stability boundary.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: Online calculation methods for the principal-distributor coordinated integrated stability boundary considering source load uncertainties include: S1. Based on the historical prediction errors and real-time operation data of new energy output and load, a joint uncertainty set of source and load is constructed using a rolling time window to determine the uncertain operating states of multiple source and load; S2. Calculate the static voltage stability margin, frequency stability margin, and transient voltage recovery margin under uncertain operating conditions of each source load. Construct a relative safety margin based on the corresponding safety limits. Determine the most unfavorable source load operating condition and restrictive safety and stability constraints based on the minimum relative safety margin. S3. Using the active and reactive power exchange at the main distribution network connection boundary and the active and reactive power regulation of new energy sources as variables, calculate the associated sensitivity corresponding to the restrictive security and stability constraints based on the dynamic differential-algebraic model. S4. Determine the boundary tracking direction based on the accompanying sensitivity and the power consistency relationship between the main and distribution network interconnection boundary, and use the pseudo-arc length prediction method to calculate adjacent candidate boundary points. S5. The candidate boundary points are corrected by the power flow and safety and stability verification, and the comprehensive stable boundary is obtained iteratively. The comprehensive stable boundary is then updated on a rolling basis according to the real-time source load status.

[0009] As an improvement, in S1, historical predicted active power, actual active power, and current real-time operating data of wind power, photovoltaic power, and load are obtained. The source load prediction error is constructed based on the deviation between the actual active power and the corresponding predicted active power in the same time window, forming a source load prediction residual vector. A rolling time window is used to obtain the source load prediction residual vectors at multiple consecutive moments. Based on the variation range of various prediction residuals within the rolling time window and the correlation between different source load prediction residuals, the source load joint uncertainty set corresponding to the current calculation period is constructed.

[0010] As an improvement, in S2, the static voltage stability margin represents the distance between the current operating state and the critical state of static voltage instability; the frequency stability margin is represented by the lowest value of the system frequency after a preset disturbance; and the transient voltage recovery margin is represented by the lowest voltage at the key node or the grid connection point of the new energy power station after a preset disturbance.

[0011] As an improvement, in S2, the distance between different stability margins and the corresponding safety thresholds is processed using a uniform positive and negative direction. When the corresponding safety stability margin is greater than zero, it indicates that the corresponding safety stability constraint still has a safety margin; when it is equal to zero, it indicates that the corresponding stability index has reached the corresponding safety limit; when it is less than zero, it indicates that the corresponding safety stability constraint has been violated. In S2, the minimum value among the static voltage stability margin, frequency stability margin, and transient voltage recovery margin is determined as the relative safety margin. The source load uncertain operating state with the smallest relative safety margin is determined as the most unfavorable source load operating state. The corresponding safety and stability constraint is determined as the restrictive safety and stability constraint. The safety and stability margin corresponding to the restrictive safety and stability constraint is constructed as the restrictive safety and stability constraint function.

[0012] As an improvement, in S3, the dynamic differential-algebraic model is expressed as:

[0013]

[0014] In the formula, Represents dynamic state variables The derivative with respect to time; Represents the dynamic state variables of the main and distribution power systems; Represents algebraic state variables; This represents the power vector exchanged at the boundary between the main and distribution networks; This represents the active and reactive power regulation variables of new energy sources, which consist of the active and reactive power regulation quantities of the new energy equipment involved in the regulation. This indicates the most unfavorable operating state of the source load.

[0015] As an improvement, in S3, the dynamic differential-algebraic model is represented in a unified residual form:

[0016] In the formula, Represents dynamic state variables and algebraic state variables The combined state variables; This represents the residual function corresponding to the dynamic differential-algebraic model of the main and distribution power systems. Based on the linearization relationship of the dynamic differential-algebraic model and the restricted security and stability constraint functions, the adjoint equation is constructed as follows:

[0017] In the formula, Represents the residual function with respect to the combined state variables. The Jacobian matrix; Indicates the accompanying variable; Calculate the accompanying sensitivity of restrictive safety and stability constraints relative to the active and reactive power adjustment variables of new energy sources:

[0018]

[0019] In the formula, It represents the accompanying sensitivity corresponding to the switching power at the main distribution network boundary, which is used to determine the local tracking direction of the stable boundary in the active-reactive switching power plane at the main distribution network boundary. This represents the accompanying sensitivity corresponding to the active and reactive power adjustment variables of new energy sources, used to characterize the local impact of changes in the active and reactive power adjustment quantities of new energy sources on the current restrictive safety and stability constraints.

[0020] As an improvement, in S4, let the first... The principal and secondary boundary adjoint sensitivities corresponding to each stable boundary operating point are:

[0021] In the formula, and These represent the accompanying sensitivity components of the current restrictive security and stability constraints relative to the active power exchange and reactive power exchange at the primary and secondary boundaries, respectively. exist At that time, the boundary tangent vector corresponding to the current stable boundary operating point is determined based on its active and reactive components:

[0022] In the formula, Indicates the first Boundary tangent vector at each stable boundary running point; Represents the direction coefficient, taken as... or This is used to maintain the continuity of the tracking direction of adjacent stable boundary tangent vectors.

[0023] As an improvement, in S4, based on the current stable boundary running point, the adjacent stable boundary prediction points are determined along the boundary tangent vector according to the pseudo-arc length prediction step size:

[0024] In the formula, Indicates the first The primary and secondary boundary exchange power vectors corresponding to each stable boundary running point; This represents the predicted adjacent stable boundary points; Indicates the first The pseudo-arc length prediction step size used in secondary boundary tracking; The direction coefficient is selected based on the directional relationship between adjacent stable boundary tangent vectors. This ensures that the continuously obtained stable boundary prediction points are sequentially expanded along the same tracking direction, avoiding back-and-forth jumps during the boundary tracking process.

[0025] As an improvement, in S5, candidate boundary points are iteratively corrected based on AC power flow conditions, primary and secondary boundary power consistency conditions, stability boundary conditions corresponding to the current restrictive security and stability constraints, and pseudo-arc length correction conditions.

[0026] As an improvement, in S5, when the candidate point cannot meet the correction conditions, the pseudo-arc length prediction step size is adjusted and the prediction and correction are performed again. In S5, after entering the next calculation period, the joint uncertainty set of source loads is updated according to the latest real-time source load operation data, and the most unfavorable uncertain operating state of source loads, restrictive safety and stability constraints, and corresponding accompanying sensitivity parameters are re-determined. The stable boundary operating point obtained in the previous calculation period is used as the initial information to realize the rolling online update of the main and auxiliary coordinated integrated stability boundary.

[0027] The beneficial effects of the online calculation method for the main-distribution coordinated comprehensive stability boundary considering the uncertainty of source and load in this invention are as follows: by constructing a joint uncertainty set of source and load and performing rolling updates, the adaptability of the comprehensive stability boundary calculation to the output of new energy sources and load changes is improved; by jointly evaluating multiple types of safety and stability margins, the identification of the most unfavorable uncertain operating state of source and load and restrictive safety and stability constraints is achieved; by using the accompanying sensitivity and pseudo-arc length prediction methods, the continuous tracking of the main-distribution coordinated comprehensive stability boundary is achieved; by using AC power flow correction and safety and stability verification, the online calculation and rolling update of the comprehensive stability boundary are achieved; it can reduce repeated boundary searches and stability calculations under changes in source and load states, improve the efficiency of online calculation of the main-distribution coordinated comprehensive stability boundary and the adaptability of operating states, and is suitable for the online calculation of the safety and stability operating boundary of a high proportion of new energy main-distribution power system. Attached Figure Description

[0028] Figure 1 This is a flowchart of an online calculation method for the main-component cooperative integrated stability boundary considering source load uncertainty, according to an embodiment of the present invention.

[0029] Figure 2 This is a circuit diagram of the master-slave collaborative testing system according to an embodiment of the present invention.

[0030] Figure 3(a) shows the convergence curves of the power consistency residuals of the master and slave boundary and the stability boundary check residuals.

[0031] Figure 3(b) shows the curves of normalized safety margin and relative safety margin under continuous operating state changes.

[0032] Figure 3(c) shows the projection of the discrete point set of the stable boundary under different source load uncertain states onto the active-reactive plane of the principal-subordinate boundary. Detailed Implementation

[0033] The technical solutions of the embodiments of the present invention will be explained and described below. However, the following embodiments are only preferred embodiments of the present invention and not all of them. Other embodiments obtained by those skilled in the art based on the embodiments in the implementation methods without creative effort are all within the protection scope of the present invention.

[0034] See Figure 1 The online calculation method for the principal-distributor cooperative integrated stability boundary considering source load uncertainty in this invention includes: S1. Based on the historical prediction errors and real-time operation data of new energy output and load, a joint uncertainty set of source and load is constructed using a rolling time window to determine the uncertain operating states of multiple source and load; S2. Calculate the static voltage stability margin, frequency stability margin, and transient voltage recovery margin under uncertain operating conditions of each source load. Construct a relative safety margin based on the corresponding safety limits. Determine the most unfavorable source load operating condition and restrictive safety and stability constraints based on the minimum relative safety margin. S3. Using the active and reactive power exchange at the main distribution network connection boundary and the active and reactive power regulation of new energy sources as variables, calculate the associated sensitivity corresponding to the restrictive security and stability constraints based on the dynamic differential-algebraic model. S4. Determine the boundary tracking direction based on the accompanying sensitivity and the power consistency relationship between the main and distribution network interconnection boundary, and use the pseudo-arc length prediction method to calculate adjacent candidate boundary points. S5. The candidate boundary points are corrected by the power flow and safety and stability verification, and the comprehensive stable boundary is obtained iteratively. The comprehensive stable boundary is then updated on a rolling basis according to the real-time source load status.

[0035] The online calculation method for the integrated stability boundary of the main and distribution systems, considering the uncertainty of source and load, improves the adaptability of the integrated stability boundary calculation to changes in new energy output and load by constructing a joint uncertainty set of source and load and performing rolling updates; it achieves the identification of the most unfavorable uncertain operating state of source and load and restrictive safety and stability constraints through joint evaluation of multiple types of safety and stability margins; it achieves continuous tracking of the integrated stability boundary of the main and distribution systems through adjoint sensitivity and pseudo-arc length prediction methods; and it achieves online calculation and rolling updates of the integrated stability boundary through AC power flow correction and safety and stability verification.

[0036] Example 1 See Figure 1 The online calculation method for the principal-assigned cooperative integrated stability boundary considering source load uncertainty in Embodiment 1 of the present invention includes: S1. Based on the historical prediction errors of new energy output and load and real-time operation data, a rolling time window is used to construct a joint uncertainty set of source and load, and determine the uncertain operating states of multiple source and load.

[0037] In this embodiment, in S1, the historical predicted active power, actual active power, and current real-time operating data of wind power, photovoltaic power, and load are obtained, and the source-load prediction error is constructed based on the deviation between the actual active power and the corresponding predicted active power in the same time window.

[0038] For the Source object of class, at time The actual active power is expressed as:

[0039] In the formula, This indicates that the first type of source payload object is at time t. The actual active power; This represents the corresponding predicted active power; Indicates the predicted residual; This indicates the type of source / load object, including wind power, solar power, and load.

[0040] In practice, the prediction errors corresponding to wind power, photovoltaic power, and load at the same time point are combined to form a source-load prediction error vector:

[0041] In the formula, , and represent the active power prediction residuals of wind power, photovoltaic power, and load at time t, respectively; superscript This indicates transpose.

[0042] Furthermore, a rolling time window is used to obtain the source load prediction residual vectors at multiple consecutive time points. Based on the variation range of various prediction residuals within the rolling time window and the correlation between different source load prediction residuals, a joint uncertainty set of source loads corresponding to the current calculation period is constructed. .

[0043] The source-load joint uncertainty set is used to characterize the range of joint changes that may be formed by wind power, photovoltaic and load forecast residuals within the current calculation period. This allows the correlation between the changes in new energy output and load changes to be included in the subsequent safety and stability analysis, rather than treating different source-load objects as independent uncertainties.

[0044] In practice, multiple uncertain operating states of the source loads that can reflect the current range of source load changes and their correlations are determined within the joint uncertainty set of the source loads:

[0045] In the formula, This indicates the uncertain operating state of the i-th source load; This indicates the number of uncertain operating states of the source load corresponding to the current calculation period.

[0046] Based on the predicted residual vectors in the uncertain operating states of each source load and the predicted active power at the current moment, the actual active power of wind power, photovoltaic power and load in each state is determined, and the physical operating state corresponding to the subsequent safe and stable calculation is formed.

[0047] When new actual operating data enters the rolling time window, the prediction residuals are recalculated based on the latest actual active power of wind power, photovoltaic power and load and the corresponding predicted active power. The earliest prediction residual sample in the rolling time window is deleted, and the range of change and correlation of the prediction residuals are re-determined using the latest prediction residuals, thereby updating the source-load joint uncertainty set and the corresponding multiple source-load uncertain operating states.

[0048] This allows the joint uncertainty set of source loads to be updated in a rolling manner as the actual source load prediction error changes, and the determined uncertain operating states of multiple source loads are used as inputs for the calculation of each stability margin in S2.

[0049] S2. Calculate the static voltage stability margin, frequency stability margin, and transient voltage recovery margin under uncertain operating conditions of each source load. Construct a relative safety margin based on the corresponding safety limits. Determine the most unfavorable source load operating state and restrictive safety and stability constraints based on the minimum relative safety margin.

[0050] In this embodiment, in S2, when implemented in practice, safety and stability calculations are performed on each source load under uncertain operating conditions determined in S1 to obtain the corresponding static voltage stability index (static voltage stability margin), the lowest system frequency after the preset disturbance (frequency stability margin), and the lowest voltage during the transient voltage recovery process of key nodes or new energy power station grid connection points after the preset disturbance (transient voltage recovery margin).

[0051] Regarding the first For an uncertain operating state of a source load, its static voltage stability margin is expressed as:

[0052] In the formula, Indicates the first Static voltage stability margin under uncertain operating conditions of individual source loads; This indicates the static voltage stability index under the corresponding operating conditions; Indicates the static voltage stability safety limit; This represents the positive normalized scale corresponding to the static voltage stability index.

[0053] In practice, the safety limits of the static voltage stability index are determined based on the target power system operation procedures, stability criteria, and simulation model configuration.

[0054] For the first A preset disturbance is applied to an uncertain operating state of a source load, and the lowest system frequency during the disturbance is obtained through dynamic time-domain calculation. The corresponding frequency stability margin is expressed as:

[0055] In the formula, Indicates the first Frequency stability margin under uncertain operating conditions of individual source loads; Indicates the lowest system frequency after the preset disturbance effect; This indicates the system's minimum frequency safety limit; This represents the positive normalization scale corresponding to the frequency stability index.

[0056] The minimum voltage is determined based on the transient voltage recovery process at key nodes or grid connection points of new energy power plants after a preset disturbance. The corresponding transient voltage recovery margin is expressed as:

[0057] In the formula, Indicates the first Transient voltage recovery margin under uncertain operating conditions of individual source loads; This indicates the lowest voltage during the transient voltage recovery process at key nodes or grid connection points of new energy power plants after a preset disturbance. Indicates the safety limit for transient voltage; This represents the positive normalized scale corresponding to the transient voltage stability index.

[0058] In practice, the static voltage stability margin, frequency stability margin, and transient voltage recovery margin are treated with a uniform positive and negative direction. When the corresponding safety stability margin is greater than zero, it means that the corresponding safety stability constraint still has a safety margin; when it is equal to zero, it means that the corresponding stability index has reached the corresponding safety limit; when it is less than zero, it means that the corresponding safety stability constraint has been violated.

[0059] Regarding the first For an uncertain operating state of a source load, the minimum value among the static voltage stability margin, frequency stability margin, and transient voltage recovery margin is determined as the relative safety margin:

[0060] In the formula, Indicates the first The relative safety margin corresponding to the uncertain operating state of each source load is used to characterize the relative distance between the current operating state and the safety and stability constraint that will first reach the safety limit.

[0061] The source load uncertain operating state with the smallest relative safety margin is determined as the most unfavorable source load operating state:

[0062] In the formula, This indicates the number of the most unfavorable source load operating state.

[0063] Under the most unfavorable source load operating conditions, the safety and stability constraint corresponding to the smallest safety and stability margin among the static voltage stability margin, frequency stability margin, and transient voltage recovery margin is determined as the restrictive safety and stability constraint:

[0064] In the formula, Indicates the current type of restrictive safety and stability constraints; , and These represent static voltage stability constraints, frequency stability constraints, and transient voltage recovery constraints, respectively.

[0065] In practice, the security and stability margins corresponding to the restrictive security and stability constraints are constructed as restrictive security and stability constraint functions. ,when: When the current restrictive safety and stability constraint reaches the corresponding safety limit, the corresponding operating state is on the stable boundary determined by the restrictive safety and stability constraint.

[0066] Therefore, the most unfavorable source load operating state and restrictive safety and stability constraints are determined based on the actual distance between different safety and stability margins and corresponding safety limits under the current uncertain source load conditions, instead of pre-fixing a certain type of stability constraint as the sole limiting factor of the comprehensive stability boundary.

[0067] S3. Using the active and reactive power exchange quantities at the main distribution network connection boundary and the active and reactive power regulation quantities of new energy sources as variables, calculate the associated sensitivity corresponding to the restrictive security and stability constraints based on the dynamic differential-algebraic model.

[0068] In this embodiment, in S3, specifically, a dynamic differential-algebraic model of the main and distribution power systems is established for the most unfavorable source load operating state determined in S2: Represents dynamic state variables The derivative with respect to time;

[0069]

[0070] In the formula, Represents dynamic state variables The derivative with respect to time; Represents the dynamic state variables of the main and distribution power systems; Represents algebraic state variables; This represents the power vector exchanged at the boundary between the main and distribution networks; This represents the active and reactive power regulation variables of new energy sources, which consist of the active and reactive power regulation quantities of the new energy equipment involved in the regulation. This represents the most unfavorable source load operating state determined by S2.

[0071] The power vector of the main and distribution network interconnection boundary is represented as:

[0072] In the formula, and These represent the active power exchange and reactive power exchange at the main and distribution network interconnection boundaries, determined according to the unified power positive direction.

[0073] The above dynamic differential-algebraic model can be expressed in a unified residual form:

[0074] In the formula, Represents dynamic state variables and algebraic state variables The combined state variables; This represents the residual function corresponding to the dynamic differential-algebraic model of the main and distribution power systems.

[0075] In practice, the adjoint equations are constructed based on the linearization relationship of the dynamic differential-algebraic model and the restrictive safety and stability constraint functions:

[0076] In the formula, Represents the residual function with respect to the combined state variables. The Jacobian matrix; This indicates an accompanying variable.

[0077] Calculate the accompanying sensitivity of restrictive safety and stability constraints relative to the active and reactive power adjustment variables of new energy sources:

[0078]

[0079] In the formula, It represents the accompanying sensitivity corresponding to the switching power at the main distribution network boundary, which is used to determine the local tracking direction of the stable boundary in the active-reactive switching power plane at the main distribution network boundary. This represents the accompanying sensitivity corresponding to the active and reactive power adjustment variables of new energy sources, used to characterize the local impact of changes in the active and reactive power adjustment quantities of new energy sources on the current restrictive safety and stability constraints.

[0080] Accompanying sensitivity of switching power at the main and distribution network interconnection boundary Used to determine the local tracking direction of the stability boundary within the active-reactive power exchange plane at the primary and secondary boundaries; accompanying sensitivity of the active and reactive power regulation variables of new energy sources. It is used to reflect the local interaction between the active and reactive power regulation directions of different new energy sources and the current restrictive safety and stability constraints.

[0081] In practice, during the stability boundary tracking process, static voltage stability, frequency stability, and transient voltage recovery calculations are recalculated for the current stability boundary operating point, and the restrictive safety and stability constraints corresponding to the current operating point are redefined.

[0082] When the restrictive safety and stability constraints at the current stable boundary operating point change relative to the previous stable boundary operating point, the restrictive safety and stability constraint function in the adjoint equation is switched to the constraint function corresponding to the current restrictive safety and stability constraint, and the adjoint variables and adjoint sensitivities are resolved according to the dynamic differential-algebraic model corresponding to the current stable boundary operating point.

[0083] This allows the local tracking direction of the integrated stability boundary to change according to the actual safety and stability constraints that limit the safe operating range of the system.

[0084] S4. Determine the boundary tracking direction based on the accompanying sensitivity and the power consistency relationship between the main and distribution network connection boundaries, and use the pseudo-arc length prediction method to calculate adjacent candidate boundary points.

[0085] In this embodiment, in S4, the power exchanged at the main and distribution network interconnection boundaries corresponding to the transmission network side and the distribution network side is converted to a unified positive power direction, and the power consistency residual at the main and distribution network interconnection boundaries is determined based on the active and reactive power exchanged on both sides for the same main and distribution network interconnection boundary.

[0086] In the formula, Indicates the first The primary and secondary boundary power consistency residuals corresponding to each stable boundary operating point; and These represent the active and reactive power exchange at the main and distribution network interconnection boundaries calculated from the transmission network side, respectively. and These represent the active and reactive power exchange at the main distribution network interconnection boundary calculated from the distribution network side.

[0087] Let the first The principal and secondary boundary adjoint sensitivities corresponding to each stable boundary operating point are:

[0088] In the formula, and These represent the accompanying sensitivity components of the current restrictive security and stability constraints relative to the active power exchange and reactive power exchange at the primary and secondary boundaries, respectively.

[0089] Since the accompanying sensitivity characterizes the local variation direction of the current restrictive security and stability constraint function in the active-reactive power exchange plane of the primary-secondary boundary, therefore, in At that time, the boundary tangent vector corresponding to the current stable boundary operating point is determined based on its active and reactive components:

[0090] In the formula, Indicates the first Boundary tangent vector at each stable boundary running point; Represents the direction coefficient, taken as... or This is used to maintain the continuity of the tracking direction of adjacent stable boundary tangent vectors.

[0091] Furthermore, using the current stable boundary running point as a reference, the adjacent stable boundary prediction points are determined along the boundary tangent vector according to the pseudo-arc length prediction step size:

[0092] In the formula, Indicates the first The primary and secondary boundary exchange power vectors corresponding to each stable boundary running point; This represents the predicted adjacent stable boundary points; Indicates the first The pseudo-arc length prediction step size is used in the secondary boundary tracing.

[0093] In practice, the direction coefficient is selected based on the directional relationship between adjacent stable boundary tangent vectors. This ensures that the continuously obtained stable boundary prediction points are sequentially expanded along the same tracking direction, avoiding back-and-forth jumps during the boundary tracking process.

[0094] Therefore, the local tangential direction of the stable boundary can be directly obtained based on the local accompanying sensitivity corresponding to the current restrictive safety and stability constraints, and the adjacent candidate boundary points can be predicted based on the already obtained stable boundary operating points, thereby reducing the amount of computation required to repeatedly perform large-scale point-by-point searches within the entire active-reactive power exchange range of the main and auxiliary boundaries.

[0095] S5. The candidate boundary points are corrected by the power flow and safety and stability verification, and the comprehensive stable boundary is obtained iteratively. The comprehensive stable boundary is then updated on a rolling basis according to the real-time source load status.

[0096] Since the candidate points obtained in step S4 are predicted values, they may not strictly satisfy the actual operating and stability boundary conditions of the system, therefore further correction is required. The correction mainly considers four types of conditions: 1. AC power flow conditions are used to ensure that the candidate operating states satisfy the active and reactive power balance of the system and the network power flow relationship. After correction, the node voltage, branch power flow, main distribution boundary exchange power and new energy operating status are obtained by resolving the AC power flow, ensuring that the corrected candidate points are physically realizable. 2. The power consistency condition of the main and distribution boundary corresponds to the power consistency residual of the main and distribution boundary defined in S4. During the correction process, by reducing this residual, the active and reactive power exchanged by the transmission network side and the distribution network side for the same tie boundary are consistent. 3. The current restrictive safety and stability constraints correspond to the stability boundary conditions, which correspond to the restrictive safety and stability constraint functions constructed in S2. When the constraint function reaches the boundary conditions, it means that the corresponding safety and stability index has just reached the safety limit, ensuring that the restrictive safety and stability index corresponding to the candidate operating state reaches its safety limit, that is, the candidate point is located on the stability boundary. 4. Pseudo-arc length correction condition, corresponding to the boundary tangent vector and pseudo-arc length prediction relationship established in S4, is used to ensure that the corrected point is the adjacent boundary point obtained along the current boundary tracing direction, avoiding returning to the previous boundary point or unconstrained drift along the boundary.

[0097] In this embodiment, in S5, when implemented in practice, the adjacent candidate boundary points obtained in S4 are used as the initial values ​​for correction, and the candidate boundary points are iteratively corrected according to the AC power flow conditions, the primary and secondary boundary power consistency conditions, the stability boundary conditions corresponding to the current restrictive safety and stability constraints, and the pseudo-arc length correction conditions.

[0098] No. The candidate physics operating state after the second correction is represented as follows:

[0099] In the formula, Indicates the first The candidate physical operating state corresponding to the next correction; It represents the state correction quantity determined based on AC power flow conditions, primary and secondary boundary power consistency conditions, stability boundary conditions, and pseudo-arc length correction conditions.

[0100] In practice, the AC power flow equations are solved for the corrected candidate physical operating states to obtain the corresponding node voltages, branch active and reactive power flows, main and distribution boundary exchange power, and active and reactive power operating states of new energy sources. Static voltage stability, frequency stability, and transient voltage recovery calculations are then performed again.

[0101] When the recalculated restrictive safety and stability constraints change relative to the previous stable boundary operating point, the restrictive safety and stability constraint function is redefined according to S3 and the corresponding associated sensitivity is recalculated. Then, subsequent boundary point prediction and correction are performed based on the updated associated sensitivity.

[0102] When the AC power flow does not converge, the candidate physical operating state violates the preset node voltage, line power flow, equipment capacity, or new energy operation constraints, or the stability boundary correction condition cannot be met within the preset number of corrections, the current pseudo-arc length prediction step size is reduced:

[0103] In the formula, This represents the reduced pseudo-arc length prediction step size; This represents the step size reduction factor, and .

[0104] After reducing the prediction step size, the prediction and correction of adjacent boundary points are re-executed using the current stable boundary running point.

[0105] Furthermore, for the corrected candidate stable boundary points, the power consistency residuals of the primary and secondary boundaries are recalculated, and the constraint function values ​​corresponding to the current restrictive safety and stability constraints are determined as the stable boundary verification residuals.

[0106] In the formula, This represents the residual for stability boundary verification.

[0107] When both conditions are met:

[0108] as well as:

[0109] Furthermore, when the candidate physical operating state satisfies the AC power flow equation and the preset operating constraints, the candidate boundary point is determined as the stable boundary operating point.

[0110] In the formula, This represents the convergence threshold of the primary-secondary boundary power consistency residual; This represents the convergence threshold of the residuals for stability boundary verification. This represents the 2-norm of a vector.

[0111] When the corrected candidate point meets the convergence threshold of the primary and secondary boundary power consistency residual and the stability boundary verification residual, and meets the AC power flow and preset operating constraints, the point is accepted as the new stability boundary operating point; if it does not meet the requirements, the correction continues, and if the preset number of corrections is still not met, the pseudo-arc length prediction step size is reduced and the prediction is restarted.

[0112] After obtaining the new stable boundary running point, the prediction of S4 and the correction of S5 are repeated based on this point, so as to obtain the set of stable boundary points for the current calculation period point by point.

[0113] In practice, starting from one or more initial stable boundary points, S4 and S5 are executed continuously along the stable boundary to obtain multiple stable boundary points corresponding to the current computation time period, forming a stable boundary point set for the current computation time period:

[0114] In the formula, This represents the set of principal-alternate collaborative stability boundary points corresponding to the current calculation period; This indicates the number of stable boundary operating points determined.

[0115] After entering the next calculation period, the source-load joint uncertainty set is updated based on the latest actual operating data in the rolling time window. S2 is re-executed to determine the updated most unfavorable source-load state and restrictive safety and stability constraints, and the associated sensitivity is recalculated. The stability boundary point set of the previous calculation period is used as the initial information for stability boundary tracking in the next calculation period. S3 to S5 are repeated to obtain the updated stability boundary point set, realizing the rolling online update of the primary and secondary cooperative stability boundary.

[0116] To further verify the effectiveness of the online calculation method for the principal-assigned cooperative integrated stability boundary considering source load uncertainties in this embodiment, a... Figure 2 The diagram shows the main and distribution network coordinated testing system circuit. The testing system adopts a 39-node structure with a voltage level of 220kV, while the distribution network adopts a 33-node structure with a voltage level of 10kV. The 18 nodes of the main network and the 1 node of the distribution network constitute the main and distribution network boundary nodes.

[0117] The settings for continuous operation status changes are shown in Table 1.

[0118] Table 1 Continuous Operation Status Change Settings

[0119] The online calculation method for the principal-assigned cooperative integrated stability boundary, considering the uncertainty of source loads in this embodiment, is used to... Figure 2 The system shown is used for calculation, and the results are as follows: Figures 3(a) to 3(c) As shown.

[0120] Figure 3(a) shows the changes in the power consistency residuals of the primary and secondary boundary and the stability boundary verification residuals during the candidate boundary point correction process. After the candidate stable boundary points are obtained through pseudo-arc length prediction, they are iteratively corrected using the AC power flow conditions, the power consistency conditions of the primary and secondary boundary, and the boundary conditions corresponding to the restrictive safety and stability constraints. As the correction process progresses, the power consistency residuals of the primary and secondary boundary and the stability boundary verification residuals gradually decrease.

[0121] When the residual of primary and secondary boundary power consistency is less than the corresponding convergence threshold, the residual of stability boundary verification is less than the corresponding convergence threshold, and the corresponding candidate physical operating state satisfies the AC power flow equation and preset operating constraints, the candidate boundary point is determined as the stable boundary operating point. This demonstrates that by combining pseudo-arc length prediction with physical operating state correction, the predicted candidate points can gradually regress to physical operating states that satisfy the primary and secondary boundary power consistency and safe and stable boundary conditions. (Primary and secondary boundary power consistency residual convergence threshold) Set to 0.0025; stability boundary check residual convergence threshold Set to 0.0030. After 8 iterations, the candidate physical operating state satisfies the AC power flow equation and the preset operating constraints, and the candidate boundary point is determined as the stable boundary operating point.

[0122] Figure 3(b) shows the changes in static voltage stability margin, frequency stability margin, transient voltage recovery margin, and relative safety margin during continuous operation.

[0123] When changes occur in photovoltaic output, wind power fluctuations, distribution network load, and main distribution boundary operating conditions, the distance between various safety and stability margins and their corresponding safety limits changes accordingly. The safety and stability margin with the smallest value may also change, causing restrictive safety and stability constraints to switch at different operating stages.

[0124] When the restrictive safety and stability constraints change, the adjoint equation is reconstructed using the constraint function corresponding to the current restrictive safety and stability constraints, and the adjoint sensitivity is calculated. This ensures that the subsequent stability boundary prediction direction can reflect the stability factors that currently limit the safe operating range of the system, rather than using fixed stability constraints throughout the entire boundary tracking process.

[0125] Figure 3(c) shows the projection results of the integrated stability boundary point set of the main and distribution forces under different uncertain operating conditions of source loads onto the active-reactive power exchange plane of the main and distribution boundaries. It can be seen that there are differences in the location of the stability boundary and the allowable power exchange range of the main and distribution boundaries corresponding to different uncertain operating conditions of source loads.

[0126] When the output of new energy sources or the load of the distribution network changes, the active-reactive power exchange range of the main and distribution boundaries that satisfy the constraints of static voltage stability, frequency stability, and transient voltage recovery changes accordingly. Upon entering the next calculation period, the set of stable boundary points from the previous calculation period is used as the new initial information for stability boundary tracking. Prediction and correction continue based on the updated source-load joint uncertainty set and restrictive security and stability constraints. This avoids having to perform a complete stability boundary search from the initial operating state again after changes in source-load conditions.

[0127] Furthermore, to verify the ability of the accompanying sensitivity of the active and reactive power regulation variables of new energy sources to characterize the local change direction of the current restrictive security and stability constraints, under the condition that the total scale of new energy regulation resources is basically the same, fixed values ​​are used respectively. The three methods of allocation, allocation based on equipment margin, and adjustment based on the direction of accompanying sensitivity are compared.

[0128] The system stability characteristics under different active-reactive power regulation modes of new energy sources are shown in Table 2.

[0129] Table 2 Comparison of System Stability Characteristics under Different Active and Reactive Power Regulation Methods from Different New Energy Sources

[0130] As shown in Table 2, under the condition that the total scale of active and reactive power regulation resources of new energy is basically the same, fixed The lowest system frequency corresponding to the allocation method is 48.87Hz, and the lowest voltage at the grid connection point of the new energy power station is 0.918pu; when allocating according to the remaining regulation capacity of the equipment, the lowest system frequency is 49.01Hz, and the lowest voltage at the grid connection point of the new energy power station is 0.937pu; when active and reactive power regulation is carried out according to the direction of local change of the current limiting safety and stability constraints reflected by the accompanying sensitivity, the lowest system frequency increases to 49.16Hz, and the lowest voltage at the grid connection point of the new energy power station increases to 0.958pu.

[0131] The beneficial effects of the online calculation method for the integrated stability boundary of the main distribution system considering source-load uncertainty in Embodiment 1 of this invention are as follows: The source-load joint uncertainty set is updated via a rolling time window, allowing the stability boundary calculation to be adjusted according to changes in wind power, photovoltaic, and load forecasting errors; the most unfavorable source-load operating state and restrictive safety and stability constraints are determined through a unified comparison of static voltage stability margin, frequency stability margin, and transient voltage recovery margin; the local change direction of the main distribution boundary is obtained through the accompanying sensitivity corresponding to the restrictive safety and stability constraints; based on this, pseudo-arc length prediction, AC power flow correction, and safety and stability verification are used to continuously determine the stability boundary operating points, and the stability boundary point set of the previous calculation period is used as the initial reference information for the next calculation period, thereby realizing online calculation and rolling update of the integrated stability boundary of the main distribution system considering source-load uncertainty; it can reduce repeated boundary searches and stability calculations under source-load state changes, improve the efficiency of online calculation of the integrated stability boundary of the main distribution system and the adaptability of operating states, and is suitable for online calculation of the safety and stability operating boundary of a high-proportion renewable energy main distribution power system.

[0132] This invention also discloses an online calculation system for stable boundary characteristics under master-slave cooperation, comprising: The source-load joint uncertainty set construction module is used to construct the source-load joint uncertainty set based on the historical prediction errors and real-time operation data of new energy output and load using a rolling time window, and to determine the uncertain operating states of multiple source loads. The stability margin calculation module is used to calculate the static voltage stability margin, frequency stability margin, and transient voltage recovery margin under uncertain operating conditions of each source load. It constructs a relative safety margin based on the corresponding safety limits and determines the most unfavorable source load operating state and restrictive safety and stability constraints with the minimum relative safety margin. The accompanying sensitivity calculation module is used to calculate the accompanying sensitivity corresponding to the restrictive security and stability constraints based on a dynamic differential-algebraic model, using the active and reactive power exchange quantities at the main distribution network connection boundary and the active and reactive power regulation quantities of new energy sources as variables. The boundary tracking direction and candidate boundary point module is used to determine the boundary tracking direction based on the accompanying sensitivity and the power consistency relationship between the main and distribution network interconnection boundary, and to calculate the adjacent candidate boundary points using the pseudo-arc length prediction method. The calibration and update module is used to calibrate candidate boundary points through AC power flow and safety and stability verification, iteratively obtain the comprehensive stable boundary, and continuously update the comprehensive stable boundary according to the real-time source load status.

[0133] This invention also discloses a computer device, including a processor and a storage medium, wherein the storage medium stores a computer program, and when the computer program is executed by the processor, it implements the aforementioned online calculation method for the main-component cooperative integrated stability boundary considering source load uncertainty.

[0134] This invention also discloses a computer-readable storage medium storing a computer program that, when executed, implements the aforementioned online calculation method for the main-allocation cooperative integrated stability boundary considering source load uncertainty.

[0135] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Those skilled in the art should understand that the present invention includes, but is not limited to, the content described in the above specific embodiments. Any modifications that do not depart from the functional and structural principles of the present invention will be included within the scope of the claims.

Claims

1. An online calculation method for the principal-distributor coordinated integrated stability boundary considering source load uncertainty, characterized in that: include: S1. Based on the historical prediction errors and real-time operation data of new energy output and load, a joint uncertainty set of source and load is constructed using a rolling time window to determine the uncertain operating states of multiple source and load; S2. Calculate the static voltage stability margin, frequency stability margin, and transient voltage recovery margin under uncertain operating conditions of each source load. Construct a relative safety margin based on the corresponding safety limits. Determine the most unfavorable source load operating condition and restrictive safety and stability constraints based on the minimum relative safety margin. S3. Using the active and reactive power exchange at the main distribution network connection boundary and the active and reactive power regulation of new energy sources as variables, calculate the associated sensitivity corresponding to the restrictive security and stability constraints based on the dynamic differential-algebraic model. S4. Determine the boundary tracking direction based on the accompanying sensitivity and the power consistency relationship between the main and distribution network interconnection boundary, and use the pseudo-arc length prediction method to calculate adjacent candidate boundary points. S5. The candidate boundary points are corrected by the power flow and safety and stability verification, and the comprehensive stable boundary is obtained iteratively. The comprehensive stable boundary is then updated on a rolling basis according to the real-time source load status.

2. The online calculation method for the main-distributor cooperative integrated stability boundary considering source load uncertainty according to claim 1, characterized in that: In S1, historical predicted active power, actual active power, and current real-time operating data of wind power, photovoltaic power, and load are obtained. The source load prediction error is constructed based on the deviation between the actual active power and the corresponding predicted active power in the same time window, forming a source load prediction residual vector. The source load prediction residual vector at multiple consecutive moments is obtained using a rolling time window. The source load joint uncertainty set corresponding to the current calculation period is constructed based on the variation range of various prediction residuals within the rolling time window and the correlation between different source load prediction residuals.

3. The online calculation method for the main-distributor cooperative integrated stability boundary considering source load uncertainty according to claim 1, characterized in that: In S2, the static voltage stability margin represents the distance between the current operating state and the critical state of static voltage instability; the frequency stability margin is represented by the lowest system frequency after a preset disturbance; and the transient voltage recovery margin is represented by the lowest voltage at the critical node or the grid connection point of the new energy power station after a preset disturbance.

4. The online calculation method for the main-distributor cooperative integrated stability boundary considering source load uncertainty according to claim 1, characterized in that: In S2, the distance between different stability margins and the corresponding safety thresholds is processed using a uniform positive and negative direction. When the corresponding safety stability margin is greater than zero, it indicates that the corresponding safety stability constraint still has a safety margin; when it is equal to zero, it indicates that the corresponding stability index has reached the corresponding safety limit; when it is less than zero, it indicates that the corresponding safety stability constraint has been violated. In S2, the minimum value among the static voltage stability margin, frequency stability margin, and transient voltage recovery margin is determined as the relative safety margin. The source load uncertain operating state with the smallest relative safety margin is determined as the most unfavorable source load operating state. The corresponding safety and stability constraint is determined as the restrictive safety and stability constraint. The safety and stability margin corresponding to the restrictive safety and stability constraint is constructed as the restrictive safety and stability constraint function.

5. The online calculation method for the main-distributor cooperative integrated stability boundary considering source load uncertainty according to claim 1, characterized in that: In S3, the dynamic differential-algebraic model is expressed as: In the formula, Represents dynamic state variables The derivative with respect to time; Represents the dynamic state variables of the main and distribution power systems; Represents algebraic state variables; This represents the power vector exchanged at the boundary between the main and distribution networks; This represents the active and reactive power regulation variables of new energy sources, which consist of the active and reactive power regulation quantities of the new energy equipment involved in the regulation. This indicates the most unfavorable operating state of the source load.

6. The online calculation method for the main-allocation cooperative integrated stability boundary considering source load uncertainty according to claim 5, characterized in that: In S3, the dynamic differential-algebraic model is represented in a unified residual form: In the formula, Represents dynamic state variables and algebraic state variables The combined state variables; This represents the residual function corresponding to the dynamic differential-algebraic model of the main and distribution power systems. Based on the linearization relationship of the dynamic differential-algebraic model and the restricted safety and stability constraint functions, the adjoint equation is constructed as follows: In the formula, Represents the residual function with respect to the combined state variables. Jacobian matrix; Indicates the accompanying variable; Calculate the accompanying sensitivity of restrictive safety and stability constraints relative to the active and reactive power adjustment variables of new energy sources: In the formula, It represents the accompanying sensitivity corresponding to the switching power at the main distribution network boundary, which is used to determine the local tracking direction of the stable boundary in the active-reactive switching power plane at the main distribution network boundary. This represents the accompanying sensitivity corresponding to the active and reactive power adjustment variables of new energy sources, used to characterize the local impact of changes in the active and reactive power adjustment quantities of new energy sources on the current restrictive safety and stability constraints.

7. The online calculation method for the principal-distributor cooperative integrated stability boundary considering source load uncertainty according to claim 6, characterized in that: In S4, let the first... The principal and secondary boundary adjoint sensitivities corresponding to each stable boundary operating point are: In the formula, and These represent the accompanying sensitivity components of the current restrictive security and stability constraints relative to the active power exchange and reactive power exchange at the primary and secondary boundaries, respectively. exist At that time, the boundary tangent vector corresponding to the current stable boundary operating point is determined based on its active and reactive components: In the formula, Indicates the first Boundary tangent vector at each stable boundary running point; Represents the direction coefficient, taken as or This is used to maintain the continuity of the tracking direction of adjacent stable boundary tangent vectors.

8. The online calculation method for the main-allocation cooperative integrated stability boundary considering source load uncertainty according to claim 7, characterized in that: In S4, using the current stable boundary running point as a reference, the adjacent stable boundary prediction points are determined along the boundary tangent vector according to the pseudo-arc length prediction step size: In the formula, Indicates the first The primary and secondary boundary exchange power vectors corresponding to each stable boundary running point; This represents the predicted adjacent stable boundary points; Indicates the first The pseudo-arc length prediction step size used in secondary boundary tracking; The direction coefficient is selected based on the directional relationship between adjacent stable boundary tangent vectors. This ensures that the continuously obtained stable boundary prediction points are sequentially expanded along the same tracking direction, avoiding back-and-forth jumps during the boundary tracking process.

9. The online calculation method for the main-distribution cooperative integrated stability boundary considering source load uncertainty according to claim 1, characterized in that: In S5, candidate boundary points are iteratively corrected based on AC power flow conditions, primary and secondary boundary power consistency conditions, stability boundary conditions corresponding to the current restrictive security and stability constraints, and pseudo-arc length correction conditions.

10. The online calculation method for the principal-distributor cooperative integrated stability boundary considering source load uncertainty according to claim 1, characterized in that: In S5, when a candidate point fails to meet the correction conditions, the pseudo-arc length prediction step size is adjusted and prediction and correction are performed again. In S5, after entering the next calculation period, the joint uncertainty set of source loads is updated according to the latest real-time source load operation data, and the most unfavorable uncertain operating state of source loads, restrictive safety and stability constraints, and corresponding accompanying sensitivity parameters are re-determined. The stable boundary operating point obtained in the previous calculation period is used as the initial information to realize the rolling online update of the main and auxiliary coordinated integrated stability boundary.

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