Transformer area safety boundary division method considering voltage constraint conditions

By constructing a Zbus linearized power flow model and calculating the node voltage partial derivative, and combining load and photovoltaic forecast data, the safety boundary of the distribution area is corrected, thus solving the voltage constraint problem in low-voltage distributed renewable energy distribution areas, ensuring node voltage qualification, and improving power supply quality.

CN121566479APending Publication Date: 2026-02-24ELECTRIC POWER SCI & RES INST OF STATE GRID TIANJIN ELECTRIC POWER CO +2
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Patent Information

Application Number
CN202511650274.X
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-11-12
Publication Date
2026-02-24

AI Technical Summary

Technical Problem

Existing technologies fail to effectively consider voltage constraints in the operation of low-voltage distributed renewable energy distribution areas, leading to node voltage exceeding limits, affecting power supply quality and potentially causing economic losses.

Method used

A Zbus linearized power flow model based on a single fixed-point iteration is constructed to calculate the partial derivative of the node voltage with respect to the injected power. Combined with distributed load and photovoltaic forecast data, the power balance safety boundary of the distribution area is corrected to ensure that the node voltage is qualified.

Benefits of technology

By reducing computational complexity, effective constraints on node voltages within the transformer area are achieved, preventing voltage exceedances and improving power supply quality and equipment utilization.

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Abstract

The invention discloses a transformer area safety boundary division method considering voltage constraint conditions. The transformer area safety boundary division method comprises the following steps: constructing a Zbus linearization power flow model based on sequential iteration of single fixed points; calculating the partial derivative of each node voltage relative to the injection power based on a power flow model to obtain the constraint expression of each node voltage, calculating the balance node voltage based on the PQ node, and determining the influence of the balance node voltage on each PQ node voltage; calculating lower network point power of a coupling point of a distribution network and a main network and a station area power balance safety boundary by using distributed load and distributed photovoltaic prediction data under the same time scale; and with the transformer area node voltage qualification as the target, correcting the transformer area power balance safety boundary based on the obtained node voltage qualification safety boundary, and obtaining the safety operation boundary considering the node voltage qualification. According to the method, the safe operation boundary of the distributed new energy element transformer area and the node voltage safety constraint are considered, and the situation that the node voltage in the transformer area is unqualified due to power balance allocation of the transformer area is avoided.
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Description

Technical Field

[0001] This invention relates to the field of power system operation and control technology, and in particular to a method for dividing the safety boundary of transformer substations taking into account voltage constraints. Background Technology

[0002] Low-voltage distributed renewable energy elements have become an important part of distribution network operation. With the increasing penetration rate of distributed photovoltaics, new energy vehicle charging stations, and residential energy storage, the operation of traditional distribution networks is becoming increasingly complex. To improve the economy and reliability of the distribution network and fully utilize existing resources to delay investment and reduce costs, the concept of a distribution network safety boundary is proposed. This is based on the maximum and minimum injected power of specific nodes within the distribution network under certain safe operating conditions. However, if the safety boundary only considers power balance and allocation, ignoring the differences in line conductance at nodes, it may cause voltage exceedances at specific nodes, further leading to power quality problems. This could result in user loads operating at off-rated voltage for extended periods, or even damage due to voltage issues, causing economic losses. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings and defects of the prior art and to provide a method for dividing the safe operation boundary of new energy distribution areas, taking into account voltage constraints.

[0004] This invention is achieved through the following technical solution:

[0005] A method for dividing the safety boundary of a transformer substation considering voltage constraints, comprising the following steps:

[0006] Step 1: Construct a Zbus linearized power flow model based on iterative iterations from a single fixed point;

[0007] Step 2: Calculate the partial derivatives of the voltage of each node with respect to the injected power based on the Zbus linearized power flow model to obtain the voltage constraint expression of each node. Calculate the voltage of the slack node based on the PQ node to determine the influence of the slack node voltage on the voltage of each PQ node and determine the qualified safety boundary of the node voltage.

[0008] Step 3: Using distributed load and distributed photovoltaic forecast data at the same time scale, calculate the downstream power of the coupling point between the distribution network and the main grid, and calculate the power balance safety boundary of the distribution area based on the downstream power. With the node voltage of the distribution area as the target, based on the calculated node voltage compliance safety boundary, correct the power balance safety boundary of the distribution area to obtain the safe operation boundary that takes node voltage compliance into account.

[0009] Preferably, the Zbus linearized power flow model based on single fixed-point iteration is as follows:

[0010]

[0011] Among them, Y LL Let be the admittance matrix of all PQ nodes. Let V be the conjugate matrix of S, where S is the injected power at the PQ node and V is the voltage at the PQ node. Let Y represent the conjugate matrix of V. L0 V0 and V0 are the mutual admittance matrix of node PQ and the voltage of the balancing node, respectively; W is the voltage constant generated by the root node.

[0012] Preferably, the partial derivatives of each node voltage with respect to injected power are calculated based on the Zbus linearized power flow model to obtain the PR proportional formula, quantifying the analytical relationship between node voltage and injected power, thereby obtaining the constraint expression of each node voltage; wherein, the partial derivatives of each node voltage with respect to injected power are calculated as follows:

[0013]

[0014] In the formula, V is the voltage matrix of each PQ node, and P and Q are the active power matrix and reactive power matrix of each PQ node, respectively. The voltage conjugate vector at the latest power flow operating point, where j represents the imaginary number, V * This represents the conjugate vector of the node voltage to be solved.

[0015] Preferably, the step of calculating the voltage of the balancing node based on the PQ node to determine the influence of the balancing node voltage on the voltage of each PQ node is determined by the linear relationship between the voltage of each PQ node and the voltage of the root node. The linear relationship between the voltage of each PQ node and the voltage of the root node is represented by calculating the voltage sensitivity of each PQ node voltage with respect to the root node.

[0016] Preferably, the voltage sensitivity of each PQ node voltage with respect to the root node is expressed by the following formula:

[0017]

[0018] Preferably, the distributed load and distributed photovoltaic prediction data at the same time scale are used to calculate the downstream power of the coupling point between the distribution network and the main network. The photovoltaic prediction data of the pre-scheduling period is converted into data at a 1-minute time scale by using cubic spline interpolation. Then, based on the photovoltaic output prediction data at a 1-minute time scale, the 1-minute prediction value of the load active power, and the sum of the distribution network loss, the downstream power of the coupling point between the distribution network and the main network is obtained.

[0019] Preferably, the photovoltaic forecast data for the pre-scheduling period is converted into data on a 1-minute time scale using cubic spline interpolation. Then, based on the 1-minute time scale photovoltaic output forecast data, the 1-minute load active power forecast value, and the sum of the distribution network losses, the downstream power of the coupling point between the distribution network and the main network is obtained, including:

[0020]

[0021] In the formula, Sp is the cubic spline interpolation function; and These are the predicted values ​​for photovoltaic output during the pre-scheduling periods of 15 minutes and 1 minute, respectively. and These are the predicted values ​​of the load active power over 1 minute, the predicted values ​​of the downstream active power over 1 minute, and the distribution network loss, respectively.

[0022] Preferably, the power calculation of the downstream point, which is the coupling point between the distribution network and the main network, is shown in the following formula.

[0023]

[0024] In the formula, Let be the active power at the network point at time t; Let f be the active power of the load on the f-th feeder. For internal network losses in the distribution network; N F N represents the total number of feeders in the distribution network. B This represents the total number of nodes in the distribution network. Let be the active power of the distributed photovoltaic system at the m-th node in the distribution network.

[0025] Preferably, the calculation of the power balance safety boundary of the transformer area includes:

[0026]

[0027] in, This represents the maximum AC load that the distribution radio station area is allowed to access at time t. This represents the actual AC load connected to the distribution radio station area at time t. This indicates the power balance safety boundary of the transformer area.

[0028] Preferably, the step of taking the qualified node voltage of the transformer area as the objective, and correcting the safe boundary of power balance of the transformer area based on the calculated safe boundary of node voltage qualification, to obtain a safe operating boundary that takes node voltage qualification into account, includes:

[0029]

[0030] In the formula: To take into account the safe operating boundary of node voltage compliance; This defines the safe operating boundary for power balance in the distribution area. This is the acceptable safety boundary for node voltage.

[0031] This invention constructs an iterative Zbus linearized power flow model for specific nodes. This model allows for the calculation of the partial derivatives of each node's voltage with respect to injected power, thereby obtaining a voltage constraint expression. This quantifies the analytical relationship between node voltage and injected power, significantly reducing computational complexity. Subsequently, by comprehensively considering voltage change prediction data and combining cubic spline interpolation, the time scale of the renewable energy element operation data within the power distribution area is aligned, thus correcting the safe operation boundary of the power distribution area. Attached Figure Description

[0032] Figure 1 This is a flowchart of the method for dividing the safety boundary of a transformer area considering voltage constraints according to the present invention.

[0033] Figure 2 This is a schematic diagram of the fixed-point iterative process of calculating the zeros of a nonlinear function by calculating the fixed point, as described in this invention.

[0034] Figure 3 This is a schematic diagram of the maximum AC load and actual AC load that the distribution radio area of ​​the present invention can be connected to.

[0035] Figure 4 This is a schematic diagram of the correction of the safe operation boundary of the transformer area according to the present invention. Detailed Implementation

[0036] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0037] In an exemplary embodiment of this application, the method for dividing the safe boundary of a transformer area considering voltage constraints includes the following steps:

[0038] Step 1: Construct a Zbus linearized power flow model based on iterative iterations from a single fixed point;

[0039] Step 2: Calculate the partial derivatives of the voltage of each node with respect to the injected power based on the Zbus linearized power flow model to obtain the voltage constraint expression of each node. Calculate the voltage of the slack node based on the PQ node to determine the influence of the slack node voltage on the voltage of each PQ node and determine the qualified safety boundary of the node voltage.

[0040] Step 3: Using distributed load and distributed photovoltaic forecast data at the same time scale, calculate the downstream power of the coupling point between the distribution network and the main grid, and calculate the power balance safety boundary of the distribution area based on the downstream power. With the node voltage of the distribution area as the target, based on the calculated node voltage compliance safety boundary, correct the power balance safety boundary of the distribution area to obtain the safe operation boundary that takes node voltage compliance into account.

[0041] In this application, the Zbus power flow model mentioned in step 1 is used to perform power flow calculations. Power flow calculation is a method used in power systems to analyze the distribution of parameters such as voltage, phase angle, and power at various nodes in the power system, in order to determine the steady-state operating state of the power system. Its goal is to solve for the voltage and phase angle at each node in the power system so that each component in the system (generator, transformer, line, load, etc.) meets the constraints of power balance and power flow balance.

[0042] In a typical distribution network system, the voltage of the slack node (usually the root node) is generally considered to remain constant, and other nodes can be considered as PQ nodes. According to the superposition principle, the voltage U of node i... i It consists of two superimposed parts: including the voltage U generated at node i by the root node (considered as a voltage source). i1 The voltage U generated at node i by the other PQ nodes (considered as current sources) i2 For a system with one slack node and N PQ nodes, the power flow equations are as follows:

[0043]

[0044] I = YU

[0045] in Let X be the conjugate matrix of X, S be the node injected power, U be the voltage phasor of each node, and I be the injected current of each node. Dividing these matrices according to the slack nodes and PQ nodes, we obtain the following form:

[0046]

[0047]

[0048] The matrix is ​​partitioned based on whether it is a balanced node, I0, S o V0 and V0 represent the injected current, injected power, and voltage at the slack node, respectively; I, S, and V represent the injected current vector, injected power vector, and voltage phasor at the PQ node, respectively; Y is the node admittance matrix of the system. 00 For the equilibrium node self-admittance, Y 00 Y L0 Y is the mutual admittance matrix between the equilibrium node and the PQ node. LL Let Y be the admittance matrix for all PQ nodes. 00 V is a 1x1 matrix. 0L Y is a 1*n matrix. L0 Y is an n*1 matrix. LL It is an n*n matrix.

[0049] Based on the above power flow equations, the power injection equation and current injection equation of node PQ are combined to eliminate the node injection current vector I, thereby obtaining the implicit expression of the voltage of node PQ, which includes the current source part affected by the power injection of node PQ and the voltage source part affected by the voltage of the balancing node.

[0050]

[0051] The first term in the formula is the voltage generated by each PQ node (current source), and the second term is the voltage generated by the root node (voltage source), which is approximately a constant denoted as W.

[0052] Therefore, the Zbus power flow model is obtained as follows: The Zbus power flow model has a clear physical concept. It utilizes a sparse Y-matrix and an equivalent current source injection form, which can reduce computational memory and improve computational efficiency.

[0053] For any nonlinear function y = f(x), when solving for its zero x0, we have f(x0) = 0. This can be written in another equivalent form: x0 = Ψ(x0). x0 is called a fixed point of the function Ψ(x0). The actual fixed point is the intersection of the original function and the function y = x. The process of calculating the zeros of a nonlinear function by calculating the fixed point is called fixed-point iteration. The iterative formula is shown in the figure. The iterative process is as follows: Figure 2 As shown.

[0054] From the Zbus power flow model expression, it can be seen that the Zbus power flow equation has obvious iterative function characteristics. The left side of the equation is the voltage V of each PQ node, and the right side is a function of V. Therefore, it can be solved by fixed point iteration. However, fixed point iteration requires multiple calculations, and the algorithm complexity is high. Therefore, in this application, the linear approximation method based on single fixed point iteration (FFPI) is adopted to construct a linearized power flow model of the Zbus nonlinear model with respect to the reference power flow point through single-step iteration.

[0055] At this point, select the latest system running point U. 0‘ As a reference power flow point, the node power is updated when the system power flow changes, and the node voltage V is obtained according to the following formula.

[0056]

[0057] In the formula Once the line topology, parameters, and reference power flow point are determined, A and W can be calculated offline. The above formula establishes a linear relationship between the node voltage V and the injected power S at each node of the system, which significantly reduces the complexity of the solution process.

[0058] This single fixed-point iteration method essentially involves iterating through two power flow points (0, W) and (S) in the system. 0’U 0‘ Linear interpolation between ) is fundamentally different from the standardized linearization method that performs a tangent plane at a feasible solution, such as a Taylor first-order expansion, which allows linear approximation methods based on a single fixed-point iteration to maintain high accuracy over a larger interval.

[0059] In this application, in step 2, based on the above model, the partial derivatives of each node voltage with respect to the injected power can be calculated to obtain the voltage constraint expression for each node. Simultaneously, based on the PQ nodes, the voltage of the balancing node is calculated to determine the influence of the balancing node voltage on the voltages of each PQ node. Specifically, this includes:

[0060] Step 2.1, Analytical Calculation of Voltage Constraint Expression

[0061] Voltage constraint expressions measure the impact of power variations on node voltages in a power system. By calculating the derivatives of node voltages with respect to factors such as load power variations, generator output power variations, or line parameter variations, the power-voltage ratio (PR) can be obtained. The traditional PR ratio is derived by inverting the Jacobian matrix, but this method is computationally intensive and difficult to use for real-time control. Therefore, based on the Zbus power flow model proposed in this application, the partial derivatives of each node voltage with respect to injected power are calculated, resulting in the following expression for the PR ratio. This quantifies the analytical relationship between node voltage and injected power, significantly reducing computational complexity.

[0062]

[0063]

[0064] In the formula, V is the voltage matrix of each PQ node, and P and Q are the active power matrix and reactive power matrix of each PQ node, respectively. This is the voltage conjugate vector of the latest power flow operating point.

[0065] In step 2, the voltage constraint of the slack node based on the PQ node is calculated quickly as follows:

[0066] Besides the power injection at each PQ node causing voltage changes, the voltage change at the root node also affects the voltages of other nodes. In the Zbus-based linearized power flow model, the node voltages of each PQ node and the voltage vector of the slack node are linearly related. Therefore, the voltage V0 of the slack node can be derived from the linearized power flow equations to quickly solve the voltage constraints of the PQ nodes on the slack node. Based on the power flow model, the voltage sensitivity of each PQ node with respect to the root node is obtained, as shown below:

[0067]

[0068] The above equation establishes a linear relationship between the voltage of each PQ node and the voltage of the root node. Using this relationship, the impact of the change in the voltage of the equilibrium node on the change in the voltage of each PQ node can be quantitatively determined.

[0069] In a distribution network, the voltage of the PQ nodes is mainly affected by two factors. Firstly, the adjustment of the on-load tap changer (OLTC) in the substation causes changes in the voltage of the balancing node, thus leading to changes in the voltage of each PQ node. Secondly, changes in load power also cause changes in node voltage. Due to the high R / X ratio of distribution network lines, there is a strong coupling relationship between voltage and active and reactive power.

[0070] In summary, the voltages of each PQ node are closely related to the voltage of the slack node and the active and reactive power of each node. Through analysis based on the Zbus power flow model proposed in this application, voltage constraint expressions can be obtained, and a linear relationship between these variables can be established, providing theoretical support for the calculation of substation voltage regulation boundaries.

[0071] Distributed photovoltaic (PV) output is characterized by randomness and volatility due to external environmental influences. If the distribution network lacks measures to mitigate these fluctuations, the power output volatility will be directly reflected at the coupling point between the distribution network and the main grid, i.e., the downstream grid connection point. Therefore, effectively mitigating drastic power fluctuations at the downstream grid connection point is crucial for improving local PV consumption, ensuring equipment utilization, and reducing the impact of the distribution network on the main grid. This necessitates calculating the function of the downstream grid connection point.

[0072] In this application, the power of the lower grid point is calculated as shown in the following formula.

[0073]

[0074] In the formula, Let be the active power at the network point at time t; Let f be the active power of the load on the f-th feeder. For internal network losses in the distribution network; N F N represents the total number of feeders in the distribution network. F This represents the total number of nodes in the distribution network. This refers to the active power of the distributed photovoltaic system at the m-th node in the distribution network; to align with the load power direction standard, when the photovoltaic system outputs power... This is equivalent to a negative power load.

[0075] The pre-dispatch phase of the power system relies on short-term forecasts of load and photovoltaic output. To ensure accuracy, the current short-term forecast period for load and photovoltaic output is 15 minutes; therefore, this application selects a pre-dispatch period of 15 minutes. In real-time control, feedback control is performed using actual data collected from power grid measurement equipment, with a real-time control step size T. cIt is related to the sampling frequency of the measurement devices within the system.

[0076] As mentioned earlier, the power at the downstream distribution point is the sum of the load power, photovoltaic power, and distribution network losses. Distribution network losses are relatively fixed and account for a small proportion of the downstream power; under certain accuracy, they can be considered constant. Load power exhibits strong regularity, and current load forecasting accuracy can reach a 1-minute timescale. However, due to the strong volatility and randomness of photovoltaic output, current mature forecasting levels can only achieve a 15-minute timescale. To ensure the accuracy of pre-dispatch, a pre-dispatch period T is selected. p The time scale is 15 minutes. However, since the prediction step size of photovoltaic and load is not consistent, in order to obtain the power fluctuation rate of the grid points per minute within the pre-scheduling period, it is necessary to align the time scale of photovoltaic and load prediction data.

[0077] Therefore, this application proposes to process the data of new energy elements based on cubic spline interpolation. Cubic spline interpolation is the main processing method for photovoltaic data. First, cubic spline interpolation is used to process the 15-minute photovoltaic prediction data to transform it into data on a 1-minute time scale. Then, the predicted power value of the grid point is calculated. The calculation process is shown in the formula.

[0078]

[0079] In the formula, Sp is the cubic spline interpolation function; and These are the predicted values ​​of photovoltaic output for 15 minutes and 1 minute, respectively. and These are the predicted values ​​of the load active power over 1 minute, the predicted values ​​of the downstream active power over 1 minute, and the distribution network loss, respectively.

[0080] With the widespread application of renewable energy, especially photovoltaic (PV) power generation, in distribution networks, distribution substations have become more complex. The volatility of PV power generation and the dynamic changes in load active power pose new challenges to the voltage stability of the power grid. Against this backdrop, assessing the safe operating boundary of substations combining active power and PV power generation becomes particularly important.

[0081] In power distribution networks, due to the much larger resistance than reactance, there is a strong coupling relationship between system voltage and active power. Therefore, by regulating the OLTC (Optical Voltage Controlled Transmission System), not only can the bus voltage be adjusted, but active power can also be indirectly controlled. To ensure the safe and stable operation of the power grid, it is necessary to calculate the upper and lower limits of substation voltage regulation, i.e., the voltage regulation range. In practical applications, evaluating the voltage regulation range of a substation usually requires calculating the voltage sensitivity of each node, as node voltage is affected by changes in load power and photovoltaic power generation. The dynamics of load active power and photovoltaic output place new demands on maximizing the voltage regulation range. The safe operating boundary is shown in the following equation:

[0082]

[0083] in, This represents the maximum AC load that the distribution radio station area is allowed to access at time t. This represents the actual AC load connected to the distribution transformer area at time t. The safe operating boundary of the distribution transformer area can be obtained from the sampling points based on time t.

[0084] Since the voltages of each PQ node are closely related to the voltage of the slack node and the active and reactive power of each node, as mentioned earlier, the voltage constraint expression can be obtained through analysis based on the Zbus power flow model, thereby establishing the linear relationship between relevant variables. Therefore, at time t, the boundary of safe operation of the transformer area, the voltage of each node can be solved according to the voltage constraint expression; then, assuming the voltage is within acceptable limits (U < 263V), the voltage can be calculated. ac With the goal of ensuring the voltage of each node is qualified, a boundary is formed to correct the safe operation of the transformer area.

[0085] The safe operation boundary of the transformer area is revised as follows:

[0086]

[0087] In the formula: To take into account the safe operating boundary of node voltage compliance; This defines the safe operating boundary for power balance in the distribution area. This is the acceptable safety boundary for node voltage.

[0088] The technology of this invention provides a Zbus linearized power flow model applicable to the computing power at the edge of the distribution area. It constructs a linearized iterative solution based on a single fixed point, calculates the partial derivatives of each node with respect to the injected power based on the Zbus linearized power flow model, obtains the voltage constraint expression, calculates the allowable distributed energy power adjustment range of the distribution area, and takes into account the safe operation boundary of the distributed new energy element distribution area and the node voltage safety constraint, so as to avoid the occurrence of unqualified node voltage in the distribution area due to the power balance allocation of the distribution area.

[0089] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. It will be apparent to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or basic features of the present invention.

[0090] Therefore, the embodiments should be regarded as exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of the equivalents of the claims be included within the invention.

[0091] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for dividing the safety boundary of a transformer substation considering voltage constraints, characterized in that, Includes the following steps: Step 1: Construct a Zbus linearized power flow model based on iterative iterations from a single fixed point; Step 2: Calculate the partial derivatives of the voltage of each node with respect to the injected power based on the Zbus linearized power flow model to obtain the voltage constraint expression of each node. Calculate the voltage of the slack node based on the PQ node to determine the influence of the slack node voltage on the voltage of each PQ node and determine the qualified safety boundary of the node voltage. Step 3: Using distributed load and distributed photovoltaic forecast data at the same time scale, calculate the downstream power of the coupling point between the distribution network and the main grid, and calculate the power balance safety boundary of the distribution area based on the downstream power. With the goal of ensuring the compliance of node voltage in the transformer substation, the power balance safety boundary of the transformer substation is modified based on the calculated safety boundary of node voltage compliance, thus obtaining a safe operating boundary that takes into account node voltage compliance.

2. The method for dividing the safety boundary of a transformer substation considering voltage constraints according to claim 1, characterized in that, The Zbus linearized power flow model based on sequential iteration from a single fixed point is as follows: Among them, Y LL Let be the admittance matrix of all PQ nodes. Let V be the conjugate matrix of S, where S is the injected power at the PQ node and V is the voltage at the PQ node. Let Y represent the conjugate matrix of V. L0 V0 and V0 are the mutual admittance matrix of node PQ and the voltage of the balancing node, respectively; W is the voltage constant generated by the root node.

3. The method for dividing the safety boundary of a transformer substation considering voltage constraints according to claim 2, characterized in that, The partial derivatives of each node voltage with respect to injected power are calculated based on the Zbus linearized power flow model to obtain the PR proportional formula, quantifying the analytical relationship between node voltage and injected power, thereby obtaining the constraint expression of each node voltage; wherein, the partial derivatives of each node voltage with respect to injected power are calculated as follows: In the formula, V is the voltage matrix of each PQ node, and P and Q are the active power matrix and reactive power matrix of each PQ node, respectively. The voltage conjugate vector at the latest power flow operating point, where j represents the imaginary number, V * This represents the conjugate vector of the node voltage to be solved.

4. The method for dividing the safety boundary of a transformer substation considering voltage constraints according to claim 3, characterized in that, The calculation of the balancing node voltage based on the PQ node determines the impact of the balancing node voltage on the voltage of each PQ node. This impact is determined by the linear relationship between the voltage of each PQ node and the voltage of the root node. The linear relationship between the voltage of each PQ node and the voltage of the root node is expressed by calculating the voltage sensitivity of each PQ node voltage with respect to the root node.

5. The method for dividing the safety boundary of a transformer substation considering voltage constraints according to claim 4, characterized in that, The voltage sensitivity of each PQ node voltage with respect to the root node is expressed by the following formula:

6. The method for dividing the safety boundary of a transformer substation considering voltage constraints according to claim 1, characterized in that, The distributed load and distributed photovoltaic prediction data at the same time scale are used to calculate the downstream power of the coupling point between the distribution network and the main network. The photovoltaic prediction data of the pre-scheduling period is converted into data at a 1-minute time scale by using cubic spline interpolation. Then, based on the photovoltaic output prediction data at a 1-minute time scale, the 1-minute prediction value of the load active power, and the sum of the distribution network loss, the downstream power of the coupling point between the distribution network and the main network is obtained.

7. The method for dividing the safety boundary of a transformer substation considering voltage constraints according to claim 1, characterized in that, The photovoltaic forecast data for the pre-scheduling period is converted into 1-minute time-scale data using cubic spline interpolation. Then, based on the 1-minute time-scale photovoltaic output forecast data, the 1-minute load active power forecast value, and the sum of distribution network losses, the downstream power of the coupling point between the distribution network and the main network is obtained, including: In the formula, Sp is the cubic spline interpolation function; and These are the predicted values ​​for photovoltaic output during the pre-scheduling periods of 15 minutes and 1 minute, respectively. and These are the predicted values ​​of the load active power over 1 minute, the predicted values ​​of the downstream active power over 1 minute, and the distribution network loss, respectively.

8. The method for dividing the safety boundary of a transformer substation considering voltage constraints according to claim 1, characterized in that, The power calculation for the downstream point, which is the coupling point between the distribution network and the main network, is shown in the following formula. In the formula, Let be the active power at the network point at time t; Let f be the active power of the load on the f-th feeder. For internal network losses in the distribution network; N F N represents the total number of feeders in the distribution network. F This represents the total number of nodes in the distribution network. Let be the active power of the distributed photovoltaic system at the m-th node in the distribution network.

9. The method for dividing the safety boundary of a transformer substation considering voltage constraints according to claim 1, characterized in that, The calculation of the power balance safety boundary of the transformer area includes: in, This represents the maximum AC load that the distribution radio station area is allowed to access at time t. This represents the actual AC load connected to the distribution radio station area at time t. This indicates the power balance safety boundary of the transformer area.

10. The method for dividing the safety boundary of a transformer substation considering voltage constraints according to claim 9, characterized in that, The method aims to achieve qualified node voltage in the transformer substation area. Based on the calculated safe boundary for qualified node voltage, the safe boundary for power balance in the transformer substation area is modified to obtain a safe operating boundary that takes node voltage qualification into account. include: In the formula: To take into account the safe operating boundary of node voltage compliance; This defines the safe operating boundary for power balance in the distribution area. This is the acceptable safety boundary for node voltage.