A two-stage power distribution network distributed photovoltaic carrying capacity improvement method considering operation risk

Abstract

This invention relates to the technical field of new energy power systems, and particularly to a two-stage method for enhancing the distributed photovoltaic (PV) carrying capacity of distribution networks, taking into account operational risks. Specifically, it includes: establishing a system operational risk model based on the robust feasible region of PV output; constructing a two-stage distributed PV carrying capacity enhancement model; and constructing a data-driven improved ellipsoidal uncertainty set. This invention quantifies the economic losses caused by curtailment and load abandonment into operational risks by constructing a system operational risk model based on the robust feasible region of PV output, and incorporates these risks into the optimization objective of the two-stage distributed PV carrying capacity enhancement model. Compared to existing methods that rely on the probability distribution of PV output and do not adequately assess operational risks, this invention collaboratively optimizes investment and operating costs and operational risks during the day-ahead planning and intraday adjustment phases, effectively avoiding problems such as voltage exceeding limits and equipment overload caused by PV uncertainties, and significantly improving economic efficiency while ensuring safe system operation.

Description

Technical Field

[0001] This invention relates to the technical field of new energy power systems, and in particular to a two-stage method for improving the distributed photovoltaic carrying capacity of distribution networks, taking into account operational risks. Background Technology

[0002] Driven by global energy structure transformation and the "dual carbon" goal, distributed photovoltaic (DPV) has achieved large-scale integration into distribution networks due to its core advantages such as cleanliness, flexibility, and local consumption. However, the intermittency and volatility of photovoltaic output, coupled with its continuously increasing penetration rate, pose serious challenges to traditional distribution network operation modes. On the one hand, the reverse power flow of DPV can easily cause safety issues such as voltage exceeding limits and line overload, severely restricting the distribution network's capacity to support distributed photovoltaic power. On the other hand, the significantly increased randomness and complexity of system operation states lead to a continuous rise in operational risks such as voltage fluctuations and equipment overload, threatening power supply reliability and grid security. Therefore, how to effectively improve the distribution network's capacity to support distributed photovoltaic power while ensuring the safe and economical operation of the system has become a critical issue that urgently needs to be addressed in the current planning and operation of distribution networks.

[0003] The following problems exist in the research on the carrying capacity assessment of distributed photovoltaic power in distribution networks: 1. Existing studies often involve high investment costs and limited adjustment range or response speed when configuring controllable distributed power sources, such as micro gas turbines and fuel cell energy storage; 2. Existing studies on improving the photovoltaic carrying capacity of distribution networks do not adequately consider the full-cycle and multi-scenario collaborative scheduling capabilities of reactive power compensation and flexible control equipment such as capacitor banks and smart soft switches, and there is still room for further improvement in related planning schemes; 3. The accuracy of renewable energy output and load forecasting is the main factor limiting the renewable energy capacity level of the system. The current assessment of the carrying capacity of distributed photovoltaic power in distribution networks mainly relies on the probability distribution of its output, failing to fully consider the operational risk assessment and not covering all possible output scenarios. Summary of the Invention

[0004] To address the problem that current assessments of the carrying capacity of distributed photovoltaic (PV) power grids mainly rely on the probability distribution of their output, failing to adequately consider operational risk assessments and not covering all possible output scenarios, this invention provides a two-stage method for enhancing the carrying capacity of distributed PV power grids that takes operational risks into account.

[0005] This invention is achieved through the following technical solution: a two-stage method for enhancing the distributed photovoltaic carrying capacity of a distribution network, taking into account operational risks, comprising the following steps:

[0006] S1. Establish a system operation risk model based on the robust feasible region of photovoltaic output: The robust feasible region of photovoltaic output is defined as follows: if the photovoltaic output exceeds the maximum allowable threshold, the system needs to curtail photovoltaic power for safe operation; if the photovoltaic output is lower than the minimum allowable threshold, the system needs to curtail load.

[0007] S2. Construct a two-stage distributed photovoltaic carrying capacity enhancement model: In the day-ahead planning stage, by coordinating the configuration of capacitor banks, smart soft switches and energy storage, a static configuration scheme with multiple flexible resources is formulated with the goal of minimizing system investment and operating costs; In the day-ahead adjustment stage, combined with the actual operating scenarios of curtailment and load reduction, the distributed photovoltaic access capacity is maximized while minimizing system operating risks.

[0008] S3. Construct an improved ellipsoidal uncertainty set based on data-driven approach: Divide the collected historical data into days and establish a high-dimensional ellipsoid set based on the historical data. Rotate the high-dimensional ellipsoid to make its axis of symmetry coincide with the coordinate axis, thereby obtaining the vertices of the high-dimensional ellipsoid uncertainty set. Finally, construct a linear polyhedral uncertainty set from the coordinates of the high-dimensional ellipsoid vertices.

[0009] As a further improvement to the technical solution of the present invention, the robust feasible region of photovoltaic output is equivalently described by the following two-layer model, the specific formula of which is:

[0010] ;

[0011] In the formula: Indicates photovoltaic power station At any moment The upper limit of the decision variable; Indicates photovoltaic power station At any moment The lower bound decision variable; Indicates pumped storage power station At any moment ; output power; Indicates photovoltaic power station At any moment The power of abandoned light; Indicates load At any moment The power of abandoned load; Indicates time period, Represents a set of nodes

[0012] As a further improvement to the technical solution of the present invention, constraints are established for the robust feasible domain of photovoltaic power output. The constraints specifically include: the actual power output of the photovoltaic power station, curtailment and load abandonment constraints, the power output range of the pumped storage power station, and the ramping constraints of the pumped storage power station.

[0013] The specific formula for the actual output of a photovoltaic power station is as follows:

[0014] ;

[0015] In the formula: Indicates photovoltaic power station At any moment ; output power; Indicates photovoltaic power station At any moment The robust feasible domain upper limit; Indicates photovoltaic power station At any moment The predicted power; Indicates photovoltaic power station At any moment The robust feasible lower bound; Indicates any time; Indicates an uncertain budget; This represents the total number of uncertain nodes;

[0016] The specific formulas for light curtailment and load curtailment constraints are as follows:

[0017] ;

[0018] In the formula: Indicates load At any moment The predicted power;

[0019] The specific formula for the output range of a pumped storage power station is as follows:

[0020] ;

[0021] In the formula: Indicates pumped storage power station At any moment The running status; Indicates pumped storage power station At any moment The lower limit of output power; Indicates pumped storage power station At any moment ; output power; Indicates pumped storage power station At any moment The upper limit of output power;

[0022] The specific formula for the ramp constraint of pumped storage power stations is as follows:

[0023] ;

[0024] In the formula: Indicates pumped storage power station At any moment ; output power; Indicates pumped storage power station At any moment The running status; Indicates pumped storage power station Downhill power; Indicates pumped storage power station The power of climbing uphill.

[0025] As a further improvement to the technical solution of this invention, the system operation risk in the system operation risk model is defined as: the economic loss caused by curtailment of solar power and load when the photovoltaic output exceeds the robust feasible range allowed by the system; wherein the specific formula for system operation risk is:

[0026] ;

[0027] In the formula: This indicates system operational risks; This represents the cost coefficient for wasted light. This represents the cost coefficient for abandoned loads; Indicates photovoltaic power station Maximum output power; yes The probability density function;

[0028] The specific formula for system operational risk is equivalently processed using a discretization method. Specifically, the predicted value is used as the boundary to divide the system into a lower bound interval and an upper bound interval. The lower bound interval and the upper bound interval are then divided into equal parts. and There are several risk units, and the specific formula for the system operation risk value of each risk unit is as follows:

[0029] ;

[0030] ;

[0031] In the formula: Indicates photovoltaic power station At any moment When the output power falls to the first Operational risks of each risk unit; Indicates any time; Represents a risk unit within any upper bound interval; Indicates photovoltaic power station At any moment When the output power falls to the first Operational risks of each risk unit; Represents a risk unit within any lower bound interval; , The actual photovoltaic output appears in the risk unit. , The probability is multiplied by the interval width of the corresponding risk unit;

[0032] Then, based on the predicted photovoltaic output and the system operation risk value of each risk unit, the specific formula for the system operation risk of the entire scheduling cycle is as follows:

[0033] ;

[0034] in ;

[0035] The robust feasible region for photovoltaic power plant output is represented as follows:

[0036] ;

[0037] In the formula: This indicates the operational risk of the system after processing by the discretization method; Indicates photovoltaic power station At any moment When it falls in the first Upward decision variables for each risk unit; Indicates photovoltaic power station At any moment When the output power falls to the first Operational risks of each risk unit; Indicates photovoltaic power station At any moment When it falls in the first Downward decision variables for each risk unit; Indicates photovoltaic power station At any moment When the output power falls to the first Operational risks of each risk unit; Indicates photovoltaic power station At any moment When the output power falls to the first The output limit of each risk unit; Indicates photovoltaic power station At any moment When the output power falls to the first The lower limit of the output of each risk unit.

[0038] As a further improvement to the technical solution of this invention, the expression of the two-stage distributed photovoltaic carrying capacity enhancement model is as follows:

[0039] ;

[0040] in: ;

[0041] ;

[0042] ;

[0043] ;

[0044] ;

[0045] In the formula: For capacitor bank operating costs; For the operating cost of intelligent soft switches; For energy storage operating costs; The annual cost of configuring energy storage; The annual operating cost of energy storage; This refers to the total capacity of distributed photovoltaic power grid connection. , and These are 0-1 variables representing whether the capacitor bank, smart soft switch, and energy storage are installed. A value of 1 indicates that the equipment is installed, and a value of 0 indicates that the equipment is not installed. Let U be the set of nodes; U is the uncertainty set of photovoltaic output. For nodes The capacitor bank at time Unproductive efforts; and Representing nodes respectively The intelligent soft switch is always The meritorious and the ineffective contributions; Configure a cost coefficient for each unit of capacity; Configure a cost factor per unit power; and Representing nodes respectively The energy storage configuration capacity and maximum charging and discharging power; For energy storage lifespan; Operating cost per unit power; and Representing nodes respectively Energy storage at time The charging and discharging power; For nodes The permitted capacity of the connected photovoltaic system; This is the unit operating cost coefficient for the capacitor bank; This represents the unit operating cost coefficient for intelligent soft switches.

[0046] As a further improvement to the technical solution of this invention, constraints are established for the two-stage distributed photovoltaic carrying capacity enhancement model. These constraints include: flexibility resource planning constraints, distributed photovoltaic access capacity constraints, distribution network operation constraints, capacitor bank operation constraints, smart soft switching operation constraints, distribution network topology constraints, and energy storage constraints.

[0047] As a further improvement to the technical solution of this invention, the specific formula for the flexibility resource planning constraint is as follows:

[0048] ;

[0049] In the formula: , and These represent capacitor banks, smart soft switches, and energy storage nodes, respectively. ,node and Between or nodes Candidate installation locations; , , Representing nodes respectively Whether to install capacitor banks, at the nodes and Are smart soft switches installed on the lines between them, at the nodes? Whether to install energy storage; For the operator's planning budget, this indicates the number of components to be planned;

[0050] The specific formula for the capacity constraint of distributed photovoltaic power grid connection is as follows:

[0051] ;

[0052] In the formula: The photovoltaic power coefficient is determined by the intensity of sunlight.

[0053] The specific formula for the operating constraints of the distribution network is as follows:

[0054] ;

[0055] ;

[0056] in ;

[0057] ;

[0058] ;

[0059] ;

[0060] ;

[0061] ;

[0062] In the formula: Indicates the line At any moment By node Flow to Node The active power; Indicates the line At any moment By node Flow to Node The active power; Represents a node Energy storage at time The charging power; Represents a node Energy storage at time The discharge power; Indicates a time period; Indicates the line At any moment By node Flow to Node reactive power; Indicates the line At any moment By node Flow to Node reactive power; Represents a node At any moment The voltage; Represents a node At any moment The voltage; This indicates the lower limit of active power from the main grid; Indicates at time Active power from the main network; This indicates the maximum active power output from the main grid. This indicates the lower limit of reactive power from the main grid; Indicates at time Reactive power from the main grid; This indicates the upper limit of reactive power from the main grid; Indicates the line At any moment The square of apparent power; Represents the set of system lines; Indicates the line Upper limit of active power; Indicates the line Reactive power limit; and They represent the times at time 1 and 2 respectively. Active and reactive power from the main grid; and These represent the pumped storage power station at time [time]. The meritorious and the ineffective contributions; and These represent the time intervals of the intelligent soft switch. The meritorious and the ineffective contributions; Indicates the capacitor bank at time [time]. Unproductive efforts; and They represent the times at time 1 and 2 respectively. node The outflow of active and reactive power; and They represent the lines respectively. Resistance and reactance; For a moment The line status is indicated by a value of 1, which represents normal operation, and a value of 0, which represents disconnection. Indicates large The largest possible number in the law;

[0063] The specific formula for the capacitor bank operating constraints is as follows:

[0064] ;

[0065] in ;

[0066] ;

[0067] ;

[0068] In the formula: Represents a node The capacitor bank at time reactive power; Represents a node The Taiwan capacitor bank at time The switching action state; Represents a node The capacitor bank at time The entry point; Represents a node The capacitor bank at time The cutout; Indicates at node The value indicates whether the capacitor bank is installed; 1 indicates installed, and 0 indicates not installed. Indicates at node The capacitor bank at time Whether it is under control, 1 indicates controlled, 0 indicates uncontrolled; Represents a node The upper limit of reactive power of capacitor banks; For nodes The unit reactive power of the capacitor bank; Represents a node The Taiwan capacitor bank at time The switch's operational status is indicated by a value of 1, which represents connection, and a value of 0, which represents disconnection. Represents a node The Taiwan capacitor bank at time The switch's operational status is indicated by a value of 1, which represents connection, and a value of 0, which represents disconnection. Indicates the number of capacitor banks;

[0069] The specific formula for the operating constraints of intelligent soft switches is as follows:

[0070] ;

[0071] in ;

[0072] ;

[0073] In the formula: Represents a node The intelligent soft switch is always The active power; Indicates the apparent power of the intelligent soft switch; Represents a node The intelligent soft switch is always reactive power; Represents a node The lower limit of active power for intelligent soft switches; Represents a node The active power of the intelligent soft switch; Indicates at node and The indicator shows whether the smart soft switch is installed; 1 indicates installed, and 0 indicates not installed. At the node and The intelligent soft switch between them is always Whether it is under control, 1 indicates controlled, 0 indicates uncontrolled; Represents a node The upper limit of active power of the intelligent soft switch; Represents a node The lower limit of reactive power for intelligent soft switches; Represents a node The reactive power of the intelligent soft switch; Represents a node The upper limit of reactive power of intelligent soft switches; Represents a node The lower limit of reactive power for intelligent soft switches; Represents a node The reactive power of the intelligent soft switch; Represents a node The upper limit of reactive power of intelligent soft switches; Represents a node The lower limit of active power for intelligent soft switches; Represents a node The active power of the intelligent soft switch; Represents a node The upper limit of active power of the intelligent soft switch; Indicates the candidate installation locations for the intelligent soft switch;

[0074] The specific formula for distribution network topology constraints is as follows:

[0075] ;

[0076] ;

[0077] ;

[0078] ;

[0079] ;

[0080] In the formula: Represents a node At any moment Child node variables; For nodes At any moment The root node variable, a value of 1 indicates the root node; For nodes At any moment The root node variable, a value of 1 indicates the root node; Represents the set of all root nodes in the system; Indicates the lower limit of the node voltage; Indicates the upper limit of the node voltage; Indicates at time The node relationship is a 0-1 variable, where a value of 1 indicates a node. It is a node The upstream node is 0, otherwise it is 0; This represents the node voltage of node i at time t.

[0081] The specific formula for energy storage constraints is as follows:

[0082] ;

[0083] ;

[0084] In the formula: Represents a node Energy storage at time ; output power; Represents a node Energy storage at time The charge / discharge control variable is 1, which represents charging, and 0, which represents discharging. Represents a node Energy storage The SOC value at time t, where SOC represents the state of charge of the energy storage; Indicates the lower limit of the SOC of energy storage; Indicates the upper limit of the SOC of energy storage; Represents a node The SOC value of the stored energy at the initial moment; Represents a node The SOC value of the stored energy at the last moment; For charge and discharge efficiency; For nodes Energy storage at time The charge / discharge control variable, with a value of 1 indicating charging and a value of 0 indicating discharging; This is the ratio of the configured capacity to the maximum charge / discharge power. Configure the maximum capacity; For nodes Energy storage at time The SOC value.

[0085] As a further improvement to the technical solution of the present invention, step S3 specifically includes the following steps:

[0086] The collected historical data is divided by day, and all data scenarios are defined. Uncertain sets of high-dimensional ellipsoids The collected data is written in the vector form shown below:

[0087] ;

[0088] In the formula: This represents the generated photovoltaic uncertainty data; A positive definite matrix representing the direction of the deviation of the symmetry axis from the coordinate axes of an uncertain set of a high-dimensional ellipsoid; It represents the center point of the uncertain set of a high-dimensional ellipsoid; T represents the mathematical symbol for transpose;

[0089] To obtain the vertices of the uncertain set of the high-dimensional ellipsoid, the high-dimensional ellipsoid is rotated so that its axis of symmetry coincides with the coordinate axes. The equation for this rotation is:

[0090] ;

[0091] In the formula: This represents the set of uncertainties in a high-dimensional ellipsoid after rotation; express The coordinate values ​​of the coordinate axes after rotation; and It is for positive definite matrices The matrix obtained during orthogonal decomposition. The transformation matrix is... Let be a diagonal matrix, denoted as ; and The following relationship must be satisfied:

[0092] ;

[0093] It can be seen that the uncertainty set of the high-dimensional ellipsoid after rotation is known. of The coordinates of the vertices are:

[0094] ;

[0095] In the formula: Describes the set of uncertainties in a high-dimensional ellipsoid after rotation. The coordinates of the first vertex; Describes the set of uncertainties in a high-dimensional ellipsoid after rotation. The Vertex coordinates; Represents the first positive number in the diagonal matrix D; Describe the first position on the diagonal matrix D A positive number;

[0096] Uncertainty set of the rotated high-dimensional ellipsoid The vertex coordinates can be obtained through inverse transformation. The vertex coordinates; the uncertain set of a linear polyhedron constructed from the vertex coordinates. Represented as:

[0097] ;

[0098] In the formula: The first polyhedron represents the set of uncertainties. One scaling factor; Describes the set of uncertainties in a high-dimensional ellipsoid after rotation. The The coordinates of each vertex.

[0099] The technical solution provided by this invention has the following advantages compared with the prior art:

[0100] 1. This invention constructs a system operation risk model based on the robust feasible domain of photovoltaic output, quantifying the economic losses caused by curtailment and load abandonment as operational risks, and incorporating them into the optimization objective of a two-stage distributed photovoltaic carrying capacity improvement model. Compared to existing methods that rely on the probability distribution of photovoltaic output and do not fully assess operational risks, this invention can synergistically optimize investment and operating costs and operational risks during the day-ahead planning and intraday adjustment stages, effectively avoiding problems such as voltage exceeding limits and equipment overload caused by photovoltaic uncertainties, and significantly improving economic efficiency while ensuring safe system operation.

[0101] 2. This invention coordinates the configuration of capacitor banks, intelligent soft switches, and energy storage during the day-ahead planning phase to formulate a static configuration scheme for multiple flexible resources, and optimizes it in conjunction with actual scenarios of curtailment and load shedding during the day-ahead adjustment phase. Compared with existing research methods that only configure controllable distributed power sources and do not adequately consider the coordination of reactive power compensation and flexible control equipment, this invention fully leverages the complementary advantages of multiple flexible resources, significantly expands the photovoltaic absorption space, and maximizes the capacity of distributed photovoltaic grid connection.

[0102] 3. This invention employs a high-dimensional ellipsoidal uncertainty set based on historical data and constructs a linear polyhedral uncertainty set through rotational transformation, effectively characterizing the spatiotemporal correlation between adjacent photovoltaic power output periods. Compared to traditional robust optimization methods that use box sets and ignore correlations, this invention avoids the problem of overly conservative decision-making caused by dealing with extremely unlikely scenarios. It improves the economic efficiency of decision-making while ensuring robustness, and maintains a low curtailment rate and load curtailment rate within a wider range of uncertainty. Attached Figure Description

[0103] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0104] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0105] Figure 1This is a schematic diagram of the robust feasible region for photovoltaic power output provided in an embodiment of the present invention.

[0106] Figure 2 This is a schematic diagram of the probability density function of photovoltaic power output provided in an embodiment of the present invention.

[0107] Figure 3 The photovoltaic forecast values ​​and load levels provided for the experimental examples of this invention.

[0108] Figure 4 The results of the robust feasible region assessment of photovoltaic output provided for the experimental examples of this invention.

[0109] Figure 5 The impact of different numbers of risk units on system operation risk is provided for the experimental examples of this invention.

[0110] Figure 6 The impact of different uncertainty budgets on system operation risk provided for the experimental examples of this invention.

[0111] Figure 7 The impact of different uncertainty ranges on photovoltaic load-bearing capacity is provided for the experimental examples of this invention.

[0112] Figure 8 The impact of different uncertainty ranges on the light abandonment rate and load abandonment rate provided for the experimental examples of this invention.

[0113] Figure 9 A comparison of the computational efficiency of different solution algorithms provided for the experimental examples of this invention. Detailed Implementation

[0114] To better understand the above-mentioned objectives, features, and advantages of the present invention, the solutions of the present invention will be further described below. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other.

[0115] Many specific details are set forth in the following description in order to provide a full understanding of the invention, but the invention may also be practiced in other ways different from those described herein; obviously, the embodiments in the specification are only some embodiments of the invention, and not all embodiments.

[0116] Example

[0117] This invention provides a specific embodiment of a two-stage method for enhancing the distributed photovoltaic carrying capacity of a distribution network, taking into account operational risks, comprising the following steps:

[0118] S1. Establish a system operation risk model based on the robust feasible region of photovoltaic output:

[0119] 1.1 Robust Feasibility Domain for Photovoltaic Output

[0120] The robust feasible region for photovoltaic (PV) output is defined as follows: if the PV output exceeds the maximum allowable threshold, the system must curtail the PV output for safe operation; if the PV output is below the minimum allowable threshold, the system must curtail the load. In other words, once the PV output boundary is determined, fluctuations in PV output within the feasible range will not cause any loss to the system's operation.

[0121] The robust feasible region of photovoltaic output is equivalently described by the following two-layer model, the specific formula of which is:

[0122] ;

[0123] In the formula: Indicates photovoltaic power station At any moment The upper limit of the decision variable; Indicates photovoltaic power station At any moment The lower bound decision variable; Indicates pumped storage power station At any moment ; output power; Indicates photovoltaic power station At any moment The power of discarded light; Indicates load At any moment The power of abandoned load; Indicates time period, Represents a set of nodes.

[0124] Constraints are established for the robust feasible region of photovoltaic power output. These constraints specifically include: the actual output of the photovoltaic power station, curtailment and load shedding constraints, the output range of the pumped storage power station, and the ramp-up constraints of the pumped storage power station.

[0125] The specific formula for the actual output of a photovoltaic power station is as follows:

[0126] ;

[0127] In the formula: Indicates photovoltaic power station At any moment ; output power; Indicates photovoltaic power station At any moment The robust feasible domain upper limit; Indicates photovoltaic power station At any moment The predicted power; Indicates photovoltaic power station At any moment The robust feasible lower bound; Indicates any time; Indicates an uncertain budget; This represents the total number of uncertain nodes;

[0128] The specific formulas for light curtailment and load curtailment constraints are as follows:

[0129] ;

[0130] In the formula: Indicates load At any moment The predicted power;

[0131] The specific formula for the output range of a pumped storage power station is as follows:

[0132] ;

[0133] In the formula: Indicates pumped storage power station At any moment The running status; Indicates pumped storage power station At any moment The lower limit of output power; Indicates pumped storage power station At any moment ; output power; Indicates pumped storage power station At any moment The upper limit of output power;

[0134] The specific formula for the ramp constraint of pumped storage power stations is as follows:

[0135] ;

[0136] In the formula: Indicates pumped storage power station At any moment ; output power; Indicates pumped storage power station At any moment The running status; Indicates pumped storage power station Downhill power; Indicates pumped storage power station The power of climbing uphill.

[0137] 1.2 System Operation Risk Model

[0138] The system operation risk in the aforementioned system operation risk model is defined as the economic loss caused by curtailment and load abandonment when photovoltaic output exceeds the system's allowable robust feasible range. For example... Figure 1 As shown, when When the photovoltaic output exceeds the upper limit of the acceptable area, measures such as curtailment are necessary to ensure the safe operation of the system. When photovoltaic (PV) output falls below the lower limit of the acceptable range, measures such as load shedding are necessary. That is, when PV output appears to be below the acceptable range... Figure 2 In the mid-shaded areas, there is a risk of curtailment of solar power or load. Assuming the photovoltaic prediction error follows a normal distribution with a mean of 0, the specific formula for the system operation risk is:

[0139] ;

[0140] In the formula: This indicates system operational risks; This represents the cost coefficient for wasted light. This represents the cost coefficient for abandoned loads; Indicates photovoltaic power station Maximum output power; yes The probability density function.

[0141] Because the integral form of the above formula (the specific formula for system operation risk) makes the system operation risk model difficult to solve directly, the following discretization method is used for equivalent processing. At any given time, the robust feasible region of photovoltaic output is bounded by the predicted value. The lower bound interval falls within the interval... Inside. The upper bound interval falls within the interval. Within. Furthermore, the lower bound interval and the upper bound interval are each equally divided into... and Each risk unit has an upper bound risk unit containing operational risk values. and corresponding photovoltaic output The lower bound risk unit contains the operational risk value. and corresponding photovoltaic output .

[0142] The specific formula for the system operation risk value of each risk unit is as follows:

[0143] ;

[0144] ;

[0145] In the formula: Indicates photovoltaic power station At any moment When the output power falls to the first Operational risks of each risk unit; Indicates any time; Represents a risk unit within any upper bound interval; Indicates photovoltaic power station At any moment When the output power falls to the first Operational risks of each risk unit; Represents a risk unit within any lower bound interval; , The actual photovoltaic output appears in the risk unit. , The probability is multiplied by the interval width of the corresponding risk unit;

[0146] Then, based on the predicted photovoltaic output and the system operation risk value of each risk unit, the specific formula for the system operation risk of the entire scheduling cycle is as follows:

[0147] ;

[0148] in ;

[0149] The robust feasible region for photovoltaic power plant output is represented as follows:

[0150] ;

[0151] In the formula: This indicates the operational risk of the system after processing by the discretization method; Indicates photovoltaic power station At any moment When it falls in the first Upward decision variables for each risk unit; Indicates photovoltaic power station At any moment When the output power falls to the first Operational risks of each risk unit; Indicates photovoltaic power station At any moment When it falls in the first Downward decision variables for each risk unit; Indicates photovoltaic power station At any moment When the output power falls to the first Operational risks of each risk unit; Indicates photovoltaic power station At any moment When the output power falls to the first The output limit of each risk unit; Indicates photovoltaic power station At any moment When the output power falls to the first The lower limit of the output of each risk unit.

[0152] S2. Construct a two-stage distributed photovoltaic carrying capacity enhancement model:

[0153] 2.1 Objective Function of the Two-Stage Distributed Photovoltaic Carrying Capacity Enhancement Model

[0154] In the day-ahead planning phase, a static configuration scheme with multiple flexible resources is formulated by coordinating the configuration of capacitor banks, smart soft switches and energy storage to minimize system investment and operating costs. In the day-ahead adjustment phase, the distributed photovoltaic access capacity is maximized while minimizing system operating risks, taking into account the actual operating scenarios of curtailment and load reduction.

[0155] The expression for the two-stage distributed photovoltaic carrying capacity enhancement model is as follows:

[0156] ;

[0157] in: ;

[0158] ;

[0159] ;

[0160] ;

[0161] ;

[0162] In the formula: For capacitor bank operating costs; For the operating cost of intelligent soft switches; For energy storage operating costs; The annual cost of configuring energy storage; The annual operating cost of energy storage; This refers to the total capacity of distributed photovoltaic power grid connection. , and These are 0-1 variables representing whether the capacitor bank, smart soft switch, and energy storage are installed. A value of 1 indicates that the equipment is installed, and a value of 0 indicates that the equipment is not installed. Let U be the set of nodes; U is the uncertainty set of photovoltaic output. For nodes The capacitor bank at time Unproductive efforts; and Representing nodes respectively The intelligent soft switch is always The meritorious and the ineffective contributions; Configure a cost coefficient for each unit of capacity; Configure a cost factor per unit power; and Representing nodes respectively The energy storage configuration capacity and maximum charging and discharging power; For energy storage lifespan; Operating cost per unit power; and Representing nodes respectively Energy storage at time The charging and discharging power; For nodes The permitted capacity of the connected photovoltaic system; This is the unit operating cost coefficient for the capacitor bank; This represents the unit operating cost coefficient for intelligent soft switches.

[0163] 2.2 Establish constraints for the two-stage distributed photovoltaic carrying capacity improvement model. These constraints include: flexibility resource planning constraints, distributed photovoltaic access capacity constraints, distribution network operation constraints, capacitor bank operation constraints, smart soft switching operation constraints, distribution network topology constraints, and energy storage constraints.

[0164] The specific formula for the flexibility resource planning constraint is as follows:

[0165] ;

[0166] In the formula: , and These represent capacitor banks, smart soft switches, and energy storage nodes, respectively. ,node and Between or nodes Candidate installation locations; , , Representing nodes respectively Whether to install capacitor banks, at the nodes and Are smart soft switches installed on the lines between them, at the nodes? Whether to install energy storage; The operator's planning budget indicates the number of components to be planned.

[0167] The specific formula for the capacity constraint of distributed photovoltaic power grid connection is as follows:

[0168] ;

[0169] In the formula: The photovoltaic power factor is determined by the intensity of sunlight.

[0170] The specific formula for the operating constraints of the distribution network is as follows:

[0171] ;

[0172] ;

[0173] in ;

[0174] ;

[0175] ;

[0176] ;

[0177] ;

[0178] ;

[0179] In the formula: Indicates the line At any moment By node Flow to Node The active power; Indicates the line At any moment By node Flow to Node The active power; Represents a node Energy storage at time The charging power; Represents a node Energy storage at time The discharge power; Indicates a time period; Indicates the line At any moment By node Flow to Node reactive power; Indicates the line At any moment By node Flow to Node reactive power; Represents a node At any moment The voltage; Represents a node At any moment The voltage; This indicates the lower limit of active power from the main grid; Indicates at time Active power from the main network; This indicates the maximum active power output from the main grid. This indicates the lower limit of reactive power from the main grid; Indicates at time Reactive power from the main grid; This indicates the upper limit of reactive power from the main grid; Indicates the line At any moment The square of apparent power; Represents the set of system lines; Indicates the line Upper limit of active power; Indicates the line Reactive power limit; and They represent the times respectively. Active and reactive power from the main grid; and These represent the pumped storage power station at time [time]. The meritorious and the ineffective contributions; and These represent the time intervals of the intelligent soft switch. The meritorious and the ineffective contributions; Indicates the capacitor bank at time [time]. Unproductive efforts; and They represent the times respectively. node The outflow of active and reactive power; and They represent the lines respectively. Resistance and reactance; For a moment The line status is indicated by a value of 1, which represents normal operation, and a value of 0, which represents disconnection. Indicates large The largest possible number in the law.

[0180] The specific formula for the capacitor bank operating constraints is as follows:

[0181] ;

[0182] in ;

[0183] ;

[0184] ;

[0185] In the formula: Represents a node The capacitor bank at time reactive power; Represents a node The Taiwan capacitor bank at time The switching action state; Represents a node The capacitor bank at time The entry point; Represents a node The capacitor bank at time The cutout; Indicates at node The value indicates whether the capacitor bank is installed; 1 indicates installed, and 0 indicates not installed. Indicates at node The capacitor bank at time Whether it is under control, 1 indicates controlled, 0 indicates uncontrolled; Represents a node The upper limit of reactive power of capacitor banks; For nodes The unit reactive power of the capacitor bank; Represents a node The Taiwan capacitor bank at time The switch's operational status is indicated by a value of 1, which represents connection, and a value of 0, which represents disconnection. Represents a node The Taiwan capacitor bank at time The switch's operational status is indicated by a value of 1, which represents connection, and a value of 0, which represents disconnection. Indicates the number of capacitor banks.

[0186] The specific formula for the operating constraints of intelligent soft switches is as follows:

[0187] ;

[0188] in ;

[0189] ;

[0190] In the formula: Represents a node The intelligent soft switch is always The active power; Indicates the apparent power of the intelligent soft switch; Represents a node The intelligent soft switch is always reactive power; Represents a node The lower limit of active power for intelligent soft switches; Represents a node The active power of the intelligent soft switch; Indicates at node and The indicator shows whether the smart soft switch is installed; 1 indicates installed, and 0 indicates not installed. At the node and The intelligent soft switch between them is always Whether it is under control, 1 indicates controlled, 0 indicates uncontrolled; Represents a node The upper limit of active power of the intelligent soft switch; Represents a node The lower limit of reactive power for intelligent soft switches; Represents a node The reactive power of the intelligent soft switch; Represents a node The upper limit of reactive power of intelligent soft switches; Represents a node The lower limit of reactive power for intelligent soft switches; Represents a node The reactive power of the intelligent soft switch; Represents a node The upper limit of reactive power of intelligent soft switches; Represents a node The lower limit of active power for intelligent soft switches; Represents a node The active power of the intelligent soft switch; Represents a node The upper limit of active power of the intelligent soft switch; Indicates the candidate installation location for the smart soft switch.

[0191] The specific formula for distribution network topology constraints is as follows:

[0192] ;

[0193] ;

[0194] ;

[0195] ;

[0196] ;

[0197] In the formula: Represents a node At any moment Child node variables; For nodes At any moment The root node variable, a value of 1 indicates the root node; For nodes At any moment The root node variable, a value of 1 indicates the root node; Represents the set of all root nodes in the system; Indicates the lower limit of the node voltage; Indicates the upper limit of the node voltage; Indicates at time The node relationship is a 0-1 variable, where a value of 1 indicates a node. It is a node The upstream node is 0, otherwise it is 0; This represents the node voltage of node i at time t.

[0198] The specific formula for energy storage constraints is as follows:

[0199] ;

[0200] ;

[0201] In the formula: Represents a node Energy storage at time ; output power; Represents a node Energy storage at time The charge / discharge control variable is 1, which represents charging, and 0, which represents discharging. Represents a node Energy storage The SOC value at time t, where SOC represents the state of charge of the energy storage; Indicates the lower limit of the SOC of energy storage; Indicates the upper limit of the SOC of energy storage; Represents a node The SOC value of the stored energy at the initial moment; Represents a node The SOC value of the stored energy at the last moment; For charge and discharge efficiency; For nodes Energy storage at time The charge / discharge control variable, with a value of 1 indicating charging and a value of 0 indicating discharging; This is the ratio of the configured capacity to the maximum charge / discharge power. Configure the maximum capacity; For nodes Energy storage at time The SOC value.

[0202] S3. Construct an improved ellipsoidal uncertainty set based on data-driven approach: Divide the collected historical data into days and establish a high-dimensional ellipsoid set based on the historical data. Rotate the high-dimensional ellipsoid to make its axis of symmetry coincide with the coordinate axis, thereby obtaining the vertices of the high-dimensional ellipsoid uncertainty set. Finally, construct a linear polyhedral uncertainty set from the coordinates of the high-dimensional ellipsoid vertices.

[0203] In robust optimization, traditional uncertain sets often use box sets to describe uncertain variables. This method assumes that multiple random variables are independent. However, for the same renewable energy power plant, there is a certain correlation between the output of adjacent time periods. Therefore, if the uncertain set used fails to consider the spatiotemporal correlation of renewable energy output, the decision result of robust optimization will deal with many scenarios that are unlikely to occur, thus affecting the economic efficiency of the decision. To address this, this invention constructs a data-driven improved ellipsoidal uncertainty set based on historical data of photovoltaic power plant output. The specific steps are as follows:

[0204] 3.1 Construction of High-Dimensional Ellipsoid Sets Based on Historical Data

[0205] The collected historical data is divided by day, and all data scenarios are defined. Uncertain sets of high-dimensional ellipsoids The collected data is written in the vector form shown below:

[0206] ;

[0207] In the formula: This represents the generated photovoltaic uncertainty data; A positive definite matrix representing the direction of the deviation of the symmetry axis from the coordinate axes of an uncertain set of a high-dimensional ellipsoid; represents the center point of the uncertain set of a high-dimensional ellipsoid; T represents the mathematical symbol for transpose.

[0208] 3.2 Construction of Uncertain Sets for Linear Polyhedra

[0209] To obtain the vertices of the uncertain set of the high-dimensional ellipsoid, the high-dimensional ellipsoid is rotated so that its axis of symmetry coincides with the coordinate axes. The equation for this rotation is:

[0210] ;

[0211] In the formula: This represents the set of uncertainties in a high-dimensional ellipsoid after rotation; express The coordinate values ​​of the coordinate axes after rotation; and It is for positive definite matrices The matrix obtained during orthogonal decomposition. Let be the transformation matrix. Let be a diagonal matrix, denoted as ; and The following relationship must be satisfied:

[0212] ;

[0213] It can be seen that the uncertainty set of the high-dimensional ellipsoid after rotation is known. of The coordinates of the vertices are:

[0214] ;

[0215] In the formula: Represents the set of uncertainties in a high-dimensional ellipsoid after rotation. The coordinates of the first vertex; Represents the set of uncertainties in a high-dimensional ellipsoid after rotation. The Vertex coordinates; Represents the first positive number in the diagonal matrix D; Describe the first position on the diagonal matrix D A positive number;

[0216] Uncertainty set of the rotated high-dimensional ellipsoid The vertex coordinates can be obtained through inverse transformation. The vertex coordinates; the uncertain set of a linear polyhedron constructed from the vertex coordinates. Represented as:

[0217]

[0218] In the formula: The first polyhedron represents the set of uncertainties. One scaling factor; Represents the set of uncertainties in a high-dimensional ellipsoid after rotation. The The coordinates of each vertex.

[0219] The specific embodiments of the present invention will be described in detail below.

[0220] Test case

[0221] The effectiveness of the two-stage distributed photovoltaic carrying capacity enhancement model provided in this invention was verified using an improved IEEE-33 node power system. All models and algorithms were implemented in MATLAB 2023a and solved using GUROBI 10.0.1. The wind curtailment cost coefficient was [missing information]. The cost coefficient for abandoned load is The initial photovoltaic forecast values ​​(corresponding to photovoltaic power in the figure) and load levels (corresponding to load power in the figure) given by the system are as follows: Figure 3 As shown.

[0222] This experimental example sets up four cases for comparative analysis: Case 1: Robust optimization model without considering the uncertainty of photovoltaic output; Case 2: Without considering various flexible resources; Case 3: Without considering system operation risks; Case 4: Two-stage distributed photovoltaic carrying capacity improvement model (example) provided by the present invention.

[0223] Example 1 omits the uncertain budget for photovoltaic output. The relevant formulas are the same as in Example 4. That is, the specific formula for the actual output of the photovoltaic power station in Example 1 is:

[0224]

[0225] Example 2 omits the relevant formulas for capacitor bank operation constraints, intelligent soft-switching operation constraints, and energy storage constraints from Example 2.2; otherwise, it is the same as Example 4.

[0226] Example 3 omits the system operation risks after processing by the discretization method in Example 2.1. The specific formula, and the expression of the two-stage distributed photovoltaic carrying capacity improvement model does not contain The same applies to Example 4.

[0227] A. Economic Comparison

[0228] Table 1 compares the results of each example. As shown in Table 1, compared to the other three examples, Example 1 lacks robustness due to the absence of uncertainties in photovoltaic output. Although it does not explicitly consider risk constraints, the deviation between the scheduling plan and actual output leads to severe curtailment and load shedding problems. Example 2, in a scenario lacking flexible resource support, while reducing the total system cost to some extent, fails to fully unleash the potential for photovoltaic consumption and still faces high operational risks. Example 3, while relaxing cost constraints by ignoring system operational risks, suffers from a significantly increased risk of curtailment and load shedding due to excessive optimism regarding uncertainties.

[0229] Comparing the data in Table 1, the two-stage distributed photovoltaic (PV) carrying capacity enhancement model provided by this invention demonstrates significant advantages in all indicators. This indicates that the two-stage distributed PV carrying capacity enhancement model provided by this invention achieves synergistic optimization of economic efficiency and operational risk by integrating robust feasible region constraints and flexible resource scheduling. On the one hand, the model effectively avoids the risks of curtailment and load abandonment caused by PV uncertainties through dynamic boundary constraints of the robust feasible region; on the other hand, by fully exploring the potential of various flexible resources, it broadens the PV consumption space and reduces the total system cost. In summary, the two-stage distributed PV carrying capacity enhancement model provided by this invention significantly improves the renewable energy consumption level and economic efficiency while ensuring the safe and reliable operation of the system, providing a better decision-making scheme for power system scheduling with a high proportion of PV.

[0230] Table 1 Comparison of results for each example

[0231]

[0232] In the table, the total cost is based on the two-stage distributed photovoltaic carrying capacity enhancement model. And the corresponding constraints were calculated.

[0233] The photovoltaic carrying capacity and Figure 7 The photovoltaic carrying capacity in the model is also calculated based on a two-stage distributed photovoltaic carrying capacity improvement model and corresponding constraints. Because Figure 7 The result was obtained by continuously adjusting the uncertainty range, from 0.2 to 0.65. However, the two-stage distributed photovoltaic carrying capacity improvement model is based on the standard uncertainty range, meaning the uncertainty fluctuation range is a baseline value. For example, with the horizontal axis at 0.2, the 0.2 in the figure represents 0.2 times the baseline value. Example 1 does not consider photovoltaic uncertainty, while Examples 2, 3, and 4 use the standard uncertainty range. Therefore, Example 1 is naturally not included in the standard uncertainty range. Figure 7 In the middle, therefore Figure 7 The value was adjusted starting from 0.2.

[0234] in the above table The calculations are also based on a two-stage distributed photovoltaic carrying capacity improvement model and corresponding constraints. Examples 1, 2, and 4 consider system operation risks, while example 3 does not. System operation risk corresponds to the results of curtailment and load abandonment generated in the model. However, the fact that example 3 does not use the system operation risk formula to calculate the cost of exceeding limits does not mean that the model in example 3 is free from exceeding limits; example 3 does have limits, therefore the costs in example 3... This represents the normal cost of curtailing solar power and load.

[0235] Similarly, the abandoned light rate, abandoned load rate, and... in the table above... Figure 8 The curtailment rate and load curtailment rate are also calculated based on the two-stage distributed photovoltaic carrying capacity improvement model and corresponding constraints. When the uncertainty starts from 0.2 times, Figure 8 There is no example 1 in the example because example 1 does not consider uncertainty.

[0236] B. Operational Risk Assessment and Analysis

[0237] The optimization results of the robust feasible region of photovoltaic output are as follows: Figure 4 As shown, the boundary of the robust feasible region for photovoltaic (PV) output exhibits significant time-varying characteristics throughout the day, and its distance from the predicted output curve (predicted value) directly determines the risk preference of system operation. Combining the PV predicted values, it can be seen that the upper bound of the robust feasible region for PV output is closer to the predicted value between 4:00 and 5:00, 8:00, 10:00 and 12:00, and 21:00, which easily leads to a higher risk of curtailment. This phenomenon reflects the model's conservatism in dealing with PV output overestimation; it avoids over-dispatch risk by narrowing the upper bound, but at the expense of renewable energy utilization. The lower bound of the robust feasible region between 16:00 and 20:00 is close to the predicted value, meaning that the margin for actual PV output to be lower than the prediction is significantly compressed, and the system's safety margin for dealing with PV output troughs is insufficient, easily leading to a higher risk of load curtailment.

[0238] Furthermore, according to the definition of risk units, the more numerous the risk units, the more accurate the discretization method used in this invention becomes relative to integral solving, but the solution efficiency also decreases. Therefore, it is necessary to find the optimal number of risk units that satisfies both computational accuracy and solution efficiency. To select the optimal number of risk units... We compared the system operational risk values ​​when the number of upper and lower bound risk units were selected as 10, 12, 14, 16, 18, 20, 22, 24, and 26, respectively. Figure 5 As shown, the system operational risk value gradually decreases as the number of risk units increases. At that time, the system's operational risk value remained basically stable.

[0239] Depend on Figure 6 It is evident that the system operation risk value increases with the uncertainty budget of photovoltaic output. The changes exhibit a significant monotonically increasing trend. This trend indicates that the increased uncertainty in the budget leads to a continuous tightening of the robust feasible region boundary, improving the model's coverage of extreme scenarios, and consequently causing a gradual increase in the system's operational risk. Furthermore, when... At the same time, the uncertainty budget for photovoltaic output will continue to increase. The marginal benefit of reducing system operation risks has approached zero, and the improvement of the model's robustness has reached a bottleneck.

[0240] C. Photovoltaic carrying capacity assessment and analysis

[0241] like Figure 7 The figure shows the photovoltaic carrying capacity results under different uncertainty ranges. As can be seen from the figure, as the uncertainty range gradually increases from 0.2 to 0.65, the photovoltaic carrying capacity of each example shows an upward trend. This indicates that a larger uncertainty range can broaden the boundary of the robust feasible region, thereby increasing the system's tolerance for fluctuations in photovoltaic output.

[0242] Specifically, in Example 2, the photovoltaic carrying capacity consistently remained at the lowest level across the entire range, and its increase with the expansion of uncertainty was the most gradual. This indicates that in scenarios lacking flexible resource support, the system faces stricter physical constraints on photovoltaic consumption, and even relaxing the uncertainty range cannot effectively improve the carrying capacity. Example 3 exhibits a significantly higher photovoltaic carrying capacity than Example 2, but its growth rate remains relatively limited. This reflects that while ignoring operational risk constraints can relax dispatch restrictions to some extent, it cannot fundamentally overcome the system's bottleneck in adapting to uncertainty.

[0243] In contrast, the photovoltaic carrying capacity of Example 4 is significantly higher than the other two examples across all uncertainty ranges, with the most significant increase as the uncertainty range expands. This result demonstrates that the model provided in this invention, by integrating robust feasible region constraints and flexible resource scheduling, can effectively improve photovoltaic carrying capacity across a wider range of uncertainties, achieving a high degree of adaptability to fluctuations in photovoltaic output.

[0244] Depend on Figure 8 As can be seen, with the uncertainty range gradually increasing from 0.2 to 0.65, the curtailment rates and load abandonment rates in all three examples show a significant upward trend, indicating that a larger uncertainty range exacerbates the system's operational risks. Looking at the trends, the increases in curtailment rates and load abandonment rates with the expansion of uncertainty are steeper in examples 2 and 3, while the increase in example 4 is relatively gradual. This difference reflects that in scenarios lacking flexible resource support or ignoring operational risk constraints, the system's adaptability to uncertainty decreases significantly, leading to a rapid increase in curtailment and load abandonment risks as the uncertainty range expands. In contrast, the model provided in this invention, by integrating robust constraints and flexible resource scheduling, effectively mitigates the negative impact of uncertainty on system operation, maintaining a lower curtailment rate and load abandonment rate over a wider uncertainty range.

[0245] D. Comparison of solution efficiency

[0246] Figure 9This section compares the computational efficiency of different solution algorithms. The C&CG algorithm (Column and Constraint Generation Algorithm) in the figure solves the two-stage distributed photovoltaic carrying capacity improvement model by applying strong duality theory. The Benders algorithm also applies strong duality theory to the same model. The PSO algorithm (Particle Swarm Optimization) does not require strong duality theory transformation and solves directly.

[0247] Depend on Figure 9 It is evident that the optimal value of the PSO algorithm decreases rapidly in the early stages of iteration and reaches a stable state after 16 iterations, demonstrating high computational efficiency. The upper and lower bounds of the C&CG algorithm show a synchronous convergence trend during iteration, converging after 6 iterations. This trend reflects its characteristic of gradually approaching the optimal solution through iterative optimization. Compared to the C&CG algorithm, the upper and lower bounds of the Benders algorithm exhibit a slower convergence speed, only stabilizing after 18 iterations. From the perspective of convergence characteristics, the PSO algorithm, with its heuristic search mechanism, can quickly approach the optimal solution in the early stages of iteration, significantly shortening the computation time. The C&CG algorithm, through its column and constraint generation strategy, can effectively compress the feasible region, achieving synchronous convergence of the upper and lower bounds, ensuring both optimality and high efficiency. The Benders algorithm, due to the limitations of its decomposition strategy, exhibits relatively slower convergence of the upper and lower bounds during iteration, resulting in higher computational costs. It is noteworthy that all three algorithms ultimately converge to the same optimal value, indicating consistency in solution quality, but significant differences in computational efficiency.

[0248] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the present invention. Although detailed descriptions have been provided with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments, and they should all be covered within the protection scope of the claims.

Claims

1. A two-stage method for enhancing the distributed photovoltaic carrying capacity of a distribution network, taking into account operational risks, characterized in that, Includes the following steps: S1. Establish a system operation risk model based on the robust feasible region of photovoltaic output: The robust feasible region of photovoltaic output is defined as follows: if the photovoltaic output exceeds the maximum allowable threshold, the system needs to curtail photovoltaic power for safe operation; if the photovoltaic output is lower than the minimum allowable threshold, the system needs to curtail load. S2. Construct a two-stage distributed photovoltaic carrying capacity enhancement model: In the day-ahead planning stage, by coordinating the configuration of capacitor banks, smart soft switches and energy storage, a static configuration scheme of multiple flexible resources is formulated with the goal of minimizing system investment and operating costs. During the intraday adjustment phase, the maximum distributed photovoltaic access capacity is achieved while minimizing system operation risk, taking into account the actual operating scenarios of curtailment and load reduction. S3. Construct an improved ellipsoidal uncertainty set based on data-driven approach: Divide the collected historical data into days and establish a high-dimensional ellipsoid set based on the historical data. Rotate the high-dimensional ellipsoid to make its axis of symmetry coincide with the coordinate axis, thereby obtaining the vertices of the high-dimensional ellipsoid uncertainty set. Finally, construct a linear polyhedral uncertainty set from the coordinates of the high-dimensional ellipsoid vertices.

2. The method for enhancing the distributed photovoltaic carrying capacity of a two-stage distribution network, taking into account operational risks, as described in claim 1, is characterized in that... The robust feasible region of photovoltaic output is equivalently described by the following two-layer model, the specific formula of which is: ； In the formula: Indicates photovoltaic power station At any moment The upper limit of the decision variable; Indicates photovoltaic power station At any moment The lower bound decision variable; Indicates pumped storage power station At any moment ; output power; Indicates photovoltaic power station At any moment The power of abandoned light; Indicates load At any moment The power of abandoned load; Indicates time period, Represents a set of nodes.

3. The method for enhancing the distributed photovoltaic carrying capacity of a two-stage distribution network, taking into account operational risks, as described in claim 2, is characterized in that... Constraints are established for the robust feasible region of photovoltaic power output. These constraints specifically include: the actual output of the photovoltaic power station, curtailment and load shedding constraints, the output range of the pumped storage power station, and the ramp-up constraints of the pumped storage power station. The specific formula for the actual output of a photovoltaic power station is as follows: ； In the formula: Indicates photovoltaic power station At any moment ; output power; Indicates photovoltaic power station At any moment The robust feasible domain upper limit; Indicates photovoltaic power station At any moment The predicted power; Indicates photovoltaic power station At any moment The robust feasible lower bound; Indicates any time; Indicates an uncertain budget; Indicates the total number of uncertain nodes; The specific formulas for light curtailment and load curtailment constraints are as follows: ； In the formula: Indicates load At any moment The predicted power; The specific formula for the output range of a pumped storage power station is as follows: ； In the formula: Indicates pumped storage power station At any moment The running status; Indicates pumped storage power station At any moment The lower limit of output power; Indicates pumped storage power station At any moment ; output power; Indicates pumped storage power station At any moment The upper limit of output power; The specific formula for the ramp constraint of pumped storage power stations is as follows: ； In the formula: Indicates pumped storage power station At any moment ; output power; Indicates pumped storage power station At any moment The running status; Indicates pumped storage power station Downhill power; Indicates pumped storage power station The power of climbing uphill.

4. The method for enhancing the distributed photovoltaic carrying capacity of a two-stage distribution network, taking into account operational risks, as described in claim 3, is characterized in that... The system operation risk in the system operation risk model is defined as: the economic loss caused by curtailment of solar power and load when the photovoltaic output exceeds the robust feasible range allowed by the system. The specific formula for system operational risk is as follows: ； In the formula: This indicates system operational risks; This represents the cost coefficient for wasted light. This represents the cost coefficient for abandoned loads; Indicates photovoltaic power station Maximum output power; yes The probability density function; The specific formula for system operational risk is equivalently processed using a discretization method. Specifically, the predicted value is used as the boundary to divide the system into a lower bound interval and an upper bound interval. The lower bound interval and the upper bound interval are then divided into equal parts. and There are several risk units, and the specific formula for the system operation risk value of each risk unit is as follows: ； ； In the formula: Indicates photovoltaic power station At any moment When the output power falls to the first Operational risks of each risk unit; Indicates any time; Represents a risk unit within any upper bound interval; Indicates photovoltaic power station At any moment When the output power falls to the first Operational risks of each risk unit; Represents a risk unit within any lower bound interval; , The actual photovoltaic output appears in the risk unit. , The probability is multiplied by the interval width of the corresponding risk unit; Then, based on the predicted photovoltaic output and the system operation risk value of each risk unit, the specific formula for the system operation risk of the entire scheduling cycle is as follows: ； in ; The robust feasible region for photovoltaic power plant output is represented as follows: ； In the formula: This indicates the operational risk of the system after processing by the discretization method; Indicates photovoltaic power station At any moment When it falls in the first Upward decision variables for each risk unit; Indicates photovoltaic power station At any moment When the output power falls to the first Operational risks of each risk unit; Indicates photovoltaic power station At any moment When it falls in the first Downward decision variables for each risk unit; Indicates photovoltaic power station At any moment When the output power falls to the first Operational risks of each risk unit; Indicates photovoltaic power station At any moment When the output power falls to the first The output limit of each risk unit; Indicates photovoltaic power station At any moment When the output power falls to the first The lower limit of the output of each risk unit.

5. The method for enhancing the distributed photovoltaic carrying capacity of a two-stage distribution network, taking into account operational risks, as described in claim 4, is characterized in that... The expression for the two-stage distributed photovoltaic carrying capacity enhancement model is as follows: ； in: ; ； ； ； ； In the formula: For capacitor bank operating costs; For the operating cost of intelligent soft switches; For energy storage operating costs; The equivalent annual cost of energy storage; The annual operating cost of energy storage; This refers to the total capacity of distributed photovoltaic power grid connection. , and These are 0-1 variables representing whether the capacitor bank, smart soft switch, and energy storage are installed. A value of 1 indicates that the equipment is installed, and a value of 0 indicates that the equipment is not installed. Let U be the set of nodes; U is the uncertainty set of photovoltaic output. For nodes The capacitor bank at time Unproductive efforts; and Representing nodes respectively The intelligent soft switch is always The meritorious and the ineffective contributions; Configure a cost coefficient for each unit of capacity; Configure a cost factor for unit power; and Representing nodes respectively The energy storage configuration capacity and maximum charging and discharging power; For energy storage lifespan; Operating cost per unit power; and Representing nodes respectively Energy storage at time The charging and discharging power; For nodes The permitted capacity of the connected photovoltaic system; This is the unit operating cost coefficient for the capacitor bank; This represents the unit operating cost coefficient for intelligent soft switches.

6. The method for enhancing the distributed photovoltaic carrying capacity of a two-stage distribution network, taking into account operational risks, as described in claim 5, is characterized in that... Constraints are established for the two-stage distributed photovoltaic carrying capacity improvement model. These constraints include: flexibility resource planning constraints, distributed photovoltaic access capacity constraints, distribution network operation constraints, capacitor bank operation constraints, smart soft switching operation constraints, distribution network topology constraints, and energy storage constraints.

7. The method for enhancing the distributed photovoltaic carrying capacity of a two-stage distribution network considering operational risks, as described in claim 6, is characterized in that... The specific formula for the flexibility resource planning constraint is as follows: ； In the formula: , and These represent capacitor banks, smart soft switches, and energy storage nodes, respectively. ,node and Between or nodes Candidate installation locations; , , Representing nodes respectively Whether to install capacitor banks, at the nodes and Are smart soft switches installed on the lines between them, at the nodes? Whether to install energy storage; For the operator's planning budget, this indicates the number of components to be planned; The specific formula for the capacity constraint of distributed photovoltaic power grid connection is as follows: ； In the formula: The photovoltaic power coefficient is determined by the intensity of sunlight. The specific formula for the operating constraints of the distribution network is as follows: ； ； in ; ； ； ； ； ； In the formula: Indicates the line At any moment By node Flow to Node The active power; Indicates the line At any moment By node Flow to Node The active power; Represents a node Energy storage at time The charging power; Represents a node Energy storage at time The discharge power; Indicates a time period; Indicates the line At any moment By node Flow to Node reactive power; Indicates the line At any moment By node Flow to Node reactive power; Represents a node At any moment The voltage; Represents a node At any moment The voltage; This indicates the lower limit of active power from the main grid; Indicates at time Active power from the main network; This indicates the maximum active power output from the main grid. This indicates the lower limit of reactive power from the main grid; Indicates at time Reactive power from the main grid; This indicates the upper limit of reactive power from the main grid; Indicates the line At any moment The square of apparent power; Represents the set of system lines; Indicates the line Upper limit of active power; Indicates the line Reactive power limit; and They represent the times respectively. Active and reactive power from the main grid; and These represent the pumped storage power station at time [time]. The meritorious and the ineffective contributions; and These represent the time intervals of the intelligent soft switch. The meritorious and the ineffective contributions; Indicates the capacitor bank at time [time]. Unproductive efforts; and They represent the times respectively. node The outflow of active and reactive power; and They represent the lines respectively. Resistance and reactance; For a moment The line status is indicated by a value of 1, which represents normal operation, and a value of 0, which represents disconnection. Indicates large The largest possible number in the law; The specific formula for the capacitor bank operating constraints is as follows: ； in ; ； ； In the formula: Represents a node The capacitor bank at time reactive power; Represents a node The Taiwan capacitor bank at time The switching action state; Represents a node The capacitor bank at time The entry point; Represents a node The capacitor bank at time The cutout; Indicates at node The value indicates whether the capacitor bank is installed; 1 indicates installed, and 0 indicates not installed. Indicates at node The capacitor bank at time Whether it is under control, 1 indicates controlled, 0 indicates uncontrolled; Represents a node The upper limit of reactive power of capacitor banks; For nodes The unit reactive power of the capacitor bank; Represents a node The Taiwan capacitor bank at time The switch's operational status is indicated by a value of 1, which represents connection, and a value of 0, which represents disconnection. Represents a node The Taiwan capacitor bank at time The switch's operational status is indicated by a value of 1, which represents connection, and a value of 0, which represents disconnection. Indicates the number of capacitor banks; The specific formula for the operating constraints of intelligent soft switches is as follows: ； in ; ； In the formula: Represents a node The intelligent soft switch is always The active power; Indicates the apparent power of the intelligent soft switch; Represents a node The intelligent soft switch is always reactive power; Represents a node The lower limit of active power for intelligent soft switches; Represents a node The active power of the intelligent soft switch; Indicates at node and The indicator shows whether the smart soft switch is installed; 1 indicates installed, and 0 indicates not installed. At the node and The intelligent soft switch between them is always Whether it is under control, 1 indicates controlled, 0 indicates uncontrolled; Represents a node The upper limit of active power of the intelligent soft switch; Represents a node The lower limit of reactive power for intelligent soft switches; Represents a node The reactive power of the intelligent soft switch; Represents a node The upper limit of reactive power of intelligent soft switches; Represents a node The lower limit of reactive power for intelligent soft switches; Represents a node The reactive power of the intelligent soft switch; Represents a node The upper limit of reactive power of intelligent soft switches; Represents a node The lower limit of active power for intelligent soft switches; Represents a node The active power of the intelligent soft switch; Represents a node The upper limit of active power of the intelligent soft switch; Indicates the candidate installation locations for the intelligent soft switch; The specific formula for distribution network topology constraints is as follows: ； ； ； ； ； In the formula: Represents a node At any moment Child node variables; For nodes At any moment The root node variable, a value of 1 indicates the root node; For nodes At any moment The root node variable, a value of 1 indicates the root node; Represents the set of all root nodes in the system; Indicates the lower limit of the node voltage; Indicates the upper limit of the node voltage; Indicates at time The node relationship is a 0-1 variable, where a value of 1 indicates a node. It is a node The upstream node is 0, otherwise it is 0; This represents the node voltage of node i at time t; The specific formula for energy storage constraints is as follows: ； ； In the formula: Represents a node Energy storage at time ; output power; Represents a node Energy storage at time The charge / discharge control variable is 1, which represents charging, and 0, which represents discharging. Represents a node Energy storage The SOC value at time t, where SOC represents the state of charge of the energy storage; Indicates the lower limit of the SOC of energy storage; Indicates the upper limit of the SOC of energy storage; Represents a node The SOC value of the stored energy at the initial moment; Represents a node The SOC value of the stored energy at the last moment; For charge and discharge efficiency; For nodes Energy storage at time The charge / discharge control variable, with a value of 1 indicating charging and a value of 0 indicating discharging; This is the ratio of the configured capacity to the maximum charge / discharge power. Configure the maximum capacity; For nodes Energy storage at time The SOC value.

8. A two-stage method for enhancing the distributed photovoltaic carrying capacity of a distribution network, taking into account operational risks, as described in any one of claims 1 to 7, characterized in that, Step S3 specifically involves the following steps: The collected historical data is divided by day, and all data scenarios are defined. Uncertain sets of high-dimensional ellipsoids The collected data is written in the vector form shown below: ； In the formula: This represents the generated photovoltaic uncertainty data; A positive definite matrix representing the direction of the deviation of the symmetry axis from the coordinate axes of an uncertain set of a high-dimensional ellipsoid; It represents the center point of the uncertain set of a high-dimensional ellipsoid; T represents the mathematical symbol for transpose; To obtain the vertices of the uncertain set of the high-dimensional ellipsoid, the high-dimensional ellipsoid is rotated so that its axis of symmetry coincides with the coordinate axes. The equation for this rotation is: ； In the formula: This represents the set of uncertainties in a high-dimensional ellipsoid after rotation; express The coordinate values ​​of the coordinate axes after rotation; and It is for positive definite matrices The matrix obtained during orthogonal decomposition. The transformation matrix is... Let be a diagonal matrix, denoted as ; and The following relationship must be satisfied: ； It can be seen that the uncertainty set of the high-dimensional ellipsoid after rotation is known. of The coordinates of the vertices are: ； In the formula: Represents the set of uncertainties in a high-dimensional ellipsoid after rotation. The coordinates of the first vertex; Represents the set of uncertainties in a high-dimensional ellipsoid after rotation. The Vertex coordinates; Represents the first positive number in the diagonal matrix D; Describe the first position on the diagonal matrix D A positive number; Uncertainty set of the rotated high-dimensional ellipsoid The vertex coordinates can be obtained through inverse transformation. The vertex coordinates; the uncertain set of a linear polyhedron constructed from the vertex coordinates. Represented as: ； In the formula: The first polyhedron represents the set of uncertainties. One scaling factor; Represents the set of uncertainties in a high-dimensional ellipsoid after rotation. The The coordinates of each vertex.

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