A method for evaluating timing adjustment capability based on a new timing adjustment domain of a power system

Abstract

The application discloses a kind of based on novel power system timing adjustment domain's timing adjustment capacity evaluation method, comprising the following steps: constructing novel power system timing adjustment domain model;Based on topological theory systematic demonstration timing adjustment domain's boundary existence, closedness and spatial monotonicity does not decrease;Design timing up-regulation margin, timing down-regulation margin, timing adjustment domain volume index, construct timing adjustment domain-based timing adjustment capacity evaluation index system;Construct deep neural network architecture, design priori constraint regular term, realize based on priori constraint guide's timing adjustment domain boundary solution.The present application faces the major needs of the safe and stable operation of new power system, proposes a timing adjustment capacity evaluation method based on the timing adjustment domain of the new power system, which describes the adjustment space at the current time under the balance demand within the dispatching period, providing a theoretical tool for evaluating the timing adjustment capacity of the new power system.

Description

Technical Field

[0001] This invention relates to the field of novel power system balance analysis, specifically a method for evaluating the time-series regulation capability based on a novel power system time-series regulation domain. Background Technology

[0002] The continuous and rapid development of new energy sources has led to a severe shortage of power system regulation capacity. Accurately characterizing time-series regulation capacity is crucial to ensuring the safe and stable operation of new power systems. The problem of assessing the time-series regulation capacity of new power systems exhibits significant time-series dependence and high-dimensional complexity: on the one hand, the regulation measures adopted in the current period directly affect the available regulation resources in subsequent periods, making it difficult to independently assess the regulation capacity of each period; on the other hand, the collaborative optimization of multiple types of regulation resources across multiple periods constitutes a high-dimensional complex decision space, and the solution scale increases exponentially with the increase of dimension.

[0003] Existing methods primarily assess system regulation capacity from two perspectives: renewable energy absorption capacity and flexibility. Regarding renewable energy absorption capacity assessment, current research can be categorized into supply-demand balance-based assessments and safety and stability-based assessments, based on the dominant factors constraining renewable energy absorption. In terms of flexibility assessment, existing research mainly designs flexibility indicators based on the key operational characteristics of regulation resources and conducts assessment analyses. The core idea of ​​these studies is to conduct "point assessments" of system regulation capacity from different perspectives based on time-series production simulations. This approach fails to comprehensively characterize the complete regulation space of the system under time-series coupling constraints, thus limiting the scientific guidance of assessment results for system operation scheduling and resource allocation.

[0004] Therefore, domain theory is introduced to construct a novel time-series regulation domain model for power systems. Domain theory, from a global perspective of the feasible space, maps all feasible states of the system under time-coupling constraints to a specific observation space, thereby achieving a global characterization of the system's regulation capability. After years of exploration, power system domain theory has formed a systematic theoretical framework, including domains such as the security domain, dispatchable domain, wind power absorption domain, and flexible operation domain. While the above studies have characterized the system's regulation capability to some extent, research on the novel time-series regulation capability of power systems based on domain theory is still incomplete, lacking systematic modeling methods; it has failed to reveal the marginal benefit variation law of regulation cost input, making it difficult to identify the optimal range of cost input, thus restricting the economical and efficient utilization of regulation resources.

[0005] The key to applying time-series regulation domains lies in the rapid and accurate characterization of domain boundaries. However, efficient solution for domain boundaries faces severe challenges due to the temporal dependence of regulation resources and the high-dimensional complexity of the observation space. Existing methods for characterizing domain boundaries mainly include analytical methods, point-by-point simulation methods, hyperplane methods, convex hull methods, and neural network methods. Analytical methods, based on mathematical models, analytically express domain boundaries, but struggle to meet the demands for efficient solution of high-dimensional domain boundaries. Point-by-point simulation methods select a large number of sampling points to fit the domain boundary, but the fitting accuracy is limited by the number of sampling points. Hyperplane methods use multiple hyperplanes to linearly approximate the domain boundary piecewise, but there is a trade-off between the number of hyperplanes and the fitting accuracy. Convex hull methods construct convex hull approximations to fit the domain boundary, but oversimplification of the domain boundary may result in the loss of important local features. Neural network methods construct deep neural networks to fit the high-dimensional complex features of the domain boundary, demonstrating significant advantages in solving domain boundaries.

[0006] The novel power system time-series regulation domain model considers multiple time periods and various types of time-series coupling constraints, resulting in high-dimensional and complex domain boundaries. Existing mainstream solution algorithms face the following key challenges:

[0007] 1) The curse of dimensionality limits the efficiency of boundary solution. The temporal adjustment domain exhibits high-dimensional characteristics in the observation space. In order to ensure the accuracy of the domain boundary characterization, point-search-based methods such as point-by-point simulation and vertex search need to be optimized for a large number of sampling points. The computational complexity increases exponentially with the increase of dimensionality.

[0008] 2) Poor model interpretability. Data-driven deep neural network methods fail to incorporate the operating mechanisms of power systems, resulting in poor model interpretability and an inability to guarantee that the results conform to the operating laws of power systems.

[0009] To address the aforementioned issues, it is necessary to explore the concept and methods of a new power system time-series regulation domain, thereby achieving accurate characterization of time-series regulation capabilities and efficient solution of the time-series regulation domain boundary. Summary of the Invention

[0010] The purpose of this invention is to provide a method for evaluating the timing regulation capability of a power system based on a novel timing regulation domain, comprising the following steps:

[0011] Step 1) Considering various constraints on the operation of regulating resources, power flow equation constraints, security constraints, and regulation cost limits, construct a new power system time-series regulation domain model;

[0012] Step 2) Construct an evaluation index system for time series adjustment capability based on the time series adjustment domain, including time series up-adjustment margin, time series down-adjustment margin, and time series adjustment domain volume index;

[0013] Step 3) Construct a deep neural network architecture, design prior constraint regularization terms, and train the deep neural network architecture;

[0014] Step 4) Using the new power system time-series regulation domain model as constraints, the trained deep neural network architecture is used to solve the time-series regulation domain boundary based on prior constraints.

[0015] Furthermore, various constraints on the operation of regulatory resources include constraints on thermal power operation, hydropower operation, pumped storage operation, energy storage operation, wind power operation, photovoltaic operation, nuclear power output, power transmission and reception, and demand-side response.

[0016] Thermal power plant operation constraints include thermal power plant operation status constraints, thermal power plant minimum start-up and shutdown time constraints, thermal power plant ramping constraints, and thermal power plant capacity constraints.

[0017] Hydropower operation constraints include hydropower ramping constraints, hydropower capacity constraints, and hydropower generation constraints.

[0018] Pumped storage operation constraints include pumped storage operation status constraints, pumped storage capacity constraints, reservoir capacity constraints, water storage volume constraints, and initial and final water storage volume constraints.

[0019] Energy storage operation constraints include energy storage operation status constraints, energy storage capacity constraints, battery capacity constraints, battery charge constraints, and battery charge initial and final state constraints.

[0020] Power transmission and receiving constraints include upper and lower limits of power transmission, increasing upper and lower limits of power transmission, power transmission capacity constraints, upper and lower limits of power receiving, decreasing upper and lower limits of power receiving, and power receiving capacity constraints.

[0021] Demand-side response constraints include transferable load capacity constraints, transferable load power constraints, and load reduction capacity constraints.

[0022] Furthermore, the operating constraints for thermal power plants are as follows:

[0023] (1)

[0024] (2)

[0025] The minimum start-up and shutdown time constraints for thermal power plants are as follows:

[0026] (3)

[0027] (4)

[0028] The ramp-up constraint formula for thermal power plants is shown below:

[0029] (5)

[0030] (6)

[0031] The thermal power capacity constraint formula is shown below:

[0032] (7)

[0033] In the formula: Let g be the start-up variable of the thermal power unit at time t; Let g be the shutdown variable of the thermal power unit at time t; Let g be the state variable of the thermal power unit at time t; This is the minimum start-up time for the unit; This is the minimum shutdown time for the unit; Let g be the power of the thermal power unit at time t; , Let g be the uphill and downhill speeds of the thermal power unit. , For the start-up and shutdown rates of thermal power unit g; , This represents the upper and lower limits of the power output of thermal power unit g;

[0034] The hydropower ramp-up constraint in hydropower operation constraints is as follows:

[0035] (8)

[0036] (9)

[0037] The hydropower capacity constraints are as follows:

[0038] (10)

[0039] The constraints on hydropower generation are as follows:

[0040] (11)

[0041] In the formula: Let h be the power output of the hydroelectric generator unit at time t; , Let h be the uphill and downhill speeds of the hydroelectric generator unit; , is the upper and lower limits of the power output of the hydropower unit h; T is the dispatching cycle; The total power generation of the hydropower unit during the scheduling cycle h;

[0042] The pumped storage operation constraints are as follows:

[0043] (12)

[0044] Pumped storage capacity constraints are shown below:

[0045] (13)

[0046] (14)

[0047] The capacity constraints of the water storage tank are as follows:

[0048] (15)

[0049] (16)

[0050] The water storage capacity constraints are as follows:

[0051] (17)

[0052] (18)

[0053] The initial and final state constraints of water storage are as follows:

[0054] (19)

[0055] (20)

[0056] In the formula: , Let ps be the pumping and power generation state variables of the pumped storage unit at time t; , The upper and lower limits of the pumping power of the pumped storage unit (ps); , The upper and lower limits of the power generation capacity of the pumped storage unit (ps); , Let ps be the pumping and generating power of the pumped storage unit at time t; , Let be the water volume in the upper and lower reservoirs of the pumped-storage unit ps at time t; kps,c and kps,d are the pumping and power generation coefficients of the pumped-storage unit ps. , The maximum and minimum capacities of the upper reservoir of the pumped storage unit (ps); , The maximum and minimum capacities of the lower reservoir for the pumped storage unit PS; , The initial and final water volume in the reservoir for the pumped storage unit PS; , The initial and final water volume in the reservoir for the pumped storage unit PS;

[0057] The energy storage operation constraints are as follows:

[0058] (twenty one)

[0059] Energy storage capacity constraints are as follows:

[0060] (twenty two)

[0061] (twenty three)

[0062] The battery capacity constraints are as follows:

[0063] (twenty four)

[0064] The battery power constraints are as follows:

[0065] (25)

[0066] The initial and final states of the battery are constrained as follows:

[0067] (26)

[0068] In the formula: , Let be the charging and power generation state variables of the energy storage bs at time t; , The upper and lower limits of the charging power of energy storage bs; , These represent the upper and lower limits of the power generation capacity of energy storage bs. , Let be the charging and generating power of the energy storage bs at time t; Let b be the battery capacity for storing energy at time t; , The battery charging and power generation coefficient for energy storage bs; , The maximum and minimum battery capacity for energy storage bs; , The initial and final battery charge levels for energy storage BBS scheduling;

[0069] The operating constraints for wind power are as follows:

[0070] (27)

[0071] In the formula: Let w be the power of the wind turbine at time t; , This represents the upper and lower limits of the power output of the wind turbine unit w.

[0072] The photovoltaic operating constraints are as follows:

[0073] (28)

[0074] In the formula: Let be the power of the photovoltaic unit's PV at time t; , These are the upper and lower limits of the power output of the photovoltaic (PV) unit.

[0075] Nuclear power output constraints are as follows:

[0076] (29)

[0077] In the formula: Let NUC be the power of the nuclear power unit at time t; , These are the upper and lower limits of the power output of a nuclear power unit's NUC (nuclear accumulator).

[0078] In the power transmission and reception constraints, the upper and lower limits of the power transmission capacity are as follows:

[0079] (30)

[0080] The upper and lower limits of the power transmission capacity are added as follows:

[0081] (31)

[0082] The power delivery constraints are as follows:

[0083] (32)

[0084] The upper and lower limits of the received power are constrained as follows:

[0085] (33)

[0086] The following are the reductions in the upper and lower limits of the received power:

[0087] (34)

[0088] The following are the constraints imposed by the amount of electricity:

[0089] (35)

[0090] In the formula: Let be the power transmitted by node tra at time t; , These are the upper and lower limits of the power supply to the tra node; The increased power supply of the ext_tra node at time t; Increase the upper limit of the power supply for the ext_tra node; Power is supplied to the tra node during its scheduling cycle; Let be the power received by the buy node at time t; , These are the upper and lower limits of the power received by the buy node; The reduced power received by the cut_buy node at time t; Reduce the upper limit of the power received by the cut_buy node; The scheduling cycle of the buy node is affected by power consumption;

[0091] In the demand-side response constraints, the transferable load capacity constraint is as follows:

[0092] (36)

[0093] The transferable load power constraints are as follows:

[0094] (37)

[0095] The load reduction capacity constraints are as follows:

[0096] (38)

[0097] In the formula: Let be the transferable load power of node l at time t; , These are the upper and lower limits of the transferable load power of node l; Let be the load power that can be reduced at node cl at time t; , The upper and lower limits of the load power that can be reduced at node cl.

[0098] Furthermore, the power flow equation constraints are as follows:

[0099] (39)

[0100] In the formula: The set of thermal power units connected to node i; This is the set of hydroelectric generators connected to node i. This refers to the set of photovoltaic units connected to node i. This refers to the set of wind turbine units connected to node i. This refers to the set of pumped storage units connected to node i. For the energy storage collection connected to the i-node; This refers to the set of nuclear power units connected to node i. Let be the active load of node i at time t; The set of branches connected to node i; Let be the active power transmitted from node i to node j at time t;

[0101] The line transmission power is shown below:

[0102] (40)

[0103] In the formula: Let be the phase angle of the voltage at node i at time t; Let i be the line reactance of node i and node j.

[0104] Furthermore, the security constraints are as follows:

[0105] (41)

[0106] In the formula: , Phase angle of the voltage at node i The upper and lower limits.

[0107] Furthermore, the adjustment cost constraints are as follows:

[0108] (42)

[0109] In the formula: The regulation cost of the pumped storage unit (PS); The regulation cost of energy storage bs; BUY is to reduce the set of nodes receiving power; To reduce the power receiving cost of the cut_buy node; The start-up and shutdown cost of thermal power unit g; To reduce nuclear power costs for nuclear power units (NUC); TRA is to increase the set of nodes for power transmission. The additional power supply cost for the ext_tra node; CL is the set of demand-side response nodes; The demand-side response cost for the cl node; Let w be the cost of wind curtailment for the wind turbine unit; The cost of curtailment for photovoltaic (PV) units;

[0110] in:

[0111] (43)

[0112] (44)

[0113] (45)

[0114] (46)

[0115] (47)

[0116] (48)

[0117] (49)

[0118] (50)

[0119] (51)

[0120] In the formula: , Cost coefficient for charging and generating electricity for pumped storage units; , Cost coefficient for charging and generating electricity for energy storage BBS; Reduce the power consumption cost of the cut_buy node; , For the cost coefficient of starting up and shutting down thermal power unit g; To reduce the cost factor of nuclear power units (NUC); Add a cost factor for power supply to the ext_tra node; The cost factor for reducing load on the demand side response of node cl; Let w be the wind curtailment cost coefficient for wind turbine unit w; This represents the curtailment cost coefficient for photovoltaic (PV) units.

[0121] Furthermore, the boundary of the temporal adjustment domain possesses existence and closure; the space of the temporal adjustment domain possesses monotonicity and non-decreasingness.

[0122] Furthermore, the time-series adjustment margin is as follows:

[0123] (52)

[0124] In the formula: n is the observation dimension; This is the value of the boundary point on the domain in the m-th observation dimension; This represents the value of the running point in the m-th observation dimension;

[0125] The timing downsizing margin is shown below:

[0126] (53)

[0127] In the formula: This is the value of the lower boundary point of the domain in the m-th observation dimension;

[0128] The timing adjustment domain volume is shown below:

[0129] (54)

[0130] (55)

[0131] In the formula: x is the vector of observed variables; A is the matrix of equality constraint coefficients; b is the vector of equality constraint coefficients; D is the matrix of inequality constraint coefficients. To match the given adjustment cost limit The relevant inequality constraint coefficient vector; Given adjustment cost limit A subset of the next time-series adjustment domain.

[0132] Furthermore, the prior constraint regularization terms include the upper boundary prior constraint regularization term and the lower boundary prior constraint regularization term;

[0133] The upper boundary prior constraint regularization term is shown below:

[0134] (56)

[0135] In the formula: C is the cost set of different boundary points; The adjustment cost limit corresponding to the current boundary point of the input network; The adjustment cost limit for other boundary points that have the same conditional observation variables as the current boundary point, excluding adjustment costs; The upper boundary power output fitted by the neural network; The target node load power for the aforementioned boundary point samples;

[0136] The lower boundary prior constraint regularization terms are shown below:

[0137] (57)

[0138] In the formula: The lower boundary power output fitted by the neural network; The target node load power for the boundary point sample.

[0139] Furthermore, the deep neural network architecture includes a convolutional feature extraction layer and a fully connected mapping layer; the deep neural network architecture is used to realize the mapping from conditional observed load power variables to target observed load power variables;

[0140] The loss function used when training a deep neural network architecture is as follows:

[0141] (58)

[0142] In the formula, , For dynamic weighting coefficients; MAE is the mean squared error; when fitting the upper boundary, When fitting the lower boundary, .

[0143] The technical effects of this invention are undeniable. Addressing the critical need for the safe and stable operation of new power systems, this invention proposes a method for evaluating the time-series regulation capability based on the time-series regulation domain of new power systems. It characterizes the regulation space at the current moment under the condition of meeting the balance requirements within the scheduling cycle, providing a theoretical tool for evaluating the time-series regulation capability of new power systems.

[0144] This invention proposes a novel concept of a time-series regulation domain for power systems, constructing a time-series regulation domain model that considers the time-series coupling constraints of various regulation resources and the limit constraints of regulation costs. From a mathematical theoretical perspective, the boundary characteristics of the time-series regulation domain are analyzed, demonstrating its existence, closure, and spatial monotonicity. From the perspectives of time-series up-regulation capacity, down-regulation capacity, and total regulation capacity, an evaluation index system is constructed that includes time-series up-regulation margin, time-series down-regulation margin, and the volume of the time-series regulation domain.

[0145] To address the challenge of high-dimensional complexity in existing domain boundary solutions, a temporally adjusted domain boundary solution method guided by prior constraints is proposed. This method fits the domain boundary by constructing a deep neural network. The core idea is to incorporate the monotonic and non-decreasing property of the temporally adjusted domain subset space into the neural network training process, thereby combining data-driven approaches with physical constraints.

[0146] In terms of effectiveness, the time-series conditioning domain boundary solution method based on prior constraints achieves accurate capture of the complex boundary morphology features of the time-series conditioning domain by constructing a deep neural network and incorporating the spatial monotonicity of the time-series conditioning domain into the neural network training process. It also demonstrates good versatility in characterizing high-dimensional time-series conditioning domains. Attached Figure Description

[0147] Figure 1 This is a verification diagram of the accuracy of the upper boundary of the three-dimensional temporal adjustment domain;

[0148] Figure 2 This is a verification diagram of the accuracy of the lower boundary of the three-dimensional time-series adjustment domain;

[0149] Figure 3 This is a verification diagram of the accuracy of the upper boundary of the five-dimensional time-series adjustment domain;

[0150] Figure 4 This is a verification diagram of the lower boundary accuracy of the five-dimensional time-series adjustment domain;

[0151] Figure 5 It is a time-series conditioning capability evaluation diagram based on the time-series conditioning domain;

[0152] Figure 6 This is a graph showing the relationship between adjustment cost and the area of ​​the time-series adjustment domain.

[0153] Figure 7 It is a graph showing the relationship between adjustment cost and slope;

[0154] Figure 8 This is a comparison chart of time-series adjustment domains under different new energy penetration rates;

[0155] Figure 9 It is a two-dimensional projection diagram of the time-series adjustment domain under different new energy penetration rates;

[0156] Figure 10 It is a two-dimensional projection of the time-series adjustment domain under low new energy penetration rate;

[0157] Figure 11 It is a two-dimensional projection of the time-series adjustment domain under high new energy penetration rate;

[0158] Figure 12 It is the relationship between the penetration rate of new energy sources and the volume of the time-series adjustment domain. Detailed Implementation

[0159] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0160] Example 1:

[0161] See Figures 1-12 A method for evaluating the time-series regulation capability of a novel power system based on a time-series regulation domain includes the following steps:

[0162] Step 1) Considering various constraints on the operation of regulating resources, power flow equation constraints, security constraints, and regulation cost limits, construct a new power system time-series regulation domain model;

[0163] Step 2) Construct an evaluation index system for time series adjustment capability based on the time series adjustment domain, including time series up-adjustment margin, time series down-adjustment margin, and time series adjustment domain volume index;

[0164] Step 3) Construct a deep neural network architecture, design prior constraint regularization terms, and train the deep neural network architecture;

[0165] Step 4) Using the new power system time-series regulation domain model as constraints, the trained deep neural network architecture is used to solve the time-series regulation domain boundary based on prior constraints.

[0166] Example 2:

[0167] A method for evaluating the time-series regulation capability based on a novel power system time-series regulation domain, with the same technical content as in Example 1, further including various regulation resource operation constraints such as thermal power operation constraints, hydropower operation constraints, pumped storage operation constraints, energy storage operation constraints, wind power operation constraints, photovoltaic operation constraints, nuclear power output constraints, power transmission and reception constraints, and demand-side response constraints.

[0168] Thermal power plant operation constraints include thermal power plant operation status constraints, thermal power plant minimum start-up and shutdown time constraints, thermal power plant ramping constraints, and thermal power plant capacity constraints.

[0169] Hydropower operation constraints include hydropower ramping constraints, hydropower capacity constraints, and hydropower generation constraints.

[0170] Pumped storage operation constraints include pumped storage operation status constraints, pumped storage capacity constraints, reservoir capacity constraints, water storage volume constraints, and initial and final water storage volume constraints.

[0171] Energy storage operation constraints include energy storage operation status constraints, energy storage capacity constraints, battery capacity constraints, battery charge constraints, and battery charge initial and final state constraints.

[0172] Power transmission and receiving constraints include upper and lower limits of power transmission, increasing upper and lower limits of power transmission, power transmission capacity constraints, upper and lower limits of power receiving, decreasing upper and lower limits of power receiving, and power receiving capacity constraints.

[0173] Demand-side response constraints include transferable load capacity constraints, transferable load power constraints, and load reduction capacity constraints.

[0174] Example 3:

[0175] A method for evaluating the timing regulation capability of a novel power system timing regulation domain is proposed, with the technical content being the same as any one of Embodiments 1-2. Further, in the thermal power plant operation constraints, the thermal power plant operation state constraints are as follows:

[0176] (1)

[0177] (2)

[0178] The minimum start-up and shutdown time constraints for thermal power plants are as follows:

[0179] (3)

[0180] (4)

[0181] The ramp-up constraint formula for thermal power plants is shown below:

[0182] (5)

[0183] (6)

[0184] The thermal power capacity constraint formula is shown below:

[0185] (7)

[0186] In the formula: Let g be the start-up variable of the thermal power unit at time t; Let g be the shutdown variable of the thermal power unit at time t; Let g be the state variable of the thermal power unit at time t; This is the minimum start-up time for the unit; This is the minimum shutdown time for the unit; Let g be the power of the thermal power unit at time t; , Let g be the uphill and downhill speeds of the thermal power unit. , For the start-up and shutdown rates of thermal power unit g; , This represents the upper and lower limits of the power output of thermal power unit g;

[0187] The hydropower ramp-up constraint in hydropower operation constraints is as follows:

[0188] (8)

[0189] (9)

[0190] The hydropower capacity constraints are as follows:

[0191] (10)

[0192] The constraints on hydropower generation are as follows:

[0193] (11)

[0194] In the formula: Let h be the power output of the hydroelectric generator unit at time t; , Let h be the uphill and downhill speeds of the hydroelectric generator unit; , is the upper and lower limits of the power output of the hydropower unit h; T is the dispatching cycle; The total power generation of the hydropower unit during the scheduling cycle h;

[0195] The pumped storage operation constraints are as follows:

[0196] (12)

[0197] Pumped storage capacity constraints are shown below:

[0198] (13)

[0199] (14)

[0200] The capacity constraints of the water storage tank are as follows:

[0201] (15)

[0202] (16)

[0203] The water storage capacity constraints are as follows:

[0204] (17)

[0205] (18)

[0206] The initial and final state constraints of water storage are as follows:

[0207] (19)

[0208] (20)

[0209] In the formula: , Let ps be the pumping and power generation state variables of the pumped storage unit at time t; , The upper and lower limits of the pumping power of the pumped storage unit (ps); , The upper and lower limits of the power generation capacity of the pumped storage unit (ps); , Let ps be the pumping and generating power of the pumped storage unit at time t; , Let be the water volume in the upper and lower reservoirs of the pumped-storage unit ps at time t; kps,c and kps,d are the pumping and power generation coefficients of the pumped-storage unit ps. , The maximum and minimum capacities of the upper reservoir of the pumped storage unit (ps); , The maximum and minimum capacities of the lower reservoir for the pumped storage unit PS; , The initial and final water volume in the reservoir for the pumped storage unit PS; , The initial and final water volume in the reservoir for the pumped storage unit PS;

[0210] The energy storage operation constraints are as follows:

[0211] (twenty one)

[0212] Energy storage capacity constraints are as follows:

[0213] (twenty two)

[0214] (twenty three)

[0215] The battery capacity constraints are as follows:

[0216] (twenty four)

[0217] The battery power constraints are as follows:

[0218] (25)

[0219] The initial and final states of the battery are constrained as follows:

[0220] (26)

[0221] In the formula: , Let be the charging and power generation state variables of the energy storage bs at time t; , The upper and lower limits of the charging power of energy storage bs; , These represent the upper and lower limits of the power generation capacity of energy storage bs. , Let be the charging and generating power of the energy storage bs at time t; Let b be the battery capacity for storing energy at time t; , The battery charging and power generation coefficient for energy storage bs; , The maximum and minimum battery capacity for energy storage bs; , The initial and final battery charge levels for energy storage BBS scheduling;

[0222] The operating constraints for wind power are as follows:

[0223] (27)

[0224] In the formula: Let w be the power of the wind turbine at time t; , This represents the upper and lower limits of the power output of the wind turbine unit w.

[0225] The photovoltaic operating constraints are as follows:

[0226] (28)

[0227] In the formula: Let be the power of the photovoltaic unit's PV at time t; , These are the upper and lower limits of the power output of the photovoltaic (PV) unit.

[0228] Nuclear power output constraints are as follows:

[0229] (29)

[0230] In the formula: Let NUC be the power of the nuclear power unit at time t; , These are the upper and lower limits of the power output of a nuclear power unit's NUC (nuclear accumulator).

[0231] In the power transmission and reception constraints, the upper and lower limits of the power transmission capacity are as follows:

[0232] (30)

[0233] The upper and lower limits of the power transmission capacity are added as follows:

[0234] (31)

[0235] The power delivery constraints are as follows:

[0236] (32)

[0237] The upper and lower limits of the received power are constrained as follows:

[0238] (33)

[0239] The following are the reductions in the upper and lower limits of the received power:

[0240] (34)

[0241] The following are the constraints imposed by the amount of electricity:

[0242] (35)

[0243] In the formula: Let be the power transmitted by node tra at time t; , These are the upper and lower limits of the power supply to the tra node; The increased power supply of the ext_tra node at time t; Increase the upper limit of the power supply for the ext_tra node; Power is supplied to the tra node during its scheduling cycle; Let be the power received by the buy node at time t; , These are the upper and lower limits of the power received by the buy node; The reduced power received by the cut_buy node at time t; Reduce the upper limit of the power received by the cut_buy node; The scheduling cycle of the buy node is affected by power consumption;

[0244] In the demand-side response constraints, the transferable load capacity constraint is as follows:

[0245] (36)

[0246] The transferable load power constraints are as follows:

[0247] (37)

[0248] The load reduction capacity constraints are as follows:

[0249] (38)

[0250] In the formula: Let be the transferable load power of node l at time t; , These are the upper and lower limits of the transferable load power of node l; Let be the load power that can be reduced at node cl at time t; , The upper and lower limits of the load power that can be reduced at node cl.

[0251] Example 4:

[0252] A method for evaluating the timing regulation capability of a power system based on a novel power system timing regulation domain, with the same technical content as any one of embodiments 1-3, further wherein the power flow equation constraints are as follows:

[0253] (39)

[0254] In the formula: The set of thermal power units connected to node i; This is the set of hydroelectric generators connected to node i. This refers to the set of photovoltaic units connected to node i. This refers to the set of wind turbine units connected to node i. This refers to the set of pumped storage units connected to node i. For the energy storage collection connected to the i-node; This refers to the set of nuclear power units connected to node i. Let be the active load of node i at time t; The set of branches connected to node i; Let be the active power transmitted from node i to node j at time t;

[0255] The line transmission power is shown below:

[0256] (40)

[0257] In the formula: Let be the phase angle of the voltage at node i at time t; Let i be the line reactance of node i and node j.

[0258] Example 5:

[0259] A method for evaluating the timing regulation capability of a novel power system timing regulation domain is proposed, with the technical content being the same as any one of embodiments 1-4. Further, the security constraints are as follows:

[0260] (41)

[0261] In the formula: , Phase angle of the voltage at node i The upper and lower limits.

[0262] Example 6:

[0263] A method for evaluating the time-series regulation capability based on a novel power system time-series regulation domain, with the same technical content as any one of embodiments 1-5, further wherein the regulation cost constraint is as follows:

[0264] (42)

[0265] In the formula: The regulation cost of the pumped storage unit (PS); The regulation cost of energy storage bs; BUY is to reduce the set of nodes receiving power; To reduce the power receiving cost of the cut_buy node; The start-up and shutdown cost of thermal power unit g; To reduce nuclear power costs for nuclear power units (NUC); TRA is to increase the set of nodes for power transmission. The additional power supply cost for the ext_tra node; CL is the set of demand-side response nodes; The demand-side response cost for the cl node; Let w be the cost of wind curtailment for the wind turbine unit; The cost of curtailment for photovoltaic (PV) units;

[0266] in:

[0267] (43)

[0268] (44)

[0269] (45)

[0270] (46)

[0271] (47)

[0272] (48)

[0273] (49)

[0274] (50)

[0275] (51)

[0276] In the formula: , Cost coefficient for charging and generating electricity for pumped storage units; , Cost coefficient for charging and generating electricity for energy storage BBS; Reduce the power consumption cost of the cut_buy node; , For the cost coefficient of starting up and shutting down thermal power unit g; To reduce the cost factor of nuclear power units (NUC); Add a cost factor for power supply to the ext_tra node; The cost factor for reducing load on the demand side response of node cl; Let w be the wind curtailment cost coefficient for wind turbine unit w; This represents the curtailment cost coefficient for photovoltaic (PV) units.

[0277] Example 7:

[0278] A method for evaluating the timing regulation capability of a novel power system based on a timing regulation domain is provided. The technical content is the same as any one of embodiments 1-6. Furthermore, the boundary of the timing regulation domain has existence and closure; the space of the timing regulation domain has monotonicity.

[0279] Example 8:

[0280] A method for evaluating the timing regulation capability based on a novel power system timing regulation domain, with technical content identical to any one of embodiments 1-7, further wherein the timing adjustment margin is as follows:

[0281] (52)

[0282] In the formula: n is the observation dimension; This is the value of the boundary point on the domain in the m-th observation dimension; This represents the value of the running point in the m-th observation dimension;

[0283] The timing downsizing margin is shown below:

[0284] (53)

[0285] In the formula: This is the value of the lower boundary point of the domain in the m-th observation dimension;

[0286] The timing adjustment domain volume is shown below:

[0287] (54)

[0288] (55)

[0289] In the formula: x is the vector of observed variables; A is the matrix of equality constraint coefficients; b is the vector of equality constraint coefficients; D is the matrix of inequality constraint coefficients. To match the given adjustment cost limit The relevant inequality constraint coefficient vector; Given adjustment cost limit A subset of the next time-series adjustment domain.

[0290] Example 9:

[0291] A method for evaluating the timing regulation capability based on a novel power system timing regulation domain, with the same technical content as any one of embodiments 1-8, further comprising an upper boundary prior constraint regularization term and a lower boundary prior constraint regularization term;

[0292] The upper boundary prior constraint regularization term is shown below:

[0293] (56)

[0294] In the formula: C is the cost set of different boundary points; The adjustment cost limit corresponding to the current boundary point of the input network; The adjustment cost limit for other boundary points that have the same conditional observation variables as the current boundary point, excluding adjustment costs; The upper boundary power output fitted by the neural network; The target node load power for the aforementioned boundary point samples;

[0295] The lower boundary prior constraint regularization terms are shown below:

[0296] (57)

[0297] In the formula: The lower boundary power output fitted by the neural network; The target node load power for the boundary point sample.

[0298] Example 10:

[0299] A method for evaluating the time-series regulation capability based on a novel power system time-series regulation domain, with the same technical content as any one of embodiments 1-9, further comprising a deep neural network architecture including a convolutional feature extraction layer and a fully connected mapping layer; the deep neural network architecture is used to realize the mapping from conditional observed load power variables to target observed load power variables;

[0300] The loss function used when training a deep neural network architecture is as follows:

[0301] (58)

[0302] In the formula, , For dynamic weighting coefficients; MAE is the mean squared error; when fitting the upper boundary, When fitting the lower boundary, .

[0303] Example 11:

[0304] A method for evaluating the timing regulation capability of a power system based on a novel timing regulation domain includes the following steps:

[0305] 1) Considering various constraints on the operation of regulating resources, power flow equation constraints, security constraints, and regulation cost limits, a new time-series regulation domain model for the power system is constructed.

[0306] 2) Based on topological theory, systematically demonstrate the existence and closure of the boundary of the temporal adjustment domain, and the monotonicity of the temporal adjustment domain space;

[0307] 3) Design time series up-adjustment margin, time series down-adjustment margin, and time series adjustment domain volume index, and construct a time series adjustment capability evaluation index system based on the time series adjustment domain;

[0308] 4) Construct a deep neural network architecture, design prior constraint regularization terms, and realize the solution of the temporal adjustment domain boundary guided by prior constraints.

[0309] The operational constraints of various regulatory resources are as follows:

[0310] Electrical operating constraints.

[0311] The constraints on thermal power plant operation include thermal power plant operation status constraints (1) and (2), thermal power plant minimum start-up and shutdown time constraints (3) and (4), thermal power plant ramping constraints (5) and (6), and thermal power plant capacity constraints (7).

[0312] (1)

[0313] (2)

[0314] (3)

[0315] (4)

[0316] (5)

[0317] (6)

[0318] (7)

[0319] In the formula: Let g be the start-up variable of the thermal power unit at time t; Let g be the shutdown variable of the thermal power unit at time t; Let g be the state variable of the thermal power unit at time t; This is the minimum start-up time for the unit; This is the minimum shutdown time for the unit; Let g be the power of the thermal power unit at time t; , Let g be the uphill and downhill speeds of the thermal power unit. , For the start-up and shutdown rates of thermal power unit g; , This represents the upper and lower limits of the power output of thermal power unit g;

[0320] Electrical operating constraints

[0321] Hydropower operation constraints include hydropower ramp constraint (8) (9), hydropower capacity constraint (10), and hydropower generation constraint (11).

[0322] (8)

[0323] (9)

[0324] (10)

[0325] (11)

[0326] In the formula: Let h be the power output of the hydroelectric generator unit at time t; , Let h be the uphill and downhill speeds of the hydroelectric generator unit; , is the upper and lower limits of the power output of the hydropower unit h; T is the dispatching cycle; The total power generation of the hydropower unit during the scheduling cycle h;

[0327] Storage operation constraints

[0328] The constraints of pumped storage operation include pumped storage operation status constraint (12), pumped storage capacity constraint (13) (14), reservoir capacity constraint (15) (16), water storage capacity constraint (17) (18), and water storage initial and final state constraint (19) (20).

[0329] (12)

[0330] (13)

[0331] (14)

[0332] (15)

[0333] (16)

[0334] (17)

[0335] (18)

[0336] (19)

[0337] (20)

[0338] In the formula: , Let ps be the pumping and power generation state variables of the pumped storage unit at time t; , The upper and lower limits of the pumping power of the pumped storage unit (ps); , The upper and lower limits of the power generation capacity of the pumped storage unit (ps); , Let ps be the pumping and generating power of the pumped storage unit at time t; , Let be the water volume in the upper and lower reservoirs of the pumped-storage unit ps at time t; kps,c and kps,d are the pumping and power generation coefficients of the pumped-storage unit ps. , The maximum and minimum capacities of the upper reservoir of the pumped storage unit (ps); , The maximum and minimum capacities of the lower reservoir for the pumped storage unit PS; , The initial and final water volume in the reservoir for the pumped storage unit PS; , The initial and final water volume in the reservoir for the pumped storage unit PS;

[0339] Energy storage operation constraints

[0340] Energy storage operation constraints include energy storage operation state constraints (21), energy storage capacity constraints (22) (23), battery capacity constraints (24), battery power constraints (25), and battery power initial and final state constraints (26).

[0341] (twenty one)

[0342] (twenty two)

[0343] (twenty three)

[0344] (twenty four)

[0345] (25)

[0346] (26)

[0347] In the formula: , Let be the charging and power generation state variables of the energy storage bs at time t; , The upper and lower limits of the charging power of energy storage bs; , These represent the upper and lower limits of the power generation capacity of energy storage bs. , Let be the charging and generating power of the energy storage bs at time t; Let b be the battery capacity for storing energy at time t; , The battery charging and power generation coefficient for energy storage bs; , The maximum and minimum battery capacity for energy storage bs; , The initial and final battery charge levels for energy storage BBS scheduling;

[0348] Wind power operation constraints

[0349] Wind power operation constraints include wind power capacity constraints (27).

[0350] (27)

[0351] In the formula: Let w be the power of the wind turbine at time t; , This represents the upper and lower limits of the power output of the wind turbine unit w.

[0352] Photovoltaic operation constraints

[0353] The photovoltaic operating constraints include photovoltaic capacity constraints (28).

[0354] (28)

[0355] In the formula: Let be the power of the photovoltaic unit's PV at time t; , These are the upper and lower limits of the power output of the photovoltaic (PV) unit.

[0356] Nuclear power output constraints

[0357] Nuclear power operation constraints include nuclear power capacity constraints (29).

[0358] (29)

[0359] In the formula: Let NUC be the power of the nuclear power unit at time t; , These are the upper and lower limits of the power output of a nuclear power unit's NUC (nuclear accumulator).

[0360] Power supply and receiving constraints

[0361] Power supply and receiving constraints include upper and lower limit constraints for power supply (30), constraints for increasing upper and lower limit constraints for power supply (31), constraints for power supply amount (32), constraints for upper and lower limit constraints for power receiving (33), constraints for decreasing upper and lower limit constraints for power receiving (34), and constraints for power receiving amount (35).

[0362] (30)

[0363] (31)

[0364] (32)

[0365] (33)

[0366] (34)

[0367] (35)

[0368] In the formula: Let be the power transmitted by node tra at time t; , These are the upper and lower limits of the power supply to the tra node; The increased power supply of the ext_tra node at time t; Increase the upper limit of the power supply for the ext_tra node; Power is supplied to the tra node during its scheduling cycle; Let be the power received by the buy node at time t; , These are the upper and lower limits of the power received by the buy node; The reduced power received by the cut_buy node at time t; Reduce the upper limit of the power received by the cut_buy node; The scheduling cycle of the buy node is affected by power consumption;

[0369] Demand-side response constraints

[0370] Demand-side response constraints include transferable load capacity constraints (36), transferable load power constraints (37), and load reduction constraints (38).

[0371] (36)

[0372] (37)

[0373] (38)

[0374] In the formula: Let be the transferable load power of node l at time t; , These are the upper and lower limits of the transferable load power of node l; Let be the load power that can be reduced at node cl at time t; , The upper and lower limits of the load power that can be reduced at node cl.

[0375] The power flow equality constraints are as follows:

[0376] Power flow equality constraints ensure the power balance of the system, including power balance constraint equation (39).

[0377] (39)

[0378] In the formula: The set of thermal power units connected to node i; This is the set of hydroelectric generators connected to node i. This refers to the set of photovoltaic units connected to node i. This refers to the set of wind turbine units connected to node i. This refers to the set of pumped storage units connected to node i. For the energy storage collection connected to the i-node; This refers to the set of nuclear power units connected to node i. Let be the active load of node i at time t; The set of branches connected to node i; Let be the active power transmitted from node i to node j at time t;

[0379] The formula for calculating line transmission power is as follows:

[0380] (40)

[0381] In the formula: Let be the phase angle of the voltage at node i at time t; Let i be the line reactance of node i and node j.

[0382] The safety constraints are as follows:

[0383] Safety constraints ensure the safety and stability of the system, including phase angle safety constraints (41).

[0384] (41)

[0385] In the formula: , Phase angle of the voltage at node i The upper and lower limits.

[0386] The adjustment cost constraints are shown below:

[0387] The regulation cost constraint takes into account the regulation costs of various conventional and emergency regulation resources, including pumped storage regulation costs, energy storage regulation costs, reduced power receiving costs, thermal power unit start-up and shutdown costs, reduced nuclear power costs, increased power transmission costs, demand-side response costs, wind curtailment costs, and solar curtailment costs.

[0388] (42)

[0389] In the formula: The regulation cost of the pumped storage unit (PS); The regulation cost of energy storage bs; BUY is to reduce the set of nodes receiving power; To reduce the power receiving cost of the cut_buy node; The start-up and shutdown cost of thermal power unit g; To reduce nuclear power costs for nuclear power units (NUC); TRA is to increase the set of nodes for power transmission. The additional power supply cost for the ext_tra node; CL is the set of demand-side response nodes; The demand-side response cost for the cl node; Let w be the cost of wind curtailment for the wind turbine unit; The cost of curtailment for photovoltaic (PV) units;

[0390] in:

[0391] (43)

[0392] (44)

[0393] (45)

[0394] (46)

[0395] (47)

[0396] (48)

[0397] (49)

[0398] (50)

[0399] (51)

[0400] In the formula: , Cost coefficient for charging and generating electricity for pumped storage units; , Cost coefficient for charging and generating electricity for energy storage BBS; Reduce the power consumption cost of the cut_buy node; , For the cost coefficient of starting up and shutting down thermal power unit g; To reduce the cost factor of nuclear power units (NUC); Add a cost factor for power supply to the ext_tra node; The cost factor for reducing load on the demand side response of node cl; Let w be the wind curtailment cost coefficient for wind turbine unit w; This represents the curtailment cost coefficient for photovoltaic (PV) units.

[0401] The existence and closure of the boundary of the temporal adjustment domain, and the monotony and non-decreasing property of the temporal adjustment domain space are proven as follows:

[0402] For a given adjustment cost limit A subset of the timing adjustment domain can be represented as:

[0403] (52)

[0404] In the formula: x is the vector of observed variables; A is the matrix of equality constraint coefficients; b is the vector of equality constraint coefficients; D is the matrix of inequality constraint coefficients. To match the given adjustment cost limit The relevant inequality constraint coefficient vector.

[0405] Existence proof of the boundary of the temporal adjustment domain subset

[0406] Based on the compact form of the above field model, Ax=b defines an affine subspace. A bounded polyhedron is defined, and the temporal adjustment domain subset is the intersection of the affine subspace and the bounded polyhedron.

[0407] In practical power systems, the equality constraint Ax=b usually has a feasible solution, and when the adjustment cost limit is met... When configured appropriately, there exists an operating point that satisfies all constraints, i.e. Not empty. Under this premise, the relative boundary of this intersection within the affine subspace is determined by the intersection of the effective hyperplane of the inequality constraint and the affine subspace, that is, the boundary is formed by points that satisfy at least one inequality constraint. From Starting from any point within the affine subspace, any direction along the affine subspace will inevitably reach at least one boundary of an inequality constraint within a finite distance. Therefore, the subset boundary of the temporal adjustment domain exists.

[0408] Proof of the closure of the boundary of the temporal adjustment domain subset

[0409] Including all its limit points is A sufficient condition for a closed set. Let... yes The convergent sequence in and converges to ,like Then it is proved that the boundary is closed.

[0410] For any k, the following holds:

[0411] (53)

[0412] (54)

[0413] Due to the continuity of linear functions:

[0414] (55)

[0415] (56)

[0416] therefore , Including all its limit points, it is proved that... It is a closed set.

[0417] Proof that the subset space of the time-adjusted domain is monotonically nondecreasing

[0418] For two different cost limits ,like Then it is proved that the subset space of the time-order adjustment domain is monotonically non-decreasing.

[0419] Based on the physical meaning of adjustment costs, when adjustment costs increase, available adjustment resources increase, constraints loosen, and this manifests in a compact form as... Monotonicity:

[0420] (57)

[0421] For any have:

[0422] (58)

[0423] (59)

[0424] but ,therefore It is proven that the subset space of the time-series adjustment domain is monotonically non-decreasing.

[0425] The evaluation index system for time-series regulation capability based on the time-series regulation domain is as follows:

[0426] Timing margin

[0427] Timing margin This reflects the amount of upsizing space the system can provide. The sum of distances between the operating point and the domain boundary point in each observation dimension under a fixed adjustment cost is defined as the time-series upsizing margin, used to characterize the system's time-series upsizing capability. The time-series upsizing margin is calculated as shown in equation (60).

[0428] (60)

[0429] In the formula: n is the observation dimension; This is the value of the boundary point on the domain in the m-th observation dimension; This represents the value of the running point in the m-th observation dimension;

[0430] Timing downgrade margin

[0431] Timing downgrade margin This reflects the amount of downsizing space the system can provide. The sum of the distances between the operating point and the lower boundary point of the domain under fixed cost across all observation dimensions is defined as the time series downsizing margin, used to characterize the system's time series downsizing capability. The time series downsizing margin is calculated as shown in equation (61).

[0432] (61)

[0433] In the formula: This is the value of the lower boundary point of the domain in the m-th observation dimension;

[0434] Timing adjustment domain volume

[0435] The volume of the timing regulation domain reflects the size of the system's regulation space; the larger the timing regulation domain, the stronger its regulation capability. The calculation of the timing regulation domain volume is shown in equation (62).

[0436] (62)

[0437] The method for solving the boundary of the time-series conditioning domain based on prior constraints is as follows:

[0438] Based on the aforementioned proof of the monotonically non-decreasing property of the temporal adjustment domain subset space, for the upper boundary of the domain, as the adjustment cost limit increases, the boundary point monotonically expands outward in the observation space. Specifically, for any two adjustment cost limits... Under the same observed variables, the power at the upper boundary point satisfies:

[0439] (63)

[0440] Based on this, the upper boundary prior constraint regularization term is designed:

[0441] (64)

[0442] In the formula: C is the cost set of different boundary points; The adjustment cost limit corresponding to the current boundary point of the input network; The adjustment cost limit for other boundary points that have the same conditional observation variables as the current boundary point, excluding adjustment costs; The upper boundary power output fitted by the neural network; The target node load power for the aforementioned boundary point samples;

[0443] For the lower boundary of the domain, as the cost limit increases, the boundary point monotonically expands outward, but in the opposite direction. For The power at the lower boundary point satisfies:

[0444] (65)

[0445] The lower boundary prior constraint regularization term is designed as follows:

[0446] (66)

[0447] In the formula: The lower boundary power output fitted by the neural network; The target node load power for the boundary point sample.

[0448] The overall loss function is designed as follows:

[0449] (67)

[0450] In the formula, , For dynamic weighting coefficients; MAE is the mean squared error; when fitting the upper boundary, When fitting the lower boundary, .

[0451] To balance fitting accuracy and convergence speed, a dynamic weight adjustment mechanism is designed. In the early stages of training, the network lacks sufficient understanding of boundary morphology and requires strong constraints to guide training, so a large β value is set. As the number of training generations increases, the network gradually masters the monotonicity pattern, at which point the model parameters need to be finely adjusted to improve fitting accuracy, so the β value is gradually decreased and the α value is increased.

[0452] Example 12:

[0453] The verification of a novel power system time-series regulation capability assessment method based on a novel power system time-series regulation domain is as follows:

[0454] This embodiment uses an improved IEEE-118 node test model to systematically verify the effectiveness of the proposed method. The power parameters and source-load data of the model are based on actual data from a province in southwest China.

[0455] 1) Accuracy Analysis

[0456] To verify the accuracy of the proposed method, it is compared and analyzed with the point-by-point simulation method. When there are enough sampling points, the boundary point set obtained by the point-by-point simulation method is generally considered to truly reflect the domain boundary. Therefore, with the load power and regulation cost of node 40 as conditional observation variables and the load power of node 30 as the target observation variable, the upper and lower boundaries of the three-dimensional time-series regulation domain are solved based on the proposed method and the point-by-point simulation method, respectively. The solution accuracy of the proposed method in the direction of the target observation variable is analyzed, and the results are as follows. Figure 1 and Figure 2 As shown.

[0457] In the figure, the horizontal axis represents the boundary point values ​​obtained based on the point-by-point simulation method, the vertical axis represents the boundary point values ​​obtained based on the proposed method, the red dashed line represents the ideal coincidence line where the results of the two methods are consistent, and the blue scattered points represent the boundary points in the direction of the target observed variable.

[0458] Depend on Figure 1 and Figure 2 As can be seen, the blue scattered points are closely distributed near the red dashed line, indicating that the calculation results of the proposed method are highly consistent with those of the point-by-point simulation method, thus verifying the accuracy of the proposed method.

[0459] To further quantify and evaluate the fitting accuracy of the three-dimensional temporal adjustment domain boundary, sMAPE and R0 were calculated.2 The indicators and results are shown in Table 1.

[0460] Table 1. Accuracy Indicators for Boundary Solution of Three-Dimensional Temporal Adjustment Domain

[0461]

[0462] As shown in Table 1, the sMAPE index at the upper boundary is only 0.51%, and at the lower boundary it is only 1.24%, indicating that the proposed method has extremely small fitting bias. Looking at the coefficient of determination, the R² values ​​at the upper and lower boundaries are... 2 The values ​​reached 0.9989 and 0.9999 respectively, both close to 1, indicating that the model has a very strong ability to interpret the sample data and excellent goodness of fit.

[0463] In summary, the proposed method for solving the boundary of the temporal regulation domain based on prior constraints achieves accurate capture of the complex boundary morphological features of the temporal regulation domain by constructing a deep neural network and incorporating the spatial monotonicity of the temporal regulation domain into the neural network training process.

[0464] 2) Generality Analysis

[0465] To verify the applicability of the proposed method for characterizing high-dimensional time-series regulation domains, the load power and regulation cost of nodes 30, 35, and 40 were used as conditional observation variables, and the load power of node 45 was used as the target observation variable. The upper and lower boundaries of the five-dimensional time-series regulation domain were solved using both the proposed method and point-by-point simulation. The solution accuracy of the proposed method in the direction of the target observation variable was analyzed, and the results are as follows: Figure 3 and Figure 4 As shown.

[0466] Depend on Figure 3 and Figure 4 As can be seen, the blue scatter points are distributed along the red dashed line, indicating that the proposed method and the point-by-point simulation method maintain a high degree of consistency in solving the boundary of the five-dimensional time-series conditioning domain. Compared to the three-dimensional time-series conditioning domain, the dispersion of the boundary points in the five-dimensional time-series conditioning domain is increased, which is due to the increased complexity of the boundary shape caused by the increased dimension. However, the boundary scatter points are still concentrated near the ideal coincidence line, without serious deviation. Moreover, the scatter points are more densely distributed in the high-power region of the upper boundary and the low-power region of the lower boundary of the five-dimensional domain, indicating that the proposed method still maintains good characterization accuracy under common operating conditions.

[0467] To further quantify and evaluate the fitting accuracy of the five-dimensional time-series adjustment domain boundary, sMAPE and R0 were calculated. 2 The indicators and results are shown in Table 2.

[0468] Table 2. Accuracy Indicators for Solving the Boundary of the Five-Dimensional Temporal Adjustment Domain

[0469]

[0470] Comparing Tables 1 and 2, we can see that as the dimension increases from 3 to 5, the sMAPE of the upper boundary of the domain increases from 0.51% to 3.09%, and the sMAPE of the lower boundary increases from 1.24% to 5.15%. Although the fitting error increases, the sMAPE of the five-dimensional time-series conditioning domain remains below 5.15%, meeting the accuracy requirements of practical applications. In terms of the coefficient of determination, the R² values ​​for the upper and lower boundaries are 0.9984 and 0.9971, respectively. Although slightly lower than in the three-dimensional domain, they remain at a high level, indicating that the model still has strong explanatory power for high-dimensional sample data and excellent goodness of fit.

[0471] In summary, the proposed method for solving the boundary of the temporal regulation domain based on prior constraints demonstrates good versatility in characterizing high-dimensional temporal regulation domains. Although the increased dimensionality leads to more complex boundary morphology, by constructing a deep neural network and incorporating the spatial monotonicity of the temporal regulation domain into the network training process, accurate characterization of the boundary of high-dimensional complex domains can be achieved.

[0472] 3) Evaluation of temporal regulation capability based on temporal regulation domain

[0473] The time-series regulation domain can intuitively characterize the system regulation space under the time-series coupling constraints of various regulation resources within the scheduling cycle, transforming the abstract evaluation of time-series regulation capability into an intuitive geometric space metric. To evaluate the system's time-series regulation capability, a time-series regulation domain is constructed using the load power of node 30 and node 40 and the regulation cost as observation variables, as shown below. Figure 5 As shown.

[0474] The timing regulation domain provides a geometrical analytical tool for evaluating the timing regulation capabilities of novel power systems. Based on the relative positions of the observation points and the domain boundary, the system regulation state can be divided into three typical cases:

[0475] (1) Adjustable state: When the observation point is located inside the domain, the system is in an adjustable state, such as Figure 5 As shown at point A in the diagram. The projection of the line connecting the observation point and the domain boundary point onto each observation direction represents the available adjustment margin in that direction. The system can respond to wind, solar, and load fluctuations by utilizing various adjustment resources, maintaining power balance within the scheduling cycle.

[0476] (2) Critically adjustable state: When the observation point is located on the domain boundary, the system is in a critically adjustable state, such as Figure 5 Points B and C are shown in the diagram. At this point, the system's adjustment margin in a specific adjustment direction is zero, and the adjustment resources have reached the constraint boundary. In this state, even minor fluctuations in wind, solar, or load within the scheduling cycle can cause the system to exceed its limits.

[0477] (3) Unadjustable state: When the observation point is located outside the domain, the system is in an unadjustable state, such as Figure 5 As shown at point D, at this point, the system's adjustment resources are unable to meet the power balance requirements within the given cost limit, and the system faces the risk of supply-demand imbalance.

[0478] To quantitatively assess the system's time-series adjustment capability, observation point A was selected as the representative point of the current system operating state, and points B and C were selected as the upper and lower boundary points, respectively. Based on the evaluation index system proposed in Section 1.3, the time-series up-adjustment margin, time-series down-adjustment margin, and time-series adjustment domain volume were calculated, and the results are shown in Table 3.

[0479] Table 3 Evaluation Indicators of Temporal Regulation Capability Based on Temporal Regulation Domain

[0480]

[0481] As shown in Table 3, at the selected observation points, the system's time-series up-adjustment margin is 1543.92 MW, indicating that under the premise of satisfying various constraints within the scheduling cycle, the system can provide 1543.92 MW of up-adjustment power at the current moment. The time-series down-adjustment margin is 932.76 MW, indicating that the system can provide 932.76 MW of down-adjustment power at the current moment. These two indicators comprehensively consider multiple time-series coupling constraints, and compared with the traditional evaluation method that only considers the capacity margin at a single moment, they more realistically reflect the actual regulation capability of the system.

[0482] The timing adjustment domain volume is 5.54 × 10⁻⁶. 8 MW² quantifies the overall adjustability of the system. This metric condenses complex timing adjustment capabilities into a single value, facilitating horizontal comparisons across different operating scenarios and providing a quantitative basis for evaluating the overall adjustability of the system.

[0483] In summary, the time-series regulation capability assessment based on the time-series regulation domain transforms the abstract time-series regulation capability assessment into an intuitive geometric spatial metric. It can not only quantitatively calculate the regulation margin in each regulation direction, but also evaluate the overall regulation capability of the system through the domain volume index, providing more scientific decision support for power system dispatching, operation and configuration optimization.

[0484] 4) Benefit analysis of adjusting cost input

[0485] Reasonable adjustment cost input can ensure sufficient system time-series adjustment capacity while taking into account economic efficiency. Analyzing the domain area change patterns under different adjustment cost inputs reveals the characteristics of marginal benefit changes in adjustment cost inputs, providing scientific guidance for adjustment cost input.

[0486] To quantify the size of the adjustment space under a fixed adjustment cost, a three-dimensional time-series adjustment domain is constructed. Two-dimensional cross-sectional areas are extracted under different adjustment cost limits, yielding the adjustment cost-domain area relationship curve, as shown below. Figure 6 As shown.

[0487] Depend on Figure 6 It is evident that the area of ​​the adjustment zone increases with the increase of adjustment cost input, and the slope of the curve gradually decreases, exhibiting a significant characteristic of "diminishing marginal returns." Furthermore, the curve shows several sharp increases in slope, forming a "step growth" characteristic. To further analyze the changing law of marginal benefits of adjustment cost input, the first derivative of the area of ​​the adjustment zone with respect to cost is calculated, resulting in the adjustment cost-slope relationship curve as shown below. Figure 7 As shown.

[0488] Depend on Figure 7 As can be seen, the slope curve generally shows a downward trend, with diminishing marginal returns. Furthermore, the curve exhibits several significant peaks, which occur at the critical points where different types of regulatory resources begin to participate in regulation. As regulatory costs continue to increase, the temporal synergistic effect among regulatory resources causes the domain area to expand rapidly, forming slope peaks. As low-cost regulatory resources gradually become saturated, fluctuations disappear, and the curve flattens out.

[0489] In summary, as adjustment cost input increases, the system's temporal adjustment capacity exhibits two key characteristics: "step-like growth" reflects the temporal synergistic effect of multi-type adjustment resources participating in adjustment at different levels; and "diminishing marginal returns" reflects the physical law that the system's temporal adjustment capacity diminishes with increasing adjustment costs. Identifying the peak point of the adjustment cost-slope curve can provide a quantitative basis for optimizing adjustment cost input. Increasing adjustment cost input near the peak point can achieve the maximum marginal benefit, thus ensuring sufficient system temporal adjustment capacity while also considering economic efficiency.

[0490] 5) Impact analysis of new energy penetration rate

[0491] The penetration rate of new energy sources has a significant impact on the time-series regulation capability of new power systems. This study analyzes the morphological evolution of the time-series regulation domain under different new energy penetration rates, providing a reference for the rational planning of new energy construction.

[0492] The three-dimensional time-series conditioning domains were characterized when the penetration rate of new energy sources was 27%, 30%, 40%, 50%, and 60%, respectively. The results are as follows: Figure 8 As shown. With a fixed adjustment cost of 500, the two-dimensional domain boundary under different permeabilities is obtained by projecting onto the load power plane of node 30-node 40. The results are as follows. Figure 9 As shown.

[0493] Depend on Figure 8 and Figure 9It is evident that the spatial morphology of the time-series regulation domain exhibits a significant nonlinear evolution characteristic with changes in the penetration rate of new energy sources. At low penetration rates, the regulation space is relatively limited. As penetration increases, the domain boundary expands significantly, the regulation space increases substantially, and the domain shifts towards the first quadrant. With further increases in penetration rate, the domain boundary contracts sharply, and the regulation space decreases dramatically.

[0494] To further reveal the influence of permeability on domain boundary morphology, two-dimensional projected boundaries were extracted for low permeability (27%-31%) and high permeability (56%-60%), respectively. The results are as follows: Figure 10 and Figure 11 As shown.

[0495] Depend on Figure 10 It is evident that under low penetration rates, the upper limit constraint of resource regulation capacity becomes the dominant constraint, and the upper boundary of the domain exhibits an approximately linear characteristic. As the penetration rate of new energy sources increases, the system's power generation capacity increases, and the upper boundary expands rapidly.

[0496] Depend on Figure 11 It is evident that the strong volatility of new energy sources under high penetration rates leads to a surge in system downsizing demand, and the lower boundary of the domain decreases sharply, exhibiting an approximately linear characteristic.

[0497] To explore the variation characteristics of time-series regulation capability under different new energy penetration rates, the domain volume index under different penetration rates was calculated, and the results are as follows: Figure 12 As shown.

[0498] Depend on Figure 12 It is evident that the domain volume exhibits a "sharp increase-stable-rapid decrease" evolution pattern with increasing renewable energy penetration. Based on the critical points of sharp increase and rapid decrease, the penetration level can be divided into three stages. In the low penetration stage, the domain volume rapidly increases to its peak. This is because the integration of renewable energy increases the total power generation capacity of the system. With constant load demand, the system's tolerance for load fluctuations expands, and the adjustment space grows rapidly. In the medium penetration stage, the increased volatility of renewable energy leads to a decrease in the system's time-series adjustment capability, and the domain volume slowly decreases. In the high penetration stage, the strong volatility of renewable energy leads to the depletion of adjustment resources, and the domain volume decreases sharply.

[0499] In summary, the impact of renewable energy penetration rate on the time-series regulation domain exhibits a complex pattern: there exists an optimal renewable energy penetration rate range that maximizes the domain volume, within which the system's time-series regulation capability is strongest. Below this range, insufficient renewable energy capacity limits the regulation space; above this range, excessive volatility of renewable energy leads to the depletion of regulation resources.

Claims

1. A method for evaluating the timing regulation capability of a power system based on a novel timing regulation domain, characterized in that, Includes the following steps: Step 1) Considering various constraints on the operation of regulating resources, power flow equation constraints, security constraints, and regulation cost limits, construct a new power system time-series regulation domain model; Step 2) Construct an evaluation index system for time series adjustment capability based on the time series adjustment domain, including time series up-adjustment margin, time series down-adjustment margin, and time series adjustment domain volume index; Step 3) Construct a deep neural network architecture, design prior constraint regularization terms, and train the deep neural network architecture; Step 4) Using the new power system time-series regulation domain model as constraints, the trained deep neural network architecture is used to solve the time-series regulation domain boundary based on prior constraints.

2. The method for evaluating the timing regulation capability based on a novel power system timing regulation domain as described in claim 1, characterized in that, Various constraints on the operation of regulatory resources include thermal power operation constraints, hydropower operation constraints, pumped storage operation constraints, energy storage operation constraints, wind power operation constraints, photovoltaic operation constraints, nuclear power output constraints, power transmission and reception constraints, and demand-side response constraints. Thermal power plant operation constraints include thermal power plant operation status constraints, thermal power plant minimum start-up and shutdown time constraints, thermal power plant ramping constraints, and thermal power plant capacity constraints. Hydropower operation constraints include hydropower ramping constraints, hydropower capacity constraints, and hydropower generation constraints. Pumped storage operation constraints include pumped storage operation status constraints, pumped storage capacity constraints, reservoir capacity constraints, water storage volume constraints, and initial and final water storage volume constraints. Energy storage operation constraints include energy storage operation status constraints, energy storage capacity constraints, battery capacity constraints, battery charge constraints, and battery charge initial and final state constraints. Power transmission and receiving constraints include upper and lower limits of power transmission, increasing upper and lower limits of power transmission, power transmission capacity constraints, upper and lower limits of power receiving, decreasing upper and lower limits of power receiving, and power receiving capacity constraints. Demand-side response constraints include transferable load capacity constraints, transferable load power constraints, and load reduction capacity constraints.

3. The method for evaluating the timing regulation capability based on a novel power system timing regulation domain according to claim 2, characterized in that, The operating constraints for thermal power plants are as follows: （1） （2） The minimum start-up and shutdown time constraints for thermal power plants are as follows: （3） （4） The ramp-up constraint formula for thermal power plants is shown below: （5） （6） The thermal power capacity constraint formula is shown below: （7） In the formula: Let g be the start-up variable of the thermal power unit at time t; Let g be the shutdown variable of the thermal power unit at time t; Let g be the state variable of the thermal power unit at time t; This is the minimum start-up time for the unit; This is the minimum shutdown time for the unit; Let g be the power of the thermal power unit at time t; , Let g be the uphill and downhill speeds of the thermal power unit. , For the start-up and shutdown rates of thermal power unit g; , This represents the upper and lower limits of the power output of thermal power unit g; In hydropower operation constraints, the hydropower ramp-up constraint is as follows: （8） （9） The hydropower capacity constraints are as follows: （10） The constraints on hydropower generation are as follows: （11） In the formula: Let h be the power output of the hydroelectric generator unit at time t; , Let h be the uphill and downhill speeds of the hydroelectric generator unit; , is the upper and lower limits of the power output of the hydropower unit h; T is the dispatching cycle; The total power generation of the hydropower unit during the scheduling cycle h; The pumped storage operation constraints are as follows: （12） Pumped storage capacity constraints are shown below: （13） （14） The capacity constraints of the water storage tank are as follows: （15） （16） The water storage capacity constraints are as follows: （17） （18） The initial and final state constraints of water storage are as follows: （19） （20） In the formula: , Let ps be the pumping and power generation state variables of the pumped storage unit at time t; , The upper and lower limits of the pumping power of the pumped storage unit (ps); , The upper and lower limits of the power generation capacity of the pumped storage unit (ps); , Let ps be the pumping and generating power of the pumped storage unit at time t; , Let be the water volume in the upper and lower reservoirs of the pumped-storage unit ps at time t; kps,c and kps,d are the pumping and power generation coefficients of the pumped-storage unit ps. , The maximum and minimum capacities of the upper reservoir of the pumped storage unit (ps); , The maximum and minimum capacities of the lower reservoir for the pumped storage unit PS; , The initial and final water volume in the reservoir for the pumped storage unit PS; , The initial and final water volume in the reservoir for the pumped storage unit PS; The energy storage operation constraints are as follows: （21） Energy storage capacity constraints are as follows: （22） （23） The battery capacity constraints are as follows: （24） The battery power constraints are as follows: （25） The initial and final states of the battery are constrained as follows: （26） In the formula: , Let be the charging and power generation state variables of the energy storage bs at time t; , The upper and lower limits of the charging power of energy storage bs; , These represent the upper and lower limits of the power generation capacity of energy storage bs. , Let be the charging and generating power of the energy storage bs at time t; Let b be the battery capacity for storing energy at time t; , The battery charging and power generation coefficient for energy storage bs; , The maximum and minimum battery capacity for energy storage bs; , The initial and final battery charge levels for energy storage BBS scheduling; The operating constraints for wind power are as follows: （27） In the formula: Let w be the power of the wind turbine at time t; , This represents the upper and lower limits of the power output of the wind turbine unit w. The photovoltaic operating constraints are as follows: （28） In the formula: Let be the power of the photovoltaic unit's PV at time t; , These are the upper and lower limits of the power output of the photovoltaic (PV) unit. Nuclear power output constraints are as follows: （29） In the formula: Let NUC be the power of the nuclear power unit at time t; , These are the upper and lower limits of the power output of a nuclear power unit's NUC (nuclear accumulator). In the power transmission and reception constraints, the upper and lower limits of the power transmission capacity are as follows: （30） The upper and lower limits of the power transmission capacity are added as follows: （31） The power delivery constraints are as follows: （32） The upper and lower limits of the received power are constrained as follows: （33） The following are the reductions in the upper and lower limits of the received power: （34） The following are the constraints imposed by the amount of electricity: （35） In the formula: Let be the power transmitted by node tra at time t; , These are the upper and lower limits of the power supply to the tra node; The increased power supply of the ext_tra node at time t; Increase the upper limit of the power supply for the ext_tra node; Power is supplied to the tra node during its scheduling cycle; Let be the power received by the buy node at time t; , These are the upper and lower limits of the power received by the buy node; The reduced power received by the cut_buy node at time t; Reduce the upper limit of the power received by the cut_buy node; The scheduling cycle of the buy node is affected by power consumption; In the demand-side response constraints, the transferable load capacity constraint is as follows: （36） The transferable load power constraints are as follows: （37） The load capacity constraints that can be reduced are as follows: （38） In the formula: Let be the transferable load power of node l at time t; , The upper and lower limits of the transferable load power of node l; Let be the load power that can be reduced at node cl at time t; , The upper and lower limits of the load power that can be reduced at node cl.

4. The method for evaluating the timing regulation capability based on a novel power system timing regulation domain as described in claim 1, characterized in that, The power flow equality constraints are as follows: （39） In the formula: This refers to the set of thermal power units connected to node i. This is the set of hydroelectric generators connected to node i. This refers to the set of photovoltaic units connected to node i. This refers to the set of wind turbine units connected to node i. The set of pumped storage units connected to node i; For the energy storage collection connected to the i-node; This refers to the set of nuclear power units connected to node i. Let be the active load of node i at time t; The set of branches connected to node i; Let be the active power transmitted from node i to node j at time t; The line transmission power is shown below: （40） In the formula: Let be the phase angle of the voltage at node i at time t; Let i be the line reactance of node i and node j.

5. The method for evaluating the timing regulation capability based on a novel power system timing regulation domain according to claim 1, characterized in that, The safety constraints are as follows: （41） In the formula: , Phase angle of the voltage at node i The upper and lower limits.

6. The method for evaluating the timing regulation capability based on a novel power system timing regulation domain according to claim 1, characterized in that, The adjustment cost constraints are shown below: （42） In the formula: The regulation cost of the pumped storage unit (PS); The regulation cost of energy storage bs; BUY is to reduce the set of nodes receiving power; To reduce the power consumption cost of the cut_buy node; The start-up and shutdown cost of thermal power unit g; To reduce nuclear power costs for nuclear power units (NUC); TRA is to increase the set of nodes for power transmission. The additional power supply cost for the ext_tra node; CL is the set of demand-side response nodes; The demand-side response cost for node cl; Let w be the cost of wind curtailment for the wind turbine unit; The cost of curtailment for photovoltaic (PV) units; in: （43） （44） （45） （46） （47） （48） （49） （50） （51） In the formula: , Cost coefficient for charging and generating electricity for pumped storage units; , Cost coefficient for charging and generating electricity for energy storage BBS; Reduce the power consumption cost of the cut_buy node; , For the cost coefficient of starting up and shutting down thermal power unit g; To reduce the cost factor of nuclear power units (NUC); Add a cost factor for power supply to the ext_tra node; The cost factor for reducing load on the demand side response of node cl; Let w be the wind curtailment cost coefficient for wind turbine unit w; This represents the curtailment cost coefficient for photovoltaic (PV) units.

7. The method for evaluating the timing regulation capability based on a novel power system timing regulation domain according to claim 1, characterized in that, The boundary of the temporal adjustment domain has existence and closure; the temporal adjustment domain space has monotonicity.

8. The method for evaluating the timing regulation capability based on a novel power system timing regulation domain according to claim 1, characterized in that, The timing margin is as follows: （52） In the formula: n is the observation dimension; This is the value of the boundary point on the domain in the m-th observation dimension; This represents the value of the running point in the m-th observation dimension; The timing downsizing margin is shown below: （53） In the formula: This is the value of the lower boundary point of the domain in the m-th observation dimension; The timing adjustment domain volume is shown below: （54） （55） In the formula: x is the vector of observed variables; A is the matrix of equality constraint coefficients; b is the vector of equality constraint coefficients; D is the matrix of inequality constraint coefficients. To match the given adjustment cost limit The relevant inequality constraint coefficient vector; Given adjustment cost limit A subset of the next time-series adjustment domain.

9. The method for evaluating the timing regulation capability based on a novel power system timing regulation domain according to claim 1, characterized in that, Prior constraint regularization terms include upper boundary prior constraint regularization terms and lower boundary prior constraint regularization terms; The upper boundary prior constraint regularization term is shown below: （56） In the formula: C is the cost set of different boundary points; The adjustment cost limit corresponding to the current boundary point of the input network; The adjustment cost limit for other boundary points that have the same conditional observation variables as the current boundary point, excluding adjustment costs; The upper boundary power output fitted by the neural network; The target node load power for the aforementioned boundary point samples; The lower boundary prior constraint regularization terms are shown below: （57） In the formula: The lower boundary power output fitted by the neural network; The target node load power for the boundary point sample.

10. The method for evaluating the timing regulation capability based on a novel power system timing regulation domain according to claim 1, characterized in that, The deep neural network architecture includes a convolutional feature extraction layer and a fully connected mapping layer; the deep neural network architecture is used to realize the mapping from conditional observed load power variables to target observed load power variables; The loss function used when training a deep neural network architecture is as follows: （58） In the formula, , For dynamic weighting coefficients; MAE is the mean squared error; when fitting the upper boundary, When fitting the lower boundary, .

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