A method for depicting power regulation capability of a regional power grid considering nonlinear operating characteristics of a photo-thermal power generation

Abstract

The application discloses a method for depicting power regulation capability of a regional power grid by considering nonlinear operation characteristics of a photo-thermal power station, and comprises the following steps: 1) constructing an economic dispatching model of a power system by considering nonlinear operation characteristics of the photo-thermal power station; 2) linearly converting the economic dispatching model of the power system to obtain an economic dispatching linear model of the power system by considering nonlinear operation characteristics of the photo-thermal power station; and 3) solving the economic dispatching linear model of the power system to obtain multi-period power regulation capability of the regional power grid. The method can accurately calculate operation cost of the photo-thermal power station, comprehensively consider nonlinear operation characteristics of the photo-thermal power station, and accurately calculate the power regulation capability of the regional power grid containing the photo-thermal power station, thereby providing an auxiliary decision basis for cross-regional optimization and configuration of power resources.

Description

Technical Field

[0001] This invention relates to the field of economic dispatch of power systems, specifically a method for characterizing the power regulation capability of a regional power grid that takes into account the nonlinear operating characteristics of solar thermal power generation. Background Technology

[0002] Due to the fluctuating and random nature of new energy output, some renewable energy sources cannot guarantee continuous output over long periods, posing a severe challenge to the further development of multi-energy complementary systems. Solar thermal power plants equipped with thermal storage systems possess energy time-shifting and thermoelectric conversion capabilities, combining the advantages of both new energy units and thermal power units, making them one of the important technological pathways for China's energy structure transformation. By the end of 2021, the global cumulative installed capacity of solar thermal power generation was approximately 6.8 GW, while my country's cumulative installed capacity was 538 MW. "Multiple regions, including Xinjiang, Qinghai, and Gansu, are constructing solar thermal power projects with a total installed capacity exceeding 3 GW. If all are completed as planned, the year-on-year increase in the operational scale of solar thermal power plants will reach 390%. Meanwhile, new new energy projects in Northwest China are mainly integrated 'multi-energy complementary' projects. As one of my country's major power transmission regions, accurately characterizing the power grid's power regulation capabilities in areas containing solar thermal power plants is of great significance for the Northwest China power grid to clarify the space for cross-provincial and cross-regional coordination and optimization of power resources and to achieve optimal allocation of power resources."

[0003] Currently, numerous studies have been conducted by scholars both domestically and internationally regarding the operation and scheduling of concentrated solar power (CSP) plants, primarily focusing on two aspects: firstly, utilizing the scheduling capabilities of CSP plants' thermal energy storage to mitigate the volatility of renewable energy generation; and secondly, improving the system's environmental efficiency and reducing operating costs through joint scheduling with different power generation methods such as wind power, photovoltaics, traditional thermal power, and energy storage. The operating principle of CSP plant thermal energy storage systems has also been analyzed in detail during this process. Most existing economic scheduling models for CSP plants consider the heat dissipation costs in the thermal energy storage system. However, energy losses also occur during the charging and releasing processes of the thermal energy storage system, and these losses are on the same order of magnitude as the heat dissipation rate of the thermal energy storage system, making them non-negligible. However, existing economic scheduling models involving CSP plants do not yet consider the impact of energy losses during the charging and releasing processes on the scheduling results.

[0004] To characterize the power regulation capacity of regional power grids, domestic and international scholars mainly use the feasible region of tie-line transmission power to represent this capacity. The main methods include: available transmission capacity characterization, vertex search, and multi-parameter programming. The available transmission capacity characterization calculates the available transmission capacity to represent the grid's transmission power using the network current method. The vertex search method iteratively updates the feasible region of tie-line power based on the searched vertices. The multi-parameter programming method selects coupled variables such as tie-line transmission power as planning parameters to characterize the feasible region of tie-line power. However, the available transmission capacity characterization method approximates the feasible region of tie-line power at a single moment using a specific maximum injected power plane, which cannot guarantee the accuracy of characterizing the feasible region of coupled tie-lines across multiple time periods. Compared to the vertex search method, the multi-parameter programming method, in addition to obtaining the feasible region of tie-line power across multiple time periods, can also obtain the functional relationship between the optimal solution for economic dispatch and the tie-line power. This is of great significance for dispatching departments to make dispatching decisions.

[0005] However, existing multi-parameter programming methods do not consider the operational characteristics of concentrated solar power (CSP) plants. Using multi-parameter programming theory to characterize the power regulation capability of power grids in areas containing CSP plants presents two main problems: First, the economic dispatch model for CSP plants is nonlinear, requiring that the charging and releasing processes of the thermal storage system not occur simultaneously. Existing economic dispatch models often introduce integer variables to handle this nonlinear constraint, leading to the need to solve a mixed-integer linear model. Using multi-parameter programming theory in this case requires enumerating all possible combinations of integer variables, resulting in a significant computational burden. Second, solving multi-parameter programming problems requires enumerating all combinations of active and inactive constraints. When characterizing the power regulation capability of regional power grids across multiple time periods, this generates a high-dimensional solution space with an increasing number of time periods, further increasing computational burden. Currently, common solutions involve decoupling the feasible region through load clustering and load fluctuation characteristic decoupling to achieve rapid characterization of the power regulation capability of regional power grids across multiple time periods. Among these, the K-means algorithm, as one of the most widely used load clustering algorithms, is simple to operate and its effectiveness has been widely verified.

[0006] In conclusion, it is necessary to fully consider the operating costs and nonlinear characteristics of solar thermal power plants, and to study a method for characterizing the power regulation capability of regional power grids that takes into account the influence of the nonlinear operating characteristics of solar thermal power plants. Summary of the Invention

[0007] The purpose of this invention is to provide a method for characterizing the power regulation capability of a regional power grid that takes into account the nonlinear operating characteristics of concentrated solar power (CSP) generation, comprising the following steps:

[0008] 1) Construct an economic dispatch model for the power system that takes into account the nonlinear operating characteristics of solar thermal power generation;

[0009] 2) The power system economic dispatch model is linearized to obtain a power system economic dispatch linear model that takes into account the nonlinear operating characteristics of solar thermal power generation;

[0010] 3) Solve the linear model of economic dispatch of the power system to obtain the power regulation capability of the regional power grid in multiple time periods.

[0011] Furthermore, the objective function of the power system economic dispatch model that takes into account the nonlinear operating characteristics of solar thermal power generation is as follows:

[0012]

[0013] In the formula: F represents the total operating cost of the system; C CSP For the operating cost of a solar thermal power plant; ρ RN The penalty fee per unit of wind or solar power curtailment; P RNmax,i,t p RN,i,t These represent the maximum generateable power and actual output power of the i-th renewable energy power station during time period t, respectively; p TR,j,t p is the output power of the j-th conventional unit during time period t; c,r,t p d,r,t These represent the charging and discharging power of the r-th energy storage unit during time period t; c TR,j c is the operating cost coefficient of the j-th traditional unit; c,t c d,t These are the energy storage charging and discharging prices for time period t; N RN N TR and N EES These represent the number of new energy power plants, traditional generating units, and energy storage, respectively; Δt is the time interval, and T is the total number of time intervals.

[0014] Among them, the operating cost C of the solar thermal power plant CSP As shown below:

[0015]

[0016] In the formula, S CSP,m ρ is the power generation cost coefficient of the m-th solar thermal power plant; solar The penalty cost per unit of heat waste from a solar thermal power plant; p CSP,m,t P represents the power generation of the m-th solar thermal power plant; solar,m,t p is the maximum heat that can be collected by the light field. SH,m,t γ represents the energy actually received by the m-th solar thermal power plant; loss,m N represents the heat dissipation rate of the thermal energy storage system in the m-th solar thermal power plant. CSP The number of solar thermal power plants; L CSP This is the heat loss penalty coefficient for the thermal storage system.

[0017] The heat E stored in the thermal storage system of the m-th solar thermal power plant during time period tm,t And the energy loss cost C during the charging and releasing process. CSP_cd They are shown below:

[0018]

[0019]

[0020] In the formula, t = 1, 2, ..., T; m = 1, 2, ..., N CSP N CSP Indicates the number of solar thermal power plants; E m,t E m,t-1 γ represents the heat stored in the thermal storage system of the m-th solar thermal power plant during time period t and time period t-1, respectively; loss,m η is the heat dissipation rate of the thermal energy storage system in the m-th solar thermal power plant; hc,m η hd,m These represent the charging and discharging heat efficiencies of a solar thermal power plant, respectively; L CSP P is the heat loss penalty coefficient for the thermal storage system. HT，m，t P TH，m，t Let represent the heat charging power and heat dissipation power of the m-th solar thermal power plant during time period t, respectively.

[0021] Furthermore, the constraints of the power system economic dispatch model that takes into account the nonlinear operating characteristics of solar thermal power generation include solar thermal power plant operation constraints, power balance constraints, branch power constraints, wind power and photovoltaic operation constraints, and energy storage operation constraints.

[0022] Furthermore, the operational constraints of the solar thermal power plant include energy balance constraints of the thermal storage system (3), energy balance constraints of the heat transfer system (5), state constraints of the thermal storage system during the same period (6), upper limit constraints of the solar thermal power plant's charging power (7), upper limit constraints of the solar thermal power plant's thermal power (8), upper and lower limit constraints of the heat stored in the thermal storage system (9), upper and lower limit constraints of the solar thermal power plant's output power (10), upper and lower limit constraints of the solar thermal power plant's output power ramping constraints (11), and upper limit constraints of the actual thermal power received by the solar thermal power plant from the light field (12), namely:

[0023] p SH,m,t +p TH,m,t =p HT,m,t +p CSP,m,t / β HP,m (5)

[0024] p HT,m,t ·p TH,m,t =0 (6)

[0025] 0≤p HT,m,t ≤P HT,m,max (7)

[0026] 0≤p TH,m,t ≤PTH,m,max (8)

[0027] E m,min ≤E m,t ≤E m,max (9)

[0028] 0≤p CSP,m,t ≤P CSP,m,max (10)

[0029] -RD CSP,m ≤p CSP,m,t -p CSP,m,t-1 ≤RU CSP,m (11)

[0030] 0≤p SH,m,t ≤P solor,m,t (12)

[0031] In the formula, t = 1, 2, ..., T; m = 1, 2, ..., N CSP ;P HT,m,max P TH,m,max and P CSP,m,max E represents the rated charging and discharging power and rated output electrical power of the m-th solar thermal power plant, respectively; m,max and E m,min These represent the upper and lower limits of thermal storage for the m-th solar thermal power plant's thermal storage system; RU CSP,m and RD CSP,m These represent the power output ramp-up and ramp-down limits of the m-th solar thermal power plant, respectively; β HP,m p represents the thermoelectric conversion efficiency. HT,m,t p TH,m,t E represents the charge and discharge power of the solar thermal power plant, respectively. m,t The heat stored in the thermal storage system; p CSP,m,t For the output power of the solar thermal power plant; p SH,m,t P represents the actual heat power received by the solar thermal power plant from the light field. solar,m,t P is the maximum heat-collecting power of the light field; HT，m，t P TH，m，t Let represent the heat charging power and heat dissipation power of the m-th solar thermal power plant during time period t, respectively.

[0032] The power balance constraint is shown in equation (13), that is...

[0033]

[0034] Where: t=1,2,…,T; N bus N PB These represent the number of nodes connected to the load and the number of nodes at the boundary of the regional power grid, respectively; D n,t PB represents the load of the nth node during time period t. q,tp represents the transmission power of the q-th tie line during time period t; c,r,t p d,r,t These represent the charging and discharging power of the r-th energy storage unit during time period t; p RN,i,t p represents the actual output power of the i-th renewable energy power station during time period t; TR,j,t Let j be the output power of the j-th conventional unit during time period t;

[0035] The branch power constraints are shown in equations (14)-(15), namely:

[0036] F k,min ≤f k,t ≤F k,max (14)

[0037] PB q,min ≤PB q,t ≤PB q,max (15)

[0038] Where: t = 1, 2, ..., T; k = 1, 2, ..., K; q = 1, 2, ..., N PB K represents the total number of internal branches in the system; f k,t F represents the power of the k-th internal branch during time period t. k,max F k,min These are the upper and lower power limits for the k-th internal branch, respectively; PB q,max PB q,min PB represents the upper and lower power limits of the q-th tie line, respectively; q,t Let q be the power of the q-th tie line;

[0039] The power constraints of traditional generator units are shown in formulas (16)-(17), namely:

[0040] P TR,j,min ≤p TR,j,t ≤P TR,j,max (16)

[0041] -RD TR,j ≤p TR,j,t -p TR,j,t-1 ≤RU TR,j (17)

[0042] In the formula: t = 1, 2, ..., T; j = 1, 2, ..., N TR ;P TR,j,max P TR,j,min Represent the upper and lower limits of the output power of the j-th conventional unit, respectively; RU TR,j RD TR,j P represents the ramp-up and ramp-down limits of the j-th conventional unit, respectively; TR，j，t P TR，j，t-1Let represent the output power of the j-th conventional unit at time t and time t-1, respectively;

[0043] The operating constraints for wind and solar power are shown in formula (18), namely:

[0044] 0≤p RN,i,t ≤P RNmax,i,t (18)

[0045] In the formula: t = 1, 2, ..., T; i = 1, 2, ..., N RN ;P RNmax,i,t P RN，i,t These are the maximum power generation capacity and actual output power of the i-th new energy power station in time period t, respectively.

[0046] The constraints for energy storage operation are shown in equations (19)-(21), namely:

[0047] 0≤p d,r,t ,p c,r,t ≤P r,EESmax (19)

[0048] SOC r,t =SOC r,t-1 +(p c,r,t η ec,r -p d,r,t / η ed,r (20)

[0049] SOC r,min ≤SOC r,t ≤SOC r,max (twenty one)

[0050] In the formula: t = 1, 2, ..., T; r = 1, 2, ..., N EES ;P r,EESmax Represents the rated charge and discharge power of the r-th energy storage unit; SOC r,t SOC r,t-1 The state of charge (SOC) of the r-th energy storage unit during time periods t and t-1, respectively. r,max SOC r,min η represents the upper and lower limits of the r-th energy storage state of charge, respectively; ec,r η ed,r , respectively, are the charging and discharging efficiencies of the r-th energy storage unit.

[0051] Furthermore, the steps to obtain a linear model of power system economic dispatch that takes into account the nonlinear operating characteristics of concentrated solar power (CSP) include:

[0052] 1.1) The power system economic dispatch model considering the nonlinear operating characteristics of concentrated solar power (CSP) is simplified to obtain:

[0053] min(1) (22)

[0054] st(2),(5),(7)-(21) (23)

[0055] 1.2) By transforming the equality constraints (2), (5), (13), and (20) into two complementary inequality constraints, a linear model of power system economic dispatch considering the nonlinear operating characteristics of solar thermal power generation is obtained, namely:

[0056]

[0057]

[0058] In the formula: column vector x = [p RN ,p TR ,p c ,p d [,SOC,f] T p RN p TR p c p d SOC and f are both row vectors, p HT p TH E, p CSP p SH Both p and PB are column vectors, where: p RN =[p RN,i,t ]; p TR =[p TR,j,t ]; p c =[p c,r,t ]; p d =[p d,r,t ];SOC=[SOC r,t ]; f = [f k,t ]; p HT =[p HT,j,t ]; p TH =[p TH,j,t ];E=[E m,t ]; p CSP =[p CSP,j,t ]; p SH =[p SH,j,t ];PB=[PB q,t ]; t=1,2,…,T; i=1,2,…,N RN j = 1, 2, ..., N TR r = 1, 2, ..., N EES ;k=1,2,…,K; m=1,2,…,N CSP ; q = 1, 2, ..., N PBM1, M2, M3, M4, M5, and M6 are row vectors; N1, N2, N3, N4, N5, N6, and N7 are matrices; M7 is a constant; and N8 is a column vector.

[0059] Furthermore, the steps for solving the linear model of economic dispatch of the power system include:

[0060] 2.1) Simplifying the linear model of economic dispatch of the power system, we get:

[0061] min F=GX+M7 (26)

[0062] st AX≤Bw+C (27)

[0063] In the formula: X = [x; p HT ;p TH ;E;p CSP ;p SH w = PB is the planning parameter; matrix G = [M1, M2, M3, M4, M5, M6]; matrix A = [N1, N3, N4, N5, N6]; matrix B = -N7; vector C = N8;

[0064] 2.2) Set the number of clusters to S, and start from the total load Pd = {Pd1, Pd2, ..., Pd} of T system time periods. t ,…,Pd T S loads are randomly selected as the initial cluster centers K in the} J ={K1,K2,…,K s ,…,K S};K S The S-th initial cluster center;

[0065] 2.3) Calculate the distance from the total load of each system time period to the cluster center, and divide the total load of each system time period and the nearest cluster center into the same cluster time period according to the distance;

[0066] Wherein, the total load Y of the i-th system time period i To the j-th cluster center Y j The weighted Euclidean distance D(Y) i Y j As shown below:

[0067]

[0068] In the formula: C DIM The data dimension of a data point; w c Represents the weighting coefficients of the c-th dimension data; vector vector

[0069] Among them, the weighting coefficient w of the c-th dimension data c As shown below:

[0070]

[0071] In the formula: This represents the average value of the c-th dimension of data; T is the total number of time periods, i.e., the number of data points.

[0072] 2.4) Recalculate the cluster centers for the data within each clustering period to obtain new cluster centers. New cluster center and existing cluster center K J To compare, if the cluster centers change, then let If necessary, proceed to step 23); otherwise, proceed to step 25.

[0073] 2.5) Output clustering results: The total load of S consecutive system time periods is the K-means clustering result;

[0074] 2.6) Construct a low-dimensional decoupling time period model based on the load clustering results in step 2.5), where the s-th low-dimensional decoupling time period model is shown below:

[0075] min F s =G s X s +M 7,s (30)

[0076] stA s X s ≤B s w s +C s (31)

[0077] In the formula: X s =[x;p HT,s ;p TH,s E s ;p CSP,s ;p SH,s ];w s =PB s For planning parameters; G s M 7,s A s B s and C s It is a matrix. The subscript s represents the variables and coefficients in the original optimization problems (26) and (27) corresponding to the s-th low-dimensional decoupling time period.

[0078] 2.7) Solve the model for each low-dimensional decoupled time period using multi-parameter programming theory to obtain the feasible domain of tie-line transmission power CR=CR1∪CR2∪…∪CR, which characterizes the regional power grid regulation capacity. s ∪…∪CR S CR S This represents the feasible domain of tie-line transmission power corresponding to the Sth low-dimensional decoupling period.

[0079] Furthermore, the steps for solving the s-th low-dimensional decoupled time period model using multi-parameter programming theory include:

[0080] 3.1) Construct the Lagrangian function L s ,Right now:

[0081] L s =G s X s +M 7,s -λ s (A s X s -B s w s -C s (32)

[0082] In the formula: λ s The vector consisting of Lagrange multipliers;

[0083] 3.2) Establish the optimality conditions for the s-th low-dimensional decoupled time period model, including the stationary point condition (33), the complementary relaxation condition (34), the original feasibility condition (35), and the dual feasibility condition (36), namely:

[0084]

[0085] λ s (A s X s -B s w s -C s )=0 (34)

[0086] A s X s -B s w s -C s ≤0 (35)

[0087] λ s ≥0 (36)

[0088] 3.3) For optimization problems (26) and (27), when the planning parameter w s When the parameters vary within the feasible region, there are a total of M corresponding parameters. sDifferent sets of effective and ineffective constraints;

[0089] Let the optimal solution corresponding to the m-th constraint set be denoted as . Then the effective and ineffective constraints in the m-group constraint set are shown in formulas (37) and (38) respectively, that is:

[0090]

[0091]

[0092] In the formula: The subscripts Y and N represent the active and inactive constraints in the constraint set, respectively; m = 1, 2, ..., M s ;

[0093] 3.4) Establish the optimal solution corresponding to the m-th constraint set. The expression, that is:

[0094]

[0095] Where: matrix matrix

[0096] 3.5) Substituting formula (39) into formula (38) and combining like terms, we obtain the critical region, i.e.:

[0097] A s,w,m w s <B s,w,m (40)

[0098] In the formula, the matrix matrix

[0099] 3.6) Enumerate the active and inactive constraint sets of optimization problems (26) and (27), and repeat steps 3.3) to 3.5) to obtain M. s Critical domain CR s,m Then, the analytical expression of the optimal solution function for the optimization problem is established, namely:

[0100]

[0101]

[0102] In the formula: A s,w B s,w These are the coefficient matrix and coefficient vector obtained by taking the union of the critical regions and rearranging them, respectively. M s To constrain the number of sets. This is the optimal solution.

[0103] The technical effects of this invention are undeniable, and its beneficial effects are as follows:

[0104] 1) A power system economic dispatch model considering the nonlinear operating characteristics of concentrated solar power (CSP) is proposed. Firstly, based on the operating principle of the thermal storage system in a CSP plant, the energy loss cost during the charging and discharging processes of the thermal storage system is added to the objective function. Simultaneously, the nonlinear constraint that the charging and discharging processes of a CSP plant cannot occur simultaneously is considered, thus constructing a power system economic dispatch model considering the nonlinear operating characteristics of CSP. Furthermore, to prevent the introduction of integer variables into the dispatch model, which would increase the computational burden of solving multi-parameter programming methods, a linearization transformation method for the power system economic dispatch model containing CSP plants is proposed based on the concept of equivalent linearization. This achieves a linear transformation of the nonlinear economic dispatch model without integer variables.

[0105] 2) A method for characterizing the multi-period power regulation capability of a regional power grid containing a solar thermal power plant is proposed. First, to address the difficulty in solving the multi-period power regulation capability problem, the K-means algorithm is used to cluster the system loads to achieve decoupled calculation of the feasible region of tie-line transmission power across multiple time periods. Then, based on multi-parameter programming theory, using tie-line transmission power as the planning parameter, the feasible region expression of the regional power grid tie-line transmission power is solved for each clustered low-dimensional decoupled time period to characterize the regional power grid's power regulation capability. Simultaneously, the explicit functional relationship between tie-line transmission power and the optimal solution for economic dispatch is analytically derived. Furthermore, the impact of solar thermal power plants on the time-period coupling characteristics of the regional power grid's power regulation capability is analyzed, providing auxiliary decision-making basis for the cross-regional optimal allocation of power resources.

[0106] The method proposed in this invention can accurately calculate the operating cost of a solar thermal power plant, comprehensively consider the nonlinear characteristics of solar thermal power plant operation, accurately calculate the power regulation capability of the power grid in the region containing the solar thermal power plant, and thus provide auxiliary decision-making basis for cross-regional optimal allocation of power resources. Attached Figure Description

[0107] Figure 1 This is a schematic diagram of energy flow in a solar thermal power plant.

[0108] Figure 2 This is a schematic diagram of energy flow in a solar thermal power plant.

[0109] Figure 3 A schematic diagram of the feasible region of planning parameters and the optimal solution of optimization variables for the s-th low-dimensional decoupling time period;

[0110] Figure 4 To output electrical power for the solar thermal power plants of models M0 and M1 in the IEEE-30 node system;

[0111] Figure 5 The heat charging power of the solar thermal power plant for models M0 and M1 in the IEEE-30 node system;

[0112] Figure 6 The heat output power of the solar thermal power plant in models M0 and M1 of the IEEE-30 node system;

[0113] Figure 7 The results of load time clustering for the IEEE-30 node system;

[0114] Figure 8 (a)-(b) represent the power regulation capability of the No. 2 tie line in M2 during time periods 1-2;

[0115] Figure 9 (a)-(b) represent the power regulation capability of the No. 2 tie line in M3 during periods 1-2. Detailed Implementation

[0116] 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.

[0117] Example 1:

[0118] See Figures 1 to 9 A method for characterizing the power regulation capability of a regional power grid that takes into account the nonlinear operating characteristics of concentrated solar power generation includes the following steps:

[0119] 1) Construct an economic dispatch model for the power system that takes into account the nonlinear operating characteristics of solar thermal power generation;

[0120] 2) The power system economic dispatch model is linearized to obtain a power system economic dispatch linear model that takes into account the nonlinear operating characteristics of solar thermal power generation;

[0121] 3) Solve the linear model of economic dispatch of the power system to obtain the power regulation capability of the regional power grid in multiple time periods.

[0122] The objective function of the power system economic dispatch model that takes into account the nonlinear operating characteristics of solar thermal power generation is shown below:

[0123]

[0124] In the formula: F represents the total operating cost of the system; C CSP For the operating cost of a solar thermal power plant; ρ RN The penalty fee per unit of wind or solar power curtailment; P RNmax,i,t p RN,i,t These represent the maximum generateable power and actual output power of the i-th renewable energy power station during time period t, respectively; p TR,j,t p is the output power of the j-th conventional unit during time period t; c,r,tp d,r,t These represent the charging and discharging power of the r-th energy storage unit during time period t; c TR,j c is the operating cost coefficient of the j-th traditional unit; c,t c d,t These are the energy storage charging and discharging prices for time period t; N RN N TR and N EES These represent the number of new energy power plants, traditional generating units, and energy storage, respectively; Δt is the time interval, and T is the total number of time intervals.

[0125] Among them, the operating cost C of the solar thermal power plant CSP As shown below:

[0126]

[0127] In the formula, S CSP,m ρ is the power generation cost coefficient of the m-th solar thermal power plant; solar The penalty cost per unit of waste heat from a solar thermal power plant; p CSP,m,t P represents the power generation of the m-th solar thermal power plant. solar,m,t p is the maximum heat that can be collected by the light field. SH,m,t γ represents the energy actually received by the m-th solar thermal power plant; loss,m N represents the heat dissipation rate of the thermal energy storage system in the m-th solar thermal power plant. CSP The number of solar thermal power plants;

[0128] The heat E stored in the thermal storage system of the m-th solar thermal power plant during time period t m,t And the energy loss cost C during the charging and releasing process. CSP_cd They are shown below:

[0129]

[0130]

[0131] In the formula, t = 1, 2, ..., T; m = 1, 2, ..., N CSP N CSP Indicates the number of solar thermal power plants; E m,t E m,t-1 γ represents the heat stored in the thermal storage system of the m-th solar thermal power plant during time period t and time period t-1, respectively; loss,m η is the heat dissipation rate of the thermal energy storage system in the m-th solar thermal power plant; hc,m η hd,m These represent the charging and discharging heat efficiencies of a solar thermal power plant, respectively; L CSP This is the heat loss penalty coefficient for the thermal storage system.

[0132] The constraints of the power system economic dispatch model that takes into account the nonlinear operating characteristics of solar thermal power generation include solar thermal power plant operation constraints, power balance constraints, branch power constraints, wind power and photovoltaic operation constraints, and energy storage operation constraints.

[0133] The operational constraints of the solar thermal power plant include: energy balance constraints of the thermal storage system (3), energy balance constraints of the heat transfer system (5), state constraints of the thermal storage system during the same period (6), upper limit constraints of the solar thermal power plant's charging power (7), upper limit constraints of the solar thermal power plant's thermal power (8), upper and lower limit constraints of the heat stored in the thermal storage system (9), upper and lower limit constraints of the solar thermal power plant's output power (10), upper and lower limit constraints of the solar thermal power plant's output power ramp-up constraints (11), and upper limit constraints of the actual thermal power received by the solar thermal power plant from the solar field (12), namely:

[0134] p SH,m,t +p TH,m,t =p HT,m,t +p CSP,m,t / β HP,m (5)

[0135] p HT,m,t ·p TH,m,t =0 (6)

[0136] 0≤p HT,m,t ≤P HT,m,max (7)

[0137] 0≤p TH,m,t ≤P TH,m,max (8)

[0138] E m,min ≤E m,t ≤E m,max (9)

[0139] 0≤p CSP,m,t ≤P CSP,m,max (10)

[0140] -RD CSP,m ≤p CSP,m,t -p CSP,m,t-1 ≤RU CSP,m (11)

[0141] 0≤p SH,m,t ≤P solor,m,t (12)

[0142] In the formula, t = 1, 2, ..., T; m = 1, 2, ..., N CSP ;P HT,m,max P TH,m,max and P CSP,m,max E represents the rated charging and discharging power and rated output electrical power of the m-th solar thermal power plant, respectively; m,max and Em,min These represent the upper and lower limits of thermal storage for the m-th solar thermal power plant's thermal storage system; RU CSP,m and RD CSP,m These represent the power output ramp-up and ramp-down limits of the m-th solar thermal power plant, respectively; β HP,m p represents the thermoelectric conversion efficiency. HT,m,t p TH,m,t E represents the charge and discharge power of the solar thermal power plant, respectively. m,t The heat stored in the thermal storage system; p CSP,m,t For the output power of the solar thermal power plant; p SH,m,t P represents the actual heat power received by the solar thermal power plant from the light field. solar,m,t This represents the maximum heat-collecting power of the light field.

[0143] The power balance constraint is shown in equation (13), that is...

[0144]

[0145] Where: t=1,2,…,T; N bus N PB These represent the number of nodes connected to the load and the number of nodes at the boundary of the regional power grid, respectively; D n,t PB represents the load of the nth node during time period t. q,t p represents the transmission power of the q-th tie line during time period t; c,r,t p d,r,t These represent the charging and discharging power of the r-th energy storage unit during time period t; p RN,i,t p represents the actual output power of the i-th renewable energy power station during time period t; TR,j,t Let j be the output power of the j-th conventional unit during time period t;

[0146] The branch power constraints are shown in equations (14)-(15), namely:

[0147] F k,min ≤f k,t ≤F k,max (14)

[0148] PB q,min ≤PB q,t ≤PB q,max (15)

[0149] Where: t = 1, 2, ..., T; k = 1, 2, ..., K; q = 1, 2, ..., N PB K represents the total number of internal branches in the system; f k,t F represents the power of the k-th internal branch during time period t. k,max F k,min These are the upper and lower power limits for the k-th internal branch, respectively; PB q,max PB q,minPB represents the upper and lower power limits of the q-th tie line, respectively; q,t Let q be the power of the q-th tie line;

[0150] The branch power constraints are shown in equations (16)-(17), namely:

[0151] P TR,j,min ≤p TR,j,t ≤P TR,j,max (16)

[0152] -RD TR,j ≤p TR,j,t -p TR,j,t-1 ≤RU TR,j (17) Where: t=1,2,…,T; j=1,2,…,N TR ;P TR,j,max P TR,j,min Represent the upper and lower limits of the output power of the j-th conventional unit, respectively; RU TR,j RD TR,j P represents the ramp-up and ramp-down limits of the j-th conventional unit, respectively; TR，j，t P TR，j，t-1 Let represent the output power of the j-th conventional unit at time t and time t-1, respectively;

[0153] The operating constraints for wind and solar power are shown in formula (18), namely:

[0154] 0≤p RN,i,t ≤P RNmax,i,t (18)

[0155] In the formula: t = 1, 2, ..., T; i = 1, 2, ..., N RN ;P RNmax,i,t P RN，i,t These are the maximum power generation capacity and actual output power of the i-th new energy power station in time period t, respectively.

[0156] The constraints for energy storage operation are shown in equations (19)-(21), namely:

[0157] 0≤p d,r,t ,p c,r,t ≤P r,EESmax (19)

[0158] SOC r,t =SOC r,t-1 +(p c,r,t η ec,r -p d,r,t / η ed,r (20)

[0159] SOC r,min ≤SOC r,t ≤SOCr,max (twenty one)

[0160] In the formula: t = 1, 2, ..., T; r = 1, 2, ..., N EES ;P r,EESmax Represents the rated charge and discharge power of the r-th energy storage unit; SOC r,t SOC r,t-1 The state of charge (SOC) of the r-th energy storage unit during time periods t and t-1, respectively. r,max SOC r,min η represents the upper and lower limits of the r-th energy storage state of charge, respectively; ec,r η ed,r , respectively, are the charging and discharging efficiencies of the r-th energy storage unit.

[0161] The steps to obtain a linear model of power system economic dispatch that takes into account the nonlinear operating characteristics of concentrated solar power (CSP) include:

[0162] 2.1) The power system economic dispatch model considering the nonlinear operating characteristics of concentrated solar power (CSP) is simplified to obtain:

[0163] min(1) (22)

[0164] st(2),(5),(7)-(21) (23)

[0165] 2.2) The equality constraints (2), (5), (13) and (20) are transformed into two complementary inequality constraints, resulting in a linear economic dispatch model of the power system that takes into account the nonlinear operating characteristics of solar thermal power generation, namely:

[0166]

[0167]

[0168] In the formula: column vector x = [p RN ,p TR ,p c ,p d [,SOC,f] T p RN p TR p c p d SOC and f are both row vectors, p HT p TH E, p CSP p SH Both p and PB are column vectors, where: p RN =[p RN,i,t ]; p TR =[p TR,j,t ]; p c =[p c,r,t]; p d =[p d,r,t ];SOC=[SOC r,t ]; f = [f k,t ]; p HT =[p HT,j,t ]; p TH =[p TH,j,t ];E=[E m,t ]; p CSP =[p CSP,j,t ]; p SH =[p SH,j,t ];PB=[PB q,t ]; t=1,2,…,T; i=1,2,…,N RN j = 1, 2, ..., N TR r = 1, 2, ..., N EES ;k=1,2,…,K; m=1,2,…,N CSP ; q = 1, 2, ..., N PB The row vectors M1-M6, matrices N1-N7, constant M7, and column vector N8 are obtained by rearranging the objective function and constraints of optimization problems (22) and (23).

[0169] The steps for solving the linear model of economic dispatch of a power system include:

[0170] 3.1) Simplifying the linear model of economic dispatch of the power system, we get:

[0171] minF=GX+M7 (26)

[0172] stAX≤Bw+C (27)

[0173] In the formula: X = [x; p HT ;p TH ;E;p CSP ;p SH w = PB is the planning parameter; G = [M1, M2, M3, M4, M5, M6]; A = [N1, N3, N4, N5, N6]; B = -N7; C = N8;

[0174] 2) Set the number of clusters to S, and start from the total load Pd = {Pd1, Pd2, ..., Pd} of T system time periods. t ,…,Pd T S loads are randomly selected as the initial cluster centers K in the} J ={K1,K2,…,K s ,…,K S};K S The S-th initial cluster center;

[0175] 3.3) Calculate the distance from the total load of each system time period to the cluster center, and divide the total load of each system time period and the nearest cluster center into the same cluster time period according to the distance;

[0176] Wherein, the total load Y of the i-th system time period i To the j-th cluster center Y j The weighted Euclidean distance is shown below:

[0177]

[0178] In the formula: C DIM The data dimension of a data point; w c Represents the weighting coefficients of the c-th dimension data;

[0179] Among them, the weighting coefficient w of the c-th dimension data c As shown below:

[0180]

[0181] In the formula: This represents the average value of the c-th dimension of data; T is the total number of time periods, i.e., the number of data points.

[0182] 3.4) Recalculate the cluster centers for the data within each clustering period to obtain new cluster centers. New cluster center and existing cluster center K J To compare, if the cluster centers change, then let If the condition is met, proceed to step 3.3); otherwise, proceed to step 3.5.

[0183] 3.5) Output clustering results: The total load of S consecutive system time periods is the K-means clustering result;

[0184] 3.6) Construct a low-dimensional decoupling time period model based on the load clustering results in step 3.5), where the s-th low-dimensional decoupling time period model is shown below:

[0185] minF s =G s X s +M 7,s (30)

[0186] stA s X s ≤B s w s +C s (31)

[0187] In the formula: X s =[x;pHT,s ;p TH,s E s ;p CSP,s ;p SH,s ];w s =PB s For planning parameters; G s M 7,s A s B s and C s Determined by optimization problems (26) and (27). The subscript s represents the variables and coefficients in the original optimization problems (26) and (27) corresponding to the s-th low-dimensional decoupling time period.

[0188] 3.7) Solve the low-dimensional decoupled time period model using multi-parameter programming theory to obtain the feasible domain of tie-line transmission power CR=CR1∪CR2∪…∪CR, which characterizes the regional power grid regulation capacity. s ∪…∪CR S .

[0189] The steps for solving the s-th low-dimensional decoupled time-period model using multi-parameter programming theory include:

[0190] 3.7.1) Construct the Lagrangian function L s ,Right now:

[0191] L s =G s X s +M 7,s -λ s (A s X s -B s w s -C s (32)

[0192] In the formula: λ s The vector consisting of Lagrange multipliers;

[0193] 3.7.2) Establish the optimality conditions for the s-th low-dimensional decoupled time period model, including the stationary point condition (33), the complementary relaxation condition (34), the original feasibility condition (35), and the dual feasibility condition (36), namely:

[0194]

[0195] λ s (A s X s -B s w s -C s )=0 (34)

[0196] As X s -B s w s -C s ≤0 (35)

[0197] λ s ≥0 (36)

[0198] 3.7.3) For optimization problems (26) and (27), when the planning parameter w s When the parameters vary within the feasible region, there are a total of M corresponding parameters. s Different sets of effective and ineffective constraints;

[0199] Let the optimal solution corresponding to the m-th constraint set be denoted as . Then the effective and ineffective constraints in the m-group constraint set are shown in formulas (37) and (38) respectively, that is:

[0200]

[0201]

[0202] In the formula: The subscripts Y and N represent the active and inactive constraints in the constraint set, respectively; m = 1, 2, ..., M s ;

[0203] 3.7.4) Establish the optimal solution corresponding to the m-th set of constraints. The expression, that is:

[0204]

[0205] Where: matrix matrix

[0206] 3.7.5) Substituting formula (39) into formula (38) and combining like terms, we obtain the critical region, i.e.:

[0207] A s,w,m w s <B s,w,m (40)

[0208] In the formula, the matrix matrix

[0209] 3.7.6) Enumerate the active and inactive constraint sets of optimization problems (26) and (27), and repeat steps 3.7.3) to 3.7.5) to obtain M. s Critical domain CR s,m Then, the analytical expression of the optimal solution function for the optimization problem is established, namely:

[0210]

[0211]

[0212] In the formula: A s,w B s,w These are the coefficient matrix and coefficient vector obtained by taking the union of the critical regions and rearranging them.

[0213] Example 2:

[0214] First, an economic dispatch model for the power system considering the nonlinear operating characteristics of solar thermal power (CSP) is constructed. The energy loss cost of the CSP power plant's thermal storage system during charging and discharging is added to the existing economic dispatch model for power systems containing CSP plants, fully considering the nonlinear operating constraints of CSP plants. A linear transformation of the nonlinear model is achieved based on a linearization method. Then, based on load clustering algorithms and multi-parameter programming methods, a method for characterizing the multi-period power regulation capability of the regional power grid containing CSP plants is proposed. Comparative results based on data from the IEEE-30 node system and the actual 661 node system show that the proposed method can meet the requirements of the nonlinear operating characteristics of CSP plants, accurately characterize the power regulation capability of the regional power grid containing CSP plants, and effectively reduce the inter-period coupling relationship of the regional power grid's power regulation capability, verifying the effectiveness of the proposed method. The method flowchart is as follows: Figure 1 As shown, the specific steps are as follows:

[0215] Constructing an economic dispatch model for power systems that takes into account the nonlinear operating characteristics of concentrated solar power (CSP).

[0216] Constructing a nonlinear model for economic dispatch of a power system including a solar thermal power plant

[0217] This invention considers the nonlinear constraints of the thermal storage system during the operation of a solar thermal power plant and adds the energy loss cost during the charging and releasing process of the thermal storage system. With the goal of minimizing the total operating cost of the system, the following economic dispatch model of the power system considering the nonlinear operating characteristics of solar thermal power generation is established.

[0218] 1) Objective function

[0219]

[0220] In the formula: F represents the total operating cost of the system; the first term C CSP The first item is the operating cost of a concentrated solar power (CSP) plant; the second item is the penalty for wind and solar power curtailment; the third item is the operating cost of traditional generating units, such as thermal power and hydropower units; and the fourth item is the operating cost of energy storage. ρ RN The penalty fee per unit of wind or solar power curtailment; P RNmax,i,t p RN,i,tThese represent the maximum generateable power and actual output power of the i-th renewable energy power station during time period t, respectively; p TR,j,t p is the output power of the j-th conventional unit during time period t; c,r,t p d,r,t These represent the charging and discharging power of the r-th energy storage unit during time period t; c TR,j c is the operating cost coefficient of the j-th traditional unit; c,t c d,t These are the energy storage charging and discharging prices for time period t; N RN N TR and N ESS These represent the number of new energy power plants, traditional generating units, and energy storage, respectively; Δt is the time interval, and T is the total number of time intervals.

[0221] Energy flow in a solar thermal power plant with a thermal storage system, such as Figure 1 As shown. The actual energy received by the solar thermal power plant (p SH,m,t ) is determined by the maximum heat that the light field can collect (P) solar,m,t ) and discarded heat (p curt,m,t The power generation system converts the heat obtained from the heat transfer system into electrical energy (p). CSP,m,t The thermoelectric conversion efficiency is determined by β. HP,m This indicates that the heat transfer system and the heat storage system can be connected via heat charging (p HT,m,t ) and exothermic (p) TH,m,t To achieve the storage and release of heat, η hc,m η hd,m These represent the charging and releasing heat efficiencies of a solar thermal power plant, respectively; the thermal storage system also needs to meet heat balance constraints:

[0222]

[0223] In the formula: t = 1, 2, ..., T; m = 1, 2, ..., N CSP N CSP Indicates the number of solar thermal power plants; E m,t E m,t-1 γ represents the heat stored in the thermal storage system of the m-th solar thermal power plant during time period t and time period t-1, respectively; loss,m Let be the heat dissipation rate of the thermal energy storage system of the m-th solar thermal power plant.

[0224] Existing economic dispatch models for solar thermal power plants do not adequately consider the energy loss costs of the thermal storage system, only taking into account the heat stored in the system, E. m,t The cost of heat dissipation. But as Figure 1As shown, during the operation of a concentrated solar power (CSP) plant, energy losses also occur during the charging and releasing of heat in the thermal storage system. The energy loss rate of this process is roughly equivalent to that of the heat dissipation process and cannot be ignored. To fully account for this energy loss, this invention innovatively proposes to increase the cost of energy losses during the charging and releasing processes, based on the existing operating costs of CSP plants.

[0225]

[0226] In the formula: C CSP_cd Cost of energy loss during the charging and releasing process; L CSP This is the heat loss penalty coefficient for the thermal storage system.

[0227] By combining the energy loss cost of the thermal storage system during the charging and releasing process shown in equation (3) with the operating cost of the existing solar thermal power plant, the operating cost of the solar thermal power plant proposed in this invention can be obtained, as shown in equation (4):

[0228]

[0229] In the formula: the first term is the power generation cost of the solar thermal power plant; the second term is the energy loss cost of the newly added thermal storage system during the charging and discharging process, as shown in formula (3); the third term is the heat dissipation cost of the thermal storage system; and the fourth term is the heat curtailment penalty cost of the solar thermal power plant. CSP,m ρ is the power generation cost coefficient of the m-th solar thermal power plant; solar The penalty fee for the unit heat waste of a solar thermal power plant.

[0230] 2) Operational constraints of solar thermal power plants

[0231] In addition to satisfying the energy balance constraint of the thermal storage system shown in equation (2) during the operation of a solar thermal power plant, the following constraints must also be met: ① The heat transfer system must satisfy the energy balance constraint, i.e., equation (5); ② The thermal storage system can only be in a charging, releasing, or static state at the same time, i.e., equation (6); ③ The charging and releasing power p of the solar thermal power plant HT,m,t p TH,m,t There is an upper limit constraint, namely equations (7) and (8); ④ The heat stored in the thermal storage system, E m,t There are upper and lower limits, i.e., equation (9); ⑤ The output power p of the solar thermal power plant CSP,m,t There are upper and lower limits, i.e., equation (10); ⑥ The output power p of the solar thermal power plant CSP,m,t The ramp constraint needs to be satisfied, i.e., equation (11); ⑦ The actual heat power p received by the solar thermal power plant from the light field SH,m,t It cannot exceed the maximum heat-collecting power P of the light field. solar,m,t That is, equation (12).

[0232] p SH,m,t +p TH,m,t =p HT,m,t +pCSP,m,t / β HP,m (5)

[0233] p HT,m,t ·p TH,m,t =0 (6)

[0234] 0≤p HT,m,t ≤P HT,m,max (7)

[0235] 0≤p TH,m,t ≤P TH,m,max (8)

[0236] E m,min ≤E m,t ≤E m,max (9)

[0237] 0≤p CSP,m,t ≤P CSP,m,max (10)

[0238] -RD CSP,m ≤p CSP,m,t -p CSP,m,t-1 ≤RU CSP,m (11)

[0239] 0≤p SH,m,t ≤P solor,m,t (12)

[0240] In the formula: t = 1, 2, ..., T; m = 1, 2, ..., N CSP ;P HT,m,max P TH,m,max and P CSP,m,max E represents the rated charging and discharging power and rated output electrical power of the m-th solar thermal power plant, respectively; m,max and E m,min These represent the upper and lower limits of thermal storage for the m-th solar thermal power plant's thermal storage system; RU CSP,m and RD CSP,m These represent the power output ramp-up and ramp-down limits for the m-th solar thermal power plant, respectively.

[0241] 3) Power balance constraints

[0242] This invention uses a DC power flow model commonly used in industry to model the power flow constraints of the system:

[0243]

[0244] Where: t=1,2,…,T; N bus N PB These represent the number of nodes connected to the load and the number of nodes at the boundary of the regional power grid, respectively; D n,t PB represents the load of the nth node during time period t. q,tLet q be the transmission power of the q-th tie line during time period t.

[0245] 4) Branch power constraints

[0246] F k,min ≤f k,t ≤F k,max (14)

[0247] PB q,min ≤PB q,t ≤PB q,max (15)

[0248] Where: t = 1, 2, ..., T; k = 1, 2, ..., K; q = 1, 2, ..., N PB K represents the total number of internal branches in the system; f k,t F represents the power of the k-th internal branch during time period t; k,max F k,min These are the upper and lower power limits for the k-th internal branch, respectively; PB q,max PB q,min These represent the upper and lower power limits of the q-th tie line, respectively.

[0249] 5) Branch power constraints

[0250] P TR,j,min ≤p TR,j,t ≤P TR,j,max (16)

[0251] -RD TR,j ≤p TR,j,t -p TR,j,t-1 ≤RU TR,j (17)

[0252] In the formula: t = 1, 2, ..., T; j = 1, 2, ..., N TR ;P TR,j,max P TR,j,min Represent the upper and lower limits of the output power of the j-th conventional unit, respectively; RU TR,j RD TR,j These represent the ramp-up and ramp-down limits for the j-th conventional unit, respectively.

[0253] 6) Operational constraints of wind and solar power

[0254] 0≤p RN,i,t ≤P RNmax,i,t (18)

[0255] In the formula: t = 1, 2, ..., T; i = 1, 2, ..., N RN .

[0256] 7) Energy storage operation constraints

[0257] 0≤pd,r,t ,p c,r,t ≤P r,EESmax (19)

[0258] SOC r,t =SOC r,t-1 +(p c,r,t η ec,r -p d,r,t / η ed,r (20)

[0259] SOC r,min ≤SOC r,t ≤SOC r,max (twenty one)

[0260] In the formula: t = 1, 2, ..., T; r = 1, 2, ..., N EES ;P r,EESmax Represents the rated charge and discharge power of the r-th energy storage unit; SOC r,t SOC r,t-1 The state of charge (SOC) of the r-th energy storage unit during time periods t and t-1, respectively. r,max SOC r,min η represents the upper and lower limits of the r-th energy storage state of charge, respectively; ec,r η ed,r , respectively, are the charging and discharging efficiencies of the r-th energy storage unit.

[0261] After processing, the economic dispatch model of the power system taking into account the nonlinear operating characteristics of solar thermal power generation is shown in equations (22) and (23):

[0262] min(1) (22)

[0263] st(2),(5)-(21) (23)

[0264] Linearization transformation of the economic dispatch model of the power system including solar thermal power plants

[0265] In models (22) and (23), there is a nonlinear constraint (6). Usually, integer variables are introduced to solve the mixed integer linear model. At this time, multi-parameter programming theory is used to handle the problem. It is necessary to enumerate all possible combinations of integer variables. At this time, the number of integer variables is related to the number of solar thermal units N. CPS It is related to the scheduling period T, reaching N. CPS The enumeration of all possible combinations of a large number of integer variables (×T×2) makes the computational burden of solving multi-parameter programming theory enormous. If the nonlinear constraint (6) is removed, linear optimization problems (24) and (25) can be obtained without introducing integer variables, and can be solved quickly using multi-parameter programming theory.

[0266] min(1) (24)

[0267] st(2),(5),(7)-(21) (25)

[0268] The equality constraints (2), (5), (13) and (20) in optimization problems (24) and (25) are all transformed into two complementary inequality constraints, such as: equality constraint (, which is transformed into inequality constraints ( and (). Then the transformed optimization problems (24) and (25) are arranged into matrix vector form. In this process, in order to facilitate the subsequent proof, the relevant vectors of the solar thermal power plant (such as the charging and discharging power p of the solar thermal power plant) are transformed into matrix vector form. HT p TH The thermal energy storage system stores heat (E); the solar thermal power plant outputs electrical power (p). CSP Actual received power p of solar thermal power plant SH The transmission power PB of the tie line is listed separately, and the remaining variables are integrated. Then the optimization problems (24) and (25) can be reorganized into the following linear form:

[0269]

[0270]

[0271] In the formula: column vector x = [p RN ,p TR ,p c ,p d [,SOC,f] T p RN p TR p c p d SOC and f are both row vectors, p HT p TH E, p CSP p SH Both p and PB are column vectors, where: p RN =[p RN,i,t ]; p TR =[p TR,j,t ]; p c =[p c,r,t ]; p d =[p d,r,t ];SOC=[SOC r,t ]; f = [f k,t ]; p HT =[p HT,j,t ]; p TH =[p TH,j,t ];E=[E m,t ]; p CSP =[p CSP,j,t ]; p SH =[pSH,j,t ];PB=[PB q,t ]; t=1,2,…,T; i=1,2,…,N RN j = 1, 2, ..., N TR r = 1, 2, ..., N EES ;k=1,2,…,K; m=1,2,…,N CSP ; q = 1, 2, ..., N PB The row vectors M1-M6, matrices N1-N7, constant M7, and column vector N8 can be obtained by rearranging the objective function and constraints of optimization problems (24) and (25).

[0272] The following proof by contradiction demonstrates that linear models (26) and (27) are equivalent to nonlinear models (22) and (23). Assume that optimization problems (26) and (27) have an optimal solution (x). * , E * , PB * ),in That is, the nonlinear constraint (6) does not hold. Therefore, we only need to find a feasible solution (x). ^ , E ^ , PB ^ ), and its corresponding objective function value F ^ The objective function value F is less than the optimal solution. * If this is true, it can be shown that the assumption is not true, thus proving that the charging and releasing processes of a solar thermal power plant cannot be carried out simultaneously. That is, the linear models (26) and (27) are equivalent to the nonlinear models (22) and (23).

[0273] First, find a set of feasible solutions and determine their relationship with the optimal solution. The optimization model needs to satisfy the power balance constraint (13). The simplest way is to keep the power of all units in the system constant. At this time, the tie line power and the state of charge of the energy storage will not change, that is, x^=x * , PB^=PB * Furthermore, because the output power p of the solar thermal power plant... CSP,m,t (corresponding vector is p) CSP The energy balance constraint (5) of the heat transfer system of the solar thermal power plant needs to be met. When the output power p of the solar thermal power plant is... CSP,m,t When there is no change, only the charge and discharge power p of the solar thermal power plant is needed. HT,m,t p TH,m,t By simultaneously changing the same value, it is possible to ensure that the solar thermal power plant actually receives p energy. SH,m,t (corresponding vector is p) SH While remaining unchanged, it continues to satisfy the equality constraint (5), that is... (Δp is the coefficient vector, Δp=[Δp m,t ], where t = 1, 2, ..., T, m = 1, 2, ..., N CSP Furthermore, due to the existence of equation constraint (2), the charging and discharging heat power p of the solar thermal power plant HT,m,t p TH,m,t The changes will inevitably affect the heat stored in the thermal storage system, E m,t The change (corresponding to vector E), i.e., E ^ =E * -ΔE (ΔE is the coefficient vector, ΔE=[ΔE) m,t ], where t = 1, 2, ..., T; m = 1, 2, ..., N CSP Equation constraint (2) shows that the thermal system stores heat E. m,t There is a coupling relationship between the preceding and following time periods; changes in variables in the preceding period will inevitably lead to changes in variables in the following period. Therefore, the simplest approach is to change only the variable value in the last period, i.e., ΔE. m,t =0, Where t = 1, 2, ..., T-1; ΔE m,T ≠0, At this time, Δp m,t =0, Where t = 1, 2, ..., T-1; Δp m,T ≠0, Thus, a set of feasible solutions to optimization problems (26) and (27) have been found, as shown in equation (28):

[0274]

[0275] In the formula: Δp=[Δp m,t (t=1,2,…,T), Δp m,t =0 (t=1,2,…,T-1), Δp m,T ≠0; ΔE m,t =0 (t=1,2,…,T-1), ΔE m,t =0.

[0276] The optimal solution and the found feasible solutions correspond to the objective function F of optimization problems (26) and (27). * With F ^ By making subtractions and organizing the data, we can obtain:

[0277]

[0278] Substituting the optimal and feasible solutions into equation (2), we get:

[0279]

[0280] Solving the system of equations (30) yields:

[0281] ΔE m,T =(η hc,m -1 / η hd,m )ΔP m,T Δt (31)

[0282] Substituting equation (31) into equation (29) and rearranging, we get:

[0283]

[0284] Because the heat charging and discharging efficiency η of a solar thermal power plant hc,m η hd,m The value range is generally (0.95, 1), and the heat dissipation rate γ of the thermal storage system is... loss,m The value range is generally (0, 0.05), and the time interval Δt generally ranges from (0, 1], so we can obtain (1-γ). loss,m Δt)>0, (1 / η) hd,m -η hc,m Therefore, the sign of ΔF depends only on Δp > 0. m,T It is related to the positive or negative.

[0285] When Δp m,T When ΔF > 0, it can be seen from equation (32) that ΔF > 0. At this point, a feasible solution as shown in equation (28) has been found, which can make the objective function value F ^ The objective function value F is less than the optimal solution. * This contradicts the optimality of the optimization problem, so the assumption is invalid. Therefore, the charging and discharging heat power p of the solar thermal power plant is... TH p HT It cannot be greater than 0 at the same time, that is, the nonlinear constraint (6) is automatically established.

[0286] In summary, the optimal solutions of linear models (26) and (27) automatically satisfy the nonlinear constraint (6), that is, linear models (26) and (27) are equivalent to nonlinear models (22) and (23).

[0287] Method for characterizing the multi-period power regulation capability of regional power grids containing solar thermal power plants

[0288] Decoupling of regional power grid multi-period power regulation capability based on load time clustering

[0289] When using multi-parameter programming theory to characterize the multi-period regulation capacity of a regional power grid, it is necessary to enumerate all combinations of active and inactive constraints. The power regulation capacity of a regional power grid is the tie-line transmission power PB. q,t The high-dimensional space represented by (corresponding vector PB) contains scheduling period T × number of connection lines N. PBWith numerous variables and constraints, the computational burden is immense. To address this issue, this project utilizes the K-means clustering algorithm, commonly used in load clustering, to decouple and reduce the dimensionality of multi-time-period tie-line power. This decomposes the high-dimensional space into several low-dimensional spaces, while maintaining the inter-time-period coupling characteristics within each low-dimensional space. The specific steps are as follows:

[0290] For ease of derivation, the linear optimization problems (26) and (27) are first further rearranged into compact forms as shown in equations (33) and (34):

[0291] minF=GX+M7 (33)

[0292] stAX≤Bw+C (34)

[0293] In the formula: X = [x; p HT ;p TH ;E;p CSP ;p SH ]; w = PB is the planning parameter; G = [M1, M2, M3, M4, M5, M6]; A = [N1, N3, N4, N5, N6]; B = -N7; C = N8.

[0294] Let the number of clusters be S, and the total load Pd = {Pd1, Pd2, ..., Pd} for T system time periods. t ,…,Pd T S loads are randomly selected as the initial cluster centers K in the} J ={K1,K2,…,K s ,…,K S}

[0295] Calculate the total load of each system time period to the cluster center K according to the weighted Euclidean distance formula (35). J The distance is used to determine the total load of each system during a given time period, and based on the distance, the total load of each system during that time period is divided into the same cluster period as the nearest cluster center.

[0296]

[0297] In the formula: (represents Y) i and Y j The weighted Euclidean distance between two data points, where C DIM The data dimension of a data point; w c The weighting coefficient for the c-th dimension data is used to eliminate the influence of measurement scale and dimension between different dimensions of the total load data of the system period. The coefficient of variation is the ratio of the standard deviation of a set of data to its mean. Its calculation formula is shown in equation (36):

[0298]

[0299] In the formula: This represents the average value of the c-th dimension of data; T is the total number of time periods, i.e., the number of data points.

[0300] The new cluster centers are obtained by recalculating the cluster centers for the data within each clustering period. and existing cluster center K J To compare, if the cluster centers change, then let If the value is not specified, proceed to step 3; otherwise, proceed to the next step.

[0301] The output result is the total load of S consecutive system time periods, which is the K-means clustering result.

[0302] Based on the load clustering results in step 5), a low-dimensional decoupling time period model is constructed. The s-th low-dimensional decoupling time period model can be written as:

[0303] minF s =G s X s +M 7,s (37)

[0304] stA s X s ≤B s w s +C s (38)

[0305] In the formula: X s =[x;p HT,s ;p TH,s E s ;p CSP,s ;p SH,s ];w s =PB s For planning parameters; G s M 7,s A s B s and C s It can be determined by optimization problems (33) and (34). The subscript s represents the variables and coefficients in the original optimization problems (33) and (34) corresponding to the s-th low-dimensional decoupling time period.

[0306] Characterization of regional power grid power regulation capability based on multi-parameter programming theory

[0307] This project addresses each low-dimensional decoupling period by solving the feasible region of tie-line transmission power based on multi-parameter programming theory, thereby characterizing the regional power grid's regulation capability. Taking the feasible region of tie-line power in the s-th low-dimensional decoupling period as an example, the specific method is as follows.

[0308] Construct the Lagrangian function L s :

[0309] L s =G s X s +M 7,s -λ s (A s X s -B s w s -C s (39)

[0310] In the formula: λ s It is a vector composed of Lagrange multipliers.

[0311] The optimality conditions for optimization problems (37) and (38) include the stationary point condition (40), the complementary relaxation condition (41), the original feasibility condition (42), and the dual feasibility condition (43):

[0312]

[0313] λ s (A s X s -B s w s -C s )=0 (41)

[0314] A s X s -B s w s -C s ≤0 (42)

[0315] λ s ≥0 (43)

[0316] For optimization problems (34) and (35), when the planning parameter w s When the parameters vary within the feasible region, there are a total of M corresponding parameters. s A set of distinct active and inactive constraints. Let the m-th (m = 1, 2, ..., M) be the constraint set. s Taking a set of constraints as an example, let its corresponding optimal solution be denoted as... The active and inactive constraints in the m-th constraint group can be obtained by decomposing and rearranging constraint (38), as shown in equations (44) and (45) respectively:

[0317]

[0318]

[0319] In the formula: The subscripts Y and N represent the active and inactive constraints in the constraint set, respectively.

[0320] From equation (44), it can be seen that when A s,Y,m When the matrix is ​​full rank, the optimal solution This can be represented as the planning parameter w. s The affine function is shown in equation (46); and when A s,Y,m When the matrix is ​​not full rank, the ConsistentTieBreaking Rule can be used to ensure the uniqueness of the calculation results, and thus obtain equation (46).

[0321]

[0322] In the formula: Z s,m for z s,m for

[0323] Substituting equation (46) into equation (45) and combining like terms, we obtain equation (47), which is mathematically called the critical region and denoted as CR. s,m ,in

[0324] A s,w,m w s <B s,w,m (47)

[0325] As can be seen from the above derivation, by enumerating the active and inactive constraint sets of optimization problems (37) and (38), we can obtain M. s Critical domain CR s,m (m=1,2,…,M s Between each critical region, the optimization variable is represented by w. s The analytical functions are different. For example, Figure 2 As shown, the feasible region CR of the parameters s The union of all critical regions, i.e., CR s =CR s,1 ∪CR s,2 ∪…∪CR s,Ms The expression is shown in equation (48), and the corresponding analytical expression of the optimal solution function of the optimization problem is shown in equation (49).

[0326]

[0327]

[0328] In the formula: A s,w B s,wThese are the coefficient matrix and coefficient vector obtained by taking the union of the critical regions and rearranging them.

[0329] The feasible regions of tie-line transmission power obtained by the above method for the S low-dimensional clustering time periods formed by clustering and decoupling are CR1, CR2, ..., CR3, respectively. S The corresponding optimal solutions are respectively Then, the feasible region of tie-line power over the entire period is CR = CR1∪CR2∪…∪CR s ∪…∪CR S Overall optimal solution Ultimately, the multi-period power regulation capability of the regional power grid can be characterized by the multi-period tie-line power feasible region CR.

[0330] Example 3:

[0331] See Figures 1 to 9 A verification experiment of the regional power grid power regulation capability characterization method considering the nonlinear operating characteristics of solar thermal power generation as described in Embodiment 2 includes the following:

[0332] (1) Constructing a nonlinear model for economic dispatch of a power system containing solar thermal power plants

[0333] Taking full account of the energy loss in the thermal storage stage of the solar thermal system, based on the objective function of the existing economic dispatch model of solar thermal power plants (Equation (1)), the energy loss cost of the charging and releasing process in the thermal storage stage is added, as shown in Equation (3), forming a new formula for calculating the operating cost of solar thermal power plants, as shown in Equation (4). On this basis, the operating constraints of the solar thermal power plant are considered, namely Equations (2), (5)-(12); power balance constraints, namely Equation (13); branch power constraints, namely Equations (14)-(15); and other power source operating constraints, namely Equations (16)-(21). Finally, a nonlinear economic dispatch model of the power system containing the solar thermal power plant is constructed (22)-(23).

[0334] (2) Linearization transformation of the economic dispatch model of the power system including solar thermal power plants

[0335] Through equivalence transformation, the nonlinear economic dispatch model (22)-(23) of the power system containing solar thermal power plants is transformed into a linear model (24)-(25). The proof process is shown in Section 1.2 of the invention content, involving formulas (26)-(32).

[0336] (3) Decoupling of multi-period power regulation capability of regional power grid based on load time clustering

[0337] First, S loads are randomly selected from the total load of T system time periods as initial cluster centers. Then, the distance from the total load of each remaining system time period to the cluster center is calculated sequentially using formulas (35)-(36). Based on the distance, the total load of each system time period and the nearest cluster center are assigned to the same cluster period. Then, the cluster centers are recalculated for the data in each cluster period to obtain new cluster centers. If the cluster centers change, the cluster centers are updated and the clustering is performed again. Otherwise, the clustering results are output, i.e., formulas (37) and (38).

[0338] (4) Characterization of regional power grid power regulation capability based on multi-parameter programming theory

[0339] The feasible domain of tie-line transmission power for each low-dimensional clustering period is solved once using multi-parameter tree programming theory, i.e., equation (48), and the corresponding optimal solution is obtained, i.e., equation (49). Then, the feasible domain of tie-line power over the entire cycle is obtained by finding the union of the feasible domains of each low-dimensional clustering period. Finally, the multi-period power regulation capability of the regional power grid can be characterized by the feasible domain of tie-line power over the entire cycle.

[0340] Specific simulation results

[0341] 1) Introduction to simulation data and comparison methods

[0342] This invention uses an IEEE-30 node system and a real power system in a Chinese province containing 661 nodes to verify the accuracy and effectiveness of the proposed method. Each system includes one wind farm, one photovoltaic power station, and two energy storage power stations. Two thermal power units in the original system are replaced with a solar thermal power station. The wind farm's grid connection node is numbered 5, the photovoltaic power station's is numbered 11, the energy storage power stations' are numbered 7 and 9, and the solar thermal power station's are numbered 22 and 27. The IEEE-30 node system has two tie lines, with boundary nodes numbered 8 and 28. The time interval Δt = 1, and the total number of time intervals T = 24.

[0343] All the examples used in this invention were tested in a hardware environment with an Intel(R) Core(TM) i5-8250U CPU@1.60GHz and 16GB RAM. The penalty cost ρ per unit of wind or solar curtailment in the example system is... RN And the penalty fee per unit of abandoned heat from solar thermal power plants ρ solar All are 300 RMB / MWh; heat loss penalty coefficient L for thermal storage system CSP Set at 460 RMB / MWh; Cost coefficient S for solar thermal power plants CSP = 40 RMB / MWh. The parameter settings for the solar thermal power plant are shown in Table 1, and the parameter settings for the energy storage unit and the pricing for energy storage charging and discharging are shown in Tables 2 and 3, respectively.

[0344] Table 1 Parameters of the solar thermal power plant

[0345]

[0346] Table 2 Parameters of Energy Storage Power Station

[0347]

[0348] Table 3. Charging and discharging quotations for energy storage power stations

[0349]

[0350] This embodiment compares the scheduling results of the linearized model proposed in this invention with those of the mixed-integer linear model (M0, M1) to verify the effectiveness of the linearization transformation method for the economic dispatch model of the power system containing solar thermal power plants proposed in this invention. Secondly, the method proposed in this invention will be used to characterize the power regulation capabilities of different regional power grids (M2, M3), and the impact of the addition of solar thermal power plants on the spatiotemporal coupling of regional power grid power regulation capabilities will be compared and analyzed to verify the effectiveness of the proposed method for characterizing the regional power grid power regulation capabilities considering the nonlinear operating characteristics of solar thermal power generation. The cases for M0-M3 are shown below:

[0351] M0: The linearized scheduling model for solar thermal power plants proposed in this invention;

[0352] M1: A mixed-integer linear scheduling model for solar thermal power plants;

[0353] M2: Regional power grid excluding solar thermal power plants;

[0354] M3: Regional power grid including solar thermal power plants with thermal storage systems.

[0355] 2) Verification of the accuracy of the linearization transformation method for the solar thermal power plant scheduling model

[0356] Table 4 shows the scheduling results of models M0 and M1 in the IEEE-30 node system and the actual 661 node system. The output power and charging / discharging power results of the solar thermal power plant in the IEEE-30 node example are shown below. Figures 4-6 As shown.

[0357] Table 4 Comparison of calculation results between the two models in the IEEE-30 Node and 611 Node systems.

[0358]

[0359] pass Figure 5 and Figure 6 It was found that solar thermal power plant No. 1 charged heat during periods 12-18 and released heat during periods 1-5, 11, and 19-23; solar thermal power plant No. 2 charged heat during periods 11 and 13-18 and released heat during periods 1-6 and 19-23. Therefore, the charging and releasing heat power p of the thermal storage system in both models is...HT,m,t and p TH,m,t None of them will be greater than zero at the same time, which meets the requirement that the charging and releasing of heat in the thermal storage system cannot occur simultaneously during the operation of a solar thermal power plant.

[0360] Table 2 shows that the total operating cost of the scheduling schemes obtained from the two models is consistent. In the IEEE-30 energy-saving system, the scheduling cost of both models M0 and M1 is 4.257 × 10⁻⁶. 5 In a real 611-node system, the scheduling cost for both models M0 and M1 is 1.788 × 10⁻⁶ yuan. 7 Yuan. But through Figures 4-6 It can be observed that the scheduling results of individual units differ in certain time periods. For example, in time periods 2-5, the output power of the two concentrated solar power (CSP) plants shows significant differences in the two models, with the most pronounced difference in time period 3, where the scheduling results of the two models are completely opposite. This is because the initial state and related parameter settings of the units are the same, leading to different output decisions by the solver during the solution process. Nevertheless, the sum of the output power of all CSP plants and the charging and releasing power of the thermal storage system is consistent in each time period, and does not affect the overall economic efficiency and safety of the system scheduling. The above analysis verifies the effectiveness of the linearization transformation method for scheduling models containing CSP plants proposed in this invention.

[0361] 3) Application and analysis of methods for characterizing the power regulation capability of regional power grids considering the nonlinear operating characteristics of concentrated solar power (CSP) generation.

[0362] This invention, within the IEEE-30 node system, compares and analyzes the changes in regional power grid power regulation capability before and after the integration of a concentrated solar power (CSP) plant into the power system, and analyzes the impact of CSP plants on the regional power grid's power regulation capability. The power transmission capacity is measured in PB via tie lines. q,t Using the proposed method as planning parameters, the power regulation capabilities of the power grids in regions M2 and M3 are characterized. The time-period clustering results are as follows: Figure 7 As shown.

[0363] Figure 7 This represents the clustering results when the number of clustering periods S = 8. Each dot represents a load data point, and the same color indicates that the corresponding time period belongs to the same cluster. Taking the first clustering period (s = 1) as an example, it includes time periods 1-3. The regional power regulation capability of the M2 and M3 regional power grids during time periods 1-3 is as follows: Figure 8 and Figure 9 As shown.

[0364] Figure 8 and Figure 9 Each colored block represents a critical region CR as described in Section 2.2. 1,mAll critical domains combine to form the regional power regulation capacity CR1 for the current time period. From equation (47), the CR1 for each critical domain can be obtained. 1,m The expression. For example: the critical range CR of power regulation capability of tie line 2 in the M2 system during time periods 1 and 2. 1,15 It can be expressed as equation (50):

[0365] A 1,w,15 [PB 2,1 ,PB 2,2 ] T <B 1,w,15 (50)

[0366] In the formula: A 1,w,15 =[-0.7071,-0.7071;0,-1;0.7071,0.7071;0,1], B 1,w,15 = [0.4219; 0.3900; -0.3781; -0.3648].

[0367] Meanwhile, from equation (48), the expression for the overall power regulation capability of tie line 2 in the M2 system during periods 1 and 2 can be obtained, as shown in equation (51):

[0368] A 1,w [PB 2,1 ,PB 2,2 ] T <B 1,w (51)

[0369] In the formula: A 1,w =[-0.0442,0.0015;-0.318,0.318;-0.0436,0.0574;-0.0048,0.0129;-0.0002,0.0022;0,1.1335;0.023,0.0299; B 1,w = [0.0280; 0.3786; 0.0642; 0.0132; 0.0021; 1.0687; 0.0491; 0.9363; 0.0026; 0.4566; 0.6901; 0.0228; 0.0036; 0.0300; -0.6158].

[0370] Figure 8 and Figure 9The power regulation capability boundary of a regional power grid is divided into two categories: parallel to the coordinate axes and non-parallel to the coordinate axes. The regulation capability boundary parallel to the coordinate axes represents the upper and lower limits of power transmission along tie lines. This is caused by the capacity limitations of the line itself or the maximum power transmission and reception limits of the regional power grid, and is unrelated to the influence between preceding and following time periods. The regulation capability boundary non-parallel to the coordinate axes indicates that the power on the tie lines influences each other between preceding and following time periods, exhibiting a coupling relationship. Therefore, the closer the power regulation capability area is to a square, the weaker the coupling relationship between time periods in its power regulation capability. Thus, the strength of the coupling relationship between time periods in the regulation capability can be characterized by the ratio of the area of ​​the power regulation capability area to the area of ​​the square region enclosed by the upper and lower limits of transmission power, as shown in Table 5. Combined with... Figure 8 , Figure 9 Based on the data in Table 3, it can be observed that the inter-time coupling relationship of power regulation capability is stronger for M2 than for M3. This is because, compared to new energy units such as photovoltaic and wind power, solar thermal power plants with thermal storage can achieve energy time shifting, which is equivalent to combining power generation with energy storage devices. Compared to traditional thermal power units, solar thermal power plants with thermal storage have a faster ability to adjust output. When solar thermal resources are abundant, solar thermal power plants can effectively reduce the inter-time coupling characteristics of the grid's power regulation capability.

[0371] Table 5 Inter-time Coupling Relationship of Power Grid Regulation Capability

[0372]

[0373] This invention proposes an economic dispatch model for power systems that considers the nonlinear operating characteristics of concentrated solar power (CSP) generation. It achieves linearization of the economic dispatch model without integer variables through a linearization transformation method for power systems containing CSP plants. Based on this, a method for characterizing the multi-period power regulation capability of regional power grids containing CSP plants is proposed. Finally, test examples in the IEEE-30 node system and a real power system in a Chinese province verify the effectiveness of the proposed method.

Claims

1. A method for characterizing the power regulation capability of a regional power grid considering the nonlinear operating characteristics of concentrated solar power (CSP) generation, characterized in that, Includes the following steps: Step 1) Construct an economic dispatch model for the power system that takes into account the nonlinear operating characteristics of concentrated solar power (CSP); Step 2) Linearize the power system economic dispatch model to obtain a linear power system economic dispatch model that takes into account the nonlinear operating characteristics of solar thermal power generation; Step 3) Solve the linear model of economic dispatch of the power system to obtain the multi-period power regulation capability of the regional power grid; The steps to obtain a linear model of power system economic dispatch that takes into account the nonlinear operating characteristics of concentrated solar power (CSP) include: Step 2.1) Simplify the power system economic dispatch model that takes into account the nonlinear operating characteristics of solar thermal power generation, and obtain: （22） （23） （1） In the formula: F represents the total operating cost of the system; The operating cost of a solar thermal power plant; Penalty fees per unit of wind or solar power curtailment; , These are the maximum power generation capacity and actual output power of the i-th new energy power station in time period t, respectively. Let j be the output power of the j-th conventional unit during time period t; , These represent the charging and discharging power of the r-th energy storage unit during time period t; Let be the operating cost coefficient of the j-th traditional unit; , The prices for energy storage charging and discharging during time period t are respectively; , and N EES These represent the quantities of new energy power plants, traditional generating units, and energy storage, respectively. t represents the time interval, and T represents the total number of time intervals; Among them, the operating cost of solar thermal power plants As shown below: （2） In the formula, Let be the power generation cost coefficient of the m-th solar thermal power plant; Penalty for heat waste per unit of solar thermal power plant; Let m be the power generation of the m-th solar thermal power plant; This represents the maximum heat that can be collected by the light field; This represents the energy actually received by the m-th solar thermal power plant. N represents the heat dissipation rate of the thermal energy storage system in the m-th solar thermal power plant. CSP The number of solar thermal power plants; This is the heat loss penalty coefficient for the thermal storage system; （5） （7） （8） （9） （10） （11） （12） In the formula, t = 1, 2, ..., T; m = 1, 2, ... ; , and These represent the rated charging and discharging power and the rated output power of the m-th solar thermal power plant, respectively. and These are the upper and lower limits of thermal storage for the thermal storage system of the m-th solar thermal power plant, respectively. and These represent the power output ramp-up and ramp-down limits of the m-th solar thermal power plant, respectively. Indicates thermoelectric conversion efficiency; , These represent the charge and discharge power of the solar thermal power plant, respectively. The heat stored in the thermal storage system; Output power for solar thermal power plants The actual heat power received by the solar thermal power plant from the light field The maximum heat-collecting power of the light field HT，m，t , TH，m，t Let represent the heat charging power and heat dissipation power of the m-th solar thermal power plant during time period t, respectively. The power balance constraint is shown in equation (13), that is （13） In the formula: t = 1, 2, ..., T; , These represent the number of nodes connected to the load and the number of nodes at the boundary of the regional power grid, respectively. Let be the load of the nth node in time period t; Let q be the transmission power of the q-th tie line during time period t; , These represent the charging and discharging power of the r-th energy storage unit during time period t; Let be the actual output power of the i-th renewable energy power station during time period t; Let j be the output power of the j-th conventional unit during time period t; The branch power constraints are shown in equations (14)-(15), namely: （14） （15） In the formula: t=1,2,…,T; k=1,2,…,K; q=1,2,…, K represents the total number of internal branches in the system. Let be the power of the k-th internal branch during time period t; , These are the upper and lower power limits for the k-th internal branch, respectively. , PB represents the upper and lower power limits of the q-th tie line, respectively; q,t Let q be the power of the q-th tie line; The power constraints of traditional generating units are shown in formulas (16)-(17), namely: （16） （17） In the formula: t=1,2,…,T; j=1,2,…, ; , These represent the upper and lower limits of the output power of the j-th conventional unit, respectively. , P represents the ramp-up and ramp-down limits of the j-th conventional unit, respectively; TR，j，t P TR，j，t-1 Let represent the output power of the j-th conventional unit at time t and time t-1, respectively; The operating constraints for wind and solar power are shown in formula (18), namely: （18） In the formula: t=1,2,…,T; i=1,2,…, ; , RN，i,t These are the maximum power generation capacity and actual output power of the i-th new energy power station in time period t, respectively. The constraints for energy storage operation are shown in equations (19)-(21), namely: （19） （20） （21） In the formula: t=1,2,…,T; r=1,2,…, ; This represents the rated charging and discharging power of the r-th energy storage unit; , These represent the state of charge of the r-th energy storage unit during time period t and time period t−1, respectively. , These are the upper and lower limits for the r-th energy storage state of charge, respectively. , , respectively, are the charging and discharging efficiencies of the r-th energy storage unit; Step 2.2) Transform the equality constraints (2), (5), (13) and (20) into two complementary inequality constraints to obtain the linear model of power system economic dispatch that takes into account the nonlinear operating characteristics of solar thermal power generation, namely: （24） （25） Where: column vector , , , , , , All are row vectors. , E , as well as Both are column vectors, where: =[ ]; =[ ]; =[ ]; =[ ]; =[ ]; =[ ]; =[ ]; =[ ]; =[ ]; =[ ]; =[ ]; =[ ];t=1,2,…, i=1,2,…, j=1,2,…, r=1,2,…, k=1,2,…, m=1,2,…, ;q=1,2,…, M1, M2, M3, M4, M5, and M6 are row vectors; N1, N2, N3, N4, N5, N6, and N7 are matrices; M7 is a constant; and N8 is a column vector.

2. The method for characterizing the power regulation capability of a regional power grid considering the nonlinear operating characteristics of solar thermal power generation, as described in claim 1, is characterized in that... The heat stored in the thermal storage system of the m-th solar thermal power plant during time period t And the cost of energy loss during the charging and releasing process. They are shown below: （3） （4） In the formula, t = 1, 2, ..., T; m = 1, 2, ... ; Indicates the number of solar thermal power plants; , These represent the heat stored in the thermal storage system of the m-th solar thermal power plant during time periods t and t-1, respectively. Let be the heat dissipation rate of the thermal storage system of the m-th solar thermal power plant; , These represent the charging and discharging heat efficiencies of a solar thermal power plant, respectively. This is the heat loss penalty coefficient for the thermal storage system; HT，m，t , TH，m，t Let represent the heat charging power and heat dissipation power of the m-th solar thermal power plant during time period t, respectively.

3. The method for characterizing the power regulation capability of a regional power grid considering the nonlinear operating characteristics of solar thermal power generation, as described in claim 1, is characterized in that... The constraints of the power system economic dispatch model that takes into account the nonlinear operating characteristics of solar thermal power generation include solar thermal power plant operation constraints, power balance constraints, branch power constraints, wind power and photovoltaic operation constraints, and energy storage operation constraints.

4. The method for characterizing the power regulation capability of a regional power grid considering the nonlinear operating characteristics of solar thermal power generation, as described in claim 3, is characterized in that... The operating constraints of the solar thermal power plant include: energy balance constraints of the thermal storage system (3), energy balance constraints of the heat transfer system (5), state constraints of the thermal storage system at the same time (6), upper limit constraints of the thermal power charging power of the solar thermal power plant (7), upper limit constraints of the thermal power of the solar thermal power plant (8), upper and lower limit constraints of the heat stored in the thermal storage system (9), upper and lower limit constraints of the output power of the solar thermal power plant (10), ramping constraints of the output power of the solar thermal power plant (11), and upper limit constraints of the actual thermal power received by the solar thermal power plant from the light field (12). The state constraints (6) of the thermal storage system during the same period are shown below: （6） In the formula, , These represent the charging and discharging power of the solar thermal power plant, respectively.

5. The method for characterizing the power regulation capability of a regional power grid considering the nonlinear operating characteristics of solar thermal power generation according to claim 1, characterized in that, The steps for solving the linear model of economic dispatch of a power system include: Step 1) Simplify the linear model of economic dispatch of the power system to obtain: （26） （27） In the formula: =[ ; ; ;E; ; ]; For planning parameters; matrix =[ , , , , , ];matrix =[ , , , , ,];matrix ;vector ; Step 2) Set the number of clusters to S, and calculate the total load from T system time periods. S loads are randomly selected as the initial cluster centers. ;K S The S-th initial cluster center; Step 3) Calculate the distance from the total load of each system time period to the cluster center, and divide the total load of each system time period and the nearest cluster center into the same cluster time period according to the distance; Wherein, the total load of the i-th system time period To the j-th cluster center The weighted Euclidean distance D ( , As shown below: （28） In the formula: The data dimension representing a data point; Represents the weighting coefficients of the c-th dimension data; vector ;vector ; Among them, the weighting coefficients of the c-th dimension data As shown below: （29） In the formula: This represents the average value of the c-th dimension of data; T is the total number of time periods, i.e., the number of data points. Step 4) Recalculate the cluster centers for the data within each clustering period to obtain the new cluster centers. ; New cluster center and existing cluster centers To compare, if the cluster centers change, then let If the condition is met, proceed to step 3; otherwise, proceed to step 5. Step 5) Output clustering results: The total load of S consecutive system time periods is the K-means clustering result; Step 6) Construct a low-dimensional decoupling period model based on the load clustering results in Step 5), where the s-th low-dimensional decoupling period model is shown below: （30） （31） In the formula: =[ ; ; ; ; ; ]; For planning parameters; , , , and is a matrix; the subscript s represents the variables and coefficients in the original optimization problems (26) and (27) corresponding to the s-th low-dimensional decoupling time period; Step 7) Solve the low-dimensional decoupled time period model using multi-parameter programming theory to obtain the feasible region of tie-line transmission power used to characterize the regional power grid regulation capacity. ;CR S This represents the feasible domain of tie-line transmission power corresponding to the Sth low-dimensional decoupling period.

6. The method for characterizing the power regulation capability of a regional power grid considering the nonlinear operating characteristics of solar thermal power generation, as described in claim 5, is characterized in that... The steps for solving the s-th low-dimensional decoupled time period model using multi-parameter programming theory include: Step 1) Construct the Lagrange function ,Right now: （32） In the formula: The vector consisting of Lagrange multipliers; Step 2) Establish the optimality conditions for the s-th low-dimensional decoupling time period model, including the stationary point condition (33), the complementary relaxation condition (34), the original feasibility condition (35), and the dual feasibility condition (36), namely: （33） （34） （35） （36） Step 3) For optimization problems (26) and (27), when the planning parameters When the parameters vary within the feasible region, there are a total of Different sets of effective and ineffective constraints; Let the optimal solution corresponding to the m-th constraint set be denoted as . Then, the effective and ineffective constraints in the m-group constraint set are shown in formulas (37) and (38) respectively, that is: （37） （38） In the formula: , , The subscripts Y and N represent the active and inactive constraints in the constraint set, respectively; m = ; Step 4) Establish the optimal solution corresponding to the m-th constraint set. The expression, that is: （39） Where: matrix = ;matrix = ; Step 5) Substitute formula (39) into formula (38), combine like terms, and obtain the critical region, i.e.: （40） In the formula, the matrix ;matrix ; Step 6) Enumerate the active and inactive constraint sets of optimization problems (26) and (27), and repeat steps 3) to 5) to obtain Critical domains Then, the analytical expression of the optimal solution function for the optimization problem is established, namely: （41） （42） In the formula: , These are the coefficient matrix and coefficient vector obtained by combining and rearranging the sets of the critical regions, respectively; M s The number of constraint sets; This is the optimal solution.

Images