A cascade hydropower output boundary equivalence method for clearing electricity spot market

Abstract

The present invention discloses a cascade hydropower output boundary equivalent method suitable for clearing the electricity spot market, which belongs to the field of hydropower dispatching. First, a cascade power generation maximum value model is constructed and solved to obtain the daily power boundary, and the conventional hydropower constraints in the cascade power generation maximum value model are converted into output-related constraints; secondly, the peak-shaving and valley-filling characteristics and load characteristics of large-scale cascade hydropower are considered, and based on the load curve characteristics, the output curve shape of each hydropower station in response to the load demand is obtained; finally, the daily power boundary of each hydropower station is decomposed into the output boundary. The present invention gradually converts complex constraints into the boundary of the feasible range of output of a single hydropower station, thereby simplifying the constraint form of the spot market clearing model and realizing rapid clearing of the spot market under the condition of meeting the hydropower constraint. The present invention has strong engineering practicality, can effectively decompose the power station power boundary into the output boundary, reduce the complexity of the clearing model, and greatly improve the clearing efficiency.

Description

Technical Field

[0001] The invention belongs to the field of hydropower dispatching, and in particular relates to a cascade hydropower output boundary equivalence method suitable for clearing the electricity spot market. Background Art

[0002] my country has the world's largest hydropower. The Southern Power Grid is the largest regional power grid in the world and in my country in terms of installed capacity of hydropower. Sichuan and Yunnan are also power grids dominated by hydropower. How to achieve spot clearing of the world's largest hydropower is a key issue that needs to be urgently resolved in my country's new electricity reform. The difficulty of hydropower participating in spot clearing lies in the fact that there are hundreds of hydropower stations and tens of thousands of units. It is necessary to digitally map the physical parameters such as the functional relationship between the water level and reservoir capacity of the hydropower stations and units, the functional relationship between the downstream tailwater level and the power generation flow, and the unit power characteristic curve. It is necessary to model the start and stop of the unit, the output ramp, ecology, navigation, hydraulic lag, and tracking load curve. Complex constraints have generated very large-scale equality and inequality constraints. For the spot clearing problem that is usually solved by mixed integer programming, this will lead to extremely difficult clearing problems, which are difficult to clear or the clearing results are not feasible. This is the key to the difficulty of clearing hydropower internationally. Therefore, how to deal with complex constraints equivalently and efficiently has become a key issue for spot clearing of the Southern Power Grid, Yunnan Power Grid, and Sichuan Power Grid. Therefore, how to take into account the physical characteristics of cascade hydropower in the market clearing model, break through the modeling barriers of large scale, high dimension, time and space coupling of complex hydropower systems, achieve efficient modeling and efficient clearing of various physical relationships, and meet the practical needs of hydropower clearing is a key basic issue for hydropower to participate in the electricity market, and it is also the core problem that the present invention aims to solve.

[0003] Based on existing literature and technical data, in order to solve the above problems, the engineering and academic circles have formed the following modeling models: First, the self-dispatching model of hydropower stations, that is, the hydraulic constraints are not considered in the market mechanism, and the hydropower station independently determines the unit output process. For example, the Nordic power market requires that its own physical characteristics be considered when quoting quantities and quotations, and the hydropower station decides the power generation plan by itself. However, in practice, this model requires hydropower to constantly adjust its bidding and power generation strategies in the spot market, which is inconsistent with my country's power market reform ideas and market maturity. The second is to simplify the consideration of hydropower characteristics. This type of model simplifies the hydropower generation function into a linear function, thereby simplifying the mathematical structure of the clearing model. Due to over-simplification, this type of modeling method leads to large errors in the calculation results, which in turn easily makes it difficult to execute the cleared power generation contracts, resulting in structural water abandonment or power shortages. The third is to consider the characteristics of hydropower in a refined manner. This type of model constructs the nonlinear power generation characteristics of hydropower in a refined manner in the clearing algorithm. This model solves the problem of the accuracy of the clearing results, but causes the number of constraints of the clearing model represented by the mixed integer programming model to increase sharply, and the efficiency of solving the clearing model is significantly reduced. Therefore, it is generally difficult to apply directly in actual engineering. This has also been proved in the practice of spot trial operation in my country.

[0004] In view of this, the present invention discloses a cascade hydropower output boundary equivalence method suitable for clearing the electricity spot market, and has been actually applied in the trial operation of the southern regional electricity spot market. Practice has proved that the present invention can avoid the more complex non-convex constraint structure in the clearing model, greatly reduce the number of constraints, and further decompose the electricity boundary of each hydropower station into an output boundary. Summary of the invention

[0005] The technical problem to be solved by the present invention is how to take into account the physical characteristics of cascade hydropower, break through the modeling barriers, and meet the practical needs of hydropower clearing. Since the spot market needs to be declared and cleared in the form of output curves, the present invention further decomposes the power boundary of the hydropower station into the output boundary, and then provides an equivalent method for the cascade hydropower output boundary suitable for clearing the electricity spot market.

[0006] The technical solution adopted by the present invention is:

[0007] A cascade hydropower output boundary equivalence method suitable for clearing the electricity spot market, the cascade hydropower output boundary equivalence method: first, construct a cascade power generation maximum model and solve it to obtain the daily power boundary, and convert the conventional hydropower constraints in the cascade power generation maximum model into output-related constraints; secondly, consider the peak-shaving and valley-filling characteristics and load characteristics of large-scale cascade hydropower, and based on the load curve characteristics, obtain the output curve shape of each hydropower station in response to load demand; finally, decompose the daily power boundary of each hydropower station into the output boundary. The specific steps of the cascade hydropower output boundary equivalence method are as follows:

[0008] Step 1: Equivalent transformation of hydropower constraints towards time-sharing output;

[0009] The maximum value model of cascade power generation is constructed and solved to obtain the daily power boundary. The constraint unified conversion strategy is used to convert all conventional hydropower constraints in the maximum value model of cascade power generation into constraints related to output. Then, all constraints related to output are aggregated and finally the output range constraints (including output lower limit constraints and output upper limit constraints) and output amplitude constraints of each hydropower station are obtained. Specifically:

[0010] Step 1.1: Construct the maximum value model of cascade power generation;

[0011] The maximum value model of cascade power generation is constructed as shown in equations (1) to (18). Equations (1) to (18) are a whole and together constitute the model. The maximum value model of cascade power generation takes the maximum or minimum daily power generation of cascade hydropower stations as the goal, and the objective function is equation (1). Equations (2) to (18) are constraint conditions, namely conventional hydropower constraints:

[0012] (1)

[0013] The water balance equations are as follows:

[0014] (2)

[0015] (3)

[0016] The initial and final reservoir water level constraints are as shown in equations (4) and (5):

[0017] (4)

[0018] (5)

[0019] Power generation flow constraints:

[0020] (6)

[0021] Outbound traffic constraints:

[0022] (7)

[0023] Output constraints:

[0024] (8)

[0025] Output amplitude constraint:

[0026] (9)

[0027] Output change duration constraints:

[0028] (10)

[0029] Net head constraint:

[0030] (11)

[0031] Comprehensive water flow constraints:

[0032] (12)

[0033] Navigable tail water level constraints:

[0034] (13)

[0035] Navigable tail water level fluctuation constraints:

[0036] (14)

[0037] Power station maintenance constraints:

[0038] (15)

[0039] Water level and storage capacity constraints:

[0040] (16)

[0041] Tailwater level-discharge flow relationship:

[0042] (17)

[0043] Hydropower station dynamic characteristic curve:

[0044] (18)

[0045] Where: is the total daily electricity generated by the cascade hydropower stations; For hydropower station In the period contribution; is the length of the unit period; is the total number of scheduling periods; is the total number of cascade hydropower stations; the result obtained when formula (1) takes the maximum value corresponds to the upper boundary of the equivalent daily electricity , when min is taken, it corresponds to the lower boundary of the equivalent daily electricity , and Together they form a hydroelectric power station Daily electricity volume boundaries in the spot market; For hydropower station In the period Storage capacity; , , and Hydropower Station In the period The inflow, interval flow, power generation flow and abandoned water flow; For the The first hydropower station directly upstream hydropower stations; For the The set of hydropower stations directly upstream of the hydropower station. For the leading hydropower station, this set is an empty set. , , and Hydropower Station The initial water level, expected final water level, downward allowable deviation of the final water level and upward allowable deviation of the final water level; and Hydropower Station Water levels at the beginning and end of the dispatch period; and Hydropower Station In the period The lower and upper limits of the power generation quotation flow; and Hydropower Station In the period The lower and upper limits of outbound flow; , Hydropower Station In the period Minimum technical output and installed capacity; For hydropower station The upper limit of the climbing slope; is the number of duration periods; For hydropower station The minimum number of duration periods during the output increase and decrease process, and ; , , and Hydropower Station In the period water level, power generation head, tailwater level and head loss; For hydropower station Comprehensive water flow requirements; For hydropower station Minimum navigation water level requirements; For hydropower station The requirements for the fluctuation of the shipping tailwater level; For hydropower station The maximum available capacity taking into account unit maintenance during the calculation period; For hydropower station The water level-reservoir capacity relationship function; For hydropower station The tailwater level-discharge relationship function; For hydropower station The dynamic characteristic function of .

[0046] By interval flow , initial water level , Expected final water level As well as other power station parameters required in the cascade power generation maximum value model as input conditions, the cascade power generation maximum value model is solved to obtain the daily power boundary of each hydropower station and .

[0047] Step 1.2: Convert power generation flow constraints into output range constraints;

[0048] According to the functional relationship of formula (18), the power generation flow constraint formula (6) is transformed into the output range constraint formula (19)~(21):

[0049] (19)

[0050] (20)

[0051] (twenty one)

[0052] In the formula, Indicates the hydropower station estimated in advance In the period The water head of the hydropower station does not change much within a day. It can be estimated in advance based on the initial water head of the day and the historical water head fluctuation; and They are respectively the lower limit of the power generation reference flow in formula (6) and upper limit The lower output limit constraint and the upper output limit constraint are obtained by conversion.

[0053] Similarly, the comprehensive water flow constraint formula (12) is transformed into formulas (22) to (23):

[0054] (twenty two)

[0055] (twenty three)

[0056] In the formula, is the value obtained from formula (12) The lower limit constraint of the output obtained by conversion.

[0057] Step 1.3: Convert the navigation tail water level constraint into the output lower limit constraint;

[0058] First, the navigation tailwater level constraint (Equation (13)) is converted into the outflow constraint by the tailwater level-discharge flow relationship (Equation (17). Then, according to the hydropower station dynamic characteristic curve (Equation (18), the outflow constraint is converted into the output lower limit constraint, as shown in Equations (24) to (26):

[0059] (twenty four)

[0060] (25)

[0061] (26)

[0062] Where: Minimum navigation water level requirement The lower limit constraint of the output obtained by conversion; for The corresponding outbound flow; for The inverse function of .

[0063] Step 1.4: Convert the navigation tail water level amplitude constraint into output amplitude constraint;

[0064] First, the navigation tailwater level amplitude constraint, i.e., equation (14), is converted into a flow amplitude constraint through the tailwater level-discharge relationship equation (17), and then the flow amplitude constraint is converted into an output amplitude constraint through the hydropower station dynamic characteristic curve equation (18). Since equations (17) and (18) are both nonlinear relationships, the absolute value form of equation (14) is no longer symmetrical, so it is expanded into upward and downward amplitude constraints, as shown in equations (27) to (33):

[0065] (27)

[0066] (28)

[0067] (29)

[0068] (30)

[0069] (31)

[0070] (32)

[0071] (33)

[0072] In the formula, and They are respectively the output upward amplitude constraint and the output downward amplitude constraint obtained by transforming the navigation tail water level amplitude constraint of formula (14); , and They are the flow constraints obtained by transforming the navigable tailwater level upper limit, navigable tailwater level and navigable tailwater level lower limit of the tailwater level-discharge flow relationship (17).

[0073] At this point, conventional hydropower constraints affecting the operation of hydropower stations are uniformly transformed into two categories: output range constraints and output variation constraints.

[0074] Step 1.5: Equivalently merge into time-sharing output constraints;

[0075] By using set operations, equations (19) to (33) are combined with the feasible domains of equations (8), (9) and (15) into output range constraints and output amplitude constraints, namely equations (34) and (35), where the output boundary is defined as equations (36) to (39).

[0076] (34)

[0077] (35)

[0078] (36)

[0079] (37)

[0080] (38)

[0081] (39)

[0082] In the formula, and Hydropower Station In the period The upper and lower output limits; and Hydropower Station In the period The upper and lower limits of output amplitude variation.

[0083] At this point, all constraints on the complex daily operation process of the hydropower station are converted into time-sharing output-related constraints, which serve as the basis for subsequent calculation of the hydropower station output boundary.

[0084] Step 2: Determine the output shape curve that responds to load demand;

[0085] In order to fully consider the characteristics of hydropower peak shaving and valley filling, give full play to the role of hydropower peak regulation, combined with the characteristics of hydropower peak shaving and valley filling (that is, high output at peak load and low output at low load), based on the load curve, using the power station output amplitude constraint and output upper and lower limit constraints obtained in step 1, after three steps of trend simulation, geometric scaling, and shape correction, the output shape curve of each hydropower station in response to load demand is obtained. Specifically:

[0086] Step 2.1: Trend simulation;

[0087] The original 96-point load curve is normalized into a 96-point coefficient curve, and the time periods are merged to obtain a 24-point curve to express the 24-hour load change trend. The 96-point coefficient curve is then corrected into a load trend curve using the 24-point curve. The original 96-point load curve is the known input condition of each hydropower station.

[0088] First, the original 96-point load curve Normalized to 96-point coefficient curve , the calculation method is as follows:

[0089] (40)

[0090] Where: For the period The load value; is the maximum value of the load; For the period The normalization coefficient of .

[0091] Then, in order to adapt to the 1h trading period of the spot market, the 96-point coefficient curve Every 4 adjacent time periods are combined and averaged to obtain a 24-point curve ,in, For the period The coefficient values ​​of the 24-point curve are taken as the basis, and the 96-point coefficient curve is converted into Corrected to load trend curve :

[0092] (41)

[0093] Where: For the period The coefficient value of the load trend curve, For the period The 24-point curve coefficient value, is the ceiling function.

[0094] Step 2.2: Scaling in proportion;

[0095] According to the output limit of each hydropower station obtained in step 1 And load trend curve Generate the output shape curve of each hydropower station and scale it proportionally according to the range:

[0096] First, calculate the hydropower station The output process , as the preliminary proposed output shape curve, where For hydropower station In the period The output upper limit value.

[0097] Then, considering The extreme value may be large. If the output shape curve is modified directly according to the output amplitude constraint, it is easy to change the trend of load change over time. Therefore, it is necessary to use formula (42) to perform overall geometric scaling on the initially proposed output shape curve to obtain the output shape curve after geometric scaling: .

[0098] (42)

[0099] (43)

[0100] (44)

[0101] Where: For the scaled-down hydropower station In the period Output shape curve value; , They are the time periods of maximum and minimum values ​​in the output shape curve respectively; For hydropower station Minimum output amplitude constraint; For hydropower station In the period The output shape curve scaling value.

[0102] Step 2.3: Shape correction;

[0103] Taking into account the constraints of output range, output amplitude and output change duration as shown in formula (10), the output shape curve after scaling in step 2.2 is Make further corrections:

[0104] The shape correction optimization model is established as shown in equations (45) to (48), where equation (45) is the objective function, equations (46) to (48) are constraints, and the curve obtained after solving the shape correction optimization model is This is the final output shape curve that responds to load demand:

[0105] (45)

[0106] (46)

[0107] (47)

[0108] (48)

[0109] Where: Indicates the revised hydropower station In the period Output shape curve value; represents the sum of squares of the difference between the output shape curves before and after correction, and the objective function (45) represents the minimum sum of squares of the difference between the output shape curves before and after correction; the constraint formulas (46) to (48) represent the hydropower station The output range constraint, output variation constraint and output variation duration constraint come from equations (36) to (39) and equation (10), respectively.

[0110] Step 3: Decompose the daily power boundary into output boundary;

[0111] The output shape curve in response to load demand obtained in step 2 This provides a basis for determining the output boundary. On this basis, the daily power boundary of a single power station is decomposed into the output boundary. At the same time, it is also necessary to ensure that the decomposition result meets the upper and lower limit constraints of the output and the upstream and downstream connections of the cascade.

[0112] Step 3.1: Decompose the daily power boundary of a single power station and ;

[0113] According to the hydropower stations The upper and lower boundaries of daily electricity consumption of each cascade hydropower station are decomposed according to its output range constraints, output variation constraints and output variation duration constraints.

[0114] The decomposition process of the upper boundary of daily power consumption of a single power station is as follows:

[0115] Ling Hydropower Station In the period Output limit ; Calculate the hydropower station according to formula (49) Accumulated power consumption in each period :

[0116] (49)

[0117] Will The hydroelectric station obtained in step 1.1 The upper limit of daily electricity consumption For comparison, if , then As a benchmark, gradually and evenly increase the output limit of each period, and each increase or decrease in output value is , is a constant, then each time you increase the Recalculate and with Compare and improve the process, if a certain period of time Output limit , then take ,in, and satisfy ;like , then As a benchmark, gradually and evenly reduce the output value of each period, and press Recalculate and with Compare and reduce the process, if a certain period of time Output limit , then take . Repeated iteration until equal Or the output limit of all time periods is reached , at this time, the upper boundary of the output of a single power station is obtained.

[0118] Similarly, the hydropower station The lower limit of daily electricity The lower boundary of the single power station output is obtained by decomposition.

[0119] Step 3.2: Upstream and downstream water balance verification;

[0120] For non-leading power stations, it is necessary to further ensure that the decomposition results obtained in step 3.1 satisfy the water balance relationship.

[0121] The water balance constraints are checked from top to bottom according to the topological structure of the cascade hydropower stations; if the constraints are not met, the output of the downstream hydropower stations in some periods of time is adjusted.

[0122] At this point, the electricity boundaries of each cascade hydropower station are subdivided into output boundaries.

[0123] Beneficial effects of the present invention:

[0124] In view of the problem that cascade hydropower is difficult to effectively clear in the electricity spot market, the present invention discloses a cascade hydropower output boundary equivalence method suitable for clearing the electricity spot market to adapt to the calculation and solution of cascade hydropower in the electricity spot market. This method can effectively decompose the electricity boundary of the hydropower station into the output boundary, reduce the complexity of the clearing model, and greatly improve the clearing efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0125] Figure 1 It is the overall flow chart of the present invention. DETAILED DESCRIPTION

[0126] The present invention is further described below in conjunction with the accompanying drawings and implementation examples.

[0127] This embodiment takes a cascade hydropower station group participating in the spot market in a certain area in the south as the research object, including 6 hydropower stations A~F. The main parameters of each hydropower station are shown in Table 1, and the values ​​of other parameters and constraint parameters of the hydropower station are shown in Table 2. The watershed water comes from the real water flow data of a certain day. In order to explore the universality of the method of the present invention, a large number of experimental simulations are carried out, and this embodiment selects a more typical example for discussion and analysis.

[0128] Table 1 Main parameters of each hydropower station

[0129]

[0130] Table 2 Constraint parameter settings for each hydropower station

[0131]

[0132] This embodiment provides a cascade hydropower output boundary equivalence method applicable to clearing the electricity spot market. The process is as follows: Figure 1 As shown, the specific steps are as follows:

[0133] Step 1: Equivalent transformation of hydropower constraints towards time-sharing output;

[0134] A maximum cascade power generation model is constructed and solved to obtain the daily power generation boundary. A unified constraint conversion strategy is adopted to convert all conventional hydropower constraints in the maximum cascade power generation model into output-related constraints. All output-related constraints are then aggregated and finally the lower output limit constraint, upper output limit constraint and output variation constraint of each hydropower station are obtained, aiming to reduce the complexity of subsequent model calculations and avoid repeated calculations.

[0135] Step 1.1: Model construction;

[0136] Cascade power generation is closely related to water inflow. In extreme cases, flood prevention and supply guarantee are the main focus. For example, when the water inflow of cascade hydropower stations is extremely large during the flood season, in order to ensure safety, each hydropower station generally arranges full power generation; for another example, when the water inflow is extremely small during the dry season, in order to meet the comprehensive water demand of the cascade, the output is the minimum in each period. These two special situations are relatively simple for power generation scheduling and will not be discussed here.

[0137] Under normal water supply conditions, a maximum value model of cascade power generation is constructed, and the objective function is shown in formula (1). The constraints, i.e., conventional hydropower constraints, are as follows:

[0138] 1) The water balance equations are shown in equations (2) and (3).

[0139] 2) The initial and final reservoir water level constraints are as shown in equations (4) and (5).

[0140] 3) The power generation flow constraint is as shown in formula (6).

[0141] 4) The outbound flow constraint is as shown in formula (7).

[0142] 5) Output constraint is as shown in formula (8).

[0143] 6) Output amplitude constraint is as shown in formula (9).

[0144] 7) The duration constraint of output change is as shown in formula (10).

[0145] 8) Net water head constraint is as shown in formula (11).

[0146] 9) The comprehensive water flow constraint is as shown in formula (12).

[0147] 10) The navigable tail water level constraint is as shown in formula (13).

[0148] 11) The navigable tail water level fluctuation constraint is as shown in formula (14).

[0149] 12) Power station maintenance constraints are as shown in formula (15).

[0150] 13) The water level and storage capacity constraints are as shown in formula (16).

[0151] 14) The relationship between tailwater level and discharge flow is shown in equation (17).

[0152] 15) The dynamic characteristic curve of the hydropower station is shown in formula (18).

[0153] Taking the interval flow, initial water level, expected final water level and other power station parameters required in the cascade power generation maximum model as input conditions, the cascade power generation maximum model was solved using the commercial solver Lingo to obtain the daily power generation boundary of each hydropower station. and .

[0154] Step 1.2: Convert power generation flow constraints into output range constraints;

[0155] Since the water head of the power station does not change much during the day, the water head at each time period of the day can be estimated in advance based on the initial water head of the day and the historical water head fluctuation range when performing constraint transformation processing. According to the functional relationship of formula (18), the power generation flow constraint formula (6) is transformed into the output range constraint formula (19)~(21).

[0156] Similarly, the comprehensive water flow constraint equation (12) is transformed into equations (22) to (23).

[0157] Step 1.3: Convert the navigation tail water level constraint into the output lower limit constraint;

[0158] First, the navigation tailwater level constraint, i.e., equation (13), is converted into a discharge flow constraint by the tailwater level-discharge flow relationship equation (17). Then, the discharge flow constraint is converted into a lower output limit constraint according to the hydropower station power characteristic curve equation (18), as shown in equations (24) to (26).

[0159] Step 1.4: Convert the navigation tail water level amplitude constraint into output amplitude constraint;

[0160] The navigation tailwater level amplitude constraint (14) limits the tailwater level amplitude. Similarly, the equation (14) can be first converted into the flow amplitude constraint through the tailwater level-discharge relationship (17), and then the flow amplitude constraint can be converted into the output amplitude constraint through the hydropower station dynamic characteristic curve relationship (18). Since both equations (17) and (18) are nonlinear relationships, the absolute value form of equation (14) is no longer symmetrical, so it is expanded into upward and downward amplitude constraints, as shown in equations (27) to (33).

[0161] At this point, conventional hydropower constraints affecting the operation of hydropower stations are uniformly transformed into two categories: output range constraints and output amplitude constraints, which are summarized in Table 3.

[0162] Table 3 Corresponding relationship of equivalent transformation from hydropower station operation constraints to output constraints

[0163]

[0164] Step 1.5: Equivalently merge into time-sharing output constraints;

[0165] Based on Table 3, set operations are further used to merge the feasible domains of Equations (19) to (33) with Equations (8), (9), and (15) into output range constraints and output amplitude constraints, namely, Equations (34) and (35), where the definition of the edge output boundary is Equations (36) to (39).

[0166] At this point, all constraints on the complex daily operation process of the hydropower station are converted into time-sharing output-related constraints, which are the basis for the subsequent calculation of the hydropower station output boundary.

[0167] Step 2: Determine the output shape curve that responds to load demand;

[0168] Step 2.1: Trend simulation;

[0169] First, the original 96-point load curve Normalized to 96-point coefficient curve , the calculation method is as shown in formula (40), where the original 96-point load curve is the known input condition of each hydropower station.

[0170] Then, in order to adapt to the 1h trading period of the spot market, the 96-point curve Every 4 adjacent time periods are combined and averaged to obtain a 24-point curve , and based on this, the 96-point coefficient curve is transformed into Corrected to load trend curve .

[0171] Step 2.2: Scaling in proportion;

[0172] According to the output limit of each hydropower station obtained in step 1 And load trend curve Generate the output shape curve of each hydropower station and scale it proportionally according to the range:

[0173] First, calculate the force process , as the preliminary proposed output shape curve.

[0174] Then, considering The extreme value may be large. If the output shape curve is modified directly according to the output amplitude constraint, it is easy to change the trend of load change over time. Therefore, the output shape curve initially proposed is scaled proportionally according to formula (42) to obtain the output shape curve after geometric scaling: .

[0175] Step 2.3: Shape correction;

[0176] Taking into account the constraints of output range, output amplitude and output change duration as shown in formula (10), the output shape curve after scaling in step 2.2 is Make further corrections:

[0177] The shape correction optimization model is established as shown in equations (45) to (48), where equation (45) is the objective function, equations (46) to (48) are constraints, and the curve obtained by solving the shape correction optimization model using the commercial solver Lingo is This is the final output shape curve that responds to load demand.

[0178] Step 3: Decompose the daily power boundary into output boundary;

[0179] Step 3.1: Decompose the daily power boundary of a single power station and ;

[0180] According to each hydropower station The upper and lower boundaries of daily electricity consumption of each cascade hydropower station are decomposed according to its output range constraints, output variation constraints and output variation duration constraints.

[0181] First, the upper boundary of daily power consumption of a single power station is decomposed as follows:

[0182] Ling Hydropower Station In the period Output limit ; Calculate the hydropower station according to formula (49) Accumulated power consumption in each period :

[0183] (49)

[0184] Will The hydroelectric station obtained in step 1.1 The upper limit of daily electricity consumption For comparison, if , then As a benchmark, gradually and evenly increase the output limit of each period, and each increase or decrease in output value is , is a constant, then each time you increase the Recalculate and with Compare and improve the process, if a certain period of time Output limit , then take ,in, and satisfy ;like , then As a benchmark, gradually and evenly reduce the output value of each period, and press Recalculate and with Compare and reduce the process, if a certain period of time Output limit , then take . Repeated iteration until equal Or the output limit of all time periods is reached , at this time, the upper boundary of the output of a single power station is obtained.

[0185] Then, the lower boundary of daily electricity consumption is decomposed as follows:

[0186] Ling Hydropower Station In the period Output limit ; Similarly, we use formula (49) to calculate , where we need to replace Replace with .

[0187] like , then As a benchmark, gradually and evenly increase the lower limit of output in each period, and then press Recalculate and with Compare and improve the process, if a certain period of time Output limit , then take ,in, and satisfy ;like , then As a benchmark, gradually and evenly reduce the output value of each period, and press Recalculate and with Compare and reduce the process, if a certain period of time Output limit , then take . Repeated iteration until equal Or the output lower limit of all periods is reached , at this time, the lower boundary of the single power station output is obtained.

[0188] Step 3.2: Upstream and downstream water balance verification.

[0189] For non-leading power stations, it is necessary to further ensure that the decomposition results obtained in step 3.1 satisfy the water balance relationship. At this time, the water balance constraints are checked from top to bottom according to the topological structure of the cascade hydropower stations; if the constraints are not met, the output of the downstream hydropower station is adjusted in some periods.

[0190] The above method can be used to obtain the daily power boundary and output conversion calculation results of the hydropower station A~F, see Table 4.

[0191] Table 4 Calculation results of daily power boundary and output constraint transformation of each cascade hydropower station

[0192]

[0193] In order to highlight the advantages of the cascade hydropower output boundary equivalence method provided in this embodiment, a comparative analysis is conducted between the model of the present invention and the comparison model, wherein the model of the present invention is a calculation model for the upper and lower output boundaries established by the method of this embodiment, and the comparison model is a model that directly uses the average output (i.e., the electricity boundary divided by the calculation period) as the output boundary.

[0194] The Pearson correlation coefficient is used to quantify the response of the upper and lower boundaries of the power station output to the load obtained by the model of the present invention. The results are listed in Table 5. It can be seen from the table that the correlation coefficients of the model of the present invention are all greater than 0.99. This shows that the model of the present invention enables the upper and lower boundaries of the output of each hydropower station to track the load trend well, achieves the purpose of responding to load changes, and meets the actual peak regulation needs of hydropower.

[0195] Table 5 Pearson correlation coefficient between output boundary and load curve of each power station calculated by the model of the present invention

[0196]

[0197] Table 6 shows the maximum, minimum and range of the output boundaries calculated by the two models for each hydropower station. It can be seen that the output boundary range values ​​of each hydropower station calculated by the model of the present invention are 2.3, 1.78, 1.81, 1.89, 1.93 and 3.3 times of those of the comparison model respectively; and the output upper boundary value calculated by the model of the present invention is larger and the lower boundary value is smaller.

[0198] Table 6 Calculation results of output boundary maximum and range of two models

[0199]

[0200] The electricity spot market clearing model that incorporates the method of this embodiment into the spot clearing model transformation is used as Scheme 1, and the efficiency is compared with Scheme 2, where Scheme 2 is a conventional electricity spot market clearing model. The efficiency comparison of the two schemes is shown in Table 7. The number of constraints and variables in the clearing model of Scheme 1 are 13596 and 12216 respectively, and the calculation time is 95s; the number of constraints and variables in the clearing model of Scheme 2 are 52306 and 42453 respectively, and the calculation time is 2635s. It can be seen that Scheme 1 has 38710 fewer constraints and 30237 fewer variables than Scheme 2. At the same time, the calculation time is greatly reduced, and the efficiency is improved by nearly 30 times. This shows that this embodiment can effectively reduce the complexity of the clearing model and greatly improve the efficiency of solving the clearing model.

[0201] Table 7 Comparison of the efficiency of different clearing schemes

[0202]

[0203] The final results and solution process show that the present invention can guide hydropower stations to increase output during peak hours and reduce output during off-peak hours, which is more conducive to the flexible start and stop of hydropower and the role of peak shaving and valley filling. The present invention has strong engineering practicality and can effectively decompose the power generation boundary of the power station into the output boundary, reduce the complexity of the clearing model, and greatly improve the clearing efficiency.

Claims

1. A cascade hydropower output boundary equivalence method suitable for clearing the electricity spot market, characterized in that: The cascade hydropower output boundary equivalent method is as follows: first, a cascade power generation maximum value model is constructed and solved to obtain the daily power boundary, and the conventional hydropower constraints in the cascade power generation maximum value model are converted into output-related constraints; second, based on the load curve characteristics, the output curve shape of each hydropower station in response to the load demand is obtained; finally, the daily power boundary of each hydropower station is decomposed into the output boundary; The specific steps of the cascade hydropower output boundary equivalent method are as follows: Step 1: Equivalent transformation of hydropower constraints towards time-sharing output; Step 1.1: Construct the maximum value model of cascade power generation; Construct a cascade power generation maximum value model, with the maximum or minimum daily power generation of cascade hydropower stations as the goal, including the objective function such as formula (1) and conventional hydropower constraints, where conventional hydropower constraints include water balance equation, initial and final reservoir water level constraints, power generation flow constraints, outflow flow constraints, output constraints, output amplitude constraints, output variation duration constraints, net water head constraints, comprehensive water flow constraints, navigation tail water level constraints, navigation tail water level amplitude constraints, power station maintenance constraints, water level storage capacity constraints, tail water level-discharge flow relationship and hydropower station dynamic characteristic curve; （1） Where: is the total daily electricity generated by the cascade hydropower stations; For hydropower station In the period contribution; is the length of the unit period; is the total number of scheduling periods; is the total number of cascade hydropower stations; the result obtained when formula (1) takes the maximum value corresponds to the upper boundary of the equivalent daily electricity , when min is taken, it corresponds to the lower boundary of the equivalent daily electricity ; By interval flow , initial water level , Expected final water level As well as other power station parameters required in the cascade power generation maximum value model as input conditions, the cascade power generation maximum value model is solved to obtain the daily power boundary of each hydropower station and ; Step 1.2: Convert power generation flow constraints into output range constraints; According to the functional relationship of the hydropower station's dynamic characteristic curve, the power generation flow constraint is transformed into the output range constraint formula (19)~(21): （19） （20） （21） In the formula, Indicates the hydropower station estimated in advance In the period of water head; and are respectively the lower limit of the power generation reference flow in the power generation flow constraint and upper limit The output lower limit constraint and output upper limit constraint obtained by conversion; For hydropower station In the period The power generation flow; For hydropower station The dynamic characteristic function of Similarly, the comprehensive water flow constraint is transformed into equations (22) to (23): （22） （23） In the formula, Weiyou Hydropower Station Comprehensive water flow requirements The output lower limit constraint obtained by conversion is: Derived from comprehensive water flow constraints; Step 1.3: Convert the navigation tail water level constraint into the output lower limit constraint; First, the navigation tailwater level constraint is converted into the outflow constraint by the tailwater level-discharge flow relationship in the cascade power generation maximum model. Then, the outflow constraint is converted into the output lower limit constraint according to the power characteristic curve of the hydropower station, as shown in Equations (24) to (26): （24） （25） （26） Where: Weiyou Hydropower Station Minimum water level requirement for navigation The lower limit constraint of the output obtained by conversion; for The corresponding outbound flow; For hydropower station The tailwater level-discharge relationship function; for The inverse function of Step 1.4: Convert the navigation tail water level amplitude constraint into output amplitude constraint; First, the navigation tailwater level variation constraint in the cascade power generation maximum model is converted into a flow variation constraint through the tailwater level-discharge flow relationship. Then, the flow variation constraint is converted into an output variation constraint through the hydropower station dynamic characteristic curve, as shown in equations (27) to (33): （27） （28） （29） （30） （31） （32） （33） In the formula, For hydropower station The requirements for the fluctuation of the shipping tailwater level; and They are respectively the output upward amplitude constraint and the output downward amplitude constraint obtained by transforming the navigation tail water level amplitude constraint; For hydropower station In the period Tailwater level; , and They are the flow constraints obtained by converting the upper limit of the navigable tailwater level, the navigable tailwater level and the lower limit of the navigable tailwater level in the tailwater level-discharge relationship; Step 1.5: Equivalently merge into time-sharing output constraints; By using set operations, equations (19) to (33) are combined with the feasible domain of output constraints, output range constraints and power station maintenance constraints in the cascade power generation maximum model into output range constraints and output range constraints, namely equations (34) and (35), where the definition of the output boundary is equations (36) to (39); （34） （35） （36） （37） （38） （39） In the formula, and Hydropower Station In the period The upper and lower output limits; and Hydropower Station In the period The upper and lower limits of the output amplitude variation; It is a hydroelectric power station In the period Minimum technical output; For hydropower station The maximum available capacity taking into account unit maintenance during the calculation period; For hydropower station The upper limit of the climbing slope; Step 2: Determine the output shape curve that responds to load demand; Step 2.1: Trend simulation; The original 96-point load curve is normalized into a 96-point coefficient curve, and the time periods are merged to obtain a 24-point curve. The 24-point curve is then used to correct the 96-point coefficient curve into a load trend curve. ,in, For the period The coefficient value of the load trend curve, the original 96-point load curve is the known input conditions of each hydropower station; Step 2.2: Scaling in proportion; Calculation of hydropower stations The output process , as the preliminary proposed output shape curve, where For hydropower station In the period The output upper limit value; Formula (42) is used to perform geometric scaling on the initially proposed output shape curve to obtain the output shape curve after geometric scaling: ; （42） （43） （44） Where: For the scaled-down hydropower station In the period Output shape curve value; , They are the time periods of maximum and minimum values ​​in the output shape curve respectively; For hydropower station Minimum value of output amplitude constraint; For hydropower station In the period The output shape curve scaling value; Step 2.3: Shape correction; The shape correction optimization model is established as shown in equations (45) to (48), where equation (45) is the objective function, equations (46) to (48) are constraints, and the curve obtained after solving the shape correction optimization model is This is the final output shape curve that responds to load demand: （45） （46） （47） （48） Where: Indicates the revised hydropower station In the period Output shape curve value; represents the sum of squares of the difference between the output shape curves before and after correction, and the objective function (45) represents the minimum sum of squares of the difference between the output shape curves before and after correction; is the number of duration periods; constraint equations (46) to (48) represent the hydropower station The output range constraint, output amplitude constraint and output change duration constraint come from equations (36) to (39) and the output change duration constraint in the cascade power generation maximum model respectively; Step 3: Decompose the daily power boundary into output boundary; Step 3.1: Decompose the daily power boundary of a single power station and ; According to the hydropower stations The upper and lower boundaries of daily electricity output of each cascade hydropower station are decomposed according to the output range constraints, output variation constraints and output variation duration constraints; The decomposition process of the upper boundary of daily power consumption of a single power station is as follows: Ling Hydropower Station In the period Output limit , calculate the hydropower station Accumulated power consumption in each period : Will The hydroelectric station obtained in step 1.1 The upper limit of daily electricity consumption For comparison, if , then As a benchmark, gradually and evenly increase the output limit of each period, and each increase or decrease in output value is , is a constant, then after each increase, press Recalculate and with Compare and improve the process, if a certain period of time Output limit , then take ,in, and satisfy ;like , then As a benchmark, gradually and evenly reduce the output value of each period, and press Recalculate and with Compare and reduce the process, if a certain period of time Output limit , then take ; Repeated iteration until equal Or the output limit of all time periods is reached , at this time, the upper boundary of the output of a single power station is obtained; Similarly, the hydropower station The lower limit of daily electricity Decompose to get the lower boundary of single power station output; Step 3.2: Upstream and downstream water balance verification; Check the water balance constraints from top to bottom according to the topological structure of cascade hydropower stations; if the constraints are not met, adjust the output of downstream hydropower stations in some periods; At this point, the electricity boundaries of each cascade hydropower station are subdivided into output boundaries.

2. The cascade hydropower output boundary equivalence method applicable to electricity spot market clearing according to claim 1 is characterized in that: In step 1.1, conventional hydropower constraints are as follows: The water balance equations are as follows: （2） （3） The initial and final reservoir water level constraints are as shown in equations (4) and (5): （4） （5） Power generation flow constraints: （6） Outbound traffic constraints: （7） Output constraints: （8） Output amplitude constraint: （9） Output change duration constraints: （10） Net head constraint: （11） Comprehensive water flow constraints: （12） Navigable tail water level constraints: （13） Navigable tail water level fluctuation constraints: （14） Power station maintenance constraints: （15） Water level and storage capacity constraints: （16） Tailwater level-discharge flow relationship: （17） Hydropower station dynamic characteristic curve: （18） Where: For hydropower station In the period Storage capacity; , and Hydropower Station In the period The inflow, interval flow and abandoned water flow; For the The first hydropower station directly upstream hydropower stations; For the The set of hydropower stations directly upstream of the hydropower station. For the leading hydropower station, this set is an empty set. , , and Hydropower Station The initial water level, expected final water level, downward allowable deviation of the final water level and upward allowable deviation of the final water level; and Hydropower Station Water levels at the beginning and end of the dispatch period; and Hydropower Station In the period The lower and upper limits of the power generation quotation flow; and Hydropower Station In the period The lower and upper limits of outbound flow; It is a hydroelectric power station In the period installed capacity; and Hydropower Station In the period Minimum technical output and installed capacity; For hydropower station The minimum number of duration periods during the output increase and decrease process, and ; , and Hydropower Station In the period water level, generating head and head loss; For hydropower station The water level-reservoir capacity relationship function.

3. The cascade hydropower output boundary equivalence method applicable to electricity spot market clearing according to claim 1 is characterized in that: In step 1.2, It is estimated in advance based on the initial water head of the day and the historical water head fluctuations.

4. The cascade hydropower output boundary equivalence method applicable to electricity spot market clearing according to claim 1 is characterized in that: The step 2.1 is specifically as follows: The original 96-point load curve Normalized to 96-point coefficient curve , the calculation method is as follows: （40） Where: For the period The load value; is the maximum value of the load; For the period The normalization coefficient of For the 96-point coefficient curve Every 4 adjacent time periods are combined and averaged to obtain a 24-point curve ,in, For the period The coefficient values ​​of the 24-point curve are converted into the 96-point coefficient curve using formula (41). Corrected to load trend curve : （41） Where: For the period The 24-point curve coefficient value, is the ceiling function.

5. The cascade hydropower output boundary equivalence method applicable to electricity spot market clearing according to claim 1 is characterized in that: In step 3.1, the hydropower station Accumulated power consumption in each period Calculate according to formula (49): （49）。

Images