CN110472824B - Cascade hydropower station short-term multi-objective optimization scheduling method considering peak shaving requirements - Google Patents
Cascade hydropower station short-term multi-objective optimization scheduling method considering peak shaving requirements Download PDFInfo
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Abstract
The invention belongs to the field of hydropower dispatching operation, and relates to a short-term multi-objective optimization dispatching method for a cascade hydropower station in consideration of peak shaving requirements. Aiming at adjusting the peak load of a power grid and improving the hydroelectric generation efficiency, considering both the complex operation requirement of the cascade hydropower station and the constraint of a unit vibration region, constructing a multi-target short-term optimization scheduling model of the cascade hydropower station by using mixed integer nonlinear programming, solving the model by using an improved normalization method plane constraint method, and obtaining a Pareto solution set containing a plurality of non-inferior solution schemes to provide powerful support for the final decision of a scheduling staff; in addition, the invention also uses a membership value calculation method based on fuzzy evaluation to evaluate each solution in the solution set, and selects a decision proposal scheme for the reference of dispatchers. The invention starts from the practical situation of short-term optimal dispatching of hydropower station, comprehensively considers the complex power generation operation constraint of the power station, gives consideration to the comprehensive operation benefits in multiple aspects, and meets the complex dispatching operation requirement of the cascade hydropower station.
Description
Technical Field
The invention belongs to the field of hydropower dispatching operation, and particularly relates to a short-term multi-objective optimization dispatching method for a cascade hydropower station in consideration of peak shaving requirements.
Background
With the continuous and high-speed development of economic level, the energy consumption structure is changed greatly, so that the social power demand is continuously increased, and the gap between the maximum load and the minimum load of the power grid in the day is also increased sharply. The excessive peak-to-valley difference causes insufficient power generation capacity of the power grid during the peak period, and partial load needs to be disconnected from the power grid; meanwhile, the capacity of the power grid is insufficient during the load valley period, and the thermal power generating unit faces the situation of deep peak regulation, so that the safe and stable operation of the power grid is deeply threatened. Therefore, the hydropower station is a clean renewable energy source with flexible load adjustment, short unit start-stop time and low power generation cost, and plays an important role in adjusting the peak load of a power grid and reducing the peak-valley difference in the day. The hydropower short-term peak regulation optimization scheduling problem generally aims at adjusting the peak load of a power grid and smoothing the residual load process, and the power generation and operation plan of each power station and the units of the power station in each time period is determined according to the load process of the power grid and the water inflow condition of a reservoir. In addition, the hydropower short-term optimization scheduling usually needs to consider various comprehensive benefits such as power generation efficiency and income, faces the coupling relation between the water power and the electric power between the power stations and the complex operation requirements of the water power and the electric power scheduling, is a typical multi-objective optimization problem, has the characteristics of high dimensionality, multiple variables, multiple objectives, nonlinearity and complex space-time coupling, and is a key and difficult point of current research on how to effectively solve and give consideration to the solution efficiency and the solution precision, and the acquisition of a practical hydropower station power generation and operation plan is obtained.
Disclosure of Invention
In order to solve the problems, the invention provides a cascade hydropower station short-term multi-objective optimization scheduling method considering peak shaving requirements, which aims at adjusting the peak load of a power grid and improving the hydropower generation efficiency, takes the scheduling operation requirements of the cascade hydropower station and the constraint of a vibration region of a unit into consideration, can obtain a Pareto solution set containing a plurality of non-inferior solutions, and provides powerful support for the final decision of a scheduler. The method starts from the actual situation of the hydropower short-term optimized dispatching, comprehensively considers the complex power generation operation constraint of the power station, gives consideration to the comprehensive operation benefits in multiple aspects, meets the complex dispatching operation requirement of the cascade hydropower station, and provides powerful support for the multi-target short-term optimized dispatching of the cascade hydropower station.
The technical scheme of the invention is as follows:
a cascade hydropower station short-term multi-objective optimization scheduling method considering peak shaving requirements comprises the steps of constructing a cascade hydropower station multi-objective short-term optimization scheduling model considering unit vibration regions and cascade hydropower operation constraints by using mixed integer nonlinear programming, solving a Pareto solution set containing a plurality of non-inferior solution schemes by using an improved normalization method plane constraint method, and performing an optimal compromise scheme decision method based on fuzzy evaluation and membership values. The method comprises the following specific steps:
Formula 1:
formula 2:
in the formula, C t The total load of the power grid in the period t; c' t Deducting residual load after all hydropower station output for t time period; p i,t The output of the hydropower station i in the time period t is obtained; n is the number of hydropower stations; omega i The weight value of the energy storage of the power station i is generally determined by a dispatcher according to the position of a reservoir in the cascade and the size of the effective storage capacity; v i,T The storage capacity of the power station i in the T time period is obtained; t is the length of the scheduling period, i.e. the number of the last period.
And step 2, setting the daily generated energy of the cascade hydropower station. The total generating capacity E of the cascade hydropower station in the dispatching period is used as a control variable, and the constraint is satisfied:
wherein E is the total power generation of the cascade hydropower station, and the unit time interval length of delta t is generally 1 hour.
And 3, performing output domain calculation on the unit. Firstly, acquiring a set of output vibration areas of the unit
Wherein R is i,j The method comprises the following steps of (1) collecting output vibration areas of a unit j in a power station i; />
And i ROZ ,j,m respectively the upper limit and the lower limit, M, of the mth vibration zone of the unit i,j The number of the vibration areas of the unit j in the power station i is shown.
According to the output range of the unit, the output feasible region F of the unit can be obtained by complementing the combined vibration region according to the output range of the unit i,j As shown in formula 3.
Formula 3:
in the formula (I), the compound is shown in the specification,
and/or>
Respectively the minimum output and the maximum output of the unit j in the power station; pf i,j,m And/or>
Lower limit and upper limit of the mth feasible region of the ith unit j in the power station, M =0,1 i,j (ii) a The number of feasible domains of the unit j is M i,j +1。
And 4, performing domain calculation on the combination of the power station. And combining the feasible domains of all the units in the power station to obtain a combined feasible domain of the power station. For example, the combination of any two units j and l may be in the domain of
Wherein n is the number of the feasible domain of the unit l; the combined feasible region of any three machine sets can be represented as the combination of the feasible region of one machine set and the feasible region of the combination of two machine sets, and so on, the combined feasible region of the power station can be represented as ^ based on the standard value of the maximum power station>
Wherein +>
The method comprises the following steps of (1) forming a combined feasible domain containing j machine sets; />
AndFOZ i,mf respectively combining the upper limit and the lower limit of a feasible domain for the mf combination of the power station i; m i The number of feasible domains for the station i.
in the formula, V i,t 、V i,t+1 Respectively storing capacities of the power station i in a time period t and a time period t +1; i is i,t The flow rate of the power station i in the warehouse in the time period t is obtained;
for the plant k at t-TC k,i The flow rate of the warehouse; TC (tungsten carbide) k,i The water flow delay between the power station k and the power station i; k is the number of hydropower stations directly upstream of the power station i; zf i,t 、Zf i,t-1 Respectively the water level of the power station i in the time period t and the time period t-1; a. The i,0 ,A i,1 ,...,A i,4 The water level-reservoir capacity coefficient of the power station i; zf i,min And Zf i,max Respectively the lower limit and the upper limit of the water level of the power station; p i,t The output of the power station i in the time period t is obtained; p i,min And P i,max Respectively representing the lower output limit and the upper output limit of the power station i; CF (compact flash) i The combined feasible region of the power station i calculated in the step 4 is obtained; q i,min 、Q i,max Respectively representing the lower limit and the upper limit of the ex-warehouse flow of the power station i; q i,t The flow of the power station i is taken out of the warehouse in the time period t; />
And s i,t Respectively the power generation flow and the water discharge flow of the power station in the time interval; zd i,t The tail water level of the power station i in the time period t; c i,0 ,C i,1 ,...,C i,4 The tail water level-ex-warehouse flow coefficient of the power station i is obtained; d i,0 ,D i,1 ,...,D i,5 The coefficient is the power generation efficiency function coefficient of the power station i; h i,t The head of the station i during the time t.
And 6, calculating the end point of the Pareto front edge. And solving a Pareto solution set of the multi-target model by using an improved normalization method plane constraint method. Firstly, calculating the endpoint of the Pareto leading edge, respectively reserving the constraint conditions of the multi-objective optimization model and carrying out optimization solution on a single target of the multi-objective optimization model, and thus obtaining the leading edge endpoint corresponding to the target. For the multi-target model in the step 5, two endpoints A are correspondingly obtained 1 (f 1 (x 1* ),f 2 (x 1* ) And A) 2 (f 1 (x 2* ),f 2 (x 2* ) Wherein f) is 1 (x 1* )、f 2 (x 2* ) Respectively, optimization solutions of a single object, f 2 (x 1* )、f 1 (x 2* ) Respectively, the corresponding value, x, of one object when another object takes an optimal solution 1* 、x 2* The values are the corresponding decision variables, respectively.
And 7, carrying out pareto front edge endpoint optimization. The endpoint A was calculated using equations 4 and 5, respectively 1 And A 2 Of optimal value A' 1 (f 1 (x 12 ),f 2 (x 12 ))、A′ 2 (f 1 (x 21 ),f 2 (x 21 ) Wherein f) is 1 (x 12 )、f 2 (x 12 ) For the multi-objective function values obtained after solving equation 4, f 1 (x 21 )、f 2 (x 21 ) To solve the multi-objective function value obtained after equation 5.
Formula 4:
formula 5:
in the formula, epsilon 1 And epsilon 2 Calculation parameter, R, in endpoint optimization + Is a positive real number set, epsilon 1 And epsilon 2 Are respectively of 1 (x 1* )、f 2 (x 2* ) A smaller value.
And 8, performing target function solution space normalization processing. In order to prevent the difference between the orders of magnitude of the objective function from affecting the solution, the solution space needs to be normalized, as shown in equation 6. Normalized, endpoint A' 1 (f 1 (x 12 ),
A′ 2 (f 1 (x 21 ),f 2 (x 21 ) Is converted to AN' 1 (0, -1) and AN' 2 (1,0)。
Formula 6:
in the formula (I), the compound is shown in the specification,
to normalize the position coordinates of any point in the solution space, device for selecting or keeping>
Is->
The corresponding horizontal and vertical coordinate values are the normalized objective function values.
Step 9, generating equal distance points of Uutopia: make normalized endpoint AN 'defined in step 8' 1 (0, -1) pointing to AN' 2 Vector of (1, 0)
Namely the Uutopia vector; in a vector>
Top is provided with M-1 Utobang equal spacesPoint, dividing the Uutopia vector into equal M sections, and equally spaced points ^ H>
In a manner of calculating position coordinates of &>
pm＝1,2,...,M-1。
Step 10. Let pm =1.
And 11.Pareto non-inferior solution generation. For points of equal distance of Uptobang
Make a vector perpendicular to Utobang and passing through the point>
The intersection point of the straight line and the front edge of the Pareto, namely the Pareto non-inferior solution corresponding to the equal point of Utto>
Not inferior solution->
Obtained by solving equation 7.
Formula 7:
in the formula (I), the compound is shown in the specification,
the utopia vector defined in step 9; />
Means represented by equidistant points of Utotopon>
Non-inferior solution solved by directional formula 7>
Transposing the vector of (c); />
Respectively are not inferior>
The horizontal and vertical coordinates in the normalized solution space are the normalized objective function values.
Step 12. Let pm = pm +1
Step 13, judging whether pm is greater than or equal to M, if so, entering step 14, otherwise, returning to step 11 to continue calculating, and setting the equidistant points of pm =1,2
And solving the corresponding Pareto non-inferior solution to obtain a Pareto solution set of the problem.
And step 14, non-degradation reduction. For the Pareto solution sets in the normalized solution space calculated in steps 10 to 13, the solutions therein need to be reduced to the original specifications. Pareto solution for any normalization in a solution set
Its original value (f) 1 (x),f 2 (x) The formula for calculation) is: />
And step 15, after the Pareto non-inferior solution set is obtained in the step 14, evaluating each solution in the solution set by a membership value calculation method based on fuzzy evaluation, and selecting a decision proposal scheme for reference of a dispatcher. The membership value calculation method based on the fuzzy evaluation comprises two steps of single-target membership calculation and comprehensive membership calculation. First, pm =0 needs to be made.
And step 16, calculating the single-target membership degree. For each non-inferior solution in the Pareto solution set, the membership degree of each non-inferior solution in each single target needs to be calculated respectively. For any Pareto solution (f) 1 (x),f 2 (x) Membership μ of its peak shaver target) pm,1 The calculation function of (2) is shown as formula 8, and the target membership degree mu of the power generation efficiency pm,2 The calculation function of (a) is shown in equation 9.
Formula 8:
formula 9:
And step 18, judging whether pm is greater than M +1, if so, entering step 19, otherwise, returning to step 16 to continue calculating.
And 19, calculating the comprehensive membership degree. According to the single target membership value, the comprehensive membership mu of each solution in the solution set pm And (3) calculating:
and 20, selecting the optimal compromise solution. After the calculation of the steps is completed, according to the comprehensive membership degree of each solution in the Pareto solution set, the solution with the maximum comprehensive membership degree is selected as the optimal compromise solution and serves as a decision suggestion method to be provided for scheduling personnel.
The invention has the beneficial effects that: compared with the prior art, the method can give consideration to complex operation constraints of the cascade hydropower station, adjust the peak load of the power grid, improve the hydroelectric power generation efficiency, provide a non-inferior solution set approaching the actual Pareto frontier for dispatchers, select the corresponding optimal compromise solution as a decision suggestion, meet the actual dispatching requirement of the cascade hydropower station, and is an effective method for solving the multi-target short-term optimal dispatching problem of the cascade hydropower station at present.
Drawings
FIG. 1 is a schematic diagram of Pareto fronts and endpoints;
FIG. 2 is a schematic diagram of an optimized Pareto front edge endpoint;
FIG. 3 is a diagram of a normalized solution space and solution principle;
FIG. 4 is a graph of Pareto fronts solving the resulting non-inferior solution set;
FIG. 5 is a schematic illustration of a power generation plan for each plant in the cascade;
FIG. 6 is a schematic diagram of the water level process of a muddy slope power station.
Fig. 7 is a schematic diagram of the water level process of the light power station.
Fig. 8 is a schematic diagram of the water level process of the horse cliff power station.
Fig. 9 is a water level process schematic for a tussah power plant.
Detailed Description
The invention is further described with reference to the accompanying drawings and examples.
The short-term optimization scheduling of the cascade hydropower station needs to consider various comprehensive benefits such as power generation efficiency and income, faces the coupling relation between water power and electric power between the hydropower stations and complex operation requirements of water power and electric power scheduling, is a typical multi-objective optimization problem, and how to effectively solve and consider the solving efficiency and the solving precision is the key and difficult point of current research to obtain a practical hydropower station power generation and operation plan. The invention aims to provide a cascade hydropower station short-term multi-objective optimization scheduling method considering peak shaving requirements, a Pareto solution set containing a plurality of non-inferior solutions can be obtained, powerful support is provided for final decision making of scheduling personnel, and meanwhile, the optimal compromise solution is selected from the obtained solution set by the method and serves as a decision suggestion scheme for the reference of the scheduling personnel. The main constraints are as follows:
1) Water balance and water flow time lag restriction
In the formula, V i,t 、V i,t+1 Respectively storing the storage capacities of the power station i in the time period t and the time period t +1; i is i,t The warehousing flow of the power station i in the time period t;
for the plant k at t-TC k,i The flow rate of the warehouse; TC (tungsten carbide) k,i The water flow delay between the power station k and the power station i; k is the number of hydropower stations directly upstream of the power station i;
2) Maximum and minimum output limits for hydropower stations
P i,min ≤P i,t ≤P i,max
In the formula, P i,t For station i during time tThe output of (2); p is i,min And P i,max Respectively the lower output limit and the upper output limit of the power station i.
3) Warehouse-out flow limitation
Q i,min ≤Q i,t ≤Q i,max
In the formula, Q i,min 、Q i,max Respectively representing the lower limit and the upper limit of the ex-warehouse flow of the power station i; q i,t The flow of the power station i is taken out of the warehouse in the time period t;
and s i,t The power generation flow and the water discharge flow of the power station in the time interval are respectively.
4) Water level-reservoir capacity function
Zf i,min ≤Zf i,t ≤Zf i,max
In the formula, zf i,t The water level of the power station i in the time period t; a. The i,0 ,A i,1 ,...,A i,4 The water level-storage capacity coefficient of the power station i; zf i,min And Zf i,max Respectively the lower limit and the upper limit of the water level of the power station.
5) Tail water level-flow out of reservoir function
In the formula, ZD i,t The tail water level of the power station i in the time period t is obtained; c i,0 ,C i,1 ,...,C i,4 And the tail water level-ex-warehouse flow coefficient of the power station i.
6) Hydropower station generation efficiency function
H i,t ＝(Zf i,t-1 +Zf i,t )/2-Zd i,t
In the formula, zf i,t-1 The water level of the power station i in the t-1 time period; d i,0 ,D i,1 ,...,D i,5 A power generation efficiency function coefficient of the power station i; h i,t The water head of the power station i in the t period;
7) Unit vibration zone restraint
In the formula, p i,j,t The output of a unit j in a power station i in a time period t;
and ROZ i,j,m Respectively the upper limit and the lower limit of the mth vibration area of the unit j in the power station i.
And (4) solving the multi-target short-term optimization scheduling problem of the cascade hydropower station by considering the constraint conditions. During solving, the peak load of a power grid is adjusted, the hydroelectric power generation efficiency is improved, the complex operation constraint of the cascade hydropower station is considered, a Pareto solution set comprising a plurality of non-inferior solution schemes is calculated, the membership value of each solution in the solution set is calculated by using a membership value calculation method based on fuzzy evaluation, the solution with the maximum membership is selected as a final decision scheme, and powerful support is provided for multi-target short-term optimization scheduling of the cascade hydropower station. The concrete solving step is realized by the following steps:
In the formula, C t The total load of the power grid in the period t; c t ' deduction of all hydroelectric stations for period tResidual load after the force is applied; p i,t The output of the hydropower station i in the time period t is obtained; n is the number of hydropower stations; omega i The weight value of the energy storage of the power station i is generally determined according to the position of the reservoir in the step and the size of the effective storage capacity; v i,T The storage capacity of the power station i in the T time period; t is the length of the scheduling period, i.e. the number of the last period.
And 2, setting the daily generated energy of the cascade hydropower station. And setting the total generated energy of the cascade hydropower station in a dispatching period, and setting a constraint:
wherein E is the total power generation of the cascade hydropower station, and the unit time interval length of delta t is generally 1 hour. />
And 3, calculating a combined feasible region of the hydropower station according to the unit vibration region. And calculating the combined vibration area range of the hydropower station according to the unit vibration area constraint in each power station.
Firstly, acquiring a set of output vibration areas of the unit
Wherein R is i,j The method comprises the following steps of (1) collecting output vibration areas of a unit j in a power station i; />
AndROZ i,j,m respectively the upper limit and the lower limit, M, of the mth vibration zone of the unit i,j The number of the vibration areas of the unit j in the power station i is shown.
And secondly, calculating the feasible output area of the unit. And (4) obtaining the feasible output range of the unit by complementing the combined vibration area according to the output range of the unit, as shown in the following formula.
In the formula (I), the compound is shown in the specification,
and/or>
Respectively the minimum output and the maximum output of the unit j in the power station;pf i,j,m and/or>
Respectively is the lower limit and the upper limit of the mth feasible region of the i unit j in the power station; the number of feasible domains of the unit j is M i,j +1。
And then combining the feasible regions of all the units in the power station to obtain a combined feasible region of the power station. For example, the combination of any two units j and l may be in the domain of
The combined feasible region of any three machine sets can be represented as the combination of the feasible region of one machine set and the feasible region of the combination of two machine sets, and so on, the combined feasible region of the power station can be represented as ^ based on the standard value of the maximum power station>
Wherein->
The method comprises the following steps of (1) forming a combined feasible domain containing j machine sets; />
AndFOZ i,mf respectively combining the upper limit and the lower limit of a feasible domain for the mf combination of the power station i; m i The number of feasible domains for the station i.
And 4, constructing a mixed integer nonlinear programming model of the multi-target short-term optimized scheduling of the cascade hydropower station. And (2) constructing a cascade hydropower station multi-target short-term optimized dispatching model by using mixed integer nonlinear programming according to the hydropower peak regulation and power generation efficiency target function constructed in the step (1), the water balance constraint of a cascade hydropower station, the maximum and minimum output limit of the hydropower station, the ex-warehouse flow limit, the water level-reservoir capacity function, the tail water level-ex-warehouse flow function, the water flow lag time constraint and the hydropower station power generation efficiency function as well as the hydropower station combined feasible region calculated in the step (3).
And 5, solving the Pareto solution set of the multi-target model by using an improved normalization method plane constraint method. The method comprises the following substeps:
a) The endpoint of the Pareto front is calculated. And (3) aiming at the multi-objective optimization model, respectively keeping constraint conditions of the multi-objective optimization model, and carrying out optimization solution on a single objective of the multi-objective optimization model to obtain a leading edge endpoint corresponding to the objective. For the multi-target model in the invention, a corresponding endpoint A can be obtained 1 (f 1 (x 1* ),f 2 (x 1* ) And A) 2 (f 1 (x 2* ),f 2 (x 2* ) Wherein f) is 1 (x 1* )、f 2 (x 2* ) Respectively, optimization solutions of a single object, f 2 (x 1* )、f 1 (x 2* ) Then the corresponding value, x, of one object when another object gets the optimized solution 1* 、x 2* Are the dependent decision variable values, respectively. As shown in fig. 1.
b) Pareto front edge endpoint optimization. For endpoint A 1 Solving a single-objective optimization problem
(wherein ε 1 For the calculation parameter, R, in the endpoint optimization process + Is a positive real number set, epsilon 1 Should be with f 1 (x 1* ) A smaller value) to obtain the optimized endpoint A' 1 (f 1 (x 12 ),f 2 (x 12 ) Wherein f) is 1 (x 12 )、f 2 (x 12 ) And solving the corresponding function value of each obtained target. Similarly, for endpoint A 2 Solving a single-objective optimization problem
(in the formula,. Epsilon.) 2 For the calculation parameter, epsilon, in the endpoint optimization process 2 Should be with f 2 (x 2* ) Relatively small value), the optimized endpoint A 'can be obtained' 2 (f 1 (x 21 ),f 2 (x 21 ) Wherein f) is 1 (x 21 )、f 2 (x 21 ) Then the function value corresponding to each target obtained after solving is obtained. As shown in fig. 2.
c) And (5) performing target function solution space normalization processing. For preventing eye diseasesThe difference between the orders of magnitude of the scalar functions has an influence on the solution, and the solution space of the solution needs to be normalized. The normalization method is
Normalized, endpoint A' 1 、A′ 2 Will be converted to AN' 1 (0, -1) and AN' 2 (1,0). As shown in fig. 3.
d) And generating the equal distance points of the Uttopont. Is made from normalized endpoint AN' 1 Vector pointing to AN
The vector is the utopia vector. Making M-1 equal-distance points of Utobang on the vector, dividing the Utobang vector into equal M sections, and dividing the points into equal M sections
1) is calculated as->
e) Pareto non-inferior solution generation. For arbitrary Utoban equidistant points
Make a vector perpendicular to Utobang and passing through the point>
The intersection point of the straight line and the front edge of Pareto is the Pareto non-inferior solution corresponding to the Eatopob equidistant point>
This solution can be optimized by solving a single objective optimization problem>
Thus obtaining the product. Similarly, by setting pm =1,2, M-1 to be equidistant for each urotroping £ r>
And solving the corresponding Pareto non-inferior solution to obtain a Pareto solution set of the problem. As shown in fig. 3.
f) And (4) non-inferior solution reduction. For the Pareto solution set in the normalized solution space calculated by e), the solution in the Pareto solution set needs to be reduced to the original specification:
step 6: after the Pareto non-inferior solution set is obtained in the step 5, the membership value calculation method based on fuzzy evaluation evaluates each solution in the solution set, and selects a decision proposal scheme for reference of a dispatcher. The method comprises two steps:
a) And calculating the single-target membership degree. For each non-inferior solution in the Pareto solution set, firstly, the membership degree of each single target needs to be respectively calculated, and the calculation function of the membership degree of the peak regulation target is as follows:
the calculation function of the target membership of the power generation efficiency is as follows:
b) And calculating comprehensive membership degree. And according to the single-target membership value, calculating the comprehensive membership of each solution in the solution set:
after the calculation is finished, the solution with the maximum comprehensive membership degree is selected as the optimal compromise solution and is provided for the scheduling personnel as a decision suggestion method.
The method is verified by taking short-term optimized scheduling of cascade hydropower stations in the Hedijiang river basin as an example. The cascade hydropower stations in the Hedijiang river basin are located in Guizhou province and comprise four hydropower stations including a muddy slope (day regulation), light (year regulation), a Maya cliff (day regulation) and a Gong city (day regulation) from upstream to downstream, and basic parameters of the hydropower stations are shown in a table 1. Among the four hydropower stations, the muddy slope and Ma cliff hydropower station is scheduled in the Guizhou power grid, and the illumination and Dongcang hydropower station is scheduled by the southern power grid in general, is an important peak-shaving power supply for the Guizhou power grid and the southern power grid, and faces complex scheduling requirements. When the power grid carries out cascade hydropower dispatching, the peak regulation effect is generally taken as the target, as long as no water abandon is ensured, the generation income of hydropower is rarely considered, and under the condition of determining daily generated energy, the dispatching result usually has lower generation efficiency and dispatching end-of-term energy storage, the generation income of the cascade hydropower station is influenced, so that the hydropower station of the north Panjiang faces the multi-target coordination problem between peak regulation and generation efficiency. Meanwhile, the hydropower station unit of the north-fringed river water cascade power station has a complex vibration region problem, and if the point is ignored in the dispatching process of the power grid, the output plan of the hydropower station issued by the hydropower station unit cannot be implemented on the premise of not damaging the constraint of the vibration region of the unit. In addition, the optimal scheduling of the cascade hydropower station is a complex multidimensional, dynamic, non-convex and non-linear programming problem essentially, and is difficult to solve, so how to obtain a Pareto solution set meeting the scheduling requirement in limited solving time provides powerful support for scheduling decisions, and the optimal scheduling of the cascade of the north trawl river is another problem faced by short-term optimal scheduling.
The method provided by the invention is adopted to calculate the short-term scheduling plan of the north-disk river cascade power station, and the calculation result is combined for analysis.
TABLE 1 Beipan river cascade hydropower station basic parameters
The method is used for constructing an application example based on the short-term power generation plan manufacture of a hydropower station with a certain day step in the rich water period. Firstly, the feasible combination domain of the power station needs to be calculated according to the range of the unit vibration area of the power station, and the calculation result is shown in table 2.
TABLE 2 North Panjiang cascade hydropower station combination feasible region
Based on the calculation result, a multi-target short-term optimization scheduling model of the cascade hydropower station is constructed, a Pareto solution set containing a plurality of non-inferior solution schemes is solved by using an improved normalization method plane constraint method, and an optimal compromise scheme decision method based on membership values of fuzzy evaluation is used. The Pareto frontier obtained by the improved normalization method plane constraint method is shown in fig. 4, and the objective function values and corresponding objective membership degrees of the solutions in the solution set are shown in table 3. According to the method, the Pareto non-inferior solution set is calculated and distributed on the Pareto front edge uniformly by using an improved normalization plane constraint method, various operation schemes of the cascade hydropower multi-objective optimization problem under different objective inclinations and the position of the cascade hydropower multi-objective optimization problem in the whole solution space are represented, and powerful support is provided for a dispatcher to determine a final dispatching plan.
TABLE 3 improved Pareto non-inferior solution set obtained by normalization plane constraint method
According to table 3, the solution numbered 3 has the maximum comprehensive membership value and is selected as the optimal compromise solution, so that the peak shaving objective function and the power generation efficiency objective function are considered in the short-term operation scheme of the cascade hydropower station corresponding to the solution in a balanced manner, and the requirement of cascade hydropower scheduling can be fully met. The power generation plan of each power station in the scheme is shown in fig. 5, the peak shaving effect corresponding to the scheme is shown in table 4, and the water level process of each reservoir is shown in fig. 6 to 9.
TABLE 4 Peak shaving Effect analysis of optimal compromise solution
As can be seen from fig. 5, the output of the cascade hydropower stations in the optimal compromise scheme fluctuates with the load, and in the peak load period, the output of each power station is obviously increased to respond to the peak load demand of the power grid. According to the table 4, when the method provided by the invention is used for manufacturing a hydroelectric power generation plan, the maximum load of a power grid can be reduced by 16.67% and the peak-valley difference can be reduced by 29.04%; meanwhile, the output of the hydropower station enables the residual load process of the power grid to be smoother compared with the original load process, the reduction proportion of the mean square error of the load process reaches 33%, and the application of the method can guarantee that the load process of the power grid has smaller peak-valley difference and fluctuation range, reduce the deep peak-load regulation pressure of the thermal power unit to a certain extent, and improve the safety and stability of a power system. In addition, fig. 6 to 9 show that the water level process of each reservoir is gently fluctuated within the upper and lower limits of the water level, and the water level limit requirement of the step reservoir can be completely met.
In conclusion, by adopting the short-term multi-objective optimization scheduling method for the cascade hydropower station, a non-inferior solution set approaching the front edge of the actual Pareto can be obtained, and abundant operable schemes with different objective trends are provided for scheduling personnel; in addition, the multi-target membership degree evaluation method in the method can effectively solve the multi-target scheduling scheme decision problem, the selected optimal compromise solution can simultaneously give consideration to the peak regulation requirement and the power generation efficiency of hydropower, the complex operation limit of the hydropower is met, the peak-valley difference of the power grid load process is effectively reduced, the residual load process is smoothed, the subsequent formulation of the power generation plan of the thermal power generating unit and the safe and stable operation of the power grid are facilitated, and the method is one of effective ways for solving the multi-target short-term optimization scheduling problem of the cascade hydropower station.
Claims (1)
1. A method for short-term multi-objective optimal scheduling of a cascade hydropower station considering peak regulation requirements is characterized by comprising the following steps:
step 1, building a short-term optimized dispatching objective function of the cascade hydropower station: respectively constructing a hydropower peak regulation objective function f by using the minimum mean square error of the residual load process and the maximum energy storage at the end of the hydropower dispatching period as optimization objectives 1 And hydroelectric power generation efficiency objective function f 2 As shown in formula 1 and formula 2;
formula 1:
formula 2:
in the formula, C t Is power for a period of tThe total load of the net; c' t Deducting residual load after all hydropower station output for t time period; p is i,t The output of the hydropower station i in the time period t is obtained; n is the number of hydropower stations; omega i The weight value of the energy storage of the power station i is determined by a dispatcher according to the position of the reservoir in the cascade and the size of the effective storage capacity; v i,T The storage capacity of the power station i in the T time period; t is the length of the scheduling period, namely the number of the last time period;
step 2, setting the daily generated energy of the cascade hydropower station: the total generating capacity E of the cascade hydropower station in the dispatching period is used as a control variable, and the constraint is satisfied:
wherein E is the total power generation of the cascade hydropower station and the unit time interval length of delta t;
and 3, calculating the feasible output area of the unit: firstly, acquiring a set of output vibration areas of the unit
Wherein R is i,j The method comprises the following steps of (1) collecting output vibration areas of a unit j in a power station i; />
And withROZ i,j,m Respectively the upper limit and the lower limit, M, of the mth vibration zone of the unit i,j The number of vibration areas of the unit j in the power station i is set;
according to the output range of the unit, the combined vibration area is subjected to complementary collection to obtain the output feasible region F of the unit i,j As shown in formula 3;
formula 3:
in the formula (I), the compound is shown in the specification,
and/or>
Respectively the minimum output and the maximum output of the unit j in the power station;pf i,j,m and/or>
Lower limit and upper limit of the mth feasible region of the ith unit j in the power station, M =0,1 i,j (ii) a The number of feasible domains of the unit j is M i,j +1；
And 4, calculating the combined feasible region of the power station: combining the feasible regions of all the units in the power station to obtain a combined feasible region of the power station; the combination of any two units j and l can be operated in the field of
Wherein n is the number of the feasible domain of the unit l; the combination feasible region of any three machine sets is represented as the combination of the feasible region of one machine set and the combination feasible region of two machine sets, and so on, the combination feasible region of the power station is represented as->
Wherein->
The method comprises the following steps of (1) forming a combined feasible domain containing j machine sets; />
AndFOZ i,mf respectively combining the upper limit and the lower limit of a feasible domain for the mf combination of the power station i; m i The number of the feasible domains of the power station i is obtained;
step 5, constructing a mixed integer nonlinear programming model of multi-target short-term optimized scheduling of the cascade hydropower station: according to the hydropower peak regulation and power generation efficiency target function constructed in the step 1, the water balance and water lag time constraint of the cascade hydropower station, the power station water level limit and water level-reservoir capacity function, the hydropower station output limit and the hydropower station combination feasible region constraint, the ex-warehouse flow limit and ex-warehouse flow relation, the tail water level-ex-warehouse flow function, the hydropower station power generation efficiency function and the water head calculation function which are calculated in the step 4, a mixed integer nonlinear programming is used for constructing a cascade hydropower station multi-target short-term optimization scheduling model as follows:
in the formula, V i,t 、V i,t+1 Respectively storing capacities of the power station i in a time period t and a time period t +1; i is i,t The flow rate of the power station i in the warehouse in the time period t is obtained;
for the plant k at t-TC k,i The flow rate of the warehouse; TC (tungsten carbide) k,i The water flow time lag between the power station k and the power station i; k is the number of hydropower stations directly upstream of the power station i; zf i,t 、Zf i,t-1 Respectively the water level of the power station i in the time period t and the time period t-1; a. The i,0 ,A i,1 ,...,A i,4 The water level-reservoir capacity coefficient of the power station i; zf i,min And Zf i,max Respectively the lower limit and the upper limit of the water level of the power station; p i,t The output of the power station i in the time period t is obtained; p i,min And P i,max Respectively representing the lower output limit and the upper output limit of the power station i; CF (compact flash) i The combined feasible region of the power station i calculated in the step 4 is obtained; q i,min 、Q i,max Respectively representing the lower limit and the upper limit of the ex-warehouse flow of the power station i; q i,t The flow of the power station i is taken out of the warehouse in the time period t; />
And s i,t Respectively the power generation flow and the water discharge flow of the power station in the time interval; zd i,t The tail water level of the power station i in the time period t; c i,0 ,C i,1 ,...,C i,4 The tail water level-ex-warehouse flow coefficient of the power station i is obtained; d i,0 ,D i,1 ,...,D i,5 The coefficient is the power generation efficiency function coefficient of the power station i; h i,t Water head of the power station i in a time period t;
and 6, calculating the end point of the Pareto front edge: solving a Pareto solution set of the multi-target model by using an improved normalization method plane constraint method, firstly calculating an end point of a Pareto front edge, respectively reserving constraint conditions of the multi-target optimization model and carrying out optimization solution on a single target of the multi-target optimization model to obtain a front edge end point corresponding to the target; for the multi-target model in the step 5, two endpoints A are correspondingly obtained 1 (f 1 (x 1* ),f 2 (x 1* ) And A) 2 (f 1 (x 2* ),f 2 (x 2* ) Wherein f) is 1 (x 1* )、f 2 (x 2* ) Respectively, optimization solutions of a single object, f 2 (x 1* )、f 1 (x 2* ) Respectively, the corresponding value, x, of one object when another object takes an optimal solution 1* 、x 2* The values are respectively the corresponding decision variable values;
and 7, optimizing pareto leading edge end points: the endpoint A was calculated using equations 4 and 5, respectively 1 And A 2 Of optimal value A' 1 (f 1 (x 12 ),f 2 (x 12 ))、A′ 2 (f 1 (x 21 ),f 2 (x 21 ) Wherein f) is 1 (x 12 )、f 2 (x 12 ) For the multi-objective function values obtained after solving equation 4, f 1 (x 21 )、f 2 (x 21 ) The multi-objective function value obtained after solving the formula 5 is obtained;
formula 4:
formula 5:
in the formula, epsilon 1 And epsilon 2 Calculation parameter, R, in endpoint optimization + Is a positive real number set, epsilon 1 And epsilon 2 Are respectively f 1 (x 1* )、f 2 (x 2* ) A relatively small value;
step 8, target function solution space normalization processing: as shown in formula 6; normalized, endpoint A' 1 (f 1 (x 12 ),f 2 (x 12 ))、A′ 2 (f 1 (x 21 ),f 2 (x 21 ) Is converted to AN' 1 (0, -1) and AN' 2 (1,0)；
Formula 6:
in the formula (I), the compound is shown in the specification,
to normalize the position coordinates of any point in the solution space, device for selecting or keeping>
Is->
Corresponding horizontal and vertical coordinate values are the normalized objective function values;
step 9, generating equal distance points of urotroping: make normalized endpoint AN 'defined in step 8' 1 (0, -1) pointing to AN' 2 Vector of (1, 0)
Namely the Uutopia vector; in the vector pick>
Making M-1 equal points of Utox, dividing Utox vector into equal M sections, and making equal points->
Is calculated in such a way that->
Step 10. Let pm =1;
step 11, pareto non-inferior solution generation: for urotropine equidistant points
Make a vector perpendicular to Utobang and passing through the point>
The intersection point of the straight line and the front edge of the Pareto is the Pareto non-inferior solution corresponding to the Uutopia equidistance point
Not inferior solution->
Obtained by solving equation 7;
formula 7:
in the formula (I), the compound is shown in the specification,
the utopia vector defined in step 9; />
Means is represented by points equidistant from utopia->
Non-inferior solution solved by directional formula 7>
Transposing the vector of (a); />
Respectively are not inferior>
The horizontal and vertical coordinates in the normalized solution space are the normalized objective function values;
step 12. Let pm = pm +1;
step 13, judging whether pm is greater than or equal to M, if so, entering step 14, otherwise, returning to step 11 to continue calculating, and setting the equidistant points of pm =1,2
Solving the corresponding Pareto non-inferior solution to obtain a Pareto solution set of the problem;
step 14, non-degradation reduction: for the Pareto solution sets in the normalized solution space calculated in the steps 10 to 13, the solutions in the Pareto solution sets need to be reduced to the original specifications; pareto solution for any normalization in a solution set
Its original value (f) 1 (x),f 2 (x) The formula for calculation) is: />
Step 15, after the Pareto non-inferior solution set is obtained in the step 14, evaluating each solution in the solution set based on a membership value calculation method of fuzzy evaluation, and selecting a decision proposal scheme for reference of a dispatcher; the method comprises two steps of calculating single target membership and calculating comprehensive membership; first, let pm =0;
and step 16, calculating the single-target membership degree: for each non-inferior solution in the Pareto solution set, firstly, calculating the membership degree of each non-inferior solution in each single target aspect; for any Pareto solution (f) 1 (x),f 2 (x) Membership μ of its peak shaver target) pm,1 The calculation function of (2) is shown as formula 8, and the target membership degree mu of the power generation efficiency pm,2 The calculation function of (a) is shown in equation 9;
formula 8:
formula 9:
step 17. Let pm = pm +1;
step 18, judging whether pm is larger than M +1, if so, entering step 19, otherwise, returning to step 16 to continue calculation;
and 19, calculating comprehensive membership degree: according to the single target membership value, the comprehensive membership mu of each solution in the solution set pm And (3) calculating:
and 20, selecting an optimal compromise solution: and according to the comprehensive membership degree of each solution in the obtained Pareto solution set, selecting the solution with the maximum comprehensive membership degree as the optimal compromise solution, and providing the optimal compromise solution as a decision suggestion method for scheduling personnel.
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