CN113128782A - Large-scale hydropower station group optimal scheduling dimensionality reduction method coupling feasible domain identification and random sampling - Google Patents

Large-scale hydropower station group optimal scheduling dimensionality reduction method coupling feasible domain identification and random sampling Download PDF

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CN113128782A
CN113128782A CN202110479084.1A CN202110479084A CN113128782A CN 113128782 A CN113128782 A CN 113128782A CN 202110479084 A CN202110479084 A CN 202110479084A CN 113128782 A CN113128782 A CN 113128782A
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申建建
朱文丽
程春田
蒋燕
张扬
刘双全
张聪通
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Abstract

A large-scale hydropower station group optimization scheduling dimension reduction method coupling feasible region identification and random sampling establishes a super-large-scale hydropower system scheduling model under the condition of determinacy incoming water with the maximum generated energy as a target, utilizes the feasible region identification method to perform equivalent conversion processing on various restriction constraints of water level, flow and output to obtain a model feasible solution range, and reduces the feasible solution range; and solving the model by adopting a random sampling algorithm, introducing acceptability and reliability parameters, giving water level segmentation sampling weight according to a scheduling result of many years, carrying out stochastic sampling into probability sampling, and obtaining the optimal water level and output process of the super-large-scale hydroelectric system by iterative optimization calculation. The invention can fully reduce the range of inferior decision making, greatly reduce the unnecessary calculation of the running water level state of the reservoir, and compared with the discrete differential dynamic programming and the gradual optimization method, the invention respectively reduces the calculation time by 98.73 percent and 96.86 percent under the condition of similar solution quality, thereby remarkably relieving the dimension disaster problem of hydropower optimization scheduling.

Description

Large-scale hydropower station group optimal scheduling dimensionality reduction method coupling feasible domain identification and random sampling
Technical Field
The invention belongs to the field of hydroelectric power generation dispatching, and particularly relates to a large-scale hydropower station group optimal dispatching dimension reduction method coupling feasible domain identification and random sampling.
Background
In the last two decades, the hydropower of China realizes the leap-type development, the total installation of the hydropower of China reaches 3.7 hundred million kW, the hydropower of a single regional power grid exceeds 1 hundred million kW, the single provincial power grid exceeds 7500 thousand kW, the single watershed cascade reaches 2000 thousand kW, the number of hydropower stations for the unified dispatching of regional and provincial power grids exceeds 100 or even 200, and the large hydropower system has the advantages that the calculation and storage scale of the traditional optimized dispatching method mainly based on dynamic planning and analytical planning needs to be exponentially increased, the problem of dimensionality disaster is particularly prominent, the problem is the first problem of the group power generation dispatching of the hydropower stations of the high-proportion hydropower grid and the extra large watershed cascade of the system in China, and an efficient and practical solving method is urgently needed.
With the increase of the number of the hydropower stations participating in the calculation, the state combination and the decision combination in a single time period are exponentially increased, so that the calculation amount of the system is greatly increased, and the reduction of the state combination and the decision combination in the single time period can help to solve the problem of dimension disaster. Compared with the classical dynamic programming, the discrete differential dynamic programming and the stepwise optimization algorithm reduce the state combination of each stage, and the practical application proves that the methods can effectively improve the calculation efficiency. However, the problem of dimensionality that the calculated amount and the storage amount are exponentially increased along with the increase of the number of the hydropower stations still exists, so that a new solving method and a new solving technology are urgently needed to be explored for the problem of optimizing and scheduling of the super-large-scale hydropower station group. On one hand, the reduction of the search range is important for dimension reduction, the size of the decision search range can be effectively reduced by feasible region identification on the premise of not changing an optimization algorithm optimizing mechanism, the boundary of the decision range can be redefined by the feasible region through constraint condition determination, and the calculated decision combination is reduced; on the other hand, how to avoid invalid calculation is also an important dimension reduction idea, and random sampling can reduce not only decision combination of calculation but also state combination. The two ideas can effectively reduce the calculation and the storage amount of the optimal scheduling of the water and electricity system.
Therefore, the invention provides a large-scale hydropower station group optimization scheduling dimension reduction method with strong practical value and popularization and application value by using feasible domain identification and random sampling technology and developing research aiming at the dimension disaster problem of large-scale hydropower system scheduling by taking a hydropower system in the southwest region as the background and relying on the national science fund (52079014).
Disclosure of Invention
The technical problem to be solved by the invention is to provide a large-scale hydropower station group optimization scheduling dimensionality reduction method coupling feasible domain identification and random sampling, the feasible domain is utilized to reduce the result search range, the random sampling optimization method is adopted to avoid traversing all solutions in the search range on the premise of ensuring the result reliability, the calculation efficiency is greatly improved, and the problem of dimensionality disaster in the large-scale hydropower station group optimization scheduling is solved to a certain extent.
The technical scheme of the invention is as follows: the invention discloses a large-scale hydropower station group optimal scheduling dimensionality reduction method coupling feasible domain identification and random sampling, which completes the deterministic optimal scheduling dimensionality reduction of a hydropower station group according to the following steps 1-12:
step 1, establishing a hydropower station group optimal scheduling model by taking efficient utilization of water energy as a criterion, wherein the method specifically comprises the following steps:
Figure BDA0003047988970000021
in the formula: wherein E represents the power generation of the hydroelectric system; Δ t' represents the number of hours within the time period t; i represents the hydropower station serial number; kiRepresenting the output coefficient of the hydropower station i; n is a radical ofi,tRepresenting the output of the hydropower station in the time period t; q. q.si,tRepresenting the downflow of a hydroelectric power station during a time period tAn amount; h isi,tRepresenting the average output water purification head of the hydropower station in the time period t; q. q.si,tRepresenting the generating flow of the hydropower station i in the time period t; n is a radical ofi,tRepresenting the output of the hydropower station i in the time period t; i represents the number of hydroelectric power stations.
Step 2, initializing calculation parameters including hydropower station operation parameters, water level control constraints, lower leakage flow constraints, power station output constraints and water quantity balance constraints;
Figure BDA0003047988970000022
Figure BDA0003047988970000023
Ni,min≤Ni,t≤Ni,max (4)
Vi，t+1＝Vi，t+3600(Qi，t-Ri，t)*Δt′ (5)
Figure BDA0003047988970000024
in the formula: zi,0Representing the initial water level, Z, of the hydropower station ii,TRepresenting the end water level of the hydropower station i. Zi,SAnd Zi,ZRespectively representing the minimum value and the maximum value of the water level of the hydropower station i; zi,tRepresenting the water level of the hydropower station i during a time period t; ri,minAnd Ri,maxRespectively representing the lower limit and the upper limit of the ex-warehouse flow of the hydropower station i; ri,tRepresenting the let-down flow of the hydropower station i in the time period t; q. q.si,minAnd q isi,maxRespectively representing the upper limit and the lower limit of the generating flow of the hydropower station i; q. q.si,tRepresenting the generating flow of the hydropower station i in the time period t; di,tThe water discharge rate of the hydropower station i in the time period t is shown; n is a radical ofi,minAnd Ni,maxRespectively representing the lower limit and the upper limit of the output of the hydropower station i; n is a radical ofi,tRepresenting the output of the hydropower station i in the time period t; vi,tThe initial storage capacity of the hydropower station i in the time period t is shown; qi,tWarehousing runoff of the hydropower station i in a time period t; qi,t' is the interval flow of the hydropower station i in the time period t; sigma RtRepresents the sum of the let-down flow of the upstream hydropower station in the time period t; when the hydropower station i is equal to 1, the runoff in reservoir is interval runoff, and when the hydropower station i is equal to 1, the runoff in reservoir is interval runoff>And 1, the warehousing runoff is the sum of the interval runoff and the discharge flow of the upstream hydropower station.
Step 3, setting the reliability indexes a and b and the precision epsilon 1 and epsilon 5 of the optimal solution of the sampling method and the fifth optimal solution;
step 4, determining parameter sequence { a1,a2,a3…,aMAnd the sequence of sample numbers S1,S2,S3…,SM}; where M is an array { a }1,a2,a3…,aMAnd { S }1,S2,S3…,SMThe number of elements;
step 5, setting n to 1, k to 1, t to 1, and S to Sk(ii) a Where n is the sample number of the sample and k is the array { a }1,a2,a3…,aMAnd { S }1,S2,S3…,SMThe sequence number in the sequence, S is the number of samples, SkRepresents { S1,S2,S3…,SMThe kth element in the sequence;
and 6, determining the feasible region range of the hydropower station at the end of the time period t, coupling the scheduling operation constraints of the hydropower stations, and determining the feasible region range, wherein the method comprises the following steps:
(1) and (3) constraint condition conversion:
for output constraints, the water consumption rate mu is utilizediThis is translated into a let-down flow constraint, as follows:
Figure BDA0003047988970000031
for let-down flow constraints, q is usedi,minAnd q isi,maxSeeking a feasible region, comparing the two sets of shedding flow constraints, and taking the intersection of them as a set of shedding flow constraints defining the feasible region as follows:
Figure BDA0003047988970000032
in the formula
Figure BDA0003047988970000033
q i,tRespectively representing the upper limit and the lower limit of the downward discharge flow; q. q.si,pmax,qi,pminRespectively representing the equivalent let-down flow corresponding to the upper limit and the lower limit of the output.
(3) Feasible region range determination
According to the water quantity balance equation, on the premise that other variables are determined, the runoff from the reservoir is inversely proportional to the reservoir capacity at the end of the time period, namely the upper limit value of the reservoir capacity at the end of the time period can be obtained by using the minimum downward flow, and the lower limit value of the reservoir capacity at the end of the time period can be obtained by using the maximum downward flow. As shown in the following formula, the let-down flow rate constraint is firstly converted into the reservoir capacity constraint under the condition of the known warehousing flow rate and the initial reservoir capacity in the time period by utilizing the water quantity balance. After the conversion, the data are compared with the original storage capacity constraint, and the intersection is taken as the upper limit and the lower limit of the feasible range.
Figure BDA0003047988970000034
Figure BDA0003047988970000035
In the formula
Figure BDA0003047988970000041
V i,t+1Respectively representing the upper limit and the lower limit of the storage capacity feasible region.
And converting the reservoir capacity range obtained according to the formula into an equivalent water level range through a relation curve of the water level to the reservoir capacity.
(4) Further reduction of the range of feasible regions is achieved by the following equation
Figure BDA0003047988970000042
In the formula
Figure BDA0003047988970000043
Z i,tRespectively representing the upper limit and the lower limit of a feasible region of the reservoir level; hi,normal，Hi,deadRespectively representing the normal high water level and the dead water level of the hydropower station i; a represents a water level array of the ith hydropower station under various runoff conditions in a time period t.
And 7, performing probability sampling in the range of the water level feasible region of the hydropower station to calculate the output of the faced time period: in the calculation, the probability that each bin level is located in a satisfactory solution interval is a%. Then, every time a solution is randomly extracted, the probability that the solution is not in a satisfactory solution interval is (1-a%), s candidate water levels are continuously extracted in the feasible region determined in the last step, and the probability that the water levels are not in the first a% is (1-a%)sWhen:
(1-a％)s≤b％ (12)
s reservoir levels are extracted, and in order to ensure that a satisfactory solution is contained:
Figure BDA0003047988970000044
when the number of the extracted samples is more than SminThen (1-b%) probability exists to draw a satisfactory water level.
Step 8, making t equal to t + 1; judging whether T is true or not, if so, taking the water level at the end of the whole year as the water level at the end of the time period to calculate the output, obtaining the sum of the output at each time period as a sampling result of the sample n-s, setting T as 1, and entering the step 9; if not, returning to the step 6 to continue the calculation;
step 9, judging whether n is equal to S, if so, obtaining the optimal solution and the fifth optimal solution in the S reservoir level samples, setting n to 1, entering step 10, if not, returning to step 6 to continue calculation;
step 10, judging whether k is equal to M, if so, entering step 11, if not, returning to step 6 to continue calculation;
and 11, obtaining the optimal solution sequence { f1} and the fifth optimal solution { f5} of the hydropower station scheduling, and obtaining the optimal solution and the fifth optimal solution sequence { f5} of each sampling combination1,1，f1,2，f1,3，…}，{f5,1，f5,2，f5,3…, solving the change rate d1 and d5 of the sequence, and the concrete formula is as follows:
Figure BDA0003047988970000045
Figure BDA0003047988970000051
d1<ε1 (16)
d5＜ε5 (17)
and step 12, judging the precision, outputting an optimal solution if the precision judgment is met, calculating the number of the added samples if the precision judgment is not met, setting S to be delta S and k to be M +1, and returning to the step 6 to continue the calculation.
Compared with the prior art, the technical scheme of the invention can realize the following beneficial effects: the method provided by the invention can utilize a large-scale hydropower system scheduling model to reduce the range of feasible domains, and adopts a random sampling optimization method to avoid traversing all solutions in a search range on the premise of ensuring the reliability of results, thereby greatly improving the calculation efficiency and solving the problem of dimension disaster in hydropower station group optimization scheduling to a certain extent. The invention can obviously reduce the range of poor decision making, reduce the cost of unnecessary calculation and storage, solve the problem of dimension disaster to a certain extent and realize the high-efficiency processing of the optimized dispatching of the large-scale hydropower system.
Drawings
FIG. 1 is a schematic illustration of upper and lower limits of a hydropower station water level;
FIG. 2 is a schematic diagram of a feasible domain identification method;
fig. 3 is a schematic diagram of distribution probability of an optimized scheduling result.
Detailed Description
The invention relates to a large-scale hydropower station group optimization scheduling dimension reduction method coupling feasible domain identification and random sampling, and the invention is further described by combining the attached drawings and an example.
The ultra-large-scale hydropower station group scheduling is a very challenging system optimization problem, and in order to realize efficient solution of a system, the invention mainly solves the problems in two aspects: firstly, determining a feasible solution range of a scheduling model according to a scheduling requirement and reducing the feasible solution range; and secondly, random sampling is carried out in a feasible solution range so as to avoid a large amount of invalid or inefficient calculation. The solutions to the two problems are set forth separately below.
(a) Reduction of feasible solution range of optimal scheduling model of hydropower station group
The invention aims at efficiently utilizing the water energy of a super-large scale hydropower system under the condition of determinacy water coming, and constructs a model with the maximum generated energy, which comprises the following specific steps:
Figure BDA0003047988970000052
the model is constrained as follows:
water level control constraint
Figure BDA0003047988970000061
② lower bleed flow restriction
Figure BDA0003047988970000062
② constraint of force
Ni,min≤Ni,t≤Ni,max (21)
Water quantity balance restraint
Vi，r+1＝Vi，t+3600(Qi，r-Ri，t)*Δt′ (22)
Figure BDA0003047988970000063
In the formula: zi,0Representing the initial water level, Z, of the hydropower station ii,TRepresenting the end water level of the hydropower station i. Zi,SAnd Zi,ZRespectively representing the minimum value and the maximum value of the water level of the hydropower station i; zi,tRepresenting the water level of the hydropower station i during a time period t; ri,minAnd Ri,maxRespectively representing the lower limit and the upper limit of the ex-warehouse flow of the hydropower station i; ri,tRepresenting the let-down flow of the hydropower station i in the time period t; q. q.si,minAnd q isi,maxRespectively representing the upper limit and the lower limit of the generating flow of the hydropower station i; q. q.si,tRepresenting the generating flow of the hydropower station i in the time period t; di,tThe water discharge rate of the hydropower station i in the time period t is shown; n is a radical ofi,minAnd Ni,maxRespectively representing the lower limit and the upper limit of the output of the hydropower station i; n is a radical ofi,tRepresenting the output of the hydropower station i in the time period t; vi,tThe initial storage capacity of the hydropower station i in the time period t is shown; qi,tWarehousing runoff of the hydropower station i in a time period t; qi,t' is the interval flow of the hydropower station i in the time period t; sigma RtRepresents the sum of the let-down flow of the upstream hydropower station in the time period t; when the hydropower station i is equal to 1, the runoff in reservoir is interval runoff, and when the hydropower station i is equal to 1, the runoff in reservoir is interval runoff>And 1, the warehousing runoff is the sum of the interval runoff and the discharge flow of the upstream hydropower station.
A solution that satisfies all the constraints of a mathematical model is called a feasible solution. The set composed of all feasible solutions is called a feasible region, namely the feasible region is only related to the constraint of the problem and has no direct relation with the objective function, the solving mode and the like of the problem. Therefore, the feasible region of the maximum power generation model constructed by the invention is a set of solutions meeting all the constraints.
(1) Model constraint transformation
Before reducing the feasible solution range of the model, a decision range corresponding to each constraint needs to be found, that is, the constraint is equivalently transformed. For output constraints, the water consumption rate mu is utilizediTranslates into total drainage constraint, as follows:
Figure BDA0003047988970000071
for let-down flow constraints, R is known>q, so use qi,minAnd q isi,maxSeeking a feasible region, comparing the two sets of shedding flow constraints, and taking the intersection of them as a set of shedding flow constraints defining the feasible region as follows:
Figure BDA0003047988970000072
(2) feasible set range determination
According to the water quantity balance equation, on the premise that other variables are determined, the runoff from the reservoir is inversely proportional to the reservoir capacity at the end of the time period, namely the upper limit value of the reservoir capacity at the end of the time period can be obtained by using the minimum downward flow, and the lower limit value of the reservoir capacity at the end of the time period can be obtained by using the maximum downward flow. As shown in the following formula, the let-down flow rate constraint is firstly converted into the reservoir capacity constraint under the condition of the known warehousing flow rate and the initial reservoir capacity in the time period by utilizing the water quantity balance. After the conversion, the data are compared with the original storage capacity constraint, and the intersection is taken as the upper limit and the lower limit of the feasible range.
Figure BDA0003047988970000073
Figure BDA0003047988970000074
In the invention, the water level at the end of the time interval is used as a decision variable, so that the obtained water level reservoir capacity range is converted into a water level range through a water level-reservoir capacity relation.
In addition, a sufficient runoff process is obtained by utilizing a known perennial runoff process and a manual simulation mode, and the manual simulation runoff conforms to a theoretical frequency curve of monthly runoff. A given runoff process may be considered to encompass all possible runoff processes that may occur. On the premise of determinacy of runoff water inflow, performing single-reservoir DP scheduling on the reservoir to obtain the water level change process of the reservoir for many years and taking the upper and lower limits of the water level. According to the water level scheduling process for many years, under the condition that the initial water level and the final water level of the whole year are fixed, no matter how the runoff condition changes, a part of water level can never reach. As shown in fig. 1: the water level between the upper water level limit and the normal high water level and the water level between the lower water level limit and the dead water level cannot meet the water level in the scheduling process, so the ranges can be eliminated before scheduling calculation, and the feasible area range is further reduced.
(3) Viable set range reduction
And (4) integrating the water level processes at the end of the month of all the hydropower stations to form a three-dimensional matrix A. The three dimensions are respectively: the runoff, the months and the hydropower stations, then the upper and lower limits of the water level are set for each reservoir in each period according to a. Comparing the water level range meeting the constraint condition with the water level limits, taking the overlapping area as a feasible area of the period i, and deleting any water level range not meeting the constraint condition and any range not covered by the water level range in the matrix A, wherein the specific calculation formula is as follows:
Figure BDA0003047988970000081
in the formula
Figure BDA0003047988970000082
Z i,tRespectively representing the upper limit and the lower limit of a feasible region of the reservoir level; hi,normal，Hi,deadRespectively representing the normal high water level and the dead water level of the hydropower station i; a represents a water level array of the ith hydropower station under various runoff conditions in a time period t.
And in the calculation process, determining feasible regions in sequence from small to large according to the time interval. In period 1, the feasible region at the end of the period is obtained according to the initial water level and combining the constraint condition and the water inlet amount of the first period. In conjunction with the RS optimization method, the method samples the water level from the feasible region to obtain the initial conditions for the next epoch. Therefore, the feasible region can be determined and sampled sequentially, and the feasible region range can be determined dynamically. Compared with the method for determining the feasible region of the previous stage by using the feasible region boundary of the previous stage, the method can better delete the water level range which does not meet the constraint, and the feasible region range is greatly reduced. Therefore, it is known that the calculation efficiency of the HDRS can be greatly improved by calculating the feasible region for each period in turn in this manner. The FRI method principle is shown in fig. 2.
(b) Deterministic scheduling model solution for hydropower station group
For large scale hydro-electric system scheduling problems it is difficult to calculate and compare all possible results. The invention uses RS optimization and increases result evaluation on the basis of random sampling, and dynamically adjusts the sampling number according to the search result. To ensure that the samples selected from all candidate solutions have a reasonable level of reliability, the acceptability and reliability parameters are introduced into the RS optimization. The selected water level states are iteratively evaluated to evaluate the increase in the target value that will serve as a convergence criterion for the entire search process. In order to further improve the reliability of the samples, the water level segmentation sampling weight is given according to the scheduling result of years, and random sampling is further converted into probability sampling.
(1) Satisfactory solution sequence and reliability index
In order to understand the solution distribution of reservoir scheduling and to assist in explaining the reliability indexes a% and b% of the random sampling optimization method, all solutions obtained by combining decisions and states in a certain time period of a bay, which are calculated by dynamic planning, are selected for analysis, and the specific distribution probability is as follows:
a(N)＝n_N/n_all (29)
Figure BDA0003047988970000083
in the formula: n _ N represents the number of occurrences of the output N; n _ all represents the number of all output results; a (N) represents the probability of the occurrence of a result with an output of N. A (N1) represents the probability of occurrence of a result less than N1.
As can be seen from fig. 3, the number of results is positively correlated with the quality of the results, and the closer the optimal solution is, the greater the number of results is included. The probability of each decision appearing is the same under the condition of random sampling, the probability of obtaining the optimal solution by extraction is too small, but the probability of obtaining the approximate optimal solution in the vicinity of the optimal solution by extraction is obviously improved a lot.
For large-scale reservoir scheduling problems, the decision search range is too large, and the solution cannot be directly carried out, so that the finding of an approximate solution is simpler than the finding of an optimal solution. And setting a parameter a, and considering that the solutions in the first a% interval are all satisfactory solutions when the solutions are sorted according to the advantages and the disadvantages. In the random sampling process, the samples in each interval have a certain probability to be extracted, and when the samples are completely random, the probability to be extracted of each sample is as follows:
a′％＝1/n_all (31)
correspondingly, the probability of being drawn in a satisfactory solution is:
a％＝nsatisfactory solution/n_all (32)
In the formula, nSatisfactory solutionRepresenting the number of solutions between satisfactory solutions.
The random sampling probability is only related to the number of samples, when different samples are endowed with different probabilities through objective reasons, the random sampling is changed into probability sampling according to the sample probability, and under the condition that the sampling times are enough, the random sampling result distribution is relatively even and is approximate to the overall result distribution. The distribution of the results of the probabilistic sampling is related to the probability values of the results, and when the results with better performance have higher probability, the distribution of the sampling results shows that the number of the better results is increased, and the number of the worse results is decreased. The use of probabilistic sampling can improve the reliability of the sampling when a greater probability value is assigned to a sample of a better result.
(2) Random sampling
In the calculation, the goal is to obtain a result of a satisfactory solution interval, with a probability of each solution lying in the satisfactory solution interval of a%. Then every random extraction of a solution with a probability of not being in a satisfactory solution interval of (1-a%), and successive extraction of s candidate solutions with a probability of not being in the first a%, (1-a%)sSince the sampling objective is to extract a solution that lies within a satisfactory solution interval, then when:
(1-a％)s≤b％ (33)
then S samples are drawn, and to ensure that a satisfactory solution is contained:
Figure BDA0003047988970000091
i.e. as long as the number of samples extracted is greater than SminThen there is a probability (1-b%) that a satisfactory solution is drawn.
Since the selection of the parameters in the actual calculation needs to be determined empirically, the obtained solution needs to be evaluated in order to ensure that a satisfactory solution can be extracted. During evaluation, if the effect of improving optimization is not obvious enough by continuously increasing the number of samples, the optimal solution of the samples is considered to be found, if the optimization result can be obviously improved by continuously increasing the number of samples, the number of samples needs to be continuously increased, and iteration is carried out until a satisfactory solution is found.
To complete the evaluation, the value of a is changed to form a sequence { a }1,a2,a3…,aMIs given as { S, the corresponding sample number sequence is1,S2,S3…,SM}. And sampling according to the sample numbers to obtain the optimal solution of each sampling combination and a fifth optimal solution sequence { f1,1, f1,2, f1,3, … }, { f5,1, f5,2, f5,3, … }. And (3) derivation of the solution sequence:
Figure BDA0003047988970000101
Figure BDA0003047988970000102
d1<ε1 (37)
d5＜ε5 (38)
the resulting solution was evaluated for satisfactory results from the variation of f1 and f5 with a, setting the accuracies ε 1 and ε 5. When the accuracy formula can be satisfied and f1 is closer to f5, the obtained satisfactory solution density is higher, the stage robustness is stronger, and f1 is the satisfactory solution. When the two precision formulas cannot be satisfied, the optimal solution obtained at this time cannot be determined to be a satisfactory solution, and the number of samples needs to be continuously expanded.
Figure BDA0003047988970000103
And adding the added sample solution into the existing solution set, and judging that the new solution set meets the precision requirement.
(3) Calculating step
And Step 1, setting parameters. Including the parameters a, b, ε 1 and ε 5.
Step 2. determining the parameter sequence { a1,a2,a3…,aMAnd { S }1,S2,S3…,SM}；
Step 3 according to the sequence S1,S2,S3…,SMAnd (5) sampling M-l to M elements, and calculating to obtain an optimal solution sequence { f1} and a fifth optimal solution { f5 }. m is usually 20-50;
and Step 4, solving the change rates d1 and d5 of the solution sequence, carrying out precision judgment, outputting the optimal solution if the precision judgment is met, and entering Step 5 if the precision judgment is not met.
And Step 5, increasing the number of samples, adding the solutions into the existing solution set, and returning to Step 4.
(c) Overall solution method steps
In combination with the solution idea of the above key problems, a one-time complete hydropower station group deterministic optimal scheduling dimensionality reduction process can be expressed by the following steps:
step 1, establishing a deterministic optimal scheduling model of a super-large-scale hydroelectric system, wherein the model aims to maximize the generated energy;
reading basic data, and initializing calculation parameters including hydropower station operation parameters, water level control constraints, let-down flow constraints, power station output constraints and water balance constraints;
step 3, setting parameters a, b, m, l, epsilon 1 and epsilon 5, a water level matrix A and weight distribution w of each interval;
step 4, determining parameter sequence { a1,a2,a3…,aMAnd { S }1,S2,S3…,SM}；
Step 5, setting n to 1, k to 1, t to 1, and S to Sk(ii) a Where n is the sample number of the sample and k is the array { a }1,a2,a3…,aMAnd { S }1,S2,S3…,SMThe sequence number in the sequence, S is the number of samples, SkRepresents { S1,S2,S3…,SMThe kth element in the sequence;
step 6, calculating the time interval t according to a feasible region identification principle, and determining a feasible region range at the end of the time interval;
step 7, probability sampling is carried out in a feasible region range, and a final water level is extracted to carry out output calculation in the period;
step 8, making t equal to t + 1; judging whether T is true or not, if so, taking the water level at the end of the whole year as the water level at the end of the time period to calculate the output, calculating the sum of the output at each time period as the sampling result of the sample n, setting T as 1, and entering the step 9; if not, returning to the step 6 to continue the calculation;
step 9, judging whether n is equal to S, if so, obtaining the optimal solution and the fifth optimal solution in the S samples, setting n to 1, entering step 10, if not, returning to step 6 to continue calculation;
step 10, judging whether k is equal to M, if so, entering step 11, if not, returning to step 6 to continue calculation;
step 11, obtaining an optimal solution sequence { f1} and a fifth optimal solution { f5}, and solving the change rates d1 and d5 of the sequences;
and step 12, judging the precision, outputting an optimal solution if the precision judgment is met, calculating the number of the added samples if the precision judgment is not met, setting S to be delta S and k to be M +1, and returning to the step 6 to continue the calculation.
Now, taking 21 hydropower stations, namely 12 hydropower stations in the main stream of the lanewang river, 8 hydropower stations in the Jinshajiang river and 1 hydropower station in the Nandrijiang river, as research objects, the actual runoff process of the system in 53 years, namely 1954-1959, 1961-1999 and 2008-2015, is selected for calculation so as to verify the efficiency of the method. Detailed power generation and calculation time data are shown in table 1, power generation calculation results for each hydropower station are shown in table 2, and the best results and worst results for all years are shown in table 3.
According to tables 1 and 2, compared with Discrete Differential Dynamic Programming (DDDP) and a step-by-step optimization algorithm (POA), the annual energy production calculated by the method provided by the invention is respectively improved by 4.37% and 8.74%, and the calculation time is respectively reduced by 98.73% and 96.86%. Moreover, the change of the power generation amount is found to be small in multiple calculations, which shows that the quality of the solution has better stability. The average calculation time is significantly less than the calculation time of DDDP and POA. The result shows that the method provided by the invention can obtain a better hydropower station optimal scheduling result in a shorter time.
TABLE 121 hydropower stations annual calculation result comparison
Figure BDA0003047988970000121
Table 2 comparison of power generation capacity of each hydropower station
Figure BDA0003047988970000122

Claims (1)

1. A large-scale hydropower station group optimization scheduling dimension reduction method coupling feasible domain identification and random sampling is characterized by comprising the following steps:
step 1, establishing a hydropower station group optimal scheduling model by taking efficient utilization of water energy as a criterion, wherein the method specifically comprises the following steps:
Figure FDA0003047988960000011
in the formula: e represents the power generation of all hydroelectric power stationsSumming; Δ t' represents the number of hours within the time period t; i represents the hydropower station serial number; kiRepresenting the output coefficient of the hydropower station i; h isi,tRepresenting the average output water purification head of the hydropower station in the time period t; q. q.si,tRepresenting the generating flow of the hydropower station i in the time period t; n is a radical ofi,tRepresenting the output of the hydropower station i in the time period t; i represents the number of the hydropower stations;
step 2, initializing calculation parameters including hydropower station operation parameters, water level control constraints, lower leakage flow constraints, power station output constraints and water quantity balance constraints;
Figure FDA0003047988960000012
Figure FDA0003047988960000013
Ni,min≤Ni,t≤Ni,max (4)
Vi，t+1＝Vi，t+3600(Qi，t-Ri，t)*Δt′ (5)
Figure FDA0003047988960000014
in the formula: zi,0Representing the initial water level, Z, of the hydropower station ii,TRepresenting the terminal water level of the hydropower station i; zi,SAnd Zi,ZRespectively representing the minimum value and the maximum value of the water level of the hydropower station i; zi,tRepresenting the water level of the hydropower station i during a time period t; ri,minAnd Ri,maxRespectively representing the lower limit and the upper limit of the ex-warehouse flow of the hydropower station i; ri,tRepresenting the let-down flow of the hydropower station i in the time period t; q. q.si,minAnd q isi,maxRespectively representing the upper limit and the lower limit of the generating flow of the hydropower station i; q. q.si,tRepresenting the generating flow of the hydropower station i in the time period t; di,tThe water discharge rate of the hydropower station i in the time period t is shown; n is a radical ofi,minAnd Ni,maxAre respectively asThe lower limit and the upper limit of the output of the hydropower station i; n is a radical ofi,tRepresenting the output of the hydropower station i in the time period t; vi,tThe initial storage capacity of the hydropower station i in the time period t is shown; qi,tWarehousing runoff of the hydropower station i in a time period t; qi,t' is the interval flow of the hydropower station i in the time period t; sigma RtRepresents the sum of the let-down flow of the upstream hydropower station in the time period t; when the hydropower station i is equal to 1, the runoff in reservoir is interval runoff, and when the hydropower station i is equal to 1, the runoff in reservoir is interval runoff>When 1, the warehousing runoff is the sum of the interval runoff and the discharge flow of the upstream hydropower station;
step 3, setting the reliability indexes a and b and the precision epsilon 1 and epsilon 5 of the optimal solution of the sampling method and the fifth optimal solution;
step 4, determining parameter sequence { a1,a2,a3…,aMAnd the sequence of sample numbers S1,S2,S3…,SM}; where M is an array { a }1,a2,a3…,aMAnd { S }1,S2,S3…,SMThe number of elements;
step 5, setting n to 1, k to 1, t to 1, and S to Sk(ii) a Where n is the sample number of the sample and k is the array { a }1,a2,a3…,aMAnd { S }1,S2,S3…,SMThe sequence number in the sequence, S is the number of samples, SkRepresents { S1,S2,S3…,SMThe kth element in the sequence;
and 6, determining the feasible region range of the hydropower station at the end of the time period t, coupling the scheduling operation constraints of the hydropower stations, and determining the feasible region range, wherein the method comprises the following steps:
(1) and (3) constraint condition conversion:
for output constraints, the water consumption rate mu is utilizediThis is translated into a let-down flow constraint, as follows:
Figure FDA0003047988960000021
for let-down flow constraints, q is usedi,minAnd q isi,maxSeeking a feasible region, comparing the two sets of shedding flow constraints, and taking the intersection of them as a set of shedding flow constraints defining the feasible region as follows:
Figure FDA0003047988960000022
in the formula (I), the compound is shown in the specification,
Figure FDA0003047988960000023
q i,trespectively representing the upper limit and the lower limit of the downward discharge flow; q. q.si,pmax,qi,pminRespectively representing equivalent lower bleed flow corresponding to the upper limit and the lower limit of the output;
(2) feasible region range determination
According to the water quantity balance equation, under the premise of determining other variables, the runoff from the reservoir is inversely proportional to the reservoir capacity at the end of the time period, namely, the upper limit value of the reservoir capacity at the end of the time period is obtained by using the minimum lower discharge flow, and the lower limit value of the reservoir capacity at the end of the time period is obtained by using the maximum lower discharge flow; as shown in the following formula, the lower leakage flow rate constraint is firstly converted into the reservoir capacity constraint under the condition of the known warehousing flow rate and the initial reservoir capacity in time period by utilizing water quantity balance; after the conversion, the obtained data is compared with the original storage capacity constraint, and the intersection is taken as the upper limit and the lower limit of the feasible range;
Figure FDA0003047988960000024
Figure FDA0003047988960000025
in the formula (I), the compound is shown in the specification,
Figure FDA0003047988960000026
V i,t+1respectively representing the upper limit and the lower limit of the feasible region of the storage capacity;
converting the reservoir capacity range obtained according to the formula into an equivalent water level range through a water level-reservoir capacity relation curve;
(4) further reduction of the range of feasible regions is achieved by the following equation
Figure FDA0003047988960000031
In the formula (I), the compound is shown in the specification,
Figure FDA0003047988960000032
Z i,trespectively representing the upper limit and the lower limit of a feasible region of the reservoir level; hi,normal，Hi,deadRespectively representing the normal high water level and the dead water level of the hydropower station i; a represents a water level array of the ith hydropower station under various runoff conditions within a time period t;
and 7, performing probability sampling in the range of the water level feasible region of the hydropower station to calculate the output of the faced time period: in the calculation, the probability that each reservoir level is positioned in a satisfactory solution interval is a%; then, every time a solution is randomly extracted, the probability that the solution is not in a satisfactory solution interval is (1-a%), s candidate water levels are continuously extracted in the feasible region determined in the last step, and the probability that the water levels are not in the first a% is (1-a%)sWhen:
(1-a％)s≤b％ (12)
s reservoir levels are extracted, and in order to ensure that a satisfactory solution is contained:
Figure FDA0003047988960000033
when the number of the extracted samples is more than SminWhen the water level is satisfied, the probability of (1-b%) is obtained;
step 8, making t equal to t + 1; judging whether T is true or not, if so, taking the water level at the end of the whole year as the water level at the end of the time period to calculate the output, calculating the sum of the output at each time period as the sampling result of the sample n, setting T as 1, and entering the step 9; if not, returning to the step 6 to continue the calculation;
step 9, judging whether n is equal to S, if so, obtaining the optimal solution and the fifth optimal solution in the S reservoir level samples, setting n to 1, entering step 10, if not, returning to step 6 to continue calculation;
step 10, judging whether k is equal to M, if so, entering step 11, if not, returning to step 6 to continue calculation;
and 11, obtaining the optimal solution sequence { f1} and the fifth optimal solution { f5} of the hydropower station scheduling, and obtaining the optimal solution and the fifth optimal solution sequence { f5} of each sampling combination1,1，f1,2，f1,3，…}，{f5,1，f5,2，f5,3…, solving the change rate d1 and d5 of the sequence, and the concrete formula is as follows:
Figure FDA0003047988960000034
Figure FDA0003047988960000035
d1＜ε1 (16)
d5＜ε5 (17)
and step 12, judging the precision, outputting an optimal solution if the precision judgment is met, calculating the number of the added samples if the precision judgment is not met, setting S to be delta S and k to be M +1, and returning to the step 6 to continue the calculation.
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