CN109255501B - Multi-Agent artificial fish swarm algorithm-based cascade library long-term optimization scheduling algorithm - Google Patents

Multi-Agent artificial fish swarm algorithm-based cascade library long-term optimization scheduling algorithm Download PDF

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CN109255501B
CN109255501B CN201811268417.0A CN201811268417A CN109255501B CN 109255501 B CN109255501 B CN 109255501B CN 201811268417 A CN201811268417 A CN 201811268417A CN 109255501 B CN109255501 B CN 109255501B
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吴慧军
王凌梓
李树山
李崇浩
唐红兵
廖胜利
张艳
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Dalian University of Technology
China Southern Power Grid Co Ltd
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Abstract

The invention belongs to the field of hydroelectric power generation and dispatching operation, and relates to a cascade library group long-term optimization dispatching algorithm based on a multi-Agent artificial fish swarm algorithm, which is used for improving relevant limitations such as overlong time consumption in the solving process of a cascade library group. The invention realizes a brand-new multi-Agent artificial fish swarm algorithm MAAFSA to model and solve the problem of long-term optimized scheduling of the cascade pool. The MAAFSA combines the respective advantages of the MAS and the AFSA, the Agent modules with different functions are constructed, the high-efficiency cooperation and the autonomous learning operation between the artificial fish agents are utilized, the convergence rate of the AFSA is increased, the solution of the long-term optimized scheduling of the cascade power station is realized from the aspect of man-machine interaction, and the multi-Agent evolutionary algorithm is extremely innovative. The method has the advantages of greatly improving relevant limitations such as overlong time consumption in the solving process of the cascade library group and the like, and providing a brand-new solving idea for the field of hydropower dispatching.

Description

Multi-Agent artificial fish swarm algorithm-based cascade library long-term optimization scheduling algorithm
Technical Field
The invention belongs to the technical field of hydroelectric power generation and dispatching operation, and particularly relates to a cascade library group long-term optimization dispatching algorithm based on a multi-Agent artificial fish swarm algorithm.
Technical Field
For more than 20 years, hydropower in China is always in a large-scale production stage, and the hydropower is an important peak-load and frequency-modulation power supply in a power system due to the characteristics of cleanness, no pollution, flexible adjustment process, quick response load and the like. However, the long-term optimized scheduling of the cascade hydropower station group is a multivariable, high-dimensional and large-scale multi-stage problem, and comprises extremely complicated constraint conditions, so that the solving difficulty is very high. There is currently a need to develop models and solution methods suitable for practical engineering. The achievement introduces a multi-Agent (Agent) technology into the solving process of the long-term optimized dispatching of the ladder library group, and provides a brand new solving idea for the field of hydropower dispatching.
Disclosure of Invention
The invention aims to provide a cascade library long-term optimization scheduling algorithm based on a multi-Agent (Agent) artificial fish swarm algorithm, and improve the relevant limitations of overlong time consumption and the like in the solving process of the cascade library.
The technical scheme of the invention is as follows:
a cascade library long-term optimization scheduling algorithm based on a multi-Agent artificial fish swarm algorithm comprises five modules, namely a core Agent module CA, a swarm Agent module GA, a behavior Agent module AA, an evaluation Agent module EA and a judgment Agent module JA; the AA comprises four basic behaviors, namely a foraging behavior Agent, a PAA (poly a aid), a clustering behavior Agent, an SAA (SAA), a rear-end behavior Agent, an FAA (far-end association) and a random movement behavior Agent and an MAA (mobile access Agent); and (5) realizing the purpose of solving the maximum generated energy according to the steps (1) to (5).
(1) The CA firstly receives a long-term optimization scheduling instruction of the gradient library group and starts to initialize each parameter. N GAs are randomly generated within the feasible region. Then parameters such as a maximum moving Step, a maximum Visual field of the artificial fish, a crowding factor delta, a maximum trial number Try-number and the like are transmitted to AA, and a maximum iteration number T is transmitted to JA;
(2) each GA respectively carries out information interaction with four basic behaviors of PAA, SAA, FAA and MAA, the four behaviors are simulated and executed, and maximum values generated by the respective behaviors are respectively transmitted to EA;
(3) the EA evaluates and compares the four behaviors, and selects an execution behavior;
(4) executing artificial fish behaviors, updating the artificial fish behaviors, and generating a new GA;
(5) JA judges whether the iteration time T meets the condition that T is less than or equal to T or whether the optimal solution difference value reaches the required range continuously for multiple times. If yes, turning to the step (2) and continuing the iteration operation; otherwise, ending the calculation process and outputting the current optimal result;
in an Artificial Fish Swarm Algorithm (AFSA), the convergence of the Algorithm is determined to a certain extent by the foraging behavior of Artificial Fish, the convergence is stabilized by the Swarm behavior, and the rear-end collision behavior and the evaluation behavior play a certain role in promoting the overall convergence and the convergence speed of the Algorithm. In general, the AFSA has low requirements on the properties of the problem function, and only the objective function value of the problem needs to be evaluated and updated. Meanwhile, the AFSA also has the advantages of strong robustness, strong global optimization capability and the like. However, the limitation of AFSA is that its convergence rate is relatively slow, and in order to meet the requirement of real engineering timeliness in practical application, a new technology is often combined to improve the search efficiency of AFSA.
While the main goal of MAS is to reduce complex large systems into small simple systems that are interrelated, cooperative, and coordinated. The MAS has the superior performances of autonomy, adaptability and the like, and is very suitable for solving large-scale optimization problems of cascade reservoir scheduling and the like which can be divided according to space-time and functions. Compared with the traditional AFSA, the Multi-Agent Artificial Fish Swarm Algorithm (MAAFSA) combined with the MAS combines a plurality of agents together, the problem that a single Agent cannot help is jointly solved through communication, coordination and cooperation, and the Multi-Agent Artificial Fish Swarm Algorithm has wider task field and higher efficiency than the single Agent.
Compared with the prior art, the invention has the following beneficial effects: the invention relates to a cascade pool long-term optimization scheduling algorithm based on a multi-Agent artificial fish swarm algorithm, which is used for modeling and solving a cascade pool long-term optimization scheduling problem by designing and realizing a brand-new multi-Agent artificial fish swarm algorithm on the basis of the traditional AFSA. The MAAFSA combines the respective advantages of the MAS and the AFSA, Agent modules with different functions are constructed, efficient cooperation and autonomous learning operation among the artificial fish agents are utilized, the convergence rate of the AFSA is increased, and the solution of long-term optimized scheduling of the cascade power station is realized from the aspect of man-machine interaction. Compared with the prior art, the method greatly improves the relevant limitations such as overlong time consumption in the solving process of the cascade library group.
Drawings
Fig. 1 is an architectural diagram of MAAFSA.
Fig. 2 is a flowchart of the solution of MAAFSA.
Fig. 3(a) is a station water level process.
Fig. 3(b) is a station a power take-off process.
Fig. 3(c) is a B station water level process.
FIG. 3(d) is the B station power out process.
Fig. 3(e) is the C station water level process.
FIG. 3(f) is the C plant outtake process.
FIG. 4(a) is a graph showing the output load of each power station in dry water.
FIG. 4(b) is a graph of the output load of each power station in the horizontal year.
FIG. 4(c) is the output load diagram of each power station in the rich water year.
Fig. 5 is a lower-step total power generation variation process in different typical years.
Detailed Description
The invention is further described below with reference to the figures and examples.
The method adopts the most common maximum model of the generated energy in the long-term optimized dispatching of the cascade power station to carry out research, namely the water level and the output change process of each power station in each time interval are obtained by knowing the initial and final water levels of each reservoir of the cascade power station and the interval flow of each time interval in the dispatching period, so as to achieve the purpose of maximizing the total generated energy in the dispatching period.
The objective function of the maximum model of the generated energy of the long-term optimized dispatching of the cascade power station is as follows:
Figure BDA0001845436930000031
Pi,t＝AiQi,tHi,t (2)
in the formula: e is the total power generation amount of each power station of the cascade in the dispatching period, kWh; n is the number of the cascade power stations; i is a power station serial number, i is 1, 2, …, N; t is the total number of scheduling time periods; t is the time period number, T is 1, 2, …, T; pi,tThe average output of the power station i in the time period t is kW; deltatHours of time period t, h; a. theiThe output coefficient of the power station i; qi,tFor the generation flow of station i during time t, m3/s；Hi,tIs the generating head, m, of the station i at time t.
In order to ensure the maximum power generation and the safety and stability of the power station, the maximum power generation model for the long-term optimized dispatching of the cascade power station needs to meet the following constraint conditions:
A. water balance constraint
Vi,t+1＝Vi,t+3600×(qi,t-Qi,t-di,t)×Δt (3)
In the formula: vi,t+1And Vi,tRespectively, the storage capacity m of the power station i in the time period t +1 and the time period t3；qi,t、Qi,t、di,tRespectively the warehousing flow, the power generation flow and the water discharge flow m of the power station i in the time period t3/s；ΔtThe number of hours, h, corresponding to the period t.
B. Water level restraint
Figure BDA0001845436930000032
In the formula: zi,tThe reservoir water level m of the power station i in the time period t;
Figure BDA0001845436930000033
Zi,trespectively the upper limit and the lower limit, m, of the reservoir water level of the power station i in the time period t.
C. Beginning and end water level control constraints
Figure BDA0001845436930000034
In the formula:
Figure BDA0001845436930000035
is the initial water level, m, of the power station i;
Figure BDA0001845436930000036
is the scheduling end-of-term water level, m, for station i.
D. Power generation flow restriction
Figure BDA0001845436930000037
In the formula: qi,tFor the generation flow of station i during time t, m3/s；
Figure BDA0001845436930000038
Qi,tThe upper limit and the lower limit of the generating flow of the power station i in the time period t, m3/s。
E. Outbound flow constraint
Figure BDA0001845436930000041
In the formula: qi,t、di,tRespectively the generating flow and the water discharge m of the power station i in the time period t3/s；
Figure BDA0001845436930000042
Oi,tRespectively an upper limit and a lower limit m of the ex-warehouse flow of the power station i in the time period t3/s。
F. Power station output constraints
Figure BDA0001845436930000043
In the formula: pi,tThe average output of the power station i in the time period t is kW;
Figure BDA0001845436930000044
Pi,trespectively the upper limit and the lower limit of the output of the power station i in the time period t, kW.
G. Step system output constraint
Figure BDA0001845436930000045
In the formula: pi,tThe average output of the power station i in the time period t is kW; h istThe lower output limit of the cascade system in the time period t is kW.
The multi-Agent artificial fish swarm algorithm model construction based on the maximum cascade power generation model utilizes an MAAFSA algorithm, essentially, a plurality of Agent modules with different functions are constructed from the view point of distributed computation, and then the AFSA solving step is divided into a plurality of sub-problems. And solving the subproblems hierarchically according to coordination, cooperation and intelligent interaction among the Agent modules. The MAAFSA constructs five Agent modules with different functions, including a Core Agent (CA), a Group Agent (GA), an Action Agent (AA), an Evaluation Agent (EA) and a Judgment Agent (JA). Fig. 1 is an architectural diagram of MAAFSA. Fig. 2 is a flowchart of the MAAFSA solution.
The CA has the functions of creating a living environment of the artificial fish Agent, completing the setting of parameters such as the scale N of the artificial fish Agent, the maximum Visual field of the artificial fish and the like, and initializing N GAs. Each GA represents an artificial fish Agent, and the GA state is represented by the water level X of the reservoir in front of each power station dam in cascadeiAnd (4) showing. Wherein the content of the first and second substances,
Figure BDA0001845436930000046
d represents the number of stations of the cascade station group, i represents the GA serial number,
Figure BDA0001845436930000047
representing the pre-dam reservoir level of the kth stage plant.
The AA mainly consists of four basic behaviors including a foraging Action Agent (PAA), a Swarm Action Agent (SAA), a tail-end Action Agent (FAA), and a random Movement Action Agent (MAA). The function of AA is to complete foraging, bunching, rear-end collisions and random mobility of each GA.
The task of the EA is to evaluate the current states of the GAs, then to select an execution behavior according to an optimal rule, and to realize the update of the GAs.
The evaluation of the GA state is determined by an objective function of the model with the maximum cascade power generation amount, and the GA state is better as the objective function value is larger.
Figure BDA0001845436930000051
In the formula: e is the total power generation amount of each power station of the cascade in the dispatching period, kWh; n is the number of the cascade power stations; i is a power station serial number, i is 1, 2, …, N; t is the total number of scheduling time periods; t is the time period number, T is 1, 2, …, T; pi,tThe average output of the power station i in the time period t is kW; deltatThe number of hours of time period t, h.
JA is responsible for stopping iterative computations and outputting optimal result operations.
The actions of the artificial fish Agent are basically described as follows:
a. foraging behavior
Initializing the state of the artificial fish Agent to XiFinding another state X in its field of view by close-range optimizationj，XjDetermined by the following equation:
Figure BDA0001845436930000052
Figure BDA0001845436930000053
in the formula, Xmax＝(x1,max,x2,max,…,xk,max,…,xd,max) Upper limit value, x, representing a feasible solution to the problemk,maxRepresenting the upper limit of the reservoir level of the power station k; xmin＝(x1,min,x2,min,…,xk,min,…,xd,min) Lower limit, x, representing a feasible solution to the problemk,minRepresenting the lower reservoir level limit of the power station k; r is the radius of the short-range search, r is the [0,1 ]](ii) a Rand (1-r,1+ r) represents a random number between (1-r,1+ r).
Determination of XjThereafter, the adaptive value g (X) is calculatedi) And g (X)j) If g (X)j)≥g(Xi) Then XiTo XjTo a new state to complete the foraging behavior
Figure BDA0001845436930000054
In the formula (I), the compound is shown in the specification,
Figure BDA0001845436930000055
the states of the artificial fish at the current position and the new position are respectively; xjThe optimal companion in the visual field range of the artificial fish is obtained; step is the moving Step length; rand () is a random number between 0 and 1.
Otherwise, another new state is found again through the close-range optimizing technology, whether the conditions are met or not is judged, and after Try-number operations are tried, if the foraging behavior is not executed, the random moving behavior is executed.
b. Cluster behavior
The artificial fish Agent executes the two principles of group behavior, mainly adherence: one is to try to move towards the central position of the partner in the visual field, and the other is to prevent excessive congestion. Now, the artificial fish Agent clustering behavior is described: setting the state of an artificial fish Agent as XiNumber of peers n in search field of viewfAnd central position X of the companioncenterWherein the definition of the companion in the field of view is determined in accordance with dij<Vaisul, wherein dij＝||Xi-XjAnd | l, representing the distance between two artificial fish agents. If g (X) is satisfiedcenter)/nf≥δg(Xi) If the central position of the companion is not excessively congested, XiTo XcenterDirection movement to a new position
Figure BDA0001845436930000061
The movement pattern is determined by equation (14). And if the artificial fish Agent does not conform to the principle of the clustering behavior, executing the foraging behavior.
Figure BDA0001845436930000062
In the formula (I), the compound is shown in the specification,
Figure BDA0001845436930000063
the states of the artificial fish at the current position and the new position are respectively; xcenterIs the central position of the companion; step is the moving Step length; rand () is a random number between 0 and 1.
c. Rear-end collision behavior
Setting the state of the artificial fish Agent as XiWith the optimal companion in the field of view being XjIf g (X) is satisfiedj)/nf≥δg(Xi) Then, it indicates that the vicinity of the optimal companion is not congested, XiTo XjNew position of direction movement
Figure BDA0001845436930000064
And finishing the rear-end collision behavior. The movement pattern is determined by equation (15). And if the artificial fish Agent does not meet the rear-end action condition, executing foraging action:
Figure BDA0001845436930000065
in the formula (I), the compound is shown in the specification,
Figure BDA0001845436930000066
the states of the artificial fish at the current position and the new position are respectively; xjView the artificial fishOptimal peers within range; step is the moving Step length; rand () is a random number between 0 and 1.
d. Random movement behavior
The random movement behavior refers to artificial fish Agent XiRandomly moving one step to a new state in the visual field, wherein the moving mode is determined by the following formula:
Figure BDA0001845436930000067
in the formula (I), the compound is shown in the specification,
Figure BDA0001845436930000068
the states of the artificial fish at the current position and the new position are respectively; visual artificial fish maximum Visual field; step is the moving Step length; rand () is a random number between 0 and 1.
According to the thought, the algorithm model and the solving method based on the long-term optimization scheduling of the maximum generating capacity gradient library group are realized according to the following steps (1) to (5):
(1) the CA firstly receives a long-term optimization scheduling instruction of the gradient library group and starts to initialize each parameter. N GAs are randomly generated within the feasible region. Then parameters such as a maximum moving Step, a maximum Visual field of the artificial fish, a crowding factor delta, a maximum trial number Try-number and the like are transmitted to AA, and a maximum iteration number T is transmitted to JA;
(2) each GA respectively carries out information interaction with four AA (PAA, SAA, FAA and MAA), the four behaviors are simulated and executed, and maximum values generated by the respective behaviors are respectively transmitted to EA;
(3) the EA evaluates and compares the four behaviors, and selects an execution behavior;
(4) executing artificial fish behaviors, updating the artificial fish behaviors, and generating a new GA;
(5) JA judges whether the iteration time T meets the condition that T is less than or equal to T or whether the optimal solution difference value reaches a certain range continuously for multiple times. If yes, turning to the step (2) and continuing the iteration operation; otherwise, ending the calculation process and outputting the current optimal result;
the A, B, C, D power stations in a certain territory are taken as an example for research, and the total installed capacity of the four power stations reaches 3145 MW. The D power station belongs to a daily regulation power station, the function of utilizing a water head to generate power is generally only required to be considered in the step long-term optimization scheduling calculation, and the reservoir regulation function is ignored. The plant sequence was A, B, D, C.
As can be seen from Table 1, when the MAAFSA is adopted for solving, the power generation of the whole cascade of the dry year, the open year and the rich year respectively reaches 89.47 hundred million kWh, 112.49 hundred million kWh and 129.81 hundred million kWh, and the actual scheduling results of the cascade power station are relatively met. When the MAAFSA is adopted to solve the complex cascade reservoir scheduling problem, the global optimal solution of the problem can be found under certain conditions, and the solving quality meets the actual engineering scheduling requirement. In terms of solution time, in the horizontal year as an example, MAAFSA solution requires about 29.3s, whereas conventional AFSA solution requires about 34.5 s. The calculation effect of the MAAFSA can meet the actual engineering application requirements in the aspect of calculation efficiency, and the functional Agent modules can play a very positive role through cooperation and cooperation. Therefore, ideal results can be obtained by using the MAAFSA to solve the long-term optimized scheduling of the cascade base group under different typical annual conditions, and a calculation reference can be provided for the long-term optimized scheduling of other basin cascade power stations.
Fig. 3(a) to 3(f) show the power output process of each station. Fig. 4(a) -4 (c) are graphs of the output load of each power station under three typical year conditions of dry year, open year and rich year. Fig. 5 is a lower-step total power generation variation process in different typical years. For the A of the faucet power station, in order to achieve the overall step benefit, power generation is basically not performed in the flood season, the main task of the reservoir is to participate in compensation adjustment, and the water level is gradually raised in the flood season so as to fully store water. The water level slowly falls down in the dry period, and the main task is to supplement water for a downstream reservoir while generating electricity, so that the generated energy of the whole cascade station group is increased. And after the power station B is rapidly stored in the flood season, the power station B is always maintained in a high water head state to generate power. As D of the daily regulation hydropower station, the water level is basically kept unchanged, and how much water generates electricity. The installed capacity of the C power station is large and reaches 1250 MW. Therefore, the water level amplitude is small in the whole scheduling period, and the water level is kept to operate at a high water head as far as possible so as to reduce water consumption and increase power generation quantity.
TABLE 1 comparison of optimization results under different typical annual conditions
Figure BDA0001845436930000071

Claims (1)

1. A cascade library long-term optimization scheduling method based on a multi-Agent artificial fish swarm algorithm comprises five modules, namely a core Agent module CA, a swarm Agent module GA, a behavior Agent module AA, an evaluation Agent module EA and a judgment Agent module JA; the AA comprises four basic behaviors, namely a foraging behavior Agent, a PAA (poly a aid), a clustering behavior Agent, an SAA (SAA), a rear-end behavior Agent, an FAA (far-end association) and a random movement behavior Agent and an MAA (mobile access Agent); the method is characterized by comprising the following steps:
(1) the CA firstly receives a long-term optimization scheduling instruction of the step library group and starts to initialize each parameter; randomly generating N GAs in a feasible domain range; then, transmitting the maximum moving Step length Step, the maximum Visual field Visual of the artificial fish, the crowding factor delta and the maximum trial times Try-number to AA, and transmitting the maximum iteration times T to JA;
(2) each GA respectively carries out information interaction with four basic behaviors of PAA, SAA, FAA and MAA, the four behaviors are simulated and executed, and maximum values generated by the behaviors are respectively transmitted to EA;
(3) the EA evaluates and compares the four behaviors, and selects an execution behavior;
A. foraging behavior
Figure FDA0003131103630000011
In the formula (I), the compound is shown in the specification,
Figure FDA0003131103630000012
the states of the artificial fish at the current position and the new position are respectively; xjThe optimal companion in the visual field range of the artificial fish is obtained; step is the maximum moving Step length; rand () is a random number between 0 and 1;
calculating an adaptation value g (X)i) And g (X)j) If g (X)j)≥g(Xi) Then XiTo XjIf the foraging behavior is not executed yet after Try-number operations are tried, a random moving behavior is executed;
B. cluster behavior
Figure FDA0003131103630000013
In the formula (I), the compound is shown in the specification,
Figure FDA0003131103630000014
the states of the artificial fish at the current position and the new position are respectively; xcenterIs the central position of the companion; step is the maximum moving Step length; rand () is a random number between 0 and 1;
setting the state of the artificial fish Agent as XiNumber of peers n in search field of viewfAnd central position X of the companioncenterWherein the definition of the companion in the field of view is determined in accordance with dij<Visual, wherein dij＝||Xi-Xj| |, which represents the distance between two artificial fish agents; if g (X) is satisfiedcenter)/nf≥δg(Xi) If the central position of the companion is not excessively congested, XiTo XcenterDirection movement to a new position
Figure FDA0003131103630000015
If the artificial fish Agent does not conform to the principle of the clustering behavior, executing the foraging behavior;
C. rear-end collision behavior
Figure FDA0003131103630000021
In the formula (I), the compound is shown in the specification,
Figure FDA0003131103630000022
the states of the artificial fish at the current position and the new position are respectively; xjThe optimal companion in the visual field range of the artificial fish is obtained; step is the maximum moving Step length; rand () is a random number between 0 and 1;
setting the state of the artificial fish Agent as XiWith the optimal companion in the field of view being XjIf g (X) is satisfiedj)/nf≥δg(Xi) Then, it indicates that the vicinity of the optimal companion is not congested, XiTo XjNew position of direction movement
Figure FDA0003131103630000023
Finishing the rear-end collision behavior; if the artificial fish Agent does not meet the rear-end action condition, executing foraging action;
D. random movement behavior
Figure FDA0003131103630000024
In the formula (I), the compound is shown in the specification,
Figure FDA0003131103630000025
the states of the artificial fish at the current position and the new position are respectively; visual is the maximum Visual field of the artificial fish; step is the maximum moving Step length; rand () is a random number between 0 and 1;
(4) executing artificial fish behaviors, updating the artificial fish behaviors, and generating a new GA;
(5) JA judges whether the iteration time T meets the condition that T is less than or equal to T or whether the continuous multiple optimal solution difference value reaches the required range; if yes, turning to the step (2) and continuing the iteration operation; otherwise, ending the calculation process and outputting the current optimal result;
the method comprises the following steps of taking the maximum generated energy as a target, and taking the target function of a maximum generated energy model of the long-term optimized dispatching of the cascaded power station as:
Figure FDA0003131103630000026
Pi,t＝AiQi,tHi,t
in the formula: e is the total power generation amount of each power station of the cascade in the dispatching period, kWh; n is the number of the cascade power stations; i is a power station serial number, i is 1, 2, …, N; t is the total number of scheduling time periods; t is the time period number, T is 1, 2, …, T; pi,tThe average output of the power station i in the time period t is kW; deltatHours of time period t, h; a. theiThe output coefficient of the power station i; qi,tFor the generation flow of station i during time t, m3/s；Hi,tThe power generation head m of the power station i in the time period t;
the constraint that the maximum model of the generated energy of the long-term optimized dispatching of the cascade power station needs to meet is as follows:
a. water balance constraint
Vi,t+1＝Vi,t+3600×(qi,t-Qi,t-di,t)×Δt
In the formula: vi,t+1And Vi,tRespectively, the storage capacity m of the power station i in the time period t +1 and the time period t3；qi,t、Qi,t、di,tRespectively the warehousing flow, the power generation flow and the water discharge flow m of the power station i in the time period t3/s；ΔtH is the number of hours corresponding to the time period t;
b. water level restraint
Figure FDA0003131103630000031
In the formula: zi,tThe reservoir water level m of the power station i in the time period t;
Figure FDA0003131103630000032
Z i,trespectively representing the upper limit and the lower limit m of the reservoir water level of the power station i in the time period t;
c. beginning and end water level control constraints
Figure FDA0003131103630000033
In the formula:
Figure FDA0003131103630000034
is the initial water level, m, of the power station i;
Figure FDA0003131103630000035
the scheduling end-of-term water level, m, for the power station i;
d. power generation flow restriction
Figure FDA0003131103630000036
In the formula: qi,tFor the generation flow of station i during time t, m3/s；
Figure FDA0003131103630000037
Q i,tThe upper limit and the lower limit of the generating flow of the power station i in the time period t, m3/s；
e. Outbound flow constraint
Figure FDA0003131103630000038
In the formula: qi,t、di,tRespectively the generating flow and the water discharge m of the power station i in the time period t3/s；
Figure FDA0003131103630000039
O i,tRespectively an upper limit and a lower limit m of the ex-warehouse flow of the power station i in the time period t3/s；
f. Power station output constraints
Figure FDA00031311036300000310
In the formula: pi,tThe average output of the power station i in the time period t is kW;
Figure FDA00031311036300000311
P i,trespectively representing the upper limit and the lower limit of the output power of the power station i in a time period t, kW;
g. step system output constraint
Figure FDA00031311036300000312
In the formula: pi,tThe average output of the power station i in the time period t is kW; h istThe lower output limit of the cascade system in the time period t is kW.
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