CN116227863A - Cascade hydropower station optimal scheduling method based on Harris eagle optimization algorithm - Google Patents
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Abstract
The invention relates to the technical field of cascade hydropower station optimal scheduling, in particular to a cascade hydropower station scheduling method based on a Harris eagle algorithm, which comprises the following steps: s1, establishing an optimal scheduling model of the cascade hydropower station by taking the maximum generating capacity of the cascade hydropower station in a scheduling period as an optimal target and taking the constraint conditions of the reservoir capacity constraint, the output constraint, the power generation reference flow constraint and the water balance constraint of the cascade hydropower station as constraint conditions; s2, solving the cascade hydropower station optimizing and scheduling model established in the step S1 by adopting a Harris eagle optimizing algorithm, and outputting to obtain an optimal objective function value and a water level reservoir capacity state of the cascade hydropower station in each stage. By adopting the optimized dispatching method provided by the invention, the cascade hydropower station can meet the risk constraint of each stage in the dispatching period, the water resource is reasonably utilized, the comprehensive income of the cascade hydropower station is improved, and scientific theoretical basis and technical guarantee are provided for the real-time dispatching of the cascade hydropower station.
Description
Technical Field
The invention relates to the technical field of cascade hydropower station optimal scheduling, in particular to a cascade hydropower station scheduling method based on a Harris eagle algorithm.
Background
The effective utilization of the water energy is an important ring in the development planning of renewable energy sources, and has great significance for the comprehensive treatment of rivers and lakes and the improvement of economic benefits in the river basin range. As the water resources of China are rich, the distribution pattern of cascade reservoir group joint scheduling is gradually formed since the 21 st century. The joint optimization scheduling of the cascade hydropower station group can enable the water flow field resource, the power generation flow of each hydropower station, the power generation water head and the storage capacity energy storage to be fully utilized, so that more benefits are brought to the electric power market. However, the runoff prediction of the water basin is influenced by uncertain factors in the prediction of the warehouse-in flow of each power station, and complex water quantity relations exist among all levels of hydropower stations. Over time, the time delay and loss effects of water quantity transmission become more and more severe, so that the optimization problem becomes more and more complex, and the problem generally has the characteristics of high dimensionality, multiple stages, randomness, nonlinearity and the like.
The current optimization scheduling methods for solving the cascade hydropower stations are roughly divided into two types: the first category is traditional methods, including linear programming, nonlinear programming, and dynamic programming; the second type is a population intelligent optimization algorithm, which comprises heuristic algorithms such as an ant colony algorithm, a genetic algorithm, a particle swarm algorithm and the like. However, the former has the problems of complex calculation, overlong solving time and the like, and the latter has the problems of easy sinking into local optimum, unstable result and the like. Therefore, how to accurately and effectively solve the optimal scheduling problem of the cascade hydropower station is an urgent problem to be solved by the technicians in the field.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides a cascade hydropower station optimal scheduling method based on a Harris eagle optimization algorithm, which solves the problems that the runoff prediction of a water basin and the warehouse-in flow prediction of each power station are influenced by uncertain factors, the time delay and the loss of water quantity transmission are caused as time goes on, and the like due to complex water quantity relation among hydropower stations at all levels, and specifically adopts the following technical scheme:
s1, establishing an optimal scheduling model of the cascade hydropower station by taking the maximum generating capacity of the cascade hydropower station in a scheduling period as an optimal target and taking the constraint conditions of the reservoir capacity constraint, the output constraint, the power generation reference flow constraint and the water balance constraint of the cascade hydropower station as constraint conditions;
s2, solving the cascade hydropower station optimal scheduling model in the step S1 by adopting a Harris eagle algorithm, and outputting to obtain an optimal objective function value and a water level reservoir capacity state of the cascade hydropower station in each stage.
Preferably, step S1 specifically includes:
the maximum generating capacity of the cascade hydropower station in the scheduling period is taken as an optimal target, and an objective function is established as follows:
in the formula (1), E is the total power generation amount of the cascade hydropower station, and the unit is kilowatt-hour; n is the total number of the cascade hydropower stations; t is the total time period number in the scheduling period; n (N) i，t The average output of the ith hydropower station in the t period is shown as kilowatts; Δt is the total duration of each period in seconds; k (K) i The output coefficient of the ith hydropower station; q i，t The average power generation flow of the ith hydropower station in the t period is expressed as square meters per second; h i，t The average power generation water head of the ith hydropower station in the t period is given in meters;
determining model constraint conditions by using reservoir capacity constraint, output constraint, power generation reference flow constraint and water balance constraint of a cascade hydropower station, wherein the model constraint conditions are specifically as follows:
reservoir capacity water level constraint: v (V) i，min ≤V i，t ≤V i，max (2)
Force constraint: n (N) i，min ≤N i，t ≤N i，max (3)
Power generation references flow constraints:
water balance constraint:
in the formula (5), the amino acid sequence of the compound,
in the formulae (2) to (6), V i，t For the ith hydropower station, the initial storage capacity of the ith hydropower station in the period t is measured in cubic meters, V i，min、 V i，max Limiting the storage capacity to the minimum and maximum of the ith hydropower station; n (N) i，min 、N i，max Minimum and maximum limiting output for the ith hydropower station;
limiting the power generation reference flow for the minimum and maximum of the ith hydropower station in the t period; v (V) i，t+1 For the storage capacity of the ith hydropower station at the end of the period t, +.>
The average warehouse-in flow of the ith hydropower station in the t period is the (i) th-1 th hydropower station in the t periodAverage out-of-stock flow.
It is also preferred that step S2 specifically comprises the sub-steps of:
step 2.1, initializing variables: setting the population size G of Harris eagle, and setting the maximum iteration number as T m =10000, randomly generating initial state of the Harris eagle position, i.e. initial optimal scheduling scheme { q i，t The decision variable of the model is the average power generation flow q of each stage of the cascade hydropower station i，t Generating an initial scheduling scheme according to random number simulation through generating reference flow constraint conditions:
in the formula (7), rand is [0,1]Random numbers between the two; determining the initial storage capacity { V (V) of each hydropower station in the initial stage i，1 }；
Step 2.2, adopting an elite reverse learning mechanism to optimize the population:
in the formula (8), the amino acid sequence of the compound,
in the reverse elite learning mechanism, a reverse population newly constructed by the original population; eta is [0,1]Random number, alpha i ＝min(q i，t )，β i ＝max(q i，t )；
Step 2.3, calculating a fitness function, taking the total power generation amount in the step hydropower station scheduling period as a population fitness value, and comparing F (q i，t ) And (3) with
Updating the size of population q involved in the iteration i，t And recording the population fitness value of each iteration:
in the formula (9), I t For the population fitness value calculated by the T-th iteration, E is the total power generation amount of the cascade hydropower station, N is the total number of the cascade hydropower stations, T is the total time period number in the scheduling period, and N i，t For the average output of the ith hydropower station in the t period, delta t is the total duration of each period, K i For the output coefficient of the ith hydropower station, q i，t For the average delivery flow rate of the ith hydropower station in the t period, H i，t An average power generation water head of the ith hydropower station in the t period;
and 2.4, updating the population position.
Further preferably, substep 2.4 further comprises the substeps of:
step 2.4.1, calculating the escape energy of the prey and quantitatively calculating the jumping behavior during the escape of the prey in a transition stage:
W＝2W 0 *(1-t/T m ) (10)
J＝2(1-rand) (11)
in the formulas (10) - (11), W is the energy for simulating the escape of rabbits; w (W) 0 Representing the initial state of the energy, and the calculation formula is W 0 =2rand-1; j is the jump distance during the escape of the rabbit, and rand is [0,1 ]]Random number between, T is the current iteration number, T m The maximum iteration number; if the I W I is more than 1, turning to a global exploration stage of the step 2.4.2, otherwise turning to a local development stage of the step 2.4.3;
2.4.2, in the global exploration stage, the Harriset algorithm explores based on randomly selecting one individual information and self information, or explores based on the current optimal individual information and the average information of all individuals:
in the formula (12), the amino acid sequence of the compound,
for the population position of the next iteration, +.>
In order to randomly obtain an individual from a population,
for the optimal population individuals in the iteration, UB and LB are respectively the upper limit and the lower limit of the population searching space, r 1 、r 2 、r 3 、r 4 Q are all 0,1]Random numbers between the two;
For the average position of the current population, the calculation formula is as follows:
in the formula (13), G is the population size; if T is less than T at this time m Returning to the step 2.2, otherwise, terminating the operation output result;
step 2.4.3, in the local development stage, dividing the actual attack behavior of the harris eagle into the following four strategies through parameters W and r; wherein, when r is less than 0.5, the hunting can successfully escape before the hawk attack, and when r is more than or equal to 0.5, the hunting cannot escape before the hawk attack;
strategy 1: when the |W| is more than or equal to 0.5 and r is more than or equal to 0.5, the soft attack strategy is as follows:
in formula (14), Δq i，t The calculation formula is as follows for the position difference between the optimal individual and other individuals in the population:
if T is less than T at this time m Returning to the step 2.2, otherwise, terminating the operation output result;
strategy 2: when |W| < 0.5 and r is larger than or equal to 0.5, the method is a hard attack strategy:
if T is less than T at this time m Returning to the step 2.2, otherwise, terminating the operation output result;
strategy 3: when the |W| is more than or equal to 0.5 and r is less than 0.5, the progressive rapid dive soft tapping strategy is as follows:
in the formula (17), Y is a heuristic dive made by a population, and if no effect is obtained, irregular dive Z is performed when approaching a prey; wherein, the calculation formulas of Y and Z are as follows:
Z＝Y+S*LF(D) (19)
in the formulas (18) - (19), D is the dimension of the optimization problem, and S is a 1*D-dimensional random vector; wherein, the expression of LF is:
LF(x)＝0.01*(μ*σ)/|v| 1/β (20)
in the formulas (20) - (21), τ is a gamma function; mu and v are [0,1 ]]Random number in between, β is constant 0.5; if T is less than T at this time m Returning to the step 2.2, otherwise, terminating the operation output result;
strategy 4: when the absolute W is less than or equal to 0.5 and r is less than 0.5, the progressive rapid dive hard attack strategy is as follows:
if T is less than T at this time m And returning to the step 2.2, otherwise, terminating the operation output result.
The beneficial effects of the invention are as follows:
the invention aims to avoid sinking in a local optimal solution in the convergence process, and realizes a clear scheduling scheme for maximizing the total power generation amount in a scheduling period in order to find a global optimal solution; the method can solve the dimension disaster problem existing in the multi-stage optimal scheduling problem, reduces complex calculation, improves the operation efficiency of the cascade hydropower station scheduling management, avoids the resource waste caused by nonsensical start and stop, reasonably distributes and utilizes water resources, and provides scientific theory and technical guarantee for the cascade hydropower station real-time scheduling.
Drawings
The accompanying drawings, which constitute a part of this specification, are included to provide a further understanding of the application and are not to be construed as unduly limiting the application.
FIG. 1 is a flow chart of the Harris eagle optimization algorithm of the present invention.
Detailed Description
The invention will be further described with reference to the drawings and examples.
As shown in FIG. 1, the cascade hydropower station optimal scheduling method based on the Harris eagle optimization algorithm specifically comprises the following two steps:
s1, establishing an optimal scheduling model of the cascade hydropower station by taking the maximum generating capacity of the cascade hydropower station in a scheduling period as an optimal target and taking the constraint conditions of the reservoir capacity constraint, the output constraint, the power generation reference flow constraint and the water balance constraint of the cascade hydropower station as constraint conditions;
further, the step S1 specifically includes:
the maximum generating capacity of the cascade hydropower station in the scheduling period is taken as an optimal target, and an objective function is established as follows:
in the formula (1), E is the total power generation amount of the cascade hydropower station, and the unit is kilowatt-hour; n is the total number of the cascade hydropower stations; t is the total time period number in the scheduling period; n (N) i，t The average output of the ith hydropower station in the t period is shown as kilowatts; Δt is the total duration of each period in seconds; k (K) i The output coefficient of the ith hydropower station; q i，t The average power generation flow of the ith hydropower station in the t period is expressed as square meters per second; h i，t The average power generation water head of the ith hydropower station in the t period is given in meters;
determining model constraint conditions by using reservoir capacity constraint, output constraint, power generation reference flow constraint and water balance constraint of a cascade hydropower station, wherein the model constraint conditions are specifically as follows:
reservoir capacity water level constraint: v (V) i，min ≤V i，t ≤V i，max (2)
Force constraint: n (N) i，min ≤N i，t ≤N i，max (3)
Power generation references flow constraints:
water balance constraint:
in the formula (5), the amino acid sequence of the compound,
in the formulae (2) to (6), V i，t For the ith hydropower station, the initial storage capacity of the ith hydropower station in the period t is measured in cubic meters, V i，min 、V i，max Limiting the storage capacity to the minimum and maximum of the ith hydropower station; n (N) i，min 、N i，max Minimum and maximum limiting output for the ith hydropower station;
limiting the power generation reference flow for the minimum and maximum of the ith hydropower station in the t period; v (V) i，t+1 For the storage capacity of the ith hydropower station at the end of the period t, +.>
The average warehouse-in flow of the ith hydropower station in the t period is the average warehouse-out flow of the ith-1 hydropower station in the t period.
S2, solving the cascade hydropower station optimal scheduling model established in the step S1 by adopting a Harris eagle algorithm, and outputting to obtain an optimal objective function value and a water level reservoir capacity state of the cascade hydropower station at each stage;
further, the step S2 specifically includes the following sub-steps:
step 2.1, initializing variables, and setting the population size G of Harris eagle; the maximum iteration number is set as T m =10000; randomly generating initial state of the position of the Harrissin hawk group, namely an initial optimal scheduling scheme { q i，t The decision variable of the model is the average power generation flow q of each stage of the cascade hydropower station i，t Generating an initial scheduling scheme according to random number simulation through generating reference flow constraint conditions:
in the formula (7), rand is [0,1]Random numbers between the two; determining the initial storage capacity { V (V) of each hydropower station in the initial stage i，1 }；
Step 2.2, adopting an elite reverse learning mechanism to optimize the population:
in the formula (8), the amino acid sequence of the compound,
in the reverse elite learning mechanism, a reverse population newly constructed by the original population; eta is [0,1]Random number, alpha i ＝min(q i，t )，β i ＝max(q i，t )；
Step 2.3, calculating a fitness function, taking the total power generation amount in the step hydropower station scheduling period as a population fitness value, and comparing F (q i，t ) And (3) with
Size, update population q participating in iteration i，t Calculating the fitness value of each individual of the population in each iteration process and recording: />
In the formula (9), I t For the population fitness value calculated by the T-th iteration, E is the total power generation amount of the cascade hydropower station, N is the total number of the cascade hydropower stations, T is the total time period number in the scheduling period, and N i，t For the average output of the ith hydropower station in the t period, delta t is the total duration of each period, K i For the output coefficient of the ith hydropower station, q i，t For the average delivery flow rate of the ith hydropower station in the t period, H i，t An average power generation water head of the ith hydropower station in the t period;
and 2.4, updating the population position.
Still further, the substep 2.4 specifically includes the following substeps:
step 2.4.1, calculating the escaping energy of the prey and quantitatively calculating the jumping behavior (transitional phase) during the escaping process of the prey:
W＝2W 0 *(1-t/T m ) (10)
J＝2(1-rand) (11)
in the formulas (10) - (11), W is the energy for simulating the escape of rabbits, W 0 Representing the initial state of the energy, and the calculation formula is W 0 =2rand-1; j is the jump distance during the escape of the rabbit, and rand is [0,1 ]]Random number between, T is the current iteration number, T m The maximum iteration number; if the I W I is more than 1, turning to a global exploration stage of the step 2.4.2, otherwise turning to a local development stage of the step 2.4.3;
step 2.4.2, the harris eagle algorithm explores based on randomly selecting one individual information and self information, or explores based on the current optimal individual information and the average information of all individuals (global exploration phase):
in the formula (12), the amino acid sequence of the compound,
for the population position of the next iteration, +.>
In order to randomly obtain an individual from a population,
for the optimal population individuals in the iteration, UB and LB are respectively the upper limit and the lower limit of the population searching space, r 1 、r 2 、r 3 、r 4 Q are all 0,1]Random numbers between the two;
wherein,,
for the average position of the current population, the calculation formula is as follows:
in the formula (13), G is the population size; at this time T < T m Returning to the step 2.2, otherwise, terminating the operation output result;
step 2.4.3, dividing the actual attack behavior of the harris eagle into the following four strategies (local development stage) through parameters W and r; it is worth to say here that when r < 0.5, it means that the prey can successfully escape before the harris eagle attack, and when r is not less than 0.5, it means that the prey cannot escape before the harris eagle attack;
strategy 1: when the |W| is more than or equal to 0.5 and r is more than or equal to 0.5, the soft attack strategy is as follows:
in formula (14), Δq i，t The calculation formula is as follows for the position difference between the optimal individual and other individuals in the population:
if T is less than T at this time m Returning to the step 2.2, otherwise, terminating the operation output result;
strategy 2: when |W| < 0.5 and r is larger than or equal to 0.5, the method is a hard attack strategy:
if T is less than T at this time m Returning to the step 2.2, otherwise, terminating the operation output result;
strategy 3: when the |W| is more than or equal to 0.5 and r is less than 0.5, the progressive rapid dive soft tapping strategy is as follows:
in the formula (17), Y is heuristic dive made by the population; if no effect is obtained, irregular dive z is performed when approaching a prey; wherein, the calculation formula of Y and z is as follows:
Z＝Y+S*LF(D) (19)
in the formulas (18) - (19), D is the dimension of the optimization problem, and S is a 1*D-dimensional random vector; wherein, the expression of LF is:
LF(x)＝0.01*(μ*σ)/|v| 1/β (20)
in the formulas (20) - (21), τ is a gamma function; mu and v are [0,1 ]]Random number in between, β is constant 0.5; if T is less than T at this time m Returning to the step 2.2, otherwise, terminating the operation output result;
strategy 4: when the absolute W is less than or equal to 0.5 and r is less than 0.5, the progressive rapid dive hard attack strategy is as follows:
if T is less than T at this time m And returning to the step 2.2, otherwise, terminating the operation output result.
Examples:
firstly, selecting a Wujiang step hydropower station with a scheduling period of 1 month in the first ten days to 12 months in the last ten days as an optimization object, wherein specific parameters are shown in the following table 1:
TABLE 1 main parameters of Wujiang step hydropower station
By adopting the cascade hydropower station optimal scheduling method provided by the invention, each hydropower station scheduling decision scheme is obtained through a Harris eagle optimization algorithm, and the following list 2-5 is detailed:
table 2 flood home ferry hydropower station scheduling scheme
Table 3 Dongfeng hydropower station scheduling scheme
Table 4 hydropower station scheduling scheme for cableway
Table 5 Wujiang river crossing hydropower station scheduling scheme
From the data in tables 2-5, the following conclusions can be drawn:
in the table 2, the flood peak hydropower station keeps high water level water discharge to the lower power station in the dispatching period, and the total daily power generation amount is 1155.73 kilowatt-hours, compared with the average daily power generation amount 427.40 kilowatt-hours obtained by 15.6 hundred million kilowatt-hours conversion of the annual average power generation amount of the flood peak hydropower station in the table 1, the average daily power generation amount is improved by 170.41%;
similarly, in table 3, the reservoir capacity of the eastern wind hydropower station keeps rising trend in the dispatching process, and when the water storage and lifting head increase the total power generation amount, the generation of waste water caused by too much water discharge of the upstream water power station is reduced, and the total daily power generation amount is 862.23 kilowatt hours, which is improved by 35.65% compared with the average daily power generation amount 635.62 kilowatt hours obtained in table 1;
in table 4, the cableway hydropower station is the hydropower station with the minimum reservoir capacity in the Wujiang step hydropower station group, and the overall hydropower station also presents a water storage lifting water head multiple power generation trend, wherein the total daily power generation amount is 835.33 kilowatt hours, and is improved by 51.61% compared with the average daily power generation amount 550.96 kilowatt hours obtained in table 1;
in table 5, in the short-term dispatching of the Wujiang river hydropower station, the initial reservoir capacity is close to the dead water reservoir capacity, so that the water storage and lifting head is continuously carried out, the water storage and lifting head is used as the final hydropower station, the water storage is rich, meanwhile, the water storage is also high in power generation reference flow, the total daily power generation amount is 1451.57 kilowatt hours, and the average daily power generation amount is 1134.25 kilowatt hours, and is improved by 27.98% compared with the average daily power generation amount obtained in table 1.
It should be understood that the above description is not intended to limit the invention to the particular embodiments disclosed, but to limit the invention to the particular embodiments disclosed, and that the invention is not limited to the particular embodiments disclosed, but is intended to cover modifications, adaptations, additions and alternatives falling within the spirit and scope of the invention.
Claims (4)
1. The cascade hydropower station scheduling optimization method based on the Harris eagle algorithm is characterized by comprising the following steps of:
s1, establishing an optimal scheduling model of the cascade hydropower station by taking the maximum generating capacity of the cascade hydropower station in a scheduling period as an optimal target and taking the constraint conditions of the reservoir capacity constraint, the output constraint, the power generation reference flow constraint and the water balance constraint of the cascade hydropower station as constraint conditions;
s2, solving the cascade hydropower station optimal scheduling model in the step S1 by adopting a Harris eagle algorithm, and outputting to obtain an optimal objective function value and a water level reservoir capacity state of the cascade hydropower station in each stage.
2. The cascade hydropower station scheduling optimization method based on the harris eagle algorithm according to claim 1, wherein the step S1 specifically comprises:
establishing an objective function by taking the maximum power generation amount of the cascade hydropower station in the scheduling period as an optimal objective:
in the formula (1), E is the total power generation amount of the cascade hydropower station, and the unit is kilowatt-hour; n is the total number of the cascade hydropower stations; t is the total time period number in the scheduling period; n (N) i，t The average output of the ith hydropower station in the t period is shown as kilowatts; Δt is the total duration of each period in seconds; k (K) i The output coefficient of the ith hydropower station; q i，t The average power generation flow of the ith hydropower station in the t period is expressed as square meters per second; h i，t The average power generation water head of the ith hydropower station in the t period is given in meters;
determining model constraint conditions by using reservoir capacity constraint, output constraint, power generation reference flow constraint and water balance constraint of a cascade hydropower station, wherein the model constraint conditions are specifically as follows:
reservoir capacity water level constraint: v (V) i，min V i，t ≤V i，max (2)
Force constraint: n (N) i，min N i，t ≤N i，max (3)
Power generation references flow constraints:
water balance constraint:
in the formula (5), the amino acid sequence of the compound,
in the formulae (2) to (6), V i，t For the ith hydropower station, the initial storage capacity of the ith hydropower station in the period t is measured in cubic meters, V i，min 、V i，max Limiting the storage capacity to the minimum and maximum of the ith hydropower station; n (N) i，min 、N i，max Minimum and maximum limiting output for the ith hydropower station;
limiting the power generation reference flow for the minimum and maximum of the ith hydropower station in the t period; v (V) i，t+1 For the storage capacity of the ith hydropower station at the end of the period t, +.>
The average warehouse-in flow of the ith hydropower station in the t period is the average warehouse-out flow of the ith-1 hydropower station in the t period.
3. The cascade hydropower station scheduling optimization method based on the hawk algorithm according to claim 1, wherein the step S2 specifically comprises the following sub-steps:
step 2.1, initializing variables: setting the population size G of Harris eagle, and setting the maximum iteration number as T m =10000, randomly generated initial state of the group hashThe position of the Litsea, i.e. the initial optimal scheduling scheme { q } i，t The decision variable of the model is the average power generation flow q of each stage of the cascade hydropower station i，t Generating an initial scheduling scheme according to random number simulation through generating reference flow constraint conditions:
in the formula (7), rand is [0,1]Random numbers between the two; determining the initial storage capacity { V (V) of each hydropower station in the initial stage i，1 }；
Step 2.2, adopting an elite reverse learning mechanism to optimize the population:
in the formula (8), the amino acid sequence of the compound,
in the reverse elite learning mechanism, a reverse population newly constructed by the original population; eta is [0,1]Random number, alpha i ＝min(q i，t )，β i ＝max(q i，t )；
Step 2.3, calculating a fitness function, taking the total power generation amount in the step hydropower station scheduling period as a population fitness value, and comparing F (q i，t ) And (3) with
Updating the size of population q involved in the iteration i，t And recording the population fitness value of each iteration:
in the formula (9), I t For the population fitness value calculated by the t-th iteration, E is the total power generation amount of the cascade hydropower station, and N is the cascadeThe total number of the hydropower stations, T is the total time period number in the scheduling period, N i，t For the average output of the ith hydropower station in the t period, delta t is the total duration of each period, K i For the output coefficient of the ith hydropower station, q i，t For the average delivery flow rate of the ith hydropower station in the t period, H i，t An average power generation water head of the ith hydropower station in the t period;
and 2.4, updating the population position.
4. A cascade hydropower station scheduling optimization method based on a haustilago algorithm according to claim 3, wherein the substep 2.4 updates the population position, specifically comprising the following steps:
step 2.4.1, calculating the escape energy of the prey and quantitatively calculating the jumping behavior during the escape of the prey in a transition stage:
W＝2W 0 *(1-t/T m ) (10)
J＝2(1-rand) (11)
in the formulas (10) - (11), W is the energy for simulating the escape of rabbits; w (W) 0 Representing the initial state of the energy, and the calculation formula is W 0 =2rand-1; j is the jump distance during the escape of the rabbit, and rand is [0,1 ]]Random number between, T is the current iteration number, T m The maximum iteration number; if the I W I is more than 1, turning to a global exploration stage of the step 2.4.2, otherwise turning to a local development stage of the step 2.4.3;
2.4.2, in the global exploration stage, the Harriset algorithm explores based on randomly selecting one individual information and self information, or explores based on the current optimal individual information and the average information of all individuals:
in the formula (12), the amino acid sequence of the compound,
for the next iterationGroup position->
To randomly obtain an individual from a population, < +.>
For the optimal population individuals in the iteration, UB and LB are respectively the upper limit and the lower limit of the population searching space, r 1 、r 2 、r 3 、r 4 Q are all 0,1]Random numbers between the two;
For the average position of the current population, the calculation formula is as follows:
in the formula (13), G is the population size; if T is less than T at this time m Returning to the step 2.2, otherwise, terminating the operation output result;
step 2.4.3, in the local development stage, dividing the actual attack behavior of the harris eagle into the following four strategies through parameters W and r; wherein, when r is less than 0.5, the hunting can successfully escape before the hawk attack, and when r is more than or equal to 0.5, the hunting cannot escape before the hawk attack;
strategy 1: when the |W| is more than or equal to 0.5 and r is more than or equal to 0.5, the soft attack strategy is as follows:
in formula (14), Δq i，t The calculation formula is as follows for the position difference between the optimal individual and other individuals in the population:
if T is less than T at this time m Returning to the step 2.2, otherwise, terminating the operation output result;
strategy 2: when |W| < 0.5 and r is larger than or equal to 0.5, the method is a hard attack strategy:
if T is less than T at this time m Returning to the step 2.2, otherwise, terminating the operation output result;
strategy 3: when the |W| is more than or equal to 0.5 and r is less than 0.5, the progressive rapid dive soft tapping strategy is as follows:
in the formula (17), Y is a heuristic dive made by a population, and if no effect is obtained, irregular dive Z is performed when approaching a prey; wherein, the calculation formulas of Y and Z are as follows:
Z＝Y+S*LF(D) (19)
in the formulas (18) - (19), D is the dimension of the optimization problem, and S is a 1*D-dimensional random vector; wherein, the expression of LF is:
LF(x)＝0.01*(μ*σ)/|v| 1/β (20)
in the formulas (20) - (21), τ is a gamma function; mu and v are [0,1 ]]Random number in between, β is constant 0.5; if T is less than T at this time m Returning to the step 2.2, otherwise, terminating the operation output result;
strategy 4: when the absolute W is less than or equal to 0.5 and r is less than 0.5, the progressive rapid dive hard attack strategy is as follows:
if T is less than T at this time m And returning to the step 2.2, otherwise, terminating the operation output result.
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