CN112633674B - Mid-term peak regulation scheduling method for cascade reservoir group coupled with water flow time lag - Google Patents
Mid-term peak regulation scheduling method for cascade reservoir group coupled with water flow time lag Download PDFInfo
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Abstract
The invention provides a cascade reservoir medium-term peak regulation scheduling method coupled with water flow delay aiming at frequent fluctuation of power grid daytime load and complex hydraulic connection of a cascade reservoir group. Firstly, constructing a multi-target model of power grid medium-term dispatching according to the target of optimal power grid peak regulation and maximum cascade power generation amount; then, a middle-stage segmental water flow delay description method and a parameter determination method are provided based on a water quantity balance principle, and a calculation method of scheduling period and delay period cascade comprehensive benefits under the influence of water flow delay is determined according to the middle-stage segmental water flow delay description method and the parameter determination method; and finally, fitting complex nonlinear constraints in the model by using a polynomial. The calculation result of taking the 11-seat cascade hydropower station in the laneway river as a research object shows that the calculation result of the method is more consistent with the actual operation condition by introducing the water flow time-lag factor, so that the scheduling plan deviation influenced by the hysteresis is effectively reduced, the water and electricity utilization benefit is improved, and the method has a good medium-term peak regulation effect.
Description
Technical Field
The invention belongs to the field of power grid planning and dispatching operation, and particularly relates to a mid-term peak shaving dispatching method for a cascade reservoir group coupled with water flow delay.
Background
In recent years, factors such as continuous aggravation of daily load fluctuation of power demand, medium-short term heavy rainfall and the like bring severe challenges to power generation scheduling of a power grid in a water and electricity rich region in China. Extreme climatic events such as high-temperature severe summer heat, severe winter icing and the like occur frequently, so that the power load demand difference between adjacent days is larger and larger, and a large number of thermal power generating units need to be started and stopped frequently in the middle dispatching process of a power grid to cope with load changes; on the other hand, due to the influence of climate change, extreme weather such as typhoon and rainstorm causes more water to come from the middle of the basin, and a large amount of water is possibly generated due to improper hydropower dispatching. In order to fully exert the adjusting advantages and load tracking capacity of hydropower and improve the utilization efficiency of the cascade hydropower, fine modeling research needs to be carried out on the medium-term dispatching of the cascade hydropower.
The medium-term dispatching of the reservoir group generally refers to the planning and the making of a hydropower station plan which takes day as a calculation step length and takes 7-30 days as a calculation period, and is a key process for carrying out long-term and short-term dispatching. The hydropower medium-term dispatching generally models the targets such as the maximum generated energy or the maximum guaranteed output, and the research on the target of the stable medium-term load process is less. The cascade hydropower stations have a close water flow delay relation, when the upstream and downstream steps are far away, the water flow delay often reaches hours or even days, if the arrangement plan is neglected, the influence of the water flow delay can cause a great deviation between the plan and the actual situation, and further, the hydropower station can generate a great amount of water abandon or undergeneration. However, in the existing research, the water flow time lag is considered more in short-term scheduling, and the calculation modes of the water flow time lag mainly aim at the situation that the calculation step length is 1 hour or shorter, the benefit influence of the water amount in the lag phase is rarely and comprehensively considered, and the water flow time lag cannot be directly applied to medium-term scheduling taking day as the calculation step length.
Therefore, aiming at the daytime load demand of frequent fluctuation of a power grid and the complex hydraulic connection existing in a cascade hydropower station group, a middle-stage segmental water flow time lag method and a cascade time lag comprehensive benefit calculation method are provided, and a multi-target middle-stage scheduling model with the maximum generated energy and the optimal peak regulation is established on the basis of the middle-stage segmental water flow time lag method and the cascade time lag comprehensive benefit calculation method; in the solving process, a polynomial is adopted to fit complex nonlinear constraints, and finally, 11-step hydropower stations in the lankenjiang dry flow are used as research objects to perform calculation verification.
Disclosure of Invention
The invention provides a cascade reservoir group middle-term peak regulation scheduling method coupled with water flow lag, provides a segmented water flow lag time method of a scheduling period and a lag period based on a water quantity balance principle and a calculation method of cascade lag time comprehensive benefits, and simultaneously adopts a multi-target strategy to give consideration to peak regulation and power generation benefits so as to reasonably arrange a middle-term scheduling output plan, reduce scheduling plan deviation influenced by lag, solve complex peak regulation tasks and improve power generation benefits.
The technical scheme of the invention is as follows:
a coupling water flow time lag cascade reservoir medium-term multi-target peak regulation dispatching method obtains a feasible cascade reservoir medium-term peak regulation dispatching plan according to the following steps (1) - (3):
(1) and a water quantity balance principle-based sectional water flow time-delay method in a scheduling period and a lag period is adopted.
(2) And calculating the step time-lag comprehensive benefit for reducing the influence of hysteresis.
(3) And (4) characterizing the complex nonlinear constraint by using a polynomial.
Compared with the prior art, the invention has the following beneficial effects:
(1) the proposed middle-term peak regulation model fully considers the frequent fluctuation of the daytime load and the complex hydropower power constraint and utilizes the complementary coordination characteristic of the cascade hydropower. The peak regulation requirement of the power grid is met, and meanwhile, a more refined and practical medium-term cascade dispatching plan is made by considering the water flow delay factor.
(2) A water quantity balance principle-based sectional water flow time delay linearization method for a dispatching period and a delay period and a step time delay comprehensive benefit calculation method are provided, and deviation of a power station output dispatching plan and target benefits influenced by water flow time delay can be effectively reduced.
(3) The multi-target strategy is adopted to give consideration to peak regulation and power generation benefits, peak regulation pressure can be effectively reduced, hydroelectric power generation benefits can be improved, stable operation of a power grid load system is guaranteed, and certain reference and reference are provided for the mid-term optimization scheduling problem of a complex peak regulation task.
Drawings
FIG. 1 is a schematic view of a step water balance relationship;
FIG. 2 is a schematic illustration of a stepped hydraulic relationship;
FIG. 3 is a flowchart of a mid-term dispatch model solution for a gradient reservoir group;
FIG. 4(a) is a flood season power grid load schematic diagram;
FIG. 4(b) is a schematic diagram of the grid load during the dry period;
FIG. 5 is a schematic diagram of a force optimization process;
FIG. 6 is a schematic diagram of optimal solution distribution under different weighting coefficients;
FIG. 7(a) is a flood season scene diagram;
fig. 7(b) is a schematic diagram of a dry period scenario.
Detailed Description
The invention is further described in the following with reference to the accompanying drawings and examples.
The invention relates to a method for scheduling mid-term peak shaving of a cascade bank group coupled with water flow time lag, which comprises two objective functions:
1) and (4) peak shaving optimization target. The hydropower peak regulation is that under satisfying electric wire netting and power station safety constraint condition, make full use of the characteristics that the hydropower speed of regulation is fast, traceability is strong, adjust system load peak value, make the surplus process of exerting oneself for thermal power as far as possible even to reduce the number of times that the thermal power unit opens and stops, here adopt the minimum target of surplus load variance:
in the formula: i is a power station number; n is the total power station number; t is a time interval number; t is the total number of time segments in the planning period, the planning period 15d is adopted in the embodiment, and the step length is 1 d; p t System load demand, MW, for time period t; FN (FN) t The system residual load, MW, for time period t;
mean residual load, MW; n is a radical of i,t The output, MW, of the station i time period t.
2) And (5) a maximum target of step power generation. In the scheduling process of the cascade hydropower station considering the influence of water flow time lag on benefits, the maximum calculation period generating capacity is the target:
maxF 2 ＝Ea+Eb (2)
in the formula: ea is the benefit generated by participating in the dispatching operation of the cascade hydropower station in the dispatching period; eb is the balance benefit of the scheduling period out to avoid the effects of water flow hysteresis.
Converting the multi-target model into a single target by adopting a weight coefficient method, and performing normalization processing on each target solution set by using a formula (3), wherein omega is 1 ,ω 2 Is the target weight, ω 1 ,ω 2 E (0,1) and satisfies omega 1 +ω 2 If 1, the target model is established as shown in formula (4):
maxF(x)＝ω 1 F 1 ′(x)+(1-ω 1 )F 2 ′(x) (4)
the following constraints need to be satisfied:
A. water balance equation:
in the formula: Δ t is the period length, 1 d; v i,t The storage capacity m at the end of the i time period t of the power station 3 ；
I i,t 、Q i,t 、S i,t 、
Respectively the warehousing flow, the interval flow, the power generation flow, the abandoned water flow and the ex-warehouse of the power station at the i time period tFlow rate, m 3 /s；
For the delivery of upstream station k at time period n, m 3 /s；Ω i A set of direct upstream plants k being plants i;
the time lag time ex-warehouse flow of the power station k directly upstream of the power station i reaches the sum of the power station i in the time t.
B. Setting the water level at the beginning and the end:
in the formula:
the start and end water levels, m, are given for the station i, respectively.
C. Water level-reservoir capacity relationship and constraint:
V i,min ≤V i,t ≤V i,max (11)
in the formula:
the water level m of the power station i on the dam in the time period t; f. of i ZV Is the water level-reservoir capacity function of the power station i; z i,min And Z i,max Respectively representing the lower limit and the upper limit of the water level m of the power station i time period t; v i,min And V i,max Respectively the lower limit and the upper limit of the storage capacity m of the i time period t of the power station 3 。
D. Flow constraint and tail water level-let down flow relationship:
Q i,min ≤Q i,t ≤Q i,max (12)
in the formula: q i,min 、Q i,max The lower limit and the upper limit of the generating flow m of the power station i time period t respectively 3 /s；
The tail water level m of the power station i in the time period t; f. of i ZQ Is the tail water level-let down flow function of the station i.
E. Water head restraint:
in the formula: h i,t A water purification head m of the power station i in a time period t;
is the head loss of the hydropower station i in a time period t, m; f. of i hQ As a function of head loss for station i.
F. Output constraint and power station power characteristic curve:
N i,min ≤N i,t ≤N i,max (16)
N i,t ＝A i Q i,t H i,t (17)
in the formula: n is a radical of i,min And N i,max The lower limit and the upper limit of output force, MW, of the reservoir i time period t are respectively; a. the i And the comprehensive output coefficient of the power station i is obtained.
The concrete modeling solving steps of the cascade medium-term peak shaving scheduling method of the coupled water flow time lag are as follows, and the solving process is shown in figure 3:
A. initializing data input and setting basic constraints;
B. a segmented water flow time-lag method and a polynomial technique are adopted for constraint treatment;
C. coupling the step time-lag comprehensive benefit calculation method to two single-target models with minimum peak load regulation variance and maximum generated energy, and respectively calculating to obtain F i min And F i max ；
D. Converting multiple targets into a single target model by adopting a weight coefficient method, and setting a target initial weight coefficient;
E. obtaining an optimal solution under the corresponding weight coefficient by adopting a LINGO global optimization solver;
F. outputting the calculation result, judging whether the result is feasible or not, and if not, finishing the calculation; if yes, updating the weight coefficient omega to omega +0.1, and turning to the step E;
G. when ω is 1, the optimal solution set is generated and stored after the calculation is finished.
(1) Water quantity balance principle-based sectional water flow time-lag method for scheduling period and lag period
The water flow time lag makes the hydraulic connection coupling between the cascade hydropower stations more complicated, and directly influences the water balance calculation between the upstream and downstream hydropower stations, namely the distribution of the upstream warehouse-out flow in a plurality of continuous time periods of the downstream reservoir is reflected, as shown in figure 1, the water flow time lag from the direct upstream hydropower station k to the hydropower station i is tau k Step water quantity relationship of τ k ∈[0,1]。
The flow of leaving the warehouse of a certain time interval of the upstream power station reaches the downstream after a certain time lag, and the following relation is satisfied:
in the formula:
for the direct upstream station k to reach the outbound flow of station i at time t, m 3 /s；
And d is the delay time section number corresponding to the ex-warehouse flow of the k time section n of the direct upstream power station i.
The outbound flow of the direct upstream plant k to the plant i at time t, considering the effect of water flow lag, can be divided into three parts: the I part is the flow transferred to the last dispatching period, the II part is the flow in the dispatching period, and the III part is the flow transferred to the next dispatching period. These three portions of traffic can be described as:
the total delay time ex-warehouse flow of the available power station i in all direct upstream of the time t is as follows:
the expression of the cascade water flow time lag quantifies the influence of the water flow time lag from the aspects of the scheduling period and the lag period, so that an accurate warehousing flow process can be obtained by combining water quantity balance equations (5) - (7) and an equation (20).
(2) Calculation of step-lag composite benefits to reduce hysteresis effects
The time-lag imbalance relation of the optimized scheduling in the daytime of the gradient reservoir group is as follows: each stage of power station has a part of water quantity outside the dispatching period at the beginning and the end of the dispatching period, and reaches the delay accumulation effect of the upstream and the downstream of the cascade, as shown in fig. 2. Based on a segmented water flow time-lag method, determining the step time-lag comprehensive benefits of the three parts of flow generated in the dispatching period and the lag period, and specifically comprising the following steps:
1) and determining the influence benefit outside the scheduling period. Determining the roll-in flow of the last scheduling period at the beginning of the scheduling period and the roll-out flow of the last scheduling period reaching the next scheduling period according to the formula (19):
in the formula:
the outbound flow of the upstream power station at the end of the previous dispatching period is a known value,
the flow of the upstream power station at the end of the dispatching period is taken out of the warehouse. Based on the flow rate of the delay time
As the average flow out of the warehouse of the power station outside the dispatching period, the average tail water level of each time period is obtained by the formula (13), and the water head outside the dispatching period is further determined by the formula (14)
The average water consumption rate is related to the water consumption for power generation and the power generation amount, and is an important characteristic index reflecting the water level in the scheduling process. When the influence benefit of the water quantity in the lag period and the maximum power generation benefit target are measured, the calculation accuracy of the average water consumption rate in the whole period is not as good as that of a water head-water consumption rate curve, so that the calculation accuracy is higher based on the water head
Can be expressed as:
in the formula: r is a radical of hydrogen i u The average water consumption rate of the power station I in the u part is shown, and u belongs to { I, III }; f. of i rH As a function of head-rate of consumption of the station i.
Further, the influence benefits outside the scheduling period can be obtained as follows:
in the formula: e I The transfer benefit of the last scheduling period is obtained; e III And (4) transferring the benefit for the next scheduling period.
2) And determining the power generation benefit in the scheduling period. Ea is the power generation benefit generated in the process that the hydropower participates in dispatching output in the dispatching period, and whether the influence of water flow delay on the cascade power generation benefit in the dispatching period is considered can be expressed as follows:
in the formula: e II The net power generation benefit generated by the water flow in the dispatching period is obtained.
3) And calculating the step time-lag comprehensive benefit. On the basis of determining the benefits of each part of the cascade power station, in order to fully consider the power generation benefit of a hydropower system at the end of a dispatching period, Eb is taken as a benefit balance function for correcting the output plan deviation influenced by the water flow hysteresis, and the expression is as follows:
Eb＝E III -E I (27)
and (3) integrating the power generation benefits in the dispatching period and the benefit balance function outside the dispatching period, determining the step time-delay comprehensive benefits according to the formula (2), and obtaining the target function with the maximum final generated energy as follows:
(3) characterization of complex nonlinear constraints using polynomials
Describing the nonlinear constraint relation of the cascade hydropower medium-term optimization scheduling model in a polynomial form, and constructing a nonlinear model, wherein the specific constraint processing mode is as follows:
1) water level-reservoir capacity function
The relation between the water level and the reservoir capacity of the cascade hydropower station is a nonlinear function, and a quadratic polynomial fitting is selected and expressed as:
in the formula: a is 0,i ，a g,i (g ═ 1,2,3,4) are the water level-reservoir capacity curve constants and coefficients for station i, respectively.
2) Head loss function
The head loss variation curve is often expressed as a quadratic polynomial relationship, expressed as:
in the formula: b 0,i ，b 1,i Respectively, the head loss constant and coefficient of the power station i.
3) Tail water level-let down flow function
The relationship between the tail water level and the lower discharge flow of the power station is also fit by a fourth-order polynomial, and is represented as follows:
in the formula: c. C 0,i ，c g,i And (g is 1,2,3 and 4) is a tail water level downward discharge flow curve constant and a coefficient of the power station i.
Case analysis was as follows:
the Lancang river basin is one of thirteen water and electricity bases in China, and is one of important power supply points for transmitting western electricity and east electricity of a Yunnan power grid. Under the influence of the southwest monsoon climate, the runoff of the billows cang river basin is mainly precipitation, the dry and wet seasons are clear, and natural disasters such as typhoon, rainstorm and the like frequently occur in summer. At present, 11 hydropower stations are put into production in the dry stream of lan river, and only two power stations above the regulation in the year are available: the overall regulation performance of the small bay and the glutinous ferry is poor, and basic parameters of the power station are shown in a table 1.
In order to verify the effectiveness of the method, two scenes of flood season and dry season are respectively selected for calculation and analysis. The flood season scene is the affected period of typhoon "Liqima" from 8.1.2019 to 15.4.2019, and the dry season scene is selected from the spring festival period from 2.4.2019 to 18. The average load process of the power grids in the two scenes is shown in fig. 4, and it can be seen from the graph that the load of the power grids in adjacent days fluctuates frequently and huge load peak-valley differences exist. The maximum load of a flood season scene is 38249MW, the flood season scene occurs in 8 months and 3 days, the minimum load value is 36986MW, the flood season scene occurs in 8 months and 5 days, the load peak-valley difference is 1263MW, and the load process variance is 168986MW 2 (ii) a The maximum load of the withered period scene is 35045MW, which occurs at 17 days in 2 months, the minimum load value is 27587MW, which occurs at 5 days in 2 months, the load peak-valley difference is 7458MW, and the load process variance is 6724500MW 2 . Frequent daytime load fluctuation brings great difficulty to medium-term dispatching of a power grid, and peak load needs to be reduced by utilizing the complementary coordination characteristic of water and electricity, so that the residual load process to other power supplies is as uniform as possible.
The step water flow time lag parameter data are as follows:
table 2 shows the hydraulic connections between upstream and downstream of 11 cascade hydropower stations in the dry flow of laneway river, the scheduling period is 15d, the calculation step length is 1d, and the calculation results of the cascade water flow time lag parameters and the calculation results of the delivery flow in the flood withering period are shown in table 2.
Analyzing the time lag peak regulation result:
table 3 shows the power generation efficiency of each part of the staged power station in the dry period, and the staged time lag data in table 2 can be seen: the influence benefits outside the dispatching period are mainly related to the short time lag, the water flow time lags at the bottom of the upstream power station, the functional bridge and the Dachaoshan mountain are respectively 7.8h, 6h and 6h, and the transferring-in benefits and the transferring-out benefits outside the dispatching period are 21670MW & h, 8343MW & h, 9887MW & h, 22753MW & h, 28377MW & h and 29327MW & h respectively, wherein the transferring-out benefits are more obviously influenced by the water flow time lag. Comparing the power station benefits without considering the benefit balance function and the time lag, the power generation benefit deviation of the upstream power station Udalong, Huangdeng and big Huaqiao is smaller and is respectively 340MW & h, 321MW & h, 299MW & h and 252MW & h; with the accumulation of water flow time delay or longer distance of the power stations, the time delay influence on the benefits of a small bay, a diffuse bay, a glutinous rice ferry and a flood control of a downstream power station is large, and the benefits are 10700MW & h, 5078MW & h, 39614MW & h and 30901MW & h respectively; compared with the power station power generation benefits with time delay, after the benefit balance function is adjusted, although the benefit of the glutinous ferry and the scenic flood power station is not greatly increased, the benefits of other power stations are greatly increased, and the method can refine the peak regulation scheduling process and effectively improve the peak regulation power generation benefits.
The influence of water flow delay on the peak regulation effect is analyzed by using the dispatching processes of a minibay and a glutinous rice ferry power station, the output optimization processes of the two power stations are shown in fig. 5, glutinous rice ferry mainly undertakes the peak regulation task under the condition of no delay, the output of the glutinous rice ferry power station is mainly used for 1-8d under the condition of delay, the output of the minibay power station is mainly used for 9-13d, the peak regulation task is undertaken by the minibay and the glutinous rice ferry together only in the peak period of 14-15d, the output of a high peak section at the end of a dispatching period is increased, the final output process is prevented from being damaged, and the peak regulation capacity of the power stations is fully utilized. Therefore, the peak-shaving output process considering the time lag is more consistent with the actual operation requirement.
Table 4 shows the comparison of the peak shaving effect of the power grid under the condition of considering the water flow time lag, and it can be seen that: the cascade power station has good peak regulation effect on the scheduling process under the condition of time delay, and the peak-valley difference and the variance are both 0. When the benefit balance function is not considered in comparison, the scheduling benefit deviation without time lag is 89465MW & h, the comprehensive benefit deviation without time lag when the benefit balance function is considered is 5042MW & h, the peak shaving comprehensive benefit under the condition of time lag is increased, the benefit Ea without the benefit balance function is 94507MW & h, namely the target benefit deviation influenced by water flow time lag is reduced by the time lag peak shaving operation mode adjusted by the benefit balance function, and the peak shaving power generation benefit is improved.
Multi-objective optimization and peak regulation result analysis:
fig. 6 is an optimal solution distribution of the multi-objective joint scheduling model under different weight coefficients. As can be seen from the graph, with the increase of the residual load variance of the scheme, the power generation amount of the hydroelectric system is increased, the increasing speed is gradually reduced, and finally the solution of the boundary of the Pareto front edge solution set converges on the calculation result of the single target model.
In order to further analyze the result of the multi-target combined scheduling model, a scheme which is positioned in the middle weight coefficient combination is selected to be compared with the single-target model with the minimum residual load variance and the maximum power generation amount, the result can be seen in table 5, the residual load variance of the single-target model with the optimal peak regulation is considered to be 0, and the power generation amount is 2260846MW & h; the power generation amount of the optimal single-target model considering the power generation amount is 2328876MW & h, and the residual load variance is 6984033MW 2 And the load variance of the power grid is increased by 3.86% compared with the load fluctuation. Compared with a single-target model, the result of the multi-target optimal model is improved in variance and power generation so as to obtain the net benefit E in the scheduling period II The peak load regulation capacity of the power grid and the power generation benefit of the hydropower system are obviously improved.
Comparing optimization schemes of different scenes:
the peak regulation capacity result of the multi-target and single-target optimization model in the flood withering period is shown in fig. 7. Under different scene tests, the peak regulation effect of the peak regulation optimal model is relatively best, but the integral step power generation is relatively minimum; the overall hydroelectric power generation benefit of the optimal power generation model is the maximum, but the peak regulation requirement of the system is difficult to respond; the residual load variance and the generated energy of the multi-target model in the flood withering period are suboptimal and have a difference of about 0.03GW compared with the optimal single target 2 0.01TW · h and 0.11GW 2 0.01TW · h, consistent with the results of the different target optimization schemes of Table 5. The single-target optimization result cannot give consideration to peak regulation and power generation benefits, and the multi-target model can effectively reduce the peak regulation pressure of a power grid system and improve the utilization efficiency of water and electricity, so that the safe operation of a power grid is greatly guaranteed.
TABLE 1 basic parameter table of cascade hydropower station
TABLE 2 relationship between upstream and downstream water flow delay data and flow of each power station in flood season
TABLE 3 benefits of lag aging for various sections of cascaded plants
TABLE 4 comparison of Peak shaving Effect with/without Water flow lag
TABLE 5 comparison of results for different target optimization schemes during the wither period
Claims (1)
1. A mid-term peak shaving scheduling method of a cascade bank group coupled with water flow time lag is characterized by comprising the following steps:
the objective function includes two:
1) a peak shaving optimization objective; the minimum residual load variance is adopted as a target:
in the formula: i is a power station number; n is the total power station number; t is a time interval number; t is the total time period number in the planning period; p t System load demand, MW, for time period t; FN (FN) t The system residual load, MW, for time period t;
mean residual load, MW; n is a radical of i,t The output power of the power station in the period t of time i, MW;
2) a maximum target of step power generation; in the scheduling process of the cascade hydropower station considering the influence of water flow time lag on benefits, the maximum generated energy in a calculation period is a target:
max F 2 ＝Ea+Eb (2)
in the formula: ea is a benefit function generated by participating in the dispatching operation of the cascade hydropower station in the dispatching period; eb is a benefit balance function used outside the scheduling period to avoid the influence of water flow hysteresis;
converting the multi-target model into a single target by adopting a weight coefficient method, and performing normalization processing on each target solution set by using a formula (3), wherein omega is 1 ,ω 2 Is the target weight, ω 1 ,ω 2 E (0,1) and satisfies omega 1 +ω 2 When 1, the final target model is established as shown in formula (4):
max F(x)＝ω 1 F 1 ′(x)+(1-ω 1 )F 2 ′(x) (4)
the method comprises the following specific steps:
step (1) adopting a water quantity balance principle-based sectional water flow time-lag method in a scheduling period and a lag period;
step (2) step time-lag comprehensive benefit calculation for reducing the influence of hysteresis;
step (3) adopting a polynomial to represent complex nonlinear constraint;
the step (1) is as follows:
the flow of leaving the warehouse of a certain time interval of the upstream power station reaches the downstream after a certain time lag, and the following relation is satisfied:
in the formula:
ex-warehouse flow m for a direct upstream station k to reach station i at time t 3 /s；
The delay time section number d is corresponding to the ex-warehouse flow of the k time section n of the direct upstream power station i;
the flow out of the warehouse when the direct upstream power station k reaches the power station i in the time period t under the water flow time lag action is divided into three parts: the first part is the flow transferred in the last dispatching period, the second part is the flow in the dispatching period, and the third part is the flow transferred out to the next dispatching period; these three flows are described as:
the total delay time ex-warehouse flow of the available power station i in all direct upstream of the time t is as follows:
the expression of the cascade water flow time lag quantifies the influence of the water flow time lag from the aspects of a scheduling period and a lag period, so that an accurate warehousing flow process can be obtained by combining a water quantity balance equation and an equation (7);
wherein, the water balance equation:
in the formula: Δ t is the period length; v i,t The storage capacity m at the end of the i time period t of the power station 3 ；
I i,t 、Q i,t 、S i,t 、
The flow rate of warehousing, the flow rate of intervals, the flow rate of power generation, the flow rate of abandoned water and the flow rate of ex-warehouse of the power station i time period t are respectively m 3 /s；
For the delivery of upstream station k at time period n, m 3 /s；Ω i A set of direct upstream plants k being plants i;
the sum of the delayed warehouse-out flow of the time period n of the power station i directly upstream the power station k and the arrival of the flow at the power station i in the time period t;
the step (2) is specifically as follows:
based on the step (1) segmented water flow time-lag method, determining the step time-lag comprehensive benefits of the three parts of flow generated in the dispatching period and the lag period, and specifically comprising the following steps:
1) determining the influence benefit outside the scheduling period; determining the transfer-in flow of the last scheduling period at the beginning of the scheduling period and the transfer-out flow reaching the next scheduling period at the end of the scheduling period according to the formula (6):
in the formula:
the outbound flow of the upstream power station at the end of the previous dispatching period is a known value,
the flow of the upstream power station out of the warehouse at the end of the dispatching period; based on the flow rate of the delay time
As the average flow out of the warehouse of the power station outside the dispatching period, the tail water level of each time period is obtained by the formula (13), and the water head outside the dispatching period is further determined by the formula (14)
Wherein:
in the formula:
the tail water level m of the power station i in the time period t; f. of i ZQ Is the tail water level-let-down flow function of the power station i; h i,t A water purification head m of the power station i in a time period t;
is the head loss of the hydropower station i in a time period t, m;
the average water consumption rate is related to the water consumption for power generation and the generated energyIs an important characteristic index reflecting the water level in the scheduling process; when the influence benefit of the water quantity in the lag period and the maximum power generation benefit target are measured, the calculation accuracy of the average water consumption rate in the whole period is not as good as that of a water head-water consumption rate curve, so that the calculation accuracy is higher based on the water head
Can be expressed as:
in the formula: r is a radical of hydrogen i u The average water consumption rate of the power station I in the u part is shown, and u belongs to { I, III }; f. of i rH As head-water rate function for station i;
further, the influence benefits outside the scheduling period can be obtained as follows:
in the formula: e I The transfer benefit of the last scheduling period is obtained; e III The benefit is transferred out for the next scheduling period;
2) determining the power generation benefit in a scheduling period; ea is the power generation benefit generated in the process that the hydropower participates in dispatching output in the dispatching period, and whether the influence of water flow delay on the cascade power generation benefit in the dispatching period is considered can be expressed as follows:
in the formula: e II Generating net benefits generated by water flow in the dispatching period;
3) calculating the step time-lag comprehensive benefit; on the basis of determining the benefits of each part of the cascade power station, in order to fully consider the power generation benefits of the hydropower system at the end of the dispatching period, Eb is taken as a benefit balance function for correcting the output plan deviation of the influence of the water flow hysteresis, and the expression is as follows:
Eb＝E III -E I (19)
and (3) integrating the power generation benefits in the dispatching period and the benefit balance function outside the dispatching period, determining the step time-delay comprehensive benefits according to the formula (2), and obtaining the target function with the maximum final generated energy as follows:
the step (3) is specifically as follows:
describing the nonlinear constraint relation of the cascade hydropower medium-term optimization scheduling model in a polynomial form, and constructing a nonlinear model, wherein the specific constraint processing mode is as follows:
1) water level-reservoir capacity function
The relation between the water level of the cascade hydropower station and the reservoir capacity is a nonlinear function, and a quartic polynomial is selected for fitting and expressed as:
in the formula: a is 0,i ，a g,i (g ═ 1,2,3,4) are the water level-reservoir capacity curve constants and coefficients for station i, respectively;
2) head loss function
The head loss variation curve is often expressed as a quadratic polynomial relationship, expressed as:
in the formula: b 0,i ，b 1,i Respectively a head loss constant and a coefficient of the power station i;
3) tail water level-let down flow function
The relationship between the tail water level and the lower discharge flow of the power station is also fit by a fourth-order polynomial, and is represented as follows:
in the formula: c. C 0,i ，c g,i And (g is 1,2,3 and 4) is a tail water level downward discharge flow curve constant and a coefficient of the power station i.
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