CN113946792A - Reservoir group water level control method based on water abandoning probability - Google Patents

Reservoir group water level control method based on water abandoning probability Download PDF

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CN113946792A
CN113946792A CN202110995317.3A CN202110995317A CN113946792A CN 113946792 A CN113946792 A CN 113946792A CN 202110995317 A CN202110995317 A CN 202110995317A CN 113946792 A CN113946792 A CN 113946792A
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方国华
刘进
吴承君
闻昕
颜敏
张昕怡
黄显峰
谭乔凤
陈超
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Abstract

The invention discloses a reservoir group water level control method based on water abandoning probability, which comprises the following steps: according to historical forecast data of the runoff put in a reservoir of the power station, probability distribution of runoff forecast errors in different forecast periods is analyzed and fitted, a water abandon probability calculation method based on the runoff forecast error distribution is provided, the water abandon probability is converted into reservoir water level constraints according to a water quantity balance principle, and the control of the water abandon risk of each level of reservoir of the reservoir group is realized by adding extra water level constraints. The reservoir water level control method based on the water abandonment probability provided by the invention reduces the reservoir water abandonment risk caused by the runoff forecasting error in the past reservoir group optimal scheduling scheme based on the deterministic runoff process, considers the influence of the water uncertainty on reservoir scheduling, and provides important technical support and theoretical basis for improving the utilization rate of the reservoir hydroenergy resources.

Description

Reservoir group water level control method based on water abandoning probability
Technical Field
The invention belongs to the technical field of reservoir scheduling, and particularly relates to a reservoir group water level control method based on water abandoning probability.
Background
The water abandonment is an important assessment index in the operation process of the hydropower station and is also an important embodiment of the management level of the hydropower station, so that the water abandonment control is particularly important in reservoir power generation dispatching. For a reservoir mainly based on power generation, in order to fully exert the water head benefit of the reservoir, the reservoir is mostly maintained to operate at a high water level so as to obtain the theoretical maximum power generation benefit. However, the scheduling mode lacks consideration for the hidden water abandoning risk under the high water level operation condition, is limited by the scientific and technical level, and has a certain difference between the forecast value and the actual value of the warehousing runoff. Therefore, under the condition that runoff is uncertain, the probability of water abandonment generated by the reservoir in different water level processes is considered, and the coordination of the power generation benefit of the power station and the water abandonment risk has important significance in actual scheduling.
Currently, relevant scholars have more achievements in the research on the water abandoning risk. Aiming at the problems existing in the deterministic optimal scheduling of the Wujiang step in practical application, the Xiaoyan (2015) uses the water abandoning probability to evaluate the risk of the reservoir water abandoning, and provides a scheduling concept of controlling the optimal water level combination by using the water abandoning probability on the basis; caolol et al (2016) takes the risk rate of water abandon of rainfall forecast as an index, and provides a basis for the pre-discharge decision of the reservoir in the flood season; the Zhang Smart Tong (2019) assumes that runoff errors obey specific distribution, a Monte Carlo method is adopted to generate a large number of runoff series for fixed output simulation, the distribution rule of the water abandon amount is counted, and the real water abandon risk of the power generation plan is quantified according to the water abandon amount. Although the research results mostly consider the water abandoning risk of the hydropower station, the research results mostly focus on decision-making problems between the water abandoning risk and the power generation benefit in the flood season and water abandoning risk analysis based on the rainfall forecast-runoff-water level response relation, and the research results are less in application research of the water abandoning risk in dynamic water level control of the hydropower station.
In fact, under the condition that the forecast flow is known, the water abandon risk of the hydropower station in a certain time period is related to the control water level at the beginning and the end of the time period, and in the reservoir scheduling problem, the control water level at the end of the time period becomes the control water level at the beginning of the next time period, so that the calculation of the water abandon risk of the next time period is influenced. Therefore, the water abandoning risks of the hydropower station in each scheduling period are not independent and unrelated, and the water abandoning risks of the hydropower station are reduced by controlling the water level to be an integral and dynamic process. In view of the fact that water abandoning risk control is not fully considered in current power generation optimization scheduling, the invention selects the water abandoning probability as a quantitative index of water abandoning risk on the basis of analyzing runoff forecast error distribution, provides a water abandoning probability quantification method based on hydropower station warehousing runoff forecast error distribution, then converts the water abandoning probability into water level constraints in each scheduling period, and effectively controls the water abandoning risk in the hydropower station power generation scheduling process by increasing the water level constraints.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a reservoir group water level control method based on water abandon probability, which controls the water abandon probability of each reservoir within an allowable range by limiting the water level of a cascade reservoir, and reduces the risk of reservoir water abandon caused by runoff forecast error.
The technical scheme is as follows: the invention provides a reservoir group water level control method based on water abandoning probability, which specifically comprises the following steps:
(1) dividing scheduling time intervals according to the length of a scheduling period, and determining a forecast period of flow forecasting;
(2) respectively counting historical forecast data and actual runoff data of the warehousing flow of the first-level reservoir and the interval warehousing flow of the non-first-level reservoir according to different forecast periods, calculating a relative forecast error and analyzing a statistical rule of the relative forecast error;
(3) carrying out distribution fitting on runoff forecasting errors of different reservoirs in different forecasting periods;
(4) respectively calculating the water abandoning probabilities of the first-level reservoir and the non-first-level reservoir according to the fitting result of the runoff forecasting error distribution in the step (3) and by combining a water quantity balance equation;
(5) determining a calculation sequence from upstream to downstream, acquiring the water abandoning probability upper limit value of each reservoir, and finding out a critical error corresponding to the water abandoning probability upper limit value on a runoff forecasting error distribution curve to obtain the reservoir critical warehousing flow; calculating the final water level constraint according to a water quantity balance principle, and traversing all the hydropower stations in sequence to obtain reservoir water level constraints of each hydropower station of a certain period of basin cascade under the corresponding upper limit of the water abandoning probability;
(6) and (5) repeating the steps (4) to (5) for each time interval in the dispatching period to obtain a group of reservoir group water level control methods meeting the water abandoning probability constraint.
Further, the step (3) is realized by the following steps: according to the distribution function of the relative errors of the forecast flows in different forecast periods, the correlation between the forecast runoff level and the error distribution is not considered, and the obtained relative error distribution function is multiplied by the forecast runoff value in the corresponding time period to serve as the distribution function of the absolute error of the forecast runoff.
Further, the calculation process of the water abandoning probability of the primary reservoir in the step (4) is as follows:
calculating the critical warehousing flow Q' of the abandoned water according to a water quantity balance equation:
Q′＝qgen+(Vt+Δt-Vt)/Δt (1)
in the formula, VtThe reservoir capacity at the moment t; vt+ΔtThe reservoir capacity at the time of t + delta t; q. q.sgenThe full flow of the unit is obtained; Δ t is the period length;
the reservoir is at [ t, t + Δ t]The probability of water abandon in a time period can be expressed as the probability that the actual warehousing flow Q is greater than the critical warehousing flow, namely P (Q)>Q'); knowing the advance of reservoirs over timeReport the runoff in the warehouse as QforeThe runoff forecast error is epsilon, and the actual warehousing flow Q can be expressed as the difference value Q between the forecast warehousing flow and the errorfore-epsilon, then the water abandon probability is:
Figure BDA0003233658950000031
wherein, F (x) is a distribution function of the forecast absolute error of the warehousing runoff.
Further, the non-first-level reservoir water abandon probability calculation process in the step (4) is as follows:
for a non-first-level reservoir, considering the influence of the outlet flow of an upstream reservoir on the water abandoning probability of the reservoir, sequentially calculating the expected outlet flow of each level of reservoir by adopting a method of calculating from upstream to downstream, taking the expected value as a fixed warehousing flow part of the downstream reservoir, adding random variables of interval warehousing flows, and taking the sum of the expected value and the fixed warehousing flow part as the warehousing flow of a next level reservoir;
wherein, the flow q of deliveryoutIs a function of the warehousing traffic Q:
Figure BDA0003233658950000032
expected value of outbound traffic
Figure BDA0003233658950000033
Comprises the following steps:
Figure BDA0003233658950000034
wherein G (x) is a probability density function of the warehousing traffic Q, calculated according to G (x) ═ G' (x), and G (x) is a probability distribution function of the warehousing traffic Q, according to the definition of the distribution function:
G(x)＝P(Q≤x)
＝P(Qfore-ε≤x)
＝P(ε≥Qfore-x)
＝1-P(ε<Qfore-x)
＝1-F(Qfore-x) (5)
the probability density function of the warehousing traffic is:
g(x)＝G′(x)＝f(Qfore-x) (6)
wherein, F (x) is a probability density function of the forecast error of the warehousing runoff, and F (x) is F' (x);
considering the problem of probability combination between the upstream ex-warehouse random variable and the interval in-warehouse random variable, when calculating the water abandoning probability of the non-primary reservoir, taking the expected value of the upstream reservoir ex-warehouse flow as a fixed flow, and only considering the randomness of the interval in-warehouse flow; solving the critical interval warehousing flow S of the abandoned water according to the water quantity balance equationi′：
Figure BDA0003233658950000041
In the formula, Vi,tThe storage capacity of the i-th level reservoir at the time t is shown; vi,t+ΔtThe storage capacity of the i-th level reservoir at the time t + delta t; q. q.si,genThe full flow rate of the i-level reservoir unit;
Figure BDA0003233658950000042
the expected value of the delivery flow of the upstream reservoir is obtained;
the probability of water abandonment of the reservoir in the time period [ t, t + Δ t ]:
P(Si>Si′)＝P(Si,fore-ε>Si′)
＝P(ε<Si,fore-Si′)
＝F(Si,fore-Si′) (8)
in the formula, SiThe interval warehousing flow between the i-level reservoir and the upstream reservoir; si,foreThe forecast interval flow between the i-th level reservoir and the upstream reservoir.
Further, the step (5) is realized as follows:
for the first reservoir, the water level constraint converted from the water abandonment probability is calculated as follows:
Figure BDA0003233658950000043
in the formula, Z1,t、Z1,t+ΔtThe initial and final water levels of the first-level reservoir in the t-th time period; h (x) is a function of the reservoir capacity and the water level, H-1(x) Is the corresponding inverse function; q'1,tCalculating the critical warehousing flow of the first-level reservoir in the t-th time period according to the water abandoning probability;
Figure BDA0003233658950000051
the maximum power generation flow rate of the first-level reservoir is quoted;
Figure BDA0003233658950000052
forecasting the warehousing flow of the first-level reservoir in the t-th time period; f-1(x) An inverse function of the cumulative distribution function of the error for runoff forecasting; alpha is alpha1,tThe water abandon probability upper limit value of the first-level reservoir in the t-th time period;
for non-first-level reservoirs, the water level constraint converted from the water abandonment probability is calculated as follows:
Figure BDA0003233658950000053
of formula (II) S'i,tThe critical interval warehousing flow calculated by the water abandoning probability in the t-th time period is the ith-level reservoir;
Figure BDA0003233658950000054
forecasting runoff for the interval of the ith level reservoir in the t time period;
Figure BDA0003233658950000055
the expected outlet flow of the upstream reservoir; alpha is alphai,tThe water abandoning probability upper limit value of the ith-level reservoir in the t-th period.
Has the advantages that: compared with the prior art, the invention has the beneficial effects that: 1. the method for quantifying the water abandoning probability not only considers the information of each power station characteristic of the cascade reservoir group, the hydraulic connection among the reservoirs, the real-time water level state and the like, but also simulates the probability distribution of runoff forecasting errors by combining the historical forecasting characteristics of the warehousing runoff, realizes the accurate calculation of the water abandoning probability of each cascade reservoir, and intuitively reflects the water abandoning risk of each reservoir in each time period; 2. according to the definition and the connotation of the water abandoning probability, the water abandoning probability constraint is converted into the final water level constraint of the reservoir in each time interval, the water abandoning probability of each reservoir is controlled within an allowable range through the dynamic adjustment of the water level of the cascade reservoir, and the water abandoning risk control of the cascade reservoir group in each time interval is realized.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a frequency distribution histogram of runoff prediction relative errors of a large flower water reservoir according to historical data statistics;
FIG. 3 is a comparison graph of the water level process of the big flower water reservoir under the two conditions of considering the water abandon probability constraint and not considering the water abandon probability constraint;
FIG. 4 is a comparison graph of the water level process of the Grignard reservoir under the condition of considering the water abandoning probability constraint and the condition of not considering the water abandoning probability constraint.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
As shown in figure 1, the invention provides a reservoir group water level control method based on water abandonment probability, which considers reservoir water abandonment risk caused by water uncertainty, utilizes the probability distribution of runoff historical forecast data fitting errors and is applied to the calculation of the water abandonment probability, provides a reservoir group water level control method based on the water abandonment probability, and controls the water abandonment probability of each reservoir by increasing water level constraint so as to realize the control of the water abandonment risk of each time period of the reservoir group. The method specifically comprises the following steps:
step 1: and dividing scheduling time intervals according to the length of the scheduling period, and determining the forecast period of the flow forecast.
And uniformly dividing the scheduling cycle into N time intervals, wherein the length of each time interval is delta t, and the forecast periods of the warehousing traffic sequence are respectively delta t and 2 delta t … … N delta t.
Step 2: according to different forecast periods, respectively counting historical forecast data and actual runoff data of the warehousing flow of the first-level reservoir and the interval warehousing flow of the non-first-level reservoir, calculating a relative forecast error and analyzing a statistical rule of the relative forecast error.
In general, the relative prediction error is subject to a mean of 0 and a standard deviation of σtNormal distribution of (2), wherein the standard deviation σtIncreasing linearly with the extension of the anticipation period.
And step 3: and (4) performing distribution fitting on forecast errors of different reservoirs in different forecast periods.
According to the distribution function of the relative errors of the forecast flows in different forecast periods, the correlation between the forecast runoff level and the error distribution is not considered, and the obtained relative error distribution function is multiplied by the forecast runoff value in the corresponding time period to serve as the distribution function of the absolute error of the forecast runoff.
And 4, step 4: and (4) respectively calculating the water abandoning probabilities of the first-level reservoir and the non-first-level reservoir according to the fitting result of the runoff forecasting error distribution in the step (3) and by combining a water balance equation.
1) For the first-level reservoir, firstly, calculating the critical warehousing flow Q' of the abandoned water according to a water quantity balance equation:
Q′＝qgen+(Vt+Δt-Vt)/Δt (1)
in the formula: vtThe reservoir capacity at the moment t; vt+ΔtThe reservoir capacity at the time of t + delta t; q. q.sgenThe full flow of the unit is obtained; Δ t is the period length.
The reservoir is at [ t, t + Δ t]The probability of water abandon in a time period can be expressed as the probability that the actual warehousing flow Q is greater than the critical warehousing flow, namely P (Q)>Q'). Forecasting the reservoir warehousing runoff within a known time period is QforeThe runoff forecast error is epsilon, and the actual warehousing flow Q can be expressed as the difference value Q between the forecast warehousing flow and the errorforeε, the water abandon probability can be calculated as:
Figure BDA0003233658950000071
in the formula: f (x) is a distribution function of the forecast absolute error of the warehousing runoff.
2) For a non-first-stage reservoir, the influence of the outlet flow of an upstream reservoir on the water abandoning probability of the first-stage reservoir needs to be considered. And sequentially calculating expected delivery flow of each level of reservoir by adopting a method of calculating from upstream to downstream, taking the expected value as a fixed warehousing flow part of the downstream reservoir, adding random variables of interval warehousing flow to serve as warehousing flow of a lower level reservoir.
Wherein, the flow q of deliveryoutIs a function of the flow Q into the reservoir and can be calculated as follows:
Figure BDA0003233658950000072
expected value of outbound traffic
Figure BDA0003233658950000073
Can be calculated as follows:
Figure BDA0003233658950000074
in the formula: g (x) is a probability density function of the warehousing traffic Q, and can be calculated according to G (x) ═ G' (x), and G (x) is a probability distribution function of the warehousing traffic Q, and according to the definition of the distribution function, the following are provided:
G(x)＝P(Q≤x)
＝P(Qfore-ε≤x)
＝P(ε≥Qfore-x)
＝1-P(ε<Qfore-x)
＝1-F(Qfore-x) (5)
the probability density function of the warehousing traffic is:
g(x)＝G′(x)＝f(Qfore-x) (6)
in the formula: and F (x) is a probability density function of the forecast error of the warehousing runoff, and F (x) is F' (x).
Considering the problem of probability combination between the upstream ex-warehouse random variable and the interval in-warehouse random variable, when calculating the water abandoning probability of the non-primary reservoir, taking the expected value of the upstream reservoir ex-warehouse flow as a fixed flow, and only considering the randomness of the interval in-warehouse flow; solving the critical interval warehousing flow S of the abandoned water according to the water quantity balance equationi′：
Figure BDA0003233658950000081
In the formula: vi,tThe storage capacity of the i-th level reservoir at the time t is shown; vi,t+ΔtThe storage capacity of the i-th level reservoir at the time t + delta t; q. q.si,genThe full flow rate of the i-level reservoir unit;
Figure BDA0003233658950000082
-desired value of discharge flow of upstream reservoir.
The probability of water abandonment of the reservoir in the time period [ t, t + Δ t ] can be expressed as:
P(Si>Si′)＝P(Si,fore-ε>Si′)
＝P(ε<Si,fore-Si′)
＝F(Si,fore-Si′) (8)
in the formula: siThe interval warehousing flow between the i-level reservoir and the upstream reservoir; si,foreThe forecast interval flow between the i-th level reservoir and the upstream reservoir.
And 5: determining a calculation sequence from upstream to downstream, acquiring the water abandoning probability upper limit value of each reservoir, and finding out a critical error corresponding to the water abandoning probability upper limit value on a runoff forecasting error distribution curve to obtain the reservoir critical warehousing flow; and calculating the final water level constraint according to a water quantity balance principle, and traversing all the hydropower stations in sequence to obtain the reservoir water level constraint of each power station of the cascade basin in a certain period under the corresponding water abandoning probability upper limit.
For the first reservoir, the water level constraint converted from the water abandonment probability can be calculated according to the following formula:
Figure BDA0003233658950000083
in the formula: z1,t、Z1,t+ΔtThe initial and final water levels of the first-level reservoir in the t-th time period; h (x) is a function of the reservoir capacity and the water level, H-1(x) Is the corresponding inverse function; q'1,tCalculating the critical warehousing flow of the first-level reservoir in the t-th time period according to the water abandoning probability;
Figure BDA0003233658950000084
the maximum power generation flow rate of the first-level reservoir is quoted;
Figure BDA0003233658950000085
forecasting the warehousing flow of the first-level reservoir in the t-th time period; f-1(x) An inverse function of the cumulative distribution function of the error for runoff forecasting; alpha is alpha1,tIs the upper limit value of the water abandoning probability of the first-level reservoir in the t-th period.
For non-first-level reservoirs, the water level constraint transformed by the water abandonment probability can be calculated as follows:
Figure BDA0003233658950000091
in the formula: s'i,tThe critical interval warehousing flow calculated by the water abandoning probability in the t-th time period is the ith-level reservoir;
Figure BDA0003233658950000092
forecasting runoff for the interval of the ith level reservoir in the t time period;
Figure BDA0003233658950000093
the expected outlet flow of the upstream reservoir; alpha is alphai,tThe water abandoning probability upper limit value of the ith-level reservoir in the t-th period.
Step 6: and (5) repeating the step (4) and the step (5) for each time interval in the dispatching period to obtain a group of reservoir group water level control methods meeting the water abandoning probability constraint.
Taking the i-th-stage reservoir as an example, the delivery rate of the reservoir
Figure BDA0003233658950000094
Is the flow rate Q of entering warehousei,tFunction of (c):
Figure BDA0003233658950000095
in the formula: vi,tIs the initial storage capacity of a time interval; vi,t+ΔtThe storage capacity at the end of the time period.
Expected delivery rate
Figure BDA0003233658950000096
Comprises the following steps:
Figure BDA0003233658950000097
wherein g (x) is the warehousing traffic Qi,tThe probability density function of (2) may be calculated as G (x) ═ G' (x), and G (x) is the flow rate Q of the entering traffici,tAccording to the definition of the distribution function, the probability distribution function of (1) is as follows:
Figure BDA0003233658950000098
then the flow rate Q of entering warehousei,tThe probability density function of (a) is:
Figure BDA0003233658950000101
in the formula:
Figure BDA0003233658950000102
forecasting a value for the warehousing flow; epsiloni,tTo predict errors; f (x) is a distribution function of the forecast error of the warehousing flow; f (x) is a probability density function of the error of the warehouse traffic forecast.
When i is 1, namely for the first-level reservoir, the upper limit value alpha of the water abandoning probability in the time interval is firstly determined according to the risk preference of a scheduling decision maker1,tThe probability of water abandon of the reservoir can be expressed as the probability that the actual warehousing flow exceeds the critical warehousing flow, and the actual warehousing flow of the first-level reservoir is assumed to be Q1,tAnd the critical warehousing flow rate of just not generating the waste water is Q'1,tForecast and put in storage as
Figure BDA0003233658950000103
Forecast error is epsilon1,tThe cumulative distribution function of the error of the flow forecast in the warehouse is f (x), which includes:
Figure BDA0003233658950000104
critical reservoir warehousing flow Q 'of primary reservoir'1,tComprises the following steps:
Figure BDA0003233658950000105
when i ≠ 1, i.e. for non-first-level reservoirs, first acquire time interval [ t + Δ t ≠ t]Water abandon probability upper limit value alpha of internal reservoiri,tOnly the randomness of water entering the interval is considered, the probability of water abandon of the reservoir can be expressed as the probability that the actual interval warehousing flow exceeds the critical interval warehousing flow, and the actual interval warehousing flow of the reservoir is assumed to be Si,tAnd the storage flow rate of a critical interval with no waste water is S'i,tThe forecast interval warehouse entry flow is
Figure BDA0003233658950000106
Forecast error is epsiloni,tAnd the cumulative distribution function of the interval warehousing flow forecasting error is F (x), and the cumulative distribution function comprises the following components:
Figure BDA0003233658950000107
critical interval of non-first-level reservoirReservoir flow Si,t' is:
Figure BDA0003233658950000111
when i is 1, for the first reservoir, the initial and final water level of the period is assumed to be Z1,t、Z1,t+ΔtFull delivery rate of
Figure BDA0003233658950000112
The reservoir capacity function is H (x), and the water balance equation is obtained according to the following steps:
Figure BDA0003233658950000113
the joint type (16) and the formula (19) can obtain the final water level constraint of the first-level reservoir based on the water abandoning probability:
Figure BDA0003233658950000114
when i is not equal to 1, for a non-first-level reservoir, the influence of the ex-warehouse flow of an upstream reservoir needs to be considered, the ex-warehouse flow of the upstream reservoir is influenced by the randomness of the ex-warehouse flow of the upstream reservoir and is also a random variable. Assuming that the water level is Z at the beginning and end of the time periodi,t、Zi,t+ΔtFull delivery rate of
Figure BDA0003233658950000115
The expected discharge flow of the upstream reservoir is
Figure BDA0003233658950000116
The reservoir capacity function is H (x) given by the water balance equation:
Figure BDA0003233658950000117
the joint type (18) and the formula (21) can obtain the final water level constraint of the first-level reservoir based on the water abandoning probability:
Figure BDA0003233658950000118
by taking a typical flood process from 6 month, 12 days and 00 hours in 2018 to 6 month and 15 hours in the Wujiang river basin Dahua water-Guiliqiao stepped reservoir as an example, the optimal scheduling of the stepped reservoir is researched by utilizing the reservoir group reservoir control method based on the water abandon probability, combining the maximum generated energy model and taking 1h as the scheduling time interval, so that the effectiveness and the rationality of the method are verified. Aiming at the historical flood process and the historical forecast flow process, according to the water abandoning probability quantification method provided by the invention, the historical values of the water abandoning probabilities of the cascade reservoir in different scheduling time periods are calculated, and from the safety perspective, the historical minimum water abandoning probability value of each time period is selected as the time period water abandoning probability upper limit constraint, which is shown in tables 1 and 2. FIG. 2 is a frequency distribution histogram of runoff prediction relative error of a large flower water reservoir according to historical data statistics. FIG. 3 is a comparison graph of the water level process of the big flower water reservoir under the two conditions of considering the water abandon probability constraint and not considering the water abandon probability constraint; FIG. 4 is a comparison graph of the water level process of the Grignard reservoir under the condition of considering the water abandoning probability constraint and the condition of not considering the water abandoning probability constraint.
TABLE 1 calculation of water abandon probability upper limit for large-flower water reservoir at each time interval
Figure BDA0003233658950000121
TABLE 2 calculation results of water abandon probability upper limit values of each time interval of the gurley bridge reservoir
Figure BDA0003233658950000122
From the view of the water level process, for the large flower water of the first-level reservoir, the water level process line considering the water abandoning probability is always positioned above the water level process line of the result of the conventional optimized dispatching (not considering the water abandoning probability constraint). The reason is that under the same scheduling period initial and final water level boundary, the influence of runoff forecast errors is not considered in the conventional optimized scheduling, the maximum optimization accuracy of the step power generation enables the reservoir to generate power basically according to the maximum flow in each period, and the water level at the end of the period is relatively low. After the water abandoning probability constraint is considered, extra final water level lower limit constraint is added to each time interval in the optimization calculation process, and the control final water level of each time interval is improved. For non-first-level reservoir grignard bridges, the water level process generally follows the above-mentioned law, but is also influenced by the upstream reservoir scheduling manner. When the constraint action of the water abandoning probability enables the large florescent water reservoir to continuously store water so as to meet the requirement of water level lifting, the large florescent water reservoir is small in delivery, so that the water of the downstream grid bridge reservoir is insufficient, and cannot be quickly lifted to a target water level, which is the reason that the control water level of the scheme for dispatching the water abandoning probability of the medium-term grid bridge reservoir falls below the conventional scheme, and is shown in fig. 4.
In order to further analyze the control effect of the water abandoning probability constraint on the water abandoning risk of the hydropower station, according to the actual water incoming process, the water level control simulation scheduling is respectively carried out on the water abandoning probability scheme and the scheme of the conventional model with the maximum generated energy, and the results are shown in a table 3 by comparing the power generation and water abandoning conditions of different schemes under the actual water incoming condition.
Table 3 comparison result table of optimized scheduling and conventional optimized scheduling considering water abandon probability
Scheme(s) Regular optimized scheduling Optimized scheduling considering water curtailment probability
Total output (MW) 24202 24603
Total water discard (ten thousand m)3) 1692 1551
As can be seen from Table 3, in the aspect of total output, the total output of the conventional maximum power generation capacity scheme is 24202MW according to the actual water level control simulation, and the water level control simulation output of the optimal scheduling scheme considering the water abandoning probability is 24603MW, which is increased by 1.66% compared with the conventional scheme. In the aspect of the total water abandon amount, the total water abandon amount simulated according to actual incoming water by the conventional optimal scheduling scheme is 1692 ten thousand meters3The total water abandoning amount of the optimized scheduling scheme water level control simulation considering the water abandoning probability is 1551 km3The reduction is 8.33 percent compared with the conventional scheme. The reservoir group water level control method based on the water abandon probability provided by the invention can reduce the water abandon amount of the reservoir to a certain extent, reduce the water abandon loss and increase the power generation benefit of the cascade reservoir. Scheduling decision personnel can set different water abandoning probabilities for each time interval of each reservoir according to risk preference, and reservoir water abandoning risks caused by runoff forecasting errors are reduced to the greatest extent.
The method is based on the probability distribution thought of errors from the perspective of the forecast errors of the runoff storage, provides a quantitative method of the water abandonment probability, comprehensively considers the influence of the real-time state and the incoming water uncertainty of the reservoir, and realizes the accurate calculation of the water abandonment probability of the reservoir; furthermore, the invention provides a reservoir water level control method based on the water abandoning probability, which converts the water abandoning probability constraint into the reservoir water level constraint, realizes the water abandoning risk control of each stage of the reservoir group by controlling the water level process, and provides a new method and technology for reducing the water abandoning risk of the reservoir group and improving the utilization rate of water resources.

Claims (5)

1. A reservoir group water level control method based on water abandoning probability is characterized by comprising the following steps:
(1) dividing scheduling time intervals according to the length of a scheduling period, and determining a forecast period of flow forecasting;
(2) respectively counting historical forecast data and actual runoff data of the warehousing flow of the first-level reservoir and the interval warehousing flow of the non-first-level reservoir according to different forecast periods, calculating a relative forecast error and analyzing a statistical rule of the relative forecast error;
(3) carrying out distribution fitting on runoff forecasting errors of different reservoirs in different forecasting periods;
(4) respectively calculating the water abandoning probabilities of the first-level reservoir and the non-first-level reservoir according to the fitting result of the runoff forecasting error distribution in the step (3) and by combining a water quantity balance equation;
(5) determining a calculation sequence from upstream to downstream, acquiring the water abandoning probability upper limit value of each reservoir, and finding out a critical error corresponding to the water abandoning probability upper limit value on a runoff forecasting error distribution curve to obtain the reservoir critical warehousing flow; calculating the final water level constraint according to a water quantity balance principle, and traversing all the hydropower stations in sequence to obtain reservoir water level constraints of each hydropower station of a certain period of basin cascade under the corresponding upper limit of the water abandoning probability;
(6) and (5) repeating the steps (4) to (5) for each time interval in the dispatching period to obtain a group of reservoir group water level control methods meeting the water abandoning probability constraint.
2. The method for controlling the water abandonment probability-based reservoir group water level according to claim 1, wherein the step (3) is implemented by the following steps: according to the distribution function of the relative errors of the forecast flows in different forecast periods, the correlation between the forecast runoff level and the error distribution is not considered, and the obtained relative error distribution function is multiplied by the forecast runoff value in the corresponding time period to serve as the distribution function of the absolute error of the forecast runoff.
3. The method for controlling the water abandon probability of the reservoir group according to claim 1, wherein the calculation process of the water abandon probability of the first-stage reservoir in the step (4) is as follows:
calculating the critical warehousing flow Q' of the abandoned water according to a water quantity balance equation:
Q′＝qgen+(Vt+Δt-Vt)/Δt (1)
in the formula, VtThe reservoir capacity at the moment t; vt+ΔtThe reservoir capacity at the time of t + delta t; q. q.sgenThe full flow of the unit is obtained; Δ t is the period length;
the reservoir is at [ t, t + Δ t]The probability of water abandon in a time period can be expressed as the probability that the actual warehousing flow Q is greater than the critical warehousing flow, namely P (Q)>Q'); forecasting the reservoir warehousing runoff within a known time period is QforeThe runoff forecast error is epsilon, and the actual warehousing flow Q can be expressed as the difference value Q between the forecast warehousing flow and the errorfore-epsilon, then the water abandon probability is:
Figure FDA0003233658940000021
wherein, F (x) is a distribution function of the forecast absolute error of the warehousing runoff.
4. The method for controlling the water cut probability-based reservoir group water level according to claim 1, wherein the non-primary reservoir water cut probability calculation process of step (4) is as follows:
for a non-first-level reservoir, considering the influence of the outlet flow of an upstream reservoir on the water abandoning probability of the reservoir, sequentially calculating the expected outlet flow of each level of reservoir by adopting a method of calculating from upstream to downstream, taking the expected value as a fixed warehousing flow part of the downstream reservoir, adding random variables of interval warehousing flows, and taking the sum of the expected value and the fixed warehousing flow part as the warehousing flow of a next level reservoir;
wherein, the flow q of deliveryoutIs a function of the warehousing traffic Q:
Figure FDA0003233658940000022
expected value of outbound traffic
Figure FDA0003233658940000023
Comprises the following steps:
Figure FDA0003233658940000024
wherein G (x) is a probability density function of the warehousing traffic Q, calculated according to G (x) ═ G' (x), and G (x) is a probability distribution function of the warehousing traffic Q, according to the definition of the distribution function:
G(x)＝P(Q≤x)
＝P(Qfore-ε≤x)
＝P(ε≥Qfore-x)
＝1-P(ε<Qfore-x)
＝1-F(Qfore-x) (5)
the probability density function of the warehousing traffic is:
g(x)＝G′(x)＝f(Qfore-x) (6)
wherein, F (x) is a probability density function of the forecast error of the warehousing runoff, and F (x) is F' (x);
considering the problem of probability combination between the upstream ex-warehouse random variable and the interval in-warehouse random variable, when calculating the water abandoning probability of the non-primary reservoir, taking the expected value of the upstream reservoir ex-warehouse flow as a fixed flow, and only considering the randomness of the interval in-warehouse flow; solving the critical interval warehousing flow S of the abandoned water according to the water quantity balance equationi′：
Figure FDA0003233658940000031
In the formula, Vi,tThe storage capacity of the i-th level reservoir at the time t is shown; vi,t+ΔtThe storage capacity of the i-th level reservoir at the time t + delta t; q. q.si,genThe full flow rate of the i-level reservoir unit;
Figure FDA0003233658940000032
the expected value of the delivery flow of the upstream reservoir is obtained;
the probability of water abandonment of the reservoir in the time period [ t, t + Δ t ]:
P(Si>Si′)＝P(Si,fore-ε>Si′)
＝P(ε<Si,fore-Si′)
＝F(Si,fore-Si′) (8)
in the formula, SiThe interval warehousing flow between the i-level reservoir and the upstream reservoir; si,foreThe forecast interval flow between the i-th level reservoir and the upstream reservoir.
5. The method for controlling the water abandonment probability-based reservoir group water level according to claim 1, wherein the step (5) is implemented as follows:
for the first reservoir, the water level constraint converted from the water abandonment probability is calculated as follows:
Figure FDA0003233658940000033
in the formula, Z1,t、Z1,t+ΔtThe initial and final water levels of the first-level reservoir in the t-th time period; h (x) is a function of the reservoir capacity and the water level, H-1(x) Is the corresponding inverse function; q'1,tCalculating the critical warehousing flow of the first-level reservoir in the t-th time period according to the water abandoning probability;
Figure FDA0003233658940000034
the maximum power generation flow rate of the first-level reservoir is quoted;
Figure FDA0003233658940000035
forecasting the warehousing flow of the first-level reservoir in the t-th time period; f-1(x) An inverse function of the cumulative distribution function of the error for runoff forecasting; alpha is alpha1,tThe water abandon probability upper limit value of the first-level reservoir in the t-th time period;
for non-first-level reservoirs, the water level constraint converted from the water abandonment probability is calculated as follows:
Figure FDA0003233658940000036
of formula (II) S'i,tThe critical interval warehousing flow calculated by the water abandoning probability in the t-th time period is the ith-level reservoir;
Figure FDA0003233658940000041
forecasting runoff for the interval of the ith level reservoir in the t time period;
Figure FDA0003233658940000042
the expected outlet flow of the upstream reservoir; alpha is alphai,tThe water abandoning probability upper limit value of the ith-level reservoir in the t-th period.
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Publication number Priority date Publication date Assignee Title
CN115187145A (en) * 2022-09-09 2022-10-14 南京华盾电力信息安全测评有限公司 Method for controlling water level of end-of-day scheduling reservoir of cascade reservoir by considering water abandon risk

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115187145A (en) * 2022-09-09 2022-10-14 南京华盾电力信息安全测评有限公司 Method for controlling water level of end-of-day scheduling reservoir of cascade reservoir by considering water abandon risk

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