CN110854929B - Day-ahead scheduling method considering uncertainty in time period - Google Patents

Day-ahead scheduling method considering uncertainty in time period Download PDF

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CN110854929B
CN110854929B CN201911099171.3A CN201911099171A CN110854929B CN 110854929 B CN110854929 B CN 110854929B CN 201911099171 A CN201911099171 A CN 201911099171A CN 110854929 B CN110854929 B CN 110854929B
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文劲宇
周博
艾小猛
方家琨
姚伟
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Huazhong University of Science and Technology
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Abstract

The invention discloses a day-ahead scheduling method for counting uncertainty in time period, which comprises the following steps: establishing a day-ahead scheduling model considering uncertainty in a time period based on parameters of a power system; converting the day-ahead scheduling model considering uncertainty in a time period into a discrete form; and optimizing the discrete day-ahead scheduling model considering uncertainty in the time period by adopting a robust optimization algorithm to obtain an optimal day-ahead scheduling result capable of coping with the uncertainty in the time period. The day-ahead scheduling method considering uncertainty in the time interval provided by the invention considers uncertainty in the random power supply output time interval, so that a more robust scheduling result can be given, and when the random power supply output fluctuates greatly in the time interval, the safety of system operation is ensured.

Description

Day-ahead scheduling method considering uncertainty in time period
Technical Field
The invention belongs to the field of electrical engineering, and particularly relates to a day-ahead scheduling method for counting uncertainty in time intervals.
Background
In order to realize energy conservation, emission reduction and energy crisis relief, renewable energy sources are rapidly developed in the world, wherein uncertainty of random power output such as wind power, photovoltaic power and the like brings great challenges to the operation safety of a power system. With the increasing of the renewable energy power generation ratio, a power system dispatching mechanism needs to make a reasonable day-ahead dispatching plan to ensure the operation safety of a power system.
Robust day-ahead scheduling is a scheduling method that can account for randomness of power output and has led to extensive research. However, the existing scheduling methods are limited by the technical level and the computational efficiency, each day is divided into 24 or more time periods, and a scheduling plan is made by assuming that the load and the random power output within each time period are unchanged and the output is changed in steps when the time periods are alternated. The existing scheduling method has two problems, one is that the stepped scheduling method is not in accordance with the actual physical process and cannot reflect the change of the actual physical process, thereby possibly causing operation risk; secondly, with the high and intermittent random power supply occupation ratio, the uncertainty of the random power supply in the output time period cannot be considered by the conventional robust scheduling method, so that the operation safety of the power system when the random power supply output fluctuates greatly in the time period may not be ensured by the scheduling plan made by the conventional robust scheduling method.
Some studies propose to further subdivide the scheduling period, but still cannot account for uncertainty in the subdivided period, and are limited by computational efficiency. In addition, a few studies propose scheduling methods under continuous time, but all the scheduling methods are random optimization based on generated scenes, and the robustness of a scheduling plan is limited by the balance between the number of generated scenes and the computational efficiency. If the continuous time method and the robust scheduling method can be combined, uncertainty in a time period can be considered better, and a more robust scheduling plan is given.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a day-ahead scheduling method for counting uncertainty in a time period, and aims to solve the problem of operation safety of a power system possibly caused by the fact that uncertainty in a random power output time period cannot be counted in the prior art.
In order to achieve the above object, the present invention provides a day-ahead scheduling method for accounting uncertainty in a time period, comprising the following steps:
s1, establishing a day-ahead scheduling model considering uncertainty in a time period based on power system parameters, load requirements and random power supply output;
the day-ahead scheduling model for calculating uncertainty in a time period comprises a continuous time unit model, a continuous time power grid model, a continuous time stochastic power supply model and an objective function;
s2, converting the day-ahead scheduling model considering uncertainty in the time period into a discrete form;
and S3, optimizing the discrete-form day-ahead scheduling model considering uncertainty in the time interval by adopting a robust optimization algorithm to obtain an optimal day-ahead scheduling result capable of coping with uncertainty in the time interval.
Preferably, the power system parameters include: number of nodes NbTotal number of lines NlReactance x of jth linejUpper and lower limits P of active power output of generator at ith nodegmin,i、Pgmax,iMaximum up-down climbing speed Rru,i、Rrd,iMaximum ramp rate R at start-up and shutdownsu,i、Rsd,iMinimum boot and minimum downtime Ton,i、Toff,iCost V of single start-up and single shut-downsu,i、Vsd,iCoal consumption cost per unit generated energy of the generator at the ith nodeiRated capacity Plmax,j(ii) a Load P at ith nodedi(τ), stochastic power supply predicted contribution P at ith nodeue,i(τ)。
Preferably, the load at the ith node is Pdi(τ) the predicted random power contribution at the ith node is Pue,iAnd (tau), wherein tau is a continuous variable representing time and ranges from 0 to the length of the whole scheduling time.
Preferably, the continuous-time unit model is:
Figure BDA0002269294050000021
Pgmin,iUi(τ)≤Pgi(τ)≤Pgmax,iUi(τ)
Figure BDA0002269294050000031
wherein, Ui(tau) is the starting and stopping state of the unit at the ith node, Pgi(τ) is the unit output force, ε is infinitesimal quantity, U'iU of (τ)i(τ) derivatives, which represent the minimum on-time and off-time constraints of the unit, the unit output range constraints, and the unit ramp capacity limits, respectively.
Preferably, the continuous-time grid model is:
-Plmax,j≤Sji(Pgi(τ)+Pui(τ)-Pdi(τ))≤Plmax,j
wherein, Pui(τ) is the stochastic power output at the ith node, which is the line flow constraint, SjiThe method is a power flow sensitivity matrix commonly used in a direct current power flow model.
Preferably, the continuous-time stochastic power model is:
(1-γ)Pue,i(τ)≤Pui(τ)≤(1+γ)Pue,i(τ)
where γ is the prediction error of the assumed random power output, and this equation represents the range of possible random power outputs.
Preferably, the objective function is considered to be the minimum running cost in the prediction scene, including the boot cost Csui(τ), cost of downtime Csdi(τ) and Fuel cost Cfi(τ), formulated as:
Figure BDA0002269294050000032
Figure BDA0002269294050000033
Figure BDA0002269294050000034
Cfi(τ)＝βiPgi(τ)
wherein, Csui(τ) is boot cost, Csdi(τ) cost of downtime, Cfi(τ) is Fuel cost, Pgi(τ) is the unit output.
Preferably, the day-ahead scheduling model taking uncertainty in a time period into account is an optimization problem in a continuous time form, the existing method is difficult to solve and calculate, the model is converted into a discrete form by using an interpolation method, and the day-ahead scheduling model taking uncertainty in the time period into account in the discrete form is as follows:
Figure BDA0002269294050000041
Csuit≥Vsu,i(Uit-Ui(t-1))
Csdit≥Vsd,i(Ui(t-1)-Uit)
Figure BDA0002269294050000042
wherein, CsuiFor the starting-up cost, CsdiFor the cost of shutdown, CfiFor the cost of fuel,
Figure BDA0002269294050000043
The N times of interpolation coefficients of the unit output curve are shown, T is the length of each time interval, and k is 0, 1, 2, …, N;
the constraint conditions of minimum startup and shutdown time constraint, output range constraint, output climbing constraint, tide constraint, randomness range and first-order continuity constraint are respectively as follows:
Figure BDA0002269294050000044
Figure BDA0002269294050000045
Figure BDA0002269294050000046
Figure BDA0002269294050000047
Figure BDA0002269294050000051
Figure BDA0002269294050000052
wherein
Figure BDA0002269294050000053
Can be
Figure BDA0002269294050000054
Or
Figure BDA0002269294050000055
Figure BDA0002269294050000056
Ui(t-1)There are N-1.
Through the technical scheme, compared with the prior art, the invention has the following beneficial effects:
1. the day-ahead scheduling method for counting uncertainty in time interval provided by the invention counts the uncertainty in the random power supply output time interval, so that a more robust scheduling result can be given, and when the random power supply output fluctuates greatly in time interval, the safety of system operation is ensured;
2. the day-ahead scheduling method for counting the uncertainty in the time period converts the continuous time robust optimization method for counting the uncertainty in the time period into a discrete form optimization problem, so that the existing robust optimization algorithm can be used for efficient solution;
3. the day-ahead scheduling method considering uncertainty in time periods provided by the invention adopts a continuous time modeling method, and is more in line with the actual physical process, so that a more accurate scheduling result can be given.
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FIG. 1 is a schematic flow chart of a day-ahead scheduling method for accounting for uncertainty in time periods according to the present invention;
FIG. 2 is a schematic diagram of the present invention accounting for uncertainty in time period;
FIG. 3 is a diagram illustrating a segmentation interpolation method according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention provides a day-ahead scheduling method for counting uncertainty in a time period, which comprises the following steps as shown in figure 1:
s1, establishing a day-ahead scheduling model considering uncertainty in a time period based on power system parameters, load requirements and random power supply output;
the day-ahead scheduling model for calculating uncertainty in a time period comprises a continuous time unit model, a continuous time power grid model, a continuous time stochastic power supply model and an objective function;
s2, converting the day-ahead scheduling model considering uncertainty in the time period into a discrete form;
and S3, optimizing the discrete-form day-ahead scheduling model considering uncertainty in the time interval by adopting a robust optimization algorithm to obtain an optimal day-ahead scheduling result capable of coping with uncertainty in the time interval.
Specifically, the power system parameters include: number of nodes NbTotal number of lines NlReactance x of jth linejUpper and lower limits P of active power output of generator at ith nodegmin,i、Pgmax,iMaximum up-down climbing speed Rru,i、Rrd,iMaximum ramp rate R at start-up and shutdownsu,i、Rsd,iMinimum boot and minimum downtime Ton,i、Toff,iCost V of single start-up and single shut-downsu,i、Vsd,iCoal consumption cost per unit generated energy of the generator at the ith nodeiRated capacity Plmax,j(ii) a Load R at ith nodedi(τ), stochastic power supply predicted contribution P at ith nodeue,i(τ)。
Specifically, the load at the ith node is Pdi(τ) the predicted random power contribution at the ith node is Pue,iAnd (tau), wherein tau is a continuous variable representing time and ranges from 0 to the length of the whole scheduling time.
Specifically, the continuous time unit model is as follows:
Figure BDA0002269294050000061
Pgmin,iUi(τ)≤Pgi(τ)≤Pgmax,iUi(τ)
Figure BDA0002269294050000071
wherein, Ui(tau) is the starting and stopping state of the unit at the ith node, Pgi(τ) is the unit output force, ε is infinitesimal quantity, U'i(τ) isU of (1)i(τ) derivatives, which represent the minimum on-time and off-time constraints of the unit, the unit output range constraints, and the unit ramp capacity limits, respectively.
Specifically, the continuous-time grid model is:
-Plmax,j≤Sji(Pgi(τ)+Pui(τ)-Pdi(τ))≤Plmax,j
wherein, Pui(τ) is the stochastic power output at the ith node, which is the line flow constraint, SjiThe method is a power flow sensitivity matrix commonly used in a direct current power flow model.
Specifically, assuming that the stochastic power output prediction error is γ, the continuous-time stochastic power model is:
(1-γ)Pue,i(τ)≤Pui(τ)≤(1+γ)Pue,i(τ)
wherein the formula represents the range of possible random power supply output. Take a certain time period as an example, Pui(τ) can be any one of the curves in the shaded area of the band shown in fig. 2, so that uncertainty in the random power source power-off period can be accounted for.
Specifically, the objective function is considered as the minimum running cost under the prediction scene, including the starting cost Csui(τ), cost of downtime Csdi(τ) and Fuel cost Cfi(τ), formulated as:
Figure BDA0002269294050000072
Figure BDA0002269294050000073
Figure BDA0002269294050000074
Cfi(τ)＝βiPgi(τ)
wherein, Csui(τ) is boot cost, Csdi(τ) cost of downtime, Cfi(τ) is Fuel cost, Pgi(τ) is the unit output.
The model is converted into a discrete form by combining a segmented interpolation method, the whole scheduling period H is firstly divided into H time intervals, the length of each time interval is T-H/H, and a load curve in each time interval is approximated by a cubic Bernstein interpolation method, as shown in FIG. 3. In fig. 3, the solid line is an actual predicted load curve, the dotted line is a load curve used in the conventional scheduling method, and the open line is a load curve obtained by the used piecewise interpolation method. For the tth period, i.e. (T-1) T ≦ τ ≦ tT, the curve obtained by the piecewise interpolation method is:
Figure BDA0002269294050000081
wherein τ ═ (τ - (T-1) T)/T.
Kth interpolation polynomial Bk(τ') is:
Figure BDA0002269294050000082
the interpolating polynomial vector B (τ') ═ B0(τ′),B1(τ′),B2(τ′),B3(τ′)]TInterpolation coefficient
Figure BDA0002269294050000083
Comprises the following steps:
Figure BDA0002269294050000084
wherein P'diP of (τ)di(τ) derivative, interpolation coefficient vector
Figure BDA0002269294050000085
Similarly, the stochastic power predicted output can be calculatedCurve Pue,iInterpolation coefficient of (tau)
Figure BDA0002269294050000086
And assuming that the interpolation coefficient of the unit output curve is
Figure BDA0002269294050000087
The interpolation coefficient of the random power output is
Figure BDA0002269294050000088
Since the start-stop state curve is not actually a continuous curve, it is not interpolated.
It can be observed that the day-ahead scheduling model taking into account uncertainty in a time period in the form of continuous time contains objective functions and derivation operations in the forms of equality constraints, inequality constraints, and integrals, which are converted below.
Assuming that there is a certain equality constraint F (τ) equal to 0, the interpolation coefficient of F (τ) is FBkWhen T is more than or equal to T and less than or equal to tT in (T-1), the following equivalent transformation exists according to the undetermined coefficient method:
Figure BDA0002269294050000091
assuming that there is an inequality constraint G (tau) ≦ 0, the interpolation coefficient of G (tau) is GBkThe vector of interpolation coefficients is GBConsider, for example, min { G }B}≤GBB(τ′)≤max{GBThe convex hull property of the Bernstein interpolation method shown in the description, when T is not less than (T-1) T and not more than tau and not more than tT, the method is as follows:
Figure BDA0002269294050000092
assuming that there is some integral term
Figure BDA0002269294050000093
It can be calculated as follows:
Figure BDA0002269294050000094
assuming that there is a certain derivation operation D '(τ), Bernstein quadratic interpolation method D' (τ) to (D) can be usedBB(τ))′＝D′BB(2)(τ) is described, wherein D'BThe quadratic interpolation coefficient, D' (τ), can be calculated as follows:
Figure BDA0002269294050000095
bernstein quadratic interpolation polynomial B(2)Comprises the following steps:
Figure BDA0002269294050000096
finally, a discrete day-ahead scheduling model which takes uncertainty in the time period into account is obtained:
Figure BDA0002269294050000097
Csuit≥Vsu,i(Uit-Ui(t-1))
Csdit≥Vsd,i(Ui(t-1)-Uit)
Figure BDA0002269294050000101
wherein, CsuiFor the starting-up cost, CsdiFor the cost of shutdown, CfiFor the cost of fuel,
Figure BDA0002269294050000102
And k is 0, 1, 2 and 3 which is an interpolation coefficient of the unit output curve.
The constraint conditions of minimum startup and shutdown time constraint, output range constraint, output climbing constraint, tide constraint, randomness range and first-order continuity constraint are respectively as follows:
Figure BDA0002269294050000103
Figure BDA0002269294050000104
Figure BDA0002269294050000105
Figure BDA0002269294050000106
Figure BDA0002269294050000107
Figure BDA0002269294050000108
wherein
Figure BDA0002269294050000109
Can be
Figure BDA00022692940500001010
Or
Figure BDA00022692940500001011
The discrete three-level min-max-min optimization problem can be efficiently solved through the existing robust optimization algorithm such as CCG algorithm and dual transformation, and the calculated UitI.e. the optimal way to boot.
Continuous form optimal dispatch contribution plan Pgi(τ) is:
Figure BDA0002269294050000111
the optimal starting mode and the optimal scheduling output plan are the optimal scheduling results given by the day-ahead scheduling method considering uncertainty in the time period.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (4)

1. A day-ahead scheduling method for accounting for uncertainty in a time period is characterized by comprising the following steps:
s1, establishing a day-ahead scheduling model considering uncertainty in a time period based on the power system parameters; the power system parameters include: number of nodes NbTotal number of lines NlReactance x of jth linejUpper and lower limits P of active power output of generator at ith nodegmin，i、Pgmax，iMaximum up-down climbing speed Rru，i、Rrd，iMaximum ramp rate R at start-up and shutdownsu，i、Rsd，iMinimum boot and minimum downtime Ton，i、Toff，iCost V of single start-up and single shut-downsu，i、Vsd，iCoal consumption cost per unit generated energy of the generator at the ith nodeiRated capacity Plmax，j(ii) a Load P at ith nodedi(τ), stochastic power supply predicted contribution P at ith nodeue，i(τ)；
The day-ahead scheduling model considering uncertainty in a time period comprises a continuous time unit model, a continuous time power grid model, a continuous time stochastic power supply model and an objective function; the objective function is expressed as follows according to a formula, wherein the minimum running cost is obtained under a prediction scene:
Figure FDA0002973135570000011
Figure FDA0002973135570000012
Figure FDA0002973135570000013
Cfi(τ)＝βiPgi(τ)
wherein τ is a continuous variable representing time, ε is an infinitesimal quantity, Csui(τ) is boot cost, Csdi(τ) cost of downtime, Cfi(τ) is Fuel cost, Pgi(τ) is the unit output, Pui(τ) is the random power supply output, U ', at node i'i(tau) is the starting and stopping state U of the unit at the ith nodei(τ) derivative of;
s2, converting the day-ahead scheduling model considering uncertainty in the time period into a discrete form; the discrete form day-ahead scheduling model taking uncertainty in the time period into account is as follows:
Figure FDA0002973135570000014
Csuit≥Vsu，i(Uit-Ui(t-1))
Csdit≥Vsd，i(Ui(t-1)-Uit)
Figure FDA0002973135570000021
where T is the length of each time period, CsuitFor the starting-up cost, CsditFor the cost of shutdown, CfitFor the cost of fuel,
Figure FDA0002973135570000022
The N-time interpolation coefficient of the unit output curve is k, which is 0, 1, 2, …, N;
the constraint conditions of minimum startup and shutdown time constraint, output range constraint, output climbing constraint, tide constraint, randomness range and first-order continuity constraint are respectively as follows:
Figure FDA0002973135570000023
Figure FDA0002973135570000028
Figure FDA0002973135570000024
Figure FDA0002973135570000025
Figure FDA0002973135570000026
Figure FDA0002973135570000027
wherein
Figure FDA0002973135570000031
Can be
Figure FDA0002973135570000032
Or
Figure FDA0002973135570000033
Figure FDA0002973135570000034
UitAnd Ui(t-1)Starting and stopping states, U, of the unit i in time periods t and t-1 respectivelyi(t-1)N-1; gamma is the assumed stochastic power supply output prediction error,
Figure FDA0002973135570000035
interpolation coefficient of N times for unit output curve
Figure FDA0002973135570000036
The vector of the composition is then calculated,
Figure FDA0002973135570000037
interpolation factor of N times for random power output curve
Figure FDA0002973135570000038
The vector of the composition is then calculated,
Figure FDA0002973135570000039
interpolation coefficients for predicting force curves for stochastic power supplies
Figure FDA00029731355700000310
A vector of components; sjiIs a tidal current sensitivity matrix;
and S3, optimizing the discrete-form day-ahead scheduling model considering uncertainty in the time interval by adopting a robust optimization algorithm to obtain an optimal day-ahead scheduling result for coping with uncertainty in the time interval.
2. The method of day-ahead scheduling taking into account uncertainty over a period of time of claim 1, wherein the continuous-time crew model is:
Figure FDA00029731355700000311
Pgmin，iUi(τ)≤Pgi(τ)≤Pgmax，iUi(τ)
Figure FDA00029731355700000312
wherein, Ui(tau) is the starting and stopping state of the unit at the ith node, Pgi(τ) is Unit output force, P'gi(τ) is Pgi(τ) which represents the minimum on-time and off-time constraints of the unit, the unit output range constraints, and the unit climbing capacity limits, respectively.
3. The method of day-ahead scheduling that accounts for uncertainty over a period of time of claim 1, in which the continuous-time power grid model is:
-Plmax，j≤Sji(Pgi(τ)+Pui(τ)-Pdi(τ))≤Plmax，j
wherein, Plmax，jTo rated capacity, Pgi(τ) is the unit output, Pui(τ) is the random power supply output, P, at the ith nodedi(τ) is the load at the ith node; this equation is the line flow constraint.
4. The method of day-ahead scheduling that accounts for uncertainty in time period of claim 1, in which the continuous-time stochastic power model is:
(1-γ)Pue，i(τ)≤Pui(τ)≤(1+γ)Pue，i(τ)
wherein gamma is the prediction error of the assumed random power output, Pui(τ) is the random power supply output, P, at the ith nodeue，i(τ) predicting contribution for the stochastic power source at the ith node; this formula represents the range of possible random power supply outputs.
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