CN111985686A - Power distribution network distribution robust optimization scheduling method based on probability prediction - Google Patents
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Abstract
The invention discloses a power distribution network distribution robust optimization scheduling method based on probability prediction, which comprises the following steps: adopting a probability distribution interval to construct a fuzzy set based on probability prediction; according to the constructed fuzzy set, constructing a distribution network scheduling model based on distribution robust optimization; applying an affine strategy and a strong dual theory to convert the established power distribution network scheduling model into a mixed integer linear programming problem; and solving the mixed integer linear programming problem to obtain the optimal decision of the distribution robust optimized scheduling of the power distribution network. The invention adopts the fuzzy set based on probability prediction, and can accurately depict the probability distribution of uncertain parameters, thereby improving the authenticity and the effectiveness of the solution. The method can convert the distributed robust optimization model into an easily-solved mixed integer linear programming problem, improves the calculation efficiency and reduces the solving difficulty.
Description
Technical Field
The invention belongs to the field of power system scheduling, and particularly relates to a distributed robust optimization method.
Background
With the rapid development of society, the increasing problems of environmental pollution and energy shortage, non-renewable energy sources such as fossil energy and the like are not enough to support the sustainable development of human society. According to the International Energy Outlook published by the Energy information administration in 2019, the worldwide power demand will be greatly increased in 2020 and 2050, and the power supply will be changed significantly: 1) the increment of the renewable energy power generation is in the first place, and the renewable energy power generation replaces coal-fired power generation to become the primary power generation energy in 2025 years; 2) the gas turbine is rapidly developed due to the advantages of short construction period, quick response, cleanness, environmental protection and the like.
The randomness and intermittency of the output of the renewable energy source bring great challenges to the safe and stable operation of the power system. Distribution robust optimization is used as a new uncertain optimization method, the problems that random planning is over-dependent on accurate probability distribution and the calculated amount is too large can be solved, the problem that the traditional robust optimization is over conservative is effectively avoided, and the method is gradually applied to the field of power system optimization in recent years. However, the current distribution robust optimization method mostly adopts the statistical rules of uncertain parameters (such as first-order and second-order moment information) to construct a fuzzy set, and the depiction of the uncertain parameters is rough, so that the obtained optimization result deviates from the actual situation. In addition, most of the existing solutions of the distributed robust optimization model are converted into semi-definite planning or second-order cone planning problems, so that the solutions are difficult and the calculation efficiency is low.
Disclosure of Invention
In order to solve the technical problems mentioned in the background art, the invention provides a distribution network distribution robust optimization scheduling method based on probability prediction.
In order to achieve the technical purpose, the technical scheme of the invention is as follows:
a distribution network distribution robust optimization scheduling method based on probability prediction comprises the following steps:
(1) adopting a probability distribution interval to construct a fuzzy set based on probability prediction;
(2) constructing a distribution network scheduling model based on distribution robust optimization according to the fuzzy set constructed in the step (1);
(3) applying an affine strategy and a strong dual theory to convert the power distribution network scheduling model established in the step (2) into a mixed integer linear programming problem;
(4) and (4) solving the mixed integer linear programming problem in the step (3) to obtain the optimal decision of the distribution robust optimal scheduling of the power distribution network.
Further, the specific process of step (1) is as follows:
(101) obtaining K continuous renewable energy output prediction intervals and interval probabilities thereof by adopting a probability prediction method, wherein K is the number of the intervals;
(102) according to the obtained prediction interval and interval probability, constructing a fuzzy set F based on probability prediction:
in the above formula, wtThe renewable energy output is obtained in the time period t; p is wtA probability distribution of (a); r is wtAll possible output conditions; p (R) is wtAll possible probability distributions; wkIs wtAn indeterminate set of kth intervals; p is a radical ofkIs wtProbability of kth interval; epIndicating an expected value;μ tandis wtLower and upper limits of expected values;w k,tandare respectively wtLower and upper limits of the k-th interval.
Further, the specific process of step (2) is as follows:
(201) constructing an objective function of a distribution network scheduling model based on distribution robust optimization:
in the above formula, the first and second carbon atoms are,respectively, the start, stop, fixing and unit power generation costs of the gas turbine e; boolean variable ue,t、ve,t、xe,tRespectively indicating whether the gas turbine e is started, stopped and operated in the time period t, if so, setting 1, and otherwise, setting 0;output power of gas turbine e for time period t; sup denotes supremum;
(202) constructing constraint conditions of a distribution network scheduling model based on distribution robust optimization:
a) gas turbine restraint:
xe,t-xe,t-1=ue,t-ve,t
in the above formula, the Boolean variable xe,τIndicating whether the gas turbine e is started in the period tau, if so, setting 1, otherwise, setting 0; minimum startup and shutdown times of the gas turbine e, respectively;minimum and maximum output power of the gas turbine e, respectively;the maximum upward and downward climbing rates of the gas turbine e are respectively;the output power of the gas turbine e for a period t-1; boolean variable xe,t-1Indicating whether the gas turbine e works in the period of t-1, if so, setting 1, otherwise, setting 0;
b) power flow constraint of the power distribution network:
Vj,t=Vi,t-(Pij,trij+Qij,txij)/V0
in the above formula, the first and second carbon atoms are,respectively, the active power output power and the reactive power output power of a node j in a period t, wherein,the output power and the renewable energy output of the gas turbine comprising the node j are included; pij,t、Qij,tRespectively the active power and the reactive power of the branch circuits i-j in the t period;all branch sets with head end node j; pjl,t、Qjl,tRespectively the active power and the reactive power of the branch j-l in the time period t;respectively the active load and the reactive load of a node j in the period t; vi,t、Vj,tThe voltage amplitudes of the nodes i and j in the period t are respectively; r isij、xijRespectively the resistance and reactance of the branch circuits i-j; v0Is a voltage reference value.
Further, the specific process of step (3) is as follows:
(301) applying an affine strategy and a strong dual theory to convert a target function of a power distribution network scheduling model:
according to the definition of the fuzzy set F, the supremum problem sup in the objective function is expressed as follows:
f(wt)≥0
in the above formula, f (w)t) Is wtA measure of probability of; df (w)t) Is f (w)t) Differentiation of (1); alpha is alphak,βt,γtIs a dual variable;
applying strong dual theory, the model is converted into:
according to the uncertain set WkIs defined as
Expressed as:
in the above formula, the first and second carbon atoms are,k,tandk,tis a dual variable;
and (3) applying the strong dual theory again to convert the model into:
(302) applying an affine strategy and a strong dual theory to convert the constraint conditions of the power distribution network scheduling model:
according to the uncertain set WkThe above formula is expressed as:
in the above formula, the first and second carbon atoms are,e,k,tande,k,tis a dual variable;
applying strong dual theory, the model is converted into:
for other constraints, the conversion process is basically consistent and is not repeated.
Adopt the beneficial effect that above-mentioned technical scheme brought:
the invention adopts the probability interval to construct the fuzzy set, and can more accurately depict the probability distribution of uncertain parameters, thereby leading the optimization result to be more in line with the practice. In addition, the power distribution network scheduling model based on distribution robust optimization is converted into the mixed integer linear programming problem through an affine strategy and a strong dual theory, and compared with the mixed integer semi-definite programming or second-order cone programming problem, the mixed integer linear programming problem has lower solving difficulty and higher solving efficiency.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
fig. 2 is a schematic diagram of an IEEE33 node power distribution network test system.
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings.
The invention designs a distribution network distribution robust optimization scheduling method based on probability prediction, which comprises the following specific steps as shown in figure 1:
step 1: adopting a probability distribution interval to construct a fuzzy set based on probability prediction;
step 2: constructing a distribution network scheduling model based on distribution robust optimization according to the fuzzy set constructed in the step 1;
and step 3: applying an affine strategy and a strong dual theory to convert the power distribution network scheduling model established in the step 2 into a mixed integer linear programming problem;
and 4, step 4: and (4) solving the mixed integer linear programming problem in the step (3) to obtain the optimal decision of the distribution robust optimal scheduling of the power distribution network.
An IEEE33 node power distribution network test system is taken as an example, and a schematic diagram is shown in FIG. 2. Renewable energy generator sets that are considered include wind turbines and photovoltaic sets. The gas turbine GT1, the gas turbine GT2, the wind turbine WT and the photovoltaic generator PV are respectively connected to the nodes 17, 32, 24 and 21. The gas turbine parameters are shown in table 1. The model was solved using GAMS software, and the results were as follows.
TABLE 1 gas turbine parameters
The objective function values (costs) of the probability prediction-based distributed robust optimization method and the conventional statistical rule-based distributed robust optimization method (mixed integer second-order cone programming problem) are shown in table 2. It can be seen that the method of the present invention has a lower cost, because the method can more accurately depict the probability distribution of the renewable energy output, thereby effectively reducing the conservation of the solution and improving the effectiveness of the solution.
TABLE 2 comparison of objective function values for different methods
The calculated times for both methods are shown in table 3. It can be seen that the calculation time of the method of the present invention is only half of that of the conventional method, because the solving speed of the mixed integer linear programming problem obtained by the method of the present invention is much higher than that of the mixed integer second-order cone programming problem obtained by the conventional method. The method of the invention can improve the calculation efficiency.
TABLE 3 comparison of calculation times by different methods
The embodiments are only for illustrating the technical idea of the present invention, and the technical idea of the present invention is not limited thereto, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the scope of the present invention.
Claims (4)
1. A distribution network distribution robust optimization scheduling method based on probability prediction is characterized by comprising the following steps:
(1) adopting a probability distribution interval to construct a fuzzy set based on probability prediction;
(2) constructing a distribution network scheduling model based on distribution robust optimization according to the fuzzy set constructed in the step (1);
(3) applying an affine strategy and a strong dual theory to convert the power distribution network scheduling model established in the step (2) into a mixed integer linear programming problem;
(4) and (4) solving the mixed integer linear programming problem in the step (3) to obtain the optimal decision of the distribution robust optimal scheduling of the power distribution network.
2. The distribution network distribution robust optimization scheduling method based on probability prediction as claimed in claim 1 is characterized in that the specific process of step (1) is as follows:
(101) obtaining K continuous renewable energy output prediction intervals and interval probabilities thereof by adopting a probability prediction method, wherein K is the number of the intervals;
(102) according to the obtained prediction interval and interval probability, constructing a fuzzy set F based on probability prediction:
in the above formula, wtThe renewable energy output is obtained in the time period t; p is wtA probability distribution of (a); r is wtAll possible output conditions; p (R) is wtAll possible probability distributions; wkIs wtAn indeterminate set of kth intervals; p is a radical ofkIs wtProbability of kth interval; epIndicating an expected value;μ tandis wtLower and upper limits of expected values;w k,tandare respectively wtLower and upper limits of the k-th interval.
3. The distribution network distribution robust optimization scheduling method based on probability prediction as claimed in claim 2, wherein the specific process of step (2) is as follows:
(201) constructing an objective function of a distribution network scheduling model based on distribution robust optimization:
in the above formula, the first and second carbon atoms are,respectively, the start, stop, fixing and unit power generation costs of the gas turbine e; boolean variable ue,t、ve,t、xe,tRespectively indicating whether the gas turbine e is started, stopped and operated in the time period t, if so, setting 1, and otherwise, setting 0;output power of gas turbine e for time period t; sup denotes supremum;
(202) constructing constraint conditions of a distribution network scheduling model based on distribution robust optimization:
a) gas turbine restraint:
xe,t-xe,t-1=ue,t-ve,t
in the above formula, the Boolean variable xe,τIndicating whether the gas turbine e is started in the period tau, if so, setting 1, otherwise, setting 0; minimum startup and shutdown times of the gas turbine e, respectively;minimum and maximum output power of the gas turbine e, respectively;the maximum upward and downward climbing rates of the gas turbine e are respectively;the output power of the gas turbine e for a period t-1; boolean variable xe,t-1Indicating whether the gas turbine e works in the period of t-1, if so, setting 1, otherwise, setting 0;
b) power flow constraint of the power distribution network:
Vj,t=Vi,t-(Pij,trij+Qij,txij)/V0
in the above formula, the first and second carbon atoms are,respectively, the active power output power and the reactive power output power of a node j in a period t, wherein,the output power and the renewable energy output of the gas turbine comprising the node j are included; pij,t、Qij,tRespectively the active power and the reactive power of the branch circuits i-j in the t period;all branch sets with head end node j; pjl,t、Qjl,tRespectively the active power and the reactive power of the branch j-l in the time period t;respectively the active load and the reactive load of a node j in the period t; vi,t、Vj,tThe voltage amplitudes of the nodes i and j in the period t are respectively; r isij、xijRespectively the resistance and reactance of the branch circuits i-j; v0Is a voltage reference value.
4. The distribution network distribution robust optimization scheduling method based on probability prediction as claimed in claim 3, wherein the specific process of step (3) is as follows:
(301) applying an affine strategy and a strong dual theory to convert a target function of a power distribution network scheduling model: applying an affine policy, willIs denoted by wtLinear affine function of (1):
according to the definition of the fuzzy set F, the supremum problem sup in the objective function is expressed as follows:
f(wt)≥0
in the above formula, f (w)t) Is wtA measure of probability of; df (w)t) Is f (w)t) Differentiation of (1); alpha is alphak,βt,γtIs a dual variable;
applying strong dual theory, the model is converted into:
βt≤0,γt≥0
according to the uncertain set WkIs defined as
Expressed as:
wt≥w k,t:k,t
in the above formula, the first and second carbon atoms are,k,tandk,tis a dual variable;
and (3) applying the strong dual theory again to convert the model into:
k,t≤0,k,t≥0
(302) applying an affine strategy and a strong dual theory to convert the constraint conditions of the power distribution network scheduling model: for constraint conditionsAccording to the affine strategy, it is expressed as:
according to the uncertain set WkThe above formula is expressed as:
wt≥w k,t:e,k,t
in the above formula, the first and second carbon atoms are,e,k,tande,k,tis a dual variable;
applying strong dual theory, the model is converted into:
e,k,t≤0,e,k,t≥0。
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CN117688793A (en) * | 2024-02-04 | 2024-03-12 | 中国地质大学(武汉) | Combined modeling and solving method and equipment for distributed robust unit and storage equipment |
CN117688793B (en) * | 2024-02-04 | 2024-05-10 | 中国地质大学(武汉) | Combined modeling and solving method and equipment for distributed robust unit and storage equipment |
CN118297439B (en) * | 2024-06-04 | 2024-07-30 | 国网经济技术研究院有限公司 | Multi-stage transmission and storage collaborative distribution robust planning method and system for power system |
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