CN117195605A - Electric power system bilinear model relaxation solving method based on linear interpolation - Google Patents
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Abstract
The invention belongs to the technical field of power system energy optimization, and particularly relates to a linear interpolation-based bilinear model relaxation solving method of a power system, which comprises the following steps: s1, constructing an economic dispatch model of a power system, and guaranteeing the mutual exclusion state of energy storage charge and discharge by utilizing the fact that the product of charge and discharge variables is zero; s2, dividing the hour level scheduling into a plurality of minute level scheduling by using a linear interpolation method, and solving the relaxed linear programming model by using a commercial solver; s3, representing a mutual exclusion decision state by using a 0-1 variable; s4, judging the validity of the state variable value by utilizing the fact that the sum of the charge and discharge state variables of the same time node is not more than 1; s5, the original non-male model is loosened again to be a linear programming model, and then a business solver is called again to perform effective calculation of the linear programming model. The method can quickly and effectively realize the relaxation solution of the bilinear model of the power system, and is expected to be widely applied to the relaxation solution of the non-convex model.
Description
Technical Field
The invention belongs to the technical field of power system energy optimization, and particularly relates to a linear interpolation-based bilinear model relaxation solving method of a power system.
Background
At present, with the increase of the permeability of new energy sources at the distribution side, the uncertainty of the generated power of the new energy sources can cause problems such as line congestion or overvoltage, and the like, so that the stable operation of a power system is adversely affected.
The energy storage device is deployed in the power system, so that the running state of the power grid is improved, the running reliability of the power grid is improved, and the mutually exclusive running states such as charging and discharging of the energy storage system need to be represented in the running process of the power system. In the prior art, constraint is generally carried out by adopting zero charge and discharge power products, and a bilinear term formed by two continuous variable products causes non-convex model, so that mathematical complexity of model solving is increased.
In order to eliminate the solving problem caused by bilinear terms, when the objective function of the energy optimization model monotonically increases, the non-convex terms can be eliminated without affecting the optimization result. However, as the permeability of new energy increases, the reverse flow on its distribution side causes the relaxation method to fail. In order to characterize the mutual exclusion constraint of charge and discharge, a 0-1 variable is introduced to describe the running state of energy storage. However, as the scale of systems increases, the presence of a large number of 0-1 variables causes dimensional disasters to occur in the model, making the model challenging to compute.
Therefore, a quick and effective relaxation solving method needs to be explored, and quick solving of the model is realized on the basis of guaranteeing the energy storage constraint charge and discharge mutual exclusion state.
In the prior patent, CN115759668A discloses a non-isothermal power-natural gas optimal power flow calculation method based on a convex relaxation method, and a non-isothermal natural gas system model is constructed; based on the convex envelope, relaxing the tertiary and bilinear constraints of the non-isothermal natural gas system model into a group of linear constraints to obtain a natural gas system convex model; and coupling the direct current power flow model of the power system with the built male model of the natural gas system, building a non-isothermal power natural gas optimal power flow male model, and carrying out power flow calculation based on the non-isothermal power-natural gas optimal power flow male model.
However, the model in the patent does not relate to an energy storage device, and does not consider the mutual exclusion state of energy storage constraint charge and discharge, so the model is different from the model to be solved in the invention.
Disclosure of Invention
According to the defects in the prior art, the invention provides a linear interpolation-based power system bilinear model relaxation solving method, which can quickly and effectively realize relaxation solving of a power system bilinear model.
In order to achieve the above purpose, the invention provides a linear interpolation-based power system bilinear model relaxation solving method, which comprises the following steps:
s1, constructing an economic dispatch model of a power system, setting constraint conditions comprising energy storage constraint, and ensuring mutual exclusion states of energy storage charge and discharge by utilizing zero charge and discharge variable product in the energy storage constraint;
s2, dividing the hour level scheduling into a plurality of minute level scheduling by using a linear interpolation method, eliminating the constraint that the product of charging and discharging variables is 0 according to the characteristic of continuous change of the energy storage charging and discharging power in a small time interval, performing non-male type linearization relaxation on the basis of guaranteeing that the constraint meets a mutual exclusion state (namely, linearization relaxation of an economic scheduling model is a linear programming model, and the same applies), and solving the relaxed linear programming model by using a commercial solver;
according to the characteristic that the power generation and the load power in the small area cannot be suddenly changed and the power balance constraint, the energy storage cannot be continuously suddenly changed in a quick charge and a quick discharge. According to the characteristics of the system, the constraint that the product of energy storage charging and discharging is 0 is eliminated, so that the simultaneous charging and discharging conditions are not caused;
s3, extracting energy storage charge and discharge power values at an original time node in an economic dispatch model, using a 0-1 variable to represent a mutual exclusion decision state, if the power value is not 0, setting the charge and discharge state variable at the corresponding time node as 1, otherwise setting the state variable as 0;
s4, judging the validity of the state variable values by utilizing that the sum of the charge state variable and the discharge state variable of the same time node is not more than 1, if the validity is met, continuing to solve the model, otherwise, increasing the number of interpolation points, and repeating the step S2 again;
s5, after the relaxation solution of S2 and the validity verification of S4, the original non-male model is relaxed again to be a linear programming model according to the solution of the 0-1 variable in S4, and then a business solver is called again to carry out the effective calculation of the linear programming model.
And after solving again, obtaining an effective relaxation solution of the economic dispatch model constructed in the step S1.
In the step S1, an economic dispatching model of the electric power system is constructed with the aim of minimizing the electricity generation and wind abandon punishment cost, and constraint conditions to be met by the model also comprise power balance constraint, electricity generation power constraint, climbing constraint and wind abandon constraint.
In the step S1, the step of constructing an economic dispatch model of the power system is as follows:
s11, determining an objective function as:
（1）；
on the basis of the objective function, establishing an optimal decision aiming at minimizing the running cost as follows:
（2）；
wherein a is g 、b g And c g For a given power generation parameter,punishing costs for wind curtailment; p (P) g，t For generating power of unit, P c，t Charging power for energy storage, P d，t For storing energy, discharging power, SOC t Is in charge state, P wc，t The air quantity is discarded:
s12, setting power balance constraint as follows:
（3）；
wherein P is w，t Andrespectively->Predicted values of wind power utilization amount and load at moment;
s13, setting upper and lower limit constraints of the generated power of the generating set as follows:
（4）；
i.e. generating capacity P of unit g，t Located at []The interval is within;
s14, setting climbing constraint of the unit as follows:
（5）；
（6）；
i.e. the output increased or decreased per unit time of the unit cannot exceed the upper limit RU of climbing g 、RD g ；
S15, setting air discarding quantity constraint as follows:
（7）；
disposable air volume P wc，t And wind-electricity utilization amount P w，t The sum is not more than the total wind power；
S16, setting energy storage constraint as follows:
（8）；
（9）；
（10）；
（11）；
（12）；
wherein, the energy storage charging and discharging power P c，t 、P d，t Satisfies the upper and lower limits of the formulas (8) and (9)Constraint, wherein constraint of formula (10) is to represent mutually exclusive running states by utilizing the energy storage charge and discharge variable product of zero, and constraint of formula (11) is energy storage state of charge (SOC) t In the formula (I)Respectively the energy storage charging and discharging efficiency and the SOC t Satisfies the upper and lower limit constraints of equation (12).
In the S2, by timeInterpolation processing, dividing the hour level time interval into smaller minute level intervals +.>Interpolation processing is performed on the formulas other than the formula (10) in S1:
（13）；
（14）；
（15）；
（16）；
（17）；
（18）；
（19）；
（20）；
（21）；
（22）；
（23）；
after interpolation processing, the economic dispatch model eliminates the constraint of the charge and discharge products of (10) and utilizes the energy storage to store energy in a smaller interval t in The characteristic of internal continuous change ensures that charge and discharge mutual exclusion decisions cannot occur simultaneously, non-male mould type relaxation is used as a linear programming model, and a commercial solver is utilized for quickly solving the linear programming model.
In the formulas (13) - (23), each character is an interpolated character of the corresponding character in S1, for exampleRespectively, the climbing parameters after interpolation, +.>Respectively the energy storage charging and discharging efficiency after interpolation.
In the step S3, the energy storage charge and discharge power at the time node t before the corresponding interpolation is extracted according to the optimal solution obtained in the step S2And->By binary variable->、/>Limiting the mutual exclusion state of the charge and discharge of the energy storage, and if the power values of the charge and discharge of the energy storage are not 0, corresponding state variables +.>、/>Set to 1, otherwise set to 0.
In the step S4, the validity judging process is that the optimal solution obtained in the step S2 is subjected to mutual exclusion state verification, and mutual exclusion constraint verification is carried outWhether or not it is true, if the charge and discharge power +.>、/>If the sum is not more than 1, the mutual exclusion constraint is established, and the relaxation method is effective; otherwise, the number of interpolation points is increased, and S2 is repeated again.
In S5, by means of variables、/>Relaxing the bilinear term in the formulas (8) and (9), and rewriting the constraint of the formulas (8) and (9) to be:
（24）；
（25）；
therefore, the original non-male model is loosened again to be a linear programming model, a business solver is called again to calculate the linear programming model, and the obtained result is an effective relaxation solution of the original model (economic dispatch model).
In the S2 and S5, the commercial solver adopts Gurobi.
The algorithms involved in the modeling of the present invention may be executed by an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, the algorithms being implemented by the processor executing the program.
The invention has the beneficial effects that:
the invention divides the original time interval into smaller time intervals by utilizing linear interpolation, and generates power and continuously changes load power in the smaller time intervals. The power balance constraint proves that the charging and discharging power of the stored energy is continuously changed without abrupt change.
The invention considers the continuous change characteristics of the charge and discharge of the energy storage, eliminates the constraint that the product of the charge and discharge is 0 in a smaller area, and does not cause the simultaneous charge and discharge. The energy optimization model after relaxation is a linear programming model, and the Gurobi solver can be used for quickly solving the linear programming model after interpolation.
According to the method, the charging and discharging operation decision states of each time node in the original model are judged according to the optimal solution of the interpolated model, the non-male model is relaxed into a linear programming model meeting the charging and discharging mutual exclusion decision states through fixing the 0-1 variable solution, and the quick solving of the model can be realized by utilizing a Gurobi solver.
In summary, the method can quickly and effectively realize the relaxation solution of the bilinear model of the power system, is beneficial to the stable operation of the power system, and is expected to be widely applied to the relaxation solution of the non-convex model.
Drawings
FIG. 1 is a schematic diagram of an interpolation solution of the present invention;
FIG. 2 is a schematic diagram of linear interpolation of an embodiment of the present invention;
FIG. 3 is a graph of predicted data for wind power and load according to an embodiment of the present invention;
FIG. 4 is a graph of simultaneous charging and discharging of energy storage according to an embodiment of the present invention;
FIG. 5 is a graph of the mutual exclusion result of stored energy charge and discharge after interpolation processing according to an embodiment of the present invention.
Detailed Description
Embodiments of the invention are further described below with reference to the accompanying drawings:
as shown in fig. 1 and 2, a linear interpolation-based power system bilinear model relaxation solving method includes the following steps:
s1, constructing an economic dispatch model of an electric power system with the aim of minimizing the electricity generation and wind abandoning punishment cost, wherein constraint conditions to be met by the model include energy constraint, power balance constraint, electricity generation power constraint, climbing constraint and wind abandoning constraint, and in energy storage constraint, the mutual exclusion state of energy storage charge and discharge is ensured by utilizing zero charge and discharge variable product;
s2, dividing the hour level scheduling into a plurality of minute level scheduling by using a linear interpolation method, eliminating the constraint that the product of the charging and discharging variables is 0 according to the characteristic of continuous change of the energy storage charging and discharging power in a small time interval, carrying out non-male-mold type linearization relaxation on the basis of guaranteeing that the constraint meets the mutual exclusion state, and solving a relaxed linear programming model by using a Gurobi business solver;
s3, extracting energy storage charge and discharge power values at an original time node in an economic dispatch model, using a 0-1 variable to represent a mutual exclusion decision state, if the power value is not 0, setting the charge and discharge state variable at the corresponding time node as 1, otherwise setting the state variable as 0;
s4, judging the validity of the state variable values by utilizing that the sum of the charge state variable and the discharge state variable of the same time node is not more than 1, if the validity is met, continuing to solve the model, otherwise, increasing the number of interpolation points, and repeating the step S2 again;
s5, after the relaxation solution of S2 and the validity verification of S4, the original non-male model is relaxed again to be a linear programming model according to the solution of the 0-1 variable in S4, and then the Gurobi business solver is called again to carry out the effective calculation of the linear programming model.
In S1, the steps of constructing an economic dispatch model of a power system are as follows:
s11, determining an objective function as:
（1）；
on the basis of the objective function, establishing an optimal decision aiming at minimizing the running cost as follows:
（2）；
wherein a is g 、b g And c g For a given power generation parameter,punishing costs for wind curtailment; p (P) g，t For generating power of unit, P c，t Charging power for energy storage, P d，t For storing energy, discharging power, SOC t Is in charge state, P wc，t The air quantity is discarded:
s12, setting power balance constraint as follows:
（3）；
wherein P is w，t Andrespectively->Predicted values of wind power utilization amount and load at moment;
s13, setting upper and lower limit constraints of the generated power of the generating set as follows:
（4）；
i.e. generating capacity P of unit g，t Located at []The interval is within;
s14, setting climbing constraint of the unit as follows:
（5）；
（6）；
i.e. the output increased or decreased per unit time of the unit cannot exceed the upper limit RU of climbing g 、RD g ；
S15, setting air discarding quantity constraint as follows:
（7）；
disposable air volume P wc，t And wind-electricity utilization amount P w，t The sum is not more than the total wind power；
S16, setting energy storage constraint as follows:
（8）；
（9）；
（10）；
（11）；
（12）；
wherein, the energy storage charging and discharging power P c，t 、P d，t Satisfies the upper and lower limit constraints of the formulas (8) and (9), wherein the constraint of the formula (10) is that the mutual exclusion running state is represented by using the energy storage charge and discharge variable product of zero, and the formula (11) is thatEnergy storage state of charge SOC t In the formula (I)Respectively the energy storage charging and discharging efficiency and the SOC t Satisfies the upper and lower limit constraints of equation (12).
S2, by timeInterpolation processing, dividing the hour level time interval into smaller minute level intervalsInterpolation processing is performed on the formulas other than the formula (10) in S1:
（13）；
（14）；
（15）；
（16）；
（17）；
（18）；
（19）；
（20）；
（21）；
（22）；
（23）；
after interpolation processing, the economic dispatch model eliminates the constraint of the charge and discharge products of (10) and utilizes the energy storage to store energy in a smaller interval t in The characteristic of internal continuous change ensures that charge and discharge mutual exclusion decisions cannot occur simultaneously, non-male mould type relaxation is used as a linear programming model, and a commercial solver is utilized for quickly solving the linear programming model.
S3, extracting energy storage charging and discharging power at the time node t before corresponding interpolation according to the optimal solution obtained in the step S2And->By binary variable->、/>Limiting the mutual exclusion state of the charge and discharge of the energy storage, and if the power values of the charge and discharge of the energy storage are not 0, corresponding state variables +.>、/>Set to 1, otherwise set to 0.
S4, the effectiveness judging process is that the optimal solution obtained in the step S2 is subjected to mutual exclusion state verification, and mutual exclusion constraint is verifiedWhether or not it is true, if the charge and discharge power +.>、/>If the sum is not more than 1, the mutual exclusion constraint is established, and the relaxation method is effective; otherwise, the number of interpolation points is increased, and S2 is repeated again.
S5, by means of variables、/>Relaxing the bilinear term in the formulas (8) and (9), and rewriting the constraint of the formulas (8) and (9) to be:
（24）；
（25）；
and the original non-male model is relaxed again to be a linear programming model, a business solver is called again to calculate the linear programming model, and the obtained result is an effective relaxation solution of the original model.
Taking simulation experiments as examples for verification:
a typical economic dispatch model was selected for analysis, table 1 shows thermal power plant parameter settings for the examples, and table 2 shows energy storage parameter settings for the examples. In this embodiment, certain typical day-ahead prediction data is selected for analysis of the validity of the proposed method.
FIG. 3 is predicted data of wind power and load, and thus simulation verification of an economic dispatch model is achieved. To contrast the necessity of the bilinear term constraint, the decision result after ignoring the constraint of equation (10) is shown in FIG. 4. As can be seen from fig. 4, directly neglecting the constraint of equation (10) can lead to the simultaneous charging and discharging of the stored energy; as can be seen from fig. 5, considering the interpolated relaxation model, dividing the time zone into smaller time zones with 15 minutes as the time interval can limit the simultaneous charging and discharging by utilizing the characteristic that the charging and discharging states of the stored energy do not continuously change suddenly.
The linear interpolation-based linear model relaxation solving method for the electric power system provided by the invention realizes non-male-type linear relaxation formed by charge and discharge variables by utilizing the characteristic that the charge and discharge states of stored energy in an interpolation time interval cannot be suddenly changed. On the basis, the charging and discharging states of the energy storage are determined according to the optimal solution of the linear programming model after relaxation, the non-convex problem is converted into the linear programming problem with fixed charging and discharging states, and the problem solving is realized by utilizing Gurobi. In the process, the energy storage charging and discharging model relaxation solving method considering linear interpolation improves the engineering practicability of the model.
Claims (8)
1. A linear interpolation-based bilinear model relaxation solving method of an electric power system is characterized by comprising the following steps:
s1, constructing an economic dispatch model of a power system, setting constraint conditions comprising energy storage constraint, and ensuring mutual exclusion states of energy storage charge and discharge by utilizing zero charge and discharge variable product in the energy storage constraint;
s2, dividing the hour level scheduling into a plurality of minute level scheduling by using a linear interpolation method, eliminating the constraint that the product of the charging and discharging variables is 0 according to the characteristic of continuous change of the energy storage charging and discharging power in a small time interval, carrying out non-male-mold type linearization relaxation on the basis of guaranteeing that the constraint meets the mutual exclusion state, and solving the relaxed linearization programming model by using a commercial solver;
s3, extracting energy storage charge and discharge power values at an original time node in an economic dispatch model, using a 0-1 variable to represent a mutual exclusion decision state, if the power value is not 0, setting the charge and discharge state variable at the corresponding time node as 1, otherwise setting the state variable as 0;
s4, judging the validity of the state variable values by utilizing that the sum of the charge state variable and the discharge state variable of the same time node is not more than 1, if the validity is met, continuing to solve the model, otherwise, increasing the number of interpolation points, and repeating the step S2 again;
s5, after the relaxation solution of S2 and the validity verification of S4, the original non-male model is relaxed again to be a linear programming model according to the solution of the 0-1 variable in S4, and then a business solver is called again to carry out the effective calculation of the linear programming model.
2. The linear interpolation-based power system bilinear model relaxation solving method as claimed in claim 1, wherein the method comprises the following steps: in the step S1, an economic dispatching model of the electric power system is constructed with the aim of minimizing the electricity generation and wind abandon punishment cost, and constraint conditions to be met by the model also comprise power balance constraint, electricity generation power constraint, climbing constraint and wind abandon constraint.
3. The linear interpolation-based power system bilinear model relaxation solving method as claimed in claim 2, wherein the method is characterized by comprising the following steps: in the step S1, the step of constructing an economic dispatch model of the power system is as follows:
s11, determining an objective function as:
（1）；
on the basis of the objective function, establishing an optimal decision aiming at minimizing the running cost as follows:
（2）；
wherein a is g 、b g And c g For a given power generation parameter,punishing costs for wind curtailment; p (P) g，t For generating power of unit, P c，t Charging power for energy storage, P d，t For storing energy, discharging power, SOC t Is in charge state, P wc，t The air quantity is discarded:
s12, setting power balance constraint as follows:
（3）；
wherein P is w，t Andrespectively->Predicted values of wind power utilization amount and load at moment;
s13, setting upper and lower limit constraints of the generated power of the generating set as follows:
（4）；
i.e. generating capacity P of unit g，t Located at []The interval is within;
s14, setting climbing constraint of the unit as follows:
（5）；
（6）；
i.e. the output increased or decreased per unit time of the unit cannot exceed the upper limit RU of climbing g 、RD g ；
S15, setting air discarding quantity constraint as follows:
（7）；
disposable air volume P wc，t And wind-electricity utilization amount P w，t The sum is not more than the total wind power；
S16, setting energy storage constraint as follows:
（8）；
（9）；
（10）；
（11）；
（12）；
wherein, the energy storage charging and discharging power P c，t 、P d，t Satisfies the upper and lower limit constraints of the formulas (8) and (9), wherein the constraint of the formula (10) is to represent the mutually exclusive running state by utilizing the energy storage charge and discharge variable product of zero, and the formula (11) is the energy storage charge state SOC t In the formula (I)Respectively the energy storage charging and discharging efficiency and the SOC t Satisfies the upper and lower limit constraints of equation (12).
4. A linear interpolation based power system bilinear model relaxation solution method as claimed in claim 3, wherein: in the S2, by timeInterpolation processing, dividing the hour level time interval into smaller minute level intervals +.>Interpolation processing is performed on the formulas other than the formula (10) in S1:
（13）；
（14）；
（15）；
（16）；
（17）；
（18）；
（19）；
（20）；
（21）；
（22）；
（23）；
after interpolation processing, the economic dispatch model eliminates the constraint of the charge and discharge products of (10) and utilizes the energy storage to store energy in a smaller interval t in The characteristic of internal continuous change ensures that charge and discharge mutual exclusion decisions cannot occur simultaneously, non-male mould type relaxation is used as a linear programming model, and a commercial solver is utilized for quickly solving the linear programming model.
5. The linear interpolation-based power system bilinear model relaxation solving method as claimed in claim 4, wherein the method comprises the following steps: in the step S3, the energy storage charge and discharge power at the time node t before the corresponding interpolation is extracted according to the optimal solution obtained in the step S2And->By binary variable->、/>Limiting the mutual exclusion state of the charge and discharge of the energy storage, and if the power values of the charge and discharge of the energy storage are not 0, corresponding state variables +.>、/>Set to 1, otherwise set to 0.
6. The linear interpolation-based power system bilinear model relaxation solving method of claim 5, wherein the method comprises the following steps of: in the step S4, the validity judging process is that the optimal solution obtained in the step S2 is subjected to mutual exclusion state verification, and mutual exclusion constraint verification is carried outWhether or not it is true, if the charge and discharge power +.>、/>If the sum is not more than 1, the mutual exclusion constraint is established, and the relaxation method is effective; otherwise, the number of interpolation points is increased, and S2 is repeated again.
7. The linear interpolation-based power system bilinear model relaxation solving method of claim 6, wherein the method comprises the following steps of: in S5, by means of variables、/>Relaxing the bilinear term in the formulas (8) and (9), and rewriting the constraint of the formulas (8) and (9) to be:
（24）；
（25）；
and the original non-male model is relaxed again to be a linear programming model, a business solver is called again to calculate the linear programming model, and the obtained result is an effective relaxation solution of the original model.
8. The linear interpolation-based power system bilinear model relaxation solving method as claimed in claim 1, wherein the method comprises the following steps: in the S2 and S5, the commercial solver adopts Gurobi.
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