Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an economic dispatching method of an electric power system based on opportunity constraint. The invention provides an effective solving method for sequentially determining the electricity abandonment amount of the renewable energy source and the output of the traditional generator, considers the fluctuation of the renewable energy source in the power system, ensures the safety of the power system, is suitable for being applied to the economic dispatching scene of the power system with high renewable energy source permeability, and has high application value.
The invention provides an opportunity constraint-based power system economic dispatching method which is characterized in that the method comprises the steps of firstly establishing an opportunity constraint-based power system economic dispatching model composed of an objective function and constraint conditions, then converting the model, writing opportunity constraints in the model into a quantile form, introducing relaxation variables, establishing a relaxed opportunity constraint-based power system economic dispatching model, and solving to obtain values of the relaxation variables; and obtaining a constraint condition that an economic dispatching model of the power system based on opportunity constraint has a feasible solution by using the values of the relaxation variables, then sequentially establishing a renewable energy power curtailment dispatching model and a generator output optimization model and respectively solving the models to obtain the power curtailment of each renewable energy source and the active power of each generator in each time period, thereby obtaining a final dispatching result. The method comprises the following steps:
1) establishing an opportunity constraint-based economic dispatching model of the power system, wherein the model consists of an objective function and constraint conditions; the method comprises the following specific steps:
1-1) determining an objective function of an economic dispatching model of the power system, wherein the expression is as follows:
wherein T is the number of time segments of the optimization period, N
GIn order to access the set of nodes of the generator,
for the active power of the ith generator during time period t,
for the generating cost of the ith generator in the time period t, N
RIn order to access the set of nodes of the renewable energy source,
the active power output upper limit of the jth renewable energy source,
a power abandon penalty cost for the jth renewable energy source in the time period t;
wherein the content of the first and second substances,
wherein A isgi,Bgi,CgiThe power generation cost coefficient of the ith generator is obtained;
wherein, K
jPenalty cost coefficient for jth renewable energy source, C
jIs the maximum capacity of the jth renewable energy source,
a probability density function of available capacity for the jth renewable energy source over time period t;
1-2) determining the constraint conditions of the economic dispatching model of the power system, comprising the following steps:
1-2-1) generator power constraint:
wherein the content of the first and second substances,
upper and lower power limits, Rup, of the ith generator, respectively
i,Rdown
iThe power limit of the ith generator is limited by upward climbing power and downward climbing power;
1-2-2) renewable energy power constraints:
wherein the content of the first and second substances,
the power is scheduled for the jth renewable energy source for time period t,
the predicted power for the jth renewable energy source over time period t,
the actual power for the jth renewable energy source during time period t,
available power for the jth renewable energy source for time period t;
1-2-3) power balance constraints:
wherein the content of the first and second substances,
for node k load demand over time period t, N
DA node set for accessing a load;
1-2-4) affine control and backup constraints:
wherein the content of the first and second substances,
actual power, beta, in consideration of affine control for the ith generator
iAffine control participation factor, alpha, for the i-th generator
UR,α
DRRespectively the maximum allowable probability of the shortage of the up-regulation equipment and the maximum allowable probability of the shortage of the down-regulation equipment;
1-2-5) line transmission capacity constraints:
wherein N is
WIn order to be a set of lines,
power transfer factors, P, of the line L with respect to the nodes i, j, k, respectively
LFor the maximum transmission capacity of the line L,
respectively the maximum allowable probability of forward out-of-limit and the maximum allowable probability of reverse out-of-limit of the transmission capacity of the line L;
2) converting the model established in the step 1), establishing a relaxed opportunity constraint-based power system economic dispatching model and solving the model; the method comprises the following specific steps:
2-1) by substitution in formula (10)
Writing the opportunistic constraints (11) - (14) of the model in step 1) into the form of quantiles as follows:
wherein Q (xi | p) is the p-quantile of the random variable xi,
for equivalent power transfer of line L relative to node j under consideration of affine controlShift factor, M
LCorrection coefficients for affine control to the branch L power transfer factors;
let the joint distribution of renewable energy power over time period t be as follows:
wherein the content of the first and second substances,
a random variation of the available power composition for each renewable energy source over time t,
random variables composed of power output of each renewable energy source in a time period t;
2-2) use
In alternative quantiles (15) - (18)
And introducing relaxation variables with the constraints (16) and the transmission power constraints (17) - (18) in the down-regulation to obtain the equations (23) - (26);
wherein, drs
tSlack variables in the standby constraints are adjusted for a period of time t,
the slack variable in the forward constraint and the slack variable in the reverse constraint of the line transmission capacity in the t period are respectively;
2-3) establishing a relaxed opportunity constraint economic dispatching model and solving;
wherein the model objective function is formula (27), the constraint conditions include formulas (4) to (7), formula (9), formulas (23) to (26), and formula (28), and the expression is as follows:
s.t. formulae (4) - (7), (9), (23) - (26) and (28)
Wherein the content of the first and second substances,
wherein, among others,
respectively adjusting the standby weight coefficient and the cross section risk weight coefficient in the t time period;
solving the model to obtain
The optimal solution of (2);
3) determining the electric quantity discarded by each renewable energy source and the active power of each generator to obtain a scheduling result of the power system; the method comprises the following specific steps:
3-1) utilizing the solving result of the model in the step 2-3) and relaxing the variable
Obtaining the constraint condition that the power system economic dispatching model based on the opportunity constraint established in the step 1) has a feasible solution:
if the slack variable drstAfter the renewable energy is abandoned, if the model in the step 1) has a feasible solution, the inequality constraint shown in the following formula is satisfied:
if the relaxation variable is changed
If not zero, the quantile in equation (17) satisfies the inequality constraint shown in equation (30) below:
if the relaxation variable is changed
If not, the quantile in equation (18) satisfies the inequality constraint shown in equation (31) below:
the constraints (29) to (31) are written as shown in the following formula:
wherein Ω is a subscript set of renewable energy sources participating in electricity abandonment, cj,ckIs a constant coefficient;
3-2) establishing a renewable energy power abandoning amount scheduling model and solving;
the objective function of the renewable energy power curtailment scheduling model is shown as the following formula:
the first and second derivatives of equation (33) are respectively as follows:
the curtailment penalty in equation (33) is approximated by a linear inequality as shown in equation (36):
obtaining the electric quantity abandoned by each renewable energy source in each time period t through solving the formula (36)
Then, based on the probability distribution of the available power of the renewable energy source obtained by the probability prediction and quantiles in the electric quantity abandoning calculation formulas (15) to (18) obtained by solving the formula (36), the constraint formulas (15) to (18) become deterministic linear constraints;
3-3) utilizing the result of the step 3-2) to establish a generator output optimization model and solve to obtain the active power of each generator in each time period
Wherein, the objective function of the optimization model is formula (37), and the constraint conditions include: formulae (4) to (7), formula (9), formulae (15) to (18), and formula (38), the expressions are as follows:
s.t. formulae (4) - (7), (9), (15) - (18) and (38)
3-4) the electric energy abandon amount of each renewable energy source obtained in the step 3-2) in each time interval and the active power of each generator obtained in the step 3-3) in each time interval are the dispatching results of the power system.
The invention provides an opportunity constraint-based economic dispatching method for an electric power system, which has the following advantages:
(1) the power system economic dispatching method based on opportunity constraint provided by the invention optimizes the output of the conventional generator and the renewable energy power-abandoning strategy at the same time so as to reduce the total operation cost to the maximum extent and limit the operation risk.
(2) The invention provides an effective solving method for sequentially determining the electricity abandonment amount of renewable energy sources and the output of a traditional generator, establishes an easily-solved optimization model for each step, and is suitable for being applied to an economic dispatching scene of a power system with high renewable energy permeability.
Detailed Description
The invention provides an opportunity constraint-based power system economic dispatching method which comprises the steps of firstly establishing an opportunity constraint-based power system economic dispatching model consisting of an objective function and constraint conditions, then converting the model, writing opportunity constraints in the model into quantiles and introducing relaxation variables, establishing a relaxed opportunity constraint-based power system economic dispatching model, and solving to obtain values of the relaxation variables; and obtaining a constraint condition that an economic dispatching model of the power system based on opportunity constraint has a feasible solution by using the values of the relaxation variables, then sequentially establishing a renewable energy power curtailment dispatching model and a generator output optimization model and respectively solving the models to obtain the power curtailment of each renewable energy source and the active power of each generator in each time period, thereby obtaining a final dispatching result. The method comprises the following steps:
1) establishing an opportunity constraint-based economic dispatching model of the power system, wherein the model consists of an objective function and constraint conditions; the method comprises the following specific steps:
1-1) determining a target function of an economic dispatching model of the power system;
the objective of economic dispatch of the power system is to minimize the total cost, which includes the cost of generating power and the penalty cost of renewable energy power abandonment, and the objective function is shown as the following formula:
wherein T is the number of time segments of the optimization period, N
GIn order to access the set of nodes of the generator,
for the active power of the ith generator during time period t,
for the generating cost of the ith generator in the time period t, N
RIn order to access the set of nodes of the renewable energy source,
the active power output upper limit of the jth renewable energy source,
a charge is penalized for the j-th renewable energy source for the power curtailment at time t.
Wherein the power generation cost can be represented by a quadratic function of the following formula:
wherein A isgi,Bgi,CgiThe power generation cost coefficient of the ith generator.
The penalty charge for electricity abandonment of renewable energy sources is shown as follows:
wherein, K
jPenalty cost coefficient for jth renewable energy source, C
jIs the maximum capacity of the jth renewable energy source,
the available capacity probability density function for the jth renewable energy source over time period t.
1-2) determining the constraint conditions of the economic dispatching model of the power system, comprising the following steps:
1-2-1) generator power constraint:
wherein the content of the first and second substances,
upper and lower power limits, Rup, of the ith generator, respectively
i,Rdown
iThe power limit of the ith generator is limited by the upward climbing power and the downward climbing power respectively.
1-2-2) renewable energy power constraints:
wherein the content of the first and second substances,
the power is scheduled for the jth renewable energy source for time period t,
the predicted power for the jth renewable energy source over time period t,
the actual power for the jth renewable energy source during time period t,
available power for the jth renewable energy source for time period t.
1-2-3) power balance constraints:
wherein the content of the first and second substances,
for node k load demand over time period t, N
DIs the set of nodes accessing the load.
1-2-4) affine control and backup constraints:
wherein the content of the first and second substances,
actual power, beta, in consideration of affine control for the ith generator
iAffine control participation factor, alpha, for the i-th generator
UR,α
DRThe maximum allowable probability of under-provisioning and the maximum allowable probability of under-provisioning are respectively up-provisioning and down-provisioning.
1-2-5) line transmission capacity constraints:
wherein N is
WIn order to be a set of lines,
the power transfer factors of the line L with respect to the nodes i, j, k,
for the maximum transmission capacity of the line L,
respectively, a maximum allowed probability of the transmission capacity of the line L being out of limit in the forward direction and a maximum allowed probability of the transmission capacity being out of limit in the reverse direction.
2) Checking infeasible constraints and renewable energy power abandon quantities, converting the model established in the step 1), establishing a relaxed power system economic dispatching model based on opportunity constraints, and solving; the method comprises the following specific steps:
2-1) by substitution in formula (10)
The opportunity constraints (11) - (14) are written in the form of quantiles as follows:
wherein Q (xi | p) is the p-quantile of the random variable xi,
to account for the equivalent power transfer factor of line L relative to node j in affine control, M
LAnd the correction coefficient of the power transfer factor of the branch L is affine control.
Assuming that the joint distribution of renewable energy power over time period t is known, as follows:
wherein the content of the first and second substances,
a random variation of the available power composition for each renewable energy source over time t,
random variables composed of power output of each renewable energy source in a time period t;
actual renewable energy power in traditional opportunistic constrained economic dispatch without considering renewable energy power curtailment
Equal to available renewable energy power
However, the calculation of the quantiles in equations (16) - (18) is based on the assumption that renewable energy sources do not have a power dump, which may result in conventional generator power
There is no feasible solution.
2-2) renewable energy power can be cut down by reducing the quantile on the right of the equations (16) - (18), thereby reducing the risk of down-regulation of backup shortages and transmission blockages. By using
In alternative quantiles (15) - (18)
And introducing relaxation variables in the down-regulation by the constraint (16) and the transmission power constraints (17) to (18), the following formulas (23) to (26) can be obtained:
wherein, drs
tSlack variables in the standby constraints are adjusted for a period of time t,
the slack variable in the forward constraint and the slack variable in the reverse constraint of the line transmission capacity in the t period are respectively;
2-3) establishing a relaxed power system economic dispatching model based on opportunity constraint and solving;
wherein the model objective function is equation (27), and the objective of equation (27) is to minimize the weighted sum of the relaxation variables to solve the generator active power
There is no feasible solution. In the calculation of linear combination
After quantiles of (a), the following relaxed opportunity constraint-based power system economic dispatch model can be solved directly with linear programming.
s.t. formulae (4) - (7), (9), (23) - (26) and (28)
Wherein the content of the first and second substances,
wherein the content of the first and second substances,
and respectively adjusting the standby weight coefficient and the section risk weight coefficient for the t time period.
Solving the model to obtain
The optimal solution of (2);
3) determining the electric quantity discarded by each renewable energy source and the active power of each generator to obtain a scheduling result of the power system; the method comprises the following specific steps:
3-1) after solving the power system economic dispatching model based on the opportunity constraint after the relaxation in the step 2-3), obtaining the economic dispatching model through relaxation variables
Obtaining the constraint conditions of feasible solutions of the power system economic dispatching model based on the opportunity constraint established in the step 1):
if the slack variable drs in the backup constraint is adjusted downwardtAfter the renewable energy is abandoned, in order to make the model of step 1) feasible, the inequality constraint shown in the following formula must be satisfied:
if the relaxation variable is changed
If the value is not zero, the quantile in the transmission capacity constraint equation (17) satisfies an inequality constraint shown in the following equation (30):
if the relaxation variable is changed
Is not zero, thenThe quantile in the transmission capacity constraint equation (18) satisfies an inequality constraint shown in the following equation (31):
the constraints (29) - (31) can be written as shown in the following formula:
wherein Ω is a subscript set of renewable energy sources participating in electricity abandonment, cj,ckIs a constant coefficient.
3-2) establishing a renewable energy power abandoning amount scheduling model and solving;
the objective function of renewable energy power curtailment scheduling is to minimize the overall power curtailment penalty cost as shown in the following formula:
the quantile in equation (32) and the objective function in equation (33) are with respect to the upper limit of renewable energy power
The linear approximation of equations (32) and (33) can be used to obtain a solvable renewable energy power curtailment scheduling model, whose first and second derivatives of objective function equation (33) are respectively as follows:
the second derivative of the objective function (33) is greater than or equal to zeroThe power dump penalty is therefore related to the upper power limit of the renewable energy source
A convex function of (a). The curtailment penalty in equation (33) is approximated by a linear inequality shown in equation (36) below, according to the nature of the convex function:
by solving the formula (36), the electricity abandon quantity of each renewable energy source in each time period can be obtained
Then, based on the probability distribution of the renewable energy available power obtained by the probability prediction and the quantiles in the electricity curtailment calculation equations (15) to (18) obtained by solving equation (36), the constraints equations (15) to (18) become deterministic linear constraints.
3-3) obtaining the active power of each generator in each time period by solving a generator output optimization model shown as the following step by using the result of the step 3-2)
Thereby obtaining the dispatching output of the generator.
The objective function of the optimization model is equation (37), and equation (38) is used to limit the dispatch output of the renewable energy source to be lower than the upper power limit thereof in the constraint condition.
s.t. formulae (4) - (7), (9), (15) - (18) and (38)
3-4) the electric energy abandon amount of each renewable energy source obtained in the step 3-2) in each time interval and the active power of each generator obtained in the step 3-3) in each time interval are the dispatching results of the power system.