CN107887903B - Micro-grid robust optimization scheduling method considering element frequency characteristics - Google Patents

Micro-grid robust optimization scheduling method considering element frequency characteristics Download PDF

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CN107887903B
CN107887903B CN201711045435.8A CN201711045435A CN107887903B CN 107887903 B CN107887903 B CN 107887903B CN 201711045435 A CN201711045435 A CN 201711045435A CN 107887903 B CN107887903 B CN 107887903B
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卢艺
梁俊文
卢苑
程韧俐
何晓峰
林小朗
林舜江
刘明波
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South China University of Technology SCUT
Shenzhen Power Supply Bureau Co Ltd
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Abstract

The invention discloses a micro-grid robust optimization scheduling method considering element frequency characteristics, which is characterized in that under the condition of considering uncertain fluctuation characteristics of wind power and photovoltaic power generation output, a micro-grid robust optimization scheduling model considering various element frequency response characteristics is established, a Benders decomposition method is adopted to solve the robust optimization scheduling model, and an original problem is decomposed into a sub-problem and a main problem to be subjected to alternate iteration so as to obtain a robust optimization scheduling scheme. The objective function of the robust optimization model is that the total operation cost of the microgrid is the minimum in an extreme scene with the largest network loss, the constraint conditions comprise active balance constraint, diesel engine unit operation characteristic, energy storage device operation characteristic, line frequency characteristic, load frequency characteristic, voltage safety constraint and frequency safety constraint, the obtained scheduling scheme can ensure that the system cannot generate frequency out-of-limit in the uncertain fluctuation range of distributed wind power and photovoltaic power generation output, and the frequency safety of the microgrid is ensured.

Description

Micro-grid robust optimization scheduling method considering element frequency characteristics
Technical Field
The invention relates to the technical field of power grid dispatching, in particular to a micro-grid robust optimization dispatching method considering element frequency characteristics.
Background
Throughout the world, most areas are supplied with power by a traditional large-scale power grid, a large-capacity generator set is basically installed in a remote power plant close to a power generation resource area, most loads are concentrated in urban areas with high population density and developed economy, and a large amount of power is transmitted to a load center area from the power plant through a high-voltage power transmission line. When faults in the traditional power grid are not processed in time, the faults can be gradually changed into major accidents, so that most areas of the whole power grid are powered off, and great economic loss is caused. In addition, a thermal power generator is mainly used in the traditional power grid, and a large amount of atmospheric pollutants such as carbon dioxide and sulfur dioxide and the like can be generated in coal-fired and gas-fired power generation, so that the atmospheric environment is polluted, and the healthy life of people is influenced.
Unlike traditional centralized large-scale power grids, micro-grids are modern local small-scale power grids. The micro-grid comprising the distributed energy system effectively solves the problems in the large power grid, and is widely applied. The system is used as a relatively independent small-sized system, can realize self-management, control and protection functions, can be operated in a grid-connected mode, can be switched off and connected in an autonomous operation state, is beneficial to enhancing the capability of restoring stability of a power grid, and is also beneficial to reducing the interference of the power grid; in addition, the micro-grid increasingly adopts different types of distributed energy sources for power generation, such as a solar power generation system, a wind power generation system and the like, so that the emission of carbon dioxide is remarkably reduced, the environment is protected, and the requirements of sustainable development are met. Because the micro-grid can integrate various forms of energy and meet the requirement of flexible load access, and a good solution with flexible and free switching capability between an island mode and a grid-connected mode under emergency is provided, the discussion of the operation scheduling of the micro-grid has a particularly important practical value.
The output of intermittent energy sources such as distributed wind power and photovoltaic power stations has large uncertainty and low prediction precision, and brings great challenges to maintaining qualified voltage and frequency during the operation of a microgrid. The existing microgrid optimal scheduling method basically does not consider the influence of a scheduling scheme on the frequency of a microgrid, and if the fluctuation of the frequency of the microgrid exceeds a safety allowable range, serious electric power safety accidents can be caused. Therefore, the micro-grid dynamic optimization scheduling needs to consider not only the uncertainty of the wind-solar power generation power, but also the frequency response characteristics of various elements.
At present, the optimization scheduling of the microgrid considering the uncertainty of intermittent energy sources such as photovoltaic energy, wind power energy and the like is usually implemented by uncertainty optimization methods such as random planning, fuzzy planning, robust optimization and the like. The random optimization considers uncertainty factors through a mode of combining probability density function analysis and random simulation, but random planning needs to accurately know a probability distribution model of uncertainty variables, statistical calculation is carried out on a large number of sampling results, uncertainty is expressed as fuzzy variables through fuzzy optimization, constraint conditions are expressed as fuzzy sets, the satisfaction degree of the constraint conditions is represented by fuzzy membership, but the determination of the uncertainty membership function of the fuzzy planning depends on limited sample data and the experience of a decision maker, and result errors are easily caused. The robust optimization describes the uncertain variables in the problem in a form of a set, the probability distribution of the uncertain variables does not need to be known, and the method has good generalization performance.
The above-mentioned techniques have the following disadvantages: existing microgrid optimization scheduling considering photovoltaic and wind power usually ignores frequency characteristics of a diesel set, an energy storage device, a line and a load, and when the load and distributed generation power are changed violently, the problem of frequency out-of-limit of a microgrid system can be caused, and potential safety hazards are caused. On the other hand, uncertainty is considered through random planning, a probability distribution model of uncertain variables needs to be accurately known, the uncertain variables are considered through fuzzy optimization, the membership function of the uncertain variables is determined depending on limited sample data and experience of a decision maker, and result errors are easily caused.
Disclosure of Invention
In view of the defects of the prior art, it is necessary to provide a robust optimal scheduling method for a microgrid, which takes the frequency response characteristics of various elements into consideration and obtains an optimal scheduling scheme for the microgrid.
In order to solve the above problems, the present invention adopts the following technical solutions.
A micro-grid robust optimization scheduling method considering element frequency characteristics comprises the following steps:
under the condition that uncertain fluctuation characteristics of wind power and photovoltaic power generation output are considered, a micro-grid robust optimization scheduling model considering frequency response characteristics of various elements is established;
solving the micro-grid robust optimization scheduling model by adopting a Benders decomposition method, decomposing the model into sub-problems and main problems to carry out alternate iteration so as to obtain a micro-grid robust optimization scheduling scheme,
the micro-grid robust optimization scheduling model comprises an objective function and constraint conditions, wherein the objective function is that the total operation cost of the micro-grid system is minimum under the scene of maximum network loss:
Figure BDA0001452168590000031
on the right side of the equation, the first part is the power generation cost of the diesel generator set, the second part is depreciation cost of the operation of the storage battery, and the third part is network loss cost; t is the total time period number in the scheduling period; pg,j,tRepresents the output of the node j diesel generator set in the time period t, ag,jAnd bg,jA secondary coefficient and a primary coefficient respectively representing the power generation cost of the diesel generator set, SgRepresenting a node set of a diesel generator set in the microgrid; pd,j,tAnd Pc,j,tRespectively represents the discharge power and the charge power of the node j storage battery energy storage device in the t period, sigmacAnd σdThe unit depreciation cost for charging and discharging the storage battery energy storage device is related to the state of charge (SOC) of the storage battery, and the higher the SOC is, the higher the depreciation cost of the unit charging amount is; the lower the SOC, the higher the depreciation cost per unit discharge capacity; sbRepresenting a node set of a storage battery energy storage device in the microgrid;
Figure BDA0001452168590000032
representing the active power output of the photovoltaic power station at the node j in the time period t,
Figure BDA0001452168590000033
represents the active output, P, of the node j wind farm in the period of tl,j,tRepresenting the load real power of node j in the period t, ClIs the unit network loss cost; n is the total number of all nodes in the microgrid;
the constraint conditions include:
node active power balance constraint:
Figure BDA0001452168590000034
in the formula: vi,tAnd Vj,tVoltage amplitudes of a node i and a node j in a time period t are respectively;ij,tvoltage phase angle difference between node i and node j for time period t; gijAnd BijCorresponding elements of the node admittance matrix are obtained;
operation constraint of the diesel generator set:
Figure BDA0001452168590000041
in the formula (I), the compound is shown in the specification,P g,jand
Figure BDA0001452168590000042
respectively is the lower limit and the upper limit r of the active power output of the diesel generator set at the node juAnd rdRespectively diesel generator setThe climbing rate and the landslide rate, and delta T is the time interval of each time interval;
active power output-frequency characteristic of the diesel generator set:
Pg,j,t＝Pg,jN+Kg,j(ft-fN)
in the formula (f)tAnd fNRespectively representing the frequency and the rated frequency of the micro-grid in a time period t; kg,jAdjusting the effect coefficient for the frequency of the node j diesel generator set; pg,j,tAnd Pg,jNAnd respectively representing the actual output and the rated output of the node j diesel generator set in the time period t. Considering the quadratic adjustment effect of frequency, Pg,jNAs a variable;
and (3) operation restraint of the storage battery energy storage device:
Figure BDA0001452168590000043
in the formula (I), the compound is shown in the specification,
Figure BDA0001452168590000044
and
Figure BDA0001452168590000045
maximum charge and discharge power of the accumulator, respectively, Eb,tThe amount of charge stored in the battery for the period t,
Figure BDA0001452168590000046
is the maximum charge capacity, SOC, of the batteryb,tFor a time period t the state of charge of the battery,
Figure BDA0001452168590000047
andSOC bupper and lower limits, eta, of the state of charge of the accumulatorcThe charging efficiency of the storage battery;
active output-frequency characteristics of the storage battery energy storage device:
Pd,t＝PdN+Kd(ft-fN)
in the formula, KdTo store electricityFrequency regulation effect coefficient of the cell discharge power; pdNThe rated discharge power of the storage battery;
frequency characteristics of the load:
Pl＝PlN+Kl(ft-fN)
in the formula, KlFrequency-regulating effect coefficient, P, of loadlAnd PlNRespectively loading actual power and rated power;
frequency characteristics of line impedance:
Z＝(R0+j2πftL0)l
wherein Z represents a line impedance; l represents the length of the line; r0And L0The lines respectively represent the resistance and the inductance of the single length of the line;
and (4) system safe operation constraint:
Figure BDA0001452168590000051
in the formula (I), the compound is shown in the specification, iVand
Figure BDA0001452168590000052
respectively the lower limit and the upper limit of the voltage safety limit of the node i,fand
Figure BDA0001452168590000053
respectively, a lower limit and an upper limit of the frequency safety limit;
constraint of uncertain variables: c is an uncertain variable set including photovoltaic power station output
Figure BDA0001452168590000054
Power of wind power field
Figure BDA0001452168590000055
The method adopts a box type uncertain set, and expresses uncertain variables as two parts of expected values and disturbance
Figure BDA0001452168590000056
Figure BDA0001452168590000057
According to the meteorological historical data and the daily load curve rule of statistics of the photovoltaic power station and the wind power plant of the power distribution network, the expected value and the disturbance variable range of the active power output of the photovoltaic power station and the wind power plant can be determined, the uncertain variable change range is obtained, and then the uncertain variable set C can be expressed as follows:
Figure BDA0001452168590000058
the sub-problem is that the distributed wind power and photovoltaic power generation output extreme scene with the maximum loss of the microgrid network is achieved, and the objective function is as follows:
Figure BDA0001452168590000059
in the formula, lambda is the current iteration frequency;
the constraint conditions containing the unknown variables are all used as constraints of subproblems and comprise node active power balance constraints, active output-frequency characteristics of a diesel generator set, active output-frequency characteristics of a storage battery energy storage device, frequency characteristics of loads, frequency characteristics of line impedance and uncertain variable constraints;
if the result of solving the subproblem has the optimal solution set U, adding an optimal cut set in the constraint condition of the main problem as follows:
Figure BDA0001452168590000061
in the formula (I), the compound is shown in the specification,
Figure BDA0001452168590000062
for solving the auxiliary variables constructed in the process;
if the solved subproblem only has a feasible solution V, adding a feasible cut set in the constraint condition of the main problem as follows:
Figure BDA0001452168590000063
the main problem is that the total running cost of the microgrid is the minimum under the condition that the random variable is in an extreme scene, and the objective function is as follows:
Figure BDA0001452168590000064
the constraint conditions of the main problem comprise node active power balance constraint, diesel generator set operation constraint, active output-frequency characteristic of the diesel generator set, battery energy storage device operation constraint, active output-frequency characteristic of the battery energy storage device, load frequency characteristic, line impedance frequency characteristic and system safety operation constraint besides the optimal cut set or the feasible cut set returned by the sub-problem.
Under the condition of considering uncertain fluctuation characteristics of wind power and photovoltaic power generation output, the method establishes a microgrid robust optimization scheduling model considering frequency response characteristics of various elements, solves the robust optimization scheduling model by adopting a Benders decomposition method, and decomposes an original problem into a sub-problem and a main problem to perform alternate iteration so as to obtain a robust optimization scheduling scheme. The objective function of the robust optimization model is that the total operation cost of the microgrid is the minimum in an extreme scene with the largest network loss, the constraint conditions comprise active balance constraint, diesel engine unit operation characteristic, energy storage device operation characteristic, line frequency characteristic, load frequency characteristic, voltage safety constraint and frequency safety constraint, the obtained scheduling scheme can ensure that the system cannot generate frequency out-of-limit in the uncertain fluctuation range of distributed wind power and photovoltaic power generation output, and the frequency safety of the microgrid is ensured.
Drawings
FIG. 1 is a calculation flow for solving a robust optimized scheduling problem by a Benders decomposition method;
FIG. 2 is a wiring diagram of an island microgrid;
FIG. 3 is a power variation curve of each load node at a rated frequency;
FIG. 4 is a photovoltaic output prediction curve for nodes 1 and 9;
FIG. 5 is a wind power output prediction curve for node 10;
FIG. 6 is a plan curve of a diesel generator node in each optimization scheme;
FIG. 7 is a plan curve of the energy storage of the node 11 in each optimization scheme;
FIG. 8 is a plan curve of the energy storage of the node 13 in each optimization scheme;
fig. 9 is a frequency comparison of deterministic and robust optimization in an extreme scenario.
Detailed Description
The invention is further explained below with reference to the figures and examples.
1.1 micro-grid robust optimization scheduling model considering element frequency characteristics
A. Objective function
And the total operation cost of the micro-grid system is the minimum under the scene that the target function is the maximum network loss.
Figure BDA0001452168590000071
In the formula, the first part is the power generation cost of the diesel generator set, the depreciation cost of the operation of the second part of storage batteries and the loss cost of the third part of networks; t is the total time period number in the scheduling period; pg,j,tRepresents the output of the node j diesel generator set in the time period t, ag,jAnd bg,jA secondary coefficient and a primary coefficient respectively representing the power generation cost of the diesel generator set, SgRepresenting a node set of a diesel generator set in the microgrid; pd,j,tAnd Pc,j,tRespectively represents the discharge power and the charge power of the node j storage battery energy storage device in the t period, sigmacAnd σdThe unit depreciation costs for charging and discharging the battery energy storage device are respectively related to the State of Charge (SOC) of the battery, and the higher the SOC, the higher the depreciation cost of the unit charging amount; the lower the SOC, the higher the depreciation cost per unit discharge capacity; sbRepresenting a node set of a storage battery energy storage device in the microgrid;
Figure BDA0001452168590000081
representing the active power output of the photovoltaic power station at the node j in the time period t,
Figure BDA0001452168590000082
represents the active output, P, of the node j wind farm in the period of tl,j,tRepresenting the load real power of node j in the period t, ClIs the unit network loss cost; and n is the total number of all nodes in the microgrid.
B. Constraint conditions
1) And (5) node active power balance constraint. The power balance of each node must be satisfied in the optimization scheduling of the microgrid, as shown in formula (2).
Figure BDA0001452168590000083
In the formula: vi,tAnd Vj,tVoltage amplitudes of a node i and a node j in a time period t are respectively;ij,tvoltage phase angle difference between node i and node j for time period t; gijAnd BijCorresponding elements of the admittance matrix for the node.
2) And (5) operation restriction of the diesel generator set. The method comprises the steps of generating power limit constraint and power climbing constraint, as shown in a formula (3).
Figure BDA0001452168590000084
In the formula (I), the compound is shown in the specification,P g,jand
Figure BDA0001452168590000085
respectively is the lower limit and the upper limit r of the active power output of the diesel generator set at the node juAnd rdThe ramp rate and the landslide rate of the diesel generating set respectively, and the time interval of each period of the delta T.
The active output-frequency characteristic of the diesel generator set is as shown in formula (4).
Pg,j,t＝Pg,jN+Kg,j(ft-fN) In the formula (4), ftAnd fNRespectively representing the frequency and the rated frequency of the micro-grid in a time period t; kg,jAdjusting the effect coefficient for the frequency of the node j diesel generator set; pg,j,tAnd Pg,jNAnd respectively representing the actual output and the rated output of the node j diesel generator set in the time period t. Considering the quadratic adjustment effect of frequency, Pg,jNAs variables.
3) And (5) restraining the operation of the storage battery energy storage device. In order to stabilize uncertain fluctuation of renewable energy power generation in a microgrid, a storage battery energy storage device is introduced, model constraints of the storage battery energy storage device comprise maximum charge-discharge power constraint, energy storage device charge state constraint and running state complementary constraint: the battery can be charged or discharged only in one of the states per time period t in actual operation.
Figure BDA0001452168590000091
In the formula, Pd,tAnd Pc,tRespectively representing the discharge power and the charge power of the storage battery in the t period,
Figure BDA0001452168590000092
and
Figure BDA0001452168590000093
maximum charge and discharge power of the accumulator, respectively, Eb,tThe amount of charge stored in the battery for the period t,
Figure BDA0001452168590000094
is the maximum charge capacity, SOC, of the batteryb,tFor a time period t the state of charge of the battery,
Figure BDA0001452168590000095
andSOC bupper and lower limits, eta, of the state of charge of the accumulatorcThe charging efficiency of the storage battery.
The active output-frequency characteristic of the storage battery energy storage device is that the fluctuation of the frequency does not cause the change of the charging power when the storage battery energy storage device is in a charging state; and the active output and the frequency of the energy storage device are considered to meet the droop control in the discharging state. As shown in formula (6).
Pd,t＝PdN+Kd(ft-fN) In the formula (6), KdAdjusting the effect coefficient for the frequency of the battery discharge power; pdNThe rated discharge power of the storage battery.
4) Frequency characteristics of the load.
Pl＝PlN+Kl(ft-fN) In the formula (7), KlFrequency-regulating effect coefficient, P, of loadlAnd PlNAnd respectively loading actual power and rated power.
5) Frequency characteristics of the line impedance.
Z＝(R0+j2πftL0)l (8)
Wherein Z represents a line impedance; l represents the length of the line; r0And L0The lines represent the resistance and inductance of the line per unit length, respectively. The change of the frequency can cause the change of the line reactance, thereby changing the network node admittance matrix and having influence on the operation state of the system.
6) And (5) system safe operation constraint. The voltage deviation of each node cannot exceed a safety allowable range, and the frequency deviation of the microgrid cannot exceed the safety allowable range, as shown in formula (9).
Figure BDA0001452168590000101
In the formula (I), the compound is shown in the specification, iVand
Figure BDA0001452168590000102
respectively the lower limit and the upper limit of the voltage safety limit of the node i,fand
Figure BDA0001452168590000103
respectively, the lower limit and the upper limit of the frequency safety limit.
7) The variable constraints are not determined. C is a set of uncertain variables comprisingThe random variables such as photovoltaic power station output and wind power plant output are represented as expected values and disturbance by adopting a box-type uncertain set
Figure BDA0001452168590000104
According to the meteorological historical data and the daily load curve rule of the distribution network photovoltaic power station and the wind power plant, the expected value and the disturbance variable range of the active power output of the photovoltaic power station and the wind power plant can be determined, the uncertain variable range can be obtained, and the uncertain variable set C can be represented as an expression (10).
Figure BDA0001452168590000105
1.2 solving algorithm for robust optimization scheduling problem
The objective function of the micro-grid robust optimization scheduling model considering the frequency characteristics of the elements contains a Min-Max double-layer optimization problem, and the existing solver cannot be used for directly solving the problem. The key for solving the robust optimization scheduling model is as follows: 1) how to find 1 group of uncertain variable values in the uncertain variable set, which correspond to the extreme scene with the largest network loss; 2) how to find 1 group of decision variable values in the decision variable set enables the group of decision variables to meet constraint conditions in the optimization model under any value of uncertain variables, and enables the corresponding objective function to be minimum in an extreme scene. The robust optimization model is solved by adopting a Benders decomposition algorithm. According to the idea of Benders decomposition algorithm, the Min-Max structure optimization model can be decomposed into two parts of a main problem and a subproblem. The subproblem searches for an uncertain variable extreme scene which enables the loss of the microgrid network to be maximum; and solving the scheduling scheme which enables the total cost of the micro-grid to be minimum under the operation of an extreme scene by the main problem. The sub-problem and the main problem are described as follows:
A. sub-problems
In order to find an extreme scene of distributed wind power and photovoltaic power generation output which enables the loss of a microgrid network to be maximum, the objective function of a subproblem is as follows:
Figure BDA0001452168590000111
where λ is the number of current iterations.
In the subproblems, random variables such as distributed wind power and photovoltaic power generation output and state variables such as frequency, voltage amplitude and phase angle serve as unknown variables, decision variables such as power generation power of a diesel generator set and charge and discharge power of an energy storage device serve as known variables, and constraint conditions containing the unknown variables serve as constraints of the subproblems and comprise (2), (4), (6), (7), (8) and (10).
If the result of solving the sub-problem has the optimal solution set U (including
Figure BDA0001452168590000112
) (ii) a Then add an optimal cut set to the main problem constraint as follows:
Figure BDA0001452168590000113
in the formula (I), the compound is shown in the specification,
Figure BDA0001452168590000114
to solve for the auxiliary variables constructed during the process.
If the solved subproblem has only a feasible solution V (comprising
Figure BDA0001452168590000115
) (ii) a Then add a feasible cut set to the main problem constraint as follows:
Figure BDA0001452168590000121
B. major problems
The objective function of the main problem is the total running cost of the microgrid under the condition that random variables such as wind-solar power generation output are in an extreme scene, so the objective function of the main problem can be set as follows:
Figure BDA0001452168590000122
the constraint conditions of the main problem include equations (2) to (9) in addition to the optimal cut set equation (12) or the feasible cut set equation (13) returned by the subproblems.
The calculation flow for solving the robust optimization scheduling problem by adopting the Benders decomposition algorithm is shown in fig. 1, and the detailed steps are as follows:
1) initialization: first, the lowest limit LB of the original problem objective function is set to- ∞, the highest limit UB is set to + ∞, and the method is carried out in the expected value scene (P) of uncertain variabless,t,ref，Pw,t,ref) Then, solving the deterministic optimization problem to obtain the initial value of the decision variable
Figure BDA0001452168590000123
2) Initial values of decision variables
Figure BDA0001452168590000124
Substituting the known quantity into the subproblem and solving to obtain the current value of the uncertain variable which enables the network loss to be maximum
Figure BDA0001452168590000125
Let the iteration number λ be 0.
3) If the sub-problem is solved to obtain the optimal solution, an optimal cut set (12) is added to the constraint condition of the main problem, and if the sub-problem is solved to obtain the feasible solution, a feasible cut set (13) is added to the constraint condition of the main problem. Uncertain variable values obtained by solving subproblems
Figure BDA0001452168590000126
Substituting the known quantity into the main problem, solving the main problem to obtain the optimal solution of the decision variables
Figure BDA0001452168590000127
And updating the minimum bounds
Figure BDA0001452168590000128
4) Solving the decision variables of the main problem
Figure BDA0001452168590000129
Solving the subproblem to obtain the optimal solution of the uncertain variables as the known quantity substitution subproblem
Figure BDA00014521685900001210
The highest bound UB is updated as in equation (15).
Figure BDA0001452168590000131
5) And if the UB and the LB meet the condition that the UB-LB is less than or equal to the LB, stopping iteration and returning to the optimal solution. Otherwise, let λ ═ λ +1, return to step 3). Is a convergence criterion constant in Benders' decomposition method and is set to 10-5。
2.1 example analysis verification
Taking a certain island microgrid as an example for simulation analysis, the microgrid wiring diagram is shown in fig. 2, and comprises one diesel generator set of a node 10, two storage battery energy storage devices of a node 11 and a node 13, two distributed photovoltaic power stations of a node 1 and a node 9, distributed wind power generation of a node 12, and 4 loads of nodes 6, 7, 8 and 10. Loss of network charge ClTake 0.65/(yuan/(kWh)). The charging efficiency of the storage battery is 0.85, the parameters of the diesel generator set are shown in table 1, the parameters of the energy storage device are shown in table 2, the load data are shown in table 3, and the network related parameters are shown in table 4; the power of each load node at the rated frequency is shown in fig. 3, and the prediction curves of the photovoltaic and wind power output are shown in fig. 4 and 5. The frequency safety limit range is set to be 49.5-50.5 Hz.
TABLE 1 parameters associated with diesel-electric sets
Figure BDA0001452168590000132
Table 2 relevant parameters of the nodes 11 and 13 energy storage device
Figure BDA0001452168590000133
TABLE 3 relevant parameters of load nodes
Figure BDA0001452168590000134
TABLE 4 parameters associated with transformers
Figure BDA0001452168590000135
Considering that the uncertain fluctuation range of photovoltaic output and wind power output is +/-10% of a predicted value, comparing optimal scheduling under a microgrid deterministic prediction scene, scene method optimal scheduling and the robust optimal scheduling method provided by the invention, and obtaining an optimal result shown in a table 5; the scheduling scheme pair is shown in fig. 6-8, where the scenario method is the result curve of 10 error scenarios.
TABLE 5 comparison of simulation results of various methods under 10% fluctuation of wind and solar power
Figure BDA0001452168590000141
As can be seen from Table 5:
1) under the condition that the wind and light power fluctuates by 10%, the network loss cost of robust optimization is 3620.223 yuan, which is larger than the network loss cost 2947.911 yuan of deterministic optimization and is also larger than the network loss cost optimized by a scene method, and the conclusion of an extreme scene with the maximum network loss cost of a robust optimization minimized system is met. Meanwhile, the running total cost of robust optimization is 11428.216 yuan, which is larger than the running total cost 10836.781 yuan of deterministic optimization and is also larger than the running total cost of scene method optimization. The robust optimization solves the scheduling result of the minimum running total cost in the maximum network loss scene, the result meets the constraint condition under the condition of output fluctuation of any distributed wind power and photovoltaic power generation, and the conservatism is high.
2) Compared with the total running cost obtained by robust optimization and scene method optimization, when the number of error scenes in the scene method is larger, the total running cost is closer to the total running cost of the robust optimized system. Because when the number of scenes in the scene method is sufficiently large, it is equivalent to finding the optimal scheduling result in a set of wind-solar output fluctuations, and the result should satisfy all the constraints in this set. And the robust optimization is to find an extreme scene in the wind-solar output fluctuation set and solve an optimal result so as to ensure that the result meets all constraints of the set. At this time, the scene method with enough samples is consistent with the core idea of the robust optimization method, so that the results of the scene method and the robust optimization method are close.
3) Comparing the calculation time of deterministic optimization, scene optimization and robust optimization, the calculation time of deterministic optimization is shortest, the calculation time of robust optimization is longer, and the calculation time of scene optimization is longest. Because deterministic optimized wind-solar power is a single prediction scenario, while robust optimized wind-solar power is a set, the scenario method is multi-scenario, and therefore the computational time for deterministic optimization should be minimal. As can be seen from the calculation time of the scene method, the calculation time is rapidly increasing as the number of error scenes increases. The more scenes the scene method is, the more the constraint conditions need to be satisfied, the more the computation amount is increased, and the program running time is increased. The computation time of the scene method is significantly longer than for robust optimization.
4) Comparing the robust optimized dispatch plan with other optimized dispatch plans, the plan curves of the diesel generator nodes are shown in fig. 6, and the plan curves of the two energy storage device nodes are shown in fig. 7 and 8. As can be seen from fig. 7 and 8, compared with the scenario method, the energy storage device with the robust optimization result has a small output most of the time to reserve a large adjustment capacity to cope with the uncertain fluctuation of the photovoltaic and wind power outputs, and because the output of the energy storage device is small, the diesel generator set has to output more power to supply power during the peak load period.
The frequency comparison of the micro-grid obtained by the deterministic optimization scheduling scheme and the robust optimization scheduling scheme in the extreme scenario with the largest network loss is shown in fig. 9. When uncertain variables photovoltaic and wind power output are in extreme scenes, the lower limit of frequency occurs in a time period 19 in a deterministic optimization scheduling scheme, and a robust optimization scheduling scheme can ensure that the micro-grid can meet the frequency safety requirement in each time period. Because the deterministic optimization scheduling scheme can only ensure that all constraint conditions are met in the scene of wind and light output prediction, and can not necessarily meet all constraint conditions under the condition of uncertain fluctuation of wind and light output. Therefore, the scheduling scheme obtained by the robust optimization scheduling method provided by the invention can effectively cope with uncertain fluctuation of wind and light output, and has robustness.
In conclusion, under the condition that a photovoltaic and wind power predicted output curve and a load predicted curve are known, by solving the microgrid robust optimization scheduling model considering the frequency characteristics of elements, the day-ahead output planning scheduling scheme of the diesel generator set and the energy storage device in the microgrid can be obtained. The scheduling scheme can minimize the total operation cost of the microgrid under the extreme scene of the maximum loss of the microgrid network, and can ensure that the system can meet the frequency safety requirement under any scene within the uncertain fluctuation range of distributed photovoltaic and wind power output.
The above-mentioned embodiments only express the embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (2)

1. A micro-grid robust optimization scheduling method considering element frequency characteristics is characterized by comprising the following steps:
under the condition that uncertain fluctuation characteristics of wind power and photovoltaic power generation output are considered, a micro-grid robust optimization scheduling model considering frequency response characteristics of various elements is established;
solving the micro-grid robust optimization scheduling model by adopting a Benders decomposition method, decomposing the model into sub-problems and main problems to carry out alternate iteration so as to obtain a micro-grid robust optimization scheduling scheme,
the micro-grid robust optimization scheduling model comprises an objective function and constraint conditions, wherein the objective function is that the total operation cost of the micro-grid system is minimum under the scene of maximum network loss:
Figure FDA0002648555360000011
on the right side of the equation, the first part is the power generation cost of the diesel generator set, the second part is depreciation cost of the operation of the storage battery, and the third part is network loss cost; t is the total time period number in the scheduling period; pg,j,tRepresents the output of the node j diesel generator set in the time period t, ag,jAnd bg,jA secondary coefficient and a primary coefficient respectively representing the power generation cost of the diesel generator set, SgRepresenting a node set of a diesel generator set in the microgrid; pd,j,tAnd Pc,j,tRespectively represents the discharge power and the charge power of the node j storage battery energy storage device in the t period, sigmacAnd σdThe unit depreciation cost for charging and discharging the storage battery energy storage device is related to the state of charge (SOC) of the storage battery, and the higher the SOC is, the higher the depreciation cost of the unit charging amount is; the lower the SOC, the higher the depreciation cost per unit discharge capacity; sbRepresenting a node set of a storage battery energy storage device in the microgrid;
Figure FDA0002648555360000012
representing the active power output of the photovoltaic power station at the node j in the time period t,
Figure FDA0002648555360000013
represents the active output, P, of the node j wind farm in the period of tl,j,tRepresenting the load real power of node j in the period t, ClIs the unit network loss cost; n is the total number of all nodes in the microgrid;
the constraint conditions include:
node active power balance constraint:
Figure FDA0002648555360000021
in the formula: vi,tAnd Vj,tVoltage amplitudes of a node i and a node j in a time period t are respectively;ij,tvoltage phase angle difference between node i and node j for time period t; gijAnd BijCorresponding elements of the node admittance matrix are obtained;
operation constraint of the diesel generator set:
Figure FDA0002648555360000022
in the formula (I), the compound is shown in the specification,P g,jand
Figure FDA0002648555360000023
respectively is the lower limit and the upper limit r of the active power output of the diesel generator set at the node juAnd rdRespectively representing the climbing speed and the landslide speed of the diesel generator set, wherein delta T is the time interval of each time interval;
active power output-frequency characteristic of the diesel generator set:
Pg,j,t＝Pg,jN+Kg,j(ft-fN)
in the formula (f)tAnd fNRespectively representing the frequency and the rated frequency of the micro-grid in a time period t; kg,jAdjusting the effect coefficient for the frequency of the node j diesel generator set; pg,j,tAnd Pg,jNRespectively the actual output and rated output of the node j diesel generator set in the time period t, and considering the secondary adjustment effect of the frequency, the P is adjustedg,jNAs a variable;
and (3) operation restraint of the storage battery energy storage device:
Figure FDA0002648555360000024
in the formula (I), the compound is shown in the specification,
Figure FDA0002648555360000025
and
Figure FDA0002648555360000026
maximum charge and discharge powers, E, of the jth battery, respectivelyb,j,tThe charge capacity of the jth battery for the period tth,
Figure FDA0002648555360000027
is the maximum charge capacity, SOC, of the jth batteryb,j,tFor the time period tth battery state of charge,
Figure FDA0002648555360000028
andSOC b,jupper and lower limits, eta, of the state of charge of the jth batteryc,jThe charging efficiency of the jth storage battery;
active output-frequency characteristics of the storage battery energy storage device:
Pd,j,t＝PdN+Kd(ft-fN)
in the formula, KdAdjusting the effect coefficient for the frequency of the battery discharge power; pdNThe rated discharge power of the storage battery;
frequency characteristics of the load:
Pl＝PlN+Kl(ft-fN)
in the formula, KlFrequency-regulating effect coefficient, P, of loadlAnd PlNRespectively loading actual power and rated power;
frequency characteristics of line impedance:
Z＝(R0+j2πftL0)l
wherein Z represents a line impedance; l represents the length of the line; r0And L0Respectively representing the resistance and the inductance of the line per unit length;
and (4) system safe operation constraint:
Figure FDA0002648555360000031
in the formula (I), the compound is shown in the specification, iVand
Figure FDA0002648555360000032
respectively the lower limit and the upper limit of the voltage safety limit of the node i,fand
Figure FDA0002648555360000033
respectively, a lower limit and an upper limit of the frequency safety limit;
constraint of uncertain variables: c is an uncertain variable set including photovoltaic power station output
Figure FDA0002648555360000034
Power of wind power field
Figure FDA0002648555360000035
The method adopts a box type uncertain set, and expresses uncertain variables as two parts of expected values and disturbance
Figure FDA0002648555360000036
Figure FDA0002648555360000037
According to the meteorological historical data of the photovoltaic power station and the wind power plant of the power distribution network and the daily load curve rule of statistics, the expected value of the active power output of the photovoltaic power station and the wind power plant and the change range of the disturbance quantity can be determined, further, the change range of uncertain variables is obtained, and then the set C of uncertain variables can be expressed as:
Figure FDA0002648555360000038
the sub-problem is that the distributed wind power and photovoltaic power generation output extreme scene with the maximum loss of the microgrid network is achieved, and the objective function is as follows:
Figure FDA0002648555360000041
in the formula, lambda is the current iteration frequency;
the constraint conditions containing the unknown variables are all used as constraints of subproblems and comprise node active power balance constraints, active output-frequency characteristics of a diesel generator set, active output-frequency characteristics of a storage battery energy storage device, frequency characteristics of loads, frequency characteristics of line impedance and uncertain variable constraints;
if the result of solving the subproblem has the optimal solution set U, adding an optimal cut set in the constraint condition of the main problem as follows:
Figure FDA0002648555360000042
in the formula (I), the compound is shown in the specification,
Figure FDA0002648555360000043
for solving the auxiliary variables constructed in the process;
if the solved subproblem only has a feasible solution V, adding a feasible cut set in the constraint condition of the main problem as follows:
Figure FDA0002648555360000044
the main problem is that the total running cost of the microgrid is the minimum under the condition that the random variable is in an extreme scene, and the objective function is as follows:
Figure FDA0002648555360000045
the constraint conditions of the main problem comprise node active power balance constraint, diesel generator set operation constraint, active output-frequency characteristic of the diesel generator set, battery energy storage device operation constraint, active output-frequency characteristic of the battery energy storage device, load frequency characteristic, line impedance frequency characteristic and system safety operation constraint besides the optimal cut set or the feasible cut set returned by the sub-problem.
2. The method of claim 1, wherein the frequency characteristic of the element is considered in the method for the robust optimal scheduling of the microgrid,
the detailed steps for solving the microgrid robust optimization scheduling model by adopting a Benders decomposition method are as follows:
step 1, setting a minimum limit LB of an objective function of the micro-grid robust optimization scheduling model to- ∞, setting a maximum limit UB to + ∞, and setting the minimum limit LB and the maximum limit UB to + ∞inan expected value scene (P) of an uncertain variables,t,ref，Pw,t,ref) Then, solving the deterministic optimization problem to obtain the initial value of the decision variable
Figure FDA0002648555360000051
Step 2, initial values of decision variables
Figure FDA0002648555360000052
Substituting the known quantity into the subproblem and solving to obtain the current value of the uncertain variable which enables the network loss to be maximum
Figure FDA0002648555360000053
Let the iteration number λ be 0;
step 3, if solving the subproblems to obtain the optimal solution, adding one optimal cut set into the constraint condition of the main problem, if solving the subproblems to obtain the feasible solution, adding one feasible cut set into the constraint condition of the main problem, and solving the subproblems to obtain the uncertain variable values
Figure FDA0002648555360000054
Substituting the known quantity into the main problem, solving the main problem to obtain the optimal solution of the decision variables
Figure FDA0002648555360000055
And updating the minimum bounds
Figure FDA0002648555360000056
Step 4, solving decision variables obtained by the main problems
Figure FDA0002648555360000057
Solving the subproblem to obtain the optimal solution of the uncertain variables as the known quantity substitution subproblem
Figure FDA0002648555360000058
Updating the highest bound
Figure FDA0002648555360000059
And 5, if the updated highest boundary UB and the updated lowest boundary LB meet the condition that UB-LB is less than or equal to the lowest boundary LB, stopping iteration and returning to an optimal solution, otherwise, making lambda equal to lambda +1, returning to the step 3, setting a convergence criterion constant in the Benders decomposition method as 10-5。
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