CN116505596A - Multi-region power system trans-regional support time sequence production simulation method and system - Google Patents
Multi-region power system trans-regional support time sequence production simulation method and system Download PDFInfo
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- H—ELECTRICITY
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- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract
The invention provides a multi-region power system cross-region support time sequence production simulation method and system, wherein the method comprises the following steps: based on the established conventional unit output model and new energy output sequential model, randomly generating simulation output scenes of the multi-region power system in any time sequence according to conventional unit information and new energy unit information to serve as sampling scenes for cross-region support time sequence production simulation; and based on each sampling scene, carrying out time sequence production simulation on the multi-region power system according to the established tie fault probability model and the tie transregional support model, and determining a tie transregional power transmission result and a regional power balance result. According to the method and the system, the randomness of the new energy, the conventional unit and the connecting lines is considered, the time sequence production simulation is carried out on the multi-region power system, and the simulation of the reliability of the contribution output of the new energy under the future running condition of the multi-region power system is realized.
Description
Technical Field
The present invention relates to the field of random production simulation of a multi-region power system, and more particularly, to a method and system for simulating trans-regional support timing production of a multi-region power system.
Background
The random production simulation of the power system can be used for considering random fluctuation of load and random shutdown of the unit, simulating the power generation scheduling process in the actual operation of the power system, calculating the load loss index, and is an important tool for reliability assessment. At present, various mature and common simulation methods for random production of the power system, including a semi-invariant method, a frequency-duration method, an equivalent electric quantity function method and the like, are widely applied to the traditional power system.
When production simulation is carried out in a power generation framework considering new energy, the unit scheduling process needs to meet load fluctuation and consider the influence of the new energy. Under the condition that only randomness of new energy output is considered, uncertainty of forced outage of a conventional unit is still processed according to a reserved enough accident standby model, system power and electricity balance under the influence of new energy can be analyzed in a targeted manner, power transmission capacity among areas is randomly simulated through a multi-area power system cross-region support model, networking benefits of an interconnection system are fully exerted, and new energy consumption indexes and the like are evaluated more comprehensively. Compared with the current principle of ensuring the participation of the output in the power balance according to the certainty, the random method can provide more information about the reliability of the power contribution of the new energy, consumes time and is acceptable, and has certain reference significance for the guidance planning of the novel power system with the gradually improved new energy output ratio under the 'double-carbon' target.
Disclosure of Invention
The invention provides a multi-region power system trans-regional support time sequence production simulation method and system, which are used for solving the technical problems that the output of new energy sources in a power system is not fully considered according to the certainty principle of guaranteeing the participation of the output in power balance and the evaluation flexibility is insufficient in the prior art.
According to an aspect of the present invention, there is provided a method for simulating production of a multi-region power system with a cross-region support timing, the method comprising:
the method comprises the steps of obtaining partition data and tie line data of a multi-region power system, and conventional unit information and new energy unit information in each partition;
based on the established conventional unit output model and new energy output sequential model, randomly generating simulated output scenes of a plurality of multi-region power systems in any time sequence according to the conventional unit information and the new energy unit information, and taking the simulated output scenes as sampling scenes of cross-region support time sequence production simulation;
based on a sampling scene of each transregional support time sequence production simulation, performing time sequence production simulation on the multi-region power system according to the established tie line fault probability model and the tie line transregional support model, and determining a tie line transregional power transmission result and a regional power balance result;
And calculating and considering probability evaluation indexes of the multi-region power system conservation and new energy consumption level according to the cross-region power transmission result and the regional power balance result of the connecting line of the sampling scene of each cross-region support time sequence production simulation, and outputting the probability evaluation indexes.
According to another aspect of the present invention, there is provided a multi-zone power system cross-zone support timing production simulation system, the system comprising:
the data acquisition module is used for acquiring partition data and tie line data of the multi-region power system, and conventional unit information and new energy unit information in each partition;
the sampling scene module is used for randomly generating simulated output scenes of a plurality of multi-region power systems in any time sequence according to the conventional unit information and the new energy unit information based on the established conventional unit output model and the new energy output sequential model, and taking the simulated output scenes as sampling scenes of cross-region support time sequence production simulation;
the cross-region supporting module is used for carrying out time sequence production simulation on the multi-region power system according to the established tie line fault probability model and the tie line cross-region supporting model based on the sampling scene of each cross-region supporting time sequence production simulation, and determining a tie line cross-region power transmission result and a partition electric quantity balance result;
And the output result module is used for calculating and considering probability evaluation indexes of the multi-region power system conservation level and the new energy consumption level according to the cross-region power transmission result and the regional power balance result of the connecting line of the sampling scene simulated by each cross-region support time sequence production and outputting the probability evaluation indexes.
The invention provides a multi-region power system cross-region support time sequence production simulation method and a system, wherein the method comprises the following steps: the method comprises the steps of obtaining partition data and tie line data of a multi-region power system, and conventional unit information and new energy unit information in each partition; based on the established conventional unit output model and new energy output sequential model, randomly generating simulated output scenes of a plurality of multi-region power systems in any time sequence according to the conventional unit information and the new energy unit information, and taking the simulated output scenes as sampling scenes of cross-region support time sequence production simulation; based on a sampling scene of each transregional support time sequence production simulation, performing time sequence production simulation on the multi-region power system according to the established tie line fault probability model and the tie line transregional support model, and determining a tie line transregional power transmission result and a regional power balance result; and calculating and considering probability evaluation indexes of the multi-region power system conservation and new energy consumption level according to the cross-region power transmission result and the regional power balance result of the connecting line of the sampling scene of each cross-region support time sequence production simulation, and outputting the probability evaluation indexes. According to the method and the system, the randomness of the new energy, the conventional unit and the connecting lines is considered, the time sequence production simulation is carried out on the multi-region power system through the connecting line fault probability model and the connecting line trans-regional support model, the simulation of the reliability of the contribution output of the new energy under the future running condition of the multi-region power system is realized, and the method and the system have important reference significance for the guidance planning of the novel power system with the gradually improved new energy output ratio.
Drawings
Exemplary embodiments of the present invention may be more completely understood in consideration of the following drawings:
FIG. 1 is a flow chart of a multi-zone power system cross-zone support timing production simulation method according to a preferred embodiment of the present invention;
FIG. 2 is a flow chart of a time series production simulation of a multi-zone power system based on a sampling scenario of a plurality of cross-zone support time series production simulations in accordance with a preferred embodiment of the present invention;
FIG. 3 is a flow chart of a multi-zone power system cross-zone support timing production simulation method according to another preferred embodiment of the present invention;
FIG. 4 is a schematic diagram of the topology of a multi-zone power system according to another preferred embodiment of the present invention;
fig. 5 is a schematic diagram of a link transregional transmission result according to another preferred embodiment of the present invention;
fig. 6 is a schematic diagram of another link transregional transmission result according to another preferred embodiment of the present invention;
FIG. 7 is a schematic diagram of sample results of evaluation index for a multi-zone power system cross-zone support timing production simulation in accordance with another preferred embodiment of the present invention;
fig. 8 is a schematic structural diagram of a multi-zone power system cross-zone support timing production simulation system according to a preferred embodiment of the present invention.
Detailed Description
The exemplary embodiments of the present invention will now be described with reference to the accompanying drawings, however, the present invention may be embodied in many different forms and is not limited to the examples described herein, which are provided to fully and completely disclose the present invention and fully convey the scope of the invention to those skilled in the art. The terminology used in the exemplary embodiments illustrated in the accompanying drawings is not intended to be limiting of the invention. In the drawings, like elements/components are referred to by like reference numerals.
Unless otherwise indicated, terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art. In addition, it will be understood that terms defined in commonly used dictionaries should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense.
Exemplary method one
Fig. 1 is a flowchart of a multi-zone power system cross-zone support timing production simulation method according to a preferred embodiment of the present invention. As shown in fig. 1, the multi-region power system cross-region support timing production simulation method according to the preferred embodiment starts in step 101.
In step 101, zone data and tie line data of a multi-zone power system are acquired, as well as regular unit information and new energy unit information in each zone.
In step 102, based on the established conventional unit output model and new energy output sequential model, a plurality of simulated output scenes of the multi-region power system in any time sequence are randomly generated according to the conventional unit information and the new energy unit information, and the simulated output scenes are used as sampling scenes for the cross-region support time sequence production simulation.
In the preferred embodiment, the conventional unit output model is obtained by training and verifying the established conventional unit output model based on historical output data of the conventional unit, and after model parameters are determined, the number of times that the established conventional unit output model fails in a set time period is subject to poisson distribution, and the time for maintaining unit faults is subject to exponential distribution. The new energy output sequential model is also generated based on the same principle, and is not described herein.
And 103, carrying out time sequence production simulation on the multi-region power system according to the established tie line fault probability model and the tie line cross-region support model based on the sampling scene of each cross-region support time sequence production simulation, and determining the tie line cross-region power transmission result and the regional power balance result.
Preferably, the time sequence production simulation is carried out on the multi-region power system according to the established tie fault probability model and the tie cross-region support model based on the sampling scene of each cross-region support time sequence production simulation, and the tie cross-region power transmission result and the regional power balance result are determined.
FIG. 2 is a flow chart of a time series production simulation of a multi-zone power system based on a sampling scenario of a plurality of cross-zone support time series production simulations in accordance with a preferred embodiment of the present invention. As shown in fig. 2, the time series production simulation of the multi-zone power system based on the sampling scenario of the plurality of cross-zone support time series production simulations according to the preferred embodiment of the present invention starts at step 201.
In step 201, an nth cross-zone support timing production simulation sampling scenario is selected, wherein N is greater than or equal to 1 and less than or equal to N. In the preferred embodiment, the total number of sampling scenes generated by random simulation according to the conventional unit output model and the new energy output sequential model is N.
In step 202, the cross-zone tie effect is ignored, the individual power balance of the new energy source of each zone is performed, and the first power surplus/gap of each zone is determined.
In step 203, according to the principle of the multi-area power system regular unit utilization hour balance, the average utilization hour number of the regular unit of each area is determined, and the second power surplus/gap of each area is calculated by combining the first power surplus/first power gap.
Since there are many well-established methods of balancing power in a region and determining surplus/gap of power in the prior art, the details are not repeated here.
At step 204, a tie-line simulated fault result for the multi-zone power system is randomly generated based on the established tie-line fault probability model.
Preferably, the generating, based on the established tie-line fault probability model, a tie-line simulation fault result of the multi-region power system randomly includes:
for each tie line of the multi-region power system, randomly generating tie line simulated fault data of the tie line based on an established tie line fault probability model according to a time sequence of a sampling scene of the nth trans-regional support time sequence production simulation, wherein the tie line fault probability model comprises a tie line fault frequency probability model and a tie line fault state maintenance time probability model, and specifically:
the number of times of occurrence of the tie line faults obeys poisson distribution, and the expression of the tie line fault number probability model is as follows:
where k represents the number of failures occurring in the corresponding time series determined based on the historical failure data of the corresponding time series, λ represents the average number of failures of the corresponding time series determined based on the historical failure data of the corresponding time series, and P (x=k) represents the probability when the number of failures occurring in the corresponding time series determined based on the historical failure data of the corresponding time series is k;
The tie line fault state maintaining time obeys an exponential distribution, and the expressions of the tie line fault state maintaining time probability models F (x) and F (x) are as follows:
wherein x represents a fault state maintenance time of the corresponding time series determined based on the historical fault data of the corresponding time series, F (x) represents a density function of the fault state maintenance time distribution, F (x) represents a probability distribution function of the fault state maintenance time distribution, θ represents a desired value of the distribution, h represents an average fault duration of the corresponding time series determined based on the historical fault data of the corresponding time series, SF represents an operation coefficient of the link line in the multi-region power system, EFOR represents an equivalent forced outage rate, and T represents a duration of the corresponding time series.
In step 205, taking into account the effect of the cross-region tie, determining the cross-region power transmission result of the tie by adopting the established tie cross-region support model according to the power transmission constraint in the tie data, the tie simulation fault result and the second power surplus/second power gap of each partition, and obtaining the final power surplus/gap of each partition.
Preferably, the cross-region link effect is considered, and according to the transmission constraint in the link data and the link simulated fault result, and the second power surplus/second power gap of each partition, the link cross-region transmission result is determined by adopting an established link cross-region support model, wherein an objective function of the link cross-region support model is obtained by superposing squares of power deviations of the partitions with the power gaps, and the objective function is expressed as follows:
Wherein P is EX -tie power scheduling vector;
P ZN -an incoming foreign power schedule vector for the partition;
N EX -number of tie lines;
N ZN -number of partitions;
P EX.i -defining the forward direction of the flow of the transmitting end to the receiving end as the positive direction by the power arrangement value of the ith interconnecting line;
P ZN.i -the ith partition is subject to the value of the extraneous power;
D ZN.i -a power supply gap of the ith partition, the value being greater than zero indicating the presence of a gap and less than zero indicating the ability to support externally;
k i -coefficient of ith tie-line power term, takingR/U is preferable when the resistance and the link voltage are known 2 ;
The objective function is constrained by an equation to be satisfied, namely, the power received by each partition is the sum of the power of each interconnection line arrangement related to the partition, and the equation expression is as follows:
wherein j represents a j-th connecting wire connected with an i-th subarea in the multi-area power system;
the objective function also needs to satisfy the inequality constraint that the transmission power of each tie line is limited by forward and reverse limit red beans, the input power of each partition is limited by a partition power gap, and the inequality expression is as follows:
wherein P is EXi.pos -upper forward power limit of the ith tie line;
P EXi.neg -upper limit of reverse transmission power of the ith link;
D i -power gap of ith partition, when D i Above 0, a gap is indicated, when D i Less than 0, indicating that there is power redundancy;
for the objective function with equality constraint and inequality constraint, obtaining an objective function expression eliminating the equality constraint by introducing a Bragg day multiplier;
generating a linear equation for eliminating the objective function expression of the equation constraint according to the Lagrange extremum condition, and solving the linear equation by adopting a principal component elimination method;
and when the solutions of the linear equations are all in a preset constraint range and the inequality constraint is met, determining the solutions of the linear equations as a cross-region transmission result of the connecting line of the multi-region power system.
In the preferred embodiment, the tie-line cross-zone support model is a quadratic optimization problem with linear equality constraints, and therefore, equality constraints can be superimposed into the objective function by introducing lagrangian multipliers. However, unlike the general quadratic optimization problem with linear equality constraints, for the tie-line trans-regional support model, when the received power cannot meet the gap, the inequality constraint of the received power variable will not be met, so strictly speaking, there is a difference in inequality constraint between the solution of the general problem and the tie-line trans-regional support model. Therefore, when solving the general problem, the inequality constraint of the cross-region support model of the connecting line should be fully considered.
The expression for the first mathematical model with equality constraints in general is as follows:
wherein, X-n dimension real variable;
a i ,b i ,c i -with respect to variable x i The coefficients of the quadratic terms of (2), the three coefficients are possibly 0 at the same time;
A m×n -coefficient matrix constrained by linear equation, m x n dimensions;
b-right constant vector of equation constraint, m dimension;
X min -is the lower limit of variable X;
X max -upper limit of variable X;
introducing m Lagrangian multipliers, and eliminating the second mathematical model expression after the equation constraint is as follows:
according to the Lagrangian extremum condition, the following first linear equation can be obtained:
the second linear equation below can be obtained by sorting the above linear equation:
solving the coefficient matrix by adopting a principal component elimination method, and when the coefficient matrix has singular, neglecting corresponding columns and rows, and setting corresponding variables as 0 to continue elimination operation;
after solving to obtain variable X, judging whether it is in the set constraint range [ X ] min ,X max ]In, if x i Out of range, x i Taking an upper limit or a lower limit value, taking the upper limit or the lower limit value as a known quantity to be brought into a first mathematical model expression, performing dimension reduction on a coefficient matrix constrained by a linear equation and a second linear equation, and re-solving; this process is repeated until the solved variables X are all within the constraint range or are all determined.
In the preferred embodiment, the link line transregional power transmission is equivalent to overall scheduling of power of the multi-region power system, so that determining the final power surplus/gap of each region by combining the respective second power surplus/gap of each region and the link line transregional power transmission result is obvious and will not be described herein.
In step 206, according to the preset internal output rule of the subareas, according to the cross-regional transmission result of the tie line, determining a unit output combination of each subarea, wherein the unit output combination is a subarea electric quantity balance result, and the unit output combination comprises at least one of a conventional unit and a new energy unit.
Preferably, according to a preset intra-partition output rule, according to the cross-region transmission result of the tie, determining a unit output combination of each partition, wherein the intra-partition output rule comprises:
according to the cross-region transmission result of the connecting line, the output of the zero-carbon unit is preferentially arranged for the conventional unit and the new energy unit in the region needing cross-region output power;
when pumped storage exists, comprehensively arranging the zero-carbon unit and the pumped storage output;
and when the output power can not meet the power output requirement of the cross region, arranging the thermal power output, wherein a gas unit and a coal-fired unit in the thermal power output are in a competitive relationship, and are arranged according to the principle of equal utilization hours.
In the preferred embodiment, under the condition that the new energy power generation is large, the situation that the curve valley formed by the new energy superposition load is deep and even smaller than zero is generated, if the peak regulation effect of various power supplies of the multi-area power system is comprehensively considered, the regulation still cannot be realized, and the balance deviation negative value at the moment forms the power discarding quantity. And the moment that the peak load is not balanced, the electric quantity is insufficient.
In step 207, the carbon emission of each partition is calculated according to the conventional unit output in the unit output combination of each partition, the set energy consumption data of the conventional unit power generation, and the average carbon emission value of the conventional unit using energy.
At step 208, let n=n+1, and go to step 1 when n+.n, where N is the total number of generated cross-zone support timing production simulation sampling scenarios.
In step 104, according to the link line cross-region transmission result and the partition electric quantity balance result of each cross-region support time sequence production simulation sampling scene, calculating and outputting probability evaluation indexes considering the multi-region electric power system conservation level and the new energy consumption level.
Preferably, the probability evaluation index considering the protection level and the new energy consumption level of the multi-region power system is calculated and output according to the link line cross-region power transmission result and the partition power balance result of the sampling scene of each cross-region support time sequence production simulation, wherein the probability evaluation index comprises the power shortage probability, the power shortage expected value, the maximum power gap value and the new energy utilization expected value of the time sequence corresponding to the sampling scene of each cross-region support time sequence production simulation.
In the preferred embodiment, the power shortage probability LOLP (Loss of load probability), the power shortage expected value EENS (expected energy not supplied), the maximum power gap value MLNS (Maximum Load Not Supplied) and the new energy utilization rate expected value ENEUR (Expectedvalue of new energy utilization rate) are selected as evaluation indexes for measuring the effect of the multi-region power system cross-region support time sequence production simulation, which comprehensively consider the power system power supply and the new energy consumption level in the system, so that the link cross-region support result in the optimal sampling scene can be selected from the power system power supply and the new energy consumption level. Since the calculation of the four evaluation indexes may be performed by a conventional method in the prior art after determining the conventional unit output and the new energy output of the multi-region power system, and the cross-region power transmission result and the regional power balance result, the description thereof is omitted here.
Exemplary method two
Fig. 3 is a flowchart of a multi-zone power system cross-zone support timing production simulation method according to another preferred embodiment of the present invention. As shown in fig. 3, the multi-region power system cross-region support timing production simulation method according to the preferred embodiment starts in step 301.
In step 301, obtaining partition data and tie line data of a multi-region power system, and conventional unit information and new energy unit information in each partition;
in step 302, based on the established conventional unit output model and new energy output sequential model, randomly generating simulated output scenes of N multi-region power systems in any time sequence according to the conventional unit information and the new energy unit information, and taking the simulated output scenes as sampling scenes of cross-region support time sequence production simulation;
in step 303, selecting an nth cross-region support timing production simulation sampling scene, wherein N is greater than or equal to 1 and less than or equal to N;
in step 304, ignoring the effect of the cross-zone interconnecting line, performing independent power balance of new energy of each zone, and determining a first power surplus/gap of each zone;
in step 305, according to the principle of using hours balance of the conventional units of the multi-region power system, determining the average number of hours used by the conventional units of each region, and calculating the second power surplus/gap of each region by combining the first power surplus/first power gap;
at step 306, based on the established tie line fault probability model, randomly generating a tie line simulation fault result of the multi-region power system;
In step 307, taking account of the cross-region tie action, determining a tie cross-region transmission result by adopting an established tie cross-region support model according to the transmission constraint in the tie data and the tie simulation fault result and the second power surplus/second power gap of each partition, and obtaining the final power surplus/gap of each partition;
in step 308, according to a preset internal output rule of the subareas, determining a unit output combination of each subarea according to the cross-regional transmission result of the tie line, wherein the unit output combination is a subarea electric quantity balance result, and comprises at least one of a conventional unit and a new energy unit;
in step 309, calculating the carbon emission of each partition according to the conventional unit output in the unit output combination of each partition, the set energy consumption data of the conventional unit power generation, and the average carbon emission value of the conventional unit using energy;
in step 310, let n=n+1, and when N is less than or equal to N, go to step 1, where N is the total number of generated cross-zone support timing production simulation sampling scenes;
in step 311, according to the link line cross-region power transmission result and the partition power balance result of the sampling scene simulated by each cross-region support time sequence production, calculating and outputting probability evaluation indexes considering the multi-region power system conservation level and the new energy consumption level.
In the preferred embodiment, the multi-zone power system is a power system comprising 4 zones and 5 tie lines. Fig. 4 is a schematic diagram of a topology of a multi-zone power system according to another preferred embodiment of the present invention. As shown in fig. 4, the 4 partitions of the multi-area power system are respectively from area 1 to area 4, and the 5 direct current connecting lines are respectively from connecting line 1 to connecting line 5, wherein connecting line 1 connects area 1 with area 2, connecting line 2 connects area 1 with area 3, connecting line 3 connects area 2 with area 3, connecting line 4 connects area 2 with area 4, and connecting line 5 connects area 3 with area 4. When the 4 partitions balance the independent electric power and the electric quantity, the area 1 and the area 2 are redundant by 20GW, and the gaps of the area 3 and the area are respectively 30GW and 10GW.
Fig. 5 is a schematic diagram of a link transregional transmission result according to another preferred embodiment of the present invention. As shown in fig. 5, the line cross-region support timing production simulation of 2025 years is performed on the multi-region power system shown in fig. 4 by using the line fault probability model and the line cross-region support model which are identical to those in the first exemplary method, and in the case that the power transmission constraint of each line is two-way 10GW, the obtained line cross-region power transmission results are that lines 2,3 and 5 respectively transmit 10GW to region 3, line 4 transmits 10GW to region 4, and line 1 transmits 0 to region 1. At this time, zone 3 gap 30GW is fully supported, while zone 4 still has a 10GW gap.
Fig. 6 is a schematic diagram of another link transregional transmission result according to another preferred embodiment of the present invention. As shown in fig. 6, for the same multi-zone power system, the capacity of the link 4 is extended to 20GW based on the link trans-zone transmission result shown in fig. 5. And (3) calculating the cross-region transmission result of the connecting lines again for the same sampling scene, so as to obtain the transmission of 10GW to the region 3 by the connecting lines 2,3 and 5, the transmission of 20GW to the region 4 by the connecting line 4, and the transmission of 10GW to the region 1 by the connecting line 1. At this time, the gaps in both the region 3 and the region 4 are supported. Therefore, by adopting the method of the embodiment, reasonable production simulation can be carried out on the power conservation and new energy consumption of the future multi-region power system, so that the power system containing the new energy can be effectively guided and planned.
Table 1 shows the results of main evaluation indexes obtained by 2025 random production simulation for the above 4 areas in one sampling scene.
TABLE 1
As shown in table 1, the average value of the LOLP samples in the area 1 is 0.02136, which indicates that the average time is about 2.14% and the expected value of the annual power shortage duration is 184.8 hours, and the expected value of the annual power shortage duration is compared with the standby rate duration, so that it can be determined whether the area is under power. An EENS index of 0.6017 hundred million kWh for region 1 indicates that region 1 has a power gap of 0.6017 hundred million kWh; the MLNS index gives a power value for the annual maximum power gap, for example, the sample mean value for the region 1 maximum power gap is 4771.1 kW; the ENEUR index gives the percentage of new energy consumption, and the new energy consumption rate in the area 1 is 100%. Through the four evaluation indexes, the power conservation and new energy consumption level of the area under each sampling scene can be accurately evaluated.
FIG. 7 is a schematic diagram of sampling results of an evaluation index for a multi-zone power system cross-zone support timing production simulation according to another preferred embodiment of the present invention. As shown in fig. 7, fig. 7 is a schematic diagram of the lol sampling result generated from the lol index obtained by performing the cross-zone support production simulation in the plurality of sampling scenarios in the area 1. From the histogram, the LOLP value is most concentrated in the interval of 120 to 140 samples. Therefore, in the future actual power planning, setting the backup rate duration of the power system with the LOLP value of the interval can effectively ensure the power conservation of the area.
According to the method, the randomness of the new energy, the conventional unit and the connecting lines is considered, the time sequence production simulation is carried out on the multi-region power system through the connecting line fault probability model and the connecting line trans-regional support model, the simulation of the reliability of the contribution output of the new energy under the future running condition of the multi-region power system is realized, and the method has important reference significance for the guidance planning of the novel power system with the gradually improved new energy output ratio.
Exemplary System
Fig. 8 is a schematic structural diagram of a multi-zone power system cross-zone support timing production simulation system according to a preferred embodiment of the present invention. As shown in fig. 8, a multi-zone power system cross-zone support timing production simulation system 800 according to the preferred embodiment includes:
The data acquisition module 801 is configured to acquire partition data and tie line data of a multi-region power system, and conventional unit information and new energy unit information in each partition;
the sampling scene module 802 is configured to randomly generate a plurality of simulated output scenes of the multi-region power system in any time sequence according to the conventional unit information and the new energy unit information based on the established conventional unit output model and the new energy output sequential model, and take the simulated output scenes as sampling scenes for cross-region support time sequence production simulation;
the cross-region supporting module 803 is configured to perform time-sequence production simulation on the multi-region power system according to the established tie-line fault probability model and the tie-line cross-region supporting model based on a sampling scenario of each cross-region supporting time-sequence production simulation, and determine a tie-line cross-region power transmission result and a partition power balance result;
and the output result module 804 is configured to calculate and output probability evaluation indexes considering the protection level and the new energy consumption level of the multi-region power system according to the link line cross-region power transmission result and the partition power balance result of the sampling scene simulated by each cross-region support time sequence production.
Preferably, the cross-region supporting module 803 performs time-series production simulation on the multi-region power system according to the established tie-line fault probability model and the tie-line cross-region supporting model based on the sampling scenario of each cross-region supporting time-series production simulation, and determines a tie-line cross-region power transmission result and a partition power balance result, including:
step 1, selecting an nth cross-region supporting time sequence production simulation sampling scene, wherein N is more than or equal to 1 and less than or equal to N;
step 2, ignoring the action of a cross-region interconnecting line, carrying out independent power balance of new energy sources of each region, and determining a first power surplus/gap of each region;
step 3, determining average utilization hours of the conventional units of each partition according to the utilization hours balancing principle of the conventional units of the multi-region power system, and calculating second power surplus/gaps of each partition by combining the first power surplus/first power gaps;
step 4, randomly generating a tie line simulation fault result of the multi-region power system based on the established tie line fault probability model;
step 5, considering the action of a cross-region tie, determining a cross-region power transmission result of the tie by adopting an established tie cross-region support model according to the power transmission constraint in the tie data, the tie simulation fault result and the second power surplus/second power gap of each partition, and obtaining the final power surplus/gap of each partition;
Step 6, determining a unit output combination of each subarea according to a preset subarea internal output rule and the cross-regional transmission result of the tie line, wherein the unit output combination is a subarea electric quantity balance result, and comprises at least one of a conventional unit and a new energy unit;
step 7, calculating the carbon emission of each partition according to the conventional unit output in the unit output combination of each partition, the set energy consumption data of the conventional unit power generation and the carbon emission average value of the conventional unit using energy;
and 8, let n=n+1, and when N is less than or equal to N, go to step 1, wherein N is the total number of generated sampling scenes simulated by the cross-region support time sequence production.
Preferably, the cross-region support module 803 randomly generates a link simulation fault result of the multi-region power system based on the established link fault probability model, including:
for each tie line of the multi-region power system, randomly generating tie line simulated fault data of the tie line based on an established tie line fault probability model according to a time sequence of a sampling scene of the nth trans-regional support time sequence production simulation, wherein the tie line fault probability model comprises a tie line fault frequency probability model and a tie line fault state maintenance time probability model, and specifically:
The number of times of occurrence of the tie line faults obeys poisson distribution, and the expression of the tie line fault number probability model is as follows:
where k represents the number of failures occurring in the corresponding time series determined based on the historical failure data of the corresponding time series, λ represents the average number of failures of the corresponding time series determined based on the historical failure data of the corresponding time series, and P (x=k) represents the probability when the number of failures occurring in the corresponding time series determined based on the historical failure data of the corresponding time series is k;
the tie line fault state maintaining time obeys an exponential distribution, and the expressions of the tie line fault state maintaining time probability models F (x) and F (x) are as follows:
wherein x represents a fault state maintenance time of the corresponding time series determined based on the historical fault data of the corresponding time series, F (x) represents a density function of the fault state maintenance time distribution, F (x) represents a probability distribution function of the fault state maintenance time distribution, θ represents a desired value of the distribution, h represents an average fault duration of the corresponding time series determined based on the historical fault data of the corresponding time series, SF represents an operation coefficient of the link line in the multi-region power system, EFOR represents an equivalent forced outage rate, and T represents a duration of the corresponding time series.
Preferably, the cross-region supporting module 803 considers cross-region tie action, determines a tie cross-region transmission result by using an established tie cross-region supporting model according to transmission constraint in the tie data and the tie simulation fault result and the second power surplus/second power gap of each partition, wherein an objective function of the tie cross-region supporting model is obtained by superposing squares of power deviations of partitions with power gaps, and the objective function is expressed as follows:
wherein P is EX -tie power scheduling vector;
P ZN -an incoming foreign power schedule vector for the partition;
N EX -number of tie lines;
N ZN -number of partitions;
P EX.i -defining the forward direction of the flow of the transmitting end to the receiving end as the positive direction by the power arrangement value of the ith interconnecting line;
P ZN.i -the ith partition is subject to the value of the extraneous power;
D ZN.i -a power supply gap of the ith partition, the value being greater than zero indicating the presence of a gap and less than zero indicating the ability to support externally;
k i the coefficient of the ith link power term, 1.0, R/U when the resistance and link voltage are known 2 ;
The objective function is constrained by an equation to be satisfied, namely, the power received by each partition is the sum of the power of each interconnection line arrangement related to the partition, and the equation expression is as follows:
Wherein j represents a j-th connecting wire connected with an i-th subarea in the multi-area power system;
the objective function also needs to satisfy the inequality constraint that the transmission power of each tie line is limited by forward and reverse limit red beans, the input power of each partition is limited by a partition power gap, and the inequality expression is as follows:
wherein P is EXi.pos -upper forward power limit of the ith tie line;
P EXi.neg -upper limit of reverse transmission power of the ith link;
D i -power gap of ith partition, when D i Above 0, a gap is indicated, when D i Less than 0, indicating that there is power redundancy;
for the objective function with equality constraint and inequality constraint, obtaining an objective function expression eliminating the equality constraint by introducing a Bragg day multiplier;
generating a linear equation for eliminating the objective function expression of the equation constraint according to the Lagrange extremum condition, and solving the linear equation by adopting a principal component elimination method;
and when the solutions of the linear equations are all in a preset constraint range and the inequality constraint is met, determining the solutions of the linear equations as a cross-region transmission result of the connecting line of the multi-region power system.
Preferably, the cross-zone support module 803 determines a unit output combination of each zone according to a preset intra-zone output rule and the cross-zone transmission result of the tie, where the intra-zone output rule includes:
according to the cross-region transmission result of the connecting line, the output of the zero-carbon unit is preferentially arranged for the conventional unit and the new energy unit in the region needing cross-region output power;
when pumped storage exists, comprehensively arranging the zero-carbon unit and the pumped storage output;
and when the output power can not meet the power output requirement of the cross region, arranging the thermal power output, wherein a gas unit and a coal-fired unit in the thermal power output are in a competitive relationship, and are arranged according to the principle of equal utilization hours.
Preferably, the output result module 804 calculates and outputs a probability evaluation index considering the protection level and the new energy consumption level of the multi-region power system according to the link line cross-region power transmission result and the partition power balance result of the sampling scene of each cross-region support time sequence production simulation, wherein the probability evaluation index comprises a power shortage probability, a power shortage expected value, a maximum power gap value and a new energy utilization expected value of a time sequence corresponding to the sampling scene of each cross-region support time sequence production simulation.
The multi-region power system cross-region support time sequence production simulation system according to the preferred embodiment generates a plurality of sampling scenes of cross-region support time sequence production simulation according to parameters of a conventional unit and a new energy unit in the multi-region power system based on the established conventional unit output model and the new energy output sequential model, and performs cross-region support time sequence production simulation on each sampling scene based on the established tie line fault probability model and the tie line cross-region support model.
The invention has been described with reference to a few embodiments. However, as is well known to those skilled in the art, other embodiments than the above disclosed invention are equally possible within the scope of the invention, as defined by the appended patent claims.
Generally, all terms used in the claims are to be interpreted according to their ordinary meaning in the technical field, unless explicitly defined otherwise therein. All references to "a/an/the [ means, component, etc. ]" are to be interpreted openly as referring to at least one instance of said means, component, etc., unless explicitly stated otherwise. The steps of any method disclosed herein do not have to be performed in the exact order disclosed, unless explicitly stated.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical aspects of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the above embodiments, it should be understood by those of ordinary skill in the art that: modifications and equivalents may be made to the specific embodiments of the invention without departing from the spirit and scope of the invention, which is intended to be covered by the claims.
Claims (10)
1. A multi-zone power system cross-zone support timing production simulation method, the method comprising:
the method comprises the steps of obtaining partition data and tie line data of a multi-region power system, and conventional unit information and new energy unit information in each partition;
based on the established conventional unit output model and new energy output sequential model, randomly generating simulated output scenes of a plurality of multi-region power systems in any time sequence according to the conventional unit information and the new energy unit information, and taking the simulated output scenes as sampling scenes of cross-region support time sequence production simulation;
based on a sampling scene of each transregional support time sequence production simulation, performing time sequence production simulation on the multi-region power system according to the established tie line fault probability model and the tie line transregional support model, and determining a tie line transregional power transmission result and a regional power balance result;
and calculating and considering probability evaluation indexes of the multi-region power system conservation and new energy consumption level according to the cross-region power transmission result and the regional power balance result of the connecting line of the sampling scene of each cross-region support time sequence production simulation, and outputting the probability evaluation indexes.
2. The method of claim 1, wherein the determining the link transregional power transmission result and the partition power balance result based on the sampling scenario of each transregional support time-series production simulation by performing time-series production simulation on the multi-region power system according to the established link fault probability model and the link transregional support model comprises:
Step 1, selecting an nth cross-region supporting time sequence production simulation sampling scene, wherein N is more than or equal to 1 and less than or equal to N;
step 2, ignoring the action of a cross-region interconnecting line, carrying out independent power balance of new energy sources of each region, and determining a first power surplus/gap of each region;
step 3, determining average utilization hours of the conventional units of each partition according to the utilization hours balancing principle of the conventional units of the multi-region power system, and calculating second power surplus/gaps of each partition by combining the first power surplus/first power gaps;
step 4, randomly generating a tie line simulation fault result of the multi-region power system based on the established tie line fault probability model;
step 5, considering the action of a cross-region tie, determining a cross-region power transmission result of the tie by adopting an established tie cross-region support model according to the power transmission constraint in the tie data, the tie simulation fault result and the second power surplus/second power gap of each partition, and obtaining the final power surplus/gap of each partition;
step 6, determining a unit output combination of each subarea according to a preset subarea internal output rule and the cross-regional transmission result of the tie line, wherein the unit output combination is a subarea electric quantity balance result, and comprises at least one of a conventional unit and a new energy unit;
Step 7, calculating the carbon emission of each partition according to the conventional unit output in the unit output combination of each partition, the set energy consumption data of the conventional unit power generation and the carbon emission average value of the conventional unit using energy;
and 8, let n=n+1, and when N is less than or equal to N, go to step 1, wherein N is the total number of generated sampling scenes simulated by the cross-region support time sequence production.
3. The method of claim 1, wherein the randomly generating a tie-line simulated fault result for the multi-zone power system based on the established tie-line fault probability model comprises:
for each tie line of the multi-region power system, randomly generating tie line simulated fault data of the tie line based on an established tie line fault probability model according to a time sequence of a sampling scene of the nth trans-regional support time sequence production simulation, wherein the tie line fault probability model comprises a tie line fault frequency probability model and a tie line fault state maintenance time probability model, and specifically:
the number of times of occurrence of the tie line faults obeys poisson distribution, and the expression of the tie line fault number probability model is as follows:
where k represents the number of failures occurring in the corresponding time series determined based on the historical failure data of the corresponding time series, λ represents the average number of failures of the corresponding time series determined based on the historical failure data of the corresponding time series, and P (x=k) represents the probability when the number of failures occurring in the corresponding time series determined based on the historical failure data of the corresponding time series is k;
The tie line fault state maintaining time obeys an exponential distribution, and the expressions of the tie line fault state maintaining time probability models F (x) and F (x) are as follows:
wherein x represents a fault state maintenance time of the corresponding time series determined based on the historical fault data of the corresponding time series, F (x) represents a density function of the fault state maintenance time distribution, F (x) represents a probability distribution function of the fault state maintenance time distribution, θ represents a desired value of the distribution, h represents an average fault duration of the corresponding time series determined based on the historical fault data of the corresponding time series, SF represents an operation coefficient of the link line in the multi-region power system, EFOR represents an equivalent forced outage rate, and T represents a duration of the corresponding time series.
4. The method of claim 2, wherein the cross-zone tie action is considered, and a tie cross-zone transmission result is determined by using an established tie cross-zone support model according to transmission constraint in the tie data and the tie simulation fault result and a second power surplus/second power gap of each zone, wherein an objective function of the tie cross-zone support model is obtained by superposing squares of power deviations of zones with the power gaps, and an objective function is expressed as:
Wherein P is EX -tie power scheduling vector;
P ZN -an incoming foreign power schedule vector for the partition;
N EX -number of tie lines;
N ZN -number of partitions;
P EX.i -defining the forward direction of the flow of the transmitting end to the receiving end as the positive direction by the power arrangement value of the ith interconnecting line;
P ZN.i -the ith partition is subject to the value of the extraneous power;
D ZN.i -a power supply gap of the ith partition, the value being greater than zero indicating the presence of a gap and less than zero indicating the ability to support externally;
k i the coefficient of the ith link power term, 1.0, R/U when the resistance and link voltage are known 2 ;
The objective function is constrained by an equation to be satisfied, namely, the power received by each partition is the sum of the power of each interconnection line arrangement related to the partition, and the equation expression is as follows:
wherein j represents a j-th connecting wire connected with an i-th subarea in the multi-area power system;
the objective function also needs to satisfy the inequality constraint that the transmission power of each tie line is limited by forward and reverse limit red beans, the input power of each partition is limited by a partition power gap, and the inequality expression is as follows:
wherein P is EXi.pos -upper forward power limit of the ith tie line;
P EXi.neg -upper limit of reverse transmission power of the ith link;
D i -power gap of ith partition, when D i Above 0, a gap is indicated, when D i Less than 0, indicating that there is power redundancy;
for the objective function with equality constraint and inequality constraint, obtaining an objective function expression eliminating the equality constraint by introducing a Bragg day multiplier;
generating a linear equation for eliminating the objective function expression of the equation constraint according to the Lagrange extremum condition, and solving the linear equation by adopting a principal component elimination method;
and when the solutions of the linear equations are all in a preset constraint range and the inequality constraint is met, determining the solutions of the linear equations as a cross-region transmission result of the connecting line of the multi-region power system.
5. The method of claim 2, wherein the unit output combination of each partition is determined according to the cross-partition transmission result of the tie according to a pre-established partition internal output rule, wherein the partition internal output rule comprises:
according to the cross-region transmission result of the connecting line, the output of the zero-carbon unit is preferentially arranged for the conventional unit and the new energy unit in the region needing cross-region output power;
When pumped storage exists, comprehensively arranging the zero-carbon unit and the pumped storage output;
and when the output power can not meet the power output requirement of the cross region, arranging the thermal power output, wherein a gas unit and a coal-fired unit in the thermal power output are in a competitive relationship, and are arranged according to the principle of equal utilization hours.
6. The method according to claim 2, wherein the probability evaluation index considering the multi-region power system conservation and new energy consumption level is calculated and output according to the link line cross-region power transmission result and the regional power balance result of the sampling scenario simulated by each cross-region support time sequence production, wherein the probability evaluation index comprises a power shortage probability, a power shortage expected value, a maximum power gap value and a new energy utilization expected value of a time sequence corresponding to the sampling scenario simulated by each cross-region support time sequence production.
7. A multi-zone power system cross-zone support timing production simulation system, the system comprising:
the data acquisition module is used for acquiring partition data and tie line data of the multi-region power system, and conventional unit information and new energy unit information in each partition;
The sampling scene module is used for randomly generating simulated output scenes of a plurality of multi-region power systems in any time sequence according to the conventional unit information and the new energy unit information based on the established conventional unit output model and the new energy output sequential model, and taking the simulated output scenes as sampling scenes of cross-region support time sequence production simulation;
the cross-region supporting module is used for carrying out time sequence production simulation on the multi-region power system according to the established tie line fault probability model and the tie line cross-region supporting model based on the sampling scene of each cross-region supporting time sequence production simulation, and determining a tie line cross-region power transmission result and a partition electric quantity balance result;
and the output result module is used for calculating and considering probability evaluation indexes of the multi-region power system conservation level and the new energy consumption level according to the cross-region power transmission result and the regional power balance result of the connecting line of the sampling scene simulated by each cross-region support time sequence production and outputting the probability evaluation indexes.
8. The system of claim 7, wherein the cross-zone support module performs time-series production simulation on the multi-zone power system according to the established tie-line fault probability model and the tie-line cross-zone support model based on the sampling scenario of each cross-zone support time-series production simulation, and determines a tie-line cross-zone power transmission result and a zone power balance result, comprising:
Step 1, selecting an nth cross-region supporting time sequence production simulation sampling scene, wherein N is more than or equal to 1 and less than or equal to N;
step 2, ignoring the action of a cross-region interconnecting line, carrying out independent power balance of new energy sources of each region, and determining a first power surplus/gap of each region;
step 3, determining average utilization hours of the conventional units of each partition according to the utilization hours balancing principle of the conventional units of the multi-region power system, and calculating second power surplus/gaps of each partition by combining the first power surplus/first power gaps;
step 4, randomly generating a tie line simulation fault result of the multi-region power system based on the established tie line fault probability model;
step 5, considering the action of a cross-region tie, determining a cross-region power transmission result of the tie by adopting an established tie cross-region support model according to the power transmission constraint in the tie data, the tie simulation fault result and the second power surplus/second power gap of each partition, and obtaining the final power surplus/gap of each partition;
step 6, determining a unit output combination of each subarea according to a preset subarea internal output rule and the cross-regional transmission result of the tie line, wherein the unit output combination is a subarea electric quantity balance result, and comprises at least one of a conventional unit and a new energy unit;
Step 7, calculating the carbon emission of each partition according to the conventional unit output in the unit output combination of each partition, the set energy consumption data of the conventional unit power generation and the carbon emission average value of the conventional unit using energy;
and 8, let n=n+1, and when N is less than or equal to N, go to step 1, wherein N is the total number of generated sampling scenes simulated by the cross-region support time sequence production.
9. The system of claim 7, wherein the trans-regional support module randomly generates a tie-line simulated fault result for the multi-regional power system based on the established tie-line fault probability model, comprising:
for each tie line of the multi-region power system, randomly generating tie line simulated fault data of the tie line based on an established tie line fault probability model according to a time sequence of a sampling scene of the nth trans-regional support time sequence production simulation, wherein the tie line fault probability model comprises a tie line fault frequency probability model and a tie line fault state maintenance time probability model, and specifically:
the number of times of occurrence of the tie line faults obeys poisson distribution, and the expression of the tie line fault number probability model is as follows:
Where k represents the number of failures occurring in the corresponding time series determined based on the historical failure data of the corresponding time series, λ represents the average number of failures of the corresponding time series determined based on the historical failure data of the corresponding time series, and P (x=k) represents the probability when the number of failures occurring in the corresponding time series determined based on the historical failure data of the corresponding time series is k;
the tie line fault state maintaining time obeys an exponential distribution, and the expressions of the tie line fault state maintaining time probability models F (x) and F (x) are as follows:
wherein x represents a fault state maintenance time of the corresponding time series determined based on the historical fault data of the corresponding time series, F (x) represents a density function of the fault state maintenance time distribution, F (x) represents a probability distribution function of the fault state maintenance time distribution, θ represents a desired value of the distribution, h represents an average fault duration of the corresponding time series determined based on the historical fault data of the corresponding time series, SF represents an operation coefficient of the link line in the multi-region power system, EFOR represents an equivalent forced outage rate, and T represents a duration of the corresponding time series.
10. The system of claim 8, wherein the cross-zone support module considers cross-zone tie actions, determines tie cross-zone transmission results using an established tie cross-zone support model based on transmission constraints in the tie data and the tie simulation fault results, and the second power surplus/second power gap for each zone, wherein an objective function of the tie cross-zone support model is obtained by summing squares of power deviations of zones where power gaps exist, and wherein the objective function is expressed as:
Wherein P is EX -tie power scheduling vector;
P ZN -an incoming foreign power schedule vector for the partition;
N EX -number of tie lines;
N ZN -number of partitions;
P EX.i -defining the forward direction of the flow of the transmitting end to the receiving end as the positive direction by the power arrangement value of the ith interconnecting line;
P ZN.i -the ith partition is subject to the value of the extraneous power;
D ZN.i -a power supply gap of the ith partition, the value being greater than zero indicating the presence of a gap and less than zero indicating the ability to support externally;
k i the coefficient of the ith link power term, 1.0, R/U when the resistance and link voltage are known 2 ;
The objective function is constrained by an equation to be satisfied, namely, the power received by each partition is the sum of the power of each interconnection line arrangement related to the partition, and the equation expression is as follows:
wherein j represents a j-th connecting wire connected with an i-th subarea in the multi-area power system;
the objective function also needs to satisfy the inequality constraint that the transmission power of each tie line is limited by forward and reverse limit red beans, the input power of each partition is limited by a partition power gap, and the inequality expression is as follows:
wherein P is EXi.pos -upper forward power limit of the ith tie line;
P EXi.neg -upper limit of reverse transmission power of the ith link;
D i -power gap of ith partition, when D i Above 0, a gap is indicated, when D i Less than 0, indicating that there is power redundancy;
for the objective function with equality constraint and inequality constraint, obtaining an objective function expression eliminating the equality constraint by introducing a Bragg day multiplier;
generating a linear equation for eliminating the objective function expression of the equation constraint according to the Lagrange extremum condition, and solving the linear equation by adopting a principal component elimination method;
and when the solutions of the linear equations are all in a preset constraint range and the inequality constraint is met, determining the solutions of the linear equations as a cross-region transmission result of the connecting line of the multi-region power system.
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