CN110429637B - Visualization method for probability static voltage stability domain - Google Patents
Visualization method for probability static voltage stability domain Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
- H02J3/48—Controlling the sharing of the in-phase component
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
- H02J3/50—Controlling the sharing of the out-of-phase component
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Abstract
A visualization method of a probability static voltage stability domain is characterized in that the power generation output of new energy is averaged, a fault scene is screened, and a serious fault set is obtained; selecting any fault scene in a serious fault set, and establishing a voltage stability probability evaluation model based on the uncertainty of the new energy power generation output; obtaining a cumulative probability distribution function of the load margin according to the voltage stability probability evaluation model; calculating a margin ordering index of a given probability under a fault scene according to the cumulative probability distribution function of the load margin; repeating the steps until obtaining margin sequencing indexes of all fault scenes; and sequencing the fault scenes according to the margin sequencing indexes. The method can truly and comprehensively consider the probability characteristics of the new energy, and effectively discriminate and sort the static voltage stability of the fault scene under the influence of random factors. By setting margin sequencing indexes, a power system probability voltage stability region based on a fault set is constructed, and the optimal operation region of the system with given instability probability can be accurately judged.
Description
Technical Field
The invention relates to the field of new energy power generation grid connection of a power system, in particular to a visualization method of a probability static voltage stability domain based on new energy power generation uncertainty.
Background
The grid connection of new energy power generation such as wind power, photovoltaic and the like is beneficial to adjusting the primary energy structure of the power system, the carbon emission level of the system can be reduced, and the cleanness and sustainability of the power generation side are realized. With the reduction of the cost of new energy power generation, the economic competitiveness of the new energy power generation is gradually enhanced compared with that of the traditional fossil energy power generation, so that the high proportion of wind power and photovoltaic power generation is permeated to become an important characteristic of a future power system. However, due to the influence of natural conditions, the new energy power generation output has strong randomness and uncertainty, and the difficulty of stable operation and regulation control of the system is increased by high-proportion grid connection.
In the prior art, in order to accurately and reasonably depict the random characteristics of new energy output and effectively evaluate the static voltage stability of a power system, uncertain quantities such as wind speed, illumination intensity, load increasing direction and the like are described as random variables based on a classical probability theory, a voltage stability probability evaluation model is established, and probability analysis means such as a Monte Carlo method and a modification method thereof, a point estimation method, unscented transformation, a random Response Surface method SRSM (stored Response Surface method) and the like are adopted for solving, so that the probability distribution of static voltage stability critical power, load margin or L index is obtained, and the probability distribution is used for judging the voltage instability occurrence probability of the system under any load level.
The rule of the faults of the equipment such as the power system line, the transformer and the like is also considered to be random, and once the equipment faults occur, the stability of the static voltage of the system is greatly influenced. In the prior art, the problem of equipment faults is not considered for a static voltage stability probability evaluation model of a power system. In the prior art, the characteristic that equipment fails is defined as a random variable which obeys 0-1 distribution, and the randomness of equipment failure and injected power can be uniformly processed. However, as can be seen from historical statistical data, the probability of equipment failure is usually small, while the probability of random fluctuation of new energy power generation or load direction is large, and the randomness of the two is considered in the static voltage stability probability analysis problem, so that the problem that the randomness of equipment failure is easily overwhelmed occurs, and it is difficult to accurately discriminate and quantify the influence of each equipment failure on the system voltage stability.
Therefore, how to consider not only uncertainty of new energy power generation output but also influence of equipment faults on static voltage stability analysis, and how to establish a visual power system probability voltage stability domain are a problem to be solved urgently.
Disclosure of Invention
The invention aims to solve the problems that the influence of the equipment fault of the power system and the uncertainty of new energy power generation on the static voltage stability of the system is effectively analyzed, and the problem that the randomness of the equipment fault is submerged is solved; and establishing a visualized power system probability voltage stability domain.
In order to solve the above problems, the invention provides a visualization method of a probability static voltage stability domain, in a first step S1, averaging the generated power of new energy, screening a fault scene, and obtaining a serious fault set; a second step S2, selecting any fault scene in the serious fault set, and establishing a voltage stability probability evaluation model based on the uncertainty of the new energy power generation output; a third step S3, obtaining a cumulative probability distribution function of the load margin according to the voltage stability probability evaluation model; a fourth step S4, calculating a margin sequencing index under a fault scene according to the cumulative probability distribution function of the load margin; a fifth step S5 of repeating the second step S2 to the fourth step S4 until margin ranking indexes of all fault scenarios are obtained; and a sixth step S6, sorting the fault scenes according to the margin sorting index and constructing a probability static voltage stability domain based on a visualized fault set.
According to an embodiment of the invention, the method further includes constructing a fault set based probabilistic static voltage stability domain according to the margin ranking index.
According to an embodiment of the present invention, the first step S1 of the method includes, in a first sub-section S11, obtaining an N-1 fault scenario to be analyzed, and constructing an original fault set; a second subsection S12, selecting the fault scene of the original fault set, correcting the network structure of the power system, and establishing a voltage stabilization critical point model; a third subsection S13, solving the problem of voltage stabilization critical point by adopting an interior point algorithm, and obtaining the load margin of the fault scene; a fourth section S14 repeating the first to third sections S11 to S13 until load margins for all fault scenarios are obtained; a fifth division S15, setting a load margin threshold value, and screening the fault scene to obtain a serious fault set;
according to one embodiment of the present invention, when the new energy power generation includes a wind farm and a photovoltaic power generation, the voltage stability probability evaluation model is:
wherein λ is a load margin; sBIs the set of all nodes of the system;
SGand SRRespectively a conventional generator and a reactive power supply node set;
PGithe active output of a conventional generator at node i;
QRithe reactive power output of the reactive power supply at the node i is obtained;
PWiand QWiRespectively injecting active power and reactive power of the wind power plant at the node i;
PSiand QSiRespectively the active power and the reactive power of photovoltaic power generation at a node i;
PLiand QLiRespectively the active and reactive loads at node i;
bPiand bQiIs the increasing direction of the load at the node i;
Uiandithe voltage amplitude and the phase angle of the node i are respectively;
Yijand alphaijThe element and phase angle of the ith row and the jth column of the node admittance matrix respectively describe the parameters of the grid structure characteristics of the power system,ij＝i-j-αij；
According to one embodiment of the invention, the mean value of the new energy power generation output is obtained by taking historical statistical data as a sample and calculating an expected value of the statistical sample.
According to one embodiment of the invention, the new energy power generation comprises at least one of a wind farm system and a photovoltaic power generation system.
According to one embodiment of the invention, the uncertainty of the new energy power generation output comprises uncertainty of a wind power plant, and a wind power plant stochastic model is as follows:
wherein N isWiThe number of wind generating sets in the wind power plant at the node i is shown;
θWithe power factor angle of each wind turbine generator set;
PWgithe actual output power of a single wind turbine generator is obtained;
a＝Prvin/(vin-vr) And b ═ Pr/(vr-vin) Is a constant;
vin、voutand vrRespectively the cut-in wind speed, the cut-out wind speed and the rated wind speed of the fan;
Pris the rated active output;
vithe actual wind speed of the wind power plant at the node i is obtained;
the probability density function for wind speed is:
K. and C is the shape parameter and the scale parameter of Weibull distribution respectively.
According to one embodiment of the invention, the new energy power generation output uncertainty comprises a photovoltaic power generation uncertainty, and the photovoltaic power generation uncertainty stochastic model is as follows:
wherein, thetaSiThe power factor angle of the photovoltaic power generation system at the node i is shown;
rithe intensity of solar radiation;
a is the total area of the solar cell matrix;
eta is the overall photoelectric conversion efficiency;
the illumination intensity probability density function is:
According to an embodiment of the present invention, the third step S3 includes solving the voltage stability probability evaluation model by using a stochastic response surface method, and transforming the voltage stability probability evaluation problem into a series of deterministic voltage stability critical point calculation problems;
and solving the problem of each voltage stabilization critical point by adopting an original dual interior point algorithm, and constructing an accumulative probability distribution function of the load margin according to the result.
According to one embodiment of the invention, the probability ranking index is a given load margin λaDetermining the probability of the static voltage instability of the power system after the fault:
pPr(λ≤λa)＝F(λa)0≤λa≤+∞
wherein p isPr(. is the probability of an event occurring, pPr(λ≤λa) Represents an event λ ≦ λaThe probability of occurrence.
According to an embodiment of the present invention, the margin ordering index is a given voltage instabilityProbability paDetermining load margins under different fault scenes:
λa＝F-1(pa)0≤pa≤1。
according to the method, the fault set is screened by assuming the power generation output of the new energy as a mean value, so that the probability characteristic of the new energy can be really and comprehensively considered; the random response surface method is adopted to convert the voltage stability probability evaluation problem into a series of deterministic voltage stability critical point calculation problems, and then the original dual interior point algorithm is adopted to solve each voltage stability critical point problem, so that the solving efficiency is improved; the method can effectively discriminate and sort the static voltage stability of the fault scene under the influence of random factors; according to the method, the margin ordering indexes are set, the power system probability voltage stability region based on the fault set is constructed and visualized, and the optimal operation region of the system given instability probability can be accurately judged.
Drawings
FIG. 1 is a schematic diagram of the steps of a probabilistic static voltage stability domain visualization method based on new energy generation uncertainty;
FIG. 2 is a schematic diagram of the steps for screening a critical failure set;
FIG. 3 is a graph of cumulative probability of load margin after fault;
FIG. 4 is a probabilistic static voltage stability domain based on a fault set; and
FIG. 5 is an enlarged view of the boundary of the stability region of FIG. 4.
Detailed Description
In the following detailed description of the preferred embodiments of the invention, reference is made to the accompanying drawings that form a part hereof, and in which is shown by way of illustration, specific features of the invention, such that the advantages and features of the invention may be more readily understood and appreciated. The following description is an embodiment of the claimed invention, and other embodiments related to the claims not specifically described also fall within the scope of the claims.
FIG. 1 shows a schematic step diagram of a visualization method of a probabilistic static voltage stability domain based on new energy power generation uncertainty.
As shown in fig. 1, a visualization method of a probabilistic static voltage stability domain includes, in a first step S1, averaging the output of new energy generated power, and screening a fault scene to obtain a serious fault set; a second step S2, selecting any fault scene in the serious fault set, and establishing a voltage stability probability evaluation model based on the uncertainty of the new energy power generation output; a third step S3, obtaining a cumulative probability distribution function of the load margin according to the voltage stability probability evaluation model; a fourth step S4, calculating a margin sequencing index under a fault scene according to the cumulative probability distribution function of the load margin; a fifth step S5 of repeating the second step S2 to the fourth step S4 until margin ranking indexes of all fault scenarios are obtained; and a sixth step S6, sorting the fault scenes according to the margin sorting index and constructing a probability static voltage stability domain based on a visualized fault set.
According to the method, the margin ordering indexes are set, the visual power system probability voltage stability region based on the fault set is constructed, the optimal operation region of the given instability probability of the system can be accurately judged, and the effect of intuitively acquiring the system probability is achieved.
The new energy power generation output refers to the power generated by the new energy power generation.
The actual fault set of the large-scale power system is huge, and if the voltage stability random characteristics under each fault scene are analyzed one by one, a large amount of calculation time needs to be consumed. The invention provides a two-stage method for fault screening and sorting.
Stage 1: considering that the mean value is a random variable probability characteristic parameter, the new energy power generation output is modeled into a random variable, and the screening of the fault set based on the output mean value is more reasonable. If a serious fault scene is screened based on the highest value of the probability density, the method also has feasibility, but because the high sampling area is excessively concerned, the probability characteristics of new energy sources are difficult to truly and comprehensively consider. Therefore, the new energy power generation output is assumed to be the average value, namely the wind speed of the wind power plant
(
Average of wind speed), illumination intensity
(
As an average of the illumination intensity). And calculating expected values of statistical samples according to historical statistical data of regional wind speed and illumination intensity respectively for average values of wind speed of the wind power plant and illumination intensity of photovoltaic power generation. Establishing a deterministic voltage stability critical point model, adopting an original dual interior point algorithm to analyze various N-1 fault scenes one by one, and screening to obtain a fault set which has a large influence on the system stability margin, namely a serious fault set.
And (2) stage: and (4) considering the random distribution of new energy power generation, establishing a voltage stability probability analysis model, and sequencing a serious fault set according to the result.
The implementation method of the stage 2 fault sequencing comprises the following steps: firstly, selecting each fault scene of a serious fault machine set, correcting the network structure of the power system, and establishing a voltage stability probability evaluation model under each fault scene; solving the problem of evaluating the stability probability of each voltage to obtain a load margin cumulative probability distribution curve after the fault; and thirdly, calculating probability indexes or margin indexes of the static voltage stability under each fault scene according to the load margin accumulated probability distribution, and sequencing according to the index values.
According to the method, the new energy power generation output is modeled into random variables, the mean value is a random variable probability characteristic parameter, and the probability characteristic of the new energy can be really and comprehensively considered, so that the method is more reasonable by screening a fault set based on the mean value of the new energy power generation output. If a serious fault scene is screened based on the highest value of the probability density, the method also has feasibility, but because the high sampling area is excessively concerned, the probability characteristics of new energy sources are difficult to truly and comprehensively consider.
In addition, in the invention, firstly, the selection of the fault set is carried out based on the mean value of the new energy generated output, so that the randomness of the equipment fault is prevented from being covered by the randomness of the new energy generated output. Meanwhile, voltage stability probability evaluation is carried out based on the screened serious fault set, so that on one hand, calculation is simplified, on the other hand, the calculation result comprehensively covers two factors of equipment faults and new energy power generation uncertainty, and the result is more effective.
Furthermore, in the invention, the random response surface method is adopted to convert the voltage stability probability evaluation problem in the voltage stability probability evaluation model into a series of deterministic voltage stability critical point calculation problems, and then the original dual interior point algorithm is adopted to solve each voltage stability critical point problem, thereby simplifying the calculation process and improving the solving efficiency.
In the invention, aiming at the situation that the power system quits operation due to equipment failure, the grid structure of the system is changed, and the load margin cumulative probability distribution curves after different failures are different, two evaluation indexes for evaluating the voltage stability after the failures are provided: the probability ranking index and the margin ranking index are evaluated from two aspects of voltage instability probability and load margin, so that the evaluation result is more effective.
FIG. 2 shows a schematic diagram of the steps for screening a critical failure set.
As shown in fig. 2, the first step S1 includes a first sub-section S11, obtaining an N-1 fault scenario to be analyzed, and constructing an original fault set; a second subsection S12, selecting the fault scene of the original fault set, correcting the network structure of the power system, and establishing a voltage stabilization critical point model; a third subsection S13, solving the problem of voltage stabilization critical point by adopting an interior point algorithm, and obtaining the load margin of the fault scene; a fourth section S14 repeating the first to third sections S11 to S13 until load margins for all fault scenarios are obtained; and a fifth part S15, setting a load margin threshold value, and screening the fault scene to obtain a serious fault set.
The N-1 fault scene refers to a fault caused by the fact that the equipment does not meet the N-1 operation principle when in operation. The original fault set is composed of a plurality of fault scenarios, for example, M N-1 fault scenarios to be analyzed are selected, and the original fault set S is constructed as { S ═ S1,s2,…,sM}。
In the present invention, it is first assumed that the new energy power generation output is an average value, for example, the wind speed of a wind farm
(
Average of wind speed), illumination intensity
(
As an average of the illumination intensity). And calculating expected values of statistical samples according to historical statistical data of regional wind speed and illumination intensity respectively for average values of wind speed of the wind power plant and illumination intensity of photovoltaic power generation. A deterministic voltage stability critical point model, i.e. a voltage stability critical point model in the second section S12, is established. Analyzing each N-1 fault scene one by adopting an original dual interior point algorithm, and screening to obtain a fault set which has a large influence on the stability margin of the system, namely a serious fault set, for example, from the original fault set S ═ S { (S) }1,s2,…,sMScreening to obtain a serious fault set H ═ H }1,h2,…,ht}。
The load margin threshold is used for judging the influence degree of a specific fault scene on the power system, the value of the load margin threshold can be set manually, the method is not limited to the determination mode of the load margin threshold, and the load margin threshold can be determined by adopting various methods in the prior art or the future invention.
The deterministic voltage stabilization critical point model is a mean value determined by the generated output of the new energy.
According to one embodiment of the invention, when the new energy comprises a wind power plant and a photovoltaic system, the invention takes a common index load margin for measuring the static voltage stability of the power system as an optimization target, takes an expanded power flow equation comprising load margin parameters as equality constraint, takes equipment and system safe operation limit as inequality constraint, considers the uncertainty of the output of the new energy such as wind power, photovoltaic power generation and the like, and the voltage stability probability evaluation model is as follows:
wherein λ is a load margin; sBIs the set of all nodes of the system;
SGand SRRespectively a conventional generator and a reactive power supply node set;
PGithe active output of a conventional generator at node i;
QRithe reactive power output of the reactive power supply at the node i is obtained;
PWiand QWiRespectively injecting active power and reactive power of the wind power plant at the node i;
PSiand QSiRespectively the active power and the reactive power of photovoltaic power generation at a node i;
PLiand QLiRespectively the active and reactive loads at node i;
bPiand bQiIs the increasing direction of the load at the node i;
Uiandithe voltage amplitude and the phase angle of the node i are respectively;
Yijand alphaijThe element and phase angle of the ith row and the jth column of the node admittance matrix respectively describe the parameters of the grid structure characteristics of the power system,ij＝i-j-αij；
Due to the output P of the wind power plantWiAnd QWiPhotovoltaic power generation output PSiAnd QSiAre all random variables, which makes the above equation a random analysis problem that is to be solved for the probability distribution characteristics of the load margin λ, i.e. the probability density distribution or the cumulative probability distribution.
The invention comprehensively considers the safety problems of equipment and systems and the uncertainty problem of new energy output of wind power, photovoltaic power generation and the like, so that the static voltage stability analysis model is more effective and practical.
According to one embodiment of the invention, the mean value of the new energy power generation output is obtained by taking historical statistical data as a statistical sample and calculating an expected value of the statistical sample. For example, for the average value of wind speed of a wind farm and illumination intensity of photovoltaic power generation, the expected value of a statistical sample can be calculated according to historical statistical data of regional wind speed and illumination intensity respectively.
According to one embodiment of the invention, the new energy power generation comprises at least one of a wind farm system and a photovoltaic power generation system.
The wind power plant refers to a system for generating power by utilizing wind power by a wind turbine generator; the photovoltaic power generation system is a power generation system which directly converts solar energy into electric energy by using a solar cell.
The new energy power generation system of the present invention is not limited to wind farm systems and photovoltaic power generation systems, but may also include other types of power generation systems, such as tidal power generation systems, as long as there is uncertainty in the power generation system, which can be evaluated according to the method of the present invention.
According to one embodiment of the invention, the new energy power generation output uncertainty comprises a wind farm uncertainty. Generally, a wind turbine generator can adopt two operation modes of constant voltage and constant power factor, the wind turbine generator can be classified into a PV node and a PQ node respectively at a corresponding access node of a system, and the two operation modes are both directly suitable for the voltage stability probability analysis model.
The invention assumes that the wind turbine generator runs in a constant power factor mode, and the power factors and the wind speeds of all the wind turbine generators are the same, so that the following wind power random model is established: the wind farm stochastic model is as follows:
wherein N isWiThe number of wind generating sets in the wind power plant at the node i is shown;
θWithe power factor angle of each wind turbine generator set;
PWgithe actual output power of a single wind turbine generator is obtained;
a＝Prvin/(vin-vr) And b ═ Pr/(vr-vin) Is a constant;
vin、voutand vrRespectively the cut-in wind speed, the cut-out wind speed and the rated wind speed of the fan;
Pris the rated active output;
vithe actual wind speed of the wind power plant at the node i is obtained;
the generated power of the wind turbine generator and the wind farm changes along with the fluctuation of the wind speed, and the output active power of the wind turbine generator and the wind farm also has high randomness and uncertainty due to the fact that the wind speed has high randomness and uncertainty.
Existing studies generally consider that wind speed approximates a Weibull distribution with a probability density function of:
k, C are the shape parameter and the scale parameter of Weibull distribution.
According to an embodiment of the present invention, the uncertainty of the new energy generated output includes uncertainty of photovoltaic power generation, and a relation between power generation power and illumination intensity of the photovoltaic power generation system may be represented as: :
wherein, thetaSiThe power factor angle of the photovoltaic power generation system at the node i is shown;
rithe intensity of solar radiation;
a is the total area of the solar cell matrix;
eta is the overall photoelectric conversion efficiency;
because the illumination intensity is influenced by weather and has strong intermittency and randomness, P is enabled to beSiAnd QSiIt is also random.
The illumination intensity is generally considered to satisfy a Beta distribution with a probability density function of:
where is the Gamma function, si＝ri/rmax，rmaxThe maximum irradiance of sunlight, wherein alpha and Beta are respectively a shape parameter and a scale parameter of Beta distribution.
According to an embodiment of the present invention, the third step S3 includes solving the voltage stability probability evaluation model by using a stochastic response surface method, and transforming the voltage stability probability evaluation problem into a series of deterministic voltage stability critical point calculation problems; and solving the problem of each voltage stabilization critical point by adopting an original dual interior point algorithm, and constructing an accumulative probability distribution function of the load margin according to the result.
In order to improve the solving efficiency, the voltage stability probability evaluation problem is solved by combining a random response surface method with an original dual interior point algorithm. The static voltage stability probability assessment model can be abstracted into a standard form of the randomness analysis problem as follows:
y＝f(x)
wherein y is a random variable to be solved, namely a load margin lambda;
x is an input random variable, i.e. wind speed v of the wind farmiAnd intensity of illumination ri。
The principle of solving the formula by adopting the random response surface method is as follows: and expressing the random variable y to be solved as a chaotic polynomial which takes a standard random variable as an independent variable and contains a parameter to be determined, and definitely outputting the mapping of the random variable y and the standard random variable, thereby establishing the chaotic relation between the random variable to be solved and the input random variable. And constructing a linear equation set and solving undetermined coefficients in the chaotic polynomial according to values of corresponding input variables x and the variables y to be solved of a small number of sample points so as to determine mapping of the random variables to be solved and the input random variables and analyze random distribution of the quantities to be solved.
Firstly, a chaotic polynomial of a random variable to be solved is constructed. The random response surface method generally selects a standard normal distribution random variable ξ as a standard random variable, and establishes a Hermite chaotic polynomial of a variable to be solved as follows:
where n is the number of input random variables, a0、
… is a chaotic polynomialDetermining parameters as constant terms;
an m-order Hermite polynomial of ξ. The larger the order m selected by the above formula is, the higher the calculation accuracy is, but the more undetermined parameters need to be determined, the more the number of required sample points and the calculation amount are greatly increased.
In order to balance the accuracy and efficiency, it is more practical to select a second-order chaotic polynomial, and the established polynomial is:
secondly, the mapping relation between the input random variable and the standard random variable is determined. The input random variable of the voltage stability probability evaluation model is the wind speed viAnd intensity of illumination riRespectively satisfying the Weibull distribution and the Beta distribution, and obtained by the following transformation according to the cumulative probability distribution function Ψ of the Weibull distribution and the Beta distribution:
x＝Ψ-1(Φ(ξ))
therein, Ψ-1An inverse function of the cumulative probability distribution function of x; Φ is the standard normal distribution function.
And thirdly, determining the undetermined parameters. Selecting wind speed v according to probability distribution ruleiAnd intensity of illumination riAnd calculating all calculation formulas in a static voltage stability analysis model, a wind power random model and a photovoltaic power generation uncertainty random model by adopting an original dual interior point algorithm to obtain output variable values corresponding to all the sample points, substituting the output variable values into the second-order chaotic polynomial to establish a linear equation set, and calculating and determining undetermined parameters of the chaotic polynomial.
According to one embodiment of the invention, the probability ranking index is a given load margin λaDetermining the probability of the static voltage instability of the power system after the fault:
pPr(λ≤λa)＝F(λa)0≤λa≤+∞
wherein p isPr(. is the probability of an event occurring, pPr(λ≤λa) Represents an event λ ≦ λaThe probability of occurrence.
The margin ordering index refers to the given voltage instability probability paDetermining load margins under different fault scenes: lambda [ alpha ]a＝F-1(pa)0≤pa≤1。
And solving each calculation formula in the static voltage stability analysis model, the wind power random model and the photovoltaic power generation uncertainty random model by adopting a random response surface method to obtain an accumulative probability distribution function F (lambda) of the system load margin. F (lambda) is a monotone increasing function, the probability of voltage instability of the system under any load margin can be determined according to F (lambda), and the F (lambda) is an inverse function-1And (lambda) determining the load margin corresponding to any voltage instability probability.
Due to the fact that the power system is out of operation when equipment faults occur, the grid structure of the system is changed, and the load margin accumulation probability distribution curves are different after different faults occur. Therefore, the present invention sets the following two evaluation indexes for evaluating the voltage stability after the failure.
(1) And (4) probability ranking index. Given load margin lambdaaDetermining the probability of the power system having the static voltage instability after the fault can be expressed as:
pPr(λ≤λa)＝F(λa)0≤λa≤+∞
wherein p isPr(. is the probability of an event occurring, pPr(λ≤λa) Represents an event λ ≦ λaThe probability of occurrence. The probability distribution of the load margin accumulation of different faults is different, so that the probability of system voltage instability is different. The smaller the voltage instability probability is, the smaller the influence of the fault on the static voltage stability of the system is; the larger the voltage instability probability is, the larger the influence of the fault on the static voltage stability of the system is.
(2) And (5) margin sorting indexes. Given voltage instability probability paDetermining the load margins under different fault scenarios can be expressed as:
λa＝F-1(pa)0≤pa≤1
the cumulative probability distribution of the load margins of different faults has difference, so that the load margins corresponding to the same instability probability are different. The higher the load margin is, the smaller the influence of the fault on the static voltage stability of the system is; the lower the load margin, the greater the effect of the fault on the static voltage stability of the system.
Examples
The voltage stabilization fault screening and sorting method provided by the invention comprises the following implementation steps:
(1) selecting M N-1 fault scenes to be analyzed, and constructing an original fault set
S＝{s1,s2,…,sM}；
(2) The wind speed of the wind farm and the illumination intensity of the photovoltaic system are assumed to be corresponding averages, i.e.
Selecting any fault scene si, correcting the network structure of the power system, and establishing a fault scene siA lower voltage stability critical point model;
(3) solving the problem of voltage stability critical point by adopting an interior point algorithm, obtaining the load margin of each fault scene, and screening to obtain a serious fault set H ═ H1,h2,…,ht}；
(4) Selecting any fault scene h in a serious fault setiCorrecting the network structure, considering the uncertainty of new energy power generation such as wind power and photovoltaic, and establishing a fault scene hiA voltage stability probability evaluation model;
(5) converting the voltage stability probability evaluation problem into a series of deterministic voltage stability critical point calculation problems by adopting a random response surface method;
(6) solving the problem of each voltage stable critical point by adopting an original dual interior point algorithm, and constructing an accumulative probability distribution function F of load margin according to the resulti(λ)；
(7) Calculating a failure scenario h according to equation (11) or equation (12)iA lower probability ranking index or a margin ranking index;
(8) repeating the steps 4-7 until the analysis of all fault scenes in the serious fault set H is completed;
(9) and sequencing the fault scenes in the fault set according to the probability sequencing index or the margin sequencing index.
The model and the method provided by the invention are realized by writing a program by using MATLABR2016b, the CPU dominant frequency of a computing platform is 3.2GHz multiplied by 2, and the memory is 8 GB. The main parameters of each wind farm and photovoltaic power generation and the access positions in the IEEE 118 node system are respectively shown in tables 1 and 2. The load direction studied is to increase with constant power factor, four node loads simultaneously in equal proportion.
Table 1.
Table 2.
In order to verify the solving precision and efficiency of the random response surface method, 10000 Monte Carlo simulations are used as comparison bases, the Monte Carlo method, the random response method and the point estimation method are respectively adopted to calculate the stability margin mean value and the standard deviation of the power system in the normal state, the solving effects of the three methods are shown in the table 3, and therefore the advantages of the random response surface method in the calculating efficiency and the calculating precision are verified.
Table 3.
| Method of producing a composite material | Mean value of load margin | Error/%) | Standard deviation of load margin | Error/%) | Calculating time/s |
| Monte Carlo method | 1.6922 | 0 | 0.0107 | 0 | 420.54 |
| Point estimation method | 1.6950 | 0.17 | 0.0113 | 5.61 | 3.78 |
| Random response surface method | 1.6928 | 0.04 | 0.0109 | 1.87 | 3.92 |
The load margin under the normal state and the N-1 fault state of the power system is solved by adopting a random response surface method, and a Hermite polynomial of the load margin can be constructed as follows:
the determined undetermined parameter a is different due to different fault scenes0、ai、aii、aijMay vary from one another. Table 4 shows a serious failure set of the IEEE-118 node system.
Table 4.
FIG. 3 shows the resulting cumulative probability distribution of load margins after a fault, taking as an example the retirement of branches 76-118 due to a fault.
According to FIG. 3, the current load margin λ can be determinedaWhen the static voltage instability of the system is 1.660, 1.665, 1.670 and 1.675, the probability of the static voltage instability of the system is 0.114, 0.585, 0.941 and 1.000 respectively, and the probability index of the fault scene can be determined.
Thus, the probability indexes under each fault scenario are determined one by one as shown in table 5, and the corresponding fault ranks are shown in table 6.
Table 5.
Table 6.
As can be seen from table 6, since the severity of the influence of different fault scenarios on the system voltage stability is different, the cumulative probability distribution of the fault scenarios is very different, and it is difficult to select the proper load margin λaAs a unified decision criterion. And if selectedWhen the load margin is not appropriate, the same sequence of multiple faults such as branches 8-9, 12-17, 110, 112, 75-118 in Table 6 is easy to occur.
Also for the example of a fallback of branch 76-118 due to a fault, the voltage instability probability p is givenaAt 0.6, 0.7, 0.8 and 0.9, the load levels of the system are 1.6652, 1.6662, 1.6674 and 1.6690 respectively, i.e. the margin index of the fault scene can be determined.
Table 7 shows the probability indicators for each failure scenario determined one by one, and the corresponding failure rankings are shown in table 8.
Table 7.
Table 8.
Compared with the probability sequencing index, the margin sequencing index is more flexible, the given voltage instability probability pa is easier to select, the problem that the sequencing of a plurality of faults is the same is solved, and the method is particularly suitable for large-scale power systems with different fault results having large differences.
According to the method, the load margin index is set, the visual power system probability voltage stability region based on the fault set is constructed, the optimal operation region of the given instability probability of the system can be accurately judged, and the effect of intuitively acquiring the system question probability is achieved.
The voltage stability probabilities of 0.6, 0.7, 0.8 and 0.9 obtained by the method are obtained based on the fault scene of the system, and the voltage stability probability of the actual system in the normal state is close to 1.0. The voltage instability probability under the fault scene of the fault scene is mastered, and the probability stable region and the probability unstable region of the static voltage stability of the system can be drawn beneficially, so that the system is guided to adjust and operate in the optimal region.
According to the margin ranking indexes of table 7, the invention constructs a probability static voltage stability domain based on a fault set as shown in fig. 4, and the stability domain boundary is enlarged as shown in fig. 5. In fig. 5, the left side of the curve is the probability static voltage stability region, and the right side is the probability static voltage instability region.
When the power system operates in the boundary of the probability voltage stability region, the maximum probability of the system for generating static voltage instability is a given value. With paFor example, when the system load level and the network structure operate at p, 0.6aWhen the left side of the curve is 0.6, the maximum probability of voltage instability of the system is 0.6, and the minimum probability of voltage stability of the system is 0.4. And when the system load level and network structure operate at paWhen the voltage is stabilized, the maximum probability of occurrence of voltage instability is 0.8 and the minimum probability of maintaining voltage stability is 0.2.
The calculation result of the IEEE 118 node standard system shows that the method provided by the invention can effectively discriminate and sort the static voltage stability of the fault scene under the influence of random factors. Meanwhile, based on a fault sequencing result, a power system probability voltage stability region based on a fault set is constructed and used for judging an optimal operation region of a given instability probability of the system.
According to the method, the fault set is screened by assuming the power generation output of the new energy as a mean value, so that the probability characteristic of the new energy can be really and comprehensively considered; the random response surface method is adopted to convert the voltage stability probability evaluation problem into a series of deterministic voltage stability critical point calculation problems, and then the original dual interior point algorithm is adopted to solve each voltage stability critical point problem, so that the solving efficiency is improved; the method can effectively discriminate and sort the static voltage stability of the fault scene under the influence of random factors; according to the method, the margin ordering indexes are set, the visual power system probability voltage stability region based on the fault set is constructed, and the optimal operation region of the given instability probability of the system can be accurately judged.
It should be noted that the above-mentioned embodiments illustrate rather than limit the invention, and that those skilled in the art will be able to design alternative embodiments without departing from the scope of the appended claims. In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim.
Claims (7)
1. A visualization method of a probabilistic static voltage stability domain includes,
the first step (S1), new energy power generation output is averaged, fault scenes are screened, a serious fault set is obtained, including,
a first subsection (S11) for acquiring an N-1 fault scene to be analyzed and constructing an original fault set;
a second subsection (S12) selecting the fault scene in the original fault set, correcting the network structure of the power system and establishing a voltage stabilization critical point model;
a third subsection (S13) solving the problem of voltage stability critical point by adopting an interior point algorithm to obtain the load margin of the fault scene;
a fourth subsection (S14) repeating the first subsection (S11) through the third subsection (S13) until load margins for all fault scenarios are obtained;
a fifth subsection (S15) setting a load margin threshold value, screening the fault scene and obtaining a serious fault set;
a second step (S2) of selecting any fault scene in the serious fault set, and establishing a voltage stability probability evaluation model based on the uncertainty of the power generation output of the new energy;
a third step (S3) of obtaining a cumulative probability distribution function of the load margin according to the voltage stability probability evaluation model;
a fourth step (S4) of calculating a margin ranking index under a fault scene according to the cumulative probability distribution function of the load margins;
a fifth step (S5) of repeating the second step (S2) to the fourth step (S4) until obtaining a margin ranking index for all fault scenarios, the margin ranking index being that, given a voltage instability probability, load margins under different fault scenarios are determined: lambda [ alpha ]a＝F-1(pa)0≤pa≤1，
Wherein p isaFor a given voltage instability probability, F-1(λ) is the inverse of the cumulative probability distribution function F (λ) of the system load margin, λaIs a load margin;
and a sixth step (S6) of sequencing the fault scenes according to the margin sequencing indexes and constructing a probability static voltage stability domain based on the fault set.
2. The method of claim 1, when the new energy generation includes wind farms and photovoltaic generation, the voltage stability probability evaluation model is:
wherein λ is a load margin; sBIs the set of all nodes of the system;
SGand SRRespectively a conventional generator and a reactive power supply node set;
PGithe active output of a conventional generator at node i;
QRithe reactive power output of the reactive power supply at the node i is obtained;
PWiand QWiRespectively injecting active power and reactive power of the wind power plant at the node i;
PSiand QSiRespectively the active power and the reactive power of photovoltaic power generation at a node i;
PLiand QLiRespectively the active power and the reactive power of the load at the node i;
bPiand bQiIs the increasing direction of the load at the node i;
Uiandithe voltage amplitude and the phase angle of the node i are respectively;
Yijand alphaijThe element and phase angle of the ith row and the jth column of the node admittance matrix respectively describe the parameters of the grid structure characteristics of the power system,ij＝i-j-αij；
3. The method according to claim 1, wherein the mean value of the new energy power generation output is obtained by taking historical statistical data as a statistical sample and calculating expected values of the statistical sample.
4. The method of claim 1, the new energy power generation comprising at least one of a wind farm system and a photovoltaic power generation system.
5. The method of claim 4, the new energy generation output uncertainty comprising a wind farm uncertainty, the wind farm stochastic model being as follows:
wherein, PwiThe sum of the active power of all wind turbine generators in the wind power plant at the node i is obtained;
qwi is the sum of all wind turbine generator reactive powers in the wind power plant at the node i;
NWithe number of wind generating sets in the wind power plant at the node i is shown;
θWithe power factor angle of each wind turbine generator set;
PWgithe actual output power of a single wind turbine generator is obtained;
a＝Prvin/(vin-vr) And b ═ Pr/(vr-vin) Is a constant;
vin、voutand vrRespectively the cut-in wind speed, the cut-out wind speed and the rated wind speed of the fan;
Pris the rated active output;
vithe actual wind speed of the wind power plant at the node i is obtained;
the probability density function for wind speed is:
K. and C is the shape parameter and the scale parameter of Weibull distribution respectively.
6. The method of claim 4, the new energy generation output uncertainty comprising a photovoltaic generation uncertainty, the photovoltaic generation uncertainty stochastic model being as follows:
wherein, PsiThe photovoltaic power generation active power at the node i;
Qsithe photovoltaic power generation reactive power at the node i is obtained;
θSithe power factor angle of the photovoltaic power generation system at the node i is shown;
rifor irradiating the sun with light(ii) the shot strength;
a is the total area of the solar cell matrix;
eta is the overall photoelectric conversion efficiency;
the illumination intensity probability density function is:
7. The method of claim 1, said third step (S3) comprising transforming a voltage stability probability evaluation problem into a deterministic series of voltage stability critical point calculation problems by solving said voltage stability probability evaluation model using a stochastic response surface method;
and solving the problem of each voltage stabilization critical point by adopting an original dual interior point algorithm, and constructing an accumulative probability distribution function of the load margin according to the result.
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