CN105048451B - A kind of Interval Power Flow computational methods based on generation of electricity by new energy amount interval prediction - Google Patents
A kind of Interval Power Flow computational methods based on generation of electricity by new energy amount interval prediction Download PDFInfo
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Abstract
The invention discloses a kind of Interval Power Flow computational methods based on generation of electricity by new energy amount interval prediction, comprise the following steps (1) acquisition parameter data generated energy historical data；(2) two type fuzzy logic system of section is constructed；(3) initial parameter is input in system, and output obtains section two patterns paste prediction sets；(4) Interval Power Flow computation model is built；(5) will gather as the first iteration section of Interval Power Flow computation model, Krawczyk Moore operators are calculated, and sought common ground with Krawczyk Moore operators and initial section, obtain new section and as the initial section of second of iteration, judge whether the interval width meets the condition of convergence, the output interval if meeting, if being unsatisfactory for return to step (4) carries out next iteration.The present invention avoids artificially providing not restraining for the interval iteration caused by initial section, and convergence is too fast or excessively slow problem, so as to improve the accuracy of calculating.
Description
Technical Field
The invention relates to an interval power flow calculation method based on new energy power generation amount interval prediction, and belongs to the field of new energy power generation.
Background
With the gradual exhaustion of fossil energy, the important influence on environmental pollution and climate deterioration, and the development of novel power generation technologies such as solar energy, wind power, photovoltaic and other renewable energy sources, renewable new energy power generation becomes an effective way for meeting the load increase demand, reducing environmental pollution, and improving the comprehensive utilization efficiency of energy and power supply reliability, and is widely applied to power grids. The renewable energy power generation mainly utilizes solar energy, biomass energy, wind energy, water energy, wave energy and the like, is influenced by factors such as geographical conditions, weather conditions, external environments and the like, has intermittent and random output of the generated energy of the renewable power sources, is difficult to obtain an accurate output result, and can obtain a generated energy prediction interval through fuzzy prediction. Therefore, the conventional power flow calculation becomes a flow calculation including a section amount, that is, a section flow calculation.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a method for calculating the interval power flow based on the interval prediction of the new energy power generation amount, which obtains an interval two-type fuzzy prediction set of the new energy power generation amount by utilizing the capability of interval two-type fuzzy logic for processing uncertainty problems, wherein the interval two-type fuzzy prediction set defines the fluctuation interval range of the power generation amount, and the interval can be an initial iteration interval in interval power flow calculation, so that the problems of interval iteration non-convergence, too fast convergence, too slow convergence and the like caused by artificially specifying the initial interval are avoided, and the calculation accuracy is improved.
In order to achieve the purpose, the invention is realized by the following technical scheme:
the invention discloses an interval power flow calculation method based on new energy power generation amount interval prediction, which comprises the following steps of: (1) collecting parameter data (taking a photovoltaic power generation system as an example, the parameter data are illumination intensity, ambient temperature and humidity) and historical data of distributed power generation amount (taking the photovoltaic power generation system as an example, the historical data are historical illumination intensity, historical ambient temperature, historical humidity and historical photovoltaic power generation amount); (2) taking the parameter data in the step (1) as input, taking the distributed power generation amount historical data in the step (1) as output, constructing an interval type two fuzzy logic system, and setting initial parameters of the interval type two fuzzy logic system (taking a photovoltaic power generation system as an example, the initial parameters comprise illumination intensity, ambient temperature and humidity); (3) training the interval type-two fuzzy logic system, namely inputting the acquired real-time parameter data (taking a photovoltaic power generation system as an example, real-time illumination intensity, real-time environment temperature and real-time humidity) serving as initial parameters (initial illumination intensity, initial environment temperature and initial humidity) into the constructed interval type-two fuzzy logic system, and outputting to obtain a distributed power supply generated energy interval type-two fuzzy prediction set; (4) constructing an interval power flow calculation model; (5) and (3) taking the two-type fuzzy prediction set of the power generation interval of the distributed power supply obtained in the step (3) as an initial iteration interval of an interval power flow calculation model to obtain an interval extension of a Jacobian matrix, calculating according to the definition of a Krawczyk-Moore operator to obtain a Krawczyk-Moore operator, solving an intersection of the Krawczyk-Moore operator and the initial iteration interval to obtain a new interval which is taken as an initial interval of second iteration, judging whether the interval width meets a convergence condition or not, outputting the interval if the interval width meets the convergence condition, and returning to the step (4) for next iteration if the interval width does not meet the convergence condition.
In the step (2), the construction method of the interval type two fuzzy logic system is as follows: (2-1) designing a fuzzifier: the fuzzifier obtains a fuzzy interval through a main membership function, the main membership function consists of an upper membership function and a lower membership function, the main membership function of the two-type fuzzy prediction set of the distributed power supply generating capacity interval selects a Gaussian function with uncertain mean square deviation, the upper membership function and the lower membership function are shown as the following formula, a model has three inputs and one output,
wherein,it is the exact value that is input,is the mean square error variation range, K1, 2 … p is the input dimension, xkE is the system input;
(2-2) constructing a rule base: the front and rear parts of the rule select a two-type fuzzy prediction set of a distributed power generation capacity interval, the main membership function is a Gaussian function with uncertain mean value, and the form of the rule is as follows:
whereinIs a rule precursor set, Y e Y is the rule output,is the postamble set, l is 1,2 … M, M is the total number of rules;
(2-3) constructing an inference machine: the reasoning process is as follows, and the upper and lower membership functions of the two-type fuzzy prediction set of the power generation interval of the distributed power supply participate in calculation
Wherein: is t-norm, takes minimum operator,are respectively the upper part and the lower part of the back piece assembly,The function of the degree of membership of the next,respectively an upper membership function and a lower membership function of the activation set,
(2-4) obtaining an inference model of the multi-input single-output multi-strip fuzzy rule system from the steps (2-2) and (2-3) as follows:
taking η, u and v as parameter data of the distributed power generation system, taking y as predicted power generation amount,a set of data of the parameters is set,to be the set of the power generation amounts,are two-type fuzzy prediction sets of the power generation interval of the distributed power supply, wherein, as a center set reduction method is adopted,selected as the set of intervals represented by the centroid, thenThe expression (c) can be written as one of the following interval numbers:
(2-5) designing a downgrader: by adopting a center set model reduction method, the set of regular generated electricity is replaced by a center of mass, then the weighted average value of the center of mass is calculated, and finally a center of mass interval is obtained, wherein the specific expression is as follows:
in the formula:respectively an upper boundary and a lower boundary of the centroid of each regular generating set,upper and lower bounds of the activation set, respectively, L, R is a threshold.
In the step (4), the construction method of the interval power flow calculation model comprises the following steps:
for the interval extension of the jacobian matrix,representing the form of the interval of the phase angle of the voltage,the interval form representing the magnitude of the voltage,represents the upper bound of the lower bound of the phase angle of the voltage,is the lower and upper bounds of the voltage amplitude,is an interval form of Jacobian matrix elements and represents the influence of voltage phase angles on the success,is an interval form of Jacobian matrix elements, represents the active influence of voltage amplitude values,is an interval form of Jacobian matrix elements and represents the influence of voltage phase angles on reactive power,is an interval form of Jacobian matrix elements and represents the influence of voltage amplitude on reactive powerRespectively, the lower and upper bounds of the interval form of the four Jacobian matrix elements. (ii) a
To be provided withThe analysis is carried out by taking the sub-array as an example,
wherein,representing the amount of active power offset at node i,representing the form of the voltage phase angle interval at node i,representing the voltage amplitude interval form at the node i,Representing the voltage amplitude interval form, G, at node jijRepresenting the real part of the impedance between nodes i, j,interval form representing phase angle difference between node i and node j, BijThe imaginary part of the impedance between nodes i, j,representing the voltage phase angle interval form at node j.
It can be seen thatAndwith strong correlation, independent consideration increases the range of the interval, so:
in the step (5), the calculation method of the once iteration Krawczyk-Moore operator is as follows:
mixing XcosAs an initial interval X0
Wherein
I is a unit array, and I is a unit array,is a range of independent variables, m is a function of the midpoint of the range number, PiIs the active power at node i, QiIs the reactive power at node i.
In the step (5), the Krawcyzk-Moore operator and the initial interval x are utilized0Find the intersection to get the new interval x1：
Where k represents the number of iterations, xk+1,xkRepresent the interval of the independent variable of the (K + 1) th and (K) th times, KkRepresenting the K-M operator for the K-th time.
In the step (5), the convergence condition isAnd is
Where, ω represents the convergence coefficient,the upper and lower bounds of the interval for the (k + 1) th and k-th independent variables are represented, respectively.
The invention has the beneficial effects that: compared with the existing load flow calculation considering uncertainty, the method uses the interval quantity to describe the uncertainty more suitable for the actual situation, and uses the interval two-type fuzzy logic system to obtain the initial iteration interval, thereby avoiding a series of problems of iteration convergence caused by setting the initial interval according to experience, saving the iteration time and being more suitable for large-scale systems; the Krawczyk-Moore operator is suitable, has global convergence, gives an interval solution and considers estimation errors; the combination of the interval type fuzzy logic system and the interval iteration method not only can successfully obtain a load flow calculation solution considering uncertainty, but also solves some defects of the interval iteration method, and has strong practical engineering use significance.
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FIG. 1 is a flowchart of the interval power flow calculation method based on the interval prediction of new energy power generation amount according to the present invention;
FIG. 2 is a diagram of a power generation prediction structure based on a block two-type fuzzy logic system.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention is further described with the specific embodiments.
Referring to fig. 1, the interval power flow calculation method based on new energy power generation interval prediction of the invention includes the following steps:
(1) acquiring parameter data and distributed generating capacity historical data of a distributed generating system by adopting a multi-input single-output mode;
(2) taking parameter data as input and generating capacity as output, constructing an interval two-type fuzzy logic system, and setting initial parameters of the system;
(3) training an interval type II fuzzy logic system, inputting the acquired real-time parameter data serving as initial parameters into the constructed interval type II fuzzy logic system, and outputting to obtain a distributed power supply generated energy interval type II fuzzy prediction set;
(4) constructing an interval power flow calculation model;
(5) and (4) taking the two-type fuzzy prediction set of the distributed power supply generating capacity interval obtained in the step (3) as an initial iteration interval of an interval power flow calculation model to obtain an interval extension of a Jacobian matrix, calculating to obtain a Krawczyk-Moore operator, solving an intersection of the Krawczyk-Moore operator and the initial interval to obtain a new interval, taking the new interval as an initial interval of second iteration, judging whether the interval width meets a convergence condition, outputting the interval if the interval width meets the convergence condition, and returning to the step (4) to perform next iteration if the interval width does not meet the convergence condition.
Referring to fig. 2, the construction method of the interval type two fuzzy logic system is as follows:
designing a fuzzifier: the fuzzifier converts the input accurate value into an interval type two fuzzy prediction set so as to fully process the strong uncertainty of the power load. The main membership function of the interval type two fuzzy prediction set selects a Gaussian function with uncertain mean square error, and the upper membership function and the lower membership function are shown as the following formulas. The model has 3 inputs and 1 output.
Wherein,it is the exact value that is input,is the mean square error range, K1, and 2 … p is the input dimension. B, constructing a rule base: the front and back parts of the rule select interval type two fuzzy prediction sets, the main membership function is a Gaussian function with uncertain mean value, and the form of the rule is as follows:
wherein xkE.x is the system input,is that the rule precursor set Y e Y is the rule output,is a set of back-parts. l is 1,2 … M, M is the total number of rules.
C, constructing an inference machine: for the two type of interval Mamdani fuzzy model, the reasoning process is as follows, and the upper and lower membership functions of the set are involved in the calculation.
Wherein: is t-norm, takes minimum operator,respectively an upper membership function and a lower membership function of the back part set,respectively, an upper membership function and a lower membership function of the activation set.
The reasoning model of the multi-input single-output multi-strip fuzzy rule system obtained by the processes (2) and (3) is as follows:
taking x, u and v as parameter data, taking y as predicted power generation amount,a set of data of the parameters is set,is a set of generated power.All are interval type two fuzzy prediction sets, in which the center set reduction method is adoptedSelected as the set of intervals represented by the centroid, thenThe expression of (a) is:
e, designing a falling device: and (3) replacing each regular power generation amount set by a centroid by adopting a center set reduction method, and then solving a weighted average value of the centroids to finally obtain a centroid interval. The calculation is simplified by Karnik and Mendel, and the specific expression is as follows:
in the formula:respectively an upper boundary and a lower boundary of the centroid of each regular generating set,upper and lower bounds of the activation set, respectively, L, R is a threshold.
In the step (4), the construction method of the interval load flow calculation model comprises the following steps:
interval expansion of a Jacobian matrix;
to be provided withThe analysis is illustrated by taking the subarrays as an example.
It can be seen thatAndwith strong correlation, independent consideration increases the range of the interval, so:
in the step (5), the calculation method of the once iteration Krawczyk-Moore operator is as follows:
mixing XcosAs an initial interval x0
Wherein
And I is a unit array.
In the step (5), the Krawcyzk-Moore operator and the initial interval x are utilized0And solving intersection to obtain a new interval X:
in the step (5), the convergence condition isAnd is
In this embodiment, a gaussian function with uncertain mean square error is used as its upper and lower membership functions for the parameter data, and the input accurate value is blurred into a single-valued two-type blur set. The rule of the interval type two fuzzy logic system adopts an IF-THEN form and a Mamdani inference model. The activation set is generated by input and rule front piece, and then the activation set and the back piece set calculate and output, and the upper and lower membership function of each set participates in calculation. The reasoning process comprises the steps of calculating the adaptation degree, calculating the excitation intensity, calculating an effective membership function of the back part and calculating a total output membership function. And (3) replacing each regular power generation amount set by a centroid by adopting a center set reduction method, and then solving a weighted average value of the centroids to finally obtain a centroid interval. The interval quantity is used for describing uncertainty in the power flow calculation, the uncertainty is simple and practical, and the centroid interval obtained in the above can be used as an initial interval of the interval power flow calculation. And (4) solving the interval expansion of each element of the Jacobian matrix in the load flow calculation according to a calculation formula of a Newton method and a network topological structure. And obtaining a Krawczyk-Moore operator according to an interval iteration method and the Jacobian matrix interval expansion in the above and the initial interval in the above, then solving the intersection of the K-M operator and the initial interval, taking the intersection as the initial interval of the second iteration, and judging whether the convergence condition is met.
Because the generated energy of the distributed generator is difficult to establish an accurate mathematical model, the accurate prediction of the generated energy has great difficulty. The invention adopts the interval to describe the uncertain quantity, is simple and direct, better accords with the actual situation than the probability load flow, and has smaller calculated quantity. The interval two-type fuzzy logic system does not need to establish an accurate mathematical model, describes uncertainty information logic by utilizing a rule base in a language form, constructs an inference machine according to membership function fuzzy degree, and is suitable for the characteristic of uncertainty of the generated energy of a distributed power supply. The method adopts an interval iteration method based on a Newton method, has better robustness and can be globally converged; and a secondary interval type two fuzzy prediction set is used as an initial value, so that the bisection problem caused by the initial value problem is avoided, and the convergence process is simplified. The interval power flow calculation method based on the interval two-type fuzzy logic system can perform accurate interval power flow calculation, solves the problems of too fast convergence, too slow convergence and no convergence of an interval iteration method, and has high practical value.
The foregoing shows and describes the general principles and broad features of the present invention and advantages thereof. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (6)
1. An interval power flow calculation method based on new energy power generation amount interval prediction is characterized by comprising the following steps:
(1) collecting parameter data of a distributed power generation system and historical data of distributed power generation amount;
(2) taking the parameter data in the step (1) as input, taking the distributed power generation amount historical data in the step (1) as output, constructing a zone type two fuzzy logic system, and setting initial parameters of the zone type two fuzzy logic system;
(3) training the interval type-II fuzzy logic system, namely inputting the acquired real-time parameter data serving as initial parameters into the constructed interval type-II fuzzy logic system, and outputting to obtain a distributed power supply generated energy interval type-II fuzzy prediction set;
(4) constructing an interval power flow calculation model;
(5) and (3) taking the two-type fuzzy prediction set of the power generation interval of the distributed power supply obtained in the step (3) as an initial iteration interval of an interval power flow calculation model to obtain an interval extension of a Jacobian matrix, calculating according to the definition of a Krawczyk-Moore operator to obtain a Krawczyk-Moore operator, solving an intersection of the Krawczyk-Moore operator and the initial iteration interval to obtain a new interval which is taken as an initial interval of second iteration, judging whether the interval width meets a convergence condition or not, outputting the interval if the interval width meets the convergence condition, and returning to the step (4) for next iteration if the interval width does not meet the convergence condition.
2. The interval power flow calculation method based on new energy power generation amount interval prediction according to claim 1, wherein in the step (2), the interval type two fuzzy logic system is constructed by the following method:
(2-1) designing a fuzzifier: the fuzzifier obtains a fuzzy interval through a main membership function, the main membership function consists of an upper membership function and a lower membership function, the main membership function of the two-type fuzzy prediction set of the distributed power supply generating capacity interval selects a Gaussian function with uncertain mean square deviation, the upper membership function and the lower membership function are shown as the following formula, a model has three inputs and one output,
<mrow> <msub> <mover> <mi>u</mi> <mo>&OverBar;</mo> </mover> <msub> <mi>x</mi> <mi>k</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mi>exp</mi> <mo>&lsqb;</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>(</mo> <mfrac> <mrow> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>-</mo> <msubsup> <mi>x</mi> <mi>k</mi> <mo>*</mo> </msubsup> </mrow> <msub> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mi>k</mi> </msub> </mfrac> <mo>)</mo> <mo>^</mo> <mn>2</mn> <mo>&rsqb;</mo> </mrow>
<mrow> <msub> <munder> <mi>u</mi> <mo>&OverBar;</mo> </munder> <msub> <mi>x</mi> <mi>k</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mi>exp</mi> <mo>&lsqb;</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>-</mo> <msubsup> <mi>x</mi> <mi>k</mi> <mo>*</mo> </msubsup> </mrow> <msub> <munder> <mi>&sigma;</mi> <mo>&OverBar;</mo> </munder> <mi>k</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mo>^</mo> <mn>2</mn> <mo>&rsqb;</mo> </mrow>
wherein,it is the exact value that is input,is the mean square error variation range, K1, 2kE is the system input;
(2-2) constructing a rule base: the front and rear parts of the rule select a two-type fuzzy prediction set of a distributed power generation capacity interval, the main membership function is a Gaussian function with uncertain mean value, and the form of the rule is as follows:
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>I</mi> <mi>F</mi> </mrow> </mtd> <mtd> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mi>i</mi> <mi>s</mi> <msubsup> <mover> <mi>F</mi> <mo>~</mo> </mover> <mn>1</mn> <mi>l</mi> </msubsup> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo>...</mo> <mo>...</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mi>i</mi> <mi>s</mi> <msubsup> <mover> <mi>F</mi> <mo>~</mo> </mover> <mi>k</mi> <mi>l</mi> </msubsup> <mo>...</mo> <mo>...</mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mi> </mi> <msub> <mi>x</mi> <mi>p</mi> </msub> <mi>i</mi> <mi>s</mi> <msubsup> <mover> <mi>F</mi> <mo>~</mo> </mover> <mi>p</mi> <mi>l</mi> </msubsup> <mo>,</mo> <mi>t</mi> <mi>h</mi> <mi>e</mi> <mi>n</mi> <mi> </mi> <mi>y</mi> <mi> </mi> <mi>i</mi> <mi>s</mi> <msup> <mover> <mi>G</mi> <mo>~</mo> </mover> <mi>l</mi> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced>
whereinIs a rule precursor set, Y e Y is the rule output,is a back-piece set, l 1,2.. M, M being the total number of rules;
(2-3) constructing an inference machine: the reasoning process is as follows, and the upper and lower membership functions of the two-type fuzzy prediction set of the power generation interval of the distributed power supply participate in calculation
<mrow> <msub> <mi>u</mi> <msup> <mover> <mi>G</mi> <mo>~</mo> </mover> <mi>l</mi> </msup> </msub> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mo>&Integral;</mo> <mrow> <msup> <mi>b</mi> <mi>l</mi> </msup> <mo>&Element;</mo> <mo>&lsqb;</mo> <msup> <munder> <mi>f</mi> <mo>&OverBar;</mo> </munder> <mi>l</mi> </msup> <mo>*</mo> <msub> <munder> <mi>u</mi> <mo>&OverBar;</mo> </munder> <msup> <mover> <mi>G</mi> <mo>~</mo> </mover> <mrow> <mi>l</mi> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> </mrow> </msup> </msub> <mo>,</mo> <msup> <mover> <mi>f</mi> <mo>&OverBar;</mo> </mover> <mi>l</mi> </msup> <mo>*</mo> <msub> <mover> <mi>u</mi> <mo>&OverBar;</mo> </mover> <msup> <mover> <mi>G</mi> <mo>~</mo> </mover> <mrow> <mi>l</mi> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> </mrow> </msup> </msub> <mo>&rsqb;</mo> </mrow> </msub> <mfrac> <mn>1</mn> <msup> <mi>b</mi> <mi>l</mi> </msup> </mfrac> <mi>y</mi> <mo>&Element;</mo> <mi>Y</mi> </mrow>
Wherein: is t-norm, takes minimum operator,respectively an upper membership function and a lower membership function of the back part set, f lrespectively an upper membership function and a lower membership function of the activation set,
(2-4) obtaining an inference model of the multi-input single-output multi-strip fuzzy rule system from the steps (2-2) and (2-3) as follows:
taking η, u and v as parameter data of the distributed power generation system, taking y as predicted power generation amount,a set of data of the parameters is set,to be the set of the power generation amounts,are two-type fuzzy prediction sets of the power generation interval of the distributed power supply, wherein, as a center set reduction method is adopted,selected as the set of intervals represented by the centroid, thenThe expression (c) can be written as one of the following interval numbers:
<mrow> <msup> <mi>y</mi> <mi>l</mi> </msup> <mo>=</mo> <mo>&lsqb;</mo> <msup> <munder> <mi>y</mi> <mo>&OverBar;</mo> </munder> <mi>l</mi> </msup> <mo>,</mo> <msup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>l</mi> </msup> <mo>&rsqb;</mo> </mrow>
(2-5) designing a downgrader: by adopting a center set model reduction method, the set of regular generated electricity is replaced by a center of mass, then the weighted average value of the center of mass is calculated, and finally a center of mass interval is obtained, wherein the specific expression is as follows:
<mrow> <msub> <mi>X</mi> <mi>cos</mi> </msub> <mo>=</mo> <mrow> <mo>&lsqb;</mo> <mrow> <munder> <mi>y</mi> <mo>&OverBar;</mo> </munder> <mo>,</mo> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> </mrow> <mo>&rsqb;</mo> </mrow> <mo>=</mo> <mrow> <mo>&lsqb;</mo> <mrow> <mfrac> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>l</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>L</mi> </munderover> <msup> <mover> <mi>f</mi> <mo>&OverBar;</mo> </mover> <mi>l</mi> </msup> <munder> <msup> <mi>y</mi> <mi>l</mi> </msup> <mo>&OverBar;</mo> </munder> <mo>+</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>l</mi> <mo>=</mo> <mi>L</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <munder> <msup> <mi>f</mi> <mi>l</mi> </msup> <mo>&OverBar;</mo> </munder> <munder> <msup> <mi>y</mi> <mi>l</mi> </msup> <mo>&OverBar;</mo> </munder> </mrow> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>l</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>L</mi> </munderover> <msup> <mover> <mi>f</mi> <mo>&OverBar;</mo> </mover> <mi>l</mi> </msup> <mo>+</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>l</mi> <mo>=</mo> <mi>L</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <munder> <msup> <mi>f</mi> <mi>l</mi> </msup> <mo>&OverBar;</mo> </munder> </mrow> </mfrac> <mo>,</mo> <mfrac> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>l</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>R</mi> </munderover> <munder> <msup> <mi>f</mi> <mi>l</mi> </msup> <mo>&OverBar;</mo> </munder> <msup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>l</mi> </msup> <mo>+</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>l</mi> <mo>=</mo> <mi>L</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msup> <mover> <mi>f</mi> <mo>&OverBar;</mo> </mover> <mi>l</mi> </msup> <msup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>l</mi> </msup> </mrow> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>l</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>R</mi> </munderover> <munder> <msup> <mi>f</mi> <mi>l</mi> </msup> <mo>&OverBar;</mo> </munder> <mo>+</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>l</mi> <mo>=</mo> <mi>R</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msup> <mover> <mi>f</mi> <mo>&OverBar;</mo> </mover> <mi>l</mi> </msup> </mrow> </mfrac> </mrow> <mo>&rsqb;</mo> </mrow> </mrow>
in the formula: ly、respectively an upper boundary and a lower boundary of the centroid of each regular generating set, lf、upper and lower bounds of the activation set, respectively, M, L, R is a threshold.
3. The interval power flow calculation method based on the interval prediction of new energy power generation amount according to claim 2, wherein in the step (4), the interval power flow calculation model is constructed by the following method:
<mrow> <mover> <mi>x</mi> <mo>~</mo> </mover> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mover> <mi>&theta;</mi> <mo>~</mo> </mover> </mtd> </mtr> <mtr> <mtd> <mover> <mi>U</mi> <mo>~</mo> </mover> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>&lsqb;</mo> <mrow> <munder> <mi>&theta;</mi> <mo>&OverBar;</mo> </munder> <mo>,</mo> <mover> <mi>&theta;</mi> <mo>&OverBar;</mo> </mover> </mrow> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&lsqb;</mo> <mrow> <munder> <mi>U</mi> <mo>&OverBar;</mo> </munder> <mo>,</mo> <mover> <mi>U</mi> <mo>&OverBar;</mo> </mover> </mrow> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
<mrow> <msup> <mi>F</mi> <mo>&prime;</mo> </msup> <mrow> <mo>(</mo> <mover> <mi>x</mi> <mo>~</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mover> <mi>H</mi> <mo>~</mo> </mover> </mtd> <mtd> <mover> <mi>N</mi> <mo>~</mo> </mover> </mtd> </mtr> <mtr> <mtd> <mover> <mi>K</mi> <mo>~</mo> </mover> </mtd> <mtd> <mover> <mi>L</mi> <mo>~</mo> </mover> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mo>-</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>&lsqb;</mo> <mrow> <munder> <mi>H</mi> <mo>&OverBar;</mo> </munder> <mo>,</mo> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> </mrow> <mo>&rsqb;</mo> </mrow> </mtd> <mtd> <mrow> <mo>&lsqb;</mo> <mrow> <munder> <mi>N</mi> <mo>&OverBar;</mo> </munder> <mo>,</mo> <mover> <mi>N</mi> <mo>&OverBar;</mo> </mover> </mrow> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&lsqb;</mo> <mrow> <munder> <mi>K</mi> <mo>&OverBar;</mo> </munder> <mo>,</mo> <mover> <mi>K</mi> <mo>&OverBar;</mo> </mover> </mrow> <mo>&rsqb;</mo> </mrow> </mtd> <mtd> <mrow> <mo>&lsqb;</mo> <mrow> <munder> <mi>L</mi> <mo>&OverBar;</mo> </munder> <mo>,</mo> <mover> <mi>L</mi> <mo>&OverBar;</mo> </mover> </mrow> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
for the interval extension of the jacobian matrix,representing the form of the interval of the phase angle of the voltage,the interval form representing the magnitude of the voltage,θ,represents the upper bound of the lower bound of the phase angle of the voltage,U,is the lower and upper bounds of the voltage amplitude,is an interval form of Jacobian matrix elements and represents the influence of voltage phase angles on the success,is an interval form of Jacobian matrix elements, represents the active influence of voltage amplitude values,is an interval form of Jacobian matrix elements and represents the influence of voltage phase angles on reactive power,is an interval form of Jacobian matrix elements and represents the influence of voltage amplitude on reactive powerH, K, N, L,Are respectively the fourA lower bound and an upper bound of the interval form of the Jacobian matrix elements;
to be provided withThe analysis is carried out by taking the sub-array as an example,
<mrow> <msub> <mover> <mi>H</mi> <mo>~</mo> </mover> <mrow> <mi>i</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mo>&part;</mo> <mi>&Delta;</mi> <msub> <mover> <mi>P</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> </mrow> <mrow> <mo>&part;</mo> <msub> <mover> <mi>&theta;</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> </mrow> </mfrac> <mo>=</mo> <msub> <mover> <mi>U</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>&NotEqual;</mo> <mi>i</mi> </mrow> <mi>n</mi> </munderover> <msub> <mover> <mi>U</mi> <mo>~</mo> </mover> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>G</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mi>sin</mi> <msub> <mover> <mi>&theta;</mi> <mo>~</mo> </mover> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mi>cos</mi> <msub> <mover> <mi>&theta;</mi> <mo>~</mo> </mover> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mover> <mi>H</mi> <mo>~</mo> </mover> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mo>&part;</mo> <mi>&Delta;</mi> <msub> <mover> <mi>P</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> </mrow> <mrow> <mo>&part;</mo> <msub> <mover> <mi>&theta;</mi> <mo>~</mo> </mover> <mi>j</mi> </msub> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <msub> <mover> <mi>U</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <msub> <mover> <mi>U</mi> <mo>~</mo> </mover> <mi>j</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>G</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mi>sin</mi> <msub> <mover> <mi>&theta;</mi> <mo>~</mo> </mover> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <msub> <mover> <mi>&theta;</mi> <mo>~</mo> </mover> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow>
wherein,representing the amount of active power offset at node i,representing the form of the voltage phase angle interval at node i,representing the voltage amplitude interval form at the node i,Representing the voltage amplitude interval form, G, at node jijRepresenting the real part of the impedance between nodes i, j,interval form representing phase angle difference between node i and node j, BijThe imaginary part of the impedance between nodes i, j,representing the voltage phase angle interval form at the node j;
it can be seen thatAndwith strong correlation, independent consideration increases the range of the interval, so:
<mrow> <msub> <mover> <mi>H</mi> <mo>~</mo> </mover> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mo>&part;</mo> <mi>&Delta;</mi> <msub> <mover> <mi>P</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> </mrow> <mrow> <mo>&part;</mo> <msub> <mover> <mi>&theta;</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <msub> <mover> <mi>U</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <msub> <mover> <mi>U</mi> <mo>~</mo> </mover> <mi>j</mi> </msub> <msqrt> <mrow> <msup> <msub> <mi>G</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <msup> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mn>2</mn> </msup> </mrow> </msqrt> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&theta;</mi> <mo>~</mo> </mover> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&delta;</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
<mrow> <msub> <mover> <mi>H</mi> <mo>~</mo> </mover> <mrow> <mi>i</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mover> <mi>U</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>&NotEqual;</mo> <mi>i</mi> </mrow> <mi>n</mi> </munderover> <msub> <mover> <mi>U</mi> <mo>~</mo> </mover> <mi>j</mi> </msub> <msqrt> <mrow> <msup> <msub> <mi>G</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <msup> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mn>2</mn> </msup> </mrow> </msqrt> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&theta;</mi> <mo>~</mo> </mover> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&delta;</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
δij＝arctan(-Bij/Gij)。
4. the interval power flow calculation method based on the new energy power generation amount interval prediction as claimed in claim 3, wherein in the step (5), the calculation method of one iteration of Krawczyk-Moore operator is as follows:
mixing XcosAs an initial interval X0
<mrow> <mi>K</mi> <mo>=</mo> <msup> <mi>y</mi> <mi>k</mi> </msup> <mo>-</mo> <msup> <mi>Y</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msup> <mi>f</mi> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mi>k</mi> </msup> <mo>)</mo> </mrow> <mo>-</mo> <mo>&lsqb;</mo> <mi>I</mi> <mo>-</mo> <msup> <mi>Y</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msup> <msup> <mi>F</mi> <mo>&prime;</mo> </msup> <mrow> <mo>(</mo> <mover> <mi>x</mi> <mo>~</mo> </mover> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mrow> <mo>(</mo> <mover> <mi>x</mi> <mo>~</mo> </mover> <mo>-</mo> <msup> <mi>y</mi> <mi>k</mi> </msup> <mo>)</mo> </mrow> </mrow>
Wherein
<mrow> <mi>f</mi> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mi>k</mi> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>m</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>U</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mi>m</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>U</mi> <mo>~</mo> </mover> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>(</mo> <msub> <mi>G</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mrow> <mi>m</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&theta;</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>m</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&theta;</mi> <mo>~</mo> </mover> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <mrow> <mi>m</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&theta;</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>m</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&theta;</mi> <mo>~</mo> </mover> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Q</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>m</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>U</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mi>m</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>U</mi> <mo>~</mo> </mover> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>(</mo> <msub> <mi>G</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <mrow> <mi>m</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&theta;</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>m</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&theta;</mi> <mo>~</mo> </mover> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mrow> <mi>m</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&theta;</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>m</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&theta;</mi> <mo>~</mo> </mover> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow>
<mrow> <msup> <mi>Y</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msup> <mo>=</mo> <msup> <mrow> <mo>&lsqb;</mo> <mi>m</mi> <mrow> <mo>(</mo> <msup> <mi>F</mi> <mo>&prime;</mo> </msup> <mo>(</mo> <mover> <mi>x</mi> <mo>~</mo> </mover> <mo>)</mo> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> <mo>&prime;</mo> </msup> <mo>,</mo> </mrow>
I is a unit array, and I is a unit array,is a range of independent variables, m is a function of the midpoint of the range number, PiIs the active power at node i, QiIs the reactive power at node i.
5. The interval power flow calculation method based on new energy power generation amount interval prediction as claimed in claim 4, wherein in the step (5), the Krawcyzk-Moore operator and the initial interval x are utilized0Find the intersection to get the new interval x1：
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mover> <mi>x</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> <mo>=</mo> <msup> <mover> <mi>x</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msup> <mo>&cap;</mo> <msup> <mi>K</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>
Where k represents the number of iterations,represent the interval of the independent variable of the (K + 1) th and (K) th times, K(k)Represents the k-th Krawcyzk-Moore operator.
6. The method for calculating the section power flow based on the section prediction of the new energy power generation amount according to claim 5, wherein in the step (5), the convergence condition is zerox k+1-x k< omega and
where, ω represents the convergence coefficient, x k+1,x kthe upper and lower bounds of the interval for the (k + 1) th and k-th independent variables are represented, respectively.
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