CN107221933B - Probabilistic load flow calculation method - Google Patents
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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Abstract
The invention discloses a probabilistic power flow calculation method, which is based on wind power fluctuation characteristics and prediction errors and mainly comprises the following steps: step A: counting the probability distribution of wind power fluctuation; and B: counting the probability distribution of the wind power prediction error; and C: establishing a joint condition prediction error probability distribution model of the predicted wind power and the actually measured wind power; step D: establishing a wind power probability distribution model; step E: calculating a semi-invariant of the node injection power of the wind power-containing power system; step F: and calculating the probability distribution of the node voltage and the branch power flow. The method overcomes the defects caused by single model and few consideration factors in the traditional method for representing the node injection power random variable based on the wind power probability distribution, and improves the accuracy of solving the semi-invariant of the node injection power of the power system.
Description
Technical Field
The invention relates to the field of operation and control of power systems, in particular to a probabilistic power flow calculation method based on wind power fluctuation characteristics and prediction errors.
Background
The wind power plant is generally positioned at the tail end of a power grid with a weak grid structure, and the output of a wind turbine generator is random and intermittent due to the natural fluctuation of wind energy, so that the voltage stability problem and the electric energy quality problem are easily caused, and the transmission power of a power grid line and the original tidal current distribution of the power grid are changed. With the rapid development of wind power generation technology, the proportion of wind power in a power system is continuously enlarged, the influence of the wind power on the power grid is more and more obvious, and the uncertainty of the power system is directly increased, which brings unprecedented challenges to the safe and stable operation of the power grid, so that the research on the probability load flow calculation for the uncertainty analysis of the power system is increasingly and widely concerned.
The probability power flow of the power system is one of important functional modules for scheduling and controlling the smart power grid, the main function of the probability power flow is to utilize a probability statistical method to process random factors in system operation, comprehensively consider the uncertainty of variables such as a network topology structure, element parameters, node loads and generator output and the like of the power system, simultaneously analyze the randomness of the wind power output caused by wind speed fluctuation and obtain the probability statistical information of system voltage and branch power flow, and the technology plays a very important role in a scheduling automation system.
At present, the research on the probability trend of a power system containing wind power at home and abroad is more and more extensive and deeper, the simplest and most direct is to assume that the wind speed obeys Weibull distribution, and in most cases, a wind power probability model is established on the basis of a wind speed-wind power curve, and the wind power output probability model is established by accumulating the output power results of fans to obtain the semi-invariant of the output power of a wind power plant. The method is simple in model, and under most conditions, wind driven generators in a region do not all have available online data, so that the feasibility of the method for obtaining the output power of the wind power plant by accumulating the output power results of the wind driven generators cannot meet the requirement. Along with the increase of the fluctuation of the wind speed and the large-scale grid connection of the wind power plant, the error of a wind speed-wind power curve is continuously increased, the precision of a wind power output probability model is also rapidly reduced, and the actual operation state of the system is difficult to accurately reflect in real time. Therefore, a technical scheme that a wind power prediction error probability model is established by using a statistical method so as to obtain wind power output probability distribution, and the method is suitable for system online evaluation and analysis and has objective and practical results is provided.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a probabilistic power flow calculation method based on wind power fluctuation characteristics and prediction errors. The method aims at the problem of uncertainty of node injection power in probabilistic power flow calculation of a wind power system based on a semi-invariant method, utilizes wind power sampling data of a wind power plant, obtains a sample set after processing and screening, adopts a statistical method to establish a wind power fluctuation model and a prediction error probability model, obtains combined condition prediction error distribution of predicted wind power and actually-measured wind power through proper correction, and further obtains a wind power probability distribution model.
The technical scheme adopted by the invention is as follows: the following factors are comprehensively considered:
1. historical wind power actual measurement data;
2. historical wind power prediction data;
3. the power system topology structure containing wind power and data information.
On the basis of the factors, the probabilistic power flow calculation method based on the wind power fluctuation characteristics and the prediction error comprises the following steps:
step A: counting the probability distribution of wind power fluctuation;
and B: counting the probability distribution of the wind power prediction error;
and C: and establishing a joint condition prediction error probability distribution model of the predicted wind power and the actually measured wind power. (ii) a
Step D: establishing a wind power probability distribution model;
step E: calculating a semi-invariant of the node injection power of the wind power-containing power system;
step F: and calculating the probability distribution of the node voltage and the branch power flow.
And step A, counting the probability distribution of wind power fluctuation according to the actually measured wind power sample set of the wind power plant.
And B, counting the probability distribution of the wind power prediction error according to the actually measured wind power sample set and the predicted wind power sample set of the wind power plant.
And step C, weighting the probabilities of the fluctuation probability distribution and the prediction error probability distribution under the same actual measurement wind power condition by adopting the correction coefficient, and establishing a joint condition prediction error probability distribution model of the predicted wind power and the actual measurement wind power.
According to the current actually measured wind power PtThe probability that the actually measured wind power is a certain value at the t +1 time period obtained by the fluctuation probability distribution of the wind power under the condition is α, and the wind power P is predicted according to the predicted wind powerpredictThe probability that the t +1 time period obtained by predicting the error probability distribution under the condition is β and the wind power actually measured is the same value, the probability that the wind power in the t +1 time period obtained by combining the prediction error probability distribution under the condition is r, and the relation between r and α and β is as follows:
r＝r1α+r2β (1)
in the formula: r is1、r2Respectively 2 correction coefficients of distribution weight, and making r to ensure that the sum of probability distribution after weighted correction is 11+r2＝1。
And D, establishing a wind power probability distribution model by combining the joint condition prediction error probability distribution model with a wind power predicted value.
The step E comprises the following steps:
e-1, extracting original point moment information of the wind power according to a wind power probability distribution model;
e-2, calculating a semi-invariant of the node injection power change caused by wind power factors according to the corresponding relation between the origin moment and the semi-invariant;
and E-3, calculating the semi-invariant of the node injection power change of the power system by combining the semi-invariant of the node injection power change caused by the wind power factor and the semi-invariant of the node injection power change caused by the non-wind power factor.
The recurrence relation of the origin moment and the semi-invariant in the step E-2 is as follows:
in the formula αrR-order origin moment of a random variable; k is a radical ofrIs an r-order semi-invariant of a random variable;
the number of combinations of j elements out of r different elements is indicated.
The step E-2 calculates the semi-invariants of the power system node injection power through the following formula:
ΔW(k)＝ΔWwind (k)+ΔWother (k)(3)
in the formula: Δ W(k)Injecting a k-order semi-invariant of the variation of the power for the node;
and
and respectively the k-order semi-invariants of the node injection power change caused by the wind power factor and other non-wind power factors.
And F, calculating the probability distribution of the node voltage and the branch flow according to the Jacobian matrix, the output random variable node voltage and the expected value of the branch flow.
Compared with the closest prior art, the technical scheme provided by the invention has the following excellent effects:
according to the method, the prediction error probability distribution with the prediction wind power and the actually measured wind power as a joint condition is utilized, the contradiction that in the traditional wind power probability distribution statistical process, the statistical samples are too few due to too short time and the result is easy to distort due to the fact that the statistical time length is increased is relieved, the defects that in the traditional method, the model used for representing the node injection power random variable based on the wind power probability distribution is single and the consideration factor is too few are overcome, and the accuracy of solving the semi-invariant of the node injection power of the power system is improved.
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The foregoing is only an overview of the technical solutions of the present invention, and in order to make the technical solutions of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and the detailed description.
Fig. 1 is a schematic flow diagram of a probabilistic power flow calculation method based on wind power fluctuation characteristics and prediction errors according to the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
And A, counting the fluctuation probability distribution of the wind power through an actually measured sample set of the wind power plant. Counting the current actually measured wind power P in a periodtAnd the next period of time to measure the wind power Pt+1Is calculated, P is establishedtUnder the condition of different Pt+1Value (statistical physical quantity Δ P ═ P)t+1-Pt) The wind power fluctuation probability distribution model.
And B, counting the probability distribution of the wind power prediction error through actual measurement and prediction sample sets of the wind power plant. Counting the measured wind power P in a period of timet+1And predicting wind power PpredictIs calculated, P is establishedpredictUnder the condition of different Pt+1Value (statistical physical quantity Δ ζ ═ P)t+1-Ppredic) The prediction error probability distribution model of (1).
And C, weighting the probabilities of the fluctuation probability distribution and the error probability distribution under the same actual measurement wind power condition by adopting a proper correction coefficient, and establishing a joint condition prediction error probability distribution model of the predicted wind power and the actual measurement wind power. Let according to PtThe probability of a certain value of the actually measured wind power in the t +1 time period obtained by the fluctuation probability distribution of the wind power under the condition is a according to the PpredictThe probability that the actually measured wind power in the t +1 time period obtained by predicting the error probability distribution under the condition is the same value is β, and the probability that the wind power in the t +1 time period obtained by combining the prediction error probability distribution under the condition is the value is βLet r be related to a, β as follows:
r＝r1α+r2β (1)
in the formula: r is1、r2Respectively 2 correction coefficients of distribution weight, and making r to ensure that the sum of probability distribution after weighted correction is 11+r2Since a and β change over time and are both statistics, the correction coefficient is also a statistic and changes over time.
The correction coefficient can be based on the current actually measured wind power PtAnd predicting wind power PpredictUnder the condition (statistical physical quantity ═ P)t-Ppredic) Is calculated, wherein:
in the formula: p(0) is 0. After weighted correction, the predicted wind power P is formedpredictAnd actually measured wind power PtDifferent P as combined conditionst+1And (4) establishing a joint condition prediction error probability distribution model of the predicted wind power and the actually measured wind power according to the probability distribution (the statistical physical quantity is delta zeta).
D, establishing a short-term wind power probability distribution model by utilizing the joint condition prediction error probability distribution model and the wind power predicted value, superposing the joint condition prediction error value on the basis of the wind power predicted value to obtain a wind power probability distribution model,
and E, calculating a semi-invariant containing the node injection power of the wind power system, solving an original point moment of the wind power injection power, and obtaining the semi-invariant of the node injection power caused by the wind power factor according to a recursion relation of the original point moment and the semi-invariant. The recurrence relation of origin moment and semi-invariant is as follows:
in the formula αrIs randomR-order origin moment of the variables; k is a radical ofrIs an r-order semi-invariant of a random variable;
the number of combinations of j elements out of r different elements is indicated.
The semi-invariants of the power system node injection power variation are then calculated by the following equation.
ΔW(k)＝ΔWwind (k)+ΔWother (k)(3)
In the formula: Δ W(k)Injecting a k-order semi-invariant of the variation of the power for the node;
and
and respectively the k-order semi-invariants of the node injection power change caused by the wind power factor and other non-wind power factors.
And F, calculating the probability distribution of the node voltage and the branch flow by using the semi-invariant and the Jacobian matrix of the node injection power and the expectation of the node voltage and the branch flow. The method comprises the steps of performing Taylor series expansion on a power equation of typical calculated power flow of the power system at a reference operating point, neglecting high-order terms for 2 times or more to obtain a linearized model of power flow calculation, then obtaining semi-invariants of node voltage and branch power flow of the power system through the calculation properties of the semi-invariants, and obtaining probability distribution of the node voltage and the branch power flow by adopting Cornish-Fisher series expansion on the basis.
It should be noted that the above-mentioned embodiments are only for illustrating the technical solutions of the present application and not for limiting the scope of protection thereof, and although the present application is described in detail with reference to the above-mentioned embodiments, those skilled in the art should understand that after reading the present application, they can make various changes, modifications or equivalents to the specific embodiments of the application, but these changes, modifications or equivalents are all within the scope of protection of the claims to be filed.
Claims (8)
1. A probabilistic power flow calculation method, characterized in that the method comprises the following steps:
step A: counting the probability distribution of wind power fluctuation;
and B: counting the probability distribution of the wind power prediction error;
and C: establishing a joint condition prediction error probability distribution model of the predicted wind power and the actually measured wind power;
step D: establishing a wind power probability distribution model;
step E: calculating a semi-invariant of the node injection power of the wind power-containing power system;
step F: calculating the probability distribution of node voltage and branch load flow;
weighting the probabilities of the fluctuation probability distribution and the prediction error probability distribution under the same actual measurement wind power condition by adopting a correction coefficient, and establishing a joint condition prediction error probability distribution model of the predicted wind power and the actual measurement wind power;
will be based on the current measured wind power PtThe probability that the actually measured wind power is a certain value at the t +1 time period obtained by the wind power fluctuation probability distribution under the condition is α, and the wind power P is predicted according to the predicted wind powerpredictThe probability that the t +1 time period obtained by predicting the error probability distribution under the condition is the same as the actually measured wind power is β, and the probability that the wind power at the t +1 time period obtained by combining the prediction error probability distribution under the condition is the value is shown as the following formula:
r＝r1α+r2β (1)
in the formula: r is1、r2Respectively 2 correction coefficients of distribution weight, and making r to ensure that the sum of probability distribution after weighted correction is 11+r2＝1。
2. The calculation method according to claim 1, wherein the step A is to count the probability distribution of wind power fluctuation according to a wind power sample set measured in a wind farm.
3. The calculation method according to claim 1, wherein step B is to count the probability distribution of the wind power prediction error according to the measured wind power sample set and the predicted wind power sample set of the wind farm.
4. The calculation method according to claim 1, wherein step D establishes a wind power probability distribution model by combining the joint condition prediction error probability distribution model with a wind power predicted value.
5. The computing method according to claim 1, wherein the step E comprises: e-1, extracting original point moment information of the wind power according to a wind power probability distribution model;
e-2, calculating a semi-invariant of the node injection power change caused by wind power factors according to the recurrence relation of the origin moment and the semi-invariant;
and E-3, calculating the semi-invariant of the node injection power of the power system by combining the semi-invariant of the node injection power change caused by the wind power factor and the semi-invariant of the node injection power change caused by the non-wind power factor.
6. The calculation method according to claim 5, wherein the recursion relationship between the origin moment and the semi-invariant in step E-2 is represented by the following equation:
in the formula αrR-order origin moment of a random variable; k is a radical ofrIs an r-order semi-invariant of a random variable;
the number of combinations of j elements out of r different elements is indicated.
7. The method of claim 5, wherein step E-2 calculates the semi-invariance of power system node injected power using the equation:
ΔW(k)＝ΔWwind (k)+ΔWother (k)(3)
in the formula: Δ W(k)Injecting a k-order semi-invariant of the variation of the power for the node;
and
and respectively the k-order semi-invariants of the node injection power change caused by the wind power factor and other non-wind power factors.
8. The method of claim 1, wherein step F calculates the probability distribution of the node voltages and the branch flows based on the jacobian matrix and the expected values of the output random variable node voltages and the branch flows.
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| CN109117951B (en) * | 2018-01-15 | 2021-11-16 | 重庆大学 | BP neural network-based probability load flow online calculation method |
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| CN111740415B (en) * | 2020-07-03 | 2022-02-11 | 西安交通大学 | Power system steady-state power flow risk identification and prevention method, storage medium and equipment |
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