CN104504263B - A kind of photovoltaic plant harmonics level appraisal procedure based on distribution probability - Google Patents

A kind of photovoltaic plant harmonics level appraisal procedure based on distribution probability Download PDF

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CN104504263B
CN104504263B CN201410808156.2A CN201410808156A CN104504263B CN 104504263 B CN104504263 B CN 104504263B CN 201410808156 A CN201410808156 A CN 201410808156A CN 104504263 B CN104504263 B CN 104504263B
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黄晶生
张军军
陈梅
董玮
刘美茵
郑飞
张晓琳
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State Grid Corp of China SGCC
China Electric Power Research Institute Co Ltd CEPRI
State Grid Henan Electric Power Co Ltd
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State Grid Corp of China SGCC
China Electric Power Research Institute Co Ltd CEPRI
State Grid Henan Electric Power Co Ltd
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Abstract

The present invention relates to a kind of photovoltaic plant harmonics level appraisal procedure based on distribution probability, comprise the following steps：According to the test result of different capacity section harmonic current in photovoltaic DC-to-AC converter type approval test, the probability distribution curve of different subharmonic currents is fitted, determines photovoltaic DC-to-AC converter harmonic current feature；Using photovoltaic DC-to-AC converter different capacity section, the probability distribution of different subharmonic currents, the irradiance distribution on ground is built with reference to photovoltaic plant, the horizontal probability distribution of photovoltaic plant totality harmonic current is assessed, reaches the purpose for assessing the power station quality of power supply.

Description

A kind of photovoltaic plant harmonics level appraisal procedure based on distribution probability
Technical field：
The present invention relates to a kind of photovoltaic plant harmonics level appraisal procedure, is more particularly to a kind of light based on distribution probability Overhead utility harmonics level appraisal procedure.
Background technology：
In the prior art, photovoltaic Power Quality Detection is to be incited somebody to action by photovoltaic cell and photovoltaic DC-to-AC converter, photo-voltaic power generation station Solar energy is converted into industrial frequency AC electric energy and is transferred on power network.Due to using high-frequency power electronic switching device, photovoltaic inversion The waveform modulated strategy of device, topological structure, the power network background quality of power supply are horizontal and operating condition all can be to device grid-connected current harmonic wave Size has an impact.With the increase of photovoltaic plant scale and increasing for input combining inverter number, its grid-connected electricity exported Pollution of the harmonic wave to line voltage is flowed also to can not be ignored.Currently, power station large-scale photovoltaic power station electric energy quality harmonic test reference Standard GB/T/T 14549-93《Quality of power supply utility network harmonic wave》, the standard provides big with 95% probability in measurement period Value is used as test result, for evaluating the standard of the harmonic pollution order of severity.
Because photovoltaic plant current harmonic content and irradiation level power are closely related, irradiation level power situation pair during test Test result has a significant impact.By taking certain 500kW inverter laboratory test results as an example, wherein, test result is corresponding work( The big value of 95% probability of test result under rate section：
The inverter A phase current test results of table 1
It can be seen that, the inverter is relatively low in low-power section harmonic content absolute value, total harmonic current and volume from table 1 Current ratio THDIn% is determined for 0.94%.As power output rises, harmonic content is also gradually increasing, but when power reaches After more than 70% power, harmonic content no longer rises, and now THDIn% is 2.3%.If from the above, it can be seen that only with low When power interval test result assesses power station harmonics level, there is a situation where to underestimate power station harmonics level.But simultaneously if Only power station harmonics level is assessed with high power section test result, it is contemplated that the particularity of photovoltaic plant operation, operation Time under 100% power interval is also less, and institute is also excessively harsh in this way.So pass of photovoltaic plant Harmonic Assessment Key technology is how with reference to photovoltaic plant Practical Meteorological Requirements situation to combine each power interval stress_responsive genes result, to photovoltaic plant Harmonics level carries out comprehensive assessment.
The content of the invention：
It is an object of the invention to provide a kind of photovoltaic plant harmonics level appraisal procedure based on distribution probability, methods described Solves the horizontal evaluation problem of the photovoltaic plant harmonic current based on inverter pattern result of the test.
To achieve the above object, the present invention uses following technical scheme：A kind of photovoltaic plant harmonic wave based on distribution probability Level evaluation method, comprise the following steps：
(1) photovoltaic DC-to-AC converter unit harmonic wave distribution probability is tested；
(2) photovoltaic electric station grid connection point harmonic current level is determined；
(3) determine that the horizontal photovoltaic electric station grid connection point harmonic current of long-term irradiation is horizontal.
A kind of photovoltaic plant harmonics level appraisal procedure based on distribution probability provided by the invention, the step (1) Test process comprises the following steps：
Obtain and be tested photovoltaic DC-to-AC converter reactive power output Q=0, harmonic current test data at photovoltaic electric station grid connection point；
Fundamental current span under photovoltaic plant different capacity is determined, and is divided according to fundamental current, by the test Data are divided under different operating modes；
Statistical analysis is carried out to individual harmonic current distribution under different capacity section using normal distribution；
Obtain probability density function of some subharmonic of photovoltaic DC-to-AC converter under different capacity section；
Determine photovoltaic DC-to-AC converter unit harmonic wave distribution probability.
A kind of photovoltaic plant harmonics level appraisal procedure based on distribution probability provided by the invention, the tested photovoltaic are inverse Become device with photovoltaic array analog DC source to be connected；The photovoltaic DC-to-AC converter and power quality analyzer with multi-tap boost transformation The low-pressure side connection of device；The multi-tap step-up transformer is connected with the primary side of the isolating transformer；The tested photovoltaic of control Inverter reactive power exports Q=0, passes through harmonic current under the power quality analyzer continuously 10 power intervals of record.
Another preferable a kind of photovoltaic plant harmonics level appraisal procedure based on distribution probability provided by the invention, passes through Photovoltaic plant is in 1%Pn≤P ＜ 10%Pn, 10%Pn described in the harmonic current distribution tests interpretation of result of the photovoltaic DC-to-AC converter ≤ P ＜ 20%Pn, 20%Pn≤P ＜ 30%Pn, 30%Pn≤P ＜ 40%Pn, 40%Pn≤P ＜ 50%Pn, 50%Pn≤P ＜ 60%Pn, 60%Pn≤P ＜ 70%Pn, 70%Pn≤P ＜ 80%Pn, 80%Pn≤P ＜ 90%Pn and 90%Pn≤P≤ Harmonic current is distributed under 100%Pn different capacities.
Another preferable a kind of photovoltaic plant harmonics level appraisal procedure based on distribution probability provided by the invention, it is assumed that Harmonic current Distribution value obeys N (μ, σ2), wherein μ and σ2The respectively unknown parameter of mathematic expectaion and variance；
E) likelihood function is
F) log-likelihood function is
G) by l (μ, σ2) respectively to μ, σ2Local derviation is sought, substitutes into primary current difference amplitude Frequency statistics result xi, try to achieve seemingly So equation group is：
Likelihood equations are solved to obtain
H) statistical analysis is set up to all sample observations, therefore replaces observed value x with sample X, obtains μ, σ2It is very big Possibility predication is respectively：
Wherein, n is number of samples；For xiAverage value；For sample second-order moment around mean.
Another preferable a kind of described a kind of photovoltaic plant harmonics level based on distribution probability provided by the invention is commented Estimate method, repeat the statistical analysis step, calculate the distribution estimation of individual harmonic current under all power intervals, obtain each Distributed constantSo as to obtain probability density of some subharmonic currents of photovoltaic DC-to-AC converter under different capacity section Function；P is power interval group；H is the number of some subharmonic currents.
Another preferable a kind of photovoltaic plant harmonics level appraisal procedure based on distribution probability provided by the invention, it is same Model photovoltaic DC-to-AC converter harmonic current phase Normal Distribution, and the equal Normal Distribution of parameter in harmonic current phase, I.e.
Wherein, σ2It is random distribution coefficient (such as 0.01,0.04), η represents test constant, and x is stochastic variable, obeys N (0,1) it is distributed.
Another preferable a kind of photovoltaic plant harmonics level appraisal procedure based on distribution probability provided by the invention, it is described Step (2) determines photovoltaic electric station grid connection point harmonic current level by Monte Carlo method；And between each photovoltaic DC-to-AC converter mutually It is independent, it is independent of each other between individual harmonic current；The photovoltaic DC-to-AC converter harmonic current and phase of same type meet same Photovoltaic DC-to-AC converter unit harmonic wave distribution probability；
Random sampling is carried out by photovoltaic DC-to-AC converter unit harmonic wave distribution probability and calculates electric station grid connection point harmonic current.
Another preferable a kind of photovoltaic plant harmonics level appraisal procedure based on distribution probability provided by the invention, it is described Harmonic current determination process is：
A) harmonic wave electricity is randomly selected according to the model inverter unit harmonic wave distribution probability under corresponding power interval
Flow amplitude and phase value；
B) the k subharmonic currents of i points injection are Ii,k(θ), total harmonic current of points of common connection are
C) above step is repeated several times, until grid entry point harmonic current sample meets convergence criterion, with variance system Number β is represented：
Wherein,NS is total frequency in sampling, xiIt is the shape of i times State is sampled, F (xi) it is to ith sample value xiExperimental result, V (F) is experiment function F variance.
Another preferable a kind of photovoltaic plant harmonics level appraisal procedure based on distribution probability provided by the invention, to light The historical data that overhead utility their location meteorological record device records more than 1 year is analyzed, and obtains solar global irradiance distribution frequency Table；
Assuming that irradiation level obeys certain distribution H~F (x), according to photovoltaic DC-to-AC converter test and the fitting knot of probability density function Fruit, try to achieve probability density function I~p of the photovoltaic DC-to-AC converter each harmonic under certain irradiation level sectionY|X(y|x)；Consider spoke When harmonic current is distributed under Illumination Distribution and certain power interval, it is any under the conditions of the amplitude distribution of harmonic current be one Two-dimensional random variable (X, Y), harmonic current distribution probability p in the case of whole irradiation levelY(y) it is two-dimensional random variable The marginal probability density function of (X, Y) on harmonic current, is determined by following formula：
Defined according to conditional probability density
The probability density function p (x, y) for trying to achieve certain harmonic current under any irradiation level is
P (x, y)=pY|X(y|x)pX(x)
Wherein, pX(x) it is the probability density function of irradiance distribution, pY|X(y | x) it is that certain specifies harmonic amplitude under irradiation level Probability density function；
By irradiation level sliding-model control, each distributed area irradiation level scope and each interval probability p are determinedX(x)；Foundation The division of different capacity irradiation level scope, is counted to harmonic current, and power station harmonic amplitude probability is close under certain irradiation level section Spend function pY|X(y|x)；
Under discrete conditions, the probability density function of certain harmonic current is under the conditions of whole irradiation level：
Defined according to accumulated probability density function, certain subharmonic current probability cumulative distribution letter under the conditions of whole irradiation level Number is：
FY(y) it is monotonically increasing function, inverse function F is presentY -1(y),y∈[0,1]；Then consider long-term irradiation degree condition The big value of 95% probability of electric station grid connection point harmonic current is：
With immediate prior art ratio, the present invention, which provides technical scheme, has following excellent effect
1st, method of the invention by the probability distribution of different subharmonic currents under photovoltaic DC-to-AC converter different capacity section and Power plant construction ground irradiation profile feature, the harmonic current injection for assessing photovoltaic plant are horizontal；
2nd, method of the invention has filled up the blank of current photovoltaic plant harmonic current level evaluation method；
3rd, method of the invention is according to the test result of different capacity section harmonic current in photovoltaic DC-to-AC converter type approval test, The probability distribution curve of different subharmonic currents is fitted, determines photovoltaic DC-to-AC converter harmonic current feature；
4th, method of the invention utilizes photovoltaic DC-to-AC converter different capacity section, the probability distribution of different subharmonic currents, knot Closing light overhead utility builds the irradiance distribution on ground, assesses the horizontal probability distribution of photovoltaic plant totality harmonic current, reaches assessment The purpose of the power station quality of power supply；
5th, method applicability of the invention is wider, and flexibility is strong.
Brief description of the drawings
Fig. 1 is the photovoltaic DC-to-AC converter electric energy quality test schematic diagram of the present invention；
Fig. 2 is the 10%Pn interval graphs of 3 primary current harmonic waves under 500kW inverter different capacities section of the invention；
Fig. 3 is the 100%Pn interval graphs of 3 primary current harmonic waves under 500kW inverter different capacities section of the invention；
Fig. 4 is the 10%Pn interval diagrams of 45 primary current harmonic waves under 500kW inverter different capacities section of the invention；
Fig. 5 is the 100%Pn sections signal of 45 primary current harmonic waves under 500kW inverter different capacities section of the invention Figure；
Fig. 6 is the 10%Pn power interval figures of the subharmonic current of grid entry point 3 of the present invention；
Fig. 7 is the 100%Pn power interval figures of the subharmonic current of grid entry point 3 of the present invention；
Fig. 8 is the 10%Pn power interval figures of the subharmonic current of grid entry point 45 of the present invention；
Fig. 9 is the 100%Pn power interval figures of the subharmonic current of grid entry point 45 of the present invention；
Figure 10 is certain irradiance data frequency table figure of the present invention in power station year；.
Embodiment
With reference to embodiment, the invention will be described in further detail.
Embodiment 1：
As Figure 1-10 shows, the invention of this example provides a kind of photovoltaic plant harmonics level assessment side based on distribution probability Method, comprise the following steps：
(1) photovoltaic DC-to-AC converter unit harmonic wave distribution probability is tested
Electric energy quality test is carried out to photovoltaic DC-to-AC converter used in photovoltaic plant, test topology is as shown in fig. 1.Set Power output that inverter is idle, tested inverter reactive power output Q=0 is controlled, by meeting IEC 61000-4-30 The power quality analyzer of ClassA standards continuously records current harmonics under 10 power intervals.
After obtaining test result, analysis inverter is in 1%Pn≤P ＜ 10%Pn, 10%Pn≤P ＜ 20%Pn, 20%Pn ≤ P ＜ 30%Pn, 30%Pn≤P ＜ 40%Pn, 40%Pn≤P ＜ 50%Pn, 50%Pn≤P ＜ 60%Pn, 60%Pn≤P ＜ Under 70%Pn, 70%Pn≤P ＜ 80%Pn, 80%Pn≤P ＜ 90%Pn and 90%Pn≤P≤power intervals of 100%Pn ten Harmonic current value.
Statistical analysis is carried out to individual harmonic current distribution under different capacity section using normal distribution, it is assumed that harmonic current Distribution value obeys N (μ,σ2), wherein μ, σ2For unknown parameter.
Likelihood function is
Log-likelihood function is
By l (μ, σ2) respectively to μ, σ2Local derviation is sought, substitutes into primary current difference amplitude Frequency statistics result xi, try to achieve likelihood Equation group is：
Likelihood equations are solved to obtain
Said process is set up to all sample observations, therefore replaces observed value with sample, just obtains μ, σ2Maximum likelihood estimate Meter is respectively：
Above step is repeated, the distribution estimation of each harmonic under other power intervals is calculated, obtains respective distributed constantObtain probability density function of the subharmonic of photovoltaic DC-to-AC converter 3~50 under different capacity section.
Table 2 unit harmonic amplitude probability density function p (μ, σ) parameter
What single inverter harmonic phase angle was to determine, it can be represented with equation below
θ (t)=αφh(t)φh(t)+βφh-δh, h=1,3,5 ... 13
Wherein φ h (t) are background harmonic voltage phases, and other are the coefficients related to invertor operation operating mode, general ginseng It is as shown in the table for number.
The harmonic phase distributed constant of table 3
When considering more current harmonics superpositions in photovoltaic plant, it is also necessary to consider inverter each harmonic phase problem, In multiple harmonic source current harmonics superpositions in calculating power distribution network, it is contemplated that harmonic wave Source Type is various, working condition is various, it is believed that The phase angle of each harmonic is obeyed and is uniformly distributed, θ~U [0,2 π].But the photovoltaic DC-to-AC converter of same model switchs in photovoltaic plant Frequency, control strategy are identical, therefore this method thinks same model photovoltaic DC-to-AC converter harmonic phase Normal Distribution, it is believed that harmonic wave The equal Normal Distribution of parameter in phase formula[5], i.e.,
Wherein, σ2It is random distribution coefficient (such as 0.01,0.04), η represents test constant αh、βφhWith δ h, x is random Variable, obey N (0,1) distributions.(2) photovoltaic electric station grid connection point current harmonics level calculation
Monte-Carlo Simulation method is to know oneself certain probability distribution (probability density function or probability-distribution function) Stochastic variable, obtain the sample data of certain capacity, make the totality of itself and the distribution there are all identical statistical properties.Will When Monte Carlo method is applied to the assessment of photovoltaic plant harmonics level, each inverter precondition is as follows：
A) it is independent mutually between each inverter, it is independent of each other between each harmonic；
B) it is general to meet same photovoltaic DC-to-AC converter unit harmonic wave distribution for the inverter harmonic current amplitude of same type, phase Rate.
On the basis of above-mentioned condition, carry out random sampling according to inverter unit harmonic wave distribution probability and calculate electric station grid connection point Harmonic current process is as follows：
C) harmonic current is randomly selected according to the model inverter unit harmonic wave distribution probability under corresponding power interval And phase value.
By taking 500kW inverters as an example, the inverter generated at random under 10% and 100% power interval 3 times and 45 subharmonic CURRENT DISTRIBUTION is as shown in Fig. 2-3 and Fig. 4-5：
In Fig. 2-3,3 subharmonic are 3.22A in low-power section harmonic amplitude average, are in high power region average 4.11A；Phase angle is big in low-power section variance higher-wattage section, more uniformly spreads.In Fig. 3,45 subharmonic are in low-power Section harmonic amplitude average is 6.1A, is 6.2A in high power region average；In low-power section harmonic amplitude and phase distribution It is basically identical.
D) the k subharmonic currents of i points injection are Ii,k(θ), total harmonic current of points of common connection are
C) above step M time (M is one big number) is repeated, it is logical until grid entry point harmonic amplitude sample meets convergence criterion Conventional coefficient of variation β is represented：
Wherein,NS is total frequency in sampling, xiIt is the shape of i times State is sampled, F (xi) it is to ith sample value xiExperimental result, V (F) is experiment function F variance.
By taking a certain 50MW power stations as an example, grid entry point voltage is 35kV, containing example 500kW inverters on 100 platforms, then grid entry point The assessment result of 3 times and 45 subharmonic is as shown in Fig. 6-7 and Fig. 8-9：
Using unit probability density function acquiring method in step 1, by parameter Estimation and inspection, power station is obtained in difference Current amplitude distribution probability function under power interval.As shown in table 4
Table 4 electric station grid connection point harmonic wave probability density function P (μ, σ) parameter
(3) the horizontal photovoltaic electric station grid connection point current harmonics level calculation of long-term irradiation is considered
Statistical analysis is carried out to power station their location long history irradiance data, obtains irradiance distribution frequency table as schemed Shown in 10, wherein transverse axis is that irradiation level is strong and weak, unit W/m2.The longitudinal axis is the irradiation level frequency in the section.
Assuming that irradiation level obeys certain distribution H~F (x), can according to inverter test and the fitting result of probability density function In the hope of probability density function I~p of the inverter each harmonic under certain irradiation level sectionY|X(y|x).Consider irradiation level When harmonic current is distributed under distribution and certain power interval, it is any under the conditions of the amplitude distribution of harmonic current be a two dimension Stochastic variable (X, Y), harmonic current distribution probability p in the case of whole irradiation levelY(y) it is two-dimensional random variable (X, Y) On the marginal probability density function of harmonic current, it is shown below：
Defined according to conditional probability density
The probability density function p (x, y) for trying to achieve certain harmonic current under any irradiation level is
P (x, y)=pY|X(y|x)pX(x)
Wherein, pX(x) it is the probability density function of irradiance distribution, pY|X(y | x) it is that certain specifies harmonic amplitude under irradiation level Probability density function.
Standard profile form is disobeyed in view of the irradiance distribution under long-term behavior, causes amount of calculation excessive, will be irradiated Spend sliding-model control, each distributed area irradiation level scope and each interval probability pX(x) it is as shown in the table：
The different capacity section irradiation level scope of table 6
Section 1 2 … 10
Irradiation level section (W/m2) 0<x≤100 100<x≤200 … 900<x≤1000
Probability pX(x) c1 c2 c10
According to the division of different capacity irradiation level scope, harmonic current is counted, power station is humorous under certain irradiation level section Wave amplitude probability density function pY|X(y | x) it may be referred to table 4.By taking 3 subharmonic as an example, harmonic current under different irradiation level Distribution probability p (y, x) is as shown in table 7：
Harmonic amplitude probability distribution under the subharmonic different capacity section of table 73
Under discrete conditions, the probability density function of certain harmonic current is under the conditions of whole irradiation level：
Defined according to accumulated probability density function, certain subharmonic current probability cumulative distribution letter under the conditions of whole irradiation level Several expression formulas are：
Obviously, FY(y) it is monotonically increasing function, inverse function F is presentY -1(y),y∈[0,1].Then consider long-term irradiation degree bar The big value of 95% probability of the electric station grid connection point harmonic current of part is：
Finally it should be noted that：The above embodiments are merely illustrative of the technical scheme of the present invention and are not intended to be limiting thereof, institute The those of ordinary skill in category field with reference to above-described embodiment although should be understood：Still can be to the embodiment of the present invention Modify or equivalent substitution, these are without departing from any modification of spirit and scope of the invention or equivalent substitution, in Shen Within claims of the invention that please be pending.

Claims (8)

  1. A kind of 1. photovoltaic plant harmonics level appraisal procedure based on distribution probability, it is characterised in that：Comprise the following steps：
    (1) photovoltaic DC-to-AC converter unit harmonic wave distribution probability is tested；
    (2) photovoltaic electric station grid connection point harmonic current level is determined；
    (3) determine that the horizontal photovoltaic electric station grid connection point harmonic current of long-term irradiation is horizontal；
    The step (2) determines photovoltaic electric station grid connection point harmonic current level by Monte Carlo method；And each photovoltaic DC-to-AC converter Between it is independent mutually, be independent of each other between individual harmonic current；The photovoltaic DC-to-AC converter harmonic current and phase of same type are equal Meet same photovoltaic DC-to-AC converter unit harmonic wave distribution probability；
    Random sampling is carried out by photovoltaic DC-to-AC converter unit harmonic wave distribution probability and calculates electric station grid connection point harmonic current.
  2. A kind of 2. photovoltaic plant harmonics level appraisal procedure based on distribution probability as claimed in claim 1, it is characterised in that： The test process of the step (1) comprises the following steps：
    Obtain and be tested photovoltaic DC-to-AC converter reactive power output Q=0, harmonic current test data at photovoltaic electric station grid connection point；
    Fundamental current span under photovoltaic plant different capacity is determined, and is divided according to fundamental current, by the test data It is divided under different operating modes；
    Statistical analysis is carried out to individual harmonic current distribution under different capacity section using normal distribution；
    Obtain probability density function of some subharmonic of photovoltaic DC-to-AC converter under different capacity section；
    Determine photovoltaic DC-to-AC converter unit harmonic wave distribution probability.
  3. A kind of 3. photovoltaic plant harmonics level appraisal procedure based on distribution probability as claimed in claim 2, it is characterised in that： The tested photovoltaic DC-to-AC converter is connected with photovoltaic array analog DC source；The photovoltaic DC-to-AC converter and power quality analyzer with The low-pressure side connection of multi-tap step-up transformer；The primary side connection of the multi-tap step-up transformer and isolating transformer；Control The tested photovoltaic DC-to-AC converter reactive power output Q=0 of system, by under the power quality analyzer continuously 10 power intervals of record Harmonic current.
  4. A kind of 4. photovoltaic plant harmonics level appraisal procedure based on distribution probability as claimed in claim 2, it is characterised in that： By photovoltaic plant described in the harmonic current distribution tests interpretation of result of the photovoltaic DC-to-AC converter 1%Pn≤P ＜ 10%Pn, 10%Pn≤P ＜ 20%Pn, 20%Pn≤P ＜ 30%Pn, 30%Pn≤P ＜ 40%Pn, 40%Pn≤P ＜ 50%Pn, 50% Pn≤P ＜ 60%Pn, 60%Pn≤P ＜ 70%Pn, 70%Pn≤P ＜ 80%Pn, 80%Pn≤P ＜ 90%Pn and 90%Pn≤ Harmonic current is distributed under P≤100%Pn different capacities.
  5. A kind of 5. photovoltaic plant harmonics level appraisal procedure based on distribution probability as claimed in claim 3, it is characterised in that： Assuming that harmonic current Distribution value obeys N (μ, σ2), wherein μ and σ2The respectively unknown parameter of mathematic expectaion and variance；
    A) likelihood function is
    <mrow> <mi>L</mi> <mrow> <mo>(</mo> <mi>&amp;mu;</mi> <mo>,</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&amp;Pi;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mfrac> <mn>1</mn> <mrow> <msqrt> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msqrt> <mi>&amp;sigma;</mi> </mrow> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mrow> </msup> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mn>2</mn> <msup> <mi>&amp;pi;&amp;sigma;</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mfrac> <mi>n</mi> <mn>2</mn> </mfrac> </mrow> </msup> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mrow> </msup> </mrow>
    B) log-likelihood function is
    <mrow> <mi>l</mi> <mrow> <mo>(</mo> <mi>&amp;mu;</mi> <mo>,</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mfrac> <mi>n</mi> <mn>2</mn> </mfrac> <mi>l</mi> <mi>n</mi> <mrow> <mo>(</mo> <mn>2</mn> <msup> <mi>&amp;pi;&amp;sigma;</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow>
    C) by l (μ, σ2) respectively to μ, σ2Local derviation is sought, substitutes into electric current difference amplitude Frequency statistics result xi, try to achieve likelihood equations For：
    <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>l</mi> <mrow> <mo>(</mo> <mi>&amp;mu;</mi> <mo>,</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <mi>&amp;mu;</mi> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mfrac> <mn>1</mn> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mfrac> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>l</mi> <mrow> <mo>(</mo> <mi>&amp;mu;</mi> <mo>,</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>=</mo> <mfrac> <mi>n</mi> <mrow> <mn>2</mn> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <mi>n</mi> <mrow> <mn>2</mn> <msup> <mi>&amp;sigma;</mi> <mn>4</mn> </msup> </mrow> </mfrac> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced>
    Likelihood equations are solved to obtain
    <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <mi>&amp;mu;</mi> <mo>^</mo> </mover> <mo>=</mo> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mover> <mi>&amp;sigma;</mi> <mo>^</mo> </mover> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced>
    D) statistical analysis is set up to all sample observations, therefore replaces observed value x with sample X, obtains μ, σ2Maximum likelihood estimate Meter is respectively：
    <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <mi>&amp;mu;</mi> <mo>^</mo> </mover> <mo>=</mo> <mover> <mi>X</mi> <mo>&amp;OverBar;</mo> </mover> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mover> <mi>&amp;sigma;</mi> <mo>^</mo> </mover> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <mover> <mi>X</mi> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>=</mo> <msubsup> <mi>S</mi> <mi>n</mi> <mn>2</mn> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced>
    Wherein, n is number of samples；For sample mean；For sample second-order moment around mean.
  6. 6. a kind of photovoltaic plant harmonics level appraisal procedure based on distribution probability as described in claim 3-5 any one, It is characterized in that：The statistical analysis step is repeated, the distribution estimation of individual harmonic current under all power intervals is calculated, obtains Respective distributed constantSo as to obtain probability of some subharmonic currents of photovoltaic DC-to-AC converter under different capacity section Density function；P is power interval group；H is the number of some subharmonic currents.
  7. A kind of 7. photovoltaic plant harmonics level appraisal procedure based on distribution probability as claimed in claim 6, it is characterised in that： Same model photovoltaic DC-to-AC converter harmonic current phase Normal Distribution, and the parameter in harmonic current phase obeys normal state point Cloth, i.e.,
    <mrow> <mi>y</mi> <mo>=</mo> <mi>&amp;eta;</mi> <msqrt> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </msqrt> <mi>x</mi> <mo>+</mo> <mi>&amp;eta;</mi> </mrow>
    Wherein, σ2It is random distribution coefficient, η represents test constant, obeys N (0,1) distributions.
  8. A kind of 8. photovoltaic plant harmonics level appraisal procedure based on distribution probability as claimed in claim 1, it is characterised in that： The harmonic current determination process is：
    A) harmonic current and phase value are randomly selected according to inverter unit harmonic wave distribution probability under corresponding power interval；
    B) the k subharmonic currents of i points injection are Ii,k(θ), total harmonic current of points of common connection are
    <mrow> <msub> <mi>I</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow>
    C) repeat above step a, b several times, until grid entry point harmonic current sample meets convergence criterion, use coefficient of variation β is represented：
    <mrow> <mi>&amp;beta;</mi> <mo>=</mo> <mfrac> <msqrt> <mrow> <mi>V</mi> <mrow> <mo>(</mo> <mover> <mi>E</mi> <mo>^</mo> </mover> <mo>(</mo> <mi>F</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </msqrt> <mrow> <mover> <mi>E</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>F</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>
    Wherein,NS is total frequency in sampling, xiIt is that the state of i times is taken out Sample, F (xi) it is to ith sample value xiExperimental result, V (F) is experiment function F variance.
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