CN110752622B - Affine state estimation method for power distribution network - Google Patents
Affine state estimation method for power distribution network Download PDFInfo
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Classifications
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E10/00—Energy generation through renewable energy sources
- Y02E10/70—Wind energy
- Y02E10/76—Power conversion electric or electronic aspects
Abstract
The invention relates to an affine state estimation method of a power distribution network, which converts an uncertainty interval containing uncertainty of output and load fluctuation of a distributed power supply of photovoltaic power generation and wind power generation into an affine number form to be used as node injection uncertainty power; aligning SCADA data and mu PMU data in consideration of timeliness, predicting the SCADA data by using an adaptive coefficient exponential smoothing method, and fusing the SCADA data with the mu PMU as complementary pseudo-measurement data; the method comprises the steps of determining an affine number model with uncertain power injected by a SCADA system and nodes to perform upper layer state estimation, combining affine number results of upper layer state estimation with aligned uPMU real-time measurement to form a lower layer state estimation model of the power distribution network with linear hybrid measurement, and converting directly solved affine number results into interval numbers to obtain state estimation results narrower than interval state estimation, wherein the results are not conserved. The invention fully considers the uncertainty of the distributed power supply output in the power distribution network, replaces a determined value with a narrower interval state estimation result, and describes the power distribution network state.
Description
Technical Field
The invention relates to the field of power distribution network state estimation, in particular to a power distribution network affine state estimation method.
Background
With the rapid development of renewable energy sources, energy storage, electric vehicles and other interactive energy facilities, the power generation grid connection of various high-permeability distributed power sources enables the traditional unidirectional radial power distribution network to be gradually changed into a multi-energy power supply system. The distributed power supply output has intermittence and randomness, the strong uncertainty presented by the injection power of the distributed power supply output brings challenges to the real-time state estimation of the power distribution network, and more uncertain factors need to be further considered in the state estimation of the power distribution network; the state sensing device is used for sensing the running state of the power distribution network through carrying out homologous acquisition on the installed measuring device, so that further work of a dispatcher and prevention of power failure are facilitated, and the state estimation is required to be capable of considering more uncertainties and providing more accurate results.
Traditional deterministic state estimation is carried out under a certain time section or a certain working condition according to measurement data of a measuring device, belongs to point estimation, cannot quantify the influence of uncertain factors on a power distribution network, and a probability model and a fuzzy number model considering uncertainty variables need to acquire probability density functions or membership functions through a large amount of historical data, and the change of the uncertainty variables is described by utilizing statistical data, so that the change is often different from the actual change condition, a large amount of historical data is needed, and the time complexity of algorithm solving is easy to increase. Therefore, all uncertainty conditions can be covered by only determining the upper and lower output bounds of the distributed power supply, namely the uncertainty interval, and the state estimation result in the interval form can replace the determined value, so that the information with the upper and lower bound ranges is provided for the scheduling personnel, and the method becomes an effective means for estimating the state of the power distribution network after the multi-type distributed power supply is connected.
In the interval operation, correlation among variables and unavoidable error explosion phenomenon in the operation process are ignored, so that interval expansion is caused, the obtained result is too conservative to reflect the real state of the structure, and in the real-time state estimation of the power distribution network, information cannot be provided in a more accurate narrow interval, so that a dispatcher cannot make correct judgment.
Disclosure of Invention
The invention aims to provide an affine state estimation method for a power distribution network, which aims to solve the problems that in the traditional interval operation, the correlation between variables is ignored, and the interval expansion is caused by an unavoidable error explosion phenomenon in the operation process, so that the obtained result is too conservative and the actual state of a structure cannot be reflected.
In order to achieve the above object, the present invention provides the following solutions:
an affine state estimation method for a power distribution network, comprising the following steps:
acquiring an uncertainty interval containing the output uncertainty of a distributed power supply for photovoltaic power generation and wind power generation and the fluctuation of load;
converting the uncertainty interval containing the output uncertainty of the photovoltaic power generation and the wind power generation and the load fluctuation into an affine number form as node injection uncertainty power;
acquiring SCADA data measured by a SCADA (supervisory control and data acquisition) and mu PMU data measured by a mu PMU (micro synchronous phasor measurement unit) of a data acquisition and monitoring control system; the SCADA data comprises branch power and node voltage amplitude values; the mu PMU data includes a voltage magnitude and a phase angle;
aligning the SCADA data with the mu PMU data based on the time ductility of the SCADA of the data acquisition and monitoring control system, predicting the SCADA data by using an adaptive coefficient index smoothing method, and determining predicted SCADA data and aligned mu PMU data;
performing upper layer state estimation according to the predicted SCADA data and the affine number model of the node injection uncertainty power, and determining an affine number result of the upper layer state estimation;
determining a power distribution network lower layer state estimation model of linear hybrid measurement by combining the affine number result of upper layer state estimation and the aligned mu PMU data;
determining an affine number result according to the power distribution network lower state estimation model;
converting the affine number result into an interval number;
and estimating the affine state of the power distribution network according to the interval number.
Optionally, the converting the uncertainty interval containing the uncertainty of the output of the photovoltaic power generation and the wind power generation distributed power supply and the fluctuation of the load into an affine number form is used as the node to inject the uncertainty power, which specifically includes:
the wind power probability model, the photovoltaic power generation probability model and the load fluctuation probability model are utilized, a 95% confidence interval is used as the interval output of the power uncertainty, and the interval output is converted into an affine number form to be used as the node injection uncertainty power;
(1) Taking a 95% confidence interval of a wind speed probability model with wind speed obeying double-parameter Weibull distribution as an interval of wind speed uncertainty, and combining the relation between output power and wind speed to output an active power intervalWherein,P i,wid the lower limit of the active power output of wind power generation; />An upper limit of active power output for wind power generation; when the fan operates with constant power factor, the output reactive power interval is +.>Wherein,q i,wid the lower limit of the reactive power output of the wind power generation is set; />The upper limit of reactive power output of wind power generation; converting the two power intervals into affine number form by utilizing affine mathematics:
wherein:the method is in an affine number form of active force of wind power generation; epsilon p，i，wid Active noise elements introduced for affine numbers of wind power generation; />The method is in a reactive power output affine number form of wind power generation; epsilon q，i，wid Reactive noise elements introduced for affine numbers of wind power generation;
(2) Taking a confidence interval of 95% of the photovoltaic cell output as the interval number form of photovoltaic power generation uncertainty, wherein the active power interval and the reactive power interval are respectivelyWherein,P i,pv the lower limit of the active power output of the photovoltaic power generation is set;q i,pv the lower limit of the output of the reactive power of the photovoltaic power generation is set; />The upper limit of the active power output of the photovoltaic power generation is set; />The upper limit of the output of the reactive power of the photovoltaic power generation is satisfied, and the following active and reactive output constraints are satisfied:
(p i,pv ) 2 +(q i,pv ) 2 ≤(S i,pv ) 2
wherein S is i,pv Is complex power;
converting into affine number form by utilizing affine mathematical method:
wherein,the method is in an affine number form of active power output of photovoltaic power generation; epsilon p,i,pv Active noise elements introduced for affine numbers of photovoltaic power generation; />The method is in a reactive power output affine number form of photovoltaic power generation; epsilon q,i,pv Is photovoltaic hairReactive noise elements introduced by the electric affine number;
(3) The 95% confidence interval of the load fluctuation probability model is taken as the interval number form of the load fluctuation, and the active power interval and the reactive power interval are respectivelyWherein P is i,load A lower active power output limit for load ripple;Q i,load a lower limit for load fluctuation reactive power output; />An upper active output limit for load fluctuation;for the upper limit of load fluctuation reactive power output, converting into an affine number form by utilizing an affine mathematical method:
wherein, the noise element satisfies-1 ∈s p，i，load ,ε Q，i，load ≤1；The method is characterized in that the method is in an active power output affine number form of load fluctuation; epsilon p,i,load Active noise elements introduced for affine numbers of load fluctuations; />Affine number form of reactive power output of load fluctuation; epsilon q,i,load Reactive noise elements are introduced for the affine number of load fluctuations.
Optionally, the aligning the SCADA data with the mu PMU data based on the time ductility of the SCADA of the data acquisition and monitoring control system, predicting the SCADA data by using an adaptive coefficient exponential smoothing method, and determining the predicted SCADA data and the aligned mu PMU data specifically includes:
acquiring the expected E of the SCADA data measurement delay d Taking time at any time as E d +T s ；T s An arrival time of the mu PMU data;
at T s Searching the SCADA data in a taking range corresponding to the moment, and determining that the data in the taking range is T if the SCADA data exists s SCADA data corresponding to the moment;
using the formulaPredicting the SCADA data, and determining the predicted SCADA data; wherein alpha is t To become the coefficient, x t Is historical data; />For predictive value +.>Predicted values for the next time.
Optionally, the aligning the SCADA data with the mu PMU data based on the time ductility of the SCADA of the data acquisition and monitoring control system, predicting the SCADA data by using an adaptive coefficient exponential smoothing method, and after determining the predicted SCADA data and the aligned mu PMU data, further includes:
and (5) aligning and fusing the predicted SCADA data serving as the complementary pseudo measurement with the mu PMU data.
Optionally, the performing upper layer state estimation according to the predicted SCADA data and the affine number model of the node injection uncertainty power, and determining an affine number result of the upper layer state estimation specifically includes:
measurement equation z using upper layer state estimation 1 ＝h 1 (x (1) ) +r determining affine number results of the upper layer estimation; wherein z is 1 The method comprises the steps of measuring the quantity, wherein the quantity comprises branch power obtained by SCADA measurement, node voltage amplitude and node injection uncertainty power; h is a 1 (x (1) ) Is not aA linear equation; x is x (1) Is the state quantity x (1) Including the magnitude of the node voltageAnd phase angle>r is the measurement error, the state variable x (1) The iterative solution can be performed as follows:
wherein H (x) (1) ) Is Jacobian matrix, W 1 Is a covariance matrix.
Optionally, the determining the affine number result according to the power distribution network lower layer state estimation model specifically includes: node voltage amplitudeAffine value of phase angle>The fluctuation interval of plus or minus alpha percent is added with the node voltage phasor measured by the mu PMU in real time and is used as affine quantity measurement of the lower layer estimation, and then the measurement equation is expressed as follows:
z 2 ＝h(x (2) )+ε 2
wherein z is 2 For the node voltage phasor affine interval, h measured in real time by the upper affine state estimation result and mu PMU 1 (x (1) ) Is a linear equation, ε 2 To measure error, the state variable resultsThe iterative solution can be performed as follows:
wherein E is a coefficient matrix of the measurement equation, W 2 Is covariance matrix;
results of the state variables obtainedThe affine form of node voltage magnitude and phase angle is expressed as:
wherein:estimating affine number results for final state, V ij 、θ ij To introduce a new noise element epsilon v,j 、ε θ,j Coefficients generated at that time.
Optionally, the converting the affine number result into an interval number specifically includes:
using the formulaConverting the affine number result into an interval number.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a method for estimating affine state of a power distribution network, which is characterized in that the influence of uncertainty of permeability multi-type distributed power supply output and load fluctuation on the estimation of the power distribution network state is emphasized, an affine mathematical method is adopted, the dependency relationship among different variables is established by utilizing noise elements of affine operators, the expansion of a section is restrained, a narrower section calculation result can be obtained, the section estimation is not conserved any more, and a section result of the state quantity of the power distribution network system is provided for a dispatcher;
in the state estimation, the difference of sampling periods of two measuring devices, the time ductility of the SCADA of the measuring device and the difference of sampling periods of the measuring system and the mu PMU measuring system are considered, and after SCADA data without a time mark and mu PMU data are aligned, fusion of data with different periods is carried out, so that the data of the measuring device can be fully utilized, and the state estimation accuracy is improved;
and establishing a double-layer state estimation model, combining mu PMU real-time measurement data with the traditional state estimation on the basis of the traditional state estimation, not changing the structure of the existing state estimation program, and obtaining a state estimation result with higher accuracy.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of an affine state estimation method of a power distribution network provided by the invention;
FIG. 2 is a flowchart of an affine state estimation method for a power distribution network, which is provided by the invention and takes the uncertainty of the output of a distributed power supply and the fluctuation of load into consideration;
FIG. 3 is a time-delay alignment chart of the hybrid measurement data according to the present invention;
FIG. 4 is a diagram showing a fusion of hybrid metrology data prediction and interpolation provided by the present invention;
fig. 5 is a flow chart of a dual-layer state estimation provided by the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a method and a system for estimating affine state of a power distribution network, which can inhibit section expansion to obtain narrower section calculation results, and the section estimation is not conserved any more, so as to provide more accurate section results of the state quantity of the power distribution network system for a dispatcher.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
Fig. 1 is a flowchart of an affine state estimation method of a power distribution network provided by the present invention, and as shown in fig. 1, the present invention provides an affine state estimation method of a power distribution network, including:
step 101: and acquiring an uncertainty interval containing the output uncertainty of the distributed power supply of photovoltaic power generation and wind power generation and the fluctuation of load.
Step 102: and converting the uncertainty interval containing the output uncertainty of the photovoltaic power generation and the wind power generation distributed power supply into an affine number form, and injecting the uncertainty power into the node.
Step 103: acquiring SCADA data measured by a data acquisition and monitoring control system (supervisory control and data acquisition, SCADA) and mu PMU data measured by a miniature synchrophasor measurement unit (phasor measurementunit, mu PMU); the SCADA data comprises branch power and node voltage amplitude values; the mu PMU data includes a voltage magnitude and a phase angle.
Step 104: and aligning the SCADA data with the mu PMU data based on the time ductility of the SCADA of the data acquisition and monitoring control system, predicting the SCADA data by using an adaptive coefficient exponential smoothing method, and determining predicted SCADA data and aligned mu PMU data.
Step 105: and performing upper layer state estimation according to the predicted SCADA data and the affine number model of the node injection uncertainty power, and determining an affine number result of the upper layer state estimation.
Step 106: and determining a power distribution network lower layer state estimation model of linear hybrid measurement by combining the affine number result of the upper layer state estimation and the aligned mu PMU data.
Step 107: and determining an affine number result according to the power distribution network lower-layer state estimation model.
Step 108: converting the affine number result into an interval number.
Step 109: and estimating the affine state of the power distribution network according to the interval number.
Based on the affine state estimation method of the power distribution network, which is provided by the invention, the affine state estimation method of the power distribution network, which considers the uncertainty of the output of the distributed power supply and the fluctuation of the load, is shown in fig. 2, and the method comprises the following steps:
step one: affine mathematics can solve the correlation problem in interval arithmetic, and affine number forms and interval number forms can be mutually converted; the wind power probability model, the photovoltaic power generation probability model and the load fluctuation probability model are utilized, a 95% confidence interval is used as the interval output of the power uncertainty, and the power is converted into an affine number form to be used as the node injection uncertainty power, and the specific method is as follows.
(1) Affine arithmetic can solve the correlation problem in interval arithmetic, and the expression is that
Wherein x is i Is a real coefficient, where i=1, 2 … n; epsilon i Has a value of [ -1,1]Is a noise element of (1); x is x 0 Is a central value. The interval number and affine number can be mutually converted to give an interval numberConversion into affine form
Given an affine numberConversion into the number of intervals
Four-law operation of two real or complex affine numbers:
for the last term of multiplication of complex affine numbers, the radius operator of affine variables can be used to approximate, i.e.:
here λ is a new noise element generated by non-affine operation, between [ -1,1 ].
For the division of an affine operation,divided by->Equivalent to->Multiplied by->The calculation formula is as follows:
wherein: ε 2n+1 and epsilon 2n+2 Is a noise element newly generated in complex affine operation, g (z i )＝|a|+j|b|。
(2) The probability distribution of wind speed obeys the double-parameter Weibull distribution, and the probability density function can be expressed as
Wherein: k and C respectively represent the shape parameter and the scale parameter of Weibull distribution and reflect the distribution characteristics of wind speed and average wind speed.
The relation between the active power of wind power generation and wind speed can be expressed as:
wherein: p (P) wid Active power output by the fan; v in ，v r ，v out Respectively representing cut-in, rated and cut-out wind speeds; p (P) r Is the rated power of the fan. Assuming that the fan operates in a constant power factor mode, the reactive power output by the fan is
Because the wind speed changes greatly at different moments in the day, the wind speed at a certain moment is difficult to accurately predict, the wind speed at a certain moment can be described by using an interval model, and the wind speed is used as the wind speedThe 95% confidence interval of the probability model is the 95% confidence interval of the interval number of the wind power generation uncertaintyCan be directly obtained according to probability density function, and output active power interval by combining the relation between output power and wind speed>Wherein,P i,wid for the lower active power output limit, +.>For the upper limit of active power output, the fan operates with a constant power factor, and the output reactive power interval isWherein,q i,wid for the lower reactive power output limit,/->For the upper limit of reactive power output, two power intervals are converted into affine number form by affine mathematics:
converting it into affine number form by affine mathematical method:
wherein: epsilon p，i，wid And epsilon q，i，wid Active and reactive noise elements introduced by affine numbers of wind power generation are respectively used.
(3) The probability distribution of the photovoltaic cell obeys the distribution characteristic that the Beta distribution represents the illumination intensity, and the probability density function can be expressed as follows:
wherein: alpha and beta are Bethe shape parameters of the ta distribution; Γ () is a Gamma function; r and r max The real illumination intensity and the maximum illumination intensity are respectively.
The theoretical expression of the photovoltaic output is:
wherein:the illumination intensity is S, the area of the photovoltaic module is S, eta is the photoelectric conversion efficiency, beta is the temperature coefficient, and T is the ambient temperature.
Active power of photovoltaic output, photovoltaic cell temperature T and illumination intensityClosely related, wherein the photovoltaic cell temperature can be expressed in terms of ambient temperature and illumination intensity:
wherein T is e Is the external environment temperature; beta is a constant coefficient. The ambient temperature will not typically change drastically in a short period of time, and thus the uncertainty in the photovoltaic output is determined mainly by the intensity of the light.
The illumination intensity of a certain area is mainly determined by the illumination intensity outside the atmosphere of the area and the cloud cover condition, and is specifically as follows:
in the method, in the process of the invention,the illumination intensity outside the atmosphere; i is the cloud cover coefficient. />Generally, the photovoltaic power generation device does not change in a short time, I can fluctuate greatly in a short time, and thus the uncertainty of the photovoltaic power generation device can be considered to be mainly determined by cloud coverage conditions.
Similar to wind speed prediction, cloud cover coefficients are often difficult to accurately predict at a certain moment, and can be described by using interval forms, wherein a confidence interval of 95% of photovoltaic cell output is used as the interval number form of photovoltaic power generation uncertainty, and active power intervals and reactive power intervals are respectivelyWherein,P i,pv 、q i,pv respectively, the lower limit of active and reactive power output, < + >>Upper limits of active power output respectively, and meets the following constraints of active and reactive power output
(p i,pv ) 2 +(q i,pv ) 2 ≤(S i,pv ) 2
Wherein S is i,pv For complex power, it is assumed that the photovoltaic system is controlled in a constant power factor mode, and photovoltaic power generation is considered to provide active power only to the power distribution network, so the power factor is set to be 1.
Converting it into affine number form by affine mathematical method:
wherein,the method is in an affine number form of active power output of photovoltaic power generation; epsilon p,i,pv Active noise elements introduced for affine numbers of photovoltaic power generation; />Is a photovoltaic deviceAffine number form of reactive power output of power generation; reactive noise elements introduced for affine numbers of photovoltaic power generation;
(4) The load fluctuation obeys the distribution characteristic of Gaussian distribution, and the probability density function can be expressed as
Wherein:average active and reactive loads; sigma (sigma) P 、σ Q Is the standard deviation of the active and reactive power.
Because most nodes in the power distribution network are not provided with load power for real-time measurement, a historical load curve is generally utilized to acquire load data at a certain moment in the future. However, the load level is affected by a series of factors, such as weather conditions, electricity price conditions, user electricity characteristics and the like, and accurate load data at a certain moment in the future are difficult to obtain, so that load fluctuation at a certain moment is predicted by load historical data, a 95% confidence interval of a load fluctuation probability model is used as the interval number form of the load fluctuation, and active power intervals and reactive power intervals are respectivelyWherein,P i,pv 、Q i,load respectively, the lower limit of active and reactive power output, < + >>Respectively the upper limits of active and reactive power output, and converting the upper limits into affine digital form by utilizing affine mathematical method
Wherein,the method is characterized in that the method is in an active power output affine number form of load fluctuation; epsilon p,i,load Active noise elements introduced for affine numbers of load fluctuations; />Affine number form of reactive power output of load fluctuation; epsilon q,i,load Reactive noise elements are introduced for the affine number of load fluctuations.
The further technical proposal is that: the step (2) comprises: the SCADA data (branch power measured by the SCADA system, node voltage amplitude obtained directly by the measuring device) and mu PMU (including voltage and phase angle obtained by a measuring device different from the SCADA measuring device) data are aligned in consideration of time ductility, and the SCADA data are predicted by an adaptive coefficient exponential smoothing method and fused with the mu PMU as complementary pseudo-measured data.
Step two: the SCADA data and the mu PMU data are aligned in consideration of the temporal ductility, and the SCADA data is predicted by an adaptive coefficient exponential smoothing method and fused with the mu PMU as complementary pseudo-measurement data.
(a) As shown in FIG. 3, the SCADA data is aligned with the mu PMU measurement data with the time scale, and the measurement delay of the SCADA system obeying uniform distribution is [ d ] min ，d max ]Corresponding to T s The distribution of time is [ T ] s +d min ，T s +d max ]T for SCADA data to reach the dispatch center s Time of day access range. The expectation of the SCADA measurement delay is E d Taking the time at a certain moment as E d +T s . Let mu PMU data arrival time be T s Then at T s Searching SCADA data in a corresponding access range at a moment, and if the SCADA data exist, considering the data in the range as T s SCADA data corresponding to the moment.
(b) As shown in fig. 4, a primary exponential smoothing sequence is defined:
s t ＝αx t +(1-α)s t-1
wherein t=1, 2, …, T represents the SCADA history data of the first T times, and α is (0, 1)Smoothing coefficient, initial value s 0 ＝x 1 The smoothed value of the t-th phase is used as the predicted value of the t+1 phase and is used as the complementary pseudo-measurement data to align with mu PMU data, namely:
replacing the predicted value with the smoothed value and changing the smoothed coefficient alpha to the variable coefficient alpha t The predictive formula becomes:
taking another constant beta, enabling 0 < beta < 1, and carrying out exponential weighted average on the prediction error before the t period, namely:
E t ＝βe t +β(1-β)e t-1 +…+β(1-β) t-1 e 1
then E t The recurrence formula of (2) is:
E t ＝βe t +(1-β)E t-1
taking M t ＝β|e t |+β(1-β)|e t-1 |+…+β(1-β) t-1 |e 1 |
M is then t The recurrence formula is:
M t ＝β|e t |+(1-β)M t-1
then get the transformation coefficient alpha t ＝|E t |/M t Thereby ensuring 0 < alpha t And < 1, the adaptive coefficient index smoothing prediction formula is that
The predicted SCADA data is aligned and fused with the mu PMU data as a supplemental pseudo-measurement.
Step three: as shown in fig. 4, the upper layer state estimation is performed by the SCADA system and the affine number model of the node injection uncertainty power, and the measurement includes the branch power measured by the SCADA system, the node voltage amplitude and the uncertainty prediction value of the node injection power. The measurement equation of the branch power is as follows:
the form of the state estimation correction equation is as follows:
the voltage amplitude is measured as follows:
ΔV i ＝ΔV
the active and reactive power affine number form of the uncertain predicted value of the node injection power and the load fluctuation is as follows:
wherein:active output affine number forms respectively representing wind power generation, photovoltaic power generation and load fluctuation; />The affine form of reactive power output representing wind power generation, photovoltaic power generation and load fluctuation. In the steady-state analysis process of the conventional load of the power distribution network, a PQ control mode is mostly adopted, and the power factor is constant (set to 0.85). The measurement equation of the node injection power is:
the measurement correction equation of the node injection power is as follows:
the measurement equation of the state estimation equation based on the weighted least square method is expressed as:
the method comprises the following steps:H v ＝[I 0]，/>jacobian matrices representing branch power, node voltage magnitude, node injection power, respectively. Status variable +.>The iterative solution can be performed as follows:
obtaining the result of upper layer state estimation by using SCADA system measurement and node injection power uncertainty prediction, wherein affine values including node voltage amplitude and phase angle areAdding a fluctuation interval of + -alpha% to the node voltage phasor measured in real time by the high-precision mu PMU, and taking the node voltage phasor and the upper layer variable value together as affine quantity measurement of lower layer estimation, wherein a measurement equation can be expressed as follows:
wherein: i is an identity matrix; i' does not configure uPMU corresponding row phase for deleting corresponding nodeA unitary matrix of quantities; e is a coefficient matrix of the measurement equation; epsilon 2 Is the measurement error.
The covariance matrix is:
the measurement equation is a linear equation so the second layer state estimate can be solved directly, resulting in:
the resulting state variable results are affine forms of node voltage magnitude and phase angle, which can be expressed as:
wherein:estimating affine number results for final state, V ij 、θ ij To introduce a new noise element epsilon v,j 、ε θ , j Coefficients generated at that time.
The converting the obtained affine number state estimation result into the interval number specifically includes:
since affine arithmetic is used to model uncertainty variables, affine operators in affine arithmeticIs the noise element epsilon (epsilon < -1, 1)]) By establishing correlations between different regional variables through a set of specific noise elements, the dependency between the uncertainty quantities can be characterizedThe method is characterized in that through carrying out double-layer affine state estimation by combining the SCADA system and mu PMU system data, on the basis of traditional state estimation, mu PMU measurement information with higher precision is added to carry out linear state estimation, the state estimation precision can be improved, a section solution narrower than a section arithmetic is obtained, and the result is not conserved.
The invention provides a state estimation method capable of fully considering uncertainty and inhibiting section expansion, which is used for solving the problem that a distributed power supply is connected to a power distribution network to cause uncertain influence on power distribution network state estimation and a conservative estimation result caused by neglecting section correlation in section calculation.
Affine arithmetic is introduced into an interval modeling mode of uncertainty factors, so that the correlation among uncertainty variables is increased, and the problems of interval expansion and conservation of interval calculation results in interval calculation are solved. Meanwhile, aiming at the problem of data fusion of two measuring devices with different acquisition periods required by state estimation, data alignment and prediction interpolation are carried out, so that the prediction accuracy can be improved. And the method of double-layer state estimation is adopted, and based on the traditional state estimation, mu PMU real-time measurement data is combined with the traditional state estimation, the structure of the existing state estimation program is not changed, and a state estimation result with higher accuracy can be obtained.
According to the section modeling mode considering the uncertainty of the distributed power supply output and the fluctuation of the load, according to probability density functions of wind power generation, photovoltaic power generation and the fluctuation of the load, predicted values of wind speed and light intensity and historical data of the fluctuation of the load, a 95% confidence interval is considered as the section number of the uncertainty output.
And affine arithmetic is introduced into the interval modeling mode of the uncertainty factors, and the distributed power supply output interval and the load fluctuation interval are converted into affine number forms according to an affine arithmetic and interval number conversion method and an affine number algorithm.
According to the data fusion problem of the two measuring devices adopted in the state estimation, the data timeliness of SCADA is considered, SCADA data without a time mark and mu PMU data with the time mark are aligned, and in a SCADA acquisition period, a smooth value number prediction method of an adaptive coefficient is adopted for prediction and interpolation in a data fusion mode by taking mu PMU data as a reference.
And the two-layer affine state estimation is carried out by an affine number model of SCADA measurement and node injection uncertainty power, an affine number result of the upper layer estimation is combined with aligned mu PMU high-precision measurement to form a lower-layer linear state estimation model of the power distribution network for linear hybrid measurement, and a directly solved affine number result is converted into an interval number, so that a state estimation result narrower than the interval state estimation can be obtained.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (5)
1. An affine state estimation method for a power distribution network is characterized by comprising the following steps of:
acquiring an uncertainty interval containing the output uncertainty of a distributed power supply for photovoltaic power generation and wind power generation and the fluctuation of load;
converting the uncertainty interval containing the output uncertainty of the photovoltaic power generation and the wind power generation and the load fluctuation into an affine number form as node injection uncertainty power;
acquiring SCADA data measured by a SCADA (supervisory control and data acquisition) and mu PMU data measured by a mu PMU (micro synchronous phasor measurement unit) of a data acquisition and monitoring control system; the SCADA data comprises branch power and node voltage amplitude values; the mu PMU data includes a voltage magnitude and a phase angle;
aligning the SCADA data with the mu PMU data based on the time ductility of the SCADA of the data acquisition and monitoring control system, predicting the SCADA data by using an adaptive coefficient index smoothing method, and determining predicted SCADA data and aligned mu PMU data;
performing upper layer state estimation according to the predicted SCADA data and the affine number model of the node injection uncertainty power, and determining an affine number result of the upper layer state estimation, wherein the method specifically comprises the following steps:
measurement equation z using upper layer state estimation 1 ＝h 1 (x (1) ) +r determining affine number results of the upper layer estimation; wherein z is 1 The method comprises the steps of measuring the quantity, wherein the quantity comprises branch power obtained by SCADA measurement, node voltage amplitude and node injection uncertainty power; h is a 1 (x (1) ) Is a nonlinear equation; x is x (1) Is the state quantity x (1) Including the magnitude of the node voltageAnd phase angle>r is the measurement error, the state variable x (1) The iterative solution can be performed as follows:
wherein H (x) (1) ) Is Jacobian matrix, W 1 Is covariance matrix;
determining a power distribution network lower layer state estimation model of linear hybrid measurement by combining the affine number result of upper layer state estimation and the aligned mu PMU data;
estimating a model according to the lower layer state of the power distribution networkThe model determination affine number result specifically comprises: node voltage amplitudeAffine value of phase angle>The fluctuation interval of plus or minus alpha percent is added with the node voltage phasor measured by the mu PMU in real time and is used as affine quantity measurement of the lower layer estimation, and then the measurement equation is expressed as follows:
z 2 ＝h(x (2) )+ε 2
wherein z is 2 For the node voltage phasor affine interval, h measured in real time by the upper affine state estimation result and mu PMU 1 (x (1) ) Is a linear equation, ε 2 To measure error, the state variable resultsThe iterative solution can be performed as follows:
wherein E is a coefficient matrix of the measurement equation, W 2 Is covariance matrix;
results of the state variables obtainedThe affine form of node voltage magnitude and phase angle is expressed as:
wherein:estimating affine number results for final state, V ij 、θ ij To introduce a new noise element epsilon v,j 、ε θ,j Coefficients generated at that time;
converting the affine number result into an interval number;
and estimating the affine state of the power distribution network according to the interval number.
2. The method for estimating affine state of a power distribution network according to claim 1, wherein the converting the uncertainty interval containing the uncertainty of the output of the distributed power source and the fluctuation of the load of the photovoltaic power generation and the wind power generation into the form of affine number as the node injection uncertainty power specifically comprises:
the wind power probability model, the photovoltaic power generation probability model and the load fluctuation probability model are utilized, a 95% confidence interval is used as the interval output of the power uncertainty, and the interval output is converted into an affine number form to be used as the node injection uncertainty power;
(1) Taking a 95% confidence interval of a wind speed probability model with wind speed obeying double-parameter Weibull distribution as an interval of wind speed uncertainty, and combining the relation between output power and wind speed to output an active power intervalWherein,P i,wid the lower limit of the active power output of wind power generation; />An upper limit of active power output for wind power generation; when the fan operates with constant power factor, the output reactive power interval is +.>Wherein,q i,wid the lower limit of the reactive power output of the wind power generation is set; />The upper limit of reactive power output of wind power generation; converting two power intervals using affine mathIn the form of affine numbers:
wherein:the method is in an affine number form of active force of wind power generation; epsilon p,i,wid Active noise elements introduced for affine numbers of wind power generation; />The method is in a reactive power output affine number form of wind power generation; epsilon q,i,wid Reactive noise elements introduced for affine numbers of wind power generation;
(2) Taking a confidence interval of 95% of the photovoltaic cell output as the interval number form of photovoltaic power generation uncertainty, wherein the active power interval and the reactive power interval are respectively Wherein,P i,pv the lower limit of the active power output of the photovoltaic power generation is set;q i,pv the lower limit of the output of the reactive power of the photovoltaic power generation is set; />The upper limit of the active power output of the photovoltaic power generation is set; />The upper limit of the output of the reactive power of the photovoltaic power generation is satisfied, and the following active and reactive output constraints are satisfied:
(p i,pv ) 2 +(q i,pv ) 2 ≤(S i,pv ) 2
wherein S is i,pv Is complex power;
converting into affine number form by utilizing affine mathematical method:
wherein,the method is in an affine number form of active power output of photovoltaic power generation; epsilon p,i,pv Active noise elements introduced for affine numbers of photovoltaic power generation; />The method is in a reactive power output affine number form of photovoltaic power generation; epsilon q,i,pv Reactive noise elements introduced for affine numbers of photovoltaic power generation;
(3) The 95% confidence interval of the load fluctuation probability model is taken as the interval number form of the load fluctuation, and the active power interval and the reactive power interval are respectively Wherein,P i,load a lower active power output limit for load ripple;Q i,load a lower limit for load fluctuation reactive power output; />An upper active output limit for load fluctuation; />For the upper limit of load fluctuation reactive power output, converting into an affine number form by utilizing an affine mathematical method:
wherein, the noise element satisfies-1 ∈s p,i,load ,ε Q,i,load ≤1；The method is characterized in that the method is in an active power output affine number form of load fluctuation; epsilon p,i,load Active noise elements introduced for affine numbers of load fluctuations; />Affine number form of reactive power output of load fluctuation; epsilon Q,i,load Reactive noise elements are introduced for the affine number of load fluctuations.
3. The method for estimating affine state of a power distribution network according to claim 1, wherein the aligning the SCADA data and the μpmu data based on the temporal ductility of the SCADA of the data acquisition and monitoring control system, predicting the SCADA data by using an adaptive coefficient exponential smoothing method, and determining the predicted SCADA data and the aligned μpmu data specifically includes:
acquiring the expected E of the SCADA data measurement delay d Taking time at any time as E d +T s ；T s An arrival time of the mu PMU data;
at T s Searching the SCADA data in a taking range corresponding to the moment, and determining that the data in the taking range is T if the SCADA data exists s SCADA data corresponding to the moment;
using the formulaPredicting the SCADA data, and determining the predicted SCADA data; wherein alpha is t To become the coefficient, x t Is historical data; />For predictive value +.>Predicted values for the next time.
4. The method for estimating affine state of a power distribution network according to claim 1, wherein the aligning the SCADA data and the μpmu data based on the time ductility of the SCADA of the data acquisition and monitoring control system, predicting the SCADA data by using an adaptive coefficient exponential smoothing method, and after determining the predicted SCADA data and the aligned μpmu data, further comprises:
and (5) aligning and fusing the predicted SCADA data serving as the complementary pseudo measurement with the mu PMU data.
5. The method for estimating affine state of a power distribution network according to claim 1, wherein the converting the affine number result into an interval number specifically includes:
using the formulaConverting the affine number result into an interval number.
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