CN108448568B - Power distribution network hybrid state estimation method based on multiple time period measurement data - Google Patents

Power distribution network hybrid state estimation method based on multiple time period measurement data Download PDF

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CN108448568B
CN108448568B CN201810190874.6A CN201810190874A CN108448568B CN 108448568 B CN108448568 B CN 108448568B CN 201810190874 A CN201810190874 A CN 201810190874A CN 108448568 B CN108448568 B CN 108448568B
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state
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data
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CN108448568A (en
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刘晓亮
晋飞
吴金玉
刘惯红
黄海丽
唐敏
宋战慧
王娟娟
杨君仁
辛翠芹
杨文佳
马献丽
孙守鑫
邱正美
李国强
刘忠辉
卢晓惠
杨坤
管正弦
魏玉苓
刘芊
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State Grid Corp of China SGCC
Weifang Power Supply Co of State Grid Shandong Electric Power Co Ltd
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State Grid Corp of China SGCC
Weifang Power Supply Co of State Grid Shandong Electric Power Co Ltd
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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
    • 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
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • 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
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/70—Smart grids as climate change mitigation technology in the energy generation sector
    • 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
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • 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
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • 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
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/22—Flexible AC transmission systems [FACTS] or power factor or reactive power compensating or correcting units

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  • Power Engineering (AREA)
  • Supply And Distribution Of Alternating Current (AREA)
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Abstract

The invention discloses a power distribution network mixed state estimation method based on multiple time period measurement data. The proposed method can significantly shorten the period of estimation and provide real-time status information for advanced control applications like voltage control and system congestion control. The method is helpful for detecting the sudden change of the state. The robustness of the algorithm can be further optimized, and the influence of bad data and leverage points on the estimation result can be reduced. In addition, the details of the DKF process may be further optimized.

Description

Power distribution network hybrid state estimation method based on multiple time period measurement data
Technical Field
The invention relates to a power distribution network hybrid state estimation method based on multiple time period measurement data.
Background
The concept of power system state estimation was proposed in the 70 s of the 20 th century. Since then, state estimation has become an indispensable element in EMS systems, which can provide the operator of the power system with the current real-time state information of the system, and control and development of high-level applications of the system are performed on the basis of system state perception. The use of these techniques maximizes the utilization of current system assets and provides safeguards for safe, stable operation of the system. In traditional research, the distribution network is regarded as a single passive network, and the flow of energy is unidirectional only as a link from the transmission network to the users. In addition, the influence of the traditional power distribution network fault on the stability of a large power grid is very limited, so that the attention degree is low. In recent years, with the application of a large number of renewable energy power sources in a power distribution network system, the increase of new loads and the development of demand side response technologies and policies, the functions of a power distribution network are more comprehensive, and the importance of the power distribution network in the energy system is higher and higher. As the importance of power distribution networks has increased, the measurement and communication infrastructure in power distribution network systems has also improved.
The observability of the system is satisfied, certain redundancy is the basis of state estimation research, calculation of observability guarantee can be solved theoretically, and the redundancy of information can improve the estimation quality and facilitate identification and detection of bad data. In a power distribution network system, in order to make up for the deficiency of measured information, many Pseudo measurement information (Pseudo Measurements) are added in the past state estimation research. Over the past few decades, a great deal of literature has been devoted to the establishment of pseudo-metrology information and weight determination. The early pseudo measurement information is derived from load survey information based on an electric charge metering system, several load characteristic curves with typical characteristics are obtained by combining the influences of the load, the season, the time period and other factors on the load, which are obtained in the long-term power system operation process, and the pseudo measurement information set in the calculation is further determined by combining the capacity of each distribution transformer in a power distribution network. The obtained pseudo measurement information has high uncertainty and often has large access to actual load information. For a modern power distribution network system, because the controllability of a user on loads is greatly enhanced, and the number of movable loads such as type electric vehicles is increased, the traditional pseudo measurement information cannot adapt to the operation management requirements of the modern power distribution network.
The energy internet system comprises a primary energy system, an electric power system and an information system, and emphasizes the maximization of comprehensive energy efficiency. From the perspective of the energy internet, the power distribution network system becomes an interface between a large power grid system and a primary energy system and a data system. The energy internet is an information System (Cyber-Physical System) and has an open interface, and power enterprises and various users participate together to ensure that more information and data are reliably processed. The change of the operating conditions of the power system has certain influence on the optimal operating state of the energy system. New measurement technologies, including synchrophasor measurement technologies and advanced measurement systems (AMI), offer great possibilities for better performing state estimation studies.
The synchronous phasor measurement technology provides an accurate time synchronization characteristic by a GPS signal, can accurately measure amplitude and phase information in a power system and has high information uploading frequency. PMUs (power management units) are currently used as terminals for synchrophasor measurement technologies, covering all substations of 500KV and higher voltage levels and most 220KV substations. With the technical development and the continuous reduction of the cost of the Micro-PMU, the PMU is expected to play an important role in the state estimation of the power distribution network. An RTU (Remote Terminal Unit) is used for monitoring, controlling and data acquisition. Has the functions of remote measurement, remote signaling, remote regulation and remote control. The AMI (advanced measurement infrastructure) comprises a smart meter, a data communication network and a data concentrator, and can acquire user or centralized load information and upload the information at certain time intervals (15 minutes or 30 minutes). The application of AMI technology enables the load information of the nodes not to be black boxes any more, and provides more powerful support for the pseudo-measurement information data. The current widespread use of smart meters on the consumer side has led to the power distribution network System being referred to from an Underdetermined System as an Overdetermined System.
Disclosure of Invention
The invention aims to solve the problems and provides a power distribution network mixed state estimation method based on various time period measurement data, which is used for researching a state estimation result with short time limit and high quality obtained by data fusion of various information based on the current situation of current power distribution network system measurement and an information system; on the other hand, by introducing reasonable technology, the problems of excessive investment on the infrastructure level and the maintenance difficulty caused by the excessive investment are avoided.
In order to achieve the purpose, the invention adopts the following technical scheme that:
the invention discloses a power distribution network hybrid state estimation method based on multiple time period measurement data, which comprises the following steps of:
(1) determining topological structure information of the power distribution network system and installation conditions of different measuring devices, including type and quantity information;
(2) determining the data acquisition frequency of each of PMU, RTU and AMI measuring devices in the power distribution network system according to specific manufacturer instructions and system state estimation needs;
(3) determining a system state variable used in calculation according to a topological structure of the system and a load investigation condition;
(4) carrying out load flow calculation according to the load investigation condition, and taking the calculation result as an initial value of a system state variable;
(5) determining an initial prediction model error matrix Q;
(6) predicting the state by using a Holt two-parameter exponential smoothing method to obtain a predicted state variable
Figure GDA0002288923820000031
Prediction of a measured variable
Figure GDA0002288923820000032
And predicting state variables
Figure GDA0002288923820000033
Covariance matrix of
Figure GDA0002288923820000034
(7) When the actual measurement data of the PMU is updated, whether bad data exist or the running state of the system changes is determined according to the difference value between the predicted value and the actual measurement value of the measurement variable;
if the above condition does not exist, using Kalman filter method to calculate and obtain the corrected state variable
Figure GDA0002288923820000035
And estimating a covariance matrix of the state variables
Figure GDA0002288923820000036
(8) When the RTU measured data is updated, carrying out rectangular coordinate processing on the information directly measured by the RTU by using the result of the last linear dynamic state estimation;
(9) establishing a state estimation objective function according to actual measurement data of PMU and RTU and node injection current or load current equivalent to AMI last time, and calculating system state variable by using a linear least square method
Figure GDA0002288923820000037
Figure GDA0002288923820000038
The estimated reference state vector is used as the dynamic state estimation of the next moment, and the linear prediction is carried out on the pseudo measurement data of the next RTU data updating moment;
(10) when AMI measurement data is updated, converting the information of load power or node injection power into equivalent node injection current or load current;
(11) and according to actual measurement data of the PMU, the RTU and the AMI, estimating the static linear state of the whole system to obtain a system state variable vector x.
Further, in the step (6), a predicted state variable is obtained
Figure GDA0002288923820000039
The method specifically comprises the following steps:
using Holt two-parameter exponential smoothing method to process state variable under k time
Figure GDA00022889238200000310
Performing calculations with parameters α and β between 0 and 1;
Figure GDA0002288923820000041
Fk＝α·(1+β)·I
Figure GDA0002288923820000042
Figure GDA0002288923820000043
Figure GDA0002288923820000044
predicting state variables
Figure GDA0002288923820000045
Covariance matrix of
Figure GDA0002288923820000046
The method specifically comprises the following steps:
Figure GDA0002288923820000047
wherein,
Figure GDA0002288923820000048
representing the predicted value of the state variable at time k,
Figure GDA0002288923820000049
for the state variables after correction, matrix FkIs a transition matrix of state variables from time k-1 to time k, gkIs a control variable for calculating the predicted value of the state variable; sk、bkRespectively intermediate amounts;
Figure GDA00022889238200000410
a covariance matrix representing the predicted values of the state variables at time k,
Figure GDA00022889238200000411
covariance matrix of the estimated state variable after correction.
Further, in the step (6), a predicted value of the measured variable is obtained
Figure GDA00022889238200000417
The method specifically comprises the following steps:
the measured variables include: real and imaginary parts of the node voltage; the real part and the imaginary part of the branch current; injecting real and imaginary parts of current into the nodes;
and (c) calling a function H (x) to calculate a measurement variable, wherein H (x) is H x, and H is a Jacobian matrix:
Figure GDA00022889238200000412
a) for node voltages, the corresponding h (x) function is as follows:
Figure GDA00022889238200000413
Figure GDA00022889238200000414
b) for the branch current, the corresponding h (x) function is as follows:
Figure GDA00022889238200000415
Figure GDA00022889238200000416
c) for the node injection current, the addition and subtraction of several branch current phases are written according to the KCL definition.
Wherein, Ibr、IbxRespectively the real and imaginary parts, V, of the branch currenti r、Vi xVoltage real and imaginary parts, V, of node i, respectivelys r、Vs xThe real and imaginary parts, r, of the root node voltage, respectivelykIs the resistance of branch k, xkIs the reactance of branch k, /)iRepresenting a path from the root node to node i.
Further, in the step (7), the state change after the correction is calculatedMeasurement of
Figure GDA0002288923820000051
And estimating a covariance matrix of the state variables
Figure GDA0002288923820000052
The method specifically comprises the following steps:
Figure GDA0002288923820000053
Figure GDA0002288923820000054
Figure GDA0002288923820000055
wherein R iszkAs a matrix of standard deviations of the measured information, KkReferred to as a Kalman gain matrix, is,
Figure GDA0002288923820000056
in order to correct the state variable after the correction,
Figure GDA0002288923820000057
a covariance matrix which is the state information variable after correction;
Figure GDA0002288923820000058
representing the predicted value of the state variable at time k,
Figure GDA0002288923820000059
a covariance matrix representing the predicted value of the state variable at the time k;
Figure GDA00022889238200000510
Figure GDA00022889238200000511
for measuring information zkIs estimated, corresponding toThe covariance matrix of (a) is:
Figure GDA00022889238200000512
Hkis the Jacobian matrix below time k.
Further, in the step (7), determining whether there is bad data or the operation state of the system changes, specifically:
Figure GDA00022889238200000513
calculating variable vkNormalized form of (a):
Figure GDA00022889238200000514
wherein,
Figure GDA00022889238200000515
for the predicted value of the measured variable, zkIs the measured value of the measured variable; v. ofk,iAn ith value representing a difference between an actually measured value and a predicted value of the measured variable,
Figure GDA00022889238200000516
representing the difference between the actual and predicted values of the normalized measured variable, RkThe covariance matrix of the measured data and H are the size of a Jacobian matrix;
setting a threshold t, comparing the variables
Figure GDA0002288923820000061
And a threshold value t; if it is not
Figure GDA0002288923820000062
And if the threshold value t is smaller than the threshold value t, the system is considered to be in a stable operation state, and the influence of bad data is not considered.
Further, in the step (8), the information directly measured by the RTU is processed by rectangular coordinate, specifically:
Figure GDA0002288923820000063
wherein,
Figure GDA0002288923820000064
is the real part of the voltage estimated value obtained after rectangular coordinate processing,
Figure GDA0002288923820000065
the imaginary part of the voltage estimation value is obtained after rectangular coordinate processing;
Figure GDA0002288923820000066
respectively the real part and the imaginary part of the node voltage estimated at the last moment,
Figure GDA0002288923820000067
respectively obtaining a real part and an imaginary part of the branch current estimated at the last moment; vm,iNode voltage amplitude, I, measured for RTUm,iAnd directly measuring the obtained branch current amplitude for the RTU.
Further, in the step (9), an objective function of state estimation is established, specifically:
J＝(zpmu-hpmu)TWpmu(zpmu-hpmu)+(zrtu-hrtu)TWrtu(zrtu-hrtu)+(zpseudo-hpseudo)TWpseudo(zpseudo-hpseudo)
wherein z ispmuIs a measurement data vector, h, provided by the PMUpmuIs a calculated value corresponding to a PMU data vector, WpmuIs a weight matrix for PMU data; z is a radical ofrtuIs a measurement data vector, h, provided by the RTUrtuIs a calculated value, W, corresponding to a measured data vector provided by the RTUrtuIs a weight matrix corresponding to RTU data; z is a radical ofpseudoIs the last pseudo-measured data vector, hpseudoIs a pseudo-measurement vector, W, calculated from the current state variablespseudoA pseudo metrology data weight matrix.
Further, in the step (9), the linear prediction is performed on the pseudo measurement data at the next RTU data update time, and the specific implementation method is as follows:
Figure GDA0002288923820000071
wherein, tkFrom tj-1Time tjTaking each RTU data update as an interval between moments; z is a radical ofp,kRTU measurement data corresponding to time k, zp,jRTU measurement data corresponding to time j, TpThe data update period is measured for the RTU.
Further, in the step (10), the active load, reactive load and concentrated load variables of the user directly measured by the AMI are converted into a node injection power form, specifically:
Figure GDA0002288923820000072
wherein,
Figure GDA0002288923820000073
is the real part of the equivalent current injected by the node,
Figure GDA0002288923820000074
is the imaginary part, P, of the node injected equivalent currentinj,iIs node injection active power, Q, provided by AMIinj,iIs node injected reactive power, V, provided by AMIi rIs the estimated value of the real part of the node voltage, V, obtained at the last momenti xIs the estimated value of the imaginary part of the node voltage obtained at the last moment.
Further, in the step (11), according to measured data of the PMU, the RTU, and the AMI, a full-system static linear state estimation is performed to obtain a system state variable vector x, which specifically includes:
establishing an objective function of state estimation:
J＝(zpmu-hpmu)TWpmu(zpmu-hpmu)+(zrtu-hrtu)TWrtu(zrtu-hrtu)+(zpseudo-hpseudo)TWpseudo(zpseudo-hpseudo)
wherein z ispmuIs a measurement data vector, h, provided by the PMUpmuIs a calculated value corresponding to a PMU data vector, WpmuIs a weight matrix for PMU data; z is a radical ofrtuIs a measurement data vector, h, provided by the RTUrtuIs a calculated value, W, corresponding to a measured data vector provided by the RTUrtuIs a weight matrix corresponding to RTU data; z is a radical ofpseudoIs a measurement data vector, h, provided by AMIpseudoIs a calculated value corresponding to a measured data vector provided by AMI, WpseudoA pseudo metrology data weight matrix.
The invention has the beneficial effects that:
the inventive method can significantly shorten the period of estimation and provide real-time status information for advanced control applications like voltage control and system congestion control. The method is helpful for detecting the sudden change of the state. The method can further reduce the influence of bad data and leverage points on the estimation result by optimizing the robustness of the algorithm. In addition, the details of the dkf (discrete Kalman filter) process can be further optimized.
Drawings
FIG. 1 is a schematic diagram of a hybrid power distribution network state estimation method according to the present invention;
FIG. 2 is a single line diagram of an IEEE-69 node system;
fig. 3 is the active injected power at node 38;
FIG. 4 is a graph of the voltage amplitude at node 9;
fig. 5 shows the voltage amplitude at node 5.
The specific implementation mode is as follows:
the invention will be further explained with reference to the drawings.
Kalman Filter principle
The Kalman filter is applied to the dynamic state estimation research of a linear system, and the whole process is divided into two parts: a prediction step and a filtering step. In the prediction link, the numerical value to be predicted and the corresponding covariance matrix are subjected to certain prediction,
Figure GDA0002288923820000081
Figure GDA0002288923820000082
Figure GDA0002288923820000083
wherein Fk-1The matrix connects the state variables of the system at two moments k-1 and k, qkRepresenting process errors in the prediction.
The second step is a filtering estimation part, which updates the state value by using the latest actually measured data.
Figure GDA0002288923820000084
Figure GDA0002288923820000085
Figure GDA0002288923820000086
Wherein the matrix KkIs a Gain Matrix (Gain Matrix). The estimation link of the Kalman filter is essentially a balance compromise of the predicted information and the actually measured information, and the judgment of the weight or the precision of different information is very important here.
The advantage of the Kalman filter is that it gives a reasonable interpretation to determine the weights that various information should have, and on the other hand the Kalman filter also provides more redundant information.
Holt’s Exponential Smoothing Method
Unlike the conventional linear dynamic system, the actual power system is a nonlinear system, and it is difficult to write the state variables (including node voltage vector and branch current vector) as the operating system, and the state variables are daes (differential and alternate equations) in a sequence of front and back time. Therefore, the prediction link needs to be supplemented according to the research in the aspects of statistics and linear regression.
The ARIMA (0,1,0) process model is applied to the research of partial dynamic state estimation, and the reason is that the data updating time interval of PMU is very small. This can be applied well under quasi-steady state condition, in order to capture the change characteristic of the state variable better, the invention uses the holt's linear exponential smoothing technique of two parameters. The method is characterized in that two parts of the current estimated level and the changing trend are considered simultaneously,
Sk+1＝αxk+(1-α)(Sk+bk) (7)
bk+1＝β(Sk+1-Sk)+(1-β)bk(8)
Figure GDA0002288923820000091
where the parameters a and β are directly settable, values between 0 and 1, equation (9) gives that the predicted value at time k +1 is given by two parts, i.e. the predicted estimated level and the trend of the change, equation (7) also gives that the estimated level S at time k +1 is divided into two parts, one being the final estimated result x at the previous time kkAnd the other is the predicted quantity S given at the previous momentk+bk。
Hybrid power distribution network state estimation scheme
As mentioned in the first section, there are three different measurement devices in the distribution network system, PMU, RTU and AMI. As shown in fig. 1, AMI in the present invention sets data update every 15 minutes, and if waiting for all the latest measurement information to appear, it will wait for every 15 minutes to perform static state estimation calculation, which does not meet the requirement of state sensing of modern power distribution systems. The RTU measured voltage amplitude and branch current amplitude information, the update frequency is to update data every 20 seconds. PMUs can upload 50 data per second as previously described. The whole process has three parts: only the time period when the PMU data is updated, the time when the PMU and RTU data are updated, and the time when the PMU, RTU and AMI data exist. For the first two cases, the system has a great problem in observability and data redundancy, and needs to add pseudo-metric information.
In the invention, the state estimation of the power distribution network based on branch current is selected, the state variable of the system is selected as the voltage of a root node (connected with a large power grid) and the real part and the imaginary part of each branch current, the calculation is carried out by utilizing a rectangular coordinate system, the linearization of the whole calculation process is convenient,
Figure GDA0002288923820000101
the relationship between the information measured by the PMUs and the state variables is linear and constant, and the corresponding Jacobian matrix does not need to be modified. For the current vector measurement itself, there is a relationship between 0 and 1 with the state variable, and the corresponding parameters between the voltage measurement information and the state variable are determined entirely by the topology of the system and the parameters of the line or other components.
The information measured by the RTU is a nonlinear functional relationship of state variables, and in order to make the calculation process more efficient, it is necessary to perform rectangular coordinate processing on the measured information. An ideal method is to fuse the amplitude information by using the linear dynamic estimation result to obtain the real part and the imaginary part of the electrical quantity.
Figure GDA0002288923820000102
In formula (11)
Figure GDA0002288923820000103
And
Figure GDA0002288923820000104
respectively, the node electric compaction estimated at the last momentThe real and imaginary parts of the branch current. The variable weights derived from equation (11) also need to be modified according to equation (11). Through rectangular coordinate processing, the Jacobian matrix element corresponding to the RTU measurement information is also fixed and unchangeable, and the content of the element is only 0 or 1.
Variables directly measured by AMI include active load and reactive load of users and concentrated load of a plurality of users, and are presented in a system in a node injection power form, the node injection power can be expressed into a linear function of a branch circuit (information of a Jacobian matrix needs to be updated) and can also be converted into a node injection power form, the latter method is selected in the invention to process according to a formula (12) and process uncertainty characteristics after conversion,
Figure GDA0002288923820000111
in the formula (12), the variable Pinj,i,And Qinj,iThe information is not available at every moment, and the corresponding node injection current information is obtained through the SE calculation at the previous moment when AMI does not perform data updating. After processing according to equation (12), the corresponding Jacobian matrix partial elements have a relationship only with the node-branch incidence matrix.
The reason for this is that: firstly, all elements of a Jacobian matrix are derived from parameters of 0,1 and a line, and the matrix is kept constant; the condition number of the Jacobian matrix H is reduced.
The update of AMI data is considered as a flag for one completion cycle. When new AMI data information (power injection information derived from the smart meter system) is available, the system completes the state estimation in accordance with the rigorous WLS calculations.
The detailed implementation process of the method for estimating the hybrid state of the power distribution network based on the measurement data of various time periods is described in detail below, and the method specifically comprises the following steps:
(1) determining topological structure information of the power distribution network system and installation conditions of different measuring devices, including type and quantity information;
(2) determining the data acquisition frequency of each of PMU, RTU and AMI measuring devices in the power distribution network system according to specific manufacturer instructions and system state estimation needs;
(3) determining a system state variable used in calculation according to a topological structure of the system and a load investigation condition;
(4) carrying out load flow calculation according to the load investigation condition, and taking the calculation result as an initial value of a system state variable;
(5) determining an initial prediction model error matrix Q;
the prediction model error matrix Q is a diagonal matrix with initial elements set to 1 × 10-6。
(6) Predicting the state by using a Holt two-parameter exponential smoothing method to obtain a predicted state variable
Figure GDA0002288923820000112
Prediction of a measured variable
Figure GDA0002288923820000113
And predicting state variables
Figure GDA0002288923820000114
Covariance matrix of
Figure GDA0002288923820000115
Using the Holt two-parameter exponential processing (Holt's two-parameter exponential smoothing) method, firstly, the state variable under the k time is processed
Figure GDA0002288923820000121
Calculations were performed with parameters α and β between 0-1.
Figure GDA0002288923820000122
Fk＝α·(1+β)·I
Figure GDA0002288923820000123
Figure GDA0002288923820000124
bk＝β(Sk-Sk-1)+(1-β)·bk-1
Wherein,
Figure GDA0002288923820000125
representing the predicted values of the state variables at time k, matrix FkIs the state variable transition matrix from time k-1 to time k, gkIs a control variable for calculating the predicted value of the state.
Covariance matrix for prediction
Figure GDA0002288923820000126
Figure GDA0002288923820000127
Measurement variable components: real and imaginary parts of the node voltage; the real part and the imaginary part of the branch current; the nodes inject the real and imaginary parts of the current.
The function H (x) is called to calculate the measured variable, and in the linear condition, the calculation methods of H (x) ═ H × x, the function H (x) and the Jacobian matrix H are explained as follows.
Figure GDA0002288923820000128
For node voltage, the h (x) function is as follows
Figure GDA0002288923820000129
Figure GDA00022889238200001210
The corresponding portion of Jacobian matrix H is as follows
Figure GDA00022889238200001211
Figure GDA00022889238200001212
Figure GDA00022889238200001213
Figure GDA0002288923820000131
Figure GDA0002288923820000132
For the branch current, the corresponding h (x) function is as follows
Figure GDA0002288923820000133
Figure GDA0002288923820000134
The corresponding portion of Jacobian matrix H is as follows
Figure GDA0002288923820000135
Figure GDA0002288923820000136
Figure GDA0002288923820000137
Figure GDA0002288923820000138
For the node injection current, no matter the element corresponding to the h (x) expression and the Jacobian matrix can be written into a form of addition and subtraction of several branch current phases according to the KCL definition, and details are not repeated.
(7) When the actual measurement data of the PMU is updated, whether bad data exist or the running state of the system changes is determined according to the difference value between the predicted value and the actual measurement value of the measurement variable;
if bad data exist or the operation state of the system changes, a proper method is selected for processing according to the data redundancy condition. Otherwise, calculating to obtain the corrected state variable by using a Kalman filter method
Figure GDA0002288923820000139
And estimating a covariance matrix of the state variables
Figure GDA00022889238200001310
The method for judging whether bad data exist or not or the operation state of the system changes comprises the following steps:
computing
Figure GDA00022889238200001311
A normalized form of the variable vk is calculated,
Figure GDA00022889238200001312
comparing the obtained variables
Figure GDA0002288923820000141
And a set threshold value t, which is set here by empirical values. If the value is less than the threshold value t, the system is considered to be in a (quasi-) stable operation state, and the influence of bad data is not considered.
Calculating the corrected state variable
Figure GDA0002288923820000142
And estimating a covariance matrix of the state variables
Figure GDA0002288923820000143
The method specifically comprises the following steps:
Figure GDA0002288923820000144
Figure GDA0002288923820000145
Figure GDA0002288923820000146
wherein R iszkAs a matrix of standard deviations of the measured information, KkReferred to as a Kalman gain matrix, is,
Figure GDA0002288923820000147
is the state variable after correction.
Figure GDA0002288923820000148
Figure GDA0002288923820000149
For the estimator of the measurement information at time k, the corresponding covariance matrix is:
Figure GDA00022889238200001410
(8) when the RTU measured data is updated, the result of the last linear dynamic state estimation is utilized to carry out rectangular coordinate processing on the information directly measured by the RTU, and the method specifically comprises the following steps:
Figure GDA00022889238200001411
wherein,
Figure GDA00022889238200001412
is a rectangular seatThe real part of the voltage estimate obtained after the normalization process,
Figure GDA00022889238200001413
the imaginary part of the voltage estimation value is obtained after rectangular coordinate processing;
Figure GDA00022889238200001414
respectively the real part and the imaginary part of the node voltage estimated at the last moment,
Figure GDA00022889238200001415
respectively obtaining a real part and an imaginary part of the branch current estimated at the last moment; vm,iNode voltage amplitude, I, measured for RTUm,iAnd directly measuring the obtained branch current amplitude for the RTU.
(9) Establishing a state estimation objective function according to actual measurement data of PMU and RTU and node injection current or load current equivalent to AMI last time, and calculating system state variable by using a linear least square method
Figure GDA0002288923820000151
Figure GDA0002288923820000152
The estimated state vector is used as a reference state vector of the dynamic state estimation at the next moment, and the linear prediction is carried out on the pseudo measurement data (node injection current) at the next RTU data updating moment;
establishing an objective function of state estimation, specifically:
J＝(zpmu-hpmu)TWpmu(zpmu-hpmu)+(zrtu-hrtu)TWrtu(zrtu-hrtu)+(zpseudo-hpseudo)TWpseudo(zpseudo-hpseudo)
wherein z ispmuIs a measurement data vector, h, provided by the PMUpmuIs a calculated value corresponding to a PMU data vector, WpmuIs a weight matrix for PMU data; z is a radical ofrtuIs RTMeasurement data vector, h, provided by UrtuIs a calculated value, W, corresponding to a measured data vector provided by the RTUrtuIs a weight matrix corresponding to RTU data; z is a radical ofpseudoIs the last pseudo-measured data vector, hpseudoIs a pseudo-measurement vector, W, calculated from the current state variablespseudoA pseudo metrology data weight matrix.
The method for linearly predicting the pseudo measurement data at the next RTU data updating moment comprises the following specific steps:
Figure GDA0002288923820000153
wherein, tkIs from tj-1Time tjOne time between the moments, with each RTU data update as an interval.
(10) When AMI measurement data is updated, converting the information of load power or node injection power into equivalent node injection current or load current; the method specifically comprises the following steps:
Figure GDA0002288923820000154
wherein,
Figure GDA0002288923820000156
is the real part of the equivalent current injected by the node,
Figure GDA0002288923820000155
is the imaginary part, P, of the node injected equivalent currentinj,iIs node injection active power, Q, provided by AMIinj,iIs node injected reactive power, V, provided by AMIi rIs the estimated value of the real part of the node voltage, V, obtained at the last momenti xIs the estimated value of the imaginary part of the node voltage obtained at the last moment.
(11) And according to actual measurement data of the PMU, the RTU and the AMI, estimating the static linear state of the whole system to obtain a system state variable vector x.
The specific implementation method comprises the following steps:
the objective function is established as follows:
Min J＝(zpmu-hpmu)TWpmu(zpmu-hpmu)+(zrtu-hrtu)TWrtu(zrtu-hrtu)+(zpseudo-hpseudo)TWpseudo(zpseudo-hpseudo)
calculation using WLS (weighted least squares method);
Figure GDA0002288923820000161
Δzk＝zmk-h(xk)
zmk＝[zpmu,zrtu,zpseudo]T
h(xk)＝[hpmu,hrtu,hpseudo]T
Figure GDA0002288923820000162
hpmusee step (6);
hrtuthe processing (voltage amplitude and branch current amplitude) of (1) is as follows:
Figure GDA0002288923820000166
Figure GDA0002288923820000163
Figure GDA0002288923820000164
representing the voltage amplitude, delta, of node iiIs the voltage phase of node i, /)iRepresenting a path from the root node to node i.
Figure GDA0002288923820000165
hpseudoSee step (6);
H＝[Hpmu；Hrtu；Hpseudo]。
it should be noted that, the least square method is used in both the step (9) and the step (11), but the corresponding scenarios are different, and the sources of the used measurement information z are not completely the same. Step (9) corresponds to the updating of only PMU and RTU real-time data, and the node injection power or the node injection current is estimated through the previous estimation result; and (11) updating PMU, RTU and AMI data, and directly using real-time data for calculation.
Simulation case analysis
In this section, two simulation analyses were performed using an IEEE 69 node power distribution network system. The first simulation case is used to illustrate the ability of the branch current and DKF based state estimation method to track the state of the system. For better illustration, results obtained with a WLS-based method were also compared together. The second simulation case gives the above-mentioned result of the power distribution network comprehensive state estimation strategy.
A. Testing for traceability
Figure 2 gives a single line diagram of a 69 node system. The IEEE 69 node system is a fully radial distributed three-phase balanced system. The relevant parameters and basic power flow information can be consulted in the existing literature.
To test the ability of the DKF method to track system state variables with a limited number of PMUs, the results of the two methods are compared: the results obtained using the DKF method and the results obtained using the conventional WLS method. Both methods were compared under the same conditions (including the load case).
The measurement error of the node injection power variable in the system is considered to follow a normal distribution law with a mean value of 0. The standard deviation of the distribution is set in such a way that the maximum error does not exceed 20% of the measured value. The results of the active injected power at node 38 are given in fig. 3, and the voltage amplitude at node 9 is given in fig. 4.
The simulation shows 50 different time points, and the result shows that the DKF-based method can obtain a method which is not inferior to the WLS method within a certain time range. It has to be noted that in a real scenario, it is not possible for the system's operational engineer to get the system's node injection power information at every moment. The purpose of this simulation is only to demonstrate the effectiveness and potential applicability of the DKF-based method.
A. Case analysis under mixed measurement information
In this section, the simulation involved three measurement techniques with different time periods. As shown in fig. 1, the state estimation calculation based on DKF is performed every two seconds. Linear WLS (weighted Least Square) state estimation is performed every 20 seconds, using information including real-time measurement information from PMUs and RTUs and pseudo-measurement information for node injection power presentation. WLS calculations based on all actual measurement information were performed every 15 minutes.
The amplitude measurement error of the PMU is set to be less than 1% of the actual value, the measurement error of the phase can be set according to the maximum error of the time synchronization signal, and the time error of the GPS is within 1 microsecond according to the current technical standard. The measurement error of the RTU information is set to be less than 2% of the true value. The error setting for the AMI actual measurement is less than 5% of the true quantity. The above errors are all considered to follow a normal distribution.
Fig. 5 gives information on the magnitude of the voltage at the fifth node in the system. The line with greater undulations represents the estimated value and the substantially smooth line represents the true value. Compared with the real numerical value, the estimated result has an error within 0.2 percent, and meets the requirement of power distribution network state estimation.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.

Claims (10)

1. The method for estimating the hybrid state of the power distribution network based on the measurement data of various time periods is characterized by comprising the following steps of:
(1) determining topological structure information of the power distribution network system and installation conditions of different measuring devices, including type and quantity information;
(2) determining the data acquisition frequency of each of PMU, RTU and AMI measuring devices in the power distribution network system according to specific manufacturer instructions and system state estimation needs;
(3) determining a system state variable used in calculation according to a topological structure of the system and a load investigation condition;
(4) carrying out load flow calculation according to the load investigation condition, and taking the calculation result as an initial value of a system state variable;
(5) determining an initial prediction model error matrix Q;
(6) predicting the state by using a Holt two-parameter exponential smoothing method to obtain a predicted state variable
Figure FDA0002306152370000011
Prediction of a measured variable
Figure FDA0002306152370000012
And predicted state variables
Figure FDA0002306152370000013
Covariance matrix of
Figure FDA0002306152370000014
(7) When the actual measurement data of the PMU is updated, whether bad data exist or the running state of the system changes is determined according to the difference value between the predicted value and the actual measurement value of the measurement variable;
if the above condition does not exist, using Kalman filter method to calculate and obtain the corrected state variable
Figure FDA0002306152370000015
And estimating a covariance matrix of the state variables
Figure FDA0002306152370000016
(8) When the RTU measured data is updated, carrying out rectangular coordinate processing on the information directly measured by the RTU by using the result of the last linear dynamic state estimation;
(9) establishing a state estimation objective function according to actual measurement data of PMU and RTU and node injection current or load current equivalent to AMI last time, and calculating system state variable by using a linear least square method
Figure FDA0002306152370000017
Figure FDA0002306152370000018
The estimated reference state vector is used as the dynamic state estimation of the next moment, and the linear prediction is carried out on the pseudo measurement data of the next RTU data updating moment;
(10) when AMI measurement data is updated, converting the information of load power or node injection power into equivalent node injection current or load current;
(11) and according to actual measurement data of the PMU, the RTU and the AMI, estimating the static linear state of the whole system to obtain a system state variable vector x.
2. The method for estimating hybrid state of distribution network based on multiple time period measurement data according to claim 1, wherein in the step (6), the predicted state variable is obtained
Figure FDA0002306152370000021
The method specifically comprises the following steps:
using Holt two-parameter exponential smoothing method to predict state variable under k time
Figure FDA0002306152370000022
Performing calculations with parameters α and β between 0 and 1;
Figure FDA0002306152370000023
Fk＝α·(1+β)·I
Figure FDA0002306152370000024
Figure FDA0002306152370000025
bk＝β(Sk-Sk-1)+(1-β)·bk-1
predicting state variables
Figure FDA0002306152370000026
Covariance matrix of
Figure FDA0002306152370000027
The method specifically comprises the following steps:
Figure FDA0002306152370000028
wherein,
Figure FDA0002306152370000029
for the state variables after correction, matrix FkIs a transition matrix of state variables from time k-1 to time k, gkIs a control variable for calculating the predicted value of the state variable; sk、bkRespectively intermediate amounts;
Figure FDA00023061523700000210
a covariance matrix representing the predicted values of the state variables at time k,
Figure FDA00023061523700000211
covariance matrix of the estimated state variable after correction.
3. The method for estimating hybrid state of distribution network based on multiple time period measurement data according to claim 1, wherein in the step (6), the predicted values of the measurement variables are obtained
Figure FDA00023061523700000212
The method specifically comprises the following steps:
the measured variables include: real and imaginary parts of the node voltage; the real part and the imaginary part of the branch current; injecting real and imaginary parts of current into the nodes;
and (c) calling a function H (x) to calculate a measurement variable, wherein H (x) is H x, and H is a Jacobian matrix:
Figure FDA00023061523700000213
for node voltages, the corresponding h (x) function is as follows:
Figure FDA00023061523700000214
Figure FDA00023061523700000215
for the branch current, the corresponding h (x) function is as follows:
Figure FDA0002306152370000031
Figure FDA0002306152370000032
for node injection current, writing a mode of adding and subtracting a plurality of branch current phases according to KCL definition;
wherein,Ibr、Ibxrespectively the real and imaginary parts, V, of the branch currenti r、Vi xRespectively the real and imaginary parts of the voltage at node i,
Figure FDA0002306152370000033
the real and imaginary parts, r, of the root node voltage, respectivelykIs the resistance of branch k, xkIs the reactance of branch k, /)iRepresenting a path from the root node to node i.
4. The method for estimating hybrid state of distribution network based on multiple time period measurement data according to claim 1, wherein in the step (7), the state variable after being corrected is calculated
Figure FDA0002306152370000034
And estimating a covariance matrix of the state variables
Figure FDA0002306152370000035
The method specifically comprises the following steps:
Figure FDA0002306152370000036
Figure FDA0002306152370000037
Figure FDA0002306152370000038
wherein R iszkAs a matrix of standard deviations of the measured information, KkIn the form of a Kalman gain matrix, the matrix,
Figure FDA0002306152370000039
in order to correct the state variable after the correction,
Figure FDA00023061523700000310
a covariance matrix which is the state information variable after correction;
Figure FDA00023061523700000311
representing the predicted value of the state variable at time k,
Figure FDA00023061523700000312
a covariance matrix representing the predicted value of the state variable at the time k;
Figure FDA00023061523700000313
Figure FDA00023061523700000314
for measuring information zkThe corresponding covariance matrix is:
Figure FDA00023061523700000315
Hkis the Jacobian matrix below time k.
5. The method for estimating the hybrid state of the power distribution network based on the measurement data of multiple time periods as claimed in claim 1, wherein in the step (7), it is determined whether there is bad data or the operation state of the system changes, specifically:
Figure FDA00023061523700000316
calculating variable vkNormalized form of (a):
Figure FDA0002306152370000041
wherein,
Figure FDA0002306152370000042
for measuring variablesPredicted value, zkIs the measured value of the measured variable; v. ofk,iAn ith value representing a difference between an actually measured value and a predicted value of the measured variable,
Figure FDA0002306152370000043
representing the difference between the actual and predicted values of the normalized measured variable, RkThe covariance matrix of the measured data and H are the size of a Jacobian matrix;
setting a threshold t, comparing the variables
Figure FDA0002306152370000044
And a threshold value t; if it is not
Figure FDA0002306152370000045
And if the threshold value t is smaller than the threshold value t, the system is considered to be in a stable operation state, and the influence of bad data is not considered.
6. The method for estimating the hybrid state of the power distribution network based on the measurement data of multiple time periods as claimed in claim 1, wherein in the step (8), the information directly measured by the RTU is processed by rectangular coordinate, specifically:
Figure FDA0002306152370000046
wherein,
Figure FDA0002306152370000047
is the real part of the voltage estimated value obtained after rectangular coordinate processing,
Figure FDA0002306152370000048
the imaginary part of the voltage estimation value is obtained after rectangular coordinate processing;
Figure FDA0002306152370000049
respectively the real part and the imaginary part of the node voltage estimated at the last moment,
Figure FDA00023061523700000410
respectively obtaining a real part and an imaginary part of the branch current estimated at the last moment; vm,iNode voltage amplitude, I, measured for RTUm,iAnd directly measuring the obtained branch current amplitude for the RTU.
7. The method for estimating the hybrid state of the power distribution network based on the measurement data of the multiple time periods as claimed in claim 1, wherein in the step (9), an objective function of state estimation is established, specifically:
J＝(zpmu-hpmu)TWpmu(zpmu-hpmu)+(zrtu-hrtu)TWrtu(zrtu-hrtu)+(zpseudo-hpseudo)TWpseudo(zpseudo-hpseudo)
wherein z ispmuIs a measurement data vector, h, provided by the PMUpmuIs a calculated value corresponding to a PMU data vector, WpmuIs a weight matrix for PMU data; z is a radical ofrtuIs a measurement data vector, h, provided by the RTUrtuIs a calculated value, W, corresponding to a measured data vector provided by the RTUrtuIs a weight matrix corresponding to RTU data; z is a radical ofpseudoIs the last pseudo-measured data vector, hpseudoIs a pseudo-measurement vector, W, calculated from the current state variablespseudoIs a pseudo metrology data weight matrix.
8. The method for estimating the hybrid state of the power distribution network based on the measurement data of multiple time periods as claimed in claim 1, wherein in the step (9), the pseudo measurement data at the next RTU data update time is linearly predicted, and the specific implementation method is as follows:
Figure FDA0002306152370000051
wherein, tkFrom tj-1Time tjTaking each RTU data update as an interval between moments; z is a radical ofp,kRTU measurement data corresponding to time k, zp,jRTU measurement data corresponding to time j, TpThe data update period is measured for the RTU.
9. The method for estimating the hybrid state of the power distribution network based on the measurement data of multiple time periods as claimed in claim 1, wherein in the step (10), the user active, reactive load and concentrated load variables directly measured by the AMI are converted into a form of node injection power, specifically:
Figure FDA0002306152370000052
wherein,
Figure FDA0002306152370000053
is the real part of the equivalent current injected by the node,
Figure FDA0002306152370000054
is the imaginary part, P, of the node injected equivalent currentinj,iIs node injection active power, Q, provided by AMIinj,iIs node injected reactive power, V, provided by AMIi rIs the estimated value of the real part of the node voltage, V, obtained at the last momenti xIs the estimated value of the imaginary part of the node voltage obtained at the last moment.
10. The method for estimating hybrid state of power distribution network based on multiple time period measurement data according to claim 1, wherein in step (11), a system-wide static linear state estimation is performed according to measured data of PMU, RTU, and AMI to obtain a system state variable vector x, specifically:
establishing an objective function of state estimation:
J＝(zpmu-hpmu)TWpmu(zpmu-hpmu)+(zrtu-hrtu)TWrtu(zrtu-hrtu)+(zpseudo-hpseudo)TWpseudo(zpseudo-hpseudo)
wherein z ispmuIs a measurement data vector, h, provided by the PMUpmuIs a calculated value corresponding to a PMU data vector, WpmuIs a weight matrix for PMU data; z is a radical ofrtuIs a measurement data vector, h, provided by the RTUrtuIs a calculated value, W, corresponding to a measured data vector provided by the RTUrtuIs a weight matrix corresponding to RTU data; z is a radical ofpseudoIs a measurement data vector, h, provided by AMIpseudoIs a calculated value corresponding to a measured data vector provided by AMI, WpseudoIs the AMI data weight matrix.
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