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Hybrid State Estimation Model Based on PMU and SCADA Measurements
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IFAC-PapersOnLine 49-27 (2016) 390–394
Hybrid State Estimation Model Based on PMU and SCADA Measurements Hybrid Hybrid State State Estimation Estimation Model Model Based Based on on PMU PMU and and SCADA SCADA Measurements Measurements Prof. Srdjan Skok*, MSc. Igor Ivankovic**, Zdeslav Cerina** Prof. Srdjan Srdjan Skok*, MSc. MSc. Igor Ivankovic**, Ivankovic**, Zdeslav Cerina** Cerina** Prof. Prof. Srdjan Skok*, Skok*, MSc. Igor Igor Ivankovic**, Zdeslav Zdeslav Cerina** Vukovarska 58,
*Faculty of Engineering, Rijeka, Croatia ([email protected]) *Faculty of Engineering, Vukovarska 58, Rijeka, ([email protected]) **Croatian Transmission System Operator, Kupska 4, Zagreb, CroatiaCroatia ([email protected], [email protected]) *Faculty of Engineering, Vukovarska 58, Rijeka, Croatia ([email protected]) *Faculty of Engineering, Vukovarska 58, ([email protected]) **Croatian Transmission System Operator, Kupska 4, Zagreb, Rijeka, CroatiaCroatia ([email protected], [email protected]) **Croatian Transmission **Croatian Transmission System System Operator, Operator, Kupska Kupska 4, 4, Zagreb, Zagreb, Croatia Croatia ([email protected], ([email protected], [email protected]) [email protected]) Abstract: In this paper, a new method of hybrid non-linear state estimation with PMU and SCADA Abstract: In this aa new method of hybrid non-linear state estimation with PMU measurements willpaper, be proposed. PMU measurements, the voltage and current phasors, are and usedSCADA for real Abstract: In paper, of state estimation with and SCADA Abstract: In this this paper, a new new method method of hybrid hybrid non-linear non-linear stateand estimation with PMU PMU and SCADA measurements will be proposed. PMU measurements, the voltage current phasors, are used for real time transmission line parameters (impedance and admittance) calculation. Transmission line parameters measurements will be proposed. PMU measurements, the voltage and current phasors, are used for measurements willline be parameters proposed. PMU measurements, the voltage and current phasors, are for real real time transmission (impedance and admittance) calculation. Transmission lineused parameters are input data for the conventional state estimator. Calculated parameters of the transmission lines based time transmission line parameters (impedance and admittance) calculation. Transmission line parameters time transmission line parameters (impedance and admittance) calculation. Transmission line parameters are input data forPMU the conventional state parametersimpedance of the transmission lines based on the real time measurements areestimator. comparedCalculated with the measured and admittance. The are input data for the state estimator. Calculated parameters of lines are input data forPMU the conventional conventional state estimator. Calculated parametersimpedance of the the transmission transmission lines based based on the real time measurements are compared with the measured and admittance. The simulation results were carried out on 400 kV Croatian power system. An index of accuracy is set and on the real time PMU measurements are compared with the measured impedance and admittance. The on the real results time PMU measurements are withpower the measured impedance admittance. simulation were carried out onmeasurements 400compared kV Croatian system. An index ofand accuracy isproposed set The and used to quantify the impact of PMU on power system state estimation by using simulation results were carried out on 400 kV Croatian power system. An index of accuracy is set and simulation resultsthe were carried out onmeasurements 400 kV Croatian powersystem system. An index of accuracy isproposed set and used quantify impact on power state by using hybridto model. Software for of thePMU proposed hybrid model was developed andestimation it is compatible with PMUs used to quantify the of PMU measurements on system estimation by proposed used to model. quantify the impact impact of PMU measurements on power power system state state estimation by using using proposed hybrid Software for the proposed hybrid model was developed and it is compatible with PMUs form different vendors. This research was made possible by implementation of 5 PMUs and restoration hybrid model. Software for proposed hybrid model developed and with PMUs hybriddifferent model. vendors. Software This for the the proposed hybrid model was was developed and it it is is 5compatible compatible with PMUs form research was made possible by implementation restoration of wide area monitoring (WAM) system in Croatian power system. Those of PMUs wereand implemented form different vendors. This research was made possible by implementation of 55 PMUs PMUs and restoration form different vendors. This research was made possible by implementation of PMUs and restoration of widethearea monitoringprocess (WAM) system in Croatian system. Those PMUszone. were implemented and 2nd UCTE synchronous during reconnection - reintegration of the 1st power of wide monitoring (WAM) system power system. Those were of widethearea area monitoringprocess (WAM) system in in Croatian Croatian system. Those PMUs PMUszone. were implemented implemented and 2nd UCTE synchronous during reconnection - reintegration of the 1ststst power nd nd UCTE synchronous zone. and 2 during the reconnection process reintegration of the 1 and 2 UCTE synchronous zone. during the reconnection process reintegration of the 1 © 2016, IFAC (International Federation Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Wide area monitoring, Stateofestimation, Line impedance, Phasor measurement units Keywords: Wide area monitoring, State estimation, Line impedance, Phasor measurement units Keywords: Wide area monitoring, State estimation, Line impedance, Phasor measurement units Keywords: Wide area monitoring, State estimation, Line impedance, Phasor measurement units
1. INTRODUCTION 1. INTRODUCTION 1. INTRODUCTION 1. INTRODUCTION Over the twenty years, electric power industry in many Over the has twenty electric power industry in due many countries beenyears, undergoing fundamental changes to Over the twenty years, electric power in many Over the has twenty years, electric power industry industry in due many countries been undergoing fundamental changes to the process of deregulation. In addition, the power system countries has been undergoing fundamental changes due to countries has been undergoing fundamental changes due to the process of deregulation. In addition, theshared powerbysystem network is growing larger and more complex, more the process of deregulation. In addition, the power system the process of deregulation. In addition, the power system network is growing larger and more complex, shared by more providers the deregulation. In this situation, the function network is growing larger complex, shared by network isafter growing larger and and more more complex, shared by more more providers after the deregulation. In this situation, the function of state estimation is becoming more important, because it is providers after the deregulation. In this situation, the function providers after the deregulation. In this situation, the function of state estimation ismonitoring becoming and morecontrol important, because it is the primary tool for based on the realof state estimation is becoming more important, because it of state estimation ismonitoring becoming and morecontrol important, because it is is the primary tool for based on the realtime data received from the measurement units. The the primary tool for monitoring and control based on the realthe primary tool for monitoring and control based on the realtime data energy receivedmanagement from the system measurement units. The advanced applications like time data received from measurement units. time data energy receivedmanagement from the the system measurement units. The The advanced applications like security analysis, economic dispatch, etc. which ensure advanced energy management system applications like advanced analysis, energy economic management system etc. applications like security dispatch, which system ensure reliability and economic operation of the power security analysis, economic dispatch, etc. which ensure security analysis, economic dispatch, etc. which ensure reliability and economic operation of the power system strongly depend on the accuracy of data by the state reliability and operation of the system reliability and economic economic operation ofprovided the power power system strongly depend on the accuracy of data provided by the state estimation. strongly depend on the accuracy of data provided by the strongly depend on the accuracy of data provided by the state state estimation. estimation. estimation. The updating of software for power system monitoring and The updating of software for power has system monitoring control (SCADA/EMS-applications) become possibleand on The updating of system monitoring and The updating of software software for for power power has system monitoring control (SCADA/EMS-applications) become possibleand on acontrol qualitatively new level owing to WAMS (Wide-Area control (SCADA/EMS-applications) has become possible (SCADA/EMS-applications) hasWAMS become (Wide-Area possible on on aMeasurement qualitatively new level owing to System), that allows the power system state to aa qualitatively new level owing to WAMS (Wide-Area qualitatively new level owing to WAMS (Wide-Area Measurement that allows the power stateThe to be controlled System), synchronously and with high system accuracy. Measurement System), that the system state to Measurement System), that allows allows the power power system stateThe to be controlled synchronously and are with high accuracy. phasor measurement units (PMU) the main measurement be controlled synchronously and with high accuracy. The be controlled synchronously and with high accuracy. The phasor measurement units (PMU) are the main measurement equipment in theseunits systems. Thethe state phasor measurement (PMU) main phasor measurement units (PMU) are are theconventional main measurement measurement equipment in these systems. The conventional state estimation results in calculation of steady state (current equipment in these systems. The conventional state equipment in these systems. The conventional state estimation results in calculation of steady state (current conditions) of power system. As compared to a standard set estimation results in calculation of steady state (current estimation results in calculation of steady state (current conditions) of power system. As SCADA, comparedPMU to a standard set of measurements received from installed in conditions) of power system. As compared to a standard set conditions) of power system. As SCADA, comparedPMU to a standard set of measurements received from installed in the node can measure voltage phasor in this node and current of measurements received from SCADA, PMU installed in of measurements received from SCADA, PMU installed in the node can measure voltage phasor in this node and current phasors in some or all branches adjacent to this node with the node can measure voltage phasor in this node and current the node can measure voltage phasor in this node and current phasorsaccuracy. in some or branches adjacent to high this node with high Theall of additional accuracy phasors in all use branches adjacent this with phasorsaccuracy. in some some or or branches adjacent to to high this node node with high Theall use of estimator additional accuracy measurements in the state (SE) improves high accuracy. The use of additional high accuracy high accuracy. The use of additional high accuracy measurements in the state estimator (SE) improves observability of in calculated network, enhances the efficiency measurements the estimator (SE) improves measurements in the state state estimator (SE) improves observability of calculated network, enhances the efficiency of methods for bad data detection, increases accuracy and observability of calculated network, enhances the efficiency observability of calculated network, enhances the efficiency of methods for bad data estimates. detection, increases accuracy and reliability of the obtained of methods for bad data detection, increases accuracy of methods bad data estimates. detection, increases accuracy and and reliability of for the obtained reliability of the obtained estimates. reliability of the obtained estimates.
In this paper a short description of a conventional non-linear In thisestimator paper a based short description of a conventional state on the measured state variablesnon-linear and data In this paper short of non-linear In thisestimator paper aa based short description description of aa conventional conventional non-linear state on the measured state variables and data mainly received from SCADA system is given. For state estimator based on the measured state variables and state estimator basedfrom on theSCADA measuredsystem state variables and data data mainly received is given. For comparison, a description of a linear state estimator based mainly received from SCADA system is given. For mainly received from SCADA system is given. For comparison, a description of a linearis state estimator based exclusively on PMU measurements given. Then, a new comparison, aa description of aa linear state estimator based comparison, description of linear state estimator based exclusively PMU measurements given. Then, new method of a on of hybrid non-linear stateis withaaaPMU exclusively on PMU is given. new exclusively on PMU measurements measurements isestimation given. Then, Then, new method of a of hybrid non-linear state estimation with PMU and SCADA measurements willstate be estimation proposed where the method of aa of hybrid non-linear with PMU method of of hybrid non-linear state estimation with PMU and SCADA measurements willused be for proposed where the voltage and current phasors are the calculation of and SCADA measurements will be proposed where and SCADA measurements willused be for proposed where the the voltage andtransmission current phasors are the calculation of real time line parameters (impedance and voltage and current phasors are used for the calculation of voltage andtransmission current phasors areparameters used for the calculationand of real time line (impedance admittance). Calculated parameters of the transmission lines real time transmission line parameters (impedance and real time transmission line parameters (impedance and admittance). of the transmission lines based on theCalculated real time parameters PMU measurements are compared admittance). Calculated parameters of lines admittance). of the the transmission transmission lines basedtheonmeasured theCalculated real impedance time parameters PMUand measurements are simulation compared with admittance. The based on the real time PMU measurements are compared based on the real time PMU measurements are compared with the measured impedance and admittance. The simulation results carried out on 400 Croatian The power system. with the measured impedance and admittance. simulation with thewere measured impedance andkV admittance. The simulation results were carried out on 400 kV Croatian power system. An index of accuracy is set and used to quantify the impact of results were carried out on 400 kV Croatian power system. results were carried out onand 400used kV to Croatian power system. An index of accuracy is set quantify the impact of PMU measurements on power system state estimation by An index of accuracy is set and used to quantify the impact of An index of accuracy is setpower and used to quantify the impact by of PMU measurements on system state estimation using proposed hybrid model. Software for the proposed PMU measurements on power system state estimation by PMU measurements on power system state estimation by using proposed model. for thewith proposed hybrid model washybrid developed and Software it is compatible PMUs using proposed hybrid model. Software for proposed using proposed hybrid model. Software for the thewith proposed hybrid model was developed and it is compatible PMUs from different vendors. hybrid model was developed and it is compatible with hybrid model was developed and it is compatible with PMUs PMUs from different vendors. from from different different vendors. vendors. 2. LINEAR AND NON-LINEAR STATE ESTIMATION 2. LINEAR AND NON-LINEAR STATE ESTIMATION 2. LINEAR LINEAR AND AND NON-LINEAR NON-LINEAR STATE STATE ESTIMATION ESTIMATION 2. The state estimator is the key application in the energy The state estimator is the key application in the of energy management system (EMS). The performance the The state is the application in energy The state estimator estimator is (EMS). the key key The application in the the of energy management system performance the advanced applications is highly dependent on the state management system (EMS). The performance of the management system (EMS). Thedependent performance of state the advanced applications is highly on the estimator robustness and the quality of the state estimator advanced applications is highly dependent on the state advanced applications is highly dependent on the state estimator and the analog quality and of the state estimator result. Therobustness SE uses real-time status telemetry in estimator robustness and quality of state estimator estimator robustness and the the analog quality and of the the state estimator result. The SE uses real-time status telemetry in order to calculate an estimate of system voltages and MW result. The SE uses real-time analog and status telemetry in result. The SE usesanreal-time analog and status telemetry in order to calculate estimate of system voltages and MW and MVAr power flows in the entire power network. Since order to calculate an estimate of system voltages and MW order to calculate an estimate of system voltages and MW and MVAr power flows in the entirefrom power network. Since inexact measurements (such as those a SCADA system) and power in entire power network. Since and MVAr MVAr power flows flows in the the entirefrom power network. Since inexact measurements (such as those a the SCADA system) are used to calculate the complex voltages, estimate will inexact measurements (such as those from aa SCADA system) inexact measurements (such as those from SCADA system) are used to calculate the complex voltages, the estimate will also be inexact. This introduces the problem of how to devise are used to the voltages, the estimate will are used to calculate calculate the complex complex voltages, the estimate will also be inexact. This introduces the problem of how to devise aalso“best” estimate for the voltages givenof the to available also be inexact. This introduces the problem how devise be inexact. This introduces the problem of how to devise aameasurements. “best” estimate for the voltages given the available “best” ameasurements. “best” estimate estimate for for the the voltages voltages given given the the available available measurements. measurements.
2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2016, 2016 IFAC 390Hosting by Elsevier Ltd. All rights reserved. Peer review©under of International Federation of Automatic Copyright 2016 responsibility IFAC 390Control. Copyright © 2016 IFAC 390 Copyright © 2016 IFAC 390 10.1016/j.ifacol.2016.10.764
2016 IFAC CTDSG October 11-13, 2016. Prague, Czech Republic Srdjan Skok et al. / IFAC-PapersOnLine 49-27 (2016) 390–394
A common choice for the objective function is the weighted sum of the measurement residual squares, which leads to the well known weighted least squares (WLS) state estimation solution. The classical WLS is a non-linear state estimator based upon non-synchronized measurements. This method is briefly described in chapter 2.1. Incorporating phasor measurements to an state estimator, if enough PMUs exist to make the entire system observable based exclusively on PMU measurements, then the state estimation problem can be formulated in a slightly simpler manner, and it becomes a linear problem. This type of estimation is described in chapter 2.2.
P P Q Q
U m U
T
2.2 State estimation using phasor measurements Observability is defined as the ability to uniquely estimate the states of a power system using given measurements. Observability analysis is required to decide meter placement in order to maintain solvability of the observation equations in various conditions. Implementation of PMU presents an opportunity for improving observability analysis and state estimation. If enough PMUs exist to make the entire system observable based exclusively on PMU measurements, then the state estimation is defined as a linear phasor state estimation model. Although, full observability based only on PMU measurements appears very impractical today, it may very well be the case in a few years when these devices become standard equipment at substations. In the case of state estimation only with PMU measurements, the relation between the measured phasors and the system states will become linear yielding the following measurement model:
(1)
R 1 z h ( x )
(2)
Where, R-1 is the weight matrix which is a diagonal matrix and the diagonal entry Ri-1 is1/σi2. The linearized correction equation of measurements using Taylor expansion is:
z H x
z H xv
(3)
To minimize the objective function, the derivation of J(x) should equal to zero, which deduces the WLS iterative formula: 1
(7)
Where, z is the measurement vector containing the real and imaginary parts of the measured voltage and current phasors, H is the measurement Jacobian which is constant and a function of the network model parameters only, x is the state vector containing the real and imaginary parts of bus voltage phasors and v is the measurement error vector.
Where, H is the Jacobian matrix of m x n dimensions.
x H T R 1 H H T R 1z
(6)
If bus i is equipped with voltage magnitude measurement device, the non-zero entry of the relative row in sub-matrix only appears in column i.
Where, z denotes the SCADA measurement vector which comprises voltage magnitude, active and reactive power flows and injections; x denotes the state variable vector which comprises the voltage magnitudes and phase angles of all buses (excepted the slack bus whose phase angle is zero); h(x) is the non-linear vector measurement function, and v is the measurement error vector. The objective function of WLS SE is the sums of the squares of the weighted residuals:
zih( x)
(5)
For the active and reactive power flow measurements, the structures of four Jacobian sub-matrix matrixes are same with the structure of node-branch incidence matrix. For the voltage magnitude measurements, its linearized correction equation is expressed as:
The weighted least squares method of power system state estimation has gained most popularity among commercial state estimators. In the traditional static SE, SCADA measurements errors are independent and assumed to yield the normal distribution with zero mean and σ2 variance. Then, the mathematical relations between the measurement vector z of m dimensions and the state variable vector x of n
J ( x)
P U Q U U
For the injection measurements, the Jacobian matrix is very similar to it of the power flow calculations, and its structure is same to the structure of node admittance matrix.
2.1 Weighted Least Squares Method
z h( x ) v
391
(4)
This measurement model will lead to a linear state estimator, which will be given by the following equation:
xˆ G 1 H T R 1 z
Where, HTR-1H is called the gain matrix or information matrix of n×n dimensions. And the diagonal entries of its inverse matrix which is also the estimation error covariance matrix can be used to assess the precision of SE. For the active and reactive power flow and injection measurements, its linearized correction equation is:
(8)
Where, xˆ is the estimated system state, G HT R1 H is the constant gain matrix and RE {v vT } : is the diagonal error covariance matrix.
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2016 IFAC CTDSG 392 Srdjan Skok et al. / IFAC-PapersOnLine 49-27 (2016) 390–394 October 11-13, 2016. Prague, Czech Republic
3. DEVELOPED HYBRID STATE ESTIMATION MODEL In this paper, a new method of hybrid non-linear state estimation with PMU and SCADA measurements is proposed. PMU measurements, the voltage and current phasors, are used for on-line transmission line parameters (impedance and admittance) calculation. Transmission line parameters are input data for the traditional state estimator. Calculated parameters of the transmission lines based on the real time PMU measurements are compared with the measured impedance and admittance. By observation it is concluded that transmission line parameters can vary 10% of rated values given by vendor (temperature of 20°C) during period of one year.
Vi
Y0i G0i jB0i
I ji
Yij
j
Vi Yij V j
(11)
Y0 2
(12)
I ij V j I ji Vi 2
Vi V j
2
(13)
The voltage along the line is determined based upon the current/voltage relationships at the terminals. Assuming that voltage and current at one end are known, and knowing the transmission line modelling with distributed parameters used in power system analysis, the series impedance and the shunt admittance in the iteration process can be defined as:
(9)
Z Z ij* ij
sh
Y0 Y0* th 2 2 2 2
(10)
(14)
(15)
Where Zij* and Y0* are the series impedance and shunt admittance calculated in the previous iteration, and θ is the propagation constant defined as:
The current vectors flowing between the terminal nodes are defined as: the current vector between
I ij ij , and the current vector between the nodes j and i: I I ji ji . ji nodes i and j , I ij
V
Y0 2
Adding the expressions [11] and [12] gives the following equation for Yij:
The shunt admittance composed of the capacitive reactance B0i and B0j and insulation admittance G0i and G0j between the conductor and the ground. The shunt admittance, normally distributed along the line or the cable, is in the equivalent representation cumulated and divided into two parts located at the two terminal nodes:
Y0 G0 B j 0 2 2 2
I ij Vi V j Yij Vi
A series admittance Yij, that is the series conductance Gij and series susceptance Bij of the electrical conductor between two terminal nodes i and j:
Y Y0 0i j
Vj
Y0j G0 j jB0 j
The expressions for currents can be written in the following manner:
The load being assumed to be equally balanced over the three phases, the characteristic of a branch may be described by a single phase equivalent circuit (Fig 1). Giving:
1 Yij Gij jBij Y ij Z ij
I ji
Fig. 1. Equivalent π schema of a transmission line
3.1 Line impedance modelling
Yij Gij jBij
Iij
Z ij* Y0* l Z ij*1 Y0*1
(16)
Combining equations [14], [15] and [16] the following equations for the series impedance and shunt admittance can be derived:
Vi i and V V j j are The vectors V i j the base phase voltages at the end nodes i and j respectively.
Zij
Y0 2
392
Zij*
sh Zij* Y0*
(17)
Zij* Y0* Y0* th 2 Zij*
(18)
* 0
Y
2016 IFAC CTDSG October 11-13, 2016. Prague, Czech Republic Srdjan Skok et al. / IFAC-PapersOnLine 49-27 (2016) 390–394
The series impedance and shunt admittance are calculated with iterative methods.
393
possible). Measured values were carried out from WAM self - developed program package shown on Fig. 3.
3.2 Simulation model The simulation results were carried out on the 400kV Croatian power system. Simulation was made possible by implementation of 5 PMUs and restoration of wide area monitoring (WAM) system in Croatian power system (in total 14 PMUs on 400 kV and 220 kV). Those PMUs were implemented during the reconnection process - reintegration of the 1st and 2nd UCTE synchronous zone.
Fig. 3. Operators console of self - developed WAM program package Table 1. Simulation results
Node Ernestinovo
Estimated value with transmission line parameters 416kV
Estimated value calculated with PMU measurements 423kV
Difference [%] 1.5
By using constant transmission line parameters calculated voltage at node Ernestinovo is 416 kV and calculation the same voltage using on-line transmission line parameters gives 423 kV. The difference between results from two calculation approaches is slightly above 1.5 %.
Fig. 2. Installed PMUs in the Croatian power system Observed are five PMUs - ABB RES 521, were installed in five significant 400 kV substations in order to record frequency and positive sequence phasor quantities such as 400-kV node voltages and currents in outgoing 400 kV transmission lines. Firstly, the main purpose of these PMU units was to contribute in optimization of energy transit without violating the voltage instability risk and to get experience of the phasor measurement technology applied to existing monitoring system in the Croatian power system. At the present, there are several projects for developing algorithms and software support for wide area control and protection of the Croatian power system. One of them deals with the enhancement of the state estimator model with PMU measurements. It will be also given up to date overview of the WAM system in Croatia.
It is assumed that new hybrid state estimation will give higher accuracy by implementing on power system grid with more transmission lines and PMU nodes.
3. CONCLUSION This paper has considered hybrid model using synchronized phasor measurements as additional data in traditional state estimator software in modern EMS. Based on measurements it was concluded that impedance and admittance can vary (during one year) more than 10% of nominal value rated by vendor. Developed hybrid model propose on-line calculation of transmission line parameters - impedance and admittance based on PMU measurements from both side of transmission line. On-line calculated transmission line parameters are input data for traditional state estimator. Hybrid model was tested on Croatian 400 kV power system. Simulation shows that difference between traditional state estimation calculation and results obtained by proposed hybrid model is significant.
3.3 Simulation results The simulation was carried out on small power system grid (only five nodes - four PMU measurement and 4 transmission lines). It was assumed that traditional SCADA measurement is missing from node Ernestinovo and should be calculated. Calculation was made by using traditional state estimation with constant line parameters of all transmission lines and with on-line calculated transmission line parameters (where 393
2016 IFAC CTDSG 394 Srdjan Skok et al. / IFAC-PapersOnLine 49-27 (2016) 390–394 October 11-13, 2016. Prague, Czech Republic
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IFAC-PapersOnLine 49-27 (2016) 390–394
Hybrid State Estimation Model Based on PMU and SCADA Measurements Hybrid Hybrid State State Estimation Estimation Model Model Based Based on on PMU PMU and and SCADA SCADA Measurements Measurements Prof. Srdjan Skok*, MSc. Igor Ivankovic**, Zdeslav Cerina** Prof. Srdjan Srdjan Skok*, MSc. MSc. Igor Ivankovic**, Ivankovic**, Zdeslav Cerina** Cerina** Prof. Prof. Srdjan Skok*, Skok*, MSc. Igor Igor Ivankovic**, Zdeslav Zdeslav Cerina** Vukovarska 58,
*Faculty of Engineering, Rijeka, Croatia ([email protected]) *Faculty of Engineering, Vukovarska 58, Rijeka, ([email protected]) **Croatian Transmission System Operator, Kupska 4, Zagreb, CroatiaCroatia ([email protected], [email protected]) *Faculty of Engineering, Vukovarska 58, Rijeka, Croatia ([email protected]) *Faculty of Engineering, Vukovarska 58, ([email protected]) **Croatian Transmission System Operator, Kupska 4, Zagreb, Rijeka, CroatiaCroatia ([email protected], [email protected]) **Croatian Transmission **Croatian Transmission System System Operator, Operator, Kupska Kupska 4, 4, Zagreb, Zagreb, Croatia Croatia ([email protected], ([email protected], [email protected]) [email protected]) Abstract: In this paper, a new method of hybrid non-linear state estimation with PMU and SCADA Abstract: In this aa new method of hybrid non-linear state estimation with PMU measurements willpaper, be proposed. PMU measurements, the voltage and current phasors, are and usedSCADA for real Abstract: In paper, of state estimation with and SCADA Abstract: In this this paper, a new new method method of hybrid hybrid non-linear non-linear stateand estimation with PMU PMU and SCADA measurements will be proposed. PMU measurements, the voltage current phasors, are used for real time transmission line parameters (impedance and admittance) calculation. Transmission line parameters measurements will be proposed. PMU measurements, the voltage and current phasors, are used for measurements willline be parameters proposed. PMU measurements, the voltage and current phasors, are for real real time transmission (impedance and admittance) calculation. Transmission lineused parameters are input data for the conventional state estimator. Calculated parameters of the transmission lines based time transmission line parameters (impedance and admittance) calculation. Transmission line parameters time transmission line parameters (impedance and admittance) calculation. Transmission line parameters are input data forPMU the conventional state parametersimpedance of the transmission lines based on the real time measurements areestimator. comparedCalculated with the measured and admittance. The are input data for the state estimator. Calculated parameters of lines are input data forPMU the conventional conventional state estimator. Calculated parametersimpedance of the the transmission transmission lines based based on the real time measurements are compared with the measured and admittance. The simulation results were carried out on 400 kV Croatian power system. An index of accuracy is set and on the real time PMU measurements are compared with the measured impedance and admittance. The on the real results time PMU measurements are withpower the measured impedance admittance. simulation were carried out onmeasurements 400compared kV Croatian system. An index ofand accuracy isproposed set The and used to quantify the impact of PMU on power system state estimation by using simulation results were carried out on 400 kV Croatian power system. An index of accuracy is set and simulation resultsthe were carried out onmeasurements 400 kV Croatian powersystem system. An index of accuracy isproposed set and used quantify impact on power state by using hybridto model. Software for of thePMU proposed hybrid model was developed andestimation it is compatible with PMUs used to quantify the of PMU measurements on system estimation by proposed used to model. quantify the impact impact of PMU measurements on power power system state state estimation by using using proposed hybrid Software for the proposed hybrid model was developed and it is compatible with PMUs form different vendors. This research was made possible by implementation of 5 PMUs and restoration hybrid model. Software for proposed hybrid model developed and with PMUs hybriddifferent model. vendors. Software This for the the proposed hybrid model was was developed and it it is is 5compatible compatible with PMUs form research was made possible by implementation restoration of wide area monitoring (WAM) system in Croatian power system. Those of PMUs wereand implemented form different vendors. This research was made possible by implementation of 55 PMUs PMUs and restoration form different vendors. This research was made possible by implementation of PMUs and restoration of widethearea monitoringprocess (WAM) system in Croatian system. Those PMUszone. were implemented and 2nd UCTE synchronous during reconnection - reintegration of the 1st power of wide monitoring (WAM) system power system. Those were of widethearea area monitoringprocess (WAM) system in in Croatian Croatian system. Those PMUs PMUszone. were implemented implemented and 2nd UCTE synchronous during reconnection - reintegration of the 1ststst power nd nd UCTE synchronous zone. and 2 during the reconnection process reintegration of the 1 and 2 UCTE synchronous zone. during the reconnection process reintegration of the 1 © 2016, IFAC (International Federation Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Wide area monitoring, Stateofestimation, Line impedance, Phasor measurement units Keywords: Wide area monitoring, State estimation, Line impedance, Phasor measurement units Keywords: Wide area monitoring, State estimation, Line impedance, Phasor measurement units Keywords: Wide area monitoring, State estimation, Line impedance, Phasor measurement units
1. INTRODUCTION 1. INTRODUCTION 1. INTRODUCTION 1. INTRODUCTION Over the twenty years, electric power industry in many Over the has twenty electric power industry in due many countries beenyears, undergoing fundamental changes to Over the twenty years, electric power in many Over the has twenty years, electric power industry industry in due many countries been undergoing fundamental changes to the process of deregulation. In addition, the power system countries has been undergoing fundamental changes due to countries has been undergoing fundamental changes due to the process of deregulation. In addition, theshared powerbysystem network is growing larger and more complex, more the process of deregulation. In addition, the power system the process of deregulation. In addition, the power system network is growing larger and more complex, shared by more providers the deregulation. In this situation, the function network is growing larger complex, shared by network isafter growing larger and and more more complex, shared by more more providers after the deregulation. In this situation, the function of state estimation is becoming more important, because it is providers after the deregulation. In this situation, the function providers after the deregulation. In this situation, the function of state estimation ismonitoring becoming and morecontrol important, because it is the primary tool for based on the realof state estimation is becoming more important, because it of state estimation ismonitoring becoming and morecontrol important, because it is is the primary tool for based on the realtime data received from the measurement units. The the primary tool for monitoring and control based on the realthe primary tool for monitoring and control based on the realtime data energy receivedmanagement from the system measurement units. The advanced applications like time data received from measurement units. time data energy receivedmanagement from the the system measurement units. The The advanced applications like security analysis, economic dispatch, etc. which ensure advanced energy management system applications like advanced analysis, energy economic management system etc. applications like security dispatch, which system ensure reliability and economic operation of the power security analysis, economic dispatch, etc. which ensure security analysis, economic dispatch, etc. which ensure reliability and economic operation of the power system strongly depend on the accuracy of data by the state reliability and operation of the system reliability and economic economic operation ofprovided the power power system strongly depend on the accuracy of data provided by the state estimation. strongly depend on the accuracy of data provided by the strongly depend on the accuracy of data provided by the state state estimation. estimation. estimation. The updating of software for power system monitoring and The updating of software for power has system monitoring control (SCADA/EMS-applications) become possibleand on The updating of system monitoring and The updating of software software for for power power has system monitoring control (SCADA/EMS-applications) become possibleand on acontrol qualitatively new level owing to WAMS (Wide-Area control (SCADA/EMS-applications) has become possible (SCADA/EMS-applications) hasWAMS become (Wide-Area possible on on aMeasurement qualitatively new level owing to System), that allows the power system state to aa qualitatively new level owing to WAMS (Wide-Area qualitatively new level owing to WAMS (Wide-Area Measurement that allows the power stateThe to be controlled System), synchronously and with high system accuracy. Measurement System), that the system state to Measurement System), that allows allows the power power system stateThe to be controlled synchronously and are with high accuracy. phasor measurement units (PMU) the main measurement be controlled synchronously and with high accuracy. The be controlled synchronously and with high accuracy. The phasor measurement units (PMU) are the main measurement equipment in theseunits systems. Thethe state phasor measurement (PMU) main phasor measurement units (PMU) are are theconventional main measurement measurement equipment in these systems. The conventional state estimation results in calculation of steady state (current equipment in these systems. The conventional state equipment in these systems. The conventional state estimation results in calculation of steady state (current conditions) of power system. As compared to a standard set estimation results in calculation of steady state (current estimation results in calculation of steady state (current conditions) of power system. As SCADA, comparedPMU to a standard set of measurements received from installed in conditions) of power system. As compared to a standard set conditions) of power system. As SCADA, comparedPMU to a standard set of measurements received from installed in the node can measure voltage phasor in this node and current of measurements received from SCADA, PMU installed in of measurements received from SCADA, PMU installed in the node can measure voltage phasor in this node and current phasors in some or all branches adjacent to this node with the node can measure voltage phasor in this node and current the node can measure voltage phasor in this node and current phasorsaccuracy. in some or branches adjacent to high this node with high Theall of additional accuracy phasors in all use branches adjacent this with phasorsaccuracy. in some some or or branches adjacent to to high this node node with high Theall use of estimator additional accuracy measurements in the state (SE) improves high accuracy. The use of additional high accuracy high accuracy. The use of additional high accuracy measurements in the state estimator (SE) improves observability of in calculated network, enhances the efficiency measurements the estimator (SE) improves measurements in the state state estimator (SE) improves observability of calculated network, enhances the efficiency of methods for bad data detection, increases accuracy and observability of calculated network, enhances the efficiency observability of calculated network, enhances the efficiency of methods for bad data estimates. detection, increases accuracy and reliability of the obtained of methods for bad data detection, increases accuracy of methods bad data estimates. detection, increases accuracy and and reliability of for the obtained reliability of the obtained estimates. reliability of the obtained estimates.
In this paper a short description of a conventional non-linear In thisestimator paper a based short description of a conventional state on the measured state variablesnon-linear and data In this paper short of non-linear In thisestimator paper aa based short description description of aa conventional conventional non-linear state on the measured state variables and data mainly received from SCADA system is given. For state estimator based on the measured state variables and state estimator basedfrom on theSCADA measuredsystem state variables and data data mainly received is given. For comparison, a description of a linear state estimator based mainly received from SCADA system is given. For mainly received from SCADA system is given. For comparison, a description of a linearis state estimator based exclusively on PMU measurements given. Then, a new comparison, aa description of aa linear state estimator based comparison, description of linear state estimator based exclusively PMU measurements given. Then, new method of a on of hybrid non-linear stateis withaaaPMU exclusively on PMU is given. new exclusively on PMU measurements measurements isestimation given. Then, Then, new method of a of hybrid non-linear state estimation with PMU and SCADA measurements willstate be estimation proposed where the method of aa of hybrid non-linear with PMU method of of hybrid non-linear state estimation with PMU and SCADA measurements willused be for proposed where the voltage and current phasors are the calculation of and SCADA measurements will be proposed where and SCADA measurements willused be for proposed where the the voltage andtransmission current phasors are the calculation of real time line parameters (impedance and voltage and current phasors are used for the calculation of voltage andtransmission current phasors areparameters used for the calculationand of real time line (impedance admittance). Calculated parameters of the transmission lines real time transmission line parameters (impedance and real time transmission line parameters (impedance and admittance). of the transmission lines based on theCalculated real time parameters PMU measurements are compared admittance). Calculated parameters of lines admittance). of the the transmission transmission lines basedtheonmeasured theCalculated real impedance time parameters PMUand measurements are simulation compared with admittance. The based on the real time PMU measurements are compared based on the real time PMU measurements are compared with the measured impedance and admittance. The simulation results carried out on 400 Croatian The power system. with the measured impedance and admittance. simulation with thewere measured impedance andkV admittance. The simulation results were carried out on 400 kV Croatian power system. An index of accuracy is set and used to quantify the impact of results were carried out on 400 kV Croatian power system. results were carried out onand 400used kV to Croatian power system. An index of accuracy is set quantify the impact of PMU measurements on power system state estimation by An index of accuracy is set and used to quantify the impact of An index of accuracy is setpower and used to quantify the impact by of PMU measurements on system state estimation using proposed hybrid model. Software for the proposed PMU measurements on power system state estimation by PMU measurements on power system state estimation by using proposed model. for thewith proposed hybrid model washybrid developed and Software it is compatible PMUs using proposed hybrid model. Software for proposed using proposed hybrid model. Software for the thewith proposed hybrid model was developed and it is compatible PMUs from different vendors. hybrid model was developed and it is compatible with hybrid model was developed and it is compatible with PMUs PMUs from different vendors. from from different different vendors. vendors. 2. LINEAR AND NON-LINEAR STATE ESTIMATION 2. LINEAR AND NON-LINEAR STATE ESTIMATION 2. LINEAR LINEAR AND AND NON-LINEAR NON-LINEAR STATE STATE ESTIMATION ESTIMATION 2. The state estimator is the key application in the energy The state estimator is the key application in the of energy management system (EMS). The performance the The state is the application in energy The state estimator estimator is (EMS). the key key The application in the the of energy management system performance the advanced applications is highly dependent on the state management system (EMS). The performance of the management system (EMS). Thedependent performance of state the advanced applications is highly on the estimator robustness and the quality of the state estimator advanced applications is highly dependent on the state advanced applications is highly dependent on the state estimator and the analog quality and of the state estimator result. Therobustness SE uses real-time status telemetry in estimator robustness and quality of state estimator estimator robustness and the the analog quality and of the the state estimator result. The SE uses real-time status telemetry in order to calculate an estimate of system voltages and MW result. The SE uses real-time analog and status telemetry in result. The SE usesanreal-time analog and status telemetry in order to calculate estimate of system voltages and MW and MVAr power flows in the entire power network. Since order to calculate an estimate of system voltages and MW order to calculate an estimate of system voltages and MW and MVAr power flows in the entirefrom power network. Since inexact measurements (such as those a SCADA system) and power in entire power network. Since and MVAr MVAr power flows flows in the the entirefrom power network. Since inexact measurements (such as those a the SCADA system) are used to calculate the complex voltages, estimate will inexact measurements (such as those from aa SCADA system) inexact measurements (such as those from SCADA system) are used to calculate the complex voltages, the estimate will also be inexact. This introduces the problem of how to devise are used to the voltages, the estimate will are used to calculate calculate the complex complex voltages, the estimate will also be inexact. This introduces the problem of how to devise aalso“best” estimate for the voltages givenof the to available also be inexact. This introduces the problem how devise be inexact. This introduces the problem of how to devise aameasurements. “best” estimate for the voltages given the available “best” ameasurements. “best” estimate estimate for for the the voltages voltages given given the the available available measurements. measurements.
2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2016, 2016 IFAC 390Hosting by Elsevier Ltd. All rights reserved. Peer review©under of International Federation of Automatic Copyright 2016 responsibility IFAC 390Control. Copyright © 2016 IFAC 390 Copyright © 2016 IFAC 390 10.1016/j.ifacol.2016.10.764
2016 IFAC CTDSG October 11-13, 2016. Prague, Czech Republic Srdjan Skok et al. / IFAC-PapersOnLine 49-27 (2016) 390–394
A common choice for the objective function is the weighted sum of the measurement residual squares, which leads to the well known weighted least squares (WLS) state estimation solution. The classical WLS is a non-linear state estimator based upon non-synchronized measurements. This method is briefly described in chapter 2.1. Incorporating phasor measurements to an state estimator, if enough PMUs exist to make the entire system observable based exclusively on PMU measurements, then the state estimation problem can be formulated in a slightly simpler manner, and it becomes a linear problem. This type of estimation is described in chapter 2.2.
P P Q Q
U m U
T
2.2 State estimation using phasor measurements Observability is defined as the ability to uniquely estimate the states of a power system using given measurements. Observability analysis is required to decide meter placement in order to maintain solvability of the observation equations in various conditions. Implementation of PMU presents an opportunity for improving observability analysis and state estimation. If enough PMUs exist to make the entire system observable based exclusively on PMU measurements, then the state estimation is defined as a linear phasor state estimation model. Although, full observability based only on PMU measurements appears very impractical today, it may very well be the case in a few years when these devices become standard equipment at substations. In the case of state estimation only with PMU measurements, the relation between the measured phasors and the system states will become linear yielding the following measurement model:
(1)
R 1 z h ( x )
(2)
Where, R-1 is the weight matrix which is a diagonal matrix and the diagonal entry Ri-1 is1/σi2. The linearized correction equation of measurements using Taylor expansion is:
z H x
z H xv
(3)
To minimize the objective function, the derivation of J(x) should equal to zero, which deduces the WLS iterative formula: 1
(7)
Where, z is the measurement vector containing the real and imaginary parts of the measured voltage and current phasors, H is the measurement Jacobian which is constant and a function of the network model parameters only, x is the state vector containing the real and imaginary parts of bus voltage phasors and v is the measurement error vector.
Where, H is the Jacobian matrix of m x n dimensions.
x H T R 1 H H T R 1z
(6)
If bus i is equipped with voltage magnitude measurement device, the non-zero entry of the relative row in sub-matrix only appears in column i.
Where, z denotes the SCADA measurement vector which comprises voltage magnitude, active and reactive power flows and injections; x denotes the state variable vector which comprises the voltage magnitudes and phase angles of all buses (excepted the slack bus whose phase angle is zero); h(x) is the non-linear vector measurement function, and v is the measurement error vector. The objective function of WLS SE is the sums of the squares of the weighted residuals:
zih( x)
(5)
For the active and reactive power flow measurements, the structures of four Jacobian sub-matrix matrixes are same with the structure of node-branch incidence matrix. For the voltage magnitude measurements, its linearized correction equation is expressed as:
The weighted least squares method of power system state estimation has gained most popularity among commercial state estimators. In the traditional static SE, SCADA measurements errors are independent and assumed to yield the normal distribution with zero mean and σ2 variance. Then, the mathematical relations between the measurement vector z of m dimensions and the state variable vector x of n
J ( x)
P U Q U U
For the injection measurements, the Jacobian matrix is very similar to it of the power flow calculations, and its structure is same to the structure of node admittance matrix.
2.1 Weighted Least Squares Method
z h( x ) v
391
(4)
This measurement model will lead to a linear state estimator, which will be given by the following equation:
xˆ G 1 H T R 1 z
Where, HTR-1H is called the gain matrix or information matrix of n×n dimensions. And the diagonal entries of its inverse matrix which is also the estimation error covariance matrix can be used to assess the precision of SE. For the active and reactive power flow and injection measurements, its linearized correction equation is:
(8)
Where, xˆ is the estimated system state, G HT R1 H is the constant gain matrix and RE {v vT } : is the diagonal error covariance matrix.
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2016 IFAC CTDSG 392 Srdjan Skok et al. / IFAC-PapersOnLine 49-27 (2016) 390–394 October 11-13, 2016. Prague, Czech Republic
3. DEVELOPED HYBRID STATE ESTIMATION MODEL In this paper, a new method of hybrid non-linear state estimation with PMU and SCADA measurements is proposed. PMU measurements, the voltage and current phasors, are used for on-line transmission line parameters (impedance and admittance) calculation. Transmission line parameters are input data for the traditional state estimator. Calculated parameters of the transmission lines based on the real time PMU measurements are compared with the measured impedance and admittance. By observation it is concluded that transmission line parameters can vary 10% of rated values given by vendor (temperature of 20°C) during period of one year.
Vi
Y0i G0i jB0i
I ji
Yij
j
Vi Yij V j
(11)
Y0 2
(12)
I ij V j I ji Vi 2
Vi V j
2
(13)
The voltage along the line is determined based upon the current/voltage relationships at the terminals. Assuming that voltage and current at one end are known, and knowing the transmission line modelling with distributed parameters used in power system analysis, the series impedance and the shunt admittance in the iteration process can be defined as:
(9)
Z Z ij* ij
sh
Y0 Y0* th 2 2 2 2
(10)
(14)
(15)
Where Zij* and Y0* are the series impedance and shunt admittance calculated in the previous iteration, and θ is the propagation constant defined as:
The current vectors flowing between the terminal nodes are defined as: the current vector between
I ij ij , and the current vector between the nodes j and i: I I ji ji . ji nodes i and j , I ij
V
Y0 2
Adding the expressions [11] and [12] gives the following equation for Yij:
The shunt admittance composed of the capacitive reactance B0i and B0j and insulation admittance G0i and G0j between the conductor and the ground. The shunt admittance, normally distributed along the line or the cable, is in the equivalent representation cumulated and divided into two parts located at the two terminal nodes:
Y0 G0 B j 0 2 2 2
I ij Vi V j Yij Vi
A series admittance Yij, that is the series conductance Gij and series susceptance Bij of the electrical conductor between two terminal nodes i and j:
Y Y0 0i j
Vj
Y0j G0 j jB0 j
The expressions for currents can be written in the following manner:
The load being assumed to be equally balanced over the three phases, the characteristic of a branch may be described by a single phase equivalent circuit (Fig 1). Giving:
1 Yij Gij jBij Y ij Z ij
I ji
Fig. 1. Equivalent π schema of a transmission line
3.1 Line impedance modelling
Yij Gij jBij
Iij
Z ij* Y0* l Z ij*1 Y0*1
(16)
Combining equations [14], [15] and [16] the following equations for the series impedance and shunt admittance can be derived:
Vi i and V V j j are The vectors V i j the base phase voltages at the end nodes i and j respectively.
Zij
Y0 2
392
Zij*
sh Zij* Y0*
(17)
Zij* Y0* Y0* th 2 Zij*
(18)
* 0
Y
2016 IFAC CTDSG October 11-13, 2016. Prague, Czech Republic Srdjan Skok et al. / IFAC-PapersOnLine 49-27 (2016) 390–394
The series impedance and shunt admittance are calculated with iterative methods.
393
possible). Measured values were carried out from WAM self - developed program package shown on Fig. 3.
3.2 Simulation model The simulation results were carried out on the 400kV Croatian power system. Simulation was made possible by implementation of 5 PMUs and restoration of wide area monitoring (WAM) system in Croatian power system (in total 14 PMUs on 400 kV and 220 kV). Those PMUs were implemented during the reconnection process - reintegration of the 1st and 2nd UCTE synchronous zone.
Fig. 3. Operators console of self - developed WAM program package Table 1. Simulation results
Node Ernestinovo
Estimated value with transmission line parameters 416kV
Estimated value calculated with PMU measurements 423kV
Difference [%] 1.5
By using constant transmission line parameters calculated voltage at node Ernestinovo is 416 kV and calculation the same voltage using on-line transmission line parameters gives 423 kV. The difference between results from two calculation approaches is slightly above 1.5 %.
Fig. 2. Installed PMUs in the Croatian power system Observed are five PMUs - ABB RES 521, were installed in five significant 400 kV substations in order to record frequency and positive sequence phasor quantities such as 400-kV node voltages and currents in outgoing 400 kV transmission lines. Firstly, the main purpose of these PMU units was to contribute in optimization of energy transit without violating the voltage instability risk and to get experience of the phasor measurement technology applied to existing monitoring system in the Croatian power system. At the present, there are several projects for developing algorithms and software support for wide area control and protection of the Croatian power system. One of them deals with the enhancement of the state estimator model with PMU measurements. It will be also given up to date overview of the WAM system in Croatia.
It is assumed that new hybrid state estimation will give higher accuracy by implementing on power system grid with more transmission lines and PMU nodes.
3. CONCLUSION This paper has considered hybrid model using synchronized phasor measurements as additional data in traditional state estimator software in modern EMS. Based on measurements it was concluded that impedance and admittance can vary (during one year) more than 10% of nominal value rated by vendor. Developed hybrid model propose on-line calculation of transmission line parameters - impedance and admittance based on PMU measurements from both side of transmission line. On-line calculated transmission line parameters are input data for traditional state estimator. Hybrid model was tested on Croatian 400 kV power system. Simulation shows that difference between traditional state estimation calculation and results obtained by proposed hybrid model is significant.
3.3 Simulation results The simulation was carried out on small power system grid (only five nodes - four PMU measurement and 4 transmission lines). It was assumed that traditional SCADA measurement is missing from node Ernestinovo and should be calculated. Calculation was made by using traditional state estimation with constant line parameters of all transmission lines and with on-line calculated transmission line parameters (where 393
2016 IFAC CTDSG 394 Srdjan Skok et al. / IFAC-PapersOnLine 49-27 (2016) 390–394 October 11-13, 2016. Prague, Czech Republic
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