State Estimation and Contingency Analysis for Extreme Operational Issues Dr. Noel Schulz TVA Endowed Professor in Power Systems Engineering Mississippi State University, USA
COMPARISON OF STATE ESTIMATION ALGORITHMS CONSIDERING PHASOR MEASUREMENTS AND DATA LOSS SrinathKamireddy Dr. Noel Schulz and Dr. AnuragSrivastava Power & Energy Research Laboratory Mississippi State University
MOTIVATION Recent blackouts have shown that the electric utility power system is vulnerable to natural catastrophes and physical disturbances It is possible to lose measurements from the power system due to failure of sensors or communication systems after the disasters. The performance of different state estimation algorithms may vary with redundancy of measurements. This research work focuses on comparing the performance of state estimation algorithms considering loss of measurement data and with phasor measurements.
INTRODUCTION • Power System Data • State Estimator • Operating condition of the power system The operating condition of a power system at any given point of time is known as the state of the power system . The operating condition can be determined from the voltage and bus angles of the power system. Measuring devices are not present at all parts of the power system network State estimation is a mathematical procedure that estimates the states from the network data and available measurements. It can also be used to calculate measurement data where sensors are not available. • 3
INTRODUCTION • Sensors in power system Basic Role of State Estimation • 4
GOALS To provide estimated values of measurements and states from the sensor data. To compare the performance of state estimation algorithms with loss of data due to communication network failure or loss of sensors To include phasor measurements along with traditional SCADA measurements into state estimation algorithms. Major contribution: Investigation of the impact of data loss on state estimation accuracy. The data loss is considered in form of clustered and scattered data points.
STATE ESTIMATION METHODS • 7 Weighted Least Square (WLS)method: • Minimizes the weighted sum of squares of the difference between measured and calculated values . • In weighted least square method, the objective function ‘f’ to be minimized is given by Iteratively Reweighted Least Square (IRLS)Weighted Least Absolute Value (WLAV)method: • Minimizes the weighted sum of the absolute value of difference between measured and calculated values. • The objective function to be minimized is given by • The weights get updated in every iteration. Least Absolute Value(LAV) method: • Minimizes the objective function which is the sum of absolute value of difference between measured and calculated values. • The objective function ‘g’ to be minimized is given by g= Subject to constraint zi= hi(x) +pi Where, σ2 = variance of the measurement W = weight of the measurement (reciprocal of variance of the measurement) ei= pi =zi-hi(x) i=1, 2, 3 ….m. h(x) = Measurement function, x = state variables and Z= Measured Value m=number of measurements
FLOW CHART FOR STATE ESTIMATION PROGRAM…. V, δ and Ybus Formation of measurement function ‘h’ Formation of measurement Jacobian J= [J1 J2; J3 J4; J5 J6; J7 J8; J9 J10] J1= 𝜕 V/𝜕δ J2= 𝜕 V/𝜕V J3= 𝜕 h21(x)/𝜕δ J4= 𝜕 h21(x)/𝜕V J5= 𝜕 h22(x)/𝜕δ J6= 𝜕 h22(x)/𝜕V J7= 𝜕 h31(x)/𝜕δ J8= 𝜕 h31(x)/𝜕V J9 = 𝜕 h32(x)/𝜕δ J10= 𝜕 h32(x)/𝜕V h=f(V, δ,Ybus) Estimated Measurements from ‘h’
FLOW CHART FOR STATE ESTIMATION PROGRAM…. Minimize ΣW*ǀ(z-h)ǀ Minimize ΣW*(z-h)^2 Minimize Σǀ (z-h) ǀ subject to constraint Method to solve states in each iteration Linearize the resultant equation Linearize the resultant equation Formulate minimization problem as Linear Programming problem Solve the linear equation for change in states Use updated weight ǀ(z-h)ǀ /W in the equation for solving states Solve for change in states Update states Update states Update states IRLS WLAV Method WLS Method LAV Method
METHOD TO INCLUDE PHASOR MEASUREMENTS |V| , P, Q |V| , δv, |I|, δi ‘h’ for classical SE measurements ‘h’ for phasor measurements Form Measurement Vector Convert to rectangular co-ordinates ‘h’ for combined measurements Form Measurement Vector Measurement Jacobian for classical SE measurements Measurement Jacobian for phasor measurements Combined Measurement Set Jacobian for combined measurements Use the combined measurement vector, measurement function and measurement jacobian in equation for solving states
LOSS OF DATA • A clustered data set is a group of measurements that belongs to a particular part of the power system • A scattered data point is a measurement from sensors distributed at different locations within the system • The wide spread data loss is simulated by removing clustered data sets from the available set of measurements. • The data loss at a local level is simulated by the loss of scattered data points from the measurement set.
Original Data Set from Power flow results with random error LOSS OF DATA K-K1c=R1 K-(K1c+K2c) =R2 K-K1s=R3 K-(K2s+ K1s) =R4 K= Total Number of available measurements K1c ,K2c =Clustered data sets K1s ,K2s =Scattered data points R1, R2 = Data sets at different redundancy levels • R1, R2, R3, R4 are given as one of the inputs to state estimation algorithms. • The norms and error indices given by following equations for every case of data loss are calculated. Infinity norm= Maximum(|z_measured - z_calculated|) L1-norm=Σ|z_measured-z_calculated| Euclidean norm=√ (Σ (z_measured-z_calculated) ^2) Error Index1 = L1-norm/ (number of measurements) Error Index 2 = Infinity norm/ (number of measurements) Revised Data Set with clustered data removed Revised Data Set with scattered data removed
TEST CASES • The test case has the following description • Generators - 2 • Loads - 5 • Lines - 7 • PMU’s at buses 1 and 4. Ward Hale 6-bus test case
TEST CASES • The IEEE 30 bus test case has the following components • Six generators • Four transformers • Forty one transmission lines. • Twenty one loads. • Three synchronous condensers. • PMU’s are assumed to be at buses 1 and 3 • IEEE 30 bus system
TEST CASES • The 137 bus test case has the following description • Transformers- 31 • Loads - 90 • Lines -159 • Generators -12 • The 137 bus test case is similar to the IEEE 118 bus system as shown. • The PMU’s are assumed to be present at buses 1 and 18.
MEASUREMENTS The measurements are obtained from a power flow program and an error is introduced by the following equation. z= A*(1+RND*σ). z= Measured value. RND=Random number with normal distribution & zero mean. A=Actual value from power flow σ = Standard deviation
RESULTS ( 6- BUS WITH LOSS OF MEASUREMENTS) % Redundancy Vs Error Index 1 for clustered data loss % Redundancy Vs Error Index 1 for scattered data loss % Redundancy = (m/n)*100 Error Index 1= (L1norm/m). m=number of measurements n=number of states.
RESULTS ( 30- BUS WITH LOSS OF MEASUREMENTS) % Redundancy Vs Error Index 1 for clustered data loss % Redundancy Vs Error Index 1 for scattered data loss
RESULTS ( 137- BUS WITH LOSS OF MEASUREMENTS) • % Redundancy Vs Error Index 1 for clustered data loss • % Redundancy Vs Error Index 1 for scattered data loss % Redundancy = (m/n)*100 Error Index 1= (L1norm/m). m=number of measurements n=number of states.
CONCLUSIONS • The comparison of state estimation algorithms on different test cases based on error indices helps to indicate the best algorithm for getting an accurate picture of the power system during extreme conditions. • Least Absolute Value algorithm was the best at most of the cases with data loss. • The Weighted Least Squares (WLS) method has almost the similar performance as that of LAV method for most of the cases. • Initial studies of state estimation results related to PMU penetration have shown impact in some cases. Additional work needs to be done to determine how placement and number of PMUs may affect results. • This work had provided the groundwork for the situational awareness needed to move forward with the help of different state estimation algorithms when the amount of data available is uncertain.
FUTURE WORK • Advanced testing related to PMU placement and numbers in various state estimation algorithms • To include multiple phasor measurements in WLS and IRLS WLAV methods when there is loss of data. • To include phasor measurements in LAV method with data loss. • The performance of the algorithms with both bad data and phasor measurements can be evaluated for the different state estimation algorithms. • To integrate state estimation with the SCADA test bed being developed at the MSU PERL lab.
Development of Corrective Actions for Higher Order Contingencies Bharath Kumar Ravulapati Dr Anurag K .Srivastava and Dr. Noel Schulz
Objectives • It is very important to maintain the power system security and operation in a normal state • Given situational awareness, developing a decision support system to take corrective actions is the objective of this work • Decision Support minimizes analysis time needed. • One of the main aims of this work is to develop an algorithm to help operators take corrective actions for multiple contingencies • Sensitivity based algorithms are developed based on AC and DC load flow model. • Objective of this work is also to include testing and validation of the developed algorithms using three test cases.
Motivation • Utilities are interconnected and are operating at their limit. • Due to this inherent nature any fault in the system may lead to multiple faults causing multiple outages called as higher order contingencies. • Blackouts occur due to cascading effect (multiple outages) • No proper tool is available for dealing with these multiple outages. • Proper planning is necessary to take corrective and preventive actions for solving those violations due to these contingencies
Remedial Action Schemes(RAS) • Remedial Action Schemes (RAS) are the key components for any power system utility planning. • These are the steps which the utilities need to take in order to get the system back to its normal operation. • Types of remedial actions • Shunt capacitor switching • Generation Re-dispatch • Load shedding • Under load tap changing (ULTC)Transformer • Islanding
Literature Review • Remedial Actions so far have only been developed for single contingencies. • In some cases AC power flow has been used which takes long time larger test cases. • Some of algorithms developed are not sufficient to deal with voltage problems by using DC power flow for solving violations. • Remedial Actions for multiple contingencies have not yet been developed.
Types of sensitivities The different types of sensitivities are • Line sensitivities ( includes transformer ) • Generator Sensitivities
Line Outage Sensitivities • DC • Power flow • AC • Power flow
Generator Outage Sensitivities • DC • Power flow • AC • Power flow
Corrective and Preventive Actions Methods ( online) • Take Corrective and Preventive Actions
MLODF FORMULATION using DC power flow • Thus we get impact on line ‘k’ using MLODF for multiple line outages
MLODF MLOBSF • MLOBSF • Suppose there is a line between bus ‘i´ and ‘j’ and its MLODF is M1 and there is a line between bus ‘i´ and ‘k’ and its MLODF is M2. Then the MLOBSF of buses i, j and k can be given as. MLOBSF of bus ‘i´ = M1+M2 MLOBSF of bus ‘j’ = M1 MLOBSF of bus ‘k’ = M2 Rank the buses according to their sensitivities.
MLOVS Formulation using AC power flow • For line ‘l’ (between buses ‘r’ and ‘s’)outage • For line ‘m’ (between buses ‘x’ and ‘y’) outage,
MLOVS con’t.. • The magnitudes of MGOVS for all the buses are obtained and ranked
MGODF MGODF ( based on DC power flow) • MGOBSF • GODF for line l ( between buses ‘m’ and ‘n’ ) is given as • Let us assume, • GODF of line l for generator at bus a is ‘G1’ • GODF of line l for generator at bus b is ‘G2’ • Base case MW of generator G1 is ‘MW1’ • Base case MW of generator G2 is ‘MW2’ • MGODF of the line l when both the generators at buses a and b are outaged • MGODF impact on line l = G1*MW1+G2*MW2 • General form when ‘n’ generators are outaged, • MGODF impact on line l = G1*MW1+G2*MW2+………G1*MWn
MGOBSF • Suppose there is a line between bus ‘i´ and ‘j’ and its MGODF is G1 and there is a line between bus ‘i´ and ‘k’ and its MGODF is G2. Then the MGOBSF of buses i, j, k can be given as. • MGOBSF of bus ‘i´ = G1+G2 • MGOBSF of bus ‘j’ = G1 • MGOBSF of bus ‘k’ = G2 Rank the buses according to their sensitivities.
Implementation of algorithms • Base case explanation • Implementation of MLOBSF algorithm on 37 bus test case system. • Implementation of MLOVS algorithm on 6 bus test case system. • Implementation of GLOBSF algorithm on 37 bus test case system. • Implementation of GLOVS algorithm on 137 bus test case system.
Figure 1: Base case without any violations • The test system consists of • 37 buses • 9 generators • 45 transmission lines (69kV, 138kV, 345kV) • Real load is 769.4MW and reactive load is 217.2MVAR • Generation 778.9 MW and 117.5 MVAR respectively.
Figure 2: 2 lines between UIUC69-BlT-69 are outaged. • Outaged lines • Limits Violated line • Outaged lines
After solving violations using MLODF/MLOBSF algorithm • List of top 5 sensitive buses • 16 • 57 • 15 • Back to normal Operating State • 54 • 24 • Sensitive buses acted upon by shedding the loads at the buses .
Implementing MLOVS on 6 bus Test case system • 6 buses • 3 generators • 11 transmission lines • 3 Loads
N-2 Contingency on 6 bus • Outaged line • Outaged line • Low voltage On Bus 4
After solving the violation using MLOVS algorithm • Algorithm results • List of top 5 sensitive buses • Improved voltage bus No 4 • Installed capacitor at bus No 4 • As seen in table the algorithm also gave bus number 4 as the most sensitive bus and when a Capacitor (42.5Mvar ) is installed at bus 4 the low voltage violation ( from 0.8428 pu to 0.9217 pu )is removed as seen in the figure
N-3 Generator Outage on 37 Bus System • As a result Slack bus generating out of limits • Outaged Generator 3 • Outaged Generator 1 • Outaged Generator 2
After solving the violations by generation increase using MGODF algorithm • 1 • List of top 5 sensitive buses • 48 • 50 • Sensitive buses acted upon by increasing the generation at the buses to supply the necessary load
Solving violation at the same buses by load shedding • List of top 5 sensitive buses • 1 • 32 • Sensitive buses acted upon
MGOVS • Let us assume there are two generators at buses i and j which are outaged • For generator at i outage, • For generator at j outage,
MGOVS contd… • The magnitudes of MGOVS for all the buses are obtained and ranked