• Imagine a student measuring current on an electrical circuit
With on meter, he measures .59 A. Being a cautious type, he measures again with a different meter, and reads
1.0 A. Which is correct?
.59
Meter 1
1.0
Meter 2

• Imagine a student measuring current on an electrical circuit
On the back of Meter 1 it says the measurement is accurate to +/- 5%
On the back of Meter 2 it says the measurement accuracy has a standard deviation of +/- 2%
What is the most probable actual current flow?
.59
1.0

The student assumed that the meaning of +/-
5% means that 99.9 % of measurements taken with that meter would be within 5%; or the
STANDARD DEVIATION of the measurements would be 5%/3 = 1.666%
What is the most probable actual current flow?
We cannot tell! All we know is that I have a bad meter! Each measurement is over 5 standard deviations from the other; making the probability of both being correct infinitesimal
Probable Error of measurements
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
0.5
0.6
0.7
0.8
0.9
1 1.1

But what if you do not know the accuracy of the instruments
• A state estimator is a minimization program, which minimizes the sum of weighted residuals. In this example, we assumed meter 1 had a measurement accuracy of +/- 1.666% standard deviation.
(i.e. 99.9% of measurements would be within 5%), and meter 2 had a measurement accuracy of +/- 2 standard deviations.

But what if you do not know the accuracy of the instruments
• If you have no idea of the expected accuracy of the instruments, then a
“reasonable” approach is to average the two measurements. (.56 + 1)/2 = 0.78 A
• This is obviously not correct from our previous analysis: so a basic requirement is to know the expected accuracy of your measurements.

Proposed Telemetry Requirement 1:
• TSP’s and QSE’s shall notify ERCOT of the expected accuracy of their analog measurements.
• Preferred format is expected accuracy of PT, CT,
A/D converter and transducer in percentage.
• TSPs & QSE’s will identify how the accuracy was calculated: i.e.
– Calculated from manufacturer specifications these devices (high confidence)
– MFG specs unavailable: estimated from typical specifications historically installed by our company
– A guess from our experience.

But what do you do when you identify a problem?
Probable Error of measurements
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
0.5
0.6
0.7
0.8
0.9
1 1.1

Proposed Telemetry Requirement 2
• When ERCOT identifies a measurement which is probably in Error, Participants shall recalibrate the device within 2 working days or provide
ERCOT with data documenting reasons that the measurement is known to be correct.
• Each TSP and QSE shall have a telemetry calibration program which can be shown to maintain the probable number of devices outside of their specified accuracy range to < 1% OR alternatively shall be re-calibrated once every 2 years.

• Imagine our student takes both meters to his Teaching Assistant, and asks him to check them. To his surprise, the instructor returns them 15 minutes later, telling him they both check out. What should he do?
• Logically he should ask how the meters were calibrated.
.59
Meter 1
1.0
Meter 2

Proposed Telemetry Requirement 3
• If a TSP or QSE examines a measurement at the request of ERCOT, and no error is detected, the TSP or QSE shall provide
ERCOT with details of how the calibration took place.

State Estimator
• Below is a single-line diagram with scada measurements.
• All measurements have equal weights (std=3%, w=1/(sd)^2=0.1111) in the uncertainty model.
• Measurements shown are red are erroneous, they are 25Mw (~28Mw) and 20 MW ( ~23MW) in reality.
15Mw 15Mw
~
20Mw
40Mw
28Mw
17Mw

State Estimator
SE solution 1 (SE values in black font and scada values in blue font)
• Objective function is to minimize sum of weighted squares of residuals (PI)
• KCL is loosened
• Equal Weights on all measurements ( 0.1111)
15Mw ( 15 ) 15Mw ( 15 )
~
20Mw
( 20 )
8Mw
28Mw
( 28 )
40Mw
( 40 )
28Mw
8Mw
17Mw ( 17 )
• PI = Σ weight(i) *residual(i) 2 =0
• Bus mismatches of 3 Mw at every bus

State Estimator
SE solution 2 (SE values in black font and scada values in blue font)
• Objective function is to minimize sum of weighted squares of residuals (PI)
• KCL is tightened to 0
• Equal Weights on all measurements ( 0.1111)
12.75Mw
( 15 ) 12.75Mw
( 15 )
20.75Mw
( 20 )
8Mw
~
25.75Mw
( 28 )
38.5Mw
( 40 )
25.75Mw
( 28 )
8Mw
17.75Mw
( 17 )
• PI = 0.1111*23 = 2.56
• Bus mismatches of 0 Mw at every bus
• Note that error on 3 measurements is spread across all estimates

State Estimator
SE solution 2 (SE values in black font and scada values in blue font)
• Objective function is to minimize sum of weighted squares of residuals (PI)
• 2 bad measurements have low weights ( std= 5%, w=0.04), all other measurements have normal weights (std=3%, w=0.111).
• KCL is normal (i.e. relaxed)
15Mw ( 15 ) ( 15 ) 15Mw
23Mw
( 20 )
8Mw
25Mw
~
( 28 )
40Mw
( 40 )
25Mw
8Mw
17Mw
( 17 )
• PI = 0.1111*0+ 0.04* 27 = 1.08
• Bus mismatches of 0 Mw at every bus

State Estimator
Weighting Calculation
Stdv =(PTE+CTE+ADCE+TRE)*Base/(Probable Max stdv based on gaussian distribution=5)
Example: If PT error = 1% (.01); CT error = 1% (.01); transducer = 1% (.01) and AD converter accuracy = 1% (.01) on a 271 MVA line than the expected standard deviation of the measurement mapped to that line is: (.01+.01+.01+.01)*271/5 = 2.61 and the weighting is 1/SD 2
= 0.14679
Now the Performance index = the sum of these weighting factors * residual or:
PI = Σ Weight Factor(i) * Residual(i) 2
So what information do we need for each measurement?
1.
Accuracy of PT (maximum error)
2.
Accuracy of CT
3.
Accuracy of A/D converter
4.
Accuracy of transducer

State Estimator

State Estimator
Default Weight Calculation
For a 1000Mva line belonging to MEAS class has
Stdv = (.01+.01+.01+.01)*1000/5=8, w=1/64
For a load with parent fraction 10 has
Stdv = (.01+.01+.01+.01)*10/5= .08, w=1/.0064