This document discusses transformer-rated metering fundamentals, including: - Transformer-rated meters measure current through current transformers and sometimes voltage transformers, unlike self-contained meters which connect directly to the load. - Blondel's theorem states that total power in a polyphase system can be measured using N-1 meters connected between each line and a common point. - Meeting Blondel's theorem ensures accurate power measurements under all conditions, while violations may cause errors if voltage and current are not balanced. - Examples show how to apply Blondel's theorem correctly for 3-phase 4-wire systems.

1. TESCO
Tuesdays
Today’s session will begin shortly

2. 2
January 28, 2019
Atlanta, GA
Transformer-Rated & Self-Contained
Metering Fundamentals
Prepared by Tom Lawton, TESCO
The Eastern Specialty Company
TESCO Tuesdays
October 6, 2020

3. 3
Topics we will be covering
• The Basics- Differences Between Self
Contained and Transformer or Instrument
Rated Meter Sites
• Transformer Rated Meter Forms
• Test Switches and CT’s
• Blondel’s Theorem and why this matters to
us in metering
• Meter Accuracy Testing in the Field
• Checking the Health of your CT’s and PT’s
• Site Verification and not just meter testing

4. 4
Self Contained Metering
•Typically found in residential
metering
•Meters are capable of handling
the direct incoming amperage
•Meter is connected directly to
the load being measured
•Meter is part of the circuit
•When the meter is removed
from the socket, power to the
customer is interrupted

5. 5
Meters Through the Years
Induction Meter Duncan Meter Meter from 1960’s
Meter from 80’s and 90’s 2000 to Present

6. 6
Back to Basics: Electrical Laws
Ohms Law
Voltage = Current times Resistance
V = I X R
THE MOST USEFUL AND THE MOST
FUNDAMENTAL OF THE ELECTRICAL LAWS

7. 7
Basic Concepts: Electricity and Water
Comparing Electricity to Water flowing from a hose
■ Voltage is the equivalent of the pressure in the hose
■ Current is water flowing through a hose (coulombs/sec vs
gal/sec). The water in a system is the “charge” (coulombs)
■ Impedance(Resistance) is the size of the hose. The nozzle
would provide a change in resistance.
■ Power is how fast water flows from a pipe (gallons per minute vs
kilowatts). Power is a rate of energy consumption

8. 8
Basic Concepts: Electricity and Water

9. 9
Practical Electricity

10. 10
Basic Electrical Laws
♦ Ohms Law Examples
■ If V = 20 volts and I = 5 amperes what is the resistance?
R = V / I = 20 / 5 = 4 ohms
■ If R = 20 ohms and V = 120 volts what is the current?
I = V / R = 120 / 20 = 6 amps
■ If I = 10 amperes and R = 24 ohms what is the voltage?
V = I x R = 10 x 24 = 240 volts
■ Problem: If V = 240 volts and R = 6 ohms what is the current?
I = V / R = 240 / 6 = 40 amps

11. 11
Basic Electrical Laws

12. 12
Basic Electrical Laws
♦ Power = Voltage x Current = V x I = I2R = V2/R
■ If V = 20 volts and I = 8 amperes what is the power?
P = V x I = 20 x 8 = 160 watts
■ If R = 5 ohms and V = 120 volts what is the power?
P = V2/R = 120 x 120 / 5 = 2880 watts
■ If I = 10 amperes and R = 20 ohms what is the power?
P = I2R = 10 x 10 x 20 = 2000 watts
1 kilowatt (kW) = 1,000 watts
1 megawatt (MW) = 1,000,000 watts

13. 13
Basic AC Theory
What is VA?
Power was measured in Watts. Power does useful work.
The power that does useful work is referred to as
“Active Power.”
VA is measured in Volt-Amperes. It is the capacity
required to deliver the Power. It is also referred to as the
“Apparent Power.”
Power Factor = Active Power / Apparent Power
VA = E x I
PF = W/VA

14. 14
Basic Meter Math
Power – VA
For a 120 Volt service drawing 60 Amps at 1.00 PF
How much power is being drawn?
Power = 120 x 60 x 1.00 = 7,200 Watts
How many VA are being drawn?
VA = 120 x 60 = 7,200 Volt Amperes

15. 15
Basic AC Theory
Power – The Simple View
E = Voltage (rms)
I = Current (rms)
PF = Power Factor
Power = Watts = E x I x PF
Power is sometimes
referred to as Demand
Sinusoidal
Waveforms
Only
NO
Harmonics
For a 120 Volt service drawing
13 Amps at Unity (1.0) PF,
how much power is being drawn?
Power = 120 x 13 x 1.0 = 1560 Watts

16. 16
Basic AC Theory
Power Factor = 1.0
AC
RVrms
Irms

17. 17
Basic Meter Math
Power – The Simple View
For a 120 Volt service drawing
13 Amps at 0.866 PF,
how much power is being drawn?
Power = 120 x 13 x 0.866 = 1351 Watts
For a 480 Volt service drawing
156 Amps at 0.712 PF,
how much power is being drawn?
Power = 480 x 156 x 0.712 = 53,315 Watts

18. 18
Basic AC Theory
Power – The Simple View
In the previous example we had:
Power = 480 x 156 x 0.712 = 53,315 Watts
Normally we don’t talk about Watts, we speak in Kilowatts
1000 Watts = 1 Kilowatt = 1 kW
Watts / 1000 = Kilowatts
For a 480 Volt service drawing
156 Amps at Unity (0.712) PF,
how many Kilowatts are being drawn?
Power = 480 x 156 x 0.712 / 1000 = 53.315 kW

19. 19
Basic AC Theory
Energy – What We Sell
If power is how fast water flows from a pipe,
then energy is how much water we have in a bucket
after the water has been flowing for a specified time.
Energy = Power x Time
1 kW for 1 Hour = 1 Kilowatt-Hour = 1 kWh
Energy (Wh) = E x I x PF x T
where T = time in hours
Energy (kW) = (E x I x PF / 1000) x T

20. 20
Basic Meter Math
Energy – What We Sell
For a 120 Volt service drawing 45 Amps at a
Power Factor of 0.9 for 1 day,
how much Energy (kWh) has been used?
Energy = (120 x 45 x 0.9 / 1000) x 24 = 116.64 kWh
For a 240 Volt service drawing 60 Amps at a
Power Factor of 1.0 for 5.5 hours,
how much Energy (kWh) has been used?
Energy = (240 x 60 x 1.0 / 1000) x 5.5 = 79.2 kWh

21. 21
Basic Meter Math
Energy – What We Sell
For a 120 Volt service drawing 20 Amps at a
Power Factor of 0.8 from 8:00AM to 6:00PM,
and 1 Amp at PF=1.0 from 6:00PM to 8:00AM
how much Energy (kWh) has been used?
8:00AM to 6:00PM = 10 hours
6:00PM to 8:00AM = 14 hours
Energy = (120 x 20 x 0.8 / 1000) x 10 = 19.2 kWh
Energy = (120 x 1 x 1 / 1000) x 14 = 1.68 kWh
Energy = 19.2 kWh + 1.68 kWh = 20.88 kWh

22. 22
Basic Energy Formula
• The essential specification of a watthour meter’s measurement
is given by the value
Kh [ Watthours per disk revolution ]
• The watthour meter formula is as follows:
   srevolutiondisk
revolutiondisk
watthours
Watthours nKE h *





23. 23
Meter Shop Accuracy Test Demo

24. 24
TESCO/Georgia Power 2017 Caribbean Meter School
Fundamentals of Polyphase Field Meter Testing and Site Verification
 Full Load
 Light Load
 Power Factor
Meter Accuracy Testing
Meter Accuracy
Testing in a Nutshell

25. 25
Transformer Rated Metering
• Meter measures scaled down
representation of the load.
• Scaling is accomplished by the use
of external current transformers
(CTs) and sometimes voltage
transformers or PTs).
• The meter is NOT part of the circuit
• When the meter is removed from
the socket, power to the customer
is not effected.

26. 26
9S Meter Installation with 400:5 CT’s
400A
400A
400A
LOAD
5A 5A 5A
SOURCE
PHASE A
PHASE B
PHASE C
The Basic Components

27. 27
CT Metering Accuracy

28. 28
Current Transformer Testing System &
Voltage Transformer Testing System
Knopp Voltage Transformer
Testing System
Knopp Current Transformer
Testing System

29. 29
Fundamentals of Polyphase Field Meter
Testing and Site Verification
Current Transformers Conceptual
Representation
Real, with core losses
Ideal. No losses

30. 30
Fundamentals of Polyphase Field Meter
Testing and Site Verification
Functionality with Burden Present on the Secondary Loop
PHASE A
• Some burden will always be
present – junctions, meter
coils, test switches, cables,
etc.
• CT’s must be able to
maintain an accurate ratio
with burden on the
secondary.

31. 31
Fundamentals of Polyphase Field Meter
Testing and Site Verification
Functionality with Burden Present on the Secondary Loop
Example Burden Spec:
0.3% @ B0.1, B0.2, B0.5
or
There should be less than the 0.3%
change in secondary current from initial
(“0” burden) reading, when up to 0.5 Ohms
of burden is applied
Fundamentals of Polyphase Field Meter
Testing and Site Verification

32. 32
Fundamentals of Polyphase Field Meter
Testing and Site Verification
Functionality with Burden Present on the Secondary Loop
0.3% @ B0.1, B0.2, B0.5
0.0000
1.0000
2.0000
3.0000
4.0000
5.0000
6.0000
0 2 4 6 8
Initial Reading = 5Amps
0.3% x 5A = 0.015A
5A – 0.015 = 4.985A
Burden Reading
0 5.0000
0.1 4.9999
0.2 4.9950
0.5 4.9900
1 4.9800
2 4.9500
4 4.0000
8 0.8000

33. 33
Ratio of Primary Current to Secondary Current
PHASE A
SOURCE LOAD
400A
400A
400A
5A5A
Calculate Ratio
Fundamentals of Polyphase Field Meter
Testing and Site Verification

34. 34
Typical Connections
Typical Connections for Common
Transformer (Instrument)
Rated Meter Forms

35. 35
Three Phase Power
Blondel’s Theorem
The theory of polyphase watthour metering was first set forth on a scientific
basis in 1893 by Andre E. Blondel, engineer and mathematician. His theorem
applies to the measurement of real power in a polyphase system of any
number of wires. The theorem is as follows:
- If energy is supplied to any system of conductors
through N wires, the total power in the system is given
by the algebraic sum of the readings of N wattmeters, so
arranged that each of the N wires contains one current
coil, the corresponding voltage coil being connected
between that wire and some common point. If this
common point is on one of the N wires, the
measurement may be made by the use of N-1
wattmeters.

36. 36
Three Phase Power
Blondel’s Theorem
• Simply – We can measure the power in a
N wire system by measuring the power in
N-1 conductors.
• For example, in a 4-wire, 3-phase system
we need to measure the power in 3
circuits.

37. 37
Three Phase Power
Blondel’s Theorem
• If a meter installation meets Blondel’s
Theorem then we will get accurate power
measurements under all circumstances.
• If a metering system does not meet
Blondel’s Theorem then we will only get
accurate measurements if certain
assumptions are met.

38. 38
Blondel’s Theorem
• Three wires
• Two voltage measurements with
one side common to Line 2
• Current measurements on lines
1 & 3.
This satisfies Blondel’s
Theorem.

39. 39
Blondel’s Theorem
• Four wires
• Two voltage measurements to
neutral
• Current measurements on lines 1 &
3. How about line 2?
This DOES NOT satisfy Blondel’s
Theorem.

40. 40
Blondel’s Theorem
• In the previous example:
– What are the “ASSUMPTIONS”?
– When do we get errors?
• What would the “Right Answer” be?
• What did we measure?
)cos()cos()cos( cccbbbaaasys IVIVIVP  
)]cos()cos([)]cos()cos([ bbcccbbaaasys IIVIIVP  

41. 41
Blondel’s Theorem
• Phase B power would be:
– P = Vb Ib cosθ
• But we aren’t measuring Vb
• What we are measuring is:
– IbVacos(60- θ) + IbVccos(60+ θ)
• cos(α + β) = cos(α)cos(β) - sin(α)sin(β)
• cos(α - β) = cos(α)cos(β) + sin(α)sin(β)
• So

42. 42
Blondel’s Theorem
• Pb = Ib Va cos(60- θ) + Ib Vc cos(60+ θ)
• Applying the trig identity
– IbVa(cos(60)cos(θ) + sin(60)sin(θ))
IbVc (cos(60)cos(θ) - sin(60)sin(θ))
– Ib(Va+Vc)0.5cos(θ) + Ib(Vc-Va) 0.866sin(θ)
• Assuming
– Assume Vb = Va = Vc
– And, they are exactly 120° apart
• Pb = Ib(2Vb)(0.5cosθ) = IbVbcosθ

43. 43
Blondel’s Theorem
• If Va ≠ Vb ≠ Vc then the error is
• %Error =
-Ib{(Va+Vc)/(2Vb) - (Va-Vc) 0.866sin(θ)/(Vbcos(θ))
How big is this in reality? If
Va=117, Vb=120, Vc=119, PF=1 then E=-1.67%
Va=117, Vb=116, Vc=119, PF=.866 then E=-1.67%

44. 44
Blondel’s Theorem
Condition % V % I Phase A Phase B
non-
Blondel
Imb Imb V φvan I φian V φvbn I φibn
% Err
All balanced 0 0 120 0 100 0 120 180 100 180 0.00%
Unbalanced voltages PF=1 18% 0% 108 0 100 0 132 180 100 180 0.00%
Unbalanced current PF=1 0% 18% 120 0 90 0 120 180 110 180 0.00%
Unbalanced V&I PF=1 5% 18% 117 0 90 0 123 180 110 180 -0.25%
Unbalanced V&I PF=1 8% 18% 110 0 90 0 120 180 110 180 -0.43%
Unbalanced V&I PF=1 8% 50% 110 0 50 0 120 180 100 180 -1.43%
Unbalanced V&I PF=1 18% 40% 108 0 75 0 132 180 125 180 -2.44%
Unbalanced voltages
PF≠1 PFa = PFb
18% 0% 108 0 100 30 132 180 100 210 0.00%
Unbalanced current
PF≠1 PFa = PFb
0% 18% 120 0 90 30 120 180 110 210 0.00%
Unbalanced V&I
PF≠1 PFa = PFb
18% 18% 108 0 90 30 132 180 110 210 -0.99%
Unbalanced V&I
PF≠1 PFa = PFb
18% 40% 108 0 75 30 132 180 125 210 -2.44%
Unbalanced voltages
PF≠1 PFa ≠ PFb
18% 0% 108 0 100 60 132 180 100 210 -2.61%
Unbalanced current
PF≠1 PFa ≠ PFb
0% 18% 120 0 90 60 120 180 110 210 0.00%
Unbalanced V&I
PF≠1 PFa ≠ PFb
18% 18% 108 0 90 60 132 180 110 210 -3.46%
Unbalanced V&I
PF≠1 PFa ≠ PFb
18% 40% 108 0 75 60 132 180 125 210 -4.63%
Power Measurements Handbook

45. 45
Testing at Transformer Rated Sites
Meter Accuracy
Full Load
Light Load
Power Factor
CT Health
Burden Testing
Ratio Testing
Admittance Testing
Site Verification

46. 46
The Importance of CT Testing in the Field
• One transformer in three wired
backwards will give the customer a
bill of 1/3rd the actual bill.
• One broken wire to a single
transformer will give the customer a
bill of 2/3rd the actual bill
• One dual ratio transformer
inappropriately marked in the billing
system as 400:5 instead of 800:5
provides a bill that is ½ of the actual
bill. And the inverse will give a bill
double of what should have been
sent. Both are lose-lose situations
for the utility.

47. 47
The Importance of CT Testing in the Field
(continued)
•Cross Phasing (wiring errors)
•Loose or Corroded Connections
•CT Mounted Backwards
•CT’s with Shorted Turns
•Wrong Selection of Dual Ratio CT
•Detect Magnetized CT’s
•Burden Failure in Secondary Circuit
•Open or Shorted Secondary
•Mislabeled CT’s
•Ensures all Shorting Blocks have been Removed

48. 48
Potential list of tasks to be completed during a Site
Verification of a Transformer Rated Metering Site
• Double check the meter number, the location the test result and the meter record
• Perform a visual safety inspection of the site. This includes utility and customer equipment. Things
to look for include intact down ground on pole, properly attached enclosure, unwanted voltage on
enclosure, proper trimming and site tidiness (absence of discarded seals, etc.)
• Visually inspect for energy diversions (intentional and not). This includes broken or missing wires,
jumpers, open test switch, unconnected wires and foreign objects on meters or other metering
equipment. Broken or missing wires can seriously cause the under measurement of energy. A
simple broken wire on a CT or VT can cause the loss of 1/3 to 1/2 of the registration on either 3
element or 2 element metering, respectively.
• Visually check lightning arrestors and transformers for damage or leaks.
• Check for proper grounding and bonding of metering equipment. Poor grounding and bonding
practices may result in inaccurate measurements that go undetected for long periods of time.
Implementing a single point ground policy and practice can reduce or eliminate this type of issue.
• Burden test CTs and voltage check PTs.

49. 49
Site Verification Checklist (continued)
• Verify service voltage. Stuck regulator or seasonal capacitor can impact service voltage.
• Verify condition of metering control wire. This includes looking for cracks in insulation, broken
wires, loose connections, etc.
• Confirm we have a Blondel compliant metering set up
• Compare the test switch wiring with the wiring at the CTs and VTs. Verify CTs and VTs not cross
wired. Be sure CTs are grounded in one location (test switch) only.
• Check for bad test switch by examining voltage at the top and bottom of the switch. Also verify
amps using amp probe on both sides of the test switch. Verify neutral connection to cabinet
(voltage).
• Check rotation by closing in one phase at a time at the test switch and observing the phase
meter for forward rotation. If forward rotation is not observed measurements may be significantly
impacted as the phases are most likely cancelling each other out.
• Test meter for accuracy. Verify demand if applicable with observed load. If meter is performing
compensation (line and/or transformer losses) the compensation should be verified either
through direct testing at the site or by examining recorded pulse data.
• Loss compensation is generally a very small percentage of the overall measurement and would
not be caught under utilities normal high/low checks. However, the small percentages when
applied to large loads or generation can really add up overtime. Billing adjustments can easily be
in the $million range if not caught early.

50. 50
Site Verification Checklist (continued)
• Verify metering vectors. Traditionally this has been done using instruments such as a circuit
analyzer. Many solid state meters today can provide vector diagrams along with volt/amp/pf and
values using meter manufacturer software or meter displays. Many of these desired values are
programmed into the meters Alternate/Utility display. Examining these values can provide much
information about the metering integrity. It may also assist in determining if unbalanced loads are
present and if CTs are sized properly. The vendor software generally has the ability to capture both
diagnostic and vector information electronically. These electronic records should be kept in the
meter shop for future comparisons.
• If metering is providing pulses/EOI pulse to customers, SCADA systems or other meters for
totalization they also should be verified vs. the known load on the meter. If present test/inspect
isolation relays/pulse splitters for things like blown fuses to ensure they are operating properly.
• Verify meter information including meter multiplier, serial number, dials/decimals, Mp, Ke, Primary
Kh, Kr and Rate. Errors in this type of information can also cause a adverse impact on
measured/reported values.
• Verify CT shunts are all opened.
• Look for signs of excessive heat on the meter base e.g.
melted plastic or discoloration related to heat

51. 51
Site Verification: Why should we invest our
limited meter service resources here
• These customers represent a
disproportionately large amount of the overall
revenue for every utility in North America.
• For some utilities the ten percent of their
customers who have transformer rated
metering services can represent over 70% of
their overall revenue.
• While these numbers will vary from utility to
utility the basic premise should be the same
for all utilities regarding where Meter
Services should focus their efforts
• This is perhaps one of the larger benefits that
AMI can provide for our Utilities – more time
to spend on C&I metering and less on
residential
Easy Answer: Money.

52. 52
Periodic Site Inspections…..
….Can Discover or Prevent:
• Billing Errors
• Bad Metering set-up
• Detect Current Diversion
• Identify Potential Safety Issues
• Metering Issues (issues not
related to meter accuracy)
• AMR/AMI Communications Issues
• The need for Unscheduled Truck Rolls
due to Undetected Field Related Issues
• Discrepancies between what is
believed to be at a given site versus the
actual setup and equipment at the site

53. 53
Topics we covered
• The Basics- Differences Between Self
Contained and Transformer or Instrument
Rated Meter Sites
• Transformer Rated Meter Forms
• Test Switches and CT’s
• Blondel’s Theorem and why this matters to
us in metering
• Meter Accuracy Testing in the Field
• Checking the Health of your CT’s and PT’s
• Site Verification and not just
meter testing

54. 54
Q&A and
Upcoming TESCO Tuesday Presentations
Presentation Date
OSHA Title 8 & Meter Testing Safety 10/13
Meter Test Switches 10/20
CT Testing: Theory & Practice 10/27
Ratio, Burden and Admittance 11/3
Asset & Inventory Management in the IoT Utility 2.0 World 11/10
Harmonics 11/17
Complete Site Testing 12/1
Electric Vehicle Trends & Calibration of Commercial Chargers 12/8
Streetlights & 5G Metering and Testing 12/15
Sign up: tescometering.com/tescotuesdays

55. #TESCOTuesdays
Thanks for tuning in!
See you at the next session.
Upcoming Session:
OSHA Title 8 & Meter Testing Safety
October 13, 2020 | 11:00 AM Eastern
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@TESCO_Metering
TESCO -The Eastern Specialty Company
TESCO -The Eastern Specialty Company