KVAh Metering Basics

kVAh Metering Basics Ashok Hattangady

Director Technology Development, Conzerv Systems Pvt Ltd, Bangalore, India

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09/20/06

© Copyright 1986-2005, ConZerv Proprietary & Confidential

Smart Energy Management

kVA 

kVA is already widely in use:   



2

kVA Demand PF Penalties. PF = kW / kVA Sizing of Transformers and Distribution

Any wrong definitions are detrimental and must be corrected, irrespective of billing kVAh directly

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Principle of kVA Eg. Motor Load needs 100kVAR of Reactive Energy 141 kVA 0.7 PF

~ 100 100 kW kVAR

100 kVA 1 PF

~ 100 kW

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Reactive Energy supplied by Source

Reactive Energy supplied by Capacitor


M 141 kVA 0.7 PF

M 100 141 kVA kVAR 0.7 PF


Spectral Constituents of kVA V A kW, kVAR, S D

Distortion

kVA- U 4

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Apparent


Effect of D on kVA, PF 

V

 

Consider the Rectifier Waveform- PCs, UPS, CFL etc S (Vector) kVA gives a PF of 1.00 U (Apparent) kVA gives a PF of 0.5

A

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Vector Constituents of kVA 1Φ Q Reactive kVAR

S Phasor kVA = + P2 + Q2 U Apparent kVA = + P 2 + Q2 + D2 = Vrms × A rms P Active kW

D Distortion kVA 6

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Polarity kept same as Q, not W per IEEE 100



IEEE 100

Six kVAs One Apparent Power (U) Uarith = 3ph Arithmetic kVA = V1A1+ V2A2+ V3A3

F

Fictitious kVA

S Phasor kVA = + P2 + Q2

= Q 2 + D2

U Apparent kVA = + P 2 + Q2 + D2 = Vrms × A rms

= ± U2 − S 2 D Distortion kVA

N Nonreactive kVA = P 2 + D2

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3Φ Apparent Power U 2

2

P3 + Q3 + D3 2

2

P2 + Q2 + D2 2

2

2

2

2

P1 + Q1 + D1 U3 φ = 8

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( P1 + P2 + P3 ) 2 + ( Q1 + Q2 + Q3 ) 2 + ( D1 + D2 + D3 ) 2



Vector & Scalar Addition Example: How far has your Taxi gone?

4 km

5 km “as the crow flies” 3 km Vector Add

7 km “the fare you pay” Scalar Add 9

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Apparent kVA (U) vs Arithmetic kVA 3ph V1A1

Arithmetic Scalar UArith = U1 + U2 + U3 = V1A 1 + V2 A 2 + V3 A 3

V2 A 2

Note that V2A2 & V3A3 are positive (no sign)

V3A3

Apparent

Vector addition in 3D

U3φ = ( P1 + P2 + P3 ) + ( Q1 + Q2 + Q3 ) + ( D1 + D2 + D3 ) 2

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2


2

Apparent kVA (U) vs Arithmetic kVA 3ph Arithmetic Scalar UArith = U1 + U2 + U3 = V1A 1 + V2 A 2 + V3 A 3

Apparent

Vector addition in 3D

U3φ = ( P1 + P2 + P3 ) + ( Q1 + Q2 + Q3 ) + ( D1 + D2 + D3 ) 2

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2


2

Apparent kVA (U) vs Arithmetic kVA 3ph 

3ph Apparent kVA =

U3φ = ( P1 + P2 + P3 ) + ( Q1 + Q2 + Q3 ) + ( D1 + D2 + D3 ) 2



2

2

3ph Arithmetic kVA = 2 1

2 1

2 1

2

2

2

2

2

UArith = P + Q + D + P2 + Q2 + D2 + P3 + Q3 + D3 = U1 + U2 + U3 = V1A 1 + V2 A 2 + V3 A 3 12

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2

kVAh Integration 



kVAh (over intervals of time) = …. = U1 + U2 + U3 2 1

2 1

2 1

2

2

2

2

= P + Q + D + P2 + Q2 + D2 + P3 + Q3 + D3 But Derived kVAh = kWh2 + kVARh2 

is much smaller

= ( P1 + P2 + P3 ) 2 + ( Q1 + Q 2 + Q3 ) 2 13

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2 1

2

2

= P + P2 + P3 + 2P1P2 + 2P1P3 + 2P2P3 .... © Copyright 1986-2005, ConZerv Proprietary & Confidential


2

Apparent kVA (U) vs Arithmetic kVA 

Apparent kVA includes Wh, PF, THD revenue 



Arithmetic kVA in addition includes “Unbalance” revenue 



14

a “Vector” quantity, but always Positive

a Scalar quantity

Uarith ≥ U ≥ S. Uarith is higher than U especially for Delta loads with unbalance

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Apparent kVA (U) vs Arithmetic kVA

• Traditional Billing

kWh

PF

• Apparent kVAh

kWh

PF

THD

• Arithmetic kVAh

kWh

PF

THD

» kWH + PF Penalty

» + THD

» + THD + Unbalance

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Unbalance Smart Energy Management

Apparent kVA (U) vs Arithmetic kVA 

Unbalance Penalization with Arithmetic kVA



Placing a single Line-Line Load (resistor) creates maximum Unbalance Uarith is 15.5% more than W, PF=0.866



Arithmetic kVA penalizes Unbalance



16

Vb

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Vr Vy


Apparent kVA (U) vs Arithmetic kVA 3ph 

Arith kVA, kVAh, Demand- insensitive to    



17

CT Polarity PT, CT Phase Shift errors Phase Sequence Better accuracies can be achieved. Tariff meter need show only V, A, Freq, Arith kVA, Arith kVAh, Arith kVA Dmd

But Apparent kVA is degraded by these

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Apparent kVA in Delta HT Systems 

kVA (S), PF in Delta systems do not fully measure Harmonic energy with   



18

Non-sinusoidal Waveforms Unbalanced Voltage Vectors / Loads A limitation today in HT kVA Demand and PF values

In Meter, compute on equivalent Star vectors

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Applications

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Expected Growth Of Electric Energy Demand GWh/Yr 4000 3500

150% Growth

3000 2500 2000 1500

Rest of World

1000 500 0 20

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Asia 1995


300% Growth 2020


Electricity Cost Rising Fastest in India 6 Steam 5 4

Coal

Electricity

Cost in India. Normalised to 1988

3 2 1 1988 21

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1990

1992


1995

1998


2001

14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 22 09/20/06



S. Africa.

Sweden.

Canada.

Norway.

Newzealand.

Finland.

Denmark.

S.Korea.

Australia.

Israel.

US Cents / kWh

Greece.

USA.

Netherlands.

France.

Ireland.

UK.

Spain.

Belgium.

Portugal.

Italy.

Austria.

Germany

India

Japan.

Power Costs Worldwide

2.5 MW supply, 40% Load

Electricity Usage in India Motors 75% Industrial + Agricultural

Arc Furnaces Others 1% 6% Electrolysis 5% 23

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Lighting 13%


Sector – wise % Consumption Others Industrial Agricultre Domestic

Normalized % : India Source: Annual Report on the Working of SEBs, Planning Commission, June 2001

21.8

19.3

17 31

50.8

41.9 32

18.4 9 24

25.9 13

1984 © Copyright 1986-2005, ConZerv Proprietary & Confidential 1989

09/20/06

20

1999 Smart Energy Management

Applications 

Arithmetic kVA  



Apparent kVA   

25

Domestic (1ph) and Commercial billing Simplicity in meeting the cost of service

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Industrial and Grid metering Not possible for 1ph services Available in the meters?



Applications 



26

Arithmetic kVA is suitable for Domestic and Commercial billing with simplicity in meeting the cost of service Apparent kVA is probably better suited to Industrial and Grid metering. It would simplify billing if available in the meters. It is also more suitable for Energy Balancing than Arithmetic kVA.

09/20/06





    

27

Arithmetic kVA Insensitive to CT Polarity, Phase shift error, phase sequence. Not Vector kVA Import / Export? kVA Polarity Star only, not Delta Energy Balancing when PF Caps added KVA Demand Includes PF, Harmonics, Unbalance

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“Cost of Service” Indicator 

kWh + PF Penalty 



kVAh Metering 



Includes PF penalty.

Arithmetic kVAh Metering 

28

Historic origin of kWh

09/20/06

Includes unbalance penalty. True cost of service



KVA Measurement

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2D VA

Arith VA

3D VA

Pythogoras √(W2+VAR2)

Europe VA1+VA2+VA3

√(W +VAR2+D2)


Ideal 2


Correct kVA Steps already known 

For 2E: Convert from Delta to Star 





Then, VA is given by: U3 φ =

( P1 + P2 + P3 )

2

+ ( Q1 + Q 2 + Q3 ) + ( D1 + D2 + D3 ) 2

Polarity of D = Polarity of VAR, not W 

30

IEEE 100

09/20/06

VAR must be directly calculated not from VA



2

kVA Test Case 1 

Unbalance Penalization with Arithmetic kVA



Placing a single Line-Line Load (resistor) creates maximum Unbalance Uarith is 15.5% more than W, PF=0.866



Arithmetic kVA penalizes Unbalance



31

Vb

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Vr Vy


KVA Test Case 2 (UPS)

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Unbalanced kVA 2D VA

Arith VA

3D VA

CBIP √(W2+VAR2)

Europe VA1+VA2+VA3

Ideal √(W2+VAR2+D2)

R

536.6

1200

1200

Y

452.4

1364

1364

B

268.3

600

600

3 Phase

1257

3164

2191

Phase

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Unbalanced PF 2D

Arith

3D

CBIP

Europe

Ideal

R

- 0.999

- 0.447

- 0.447

Y

- 0.853

- 0.283

- 0.283

B

0.999

0.447

0.447

3 Phase

- 0.947

- 0.544

+ 0.376

Phase

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KVAh Metering Basics

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