TRANSFORMER BASICS
FECA Clearwater FL June 11, 2009
1
Transformer Applications – FECA Agenda
June 11, 2009
08:30-10:00
Transformer Overview
- Basic Construction
- Lightning / LV Surges
- Voltage Regulation / Flicker
- Life Cycle Costing / DOE Efficiency Ruling
10:00-10:15
Break
10:15-12:15
Insulation Life (C57.91) + TAP Simulations
- The “Meaning of Life”the C57.91 Loading Guide
- Over Head – Residential + flicker
- Padmount – Residential + fusing + Short Circuit
- Padmount 3Φ + harmonics
- Vault 3Φ + vault restrictions
- Substation/Power Transformers
- Ratings/Cooling Modes – Settings
- Contingency Modeling
1:00 – 2:45
Power Transformer Maintenance, Monitoring & DGA
2:45 – 3:00
Exams/Discussions/wrap-up
Revised June 2009 dad
Generation Step Up - GSU
Generation…
Transmission…
Substation…
Distribution - Outdoors
Distribution - Downtown
Distribution - Indoors
Transformer Function
• Converts electricity from high voltage and low current
to low voltage and high current … or … vice versa
• Electricity is better generated and used at low voltage,
and better transported at high voltage…
• Transformers are the basic links of a T&D system…
• Electricity and Magnetism work together to produce
“transformer action”…
• Thin Electrical Grade Steel provides an excellent path
for magnetic flux…
Distribution – Wound Core
Basic Distribution Transformer Core Loop
Distribution – ‘Stacking a Core’
Wound Coil - Note “LV Crossovers”
Core and Coil (LV Side)
Shell Type … Note ‘Core Grounding’
Core and Coil (HV Side)
Distribution – Shell Type - Interlaced LV windings
core & coil
- excellent Short Circuit
strength...
SS
P
SS
SS
P
- natural impedance's
typically 1.5-2.0%
for SPS construction...
Interlaced SPS Shell Type C&C Cross-section
SS
Distribution – Non-Interlaced LV windings
core & coil
- excellent Short Circuit
strength...
S
P
S
S
P
S
- natural impedance's
typically 1.5-2.0%
for SPS construction...
Non-Interlaced SPS Shell Type C&C Cross-section
Distribution – Core Type
core & coil
P S
- good dielectric
strength...
S P P S
- typically good on
thermal performance...
- natural impedance's
typically 2.5-3.5%...
- MUST be interlaced...
Core Type C&C Cross-section
S P
Distribution - 3Φ 5 Legged Construction
3 Φ core & coil
P S
S P P S
S P P S
S P
3 Phase 5-Legged C&C Cross-section
Power – Stacked Core Form
Power – Stacked Core Form
Stacked Core – Core Cutting
Power – Disk Windings
Disk Windings
Power Transformer – Disk Winding
Power – Disk Windings
Power – Disk Windings
Power Transformer – Clean Room
Power Transformer – 667MVA 1Φ
Power – Pan-Cake Windings
Pan-Cake Windings
Power – Shell Form Construction
Transformer Function
• Converts electricity from high current and low voltage
to low current and high voltage … or … vice versa
• Electricity is better generated at low voltage, and
better transported at high voltage…
• Transformers are the basic links of a T&D system…
• Electricity and Magnetism work together to produce
“transformer action”…
Transformers – Basic Equations
Maxwell’s Equations
Differential form - General Case
δD
x H = J + δt
δβ
x E = - δt
Ampere’s Law
Faraday’s Law of Induction
·D=ρ
Gauss’s Law for Electricity
·β=0
Gauss’s Law for Magnetism
∆
∆
∆
∆
where,
H = Magnetic Field Strength
E = Electric Field
D = Electric Displacement
J = current density
β = Magnetic Field
ρ = Charge Density
Transformers – Electric and Magnetic Fields
When a wire is connected to an AC power source, current flows
through it and a magnetic field is created around the wire…
Transformer – Ratings
• Transformers are rated in Volt-Amperes @ a specified Maximum
Average Winding Temperature Rise in degrees Centigrade.
For example, a 25 kVA 65 Deg C rise transformer is rated to transform 25,000 Volt
Amperes from one voltage/current level to another voltage/current level WITHOUT
exceeding an Average Winding Rise of 65 Deg C above the Ambient.
• Liquid Filled (Mineral Oil or Natural Esters) Distribution Transformers
are rated in kVA at 65 Deg C. Typically 10-167 kVA 1Φ or 15-2500 kVA 3Φ.
• Power Transformers are usually specified in MVA (million volt
amperes). Multiple ratings can be specified at either or both 55
and/or 65 Degree C Rise.
Power Transformers can have multiple ratings based on optional cooling systems such
as
Fans or Pumps. For example OA/FA/FA (or under the new EIC definitions
ONAN/ONAF/ONAF) for the ratings based on ‘Natural Air/Oil Cooling/Forced Air Cooling/and a
second
stage of Fans’.
kVA/MVA is a ‘Thermal’ Statement!!!
Transformers – Turns Relationships
Vpri
Npri
=
Vsec
Nsec
= volts per turn
N = turns ratio =
Vpri = Vsec x N
and
Npri
Nsec
Isec = Ipri x N
Transformer - Turns/Volts/Current
25 kVA
120
7200
240
120
3240 turns
N =
Isec =
Ipri =
108 turns
3240
108
= 30 : 1
25,000 VA
240 V
25,000 VA
7200 V
= 104.7 Amps
= 3.47 Amps
Transformer - Core Loss & Exciting Current
Iex
A
Vrated
w
v
NL Watts
%Iex =
Iex
Irated
x 100
Rated Voltage is put across the LV terminals with the Primary
Open... the No Load Loss and Exciting Current are measured...
Transformer - Core Losses
No Load Loss = Hysteresis Loss + Eddy Current Losses
Hysteresis Loss is caused by the energy used in lining up
the magnetic domains in the core...
β
flux density = kl/in2
H
Hysteresis Loss is a function
of the area enclosed by the
Hysteresis Loop...
= magnetic field intensity = mmf = Ampere Turns
Eddy Currents are circulating currents in the core due to
induction. The thicker the core lamination, the more Eddy
Current losses...
Transformer – Winding Measurements
Irated
A
VIZ
w
v
low impedance
bolted short...
LL Watts
%IZ =
VIZ
Vrated
x 100
Rated Current is put into the HV terminals with the LV Shorted... the
Load Loss and Impedance Voltage (IZ) are measured...
Transformer – Winding Measurements
Load Loss = Ip2Rp + Is2Rs + Stray Losses
Stray Losses = Eddy (skin effect) Losses
+ Circulating Current Losses
+ Non-current carrying parts
being influenced by leakage flux
Load Losses produce heating within the windings and
resistance losses increase with temperature...
In order to cool the windings, oil ducts are inserted within the
windings to allow the oil to circulate and transfer the heat to
the tank walls and cooling fins...
Transformer – Eddy Current Losses
“No-Mag” plates (304L) are used in larger kVA transformers to reduce
Eddy Current Losses due to High Current Flow…
Transformers - Voltage Regulation
LL
%IR =
kVA x 10
pf = power factor
%Reg = pf x IR + q x IX +
where, K = p.u. load
%IX =
IZ2
q =
1
IR2
pf2
( pf x IX - q x IR)2
200
xK
Transformers – Resistance & Reactance in Ohms
Ft = [ kV2 / kVA ] x 10
Rt = Ft x %IR = ohms resistance
Xt = Ft x %IX = ohms reactance
Ztvector = Rt + j Xt
(vector form)
Ztscalar = √ Rt2 + Xt 2
then,
ISC AMPS =
kV x 1000
Zt
scalar
θtscalar = tan-1(Xt/Rt )
(scalar form)
(scalar form)
…which of course is “Ohms Law”
In addition to the TRANSFORMER, the LV Fault Current is also limited by the Impedances of the
SYSTEM to/from the Transformer, the LV circuit to/from the Fault, and the impedance of the
FAULT… complexity is added with Line-Line and/or Line to Neutral Faults and the connections (Y-Y
or Y-D)... And of course the transformation base levels…
Transformers - Efficiency
Efficiency =
Power OUT
Power IN
OR
% Eff = 100 x K x kVA / (kVA x K + (NL + LL x K2))
where K = per unit Load…
Transformers – Distribution Polarity
H1
H2
H1
H2
> 200kVA
> 8,660kV
X3
X2
ADDITIVE
X1
X1
X2
X3
SUBTRACTIVE
Transformer Polarity indicates the direction of current flow through the HV windings
with respect to the direction of the current flow through the LV windings…
Polarity is either “ADDITIVE” or “SUBTRACTIVE”
Lightning Surges and Protection
40
Lightning – Stroke Density Map
Lightning – Stroke Current Magnitude
Lightning Stroke Current Magnitude
Probability < Abcissa
1.2
1
0.8
0.6
0.4
0.2
0
1
10
100
1000
Stroke Curre nt (KA)
Lightning Stroke Current magnitude is a probability distribution.
Lightning - Transformer Failures
16.00%
14.00%
12.00%
10.00%
8.00%
6.00%
4.00%
2.00%
0.00%
120.00%
80.00%
60.00%
40.00%
20.00%
Cumulative Pct
100.00%
R/W
Emerg FPC
Const Equip
Emerg- Cust
Dig-In
Human Error- FPC
Vehicle
Misc
Human Error- Pub
UG PRI
UG Sec
OH Sec
Overload
Connector
Storm
Unknown
Tree
Lightning
Defective Equip
0.00%
Animal
Pct
Transformer Outages
1995-1996
Cause Code
Lightning is the most common cause of Transformer Failures...
Wildlife is the most common
cause of Transformer Outages...
Lightning
Lightning acts as a current source which deposits a large charge of electrons on the
power line. This charge appears as a current wave propagating along the power
line.
The current wave has a very steep wave front, i.e., high di/dt. The power system is
highly inductive. The voltage produced is V=L di/dt. This can result in voltages
approaching 1 million volts.
Such voltages will fail the insulation system of transformers and other equipment.
Lightning – Arrester Discharge Voltage
Lightning Arresters act to limit the voltage between conductors. This is
accomplished by transferring charge (current) between conductors. The arrester is
modeled electrically as a non-linear resistor.
MOV Arrester
Typical MOV Arrester characteristics 10 kA = 30 kV
Voltage
Silicon Carbide Arrester
L
ar
e
in
to
s
i
s
Re
r
Current
Lightning – Arrester Lead Lengths
kV
Voltage
Arrester Voltage
Across
=
+
Transformer Lead Voltage
Transformer Voltage = 30 kV + 48 kV = 78 kV
for a 10 kA stroke with a 20 kA/usec rise time.
The Transformer BIL for 12470 GRDY/7200 is 95 kV...
The probability of a stroke > 10 kA is 95%...
30kV
MOV
Arrester
#6 Copper
Lead Length +/- 6 feet
Current
- The Lead Inductance of #6 Copper is typically 4
microhenerys per foot (uh/ft)...
- The di/dt for Florida Lightning averages 20 kA per
microsecond...
- Lead Length voltage is V = L di/dt
= 4 uh x 20 kA/usec
= 8 kV per Foot.
Lead Length Voltage = 6 feet x 8 kV/ft = 48 kV
Arrester – Lead Length Reduction
Reduction of lead length voltage is accomplished by use of either Tank Mounted
or Internal Under Oil Arresters.
Voltage
= Arrester Voltage
Across
Transformer
MOV Arrester
Tank mounted or under oil arresters cannot be used on wye-delta banks due to
single phase switching over voltages. Under Oil arresters are used only on
single bushing transformers.
Low Side / Secondary Surges
48
Lightning – Transformer Winding Failures
Lightning on the High Voltage winding can produce 2 failure
modes
- Layer to Ground (anywhere in the winding)
- Layer to Layer at the H1 end of winding
Lightning on the Low Voltage winding can produce layer-to-layer
failures at either end of the High voltage winding or layer-to-ground
in the Low Voltage winding.
Lightning – Poletype Winding Failures
TRANSFORMER FAILURE CAUSES
POLE TYPE (167 UNITS)
OVRLOAD
5%
SEC
10%
NONE
4%
HVPROB
43%
LVPROB
19%
LVPOS
17%
LEAD
2%
Lightning – Padmount Winding Failures
TRANSFORMER FAILURE CAUSES
PAD-MOUNTED (84 UNITS)
HVPROB
12%
SEC
21%
LEAD
1%
OVRLOAD
1%
LVPOS
18%
NONE
11%
LVPROB
36%
Low Side Surges
• 5% of Stroke Currents Exceed 85 kA
• 50% Exceed 35 kA
• 35-50% of Surges enter on the LV side
• The Average LV Surge is 1500 amps/transformer/year?
• The Majority do not exceed 5000 amps?
Distribution – Core Type
core & coil
P S
- good dielectric
strength...
S P P S
- typically good on
thermal performance...
- natural impedance's
typically 2.5-3.5%...
- MUST be interlaced...
Core Type C&C Cross-section
S P
Distribution – Non-Interlaced LV windings
core & coil
- excellent Short Circuit
strength...
S
P
S
S
P
S
- natural impedance's
typically 1.5-2.0%
for SPS construction...
Non-Interlaced SPS Shell Type C&C Cross-section
Distribution – Shell Type - Interlaced LV windings
core & coil
- excellent Short Circuit
strength...
SS
P
SS
SS
P
- natural impedance's
typically 1.5-2.0%
for SPS construction...
Interlaced SPS Shell Type C&C Cross-section
SS
Lightning – ‘Anonymous’ Winding Failures
H1
HV
LV
“The Anonymous Failure Mode”
LV
H2
Lightning – ‘Anonymous’ Winding Failures
During the 1960’s, the Transformer
Manufacturers switched from Conductor
wound Copper LV windings to Aluminum
Sheet wound construction… COST $$$
Driven by COST, the practice of NONINTERLACED Construction found favor
with those Manufacturers who could
make this change…
S
P
S
S
P
S
During the 1970’s, the installed failure rate of distribution transformers began to rise
dramatically!!!
Teardown analysis began to show a special failure signature which became known
as “The Anonymous Failure”… this is a “turn-turn” or “layer-layer” dielectric failure
near the grounded end of a single bushing transformer…
And this seemed to be associated with the Non-Interlaced Shell Type Construction…
Lightning – ‘Anonymous’ Winding Failures
H1
HV
LV
“The Anonymous Failure Mode”
LV
H2
• Layer to Layer failures near the grounded end of the HV winding is a
“signature” of a low side surge occurrence...
Lightning – ‘Anonymous’ Winding Failures
Arrester
E=L
di
dt
= the voltage developed across
the ground leads...
• The majority of LV surges probably enter the Transformer through the LV ground
connections... either due to Primary Arrester operation or from the ground following
direct or nearby strokes...
Lightning – ‘Anonymous’ Winding Failures
HV
LV
LV
• Surge currents flowing through the LV windings of a Non-Interlaced LV
winding produce a high magnetic field across the primary coil...
Lightning – ‘Anonymous’ Winding Failures
290 kV winding voltage
to ground...
kV
10 kVA 95kV BIL
H2
HV winding layers
H1
• The rapidly changing magnetic field induces a very high voltage in the primary
winding...
• The lightning arrester connected across H1 to H2 does not see any voltage...
Lightning – ‘Anonymous’ Winding Failures
Layer to Layer Voltage
Peak 80 kV
kV
10 kVA 95kV BIL
H2
HV winding layers
H1
• The high layer to layer stress in the HV winding will cause coil failure near either
end of the coil... but usually at or near the grounded end of the winding...
Lightning – Low Side Surges
HV
LV
LV
LV
LV
• Surge currents flowing through the LV windings of an Interlaced LV winding
cancel and produce a weak magnetic field across the primary coil...
Lightning – Low Side Surges
Non-Interlaced
290 kV winding voltage
to ground...
kV
Interlaced
3 kV to ground...
H2
HV winding layers
H1
• Interlacing the LV winding balances the winding and significantly reduces the
stress due to LV Surges...
Lightning – Low Side Surges
Layer to Layer Voltage
kV
Non-Interlaced
Peak 80 kV
Interlaced
Peak 1 kV
10 kVA 95kV BIL
H2
HV winding layers
H1
• Interlacing the LV winding balances the winding and significantly reduces the
stress due to LV Surges...
Lightning – Low Side Surges
• Non-Interlaced LV windings are the major cause of Distribution
Transformer (DT) Lightning Failures...
• Small kVA’s are MORE susceptible because of more turns...
• Primary Arresters DO NOT Protect the HV against LV Surges...
• Interlacing or LV Arresters reduces DT Failure Rate...
1.0 %
0.5 %
Failure
Rate
interlaced types
non-interlaced types
Lightning - Summary
• The proper application and choice of Arresters can reduce the failure
rate significantly… especially in the Southeastern USA…
• Arrester Lead length can be very important…
• About 50% of lightning surges come from the low side… on the smaller
kVA transformers, Interlaced windings and/or LV Arresters can reduce
winding failures…
Starting Transformers and Motors
68
Motor Starting Issues
• The current required to start equipment such as Electric Motors or
Transformers requires a starting current, typically known as ‘Inrush’ or
‘locked rotor current’…
• For fusing, the typical ‘inrush’ rule is to keep the fuse melt beyond 812 times rated current at 0.1 second (about 6 cycles)…
• The short term voltage drop or ‘Flicker’ is a function of the required
‘Locked Rotor’ current required to start the equipment… a number of
papers and information is available to the user on this issue…
• In addition to the impact on the local low voltage circuits, starting
equipment such as large motors can cause voltage quality issues on
the primary circuits of the distribution feeders… which can affect
associated equipment…
• Some electronic systems may be sensitive to these changes!
Transformers – Resistance & Reactance in Ohms
Ft = [ kV2 / kVA ] x 10
Rt = Ft x %IR = ohms resistance
Xt = Ft x %IX = ohms reactance
Ztvector = Rt + j Xt
(vector form)
Ztscalar = √ Rt2 + Xt 2
then,
ISC AMPS =
kV x 1000
Zt
scalar
θtscalar = tan-1(Xt/Rt )
(scalar form)
(scalar form)
…which of course is “Ohms Law”
In addition to the TRANSFORMER, the LV Fault Current is also limited by the Impedances of the
SYSTEM to/from the Transformer, the LV circuit to/from the Fault, and the impedance of the
FAULT… complexity is added with Line-Line and/or Line to Neutral Faults and the connections (Y-Y
or Y-D)... And of course the transformation base levels…
Motor Start – calculations
The voltage drop across the transformer: %T = [1-Zm/sqrt((Rm+Rt)^2 + (Xm+Xt)^2))] x100
where, Zm is the motor impedance is calculated as,
Zm = (line-line voltage rating of the motor) / LRA
LRA = locked rotor amps
PF = motor starting power factor
Rm = Zm x PF ohms
Xm = sqrt( 1-PF^2) ohms
To translate the %Impedance ( %IZ ) into Real and Reactive components, we use the transformer impedance factor, Ft.
Ft = [ [(Secondary voltage in kV)^2] / kVA rating of Transformer ] x 10
Rt = Ft x %IR ohms
Xt = Ft x %IX ohms
%IR and %IX are calculated from the Load Loss watts (LL) and Impedance (%IZ) of the specific transformer.
%IR = LL / (kVA x 10)
%IX = sqrt[ %IZ^2 - %IR^2 ]
The voltage drop across the secondary conductor is: %C = [ [ Rc x LRA x PF ] + [ Xc x LRA x sqrt(1-PF^2) ] ] x 100 / LV where LV is the line-line secondary voltage, typically 240 volts and,
Rc = conductor resistance in ohms per 100 feet x [ 2 x length /100 ]
Xc = conductor reactance in ohms per 100 feet x [ 2 x length /100 ]
The conductor length is multiplied by 2 as the current must have a return path. If the return path conductor is not the same
size and characteristics as the line conductor the calculation must be adjusted accordingly.
Flicker
Flicker is typically the voltage drop caused by the Locked Rotor Current
required to start a air-conditioner compressor motor.
The duration of this current for residential air conditioners varies from
4 to 20 cycles. A voltage drop occurs in each component of the system,
i.e., Transformer and Conductors, based on the magnitude of the current
and the impedance of the components.
The most common occurrence is during the startup of residential air
conditioners. Customers see this as a dimming of the lights or, under
extreme conditions, as a shrinking of the TV picture.
Customer sensitivity varies based on individual perception, the
magnitude and duration of the voltage dip, and the type of
light source.
Flicker – Motor Starting Current 15-20 cycles
RAYSAC
Y1
Volts
400
Y2
Amps
300
300
200
200
100
100
0
0
-100
-100
-200
-200
-300
-400
0.00
0.05
0.10
0.15
0.20
Channel A (V)
0.25
0.30
Channel A (I)
Measured : 02/14/97 11:47:57
0.35
0.40
-300
0.45 Sec.
Motor Start – Single Phase
Capacitor Start motors utilize a capacitor in series with
the
start winding to provide phase shift in the current through
the start winding. This phase shift causes an angular
displacement in the magnetic fields between the Run and
Start windings resulting in a torque on the rotor.
Run Winding
Start Winding
Rotor
Start Winding
Run Winding
The larger the Capacitor
- the larger the phase shift
- the larger the starting torque
- the shorter the starting cycle
Motor Start – Permanent Split Capacitor Motor
Run Capacitor
Start
Run
Line
The Start winding and Run Capacitor remain
energized at all times
Motor Start – Conventional 3 wire Hard Start
Run Capacitor
Potential Relay
Start Capacitor
Start
Run
Line
The Potential Relay removes capacitor with Start
Winding back E.M.F.
Residential Air Conditioners
Residential Air Conditioners use one of two types of Motors
- Permanent Split Capacitor
- Capacitor Start / Capacitor Run
Residential Air Conditioners use one of two types of Compressors
- Reciprocating (Piston)
- Scroll (new High Efficency units)
Motor Sizing rules are Different for Different Compressors
Motor Start Flicker – Field Test Data
AC Starting Characteristics
250.0
200.0
150.0
LRA
RECIP Test Data
Recip Regression
Scroll Test DAta
Scroll Regression
100.0
50.0
0.0
2.0
2.5
3.0
3.5
4.0
Tons
4.5
5.0
5.5
Motor Start Flicker – Kickstart TO-5
Motor Start Flicker – Kickstart TO-5
Run Capacitor
Potential Relay
Start Capacitor
Start
Run
Line
The Potential Relay removes capacitor with Start
and Run Winding back E.M.F.
Flicker – Kickstart Motor Starting Current 4-6 cycles
RAYG4KS
Y1
Volts
400
Y2
Amps
400
300
300
200
200
100
100
0
0
-100
-100
-200
-200
-300
-300
-400
0.00
0.05
0.10
Channel A (V)
0.15
Channel A (I)
M easured : 02/25/97 16:39:47
0.20
-400
0.25 Sec.
Compressor/Motor Start Flicker
– Summary
• Compressor Flicker is a momentary (5-30 cycle) voltage drop caused
by Motor Start… such as a Residential Air Conditioner…
• Compressor Flicker is ‘as perceived by the user’… Not everyone can
notice it… once seen, the mind can ‘tune-in’ to it…
• Flicker is a function of the required ‘Locked Rotor’ Starting
Amperes… the High Efficiency ‘Scroll Type’ Compressors require
Higher Starting Amps… thus going to Higher Efficiencies can cause
other issues!
• Adding extra Capacitive Reactance will not reduce the magnitue of
the required starting current, but can reduce the amount of time
required to get the compressor started… thus reducing the ‘perception
of Flicker’…
Transformer Costs and Efficiencies
83
Quantifying Transformer Costs
• Capital Vs. Expense Dollars
• Financial Math Relationships
• Cost of Losses – the A and B Factors
• Band of Equivalence
• DOE Efficiency Rules
Capital Dollars
The purchase cost of a transformer is amortized over the
expected life. This is done by applying a Fixed Charge
Rate (FCR) to the purchase price...
Price x FCR = Annualize Fixed Cost
The result is an annual cost which is uniform for the life of
the unit...
FCR (%) = Fixed Charge Rate - The cost of carrying a capital investment
made up of:
- The weighted cost of capital (stocks, bonds)
- Depreciation on the investment
- Taxes (Income, Ad valorem, Gross Receipts)
- Insurance
Expense Dollars
Expense costs such as Cost of Losses or future Change-Out are
levelized to an annual form with the Capital Recovery Factor which
considers only the cost of money and time…
Change Out Cost x CRF = Annualize Change Out Cost
The result is an annual cost which is uniform for the life of
the unit...
CRF (%) = A/P = i(1+i)n /((1+i)n-1)
Note: In ANNUAL form Expense and Capital are equal!
Basic Financial Math
Capital Recovery Factor
A/P = i(1+i)n /((1+i)n-1)
Annuity
Compound Amount Factor
F/A = (1+i)n-1/i
Present Worth Factor
P/A = ((1+i)n-1)/i(1+i)n
Present
Value
Sinking Fund Factor
A/F = i/((1+i)n-1)
Compound Interest Factor
F/P = (1+i)n
Future
Value
Present Value Factor
P/F = 1/(1+i)n
Moving Money (Value) through Time
Cost of Transformer Losses
The cost to operate a Transformer over it’s life is affected
by the Cost to Supply the capacity, or Demand (SC $/kW-yr),
and the Cost incurred to supply the Energy (EC $/kW-Hour).
The No Load losses are continuous as long as the transformer
is connected to the system, typically 8760 hours/year.
The Load Losses vary with transformer load and are affected by
the annual load factor and the timing of the system peak.
The Annual cost of ownership (AOC) is:
AOC = Price x FCR + A x NL + B x LL
NOTE: draft C57.12.33 Loss Evaluation methodology currently under development by the IEEE…
The ‘A’ Factor
A = $ per No Load (excitation) Loss Watt
A =
SC + 8760 x EC
1000
$/watt
where,
SC = Avoided Cost of System Capacity ($/kW-yr) - - The levelized avoided
(incremental) cost of generation, transmission, and primary distribution
capacity required to supply the next kW of load to the distribution
transformer coincident with the peak load.
EC = Avoided Cost of Energy ($/kWh-yr) - - The levelized avoided (incremental)
cost for supplying the next kWh, which may be produced by the utility’s
generating units or purchased from an energy supplier.
The ‘B’ Factor
B = $ per Load (winding) Loss Watt
B =
( SC x RF + 8760 x LsF x EC) x PL2
$/watt
1000
where,
RF = Peak Loss Responsibility Factor - Defines the relationship between the
transformer peak load and the transformer load at the time of system peak load.
LsF = Loss Factor - A ratio of the annual average load losses to the peak
value of load losses on the transformer. LsF = [Σ(K2n*tn)/t]/K2peak
NOTE: An empirical relationship for loss factor for RESIDENTIAL transformers is the
Propst/Ganger relationship: LsF = 0.15 (Load Factor) + 0.85 (Load Factor)2
PL = Equivalent Annual Peak Load “ON THE TRANSFORMER”
Evaluation Forms
The Transformer Evaluation Equation may be written as:
Total Owning Cost (TOC) = F x Price + A x NL + B x LL
Where the factor F is a multiplier against the Price and is used to
express the owning cost equation in three forms:
Type
description
F
form
.
- EFC
Equivalent First Cost
1.0
Capital form
- PW
Present Worth
FCR/CRF
Expense form
- AC
Annual
FCR
Annuity form
Band of Equivalence
• The BOE was described by the Shincovich and Stephens (EEI 1981)
as a way to address the uncertainty of the future estimates on factors
such as Energy Costs, Loading, etc… 1% was suggested!
• “Uncertainty” of course can result in HIGHER or LOWER future costs!
• However, this idea has been expanded as a tool to force lower first prices
at the expense of future costs… 3-10% BOE is not uncommon!
• BOE reduces the actual value of the Loss Evaluation Factors…
Typically, a 3% BOE effectively reduces the A&B Factors by ½ or more!
Variances would be better addressed with tools such as
Crystal Ball… or the Economics Variance module in TAP…
A & B Variance
LCC – Mild Steel Tank vs. Stainless
DOE Transformer Efficiencies – 2010 Rule
95
Energy Policy and Conservation Act
The Energy Policy and Conservation Act (EPCA) of 1975 established an
energy conservation program for major household appliances. The National
Energy Conservation Policy Act of 1978 amended EPCA to add Part C of
Title III, which established an energy conservation program for certain
industrial equipment. The Energy Policy Act of 1992 amended EPCA to
add certain commercial equipment, including distribution transformers.
The Department of Energy, Office of Energy Efficiency and Renewable
Energy, Building Technologies Program conducts the program that
develops equipment energy conservation standards and has overall
responsibility for rulemaking activities for distribution transformers
in fulfillment of the law.
http://www.eere.energy.gov/buildings/appliance_standards/
Energy Policy and Conservation Act
Distribution Transformers
The first step in developing energy conservation standards was the
Secretarial determination in 1997 that, "Based on its analysis of the
information now available, the Department has determined that energy
conservation standards for transformers appear to be technologically
feasible and economically justified, and are likely to result in significant
savings" 62 FR 54809 (October 22, 1997).
The Department of Energy (DOE) conducted two rulemakings for
Distribution Transformers:
• an energy conservation standard
• a test procedure
http://www.eere.energy.gov/buildings/appliance_standards/
Energy Policy and Conservation Act
• In response, NEMA developed the TP-1 Minimum Efficiency
Guidelines in the early 1990’s… note: basically a 3 year payback!
• In August 2006, the DOE published the Notice of Proposed
Rulemaking with a recommendation for to the Trial Standard Level 2
(TSL-2)…
• Mixed responses… some opposed mostly based on increased cost
and material availability… some saying it doesn’t go far enough…
http://www.eere.energy.gov/buildings/appliance_standards/
Trial Standard Levels
Efficiency = Power OUT / Power IN
%E = 100 x kVA x 0.5 / [ kVA x 0.5 + ((NL + LL x 0.9 x 0.52)/1000)]
Where NL and LL are in watts…
Note: 0.9 = Load Loss Temp correction from 85 to 55 deg C…
•TSL-1 = NemaTP1
•TSL-2 = 1/3 between TP1 and TSL-4
•TSL-3 = 2/3 between TP1 and TSL-4
•TSL-4 = minimum Life Cycle Cost
•TSL-5 = max Energy Savings with no change in LCC
•TSL-6 = max Energy Savings
KVA NEMA TP1
10.0
98.40%
15.0
98.60%
25.0
98.70%
37.5
98.80%
50.0
98.40%
75.0
99.00%
100.0
99.00%
167.0
99.10%
75.0
112.5
150.0
225.0
300.0
500.0
750.0
1000.0
1500.0
2000.0
2500.0
98.70%
98.80%
98.90%
99.00%
99.00%
99.10%
99.20%
99.20%
99.30%
99.40%
99.40%
TSL-2
98.40%
98.56%
98.73%
98.85%
98.90%
99.04%
99.10%
99.21%
TSL-3
98.43%
98.59%
98.76%
98.99%
99.04%
99.18%
99.24%
99.35%
TSL-4
98.46%
98.62%
98.79%
99.14%
99.19%
99.33%
99.39%
99.50%
98.91%
99.01%
99.08%
99.17%
99.23%
99.32%
99.24%
99.29%
99.36%
99.40%
99.44%
99.09%
99.19%
99.26%
99.35%
99.41%
99.50%
99.42%
99.47%
99.42%
99.46%
99.50%
99.27%
99.37%
99.44%
99.53%
99.59%
99.68%
99.60%
99.65%
99.48%
99.50%
99.55%
Final Rule – October 12, 2007
“Effective January 1, 2010, Liquid Filled Distribution Transformers manufactured for
sale in the United States MUST meet or exceed the following Efficiency levels…”
Efficiency = Power OUT / Power IN
@ 50% Load
%Eff = 100 x kVA x 0.5 / [ kVA x 0.5 + ((NL + LL x 0.9 x 0.52)/1000)]
where NL and LL are in watts…
Note: 0.9 = Load Loss Temp correction from 85 to 55 deg C…
DOE Final Rule
• Similar rules are in place for Medium Voltage Dry type Transformers…
• The DOE rule resolves the issue between Single and Three Phase designs by
using the same Efficiency Value for the Single Phase design for the equivalent 3
Phase kVA…
For example, the required efficiency value for a 3Φ 150 kVA transformer is the same as a 50 kVA 1Φ
unit…. (3 x 50 = 150 kVA)…
• Pre-Existing Distributor Stock, Re-manufactured units, and Transformers
intended for Mining Operations are excluded from the rule…
• For Liquid Filled Transformers, the relationships to the Trial Standard Levels
are…
• 1Φ 10-167 kVA
• 1Φ 250-833 kVA
slightly above TSL-4
between TSL2 and TSL3
• 3Φ
• 3Φ
• 3Φ
• 3Φ
TSL-2
between NEMA TP-1 & TSL-2
slightly greater than TSL-3
TSL-3
45-300 kVA
500 kVA
750 kVA
1000-2500 kVA
For the final rule, DOE set average A & B values of A=3.85 and B=1.16 $/watt 1Φ and B=1.93 $/watt 3Φ
DOE Projected Benefits
TSL-1
TSL-2
TSL-3
TSL-4
TSL-5
TSL-6
Energy Saved Quads =
1.77
2.39
3.15
3.63
6.9
9.77
CO2 (Mt) reductions =
123.1
167.3
218.5
252.7
483.1
679.5
NOX (kt) reductions =
34.1
46.4
60.9
71
134.9
188
Hg (t) reductions
3
3.7
4.3
4.9
6.4
6.5
=
NOTE: The QUAD is used by the U.S. Department of Energy in discussing
world and national energy budgets. One Quad = 1015 BTU. The global primary
energy production in 2004 was 446 quads…
Conclusion
Q/A?
Don A. Duckett, P.E.
Technical Sales Engineer
HD Supply Utilities
(407) 402-0944
Don.Duckett@ieee.org