SME
Power Systems · Problem type
Transformer efficiency at part load
Use this for “A 50 kVA transformer has 300 W of core loss and 600 W of full-load copper loss. Find its efficiency at full load, pf 0.8.”
Chart
This is an example. Type your own values to start a new problem.
Pₒᵤₜ (kW)
=
x
×
S (kVA)
×
pf
Pᵢₙ (kW)
=
Pₒᵤₜ (kW)
+
Pcore (kW)
+
Pcu (kW)
η (%)
=
Pₒᵤₜ (kW)
÷
Pᵢₙ (kW)
×
100%
Pcu,fl
Full-load copper loss
example
xbest
Load for best η
calculated
Formulas
Pₒᵤₜ
=
x
×
S
×
pf
40 = 1 × 50 × 0.8
Pcu
=
x
2
×
Pcu,fl
0.6
=
1
2
×
0.6
Pᵢₙ = Pₒᵤₜ + Pcore + Pcu
40.9 = 40 + 0.3 + 0.6
η
=
Pₒᵤₜ
Pᵢₙ
×
100
97.7995
=
40
40.9
×
100
xbest
=
√(
Pcore
Pcu,fl
)
0.7071
=
√(
0.3
0.6
)
Assumptions
•
x is the load as a share of the rating (1 is full load); pf is the load’s power factor.
•
Core loss is the same at every load; copper loss grows as the square of the load current.
•
Efficiency peaks where copper loss equals core loss, at x = √(Pcore ÷ Pcu,fl).
Step-by-step
WE KNOW
S = 50 kVA, x = 1, pf = 0.8, Pcore = 0.3 kW, Pcu,fl = 0.6 kW
FIND
output power (Pₒᵤₜ), copper loss (Pcu), input power (Pᵢₙ), efficiency (η), load for best η (xbest)
Step 1 · Find output power (Pₒᵤₜ)
Use Pₒᵤₜ = x × S × pf
The
load
draws
the
share
x
of
the
rated
volt-amperes,
and
pf
of
those
are
real
power.
Pₒᵤₜ = 1 × 50 × 0.8
Pₒᵤₜ = 40 kW
Step 2 · Find copper loss (Pcu)
Use Pcu = x² × Pcu,fl
Copper
loss
is
I
2
R,
and
the
current
is
x
times
full-load
current.
Pcu
=
1
2
×
0.6
Pcu = 0.6 kW
Step 3 · Find input power (Pᵢₙ)
Use Pᵢₙ = Pₒᵤₜ + Pcore + Pcu
What goes in comes out as output or as the two losses.
Pᵢₙ = 40 + 0.3 + 0.6
Pᵢₙ = 40.9 kW
Step 4 · Find efficiency (η)
Use η = Pₒᵤₜ ÷ Pᵢₙ × 100
Efficiency is the output as a percent of the input.
η
=
40
40.9
×
100
η
=
0.978
×
100
η
=
97.7995%
Step 5 · Find load for best η (xbest)
Use xbest = √(Pcore ÷ Pcu,fl)
Losses
per
watt
delivered
are
least
where
x
2
Pcu,fl
equals
Pcore.
xbest
=
√(
0.3
0.6
)
xbest
=
√
0.5
xbest = 0.7071
Check
Put the numbers back in. Both sides should match.
40 = 1 × 50 × 0.8 ✓
0.6
=
1
2
×
0.6
✓
40.9 = 40 + 0.3 + 0.6 ✓
97.7995
=
40
40.9
×
100
✓
0.7071
=
√(
0.3
0.6
)
✓
Topic check
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