SME
Power Systems · Problem type
Rate of change of frequency
Use this for “A grid with H = 5 s loses 0.1 pu of generation at 60 Hz. How fast does the frequency start to fall?”
Chart
f(0.5) = 59.7
This is an example. Type your own values to start a new problem.
df/dt (Hz/s)
=
ΔP (pu)
×
f (Hz)
÷
(2
×
H (s)
)
f₁ (Hz)
=
f (Hz)
−
df/dt (Hz/s)
×
t (s)
Formulas
df/dt
=
ΔP
×
f
2 ×
H
0.6
=
0.1
×
60
2 × 5
f₁
=
f
−
(df/dt)
×
t
59.7 = 60 − 0.6 × 0.5
Assumptions
•
The rate of change of frequency df/dt is in hertz per second (Hz/s).
•
Before any governor acts, the lost power ΔP comes out of the energy stored in the spinning rotors.
•
ΔP and the inertia H are on the same base, the whole system’s.
•
The fall is a straight line only for the first second or so, until governors and loads respond.
Step-by-step
WE KNOW
ΔP = 0.1 pu, f = 60 Hz, H = 5 s, t = 0.5 s
FIND
rate of fall (df/dt), frequency at t (f₁)
Step 1 · Find rate of fall (df/dt)
Use df/dt = ΔP × f ÷ (2 × H)
The
swing
equation
2
H
f
×
df/dt
=
−ΔP
at
the
first
instant:
the
rotors
alone
cover
the
loss.
df/dt
=
0.1
×
60
2 × 5
df/dt
=
0.1
×
60
10
df/dt
=
6
10
df/dt = 0.6 Hz/s
Step 2 · Find frequency at t (f₁)
Use f₁ = f − (df/dt) × t
The frequency falls at the same rate the whole time, so take off rate × time.
f₁
=
60
−
0.6
×
0.5
f₁
=
60
−
0.3
f₁
=
59.7
Hz
Check
Put the numbers back in. Both sides should match.
0.6
=
0.1
×
60
2 × 5
✓
59.7 = 60 − 0.6 × 0.5 ✓
Topic check
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