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Power Grid Kinetic Energy and Inertia
Grid Cruise Control
Kinetic Energy and Inertia
Kinetic Energy Analysis
Power Grid Kinetic Energy and Inertia
Here we discuss the kinetic energy that is stored in the power grid and the inertia of the power grid.   For this level of analysis we shall ignore transient effects such as occur due to short circuits and switching operations.  In other words we consider that the measured frequency is ubiquitous, i.e., nearly the same everywhere in the interconnected power system.
Terminology
The power industry expresses the kinetic energy of the grid as follows:
H = E0 / S0 Kinetic Energy Factor of the Grid. 
Generally expressed as grid energy (E0) per grid size (S0) at nominal frequency (F0)
Typically H ≈ 5 (in seconds = MW-sec/ MVA) approximately and is not constant under all conditions.
E0 Grid Kinetic Energy in MW-seconds in our discussion
P0 Grid Size
F0 Nominal Frequency
 
E Grid Kinetic Energy expressed in MW-seconds
E = I ω^2 / 2 The kinetic energy of a rotating object (a flywheel for example)
I Moment of Inertia ( in our discussion, H serves as a proxy for I )
ω = 2 π F Angular Velocity in Radians per Second
By manipulation we get the following:
E = H * (F / F0) ^ 2 * S0
In other words, the kinetic energy of the grid varies as the square of the frequency
Example 1
What is the approximate kinetic energy of a 200,000 MVA grid operating at nominal frequency?
E = (5) (200,000) = 1,000,000 MW-seconds
Example 2
Given a loss of 1000 MW of generation on the grid of the previous example, how many seconds will it take for the frequency to drop from its nominal value of 60 Hz down to 59.5 Hz?  For this example, assume that the corresponding loss of apparent power is 1250 MVA.  Also assume that there is no corrective action taken either by the system operator or by the governors on all the generators and that the loads do not change (decrease) with the frequency drop.  This is the fastest that the frequency will decrease to 59.5 Hz.
The change in kinetic energy, starting after the loss of generation, is calculated as follows:
ΔE = H * (F / F0) ^ 2 * (S0 – 1250) -  H * (S0 – 1250) = H * (S0 – 1250) * [(F / F0) ^ 2 – 1]
ΔE = 993,750 * [(59.5/60) ^ 2 – 1]  =  -16,493 MW-seconds
T = (16,493 MW-seconds) / (1000 MW) = 16.493 seconds
In the real world the frequency would not drop this quickly because of automatic generator governor action and the decrease in load as the frequency drops.

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Session # 180036 Copyright 2008-2010, GridTrak Updated: July 22, 2009