Power Grid Cruise Control 

This is a brief explanation of the relationship between power grid frequency and power grid supply and demand.
The cost of power imbalance between supply and demand is also discussed. 
Terminology


F 
Frequency in Hz (Hertz)

F0 
Nominal Frequency: 60 Hz or 50 Hz 
ΔF 
Deviation in Frequency from “Nominal”: F minus F0 
P 
Power in MW (megawatt) 
S 
Apparent power in MVA (megavoltamp) 
P0 
Size of the Power Grid in MW 
S0 
Size of the Power Grid in MVA 
ΔP 
Power Imbalance Between Supply and Demand: Supply MW minus Demand MW 
G 
Grid Frequency Response Characteristic: Depends on Supply Governor Responses and Demand (load) Responses 
MCP 
Market Clearing Price in $/MWh (dollars per megawatthour): or other currency depending on the country 
C 
Cost in $/hour, or Other Currency Depending on the Country 

Grid Frequency Response Characteristic 

Grid frequency response, in this document, is given for steadystate conditions.
We look at grid frequency a few seconds after a disturbance. The industry
standard relationship is given as follows:


ΔP / P0 = G * ΔF / F0


“G” is a grid parameter that depends on power supply Governor Response and how demand (load) changes with grid frequency.
Typically, G = 15. Although this parameter varies for each power grid, the industry tunes
this value
for Cruise Control purposes. Too high a value for G will cause control overcorrection, while too low a value
for G will cause sluggish control.

Example 1 

F0 = 60 Hz 

P0 = 200,000 MW 

ΔP = 1000 MW (loss of a large generator) 

Calculate the Grid Frequency Response: 

ΔF = (ΔP / P0) * (F0 / G) = (1000 / 200000)
* (60 / 15) = 0.02 Hz = 20 mHz 
Example 2 

F0 = 60 Hz


P0 = 200,000 MW 

ΔF = 0.01 Hz 

MCP = 50 $/MWh 

Calculate the Power Imbalance and the Cost to Bring Frequency Back to Nominal: 

ΔP = G * (ΔF / F0)
* P0 = (15)
* (0.01 / 60) * (200000) = 500 MW (excess supply) 

Cost = MCP * ΔP = (50) * (500) = 25,000 $/h 
Example 3 

NERC considers the minimum setting for “G”
for control purposes in USA to be:
A (1%) change in power causes a (0.1 Hz) change in frequency.


Calculate G: 

ΔP / P0 = G * ΔF / F0
1% / 100% = 0.01 = G * 0.1 / 60
G = 6 