Load-loss factor

Not to be confused with Load loss or Load factor.

Load-loss factor (also loss load factor, LLF, or simply loss factor ^[1] ) is a dimensionless ratio between average and peak values of load loss (loss of electric power between the generator and the consumer in electricity distribution). Since the losses in the wires are proportional to the square of the current (and thus the square of the power), the LLF can be calculated by measuring the square of delivered power over a short interval of time (typically half an hour), calculating an average of these values over a long period (a year), and dividing by the square of the peak power exhibited during the same long period: ^[2]

${\displaystyle {LLF}={\frac {\sum _{i=1}^{NI}{Load}_{i}^{2}}{NI*{Load}_{peak}^{2}}}}$, where

• ${\displaystyle NI}$ is the total number of short intervals (there are 8760 hours or 17,520 half-hours in a year);
• ${\displaystyle {Load}_{i}}$ is the load experienced during the short interval ${\displaystyle i}$;
• ${\displaystyle {Load}_{peak}}$ is the peak load within the long interval (typically a year).

The LLF value naturally depends on the load profile. For electricity utilities, numbers about 0.2-0.3 are typical (cf. 0.22 for Toronto Hydro, ^[3] 0.33 for New Zealand ^[4] ). Multiple empirical formulae exist that relate the loss factor to the load factor (Dickert et al. in 2009 listed nine ^[5] ).

Similarly, the ratio between the average and the peak current is called form coefficient k ^[6] or peak responsibility factor k, ^[7] its typical value is between 0.2 to 0.8 for distribution networks and 0.8 to 0.95 for transmission networks. ^[8] Coefficient k describes the losses as an additional load carried by the system, and is named loss equivalent load factor in Japan. ^[6]

See also

• Line Loss Factor, a regulatory definition of the line loss in UK

References

1. Wu & Ni 2016, p. 16.
2. New Zealand Electricity Authority. Guidelines on the calculation and use of loss factors for reconciliation purposes. 26 June 2018. p. 8.
3. "Rate Design" (PDF). Toronto Hydro.
4. "Review of EGR Connection Code" (PDF). New Zealand Electricity Authority . Retrieved 8 May 2022.
5. Dickert, J.; Hable, M.; Schegner, P. (June 2009), "Energy loss estimation in distribution networks for planning purposes", 2009 IEEE Bucharest PowerTech, IEEE, p. 4, doi:10.1109/PTC.2009.5281997, ISBN   978-1-4244-2234-0, S2CID   6344874
6. Wu & Ni 2016, p. 14.
7. Pabla 2004, p. 208.
8. Pabla 2004, p. 209.

Sources

• Wu, Anguan; Ni, Baoshan (7 June 2016). Line Loss Analysis and Calculation of Electric Power Systems. John Wiley & Sons. ISBN   978-1-118-86709-9. OCLC   1062309002.
• Pabla, A. S. (2004). Electric Power Distribution. Tata McGraw-Hill Education. pp. 208–209. ISBN   978-0-07-048285-2. OCLC   54079002.