Mon 02 February 2015
By Chris Mutel
In ecoinvent .

Some math
We can write the general formula for available electricity at step n as:

\begin{equation*}
Avail_{n} = Avail_{0} - \sum_{i=1}^{n} Loss_{i} - \sum_{i=1}^{n} Use_{i}
\end{equation*}

Makes sense - the total available at any point is what we started with, minus losses and what was used. What about the relative amount of electricity lost at any particular point in the value chain? This is the number we need on ecoinvent - the fraction of one kilowatt hour gross availability which is lost. This loss coefficient (LC) is also quite easy to define:

\begin{equation*}
LC_{i} = \frac{Loss_{i}}{Avail_{i - 1}}
\end{equation*}

Remember, in both these equations, every input parameter is an absolute amount of electricity, not a fraction or percentage.

Let's look at a real world example: Lithuania, chosen because it has nice, small numbers. According to the input data used in ecoinvent, Lithuania has 11 TWh of generation, 10 TWh of consumption, and 1TWH of losses. Combined with our fixed fractions, we already know the following:

We can also compare loss coefficients versus the values in the first table.

Type
Name
Value
Loss coefficient
Transformation
High voltage - high voltage
0.06
0.0055
Transmission
High voltage
0.33
0.03
Transformation
High voltage - medium voltage
0.08
0.0075
Transmission
Medium voltage
0.05
0.0049
Transformation
Medium voltage - low voltage
0.24
0.035
Transmission
Low voltage
0.24
0.036

Cumulative losses
Sometimes we want to know how much electricity is lost throughout the value chain; say, for example, you were curious how much electricity had to be generated to get 1 kilowatthour of medium voltage electricity supplied. In this case, we don't want the loss coefficient, but rather $1 - LC$, the amount of electricity provided after losses. We need to multiply this amount for each step where electricity is lost - it is just like interest from the bank, but in reverse. The formula for total fractional loss at step n is therefore:

\begin{equation*}
TotalLossCoefficient_{n} = 1 - \prod_{i=1}^{n} \big( 1 - LC_{i} \big)
\end{equation*}

The total loss coefficient for Lithuania for usage of medium voltage would include transformation and transmission losses for high and medium voltage, and would therefore be (with some rounding):

\begin{equation*}
1 - (1 - 0.0055) \cdot (1 - 0.03) \cdot (1 - 0.0075) \cdot (1 - 0.0049) = 0.0473
\end{equation*}

In words, the generation of 1 kilowatt hour of electricity would produce only 1 - 0.0473 kilowatt hours of medium voltage electricity at the busbar ("at the busbar" is what you say when you pretend to know something about electrical engineering).

Note that this value is not applicable to other countries, but depends on the country-specific ratio of total generation to total losses.

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