[Econ] Anaerobic Digester CHP and RNG

[allisterakun]

Context

Issue(s) closed by this pull request: closes #3086

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[bradenlimb]

Calculations on the electricity to rng ratios work out for me! So we are good on that front.

However I noticed that the biophysical_aggregate value multiplied by the price_aggregate value doesn't exactly equal the line_item_by_scenario value. In the following image I get the following

495139.0225 * 0.005363327 = 2655.592727

[allisterakun]

Calculations on the electricity to rng ratios work out for me! So we are good on that front.

However I noticed that the biophysical_aggregate value multiplied by the price_aggregate value doesn't exactly equal the line_item_by_scenario value. In the following image I get the following

495139.0225 * 0.005363327 = 2655.592727

After a bit of digging, I believe the root cause is we are calculating the "price_aggregate" as simple daily average, rather than a weighted average:

Example

Using this example to demonstrate:

• bio_values: [a, b, c, d, e]
• daily_price: [x, y, y, z, z]

Therefore:

• bio_aggregate: a + b + c + d + e
• price_aggregate (average daily price): (x + 2y + 2z) / 5
• line_item_by_scenario (total_revenue): ax + by + cy + dz + ez

Here we can see bio_aggregate * price_aggregate != line_item_by_scenario

Conceptualize

Here are how we are calculating the three values:

line_item_by_scenario

line_item_by_scenario is the day-level dot product:

$$\sum_{d=1}^{\text{total sim days}} (\text{bio quantity}_{day} \cdot price_{day})$$

biophysical_aggregate

biophysical_aggregate is the sum of daily biophysical values (quantities):

$$\sum_{d=1}^{\text{total sim days}} \text{bio quantity}_{day}$$

price_aggregate

price_aggregate is the simple average of the daily price values:

$$\frac{\sum_{d=1}^{\text{total sim days}} \text{price}_{day}}{(\text{total sim days})}$$

If you have $\sum_{i=1}^{N} a_i$ and $\sum_{i=1}^{N} b_i$

$(\sum_{i=1}^{N} a_i)(\sum_{i=1}^{N} b_i)$ is not the same as $\sum_{i=1}^{N} (a_i)(b_i)$.

Therefore, when you multiply biophysical_aggregate and price_aggregate together, it is not the same as the total_revenue.

Proposed Solution

To make sure this equality holds true, we can change how we calculate the price_aggregate to use a quantity-weighted average price instead of the simply daily average:

price_aggregate_quantity_weighted = total_revenue / total_quantity if total_quantity else None

Please let me know if this explanation is easy to understand, and if we want to move forward with the quantity-weighted price average!

[bradenlimb]

Hey @allisterakun - thanks for clarifying. The calculations you have are the ones we want. Let's leave as is. This is just the first variable that I've seen with this issue. I wonder if the others aren't calculating correctly or just aren't doing daily calcs. Probably something we should look into at some point