Merge pull request #49 from switchbox-data/41-revenue-sharing-mechanism

revenue sharing mechanism

Author: alxsmith

.gitignore

@@ -222,3 +222,4 @@ outputs/
 !docs/
 !docs/**/*
 docs/.DS_Store
+.vscode/settings.json

docs/formulas.md

@@ -42,9 +42,9 @@ This document contains the  formulas implemented in the
 | Variable | Description | Units |
 |----------|-------------|-------|
 | $N_{gas}(t)$ | Number of gas customers in year $t$ | customers |
-| $N_{gas,init}$ | Initial number of gas customers | customers |
+| $N_{gas}(0)$ | Initial number of gas customers | customers |
 | $N_{electric}(t)$ | Number of electric customers in year $t$ | customers |
-| $N_{electric,init}$ | Initial number of electric customers | customers |
+| $N_{electric}(0)$ | Initial number of electric customers | customers |
 | $N_{converts}(t)$ | Cumulative number of converted households including non-npa households through year $t$ | customers |
 | $N_{NPAconverts}(t)$ | Sum of NPA households converters in year $t$ (excludes scattershot electrification) | customers |
 | $N_{customers}(t)$ | Total number of customers in year $t$ | customers |
@@ -142,12 +142,12 @@ This document contains the  formulas implemented in the
 The number of gas customers decreases over time as customers convert to
 heat pumps. There is no growth in the number of gas customers:
 
-$$N_{gas}(t) = N_{gas,init} - \sum_{i=1}^{t} N_{converts}(i)$$
+$$N_{gas}(t) = N_{gas}(0) - \sum_{i=1}^{t} N_{converts}(i)$$
 
 **Variables:**
 
 -   $N_{gas}(t)$: Number of gas customers in year $t$
--   $N_{gas,init}$: Initial number of gas customers
+-   $N_{gas}(0)$: Initial number of gas customers
 -   $N_{converts}(t)$: Sum of NPA households and scattershot converters
     in year $t$.
 
@@ -217,9 +217,9 @@ $$C_{gas,LPP,avoided}(t) = \sum_{p \in P(t)} N_{converts}(p) \times V_{pipe,user
 ### Gas Revenue Requirement
 
 The gas revenue requirement includes ratebase return, OPEX, and
-depreciation:
+depreciation. In the performance incentive scenario, it also includes performance incentives:
 
-$$R_{gas}(t) = RB_{gas}(t) \times ror_{gas} + C_{gas,opex}(t) + D_{gas}(t)$$
+$$R_{gas}(t) = RB_{gas}(t) \times ror_{gas} + C_{gas,opex}(t) + D_{gas}(t) + PI_{gas}(t)$$
 
 **Variables:**
 
@@ -228,32 +228,33 @@ $$R_{gas}(t) = RB_{gas}(t) \times ror_{gas} + C_{gas,opex}(t) + D_{gas}(t)$$
 -   $ror_{gas}$: Gas rate of return
 -   $C_{gas,opex}(t)$: Gas OPEX costs in year $t$
 -   $D_{gas}(t)$: Gas depreciation expense in year $t$
+-   $PI_{gas}(t)$: Gas performance incentive in year $t$ (performance incentive scenario only)
 
 ## Electric System Calculations
 
 ### Electric Number of customers
 
 The number of electric customers is the initial number of electric
 customers. There is no growth in the number of electric customers:
-$$N_{electric}(t) = N_{electric,init}$$
+$$N_{electric}(t) = N_{electric}(0)$$
 
 **Variables:**
 
 -   $N_{electric}(t)$: Number of electric customers in year $t$
--   $N_{electric,init}$: Initial number of electric customers
+-   $N_{electric}(0)$: Initial number of electric customers
 
 
 ### Total Electric Usage
 
 Electric usage includes both base electric needs and heating loads from
 converts:
 
-$$U_{electric}(t) = N_{electric,init} \times Q_{electric,kWh} + \frac{N_{converts}(t) \times Q_{heating,therms} \times K_{therm\to kWh}}{\eta_{HP}}$$
+$$U_{electric}(t) = N_{electric}(0) \times Q_{electric,kWh} + \frac{N_{converts}(t) \times Q_{heating,therms} \times K_{therm\to kWh}}{\eta_{HP}}$$
 
 **Variables:**
 
 -   $U_{electric}(t)$: Total electric usage in kWh in year $t$
--   $N_{electric,init}$: Initial number of electric customers
+-   $N_{electric}(0)$: Initial number of electric customers
 -   $N_{converts}(t)$: Cumulative electrification converts through year $t$
 -   $Q_{electric,kWh}$: Average per-customer electric need in kWh
 -   $Q_{heating,therms}$: Average per-customer heating need in therms
@@ -476,6 +477,29 @@ $$B_{total,nonconverts}(t) = B_{gas,nonconverts}(t) + B_{electric,nonconverts}(t
 
 ## Depreciation and Inflation Calculations
 
+### Net Present Value (NPV) Calculation
+
+The NPV calculation evaluates utility investments by considering both the return on ratebase and depreciation recovery over the investment lifetime:
+
+$$NPV = -C_0 + \sum_{t=1}^{L} \frac{R_t + D_t}{(1 + r)^t}$$
+
+where:
+
+-   $R_t = C_0 \times f_{dep}(t) \times ror$ (return on remaining ratebase value)
+-   $D_t = \frac{C_0}{L}$ (annual depreciation recovery)
+- $f_{dep}(t) = \max(0, 1 - \frac{t}{L})$ (remaining value fraction)
+
+**Variables:**
+
+-   $NPV$: Net present value of the investment
+-   $C_0$: Initial investment cost
+-   $L$: Investment lifetime in years
+-   $R_t$: Annual return on ratebase in year $t$
+-   $D_t$: Annual depreciation recovery in year $t$
+-   $ror$: Rate of return on ratebase
+-   $r$: NPV discount rate
+-   $f_{dep}(t)$: Depreciation fraction in year $t$
+
 ### Ratebase Calculation
 
 The depreciation fraction determines how much of a project's original
@@ -552,3 +576,55 @@ This creates a table of synthetic project with uniform original costs of that wo
 -   $L$: Depreciation lifetime
 -   $RB_{init}$: Initial ratebase
 -   $C_{est}$: Estimated original cost per year
+
+## Performance Incentive Calculations
+
+### Performance Incentive Mechanism
+
+The performance incentive mechanism models shared savings between utilities and ratepayers for NPA (Non-Pipe Alternative) projects. This mechanism treats NPA costs and avoided BAU (Business-As-Usual) costs differently:
+
+**NPA Costs Treatment:**
+- NPA costs are treated as gas OpEx (operating expenses)
+- Collected in the year costs are incurred
+- No rate of return earned on NPA investments
+
+**BAU Costs Treatment:**
+- Avoided BAU costs (what would have been spent replacing LPP) are treated as normal CapEx
+- User sets ROR and depreciation period equal to pipeline lifetime
+- Earns return on ratebase over depreciation lifetime
+
+**Cost Savings Calculation:**
+Cost savings are calculated as the NPV difference between avoided BAU costs and NPA costs:
+
+$$Savings_{NPV}(t) = NPV_{BAU}(t) - C_{gas,NPA,opex}(t)$$
+
+where:
+- $NPV_{BAU}(t)$ = NPV of avoided LPP spending in year $t$
+- $C_{gas,NPA,opex}(t)$ = NPA investment costs in year $t$
+
+**Performance Incentive Distribution:**
+30% of cost savings are collected from ratepayers, evenly split over a 10-year period:
+
+$$PI_{annual}(t) = \frac{0.30 \times Savings_{NPV}(t)}{10}$$
+
+**Variables:**
+
+-   $Savings_{NPV}(t)$: NPV savings from NPA projects in year $t$
+-   $NPV_{BAU}(t)$: NPV of avoided BAU costs in year $t$
+-   $C_{gas,NPA,opex}(t)$: NPA OPEX in year $t$
+-   $PI_{annual}(t)$: Annual performance incentive payment in year $t$
+
+
+### Performance Incentive Revenue Requirement Impact
+
+In the performance incentive scenario, the gas revenue requirement includes the annual performance incentive payments:
+
+$$R_{gas,PI}(t) = R_{gas}(t) + \sum_{i=0}^{9} PI_{annual}(t-i)$$
+
+where the summation includes performance incentive payments from all active savings projects (those initiated in years $t-9$ through $t$).
+
+**Variables:**
+
+-   $R_{gas,PI}(t)$: Gas revenue requirement including performance incentives in year $t$
+-   $R_{gas}(t)$: Standard gas revenue requirement in year $t$
+-   $PI_{annual}(t-i)$: Annual performance incentive payment from savings project initiated in year $t-i$