Co-Design of Electricity Rates

Daniel Shen

1.144: Applied Category Theory for Engineering Design

Introduction

Electricity rates (tariffs) for customers are set by utilities to charge customers for the holistic cost of providing electricity. Tariff designs should be “fair” — a judgment which involves multiple, possible competing, objectives. Bonbright’s 1988 work Principles of Public Utility Rates outlines ten principles for a “desirable rate structure”:

1. Effectiveness at yielding total revenue requirements under the fair return standard.
2. Revenue stability and predictability, with a minimum of unexpected changes seriously adverse to utility companies.
3. Rate stability and predictability, with a minimum of unexpected changes seriously adverse to ratepayers.
4. Discouraging wasteful use of services while promoting all justified types and amounts of use.
5. Reflection of all present and future private and social costs and benefits due to a service’s provision.
6. Fairness of apportionment of total costs of service between rate classes.
7. Avoidance of undue discrimination in rates.
8. Dynamic efficiency promoting innovation and responding economically to changing demand and supply patterns.
9. Practicality (simplicity, certainty, convenience of payment, economy in collection, understandability, public acceptability, feasibility of application).
10. Freedom from controversies of interpretation.

These principles are sometimes competing. For example, the most economically efficient way to fairly appropriation system costs amongst different customers might be to design a personalized rate for each individual customer that reflects their real-time network usage. However, such a design would not be practical for the utility to administer and it could risk yielding insufficient revenues to cover the utility’s total costs.

Given this wealth of potential tradeoffs between rate designs, this project seeks to explore how co-design can provide a framework for evaluating the “best” rate structure. In particular, we will consider the tradeoffs between effectiveness at yielding revenue, reflection of service provision, and practicality (1, 5, and 9).

Rate Components

Residential electricity rates commonly feature two components: a fixed charge which is applied regardless of usage and a volumetric charge which is billed per amount (volume) of electricity consumed. Volumetric charges disincentivize total consumption due to demand elasticity.

The volumetric price can be constant or time-varying. The latter setup is referred to as a time of use (TOU) rate and consists of pre-determined blocks of times and electricity prices during the day. An example of a TOU structure is shown below:

(from https://www.greenconvergence.com/blog/what-is-time-of-use)

Time of use rates incentivize more efficient consumption, since the price during each block can more closely reflect the wholesale marginal cost of generating power at that time. However, customers can be more hesitant to accept a TOU rate structure since it is more complex than a flat rate. Furthermore, TOU rates can require meter upgrades to be able to monitor consumption in real-time for allocating billing in each time block.

Problem Setup

For this project setup, we consider the functionalities of utility profit and customer approval provided by a rate structure applied to a single customer class. Overall customer approval is based on:

• Total customer bill
• Carbon emissions associated with generating power
• Perceived simplicity of the rate.

Rates which consist of solely a fixed charge are considered to be the most simple (higher approval) whereas “peakier” time of use structures with large differences between the on- and off-peak price are perceived as less simple.

The resources of the design problem are the maximum tolerable customer bill and a carbon credit budget. We assume the utility can purchase credits to offset CO2 grid emissions and increase the customers’ approval of the rate.

Consumption is modeled over two periods of the day. Wholesale electricity prices are more expensive during the on-peak period compared to the off-peak period and the utility must pay more to serve electricity demand during the on-peak period.

Modules

The diagram of the MCDP is shown below:

Customer Model

The customer’s demand elasticity in the on- and off-peak period is set based on an exogenous demand curve. The impact of each tariff on customer consumption is calculated in Python and input into the MCDP software as a catalog. See Jupyter notebook tariff-generator-v2.ipynb for the code used to calculate customer demand and generate the tariff catalog.

Results

Design Space

We consider three parameters of the rate:

• Fixed charges varying from $0/mo to $100/mo in increments of $10/mo.
• Off-peak volumetric charges varying from $0/kWh to $0.30/kWh in increments of $0.05/kWh (the wholesale off-peak price seen by the utility is $0.05/kWh)
• On-peak volumetric charges varying from $0/kWh to $0.30/kWh in increments of $0.05/kWh (the wholesale on-peak price seen by the utility is $0.80/kWh).

To reduce the number of rates considered by the MCDP software, we only consider rates which the utility can recover at least $30/mo in profit once the cost of purchasing the electricity is considered. This results in 141 valid rates to choose from. Even with this relatively small number of rates, it took at least one hour for the MCDP program to run on my laptop and find a solution, so a more extensive rate catalog was not considered.

Finding the Rate which Minimizes Resources

Here, we evaluate the rates which have at least a profit for the utility of at least $30/mo while utilizing under $30/mo in carbon credits and having a max bill of under $150/mo. We increase the minimum approval from 10 to 40 in increments of 10 units.

All queries were done at an optimistic and pessimistic setting of 25. Higher resolutions did not return results in a reasonable amount of time when run on my computer.

The above figure shows the pessimistic upper sets calculated as the approval requirement is gradually increased. As the approval requirement becomes more strict (darker shaded points), the utility must spend more in carbon credits to boost the approval rating. Furthermore, some time of use tariffs (T0000000000) are eliminated due to their complexity negatively affecting customer approval. Instead, at higher approval requirements the Pareto frontier favors rates with a flat volumetric charge plus a fixed charge.

Repository

This section describes the notebooks and code used to generate these results

• notebooks/tariff-generator-v2.ipynb creates the tariff catalog and evaluates the consumer behavior under each tariff.
• notebooks/plot-results.ipynb generates the plots.
• notebooks/make-queries-v2.ipynb creates the queries.z

Outputs of the queries are in queries folder.