# A Study on Reliability Differentiated Pricing of Long-Term Transactions

Abstract: Reliability differentiated pricing (RDP) is known to improve the efficiency and benefits of consumers and producers. Outage costs representing the economic and non-economic consequences of service curtailments to customers can be used as an effective parameter of RDP in electricity markets. This paper examines the theoretical aspects of an RDP scheme, and derives the optimal decisions of consumers and electric utilities for long-term transactions. The proposed RDP is demonstrated through a case study on a wheeling service.

## Summary (2 min read)

### 1. Introduction

- Electricity consumers are often given the choice of different levels of service reliability [1]-[3].
- Moreover, real systems, in general, may not recover the sufficient revenue for the utility.
- The pricing policy proposed in [5]-[8] could overcome most of the shortcomings entailed in both priority pricing and real-time pricing.
- It could also differentiate the prices for varying levels of service reliability based on consumer outage costs.
- One reason for this is the sudden shortage of supply.

### 2. Theory of Reliability Differentiated

- A single welfare-maximizing public utility is assumed to own and operate the generating plants and the transmission network of a given electric power system, which is sold independently to customers.
- It is also assumed that the utility could set and communicate the prices, as well as set a different price range for each customer class, at each moment instantaneously.
- Supply outages occur randomly in relation to the probability of a possibly known outage.
- Outages are assumed to be of short duration, such that customers who continue to access the utility service will not find it feasible or profitable to reschedule their production processes (i.e., change their electricity usage pattern) from the high production prices during outage duration.
- It is assumed that the utility could ration the supply shortages among its targeted customer classes.

### 2.1 Consumer Behavior [5]

- Customers are modeled as price-taking, profit-maximizing firms.
- Consider a short-term rational customer whose benefit from electricity usage at any time depends on consumption at that time only.
- Then, in real-time, when there is no supply shortage, the customer would choose iQ to maximize † Corresponding Author: Department of Electrical and Electronic Engeering, Hongik University, Korea. (bhkim@wow.hongik.ac.kr).
- Fig. 1 shows the expected short-run customer demand curve DD, a very short-run customer demand curve D'E, and supply curve SS of electricity.
- The outage cost function includes loss in customer benefit (the bold letters represent expected values).

### 2.2 Objective

- All decision variables, with the exception of those involving reactive power, are nonnegative. .
- For optimal operating and pricing strategies, the objective is to maximize the subject for the operating and network constraints inherent in the system.

### 3. Optimal Long-Term Prices

- Section 2 deals with the short-run problem of a welfaremaximizing utility from which optimal short-term reliability-differentiated prices are derived from.
- This section examines the long-run social welfare maximization problem of the utility developed from the previous section.
- Based on these, the authors derive the differentiated prices of long-term reliability, which considers cost of capital or other fixed costs of production.
- Long-term transactions, such as firm capacity purchased from or by the utility, or purchased from individual generators in the case of a network utility, the access to transmission services and wheeling transactions would require the provision of long-term prices in order for the participants to enter into contracts and to accommodate optimal investment decisions.
- The customer sets the expected net marginal benefit from the electricity consumption equal to the expected price of electricity.

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- Thus, by employing socially optimal investment decision-making, long-term prices of real and reactive power could coincide with short-term reliability-differentiated prices.
- Another difficulty is the unavailability of proper demand models that could capture the interdependence of intertemporal demands.
- In principle, one should utilize benefit functions that depend on the entire time stream of demand rather than a single point in time.

### 4.1 Implications for Pricing Firm Capacity

- Firm capacity refers to the generation of capacity that is purchased by the utility from neighboring utilities, namely, independent power producers (IPP) and cogenerators, in order to provide customers with long-run higher levels of service reliability.
- The price paid for firm capacity should equal the value or marginal benefit that the customers derive from the added capacity.
- Purchasing firm capacity is a long-term contract forged to protect against the loss of customer load due to unplanned outage of generating units.
- Thus, in order to determine the optimal price of firm capacity purchases, the long-run problem of welfare-maximizing utility given in Equations (9)–(10) must be considered.
- Again, this problem could be solved when obtaining the optimal values of all variab1es as functions of the parameters of the problem, in particular, piK and q iK (sensitivity theorem).

### 4.2 Numerical Example: Calculation of Long-Term Rates

- Consider the simple four-bus system in Fig. 2.
- In the model, there are two generating units (G2 and G4) and one transmission line (T3) with non-zero forced outage rates.
- Thus, at each instance over time, there are eight possible system configurations or states that the system can utilize.
- Hence, under RDP, the total expected revenue from sales to customers is exactly equal to the sum total of all expected costs/payments for the system (i.e., TR = TC).

### 5. Conclusion and Future Study

- Outage costs play an essential role in electricity pricing and in the planning of electrical power systems.
- The central role of outage costs in the optimal investment planning of the power system from a societal point of view, particularly for setting economic reliability standards in the generation, transmission, and distribution planning, has been emphasized by many studies.
- Unbundling the services by offering consumers options on trade offs for service reliability, quality, and price can potentially increase the economic efficiency of the entire system, producing benefits for both the utility and the customers.
- The authors propose RDP in examining the proposed pricing scheme of long-term transaction, putting emphasis on the long-term contract of firm capacity.

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###### Q2. What are the future works in "A study on reliability differentiated pricing of long-term transactions" ?

However, the implications of the proposed pricing scheme for the wheeling service and transmission service needs to be dealt with further by future studies.