from 3,954 randomly sampled feeders within JVVNL’s network. The data set separates technical losses from losses due to commercial and billing inefficiencies. The former component leads to an overall reductional in society’s welfare, while the latter represents a welfare transfer from households that are billed for their consumption, to household that consume electricity without a bill. We use technical losses at the feeder level to estimate the quadratic relation. Using calculations for each 15-minute period and the parameter estimates of fitted quadratic equation, we estimate marginal distribution DD ii losses. The average marginal distribution losses in our sample is 18.4% with a standard deviation of QQ 3%. Figure 15 shows the frequency distribution of marginal transmission and distribution losses based on these calculations.<sup>24</sup>

# • **Marginal cost of emissions**

The final component of SMC is the external cost associated with emissions from generating plants that increase their output in response to an increase in demand. Ideally, the cost of emissions should be calculated separately for all pollutants such as carbon dioxide, nitrogen oxide, sulfur dioxide and particulate matter. However, this paper calculates only the cost carbon dioxide emissions, as generator-wise emissions data for other pollutants is unavailable in India. Moreover, to precisely estimate the marginal cost of carbon, emissions data at 15-minute or hourly intervals for each generator are required. Such detailed data sets are unavailable in the Indian context.

Facing these limitations, the marginal cost of emissions is proxied by the average carbon dioxide emissions per unit of energy produced by each generator. A data set<sup>25</sup> that contains information on annual carbon dioxide emissions for FY2016-17 for each power generating company in India is used for this purpose. The data set uses plant-level information on the type of fuel used, the calorific value of the fuel mix and its emission and oxidation factors to calculate the total carbon dioxide emitted by the plant in a year. The annual tons of carbon dioxide divided by the total units of energy produced by a plant in a year gives a plant-level estimate of average tons of carbon dioxide per unit of energy generated. The social cost of carbon per unit of energy generated by a plant is estimated by multiplying the average tons of carbon dioxide per kWh by Rs. 2184 (Nordhaus (2018) cost estimate for a ton of carbon emission is $33.60; at approximately Rs. 65/USD this amounts to Rs. 2184 per ton of carbon dioxide). Finally, using the SLDC high-frequency data set on generator-wise energy dispatch at 15minute time intervals from Rajasthan’s system operator, the price of emission at each period<sup>26</sup> ( ) is calculated as: ccm ccggnn ii PP

> 24 The average marginal transmission loss estimate is comparable to the average annual transmission 3.95% reported by JVVNL in its FY2016-17 financial petition to the regulator: <u>http://energy.rajasthan.gov.in/content/dam/raj/energy/jaipurdiscom/pdf/tariff/2018/true/additional_submission.pdf</u> . In reporting, the average annual distribution loss, JVVNL pools commercial losses (that occur due to billing inefficiencies) with physical losses over the wire. For the estimation of social marginal costs, we are interested in measuring the physical losses that occur over the distribution network. This estimate can be found in a report by the Forum of Regulators (2012) that shows the average distribution losses over a three-month period at a representative feeder within JVVNL’s network to be 9.2%. This is lower than the 13.4% average marginal losses calculated using our methodology.

> 25 CO2 baseline database for the Indian power sector produced by the Central Electricity Authority (Version 14), available at: <u>http://www.cea.nic.in/tpeandce.html.</u>

> 26 Because we are using high-frequency plant-wise data, the carbon cost of emission in our calculation for each 15-minute interval is based only on state-owned generators.

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