Abstract
This paper develops a framework for centralized allocation of resources and production targets among firms that produce a bad output side-by-side with a good output. The production technology is specifically defined for thermal power generation sector that produces one good output (electricity) and one bad output (stack emissions) with one polluting input (coal) and two neutral inputs (installed capacity of power plants and labor). The undesirable output is modeled as an incidental by-product resulting from use of the polluting input. We use a modified Directional Distance Function of Aparicio et al. (Eur J Oper Res 226:154–162, 2013), formulated with nonparametric data envelopment analysis, to determine the extent by which good output can be increased in each region while minimizing the use of polluting inputs and the level of bad output, by increasing efficiency through reallocation. For empirical illustration, we use the data from major coal-fired power plants in India for fiscal years 2005–06 through 2014–15. Each state within India is treated as a regional jurisdiction within which inputs (only coal and labor) and outputs are reallocated under alternative structural assumptions. Our findings reveal that the thermal power sector is suboptimal, leaving a scope for emission reduction and increase in power generation in different states of India.
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Data availability
The data used in thi paper were constructed from publicly acessible data sources.
Notes
The installed capacity of renewables (excluding large hydro) as of March 2022 was about 110GW, accounting for about 27% of the total installed generating capacity in the country, In the fiscal year 2021–22, renewables constituted only 11.9% of the gross electricity generation in India (Central Electricity Authority, General Review 2023).
The authors note that operationalization of the concept presented in this paper will depend on regulatory and operating structure in the implementing economy/organization. The paper solely aims to determine technically feasible efficiency improvements from the standpoint of production economics, but the actual application mechanism will vary from country to country and is outside the scope of this study.
Sueyoshi and Goto (2012) also introduce a new concept called managerial disposability where more inputs are used to increase good outputs and at the same time reduce bad outputs by increasing managerial efforts.
The data are reported by accounting year, which runs from April 1st to March 31st of the next year. Thus, the year 2009–10 refers to the period April 1, 2009 to March 31, 2010.
Free disposability of input implies that use of additional inputs do not lower the outputs. Analogously, free disposability of emissions imply that it is possible to have higher emissions without any associated reduction in power production.
They define \({T}_{1}=\left\{\left(x, y,z\right)\in {R}_{+}^{n+m+{m}{\}^{\prime}}}|\lambda X\le x^\lambda Y\ge y \mathrm{for \, some \, \lambda }\in {{\text{R}}}_{+}^{p}\right\}\),
\(T_{2} = \left\{ {\left( {x^{1} ,x^{2} ,y,z} \right) \in R_{ + }^{{n_{1} + n_{2} + m + m\}^{\prime} }} |\mu X^{2} \ge x^{{2\mu }} Z \le z\;{\text{for}}\;{\text{some}}\;\mu \in {\text{R}}_{ + }^{p} } \right\}\), and.
$$T={T}_{1}\cap {T}_{2}=\left\{\left({x}^{1},{x}^{2}, y,z\right)\in {R}_{+}^{{n}_{1}+{n}_{2}+m+{m}{\}^{\prime}}}|\lambda \left[{X}^{1}{X}^{2}\right]\le \left({x}^{1},{x}^{2}\right), \lambda Y\ge y, \mu {X}^{2}\le {x}^{2}, \mu Z\le z, \mathrm{for some }\left(\lambda ,\mu \right)\in {{\text{R}}}_{+}^{2p} \right\}.$$Materials-balance is explained in this approach not as a mass–energy accounting identity, but rather as nature’s pollution-generating technology, which operates independently of a firm’s intended-production technology and relates emission generation to emission-causing inputs also used in production of the goods and abating output, and mitigation of emissions to abating output.
Two outputs are joint in production when for a given vector of inputs, there is no trade-off in their production. On the other hand, they are rival if increase in the production of one output implies reduced production of the other (because more resources have been consumed in the production of the first output).
See Fig. 2, Ray et al. (2018, pp–15) for detailed explanation.
A related problem was addressed in Ray et al. (2008), which involves a cost minimization problem of a multi-location firm facing heterogeneous technology and input prices across locations.
Note that an existing unit may be a candidate for shut down. But no new units are to be constructed. Thus, the number of units either stays the same or is decreased but does not increase.
In a single output case, T is often defined using a production function as: \(T=\left\{\left(x,y\right),y\le f\left(x\right)\right\}.\)
The graph of the technology in multiple outputs case is the set: \(G = \left\{ {\left( {x,y} \right):F\left( {x,y} \right) = 0} \right\}\), in a single output case the set is \(G = \left\{ {\left( {x,y} \right):y = f\left( x \right)} \right\}\)
As noted earlier, the data are reported by accounting year, which runs from April 1st to March 31st of the next year. Thus, the year 2005–06 refers to the period April 1, 2005 to March 31, 2006. For the rest of this paper, we refer to the year 2005–06 as 2005, and so on till 2014–15 (denoted as 2014).
In cases where data are available at the unit-level, we aggregate by taking a weighted average of unit-level data (weighted by the unit’s installed capacity) to obtain plant-level information.
A large number of power plants had to be dropped because of unavailability of complete information on all required variables for our models.
MUs = Million Units (One Unit is one kilowatt hour (kWh)).
The 2014–15 CEA report explicitly mentions that “main reasons for low operating availability was increased forced shut down of thermal units due to coal shortage, Transmission constraints, Vintage units closed for operation and Reserve Shutdown.”.
SHR = (specific coal consumption (in kg/kWh) x Gross calorific value of coal (in kCal/kg)) + (specific oil consumption (in ml/kWh) x Gross calorific value of oil (in kCal/liter)).
For ease of presentation, all tables in the paper report results/data from selected years−2005, 2010, and 2014. Results/data for other years can be provided upon request.
STPS: Super Thermal Power Station. Super thermal power plant is a power generating station with capacity of 1000 MW and above.
The potential improvements at the country level are computed using formulas similar to those in (11), by taking a ratio of the difference between aggregate actual and optimal levels of good output, bad output and polluting input to the observed levels of corresponding outputs and inputs.
Plant load factor (PLF) = Generation (MWh) /Capacity (MW) × 8760 (hours). Moreover, Table 2 shows that generation at the plant was lowest in the sample with highest heat rate in 2010.
It is worthwhile to remember that our sample covers only about 60% of country’s generation capacity. An optimization on a more complete dataset could entail greater potential increment in the good output. Also, the objective function simultaneously emphasizes on two contrasting policy objectives of more power and cleaner power, if maximizing generation alone constituted the focus of reallocation framework, further increases in the power production could be attainable.
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This paper was co-authored by Shilpa Sethia in her personal capacity while she was a student at the University of Connecticut. The views expressed in this paper are author’s own and does not reflect the views of National Grid.
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Ray, S.C., Sethia, S. A state-level resource allocation model for emission reduction and efficiency improvement in thermal power plants. Ind. Econ. Rev. (2024). https://doi.org/10.1007/s41775-024-00214-2
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DOI: https://doi.org/10.1007/s41775-024-00214-2