Distributed Renewable Energy Investment: The Effect of Time-of-Use Pricing.

• Date: 01 September 2023
• Author: Li, Lu-Miao

1. INTRODUCTION

   Renewable energy development, including distributed and centralized renewable generation, is one important way for energy transition towards carbon neutrality (Baudry and Bonnet. 2019; Yang et al., 2022). From the perspective of non-power generating firms, distributed renewable energy (DRE) sources have the potential to change traditional business models (Barbose and Satchwell, 2020). In the last decade, the investment cost of distributed solar photovoltaic (PV) has dropped by 60-80%, and the levelized cost of electricity in some regions is currently lower than the retail price without subsidies (IEA, 2019). Driven by cost reductions, DRE investment has become more affordable to both the public and private sectors (IEA, 2019). Owing to the benefits of DRE, a growing number of firms such as Apple, Walmart and Target Corporation, have invested on DRE for self-consumption purpose (EPA, 2020). For instance, at Apple, distributed generation has reached approximately 495 GWh per year, accounting for 24% of its annual electricity consumption (EPA, 2020).

   A critical feature of DRE technologies is their intermittency; that is, renewable energy source cannot continuously generate electricity (Parker et al., 2019). For instance, wind blows neither continuously nor in concert with demand; the output of solar panels is volatile because of their sensitivity to weather conditions, solar radiation and other factors (Aflaki and Netessine, 2017). Intermittency of renewables can substantially affect the economic value of DRE technology (Gowrisankaran et al., 2016), and thus has an impact on capacity investment in DRE technology (Aflaki and Netessine, 2017). To optimize the participation of intermittent DRE in the grid, a transition from flat rate (FR) to time-of-use (TOU) pricing is widely adopted by electric utilities (Parag and Sovacool, 2016; IRENA, 2019). In practice, TOU pricing usually sets a higher electricity tariff in the peak period and a lower one in the off-peak period. Several previous studies have found that TOU pricing can substantially affect the economic value to DRE investors and therefore foster capacity investment in DRE technology (Sioshansi, 2016; Mills et al., 2008; Darghouth et al., 2016).

   This paper contributes to investigate the effect of TOU pricing on a firm's DRE investment, taking into account the intermittency of renewables. Previous studies, e.g. Borenstein et al. (2008), Joskow (2011) and Reichelstein and Sahoo (2015) have shown that the setting of on-peak and offpeak time periods will affect the economics of renewable energy technology. For example, a TOU pricing scheme can produce a high economic value of renewable energy, as a result of a strong overlap between peak periods and renewable generation (Ramdas et al., 2019). Conversely, the generation of renewable energies is high at times when the low retail price is taken, which will, in turn, cause a low economic value of DRE investment (Ramdas et al., 2019). Notably, whether or not the peak price occurs at the right time becomes a vital aspect in evaluating the effect of TOU pricing schemes on DRE technology (CAISO, 2016). Moreover, a TOU pricing scheme covers two-period tariffs (i.e., peak and off-peak prices) or three-period tariffs (i.e., peak, off-peak and super off-peak prices). The number of time periods applied to TOU pricing scheme may be another influencing factor. In the context, the following questions naturally come out: (i) From the perspective of a nonpower generating firm, how does a firm make an optimal decision of DRE investment under TOU pricing? (ii) Which electricity pricing scheme (i.e., either two-period TOU pricing or FR pricing; either two-period TOU pricing or three-period TOU pricing) leads to higher DRE investment? (iii) Given a fixed length of the on-peak period, how does the TOU pricing structure (i.e., the different peak times and price signals) affect a firm's decisions regarding DRE investment?

   To answer these questions, this paper develops a cost-minimization model to determine the optimal level of DRE investment for a non-power generating firm. We transform the cost function into a single-period multi-newsvendor model. Similar to the newsvendor problem, a firm faces a trade-off between under-investment cost (i.e., the benefit of using the renewable electricity minus the cost of investing in DRE) and over-investment cost (i.e., the cost of investing in DRE minus the benefit of selling the surplus renewable electricity). Then, we derive the conditions under which electricity pricing (i.e., either TOU pricing or FR pricing) leads to a higher level of DRE investment. The effects of two-period TOU pricing scheme on a firm's optimal DRE investment decision have also been assessed. Next, we generalize the model to handle the case of three-period TOU pricing. Finally, we provide some policy and managerial implications from the perspectives of regulators and firms.

   In literature, many scholars have studied the effect of TOU pricing on DRE technology, such as Moon and Park (2014), Sioshansi (2016), Zhang et al. (2017), Cui et al. (2020) and Wang et al. (2020). Most existing studies (e.g. Kok et al., 2018; Ansarin et al., 2020; Liang et al., 2020; Correia-da-Silva et al., 2020) focus on exploring the effect of TOU pricing on DRE investment, particularly in contrast with FR pricing. For example. Kok et al. (2018) reveal that FR pricing will lead to a higher investment level for solar energy, but the impact of peak pricing on investing in wind energy is determined by the actual output of wind energy. Nevertheless, few studies investigate the effect of peak time and number of time periods on renewable energy investment. Boampong and Brown (2020) argue that a switch of peak time from midday to the constrained evening hours for rooftop solar plus battery storage systems will decrease solar PV investment in California. This work is structurally similar to Kok et al. (2018) and Kok et al. (2020), which contributes to the literature in the following three aspects: (i) exploring the appeal of TOU pricing for enabling DRE technology in comparison with FR pricing; (ii) discussing the effects of various peak times and price signals on a firm's DRE investment decisions, given a fixed length of peak period; (iii) comparing the effect of different periods of TOU pricing on a firm's optimal DRE investment decision (i.e., two-period versus three-period TOU pricing).

   The remainder of the paper is organized as follows. Section 2 describes the key elements of the model and displays the optimal conditions for a firm's capacity investment in DRE technology. Section 3 examines the impact of two-period TOU pricing on DRE investment and extends the model to the case of three-period TOU electricity pricing, in order to investigate the impact of TOU pricing schemes (i.e., two-period TOU pricing versus three-period TOU pricing) on a firm's DRE investment. Section 4 presents a numerical example. Section 5 concludes this paper with some managerial and policy implications and possible future research directions.

2. THE MODEL

   We consider a long-term investment horizon (e.g., 25 years) and model a representative billing cycle (e.g., one year) under a static two-period TOU pricing scheme. The firm with DRE penetration will interact bidirectionally with the connected grid (Fridgen et al., 2020). Specifically, when an underproduction of renewable electricity exists (i.e., the generation of the renewable energy source is lower than the firm's electricity consumption), a firm may purchase a portion of electricity from the connected grid, under the rules of a TOU pricing scheme; when an overproduction of renewable electricity exists (i.e., the generation of the renewable energy source is greater than the firm's electricity consumption), the firm may sell the surplus renewable electricity to the connected grid by complying with net-metering compensation.

   2.1 Time-of-use Pricing

   For ease of exposition, we consider a static TOU pricing scheme that is limited to two representative periods (i.e., peak and off-peak periods). Hence, we denote [p.sub.i], i [member of] {p,o}, as the peak and off-peak prices for one kilowatt-hour (kWh) and [t.sub.i] as the length of peak and off-peak hours, respectively. Let T = [t.sub.p] + [t.sub.0] be the total period hours (i.e., one year, T = 8760) and r be the proportion of the total period hours that constitute the peak period. Day/night (D/N) pricing is a simple case of TOU pricing scheme, which can use day and night pricing to broadly reflect peak and off-peak hours (IRENA, 2019); the number of peak hours is typically equal to the number of off-peak hours, [t.sub.p] =[t.sub.o]=t. Under FR pricing, the firm pays a flat price for electricity consumption in both peak and off-peak periods. Then, let [p.sub.f] be the FR pricing for one kilowatt-hour (kWh). We assume that [Please download the PDF to view the mathematical expression], no electricity consumer will use the TOU pricing, and electricity consumers will not choose FR pricing if p < [p.sub.f]. This assumption is also justified, based on actual prices used in real-life situations (Dong et al., 2017; Kok et al., 2018; Choi et al, 2020).

   Comparing with FR pricing, we stipulate that the ratio of peak to off-peak price (P/OP price ratio) is the price signal of TOU pricing. Let r = [p.sub.p]/ [p.sub.o] be the P/OP price ratio. From the perspective of utility, cost allocation is the pricing foundation of TOU pricing and has always been a staple of utility rate design (Rocky Mountain Institute, 2018; Lazaret al., 2020). According to Williamson (1966) and Harris (2015), the marginal operating costs for a utility are assumed to be constant, at a rate of b per kilowatt-hour per hour (kWh/h); fixed costs are assumed to be /? per kilowatt-hour per hour (kWh/h). Then, within Williamson framework, the equation of costs and revenues can be described as [Please...