Elsevier

Energy Economics

Volume 106, February 2022, 105721
Energy Economics

Valuing investments in domestic PV-Battery Systems under uncertainty

https://doi.org/10.1016/j.eneco.2021.105721Get rights and content

Highlights

  • We model households’ decision to invest in PV plants coupled with battery storage.

  • We implement a real option approach to capture the value of managerial flexibility.

  • The option of storing energy via batteries increases de facto investment value.

  • Battery storage encourages households to invest in larger PV plants.

Abstract

Renewable energy technologies are expected to play a major role in mitigating climate change and resource depletion effects as well as in contributing to domestic energy security. Due to the intermittent nature of solar photovoltaic (PV), there are often significant gaps between energy consumption and energy supply by PV plants. This makes storage systems a potential option to maximize savings and accrue managerial flexibility by increasing the share of self-consumed energy while guaranteeing adequate power levels in distribution grids.

This paper provides a theoretical framework to model households’ decision to invest in domestic PV plants coupled with battery storage. To capture the value of managerial flexibility relative to the decision to install both a PV plant and a battery, i.e., a domestic PV-Battery System (PVB), we implement a Real Options approach and propose an optimization model, which we calibrate and test according to data from the Italian energy market. Our findings show that the option of storing energy via batteries increases de facto investment value: the adoption of a PVB increases managerial flexibility, as households can optimally exercise the option to decide their consumption and storage patterns contingent on favorable market conditions. The opportunity to store energy via batteries encourages households to invest in larger plants compared to those not paired with batteries. There is indeed a positive relationship between the PVB optimal size and investment timing.

Introduction

The EU has recently established EU-wide targets and policy objectives for the period from 2021 to 2030 to reduce global warming and mitigate climate change effects. Consequently, investments in renewable energy sources (RES) have received growing attention from Governments, policymakers, academics, and practitioners. The 2030 Climate & Energy Framework set three macro targets to be reached by 2030: at least 40% cuts in greenhouse gas (GHG) emissions compared to 1990 levels, at least 27% share for renewable energy, and at least 27% improvements in energy efficiency (European Commission, 2014). In 2018, both the binding renewable energy target and the headline target for energy efficiency were revised upwards to 32% and 32.5%, respectively. The achievement of such challenging objectives requires the implementation of cost-effective solutions to limit energy demand, reduce fuel poverty, decarbonize the power sector, favor economic growth and job creation, and increase energy security by reducing dependence on energy imports. In this context, it is generally acknowledged that the power sector has the greatest potential in the reduction of CO2 emissions and the improvement of energy efficiency and security. Much of recent research has been devoted to energy production by solar and wind power plants, considered as a milestone in the transition from a fossil-based to a zero-carbon energy sector. Nonetheless, due to the growing deployment of RES, innovative design and management of traditional electricity grids are required, and new power systems are emerging, in which decarbonization, decentralization, and digitization issues are of major importance. To address these issues a shift from a centralized system with large power plants and long transmission lines to a decentralized and polycentric system, based on distributed renewable energy production plants and micro-grids, is imperative. Different from existing transmission and distribution networks, designed for unidirectional power flows, micro-grids guarantee bidirectional power flows and allow prosumers to interact among them and with the local grid. Due to their intermittent nature and variability depending on weather conditions, RES production plants can create significant mismatches between supply and demand, thus posing a challenging threat to the stability and the operational management of the grid (Hoppmann et al., 2014). In addition, the increasing number of distributed generation plants has recently increased grid and systems management costs due to e.g., inefficiency, congestion rents, power outages, and demand for continuous real-time balancing (Boampong and Brown, 2020). Flexibility measures, such as demand-side management, integration of fast-acting supply, energy storage, voltage control, and reserve capacity, are needed to ensure grid security and reliability (Eid et al., 2016, Dulout et al., 2017, Weber et al., 2017, Madlener and Specht, 2019, Dato et al., 2020). In the light of the above considerations, energy storage can represent an effective contribution to the innovation of traditional grids and better management of energy systems. It can respond to the request for a steadier electricity supply by reducing mismatches between demand and supply.

With respect to small-scale production plants, it is commonly agreed in literature that, compared to other options, solar photovoltaic (PV) plants exhibit a rather large potential for electricity generation and can play a major role in the achievement of energy efficiency targets set at EU level (Koskela et al., 2019). In recent years, PV systems considerably increased their market share due to both a rapid decline of their price by over 80% from 2008 to 2016 in most competitive markets (Schopfer et al., 2018) and to the large adoption of Feed-In-Tariffs (FITs) (Kästel and Gilroy-Scott, 2015, Lüth et al., 2018). Nonetheless, several barriers to more widespread implementation of solar PV plants persist. So far, investments have been encouraged by generous incentive policies, which have attracted investments by both institutional and private investors and by households. The recent decrease in the levelized cost of PV-produced electricity has not counterbalanced yet the continuous reduction of FITs, which are expected to be abolished in the near future (Karakaya and Sriwannawit, 2015, Schopfer et al., 2018, Nguyen et al., 2018). To offer valuable services to the grid and enable high penetration of RES, and more specifically of PV systems, Smart Grids (SGs) and energy storage via batteries are considered promising solutions. Although SGs represent the evolution of electric grids and permit an instantaneous interaction between prosumers and the grid, which in turn can contribute to the balancing of the system in real-time, their successful implementation is still far from being effective. By contrast, battery storage is rapidly diffusing due to the competitiveness of battery prices and to their scalability to different types of projects (Dulout et al., 2017, Pandžic, 2018, D’Alpaos and Andreolli, 2020a). Batteries can indeed contribute to grid management by buffering short-term variations of supply and demand and represent a worthwhile solution to increase electricity self-consumption (Braun et al., 2009, Schill and Zerrahn, 2018, Madlener and Specht, 2019, Rossi et al., 2019), which for PV plants not coupled with storage usually ranges between 30%–40% of PV energy production (See e.g., Di Pietra and Sbordone, 2015, Ciocia et al., 2016, Jäger-Waldau et al., 2018, Petrollese and Cau, 2018, D’Adamo et al., 2020a, D’Adamo et al., 2020b). Consequently, distributed battery storage has been deeply analyzed in literature and viewed as a distributed energy technology, which can further enhance environmental benefits (e.g., CO2 emission reduction) as well as private benefits (e.g., households’ energy cost savings) deriving from PV energy production (Uddin et al., 2017, Nguyen et al., 2018, Talent and Du, 2018, Koskela et al., 2019). In consequence of  the progressive reduction of policy incentives to RES, self-consumption has recently started to be a profitable solution, and has evolved into a core driver of investments in domestic PV plants, due to two main reasons: the progressive reduction of FITs to RES and the grid-parity successfully reached in many European countries, where the cost of self-produced PV electricity is nowadays lower than the retail price of electricity (Weniger et al., 2014a, Lang et al., 2016, Luthander et al., 2015, Moshövel et al., 2015, Schwarz et al., 2018). Nonetheless, investments in PV plants coupled with battery storage are affected by high uncertainty and irreversibility (e.g., high upfront investments costs, long investment cycles, high volatility of energy prices, etc.), which make strategic decisions extremely complex and puzzling (Martinez-Cesena et al., 2013, Bigerna et al., 2016).

In this paper, we analyze whether the adoption of batteries coupled with PV plants can increase PV investments value (i.e., investments profitability) and, in turn, affect the decision on the plant optimal size and investment timing. We model the decision of a (price-taker) household connected to a distributed generation system, to invest in a domestic (rooftop) PV plant and a rechargeable lithium-ion battery. In detail, we develop and implement a Real Options model to determine the investment value of a domestic PV-Battery System (PVB), namely a PV plant coupled with battery storage, in which batteries can contribute to balancing daily energy fluctuations and, consequently, guarantee a better match between demand and supply, by increasing self-consumption. We focus on the decision to invest in an ex-novo PVB, whereas we do not consider the opportunity to couple battery storage to an existing PV plant. Therefore the decision involves the choice of the optimal size of the PVB under investigation and its optimal investment timing. Specifically, in this framework the household can (a) satisfy their energy daytime demand instantaneously through PV production and (b) store excess PV production during the daytime to satisfy their nighttime energy demand. In our setting, the household aims to minimize energy costs by increasing self-consumption and reducing shares of grid-purchased energy.

In this respect, battery storage de facto generates managerial and operational flexibility, which households can exercise optimally when deciding to invest. This flexibility contributes significantly to energy savings and hedging of investment risk, thus making the investment more attractive. Batteries guarantee an increase in self-consumption, by reducing both electricity shares fed into the grid at wholesale prices and electricity shares purchased by the grid at retail prices, and consequently, they significantly contribute to increasing investment returns.

Most contributions in literature implement traditional capital budgeting techniques such as discounted cash flow analysis and the Net Present Value (NPV) rule to evaluate investments in battery storage (Colmenar-Santos et al., 2012, Hoppmann et al., 2014, Allan et al., 2015, Naumann et al., 2015, Cucchiella et al., 2016, Khalilpour and Vassallo, 2016, Cucchiella et al., 2018, Lüth et al., 2018). Nonetheless, the NPV rule has indeed a static nature because valuation refers to a specific point in time and ignores the possibility to react to changes in internal or external conditions. This possibility to revise future actions introduces an asymmetry in standard NPV probability distribution, which expands the investment opportunity value with respect to NPV and increases its profit potential while limiting losses and hedging risk. By contrast, to properly address the issues of the irreversibility of PVB investments and uncertainty over the buying price of energy, in this paper we implement the Real Options approach (Dixit and Pindyck, 1994, Trigeorgis, 1996). This approach permits to capture the value of flexibility to invest in PVBs and account for investors’ ability to adapt to new information to come. Specifically, to capture the value of PVBs in the Italian context, we calibrate and test our model according to data driven from the Italian electricity market. We show that energy storage via batteries increases investments value. It emerges indeed a positive relationship between the PVB optimal size and the optimal investment timing (i.e., the greater the PVB optimal size, the greater the investment deferral). Furthermore, in line with the Real Options theory, we observe that increasing volatility increases the option value to defer investments.

In detail, our results reveal that when households decide whether and when it is optimal to invest, they install large PVBs, whose optimal storage size ranges between 35% and 50% of the optimal PV size (expressed in kWh). This in turn assures an increase in total self-consumption (i.e., the sum of PV energy consumed during daytime plus energy stored in the battery) by about 50% compared to PV plants not coupled with battery storage. Nonetheless, at current prices, investments in PVBs are usually still not profitable.

The remainder of the paper is organized as follows. Section 2 briefly presents relevant related literature; Section 3 discusses the model set-up and assumptions; Sections 4 PVB Investment value, 5 Optimization present the Real Options model and determine the PVB investment value as well as the optimal investment size and timing, respectively; Section 6 provides model parameters and costs estimates; Section 7 illustrates numerical simulations and discusses main results; finally Section 8 concludes.

Section snippets

Relevant literature

We investigate households’ decisions to invest in PVBs by combining irreversible investments under uncertainty with optimal investment timing, and we contribute to two main strands of literature. First, we complement existing literature on the role of storage in energy systems (De Sisternes et al., 2016, Wang et al., 2017, Ghasemi and Enayatzare, 2018, D’Alpaos and Andreolli, 2020a), its integration with RES power plants (Crespo Del Granado et al., 2016, Conte et al., 2018) and its impacts on

Model set up

We investigate the investment strategy of a household, currently connected to the national grid, who has to decide whether and when to invest in a PVB to cover their energy demand. The possibility to adopt a battery storage system and store the excess PV production enables the household to reduce grid-purchased energy to the event when batteries are completely discharged, thus increasing their self-consumption share. Specifically, we model the optimal PVB size and investment timing from the

PVB Investment value

Armed with the above insights, in this section we model PVB investment value. The household’s net operating costs per unit of time t0 are given by: C(pt,a)=pt[ns(a)]+pt[dξ(a)]=pt[1ηa+(η1)ξ(a)] where the first term on the r.h.s. of (8) represents costs paid by the household to purchase energy from the national grid during nighttime, whereas the second term is the cost of grid-purchased energy during daytime. Net operating costs C(pt,a) are decreasing in a. That is, self-consumption and

Optimization

As above mentioned, self-consumption increases for increasing PV size at a decreasing rate, until it ceases to increase when day-demand is completely satisfied (Widén, 2014, Quoilin et al., 2016, Merei et al., 2016, Tervo et al., 2018). Although to our knowledge, there are no empirical estimates of the self-consumption function as a function of PV-produced energy, based on the above literature findings, we adopt and calibrate a concave logarithmic function, to determine daytime

Calibration

We consider a household connected to a national grid under a variable rate energy contract,6 whose

Main results and comparative statics

In this section, main results and comparative statics are presented and discussed. We performed comparative statics with respect to LCOE, LCOS, α, and σ. It is worth noting that T affects investment deferral. Nonetheless, as its effect is negligible, results for different PVB lifetimes are not reported. We report results exclusively for T = 25 years.

Table 7.1 shows model results obtained by implementing the original parameters reported in Table 6.1, i.e., r=4%,6%, p0=54 €/MWh, and different

Conclusions

In this paper, we modeled a household decision to invest in a PVB. The adoption of a PVB permits households to: (a) satisfy daytime energy demand through PV production; and (b) store excess PV power generation to satisfy nighttime energy demand. The novelty of our paper resides in that, differently from other contributions in literature, which implement optimization models to determine the optimal battery size and operation strategy in an NPV-based perspective, we determine the optimal PVB size

CRediT authorship contribution statement

Francesca Andreolli: Methodology, Formal analysis, Validation, Writing – original draft. Chiara D’Alpaos: Conceptualization, Methodology, Formal analysis, Validation, Writing – original draft, Writing – review & editing. Michele Moretto: Conceptualization, Methodology, Formal analysis, Validation, Writing – original draft, Writing – review & editing.

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