A Compound Real Option Approach for Determining the Optimal Investment Path for RPV-Storage Systems.

• Author: Hassi, Benjamin
• Position: Residual pressure valves

1. INTRODUCTION

   Several countries are promoting renewable energy sources and discouraging fossil-fuel-based energy generation. On the one hand, these initiatives have resulted in a large integration of non-dispatchable energy sources, such as solar power, which, in turn, is demanding more flexibility in order to balance power supply and demand. On the other hand, the adoption of energy storage systems has expanded rapidly in recent years, mainly due to the observed decrease in the cost of batteries. In this context, the implementation of systems combining solar photovoltaic (PV) modules and batteries has significantly increased at the residential level. For example, across California, the rate of storage attachment to new solar installations has increased from less than 10% in 2017 to up to 25% in 2018(Sunrun, 2018).

   An increase in the residential PV-Storage (RPV-Storage) systems' penetration rate should translate into social and environmental benefits for the entire society. In addition, the use of RPV-Storage systems may produce large economic and operational benefits to the owner (Cucchiella et al., 2017; Hesse et al., 2017; Shaw-Williams et al., 2018; Tervo et al., 2018; Truong et

   al., 2016). Furthermore, the implementation of RPV-Storage systems can also bring other types of benefits for the household, such as moral ("warm glow") and psychological ("status effect") benefits from using renewable energy (Mollendorff &Welsch, 2017; Mamkhezri et al., 2020). However, the willingness of households to privately invest in an RPV-Storage system depends mainly on its economic valuation. Roughly speaking, for households to be willing to invest, the savings in electricity bill costs plus the potential benefits from selling energy to the grid should be larger than the capital investment costs of the RPV-Storage system. Unfortunately, the current methodologies to determine the optimal investment path for RPV-Storage systems do not consider some important real-world flexibilities that these projects offer.

   A large body of studies on the economic valuation of RPV-Storage systems have been performed (Barbour & Gonzalez, 2018; Cucchiella et al., 2017; Flatley et al., 2016; Hoppmann et al., 2014; Ramteen Sioshansi, 2010; Shaw-Williams et al., 2018; Tervo et al., 2018; Truong et al., 2016; Uddin et al., 2017). However, to the best of our knowledge, none of these studies have jointly considered the flexibility of postponing the initial investment and the option to invest in a compounded way; for instance, considering the option to first invest in PV modules and then to add batteries.

   This paper proposes a new approach for approximating the value of compound real options in the context of multi-stage projects. Based on the Least Squares Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz (2001) to valuate American options, this paper proposes a new method to valuate both the flexibility of delaying the investments and the option of expanding the capacity of both PV modules and batteries during the evaluation horizon in a compounded way, considering the household can invest multiple times.

   The price of electricity, the cost of PV modules, and the cost of batteries are modeled as three independent Geometric Brownian Motions. The household can invest in different PV module and battery capacities over a period of time and then add more PV modules and/or batteries later. Accordingly, the proposed model allows us to identify the effect of having the option to invest in a compounded manner during the investment decision process, to determine the benefit-cost thresholds for different combinations of PV modules and batteries, and to evaluate the impact of feed-in tariffs (FIT) and other economic incentives on the residential customers' investment decisions.

   To show the applicability of the methodology, we implemented the model to analyze the economic viability and the optimal investment path of an RPV-Storage system in Chile. We consider that the house owner has five different investment possibilities as the result of some combinations of two levels of power capacity from PV modules (named [P.sub.min] and [P.sub.mam] as detailed later) and two levels of storage capacity from batteries (named [B.sub.min] and [B.sub.max] as detailed later). The household has the option to invest directly in multiple RPV-Storage combinations (i.e., only [P.sub.min] only [P.sub.max], [P.sub.min] + [B.sub.mim] [P.sub.mas] + [B.sub.min] and [P.sub.max] + [B.sub.mm]) and remain in that state for the rest of the evaluation horizon, or she/he can make multiple investments, upscaling to states with higher solar power production or larger battery capacity (e.g., investing [P.sub.max] first and then moving to [P.sub.max] + [B.sub.min] in a later period).

   The results in our case study show that the household should invest in an RPV-Storage system in 60% of possible future scenarios. Additionally, our results suggest that, on average, in 36% of future scenarios it is optimal to invest in two steps or more, taking advantage of the option to postpone part of the investment until more favorable future scenarios occur. And even more importantly, the analysis of the value of the compound flexibility shown in this work suggests that investors should use the proposed Compound Least Squares Monte Carlo (CLSM) method in the economic valuation of multi-stage projects, especially if they are exposed to large uncertainties, since considering only the single flexibility to postpone an investment could promote sub-optimal decisions.

   Sensitivity analyses illustrate how more favorable future scenarios encourage the household to invest in states with higher capacity PV modules and batteries and confirm that the large level of uncertainty involved in RPV-Storage systems increases the value of a flexible project.

   The rest of the paper is outlined as follow. Section 2 contains a review of the literature. Section 3 explains the valuation framework and the proposed valuation model. Section 4 presents a case study and the numerical results. Section 5 shows some sensitivity analyses. Section 6 concludes the paper.

2. LITERATURE REVIEW

   In this section, we present a literature review of three important topics related to this research work.

   2.1 Economic Valuation of RPV-Storage Systems

   Previous research on the economic valuation of RPV-Storage systems is not yet decisive in the profitability and social/private welfare generated by these systems. Hoppmann et al. (2014) reviewed several studies about the economic viability of RPV-Storage systems. Their results suggest that: (i) investments in small residential PV systems are already profitable under certain conditions (e.g., high electricity prices), (ii) policies promoting investments in batteries will not be necessary in the long run, (iii) RPV-Storage systems are likely to promote the ongoing trend toward distributed electricity generation, and (iv) more investment in technical infrastructure will be required to support this trend.

   More recently, studies are still discrepant on the benefits of the implementation of RPV-Storage systems, mainly due to the uncertainty about the cost evolution of batteries. On the one hand, some authors confirm that batteries are unprofitable to install with current tariffs for most consumers (Uddin et al., 2017) and that widespread battery adoption will not occur unless retail electricity prices rise, in addition to other conditions such as an increase in the reward for exported electricity (Barbour & Gonzalez, 2018).

   Additionally, other works indicate that pairing lithium-ion battery storage systems with residential PV modules is profitable under current conditions in the United States (Tervo et al., 2018), Germany (Hesse et al., 2017; Truong et al., 2016), Italy (Cucchiella et al., 2017), and Australia (Shaw-Williams et al., 2018). However, subsidies, FIT, self-consumption, considerations of battery degradation and costs, and the control of the ratio between PV module and battery capacities are some of the current conditions existing in these countries that are crucial for profitability to be achieved.

   In sum, previous research is not conclusive regarding the optimal investment timing and capacity of RPV-Storage systems mainly due to the variability of contextual factors. However, in recent years, the tendency in the related literature is the consideration of RPV-Storage systems as a feasible option for households to reduce electricity bill cost and the analysis of the evolution of the cost of batteries as one of the key factors influencing investment decisions.

   2.2 Real Options Analysis to Add Flexibility to RPV-Storage Projects

   The valuation of RPV-Storage systems is complex and plenty of uncertainties. However, most of the related studies do not incorporate flexibility in the economic valuation of projects, and only compute the net present value (NPV) of the rigid projected cash flows generated by a certain combination of PV module and storage devices. This rigid valuation of discounted cash flows (DCF) assumes that the investor takes a passive attitude once the initial investment is executed. However, in these types of projects, the household has usually the flexibility to react to uncertain scenarios that differ from what was originally expected. This flexibility can be incorporated into the valuation by using the real options analysis (ROA).

   ROA has been used widely on studies related to renewable energy investments. (1) However, only a few papers apply ROA to evaluate investment decisions in RPV-Storage systems (Gahrooei et al., 2016; Martinez-Cesena et al., 2013; Moon & Baran, 2018). Additionally, to the best of our knowledge, none of these studies have jointly considered the flexibility of postponing the initial investment and the option to invest in a compounded way as we do in this paper.

   2.3 Real Option Valuation and Least Squares Monte Carlo Algorithm

   Real options are...