Solar plus_ Optimization of distributed solar PV

Applied Energy 213 (2018) 11–21

Contents lists available at ScienceDirect

Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Solar plus: Optimization of distributed solar PV through battery storage and dispatchable load in residential buildings

T

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Eric O'Shaughnessya,b, , Dylan Cutlera, Kristen Ardania, Robert Margolisa a b

National Renewable Energy Laboratory, United States University of Wisconsin-Madison, Nelson Institute for Environmental Studies, United States

H I G H L I G H T S of residential PV optimization with battery storage and load control. • Analysis analysis of PV optimization in a variety of rate environments. • Economic show that load control in particular improves the economics of PV. • Findings • Storage and load control improve PV value in challenging rate contexts.

A R T I C L E I N F O

A B S T R A C T

Keywords: Solar Storage Load control Optimization Residential buildings

As utility electricity rates evolve, pairing solar photovoltaic (PV) systems with battery storage has potential to ensure the value proposition of residential solar by mitigating economic uncertainty. In addition to batteries, load control technologies can reshape customer load profiles to optimize PV system use. The combination of PV, energy storage, and load control provides an integrated approach to PV deployment, which we call “solar plus”. The U.S. National Renewable Energy Laboratory’s Renewable Energy Optimization (REopt) model is utilized to evaluate cost-optimal technology selection, sizing, and dispatch in residential buildings under a variety of rate structures and locations. The REopt model is extended to include a controllable or “smart” domestic hot water heater model and smart air conditioner model. We find that the solar plus approach improves end user economics across a variety of rate structures – especially those that are challenging for PV – including lower grid export rates, non-coincident time-of-use structures, and demand charges.

1. Introduction

proposed and implemented residential rate reforms such as time-of-use (TOU) rates and customer demand charges pose further challenges to future residential PV deployment [7]. Solar plus storage has emerged as an alternative to grid export in evolving rate environments [7,9–12]. Energy storage solves the temporal mismatch by storing excess PV output in a battery for later consumption. A growing body of literature and new PV product bundles indicate that in addition to batteries, load control technologies can reshape customer load profiles to optimize PV system use [13–19]. We use a time series optimization model formulated as a mixed integer linear program to explore the economics of solar plus storage and load control under different rate structures. The combination of PV, energy storage, and load control provides an integrated approach to PV deployment, which we call “solar plus”.1

The temporal mismatch between solar photovoltaic (PV) system output and residential electricity demand is one of the primary challenges to wide-scale residential PV deployment [1–4]. PV output often exceeds residential electric loads during the day but falls short of demand in the late afternoon and evening when residential load tends to increase. Grid export – where excess PV output is sold to the electric grid – has provided an economic solution to this temporal mismatch. Through grid export policies such as net metering (U.S.) and feed-in tariffs (Europe, Australia, Asia), customers earn returns from full PV system output regardless of whether that output is used on site [5,6]. However, grid export rates are declining in many major PV markets around the world [7,8]. Lower grid export rates incentivize customers to reduce excess output and maximize on-site PV self-use. Other

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1

Corresponding author at: National Renewable Energy Laboratory D.C. Office, 901 D Street NW Suite 930, Washington, DC 20024, United States. E-mail address: [email protected] (E. O'Shaughnessy). This paper builds on an analysis previously presented in a National Renewable Energy Laboratory working paper: “Solar Plus: A Holistic Approach to Distributed Solar PV.”

https://doi.org/10.1016/j.apenergy.2017.12.118 Received 24 October 2017; Received in revised form 12 December 2017; Accepted 30 December 2017 0306-2619/ © 2018 Elsevier Ltd. All rights reserved.


E. O'Shaughnessy et al.

Fig. 1. Customer load shifting through solar plus. Grid net load is the total customer load at the utility meter; negative grid net load reflects excess PV output exported to the grid.

2. Solar plus

some target temperature (Fig. 4, top). Programmable units can precool the home with PV output and allow temperatures to drift up toward a maximum temperature without re-cooling with grid electricity (Fig. 4, bottom). Electric vehicles (EVs) can potentially enhance the value of solar plus systems [20]. A typical EV has around 30 kWh of electrical storage capacity [21], far greater than the capacity of current residential battery offerings and the thermal capacity of smart domestic water heaters and AC units. EV owners could use this storage capacity to increase PV self-use by charging vehicles during peak PV output hours. In this sense, PV optimization is an ancillary benefit of EV ownership. EV ownership remains relatively uncommon. It is unclear whether PV owners would be willing to invest in EVs for the purposes of PV optimization. Further, to the extent that PV optimization is part of the value proposition of EV ownership, it is unclear how to apportion EV cost premiums between the added benefits of EV ownership (e.g., lower fuel costs) and the solar plus capabilities. To avoid speculating about the willingness of PV owners to invest in EVs, we exclude EVs from our analysis. EV integration into solar plus systems is a proposed area of future research. A growing body of research explores solar plus in a variety of configurations and contexts. The majority of this literature analyzes the technical capacity of solar plus to increase PV self-use, with limited economic analysis based on simplifying assumptions about the value of PV self-use [13–17,22,23]. In a review of this research, Luthander et al. [18] find that batteries (including EV batteries) generally increase PV

In solar plus systems, load control technologies shift electric load to coincide with PV output (Fig. 1) [16–18]. For instance, PV customers can manually shift load by using deferrable devices, like laundry machines, during the midday solar peak rather than in the evening. Solar plus automates this process by calibrating home devices to maximize their use of PV rather than grid electricity. Any remaining excess PV output may be delivered to a battery and then to the grid as a last resort. Solar plus can improve overall end-user economics by increasing PV self-use, reducing grid exports, performing grid arbitrage (where customers pay TOU rates), reducing demand charge payments (where applicable), and reducing customer electricity payments. A variety of home appliances can be included in a solar plus system such as domestic water heaters, air conditioning (AC) units, heat pumps, and washing machines. This study focuses on programmable or “smart” domestic water heaters and AC units (Fig. 2), given that load control through thermal storage has been shown to have greater impacts than other controllable home appliances [17,19]. Conventional electric domestic water heaters maintain a set tank temperature by heating water instantaneously following hot water draws (Fig. 3, top). Programmable domestic water heaters can preheat water with PV output then allow the tank temperature to drift down to a minimum temperature without reheating with grid electricity (Fig. 3, bottom). Conventional AC units maintain internal home temperatures around

Fig. 2. The solar plus home.

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Fig. 3. Conventional domestic water heating (top) vs. smart domestic water heating with preheating and drift functions (bottom).

first to apply the U.S. National Renewable Energy Laboratory’s (NREL) Renewable Energy Optimization Tool (REopt). Other tools have been developed to study load control and storage for PV optimization, such as the Lawrence Berkeley Laboratory’s Distributed Energy Resources Customer Adoption Model [29], TRNSYS 17 [15], and GEDELOS-PV [14,16]. Several studies develop their own optimization models for the purposes of specific solar plus-related studies [13,19,22,24,25,27]. These modeling approaches broadly fall into two categories. The first approach focuses on detailed modeling of the solar plus technologies and their optimal and coordinated dispatch. The dispatch problem is typically addressed via heuristic/algorithmic methods [14,15] or dynamic programming [13,19] and may incorporate forecasting into short-term dispatch algorithms [16]. These approaches can accommodate complex technology models, yet generally do not consider system sizing in conjunction with the dispatch. The second approach considers system size optimization in conjunction with optimal dispatch [24,29]. Our extension of the REopt model for this analysis incorporates and improves upon many of the capabilities from these extant models by integrating detailed models of building systems directly within the mixed integer linear program. Further, we use the REopt model’s ability to size systems while considering complex rate tariff designs to perform concurrent selection, sizing, and dispatch of technologies while considering the complex tariff environment that these technologies operate within.

self-use by 13–24 percentage points, while load control strategies increase self-use by 2–15 percentage points. However, at current battery costs, some studies argue that load control options optimize PV use more cost effectively than batteries [14,15,24,25]. More recently, several studies have focused on the economic impacts of solar plus, generally finding that solar plus technologies – especially load control – provide end-user economic benefits [19,24–28]. The extant literature provides a limited understanding of the effects of customer electricity rate structure on the economics of solar plus. Most studies assume flat electricity rates or simple TOU rates with simplifying assumptions about the value of PV exported to the grid [16,25,28]. However the customer’s rate structure is a key variable impinging on both the value of PV and the optimal selection of solar plus technologies [24]. Our study fills this research gap by exploring the economics of solar plus under rate structures that vary along three dimensions: the compensation rate for excess PV output delivered to the grid, the timing of peak- and off-peak rates in TOU structures, and the amount of any levied demand charge. These three rate structures were identified as characteristics of evolving rate environments that are particularly challenging for the value proposition of stand-alone residential PV systems. By analyzing solar plus in these rate structures we can study how the economics of solar plus change in evolving rate environments and how solar plus may or may not address rate structure challenges to the PV value proposition. Our study offers a further contribution to the literature by being the 13



Fig. 4. Conventional AC cooling (top) vs. smart AC with precooling and drift functions (bottom).

Fig. 5. Relationship between BEopt and REopt models in the analysis. Customer loads are generated in BEopt and used as inputs in REopt.

3. Methods

energy for a single entity by optimally selecting, sizing, and dispatching from a set of available technologies. For the purposes of our study, REopt minimizes life cycle energy costs for a residential household by deploying an optimal configuration of PV, battery storage, smart domestic water heater, and smart AC unit. The model was run with hourly

REopt is a techno-economic time-series model that provides multiple technology integration and optimization capabilities [30]. The objective function of the model is to minimize the life cycle cost of

14



grid arbitrage.

timesteps for a full year to enable the life-cycle cost optimization. Preexisting REopt PV and battery storage modeling capabilities were used in this analysis [30], however new models for smart domestic water heating and AC were developed for this study. REopt estimates local PV production based on inputs from PVWatts®, an NREL tool that estimates the energy production of gridconnected PV systems based on local insolation. REopt’s energy storage model is a “reservoir” based model that allows energy to be moved from one timestep to the next, while accounting for inverter, rectifier, and round-trip efficiency losses. The energy capacity and the inverter capacity are sized independently in the model, and minimum and maximum states of charge are observed in the model. For further discussion of the larger REopt model formulation, see [30]. The annual energy simulation software Building Energy Optimization (BEopt) is used to establish modeled electrical/thermal/ hot water loads. The modeled loads are fed into the REopt model which then selects, sizes (in the case of PV and battery storage), and dispatches the technologies to meet the calculated loads (Fig. 5). BEopt is a residential building modeling tool that utilizes the physics based simulation engine EnergyPlus to model all energy flows and interactions with environmental conditions for residential buildings. EnergyPlus provides high fidelity building system modeling and enables rapid recalculation of the residential loads in different locations. EnergyPlus has been validated against American Society of Heating Refrigerating and Air-conditioning Engineers (ASHRAE) and American National Standards Institute (ANSI) standards and research projects. It has incorporated tests outlined in the Building Energy Simulation Test (BESTest) that have not entered into ANSI/ASHRAE Standard 140. BEopt builds upon this modeling foundation and provides residential modeling assumptions as defined in the Building America House Simulation Protocols [31]. BEopt was run at 10-min timesteps for a full year, and consistency was maintained between the typical meteorological year (TMY) files used for load modeling and TMY solar resource data used for REopt PV modeling. The following sections describe the load modeling in further detail and describe the modeling approaches for the smart domestic hot water heater and the smart AC unit. Throughout this section, let h denote a single timestep. The condition “for all timesteps” (∀ h ) is applied to certain equations to specify that the constraint must be met in every timestep.

3.2. Air conditioner model Two components are added to REopt to model the smart AC unit: a simplified AC model and an energy storage component. The simplified AC model is based on the direct expansion model in EnergyPlus, which uses performance curves to capture capacity and efficiency impacts of operation at off-rated conditions. The impacts of varying outdoor drybulb (subscript odb) temperature and entering wetbulb (subscript ewb) temperature are captured by the bi-quadratic curve shown in Eq. (1), where y is a scaling factor on the rated performance of the system, T denotes temperature, and constants a through f are based on manufacturer performance data. Two of these curves are implemented in the model—one for capacity impacts and one for efficiency impacts—enabling accurate calculation of capacity and power consumption at every timestep in the model. Curve coefficients are taken from [33]. Rated system capacity and efficiency were taken from BEopt. The available system capacity and associated efficiency are pre-processed according to the TMY file assuming the indoor setpoint is maintained. These are subsequently passed to the optimization model, thus capturing the impact of ambient conditions on AC performance. 2 2 y = a + bTewb + cTewb + dTodb + eTodb + fTewb Todb

(1)

The remaining performance curves from the full EnergyPlus model (flow fraction and part load fraction) are not implemented for this analysis. An additional constraint is added to REopt to ensure that the cooling load is met in all timesteps: q

Xtĥ fthp + Xhc ̂ = δ c q Xtĥ

∀h

(2)

is the decision variable for rated production of a given where technology t in timestep h, fthp is the production factor in each timestep for technology t (scaling the rated capacity of the AC unit, based on Eq. (1)), Xhc ̂ is the energy delivered from the energy storage capacity of the house, and δ c is the cooling load determined by BEopt. The presence of the AC unit in the model enables REopt to optimally dispatch the unit to meet the cooling load, yet without an energy storage element there would be zero degrees of freedom in the constraint shown in (2), and the AC unit would be dispatched to meet the load in all timesteps. In order to capture the flexibility of a smart AC unit, we incorporated an energy storage model to allow the smart AC unit to store energy through a 19 °C to 23 °C drift (see Fig. 4). The energy storage model is modeled as a “reservoir” type model where energy can be stored during one timestep and removed during subsequent timesteps. Losses for the energy storage are handled by forcing the model to maintain setpoint, such that the state of charge (SOC) of the energy storage unit is maintained. Due to the cooling load being calculated at a constant 21 °C, there may be some additional losses when the energy storage is at full SOC (e.g. 19 °C), and reduced losses when the SOC is at minimum (e.g. 23 °C), but these were not accounted for in the model. Due to the capacity and efficiency adjustments from (1) being calculated considering a fixed indoor setpoint of 21 °C (e.g., no feedback loop from thermal storage SOC to the AC performance), there may be additional AC performance impacts that are not fully captured when SOC is high or low. This simplification retains a mixed integer linear program formulation, while still capturing the impact of air temperature on AC performance. We used a resistance–capacitance (R-C) model [34] to quantify the energy required to lower the house temperature from 23 °C down to 19 °C and to estimate the drift duration from 19 °C up to 23 °C. To isolate the home’s inherent thermal storage capacity, we calculated the energy required to move from 23 °C to 19 °C when the outdoor air temperature is at 21 °C. This removes most external loads on the system, as the outdoor temperature is already within the deadband of the thermostat. Some ambient temperature impacts remain when the

3.1. Load modeling We model a representative household based on median values for all single-family detached homes in the U.S. as documented in the Energy Information Administration’s Residential Energy Consumption Survey database. This results in a three bedroom, two bath, 199 m2 home. The modeled house conforms to the Building America Benchmark design as defined in [31]. This is generally consistent with the International Energy Conservation Code from 2009, the most widely used energy code for new construction in the United States. Accordingly, the home has R13 walls and R-30 roof (both nominal), 0.37 U-value windows, and a SEER 13 AC system. The house was modeled with an electric water heater (0.9 energy factor). While there are certainly cost-effective energy efficiency measures available to such a homeowner, the current analysis focused on controllability of loads in association with PV. There is a large body of literature dealing with the more “static” efficiency analysis that could benefit such a residence. Climatic conditions are represented by a TMY file for the selected location. The home’s energy demands – as calculated by BEopt – are disaggregated into cooling load, domestic hot water load, and all other electrical load. Hot water draw profiles in BEopt are based on the domestic hot water event schedule generator [32]. The disaggregation of AC and hot water loads allows REopt to dispatch the smart AC or water heater to meet thermal loads while also shifting the electrical demand to different periods within the day to increase PV self-use or perform 15


E. O'Shaughnessy et al. ˇ

system is at high/low SOC, yet these impacts are in opposite directions and are expected in large part to offset each other. The energy required to cross that deadband is calculated at 14.3 kWh-thermal, and defines the capacity of the energy storage system. The max rate of charge is set by the capacity of the AC unit. The max rate of discharge is determined by outdoor conditions, therefore we use the R-C model to estimate the time to cross the deadband at 37 °C as an upper thermal threshold. This time is 2.38 h or 5.97 kW-thermal (converted into power units given the 14.3 kWh-thermal of stored energy). These values are inserted into Eqs. (3) and (4) to control the charge and discharge of the energy storage system, where Xhcˇ and Xhc ̂ are decision variables for charge and discharge of the energy storage system and bcˇ and b c ̂ are the max charge (13.8 kW-thermal) and discharge (5.97 kW-thermal) parameters:

Xhc ̂ ⩽ b c ̂

∀h

(3)

Xhcˇ ⩽ bcˇ

∀h

(4)

tdhw (1−Z d ) ⩽ Xhd

where tdhw is the exact charging profile as dictated by the BEopt simulation, Z d is the binary that determines whether the smart domestic ˇ hot water heater is deployed, and Xhd is the decision variable determining charging of the domestic water heater system. Therefore if the model wants to avoid charging exactly to meet the load (i.e., shift electrical load incurred to meet the hot water demand), then Z d must resolve to 1, such that the capital cost of the smart water heater is included in the objective function. It can be noted that this constraint would not restrict a water heater from overcharging in the presence of an incentive to consume excess energy (e.g., negative electricity pricing). This type of pricing was not present in our analysis and therefore did not affect model performance. 3.4. Financial assumptions

The cost of installing the smart AC unit is included in the objective function by multiplying the cost of the improved controls by a binary variable (Z c ) that determines if the smart controls are installed. Any increase/decrease in operational costs for the adjusted AC operation (e.g., pre-cooling and drift) are captured in the energy required to operate the unit, calculated according to the AC model outlined herein. The determination of the binary costing variable is shown in Eq. (5), where W c is the decision variable determining the energy capacity of the energy storage and w c is the maximum capacity of the system (14.3 kWh-thermal in this analysis):

W cZ c ⩽ w c

System net present values (NPV) are calculated relative to the customer’s electricity costs without any PV system. System NPV represents the full discounted lifetime value of all electricity cost savings accrued from the standalone solar or solar plus system less the customer’s investment costs in PV and solar plus technologies. A discount rate of 6.2% is assumed [36], and electricity costs are escalated based on National Institute of Standards and Technology utility cost escalators [37]. The value of solar plus is determined by the difference in NPV between the standalone and solar plus scenarios, as estimated by REopt. The NPV incorporates the capital cost of all system components, the present value of operation and maintenance costs ($20/kW/year for PV system) [38], and present value of grid purchases. Of the three candidate solar plus technologies, batteries are the most versatile but also the most costly option. Modeled battery installed costs are $1060/kWh for the battery pack and $1271/kW-alternating current for the balance of system based on benchmarked costs from [39]. The smart domestic water heater upgrade is assumed to cost $250, and the smart AC unit upgrade is assumed to cost $200 [40]. These assumed costs affect REopt’s selection of batteries versus load control technologies in our analysis. These financial assumptions are based on the best available estimates of current technology costs. Battery costs, in particular, are projected to decline over time [41,42]. The implications of falling battery costs are discussed in further depth in Section 5. We use REopt to analyze the economics of solar plus under three rate structures that are less favorable to stand-alone PV: lower grid export rates, non-coincident TOU peak rate periods, and demand charges. In each analysis, we allow a single rate parameter to vary while holding all other factors constant. This approach allows us to isolate the effects of different parameters on the economics of solar plus, as determined by the differential value between the standalone and solar plus approaches. All analyses use a customer load profile based on a home in Las Vegas, NV U.S.A unless otherwise noted (see Section 4.1). Our rate assumptions reflect realistic ranges of parameters based on representative U.S. rate structures.

(5)

3.3. Domestic water heater model The water heater is modeled in REopt as an energy storage system. Similar to the energy storage system described above, the total capacity, maximum charge, and maximum discharge parameters were defined for this model. It is assumed that the water heater has an 189L tank and a 4.5 kW element. A tank temperature range of 49–82 °C is assumed. The installed cost of the smart water heater includes a mixing valve to avoid scalding and controls to enable water temperature control. The tank size and temperature range result in a total capacity of 7.32 kWh. The maximum charge is limited to the heating element in the tank (4.5 kW) and the maximum discharge is assumed to be unlimited (e.g., able to drain the whole energy storage system within a single timestep) to account for large hot water draws such as a bath or multiple showers. Eqs. (3) and (4) must hold for the water heater for these input parameters. Additionally, a losses parameter is added to capture tank jacket losses. Eq. (6) incorporates that parameter to enforce that energy diŝ charged from the system ( Xhd ) plus tank losses in every timestep ( Xhd ) are always less than the stored energy in the previous timestep ( Xhd− 1). ̂

Xhd + f d Xhd ⩽ Xhd− 1

∀h

(7)

(6)

f d,

4. Results

was calculated assuming a heat loss The losses parameter, coefficient for the tank of 0.916 W/m2-C [35] and an indoor temperature of 21 °C. This parameter ranges from 1.44%/hr at 82 °C to 2.76%/ hr at 49 °C (note that the higher percentage per hour value at lower temperatures is due to the low stored energy at the lower temperature). Given the mixed integer linear formulation of the problem, a fixed value of 2%/hr is assumed for this analysis. The smart hot water heater is included in the objective function by multiplying the cost of the improved controls by a binary variable (Z d ) that determines if the smart water heater is deployed. The smart water heater enables the model to choose when to charge the storage (and provide more capacity) versus the standard water heater that must charge exactly to meet the load. This is reflected in the constraint shown in Eq. (7):

Most major PV markets have proposed or implemented reductions to grid export compensation rates. Lower grid export rates reduce the value of residential PV systems and incentivize customers to increase PV self-use. In the United States, grid export is compensated through net metering, where customers receive utility bill credits for each kWh of excess PV output delivered to the grid. Fig. 6 illustrates how the economics of solar plus compare with the economics of standalone solar at different net metering rates. REopt deploys the smart domestic water heater and smart AC unit at every net metering rate under the solar plus approach, but does not deploy a battery at any net metering rate. The solar plus approach reduces grid exports and increases PV self-use relative to standalone solar at all net metering rates. The incentive to 16



Fig. 6. Solar plus economics under different net metering rates. Figure assumes a flat volumetric electricity rate of $0.22/kWh.

systems are ineffective at reducing on-peak electricity use for late afternoon peak periods. Solar plus systems allow customers to shift onpeak load to coincide with PV output, thus reducing on-peak grid electricity use even with non-coincident peak periods. For this reason, the incremental value of solar plus is generally higher for customers with non-coincident peak periods. In this case, solar plus system NPV is about 28% greater than standalone solar system NPV for a 9 a.m.–2 p.m. peak period, but nearly six times greater for a 5 p.m.–10 p.m. peak period. This result indicates that solar plus mitigates some of the negative impacts of non-coincident TOU peak rate periods on residential PV economics. Demand charges are a final class of residential rate reforms that can undermine the economics of residential PV. In a demand charge rate structure, customers pay a fee based on their peak power (kW) usage over some defined time period. Demand charge customers generally pay lower volumetric ($/kWh) rates. PV systems are relatively ineffective at reducing customer demand charges when peak power use does not coincide with peak PV output. At the same time, the value of PV self-use is diminished due to low volumetric rates. As a result, demand charge rate structures can significantly reduce the value of residential PV systems. Fig. 8 compares system values under both approaches at different demand charges. REopt does not deploy a standalone solar PV system under any demand charge scenario, illustrating the potentially significant implications of demand charges for

increase PV self-use is greater at lower net metering rates. As a result, the incremental value of solar plus is higher at lower net metering rates. In this case, solar plus system NPV is about 3% greater than standalone solar NPV at a net metering rate of $0.22/kWh but about 53% greater at a net metering rate of $0.02/kWh. This result indicates that solar plus mitigates the impacts of lower grid export rates on residential PV economics. In TOU rate structures, customers pay higher volumetric ($/kWh) rates during peak periods and lower rates during off-peak periods. Residential peak load typically occurs in the late afternoon when customers return home from work and engage in domestic evening activities. Residential TOU rate structures are often designed to reduce peak residential electricity use by applying peak rates in the late afternoon. This type of TOU rate structure reduces the value of standalone PV systems, as PV output mostly coincides with lower-value off-peak electricity rates. Fig. 7 compares the economics of solar plus to standalone solar for different TOU periods. Here we analyze a range of 5-h peak periods, with each period starting at a different time on the hour from 9 a.m. to 5 p.m. For instance, the point at 9 a.m. corresponds to a peak period of 9 a.m.–2 p.m. REopt deploys the smart domestic water heater and smart AC unit at all time periods, but does not deploy a battery under any scenario. System values under both approaches are highest when the TOU peak period coincides with midday PV output. System values decline for later peak periods, as standalone solar

Fig. 7. Solar plus economics under different peak and off-peak periods. Figure assumes off-peak rate is $0.08/kWh, peak rate is $0.22/kWh, and net metering rate is $0.03/kWh.

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Fig. 8. Solar plus economics under different demand charges ($/kW). Figure assumes flat volumetric rate of $0.06/kWh, and net metering rate of $0.03/kWh.

residential PV deployment. REopt deploys a PV system paired with a battery at demand charges greater than $16/kW, and deploys the smart domestic water heater and smart AC unit at every demand charge. The solar plus approach uses load shifting to more effectively reduce customer demand charges than the standalone solar approach. Therefore the incremental value of the solar plus approach increases as customer demand charges increase. To summarize, the REopt analysis shows that the solar plus approach mitigates the negative economic impacts of three types of rate reforms on residential PV. First, solar plus increases system value for customers with low grid export rates by increasing PV self-use. Second, solar plus increases system value for customers with non-coincident TOU peak periods through load shifting. Third, solar plus increases system value for customers with demand charges by using load shifting and batteries to more effectively shave customer peak demand.

Table 1 REopt results: Hawaii self-supply rate case study.

PV system size (kW) Battery size (kWh/kW) Smart water heater Smart AC PV generation (kWh/yr.) Electricity savings ($/yr.) System cost ($) NPV

Standalone solar

Solar plus

4.6 – – – 6247 $957 $5933 $5684

8.0 7.8/1.3 Deployed Deployed 11,663 $2690 $16,598 $16,851

use, particularly during the peak period, relative to the standalone solar approach. Reduced grid electricity use and TOU period arbitrage generate additional customer savings under the solar plus approach: solar plus increases system NPV by about a factor of three relative to standalone solar. Fig. 10 provides a closer view of a single day (Thursday) from the full week dispatch shown in Fig. 9. The standalone solar case shows PV output covering midday load, however additional potential output is curtailed due to the prohibition on grid exports in the self-supply rate scenario. The solar plus case clearly demonstrates a shift of late afternoon AC load back into peak PV output hours, as well as the elimination of sporadic domestic hot water draws into a consolidated midday water heater operation. The remaining excess PV is then placed into the battery, which is discharged during peak pricing (battery discharge not shown, only demand presented for clarity) to reduce the remaining AC and miscellaneous loads to zero as the PV output tails off in the late afternoon/evening. While the impact of climate on the optimal selection, sizing, and dispatch of solar plus technologies was not central to this analysis (focus was on tariff impacts), the modeling approach enables efficient analysis of other locations/climates. Re-location is achieved by running the BEopt model with the TMY file for the desired location, passing those modified loads to REopt, and updating the solar resource in REopt for the new location. This approach was utilized to enable analysis of emerging rates in three additional case studies, located in Arizona, California, and Nevada (see Table 2). In addition to these case studies, the inputs for the Hawaii scenario were run in the colder climate of Albany, NY. Consistent with results from [24], we find the reduced customer load (lower AC demand) in the cold climate reduces optimal PV and battery system size but does not otherwise change the outcome. In other words, the rate structure in the self-supply rate scenario provides substantial incentives for investments in solar plus technologies,

4.1. Solar plus case studies We further explore the potential benefits of the solar plus approach in four real world applications. We concentrate on a case study of Hawaii, where a recent rate structure reform exemplifies the evolving PV rate environment in the United States and internationally. In late 2015, the Hawaiian Public Utilities Commission (PUC) effectively ended net metering in Hawaii. The new self-supply rate prohibits PV customers from exporting excess PV output to the grid. Following the reform, SolarCity (the largest U.S. residential PV installer) began offering a bundled PV package in Hawaii that includes PV, battery storage, a smart electric water heater, and a smart thermostat. The Hawaiian solar plus market may gain additional support from proposed state incentives [43]. Further, in late 2016, the PUC approved an optional TOU rate with an evening (5 p.m.–10 p.m.) peak period. The TOU rate is lowest during the midday (9 a.m.–5 p.m.) to encourage electricity customers to use more electricity during peak PV output hours. We used REopt to design an optimized solar plus system for a customer in Honolulu, HI U.S.A. under the self-supply tariff and TOU rate. Table 1 compares the system specifications and economics of the two approaches for the Hawaiian customer. REopt deploys a 4.6-kW PV array for standalone solar and an 8-kW PV array (maximum size based on roof space available) coupled with a 7.8-kWh battery, smart AC unit, and smart domestic water heater for solar plus. Fig. 9 compares customer load profiles in the two approaches. The bottom pane of Fig. 9 depicts clear load shifting from the peak periods under the PV output curve through battery storage, home pre-cooling, and hot water preheating. The solar plus approach significantly reduces grid electricity 18



Fig. 9. Hawaii case study PV and customer load profiles under standalone solar and solar plus scenarios. Pink regions depict peak rate periods, BESS = battery energy storage system. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

plus is higher for customers facing lower grid export rates. The relatively significant value of solar plus in the demand charge scenario is consistent with the results depicted in Fig. 8.

with small changes in optimal system size correlated to specific customer load. Table 2 summarizes the results of three additional U.S. case studies exploring how the solar plus approach can alleviate the economic impacts of certain rate reforms in real world applications. The three additional case studies correspond to three challenging rate environments: lower net metering rates (falling grid export rate), TOU rates (non-coincident “super” peak), and a residential demand charge. Consistent with the other analyses presented in this section, REopt deploys the smart domestic water heater and smart AC unit in all three scenarios but only deploys a battery in the demand charge reduction. The relative impact of solar plus on system NPV is higher in the Hawaii case study than in the low net metering and TOU cases in Table 2. This outcome is consistent with the results depicted in Fig. 6, where the value of solar

5. Discussion and conclusion Evolving rate environments in major PV markets around the world are changing and, in some cases, undermining the economics of residential PV. The reliance of standalone solar PV systems on favorable grid export rates may no longer be a tenable model for future wide-scale residential PV deployment. Solar plus offers an alternative approach to sustain the economic case for residential PV in these evolving rate environments. Using an NREL optimization model we show that solar plus increases customer system value under a variety of rate structures. The Fig. 10. Detail of Hawaii dispatch, showing operation for Thursday of example week, pink region depicts peak rate period. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Table 2 Case study results. Case study

Assumptions

REopt results

Falling grid export rate: In 2015 the Public Utilities Commission of Nevada approved a new rate structure with declining net metering payments, falling volumetric rates, and increasing basic service charges Non-coincident “super” peak: The Arizona “super peak” tariff is designed to incentivize customers to reduce electricity use during peak hours of the summer months

Volumetric rate: $0.106/kWh; service charge: $29.23/ month; net metering: $0.055/kWh. Load profile based on a home in Las Vegas, NV

REopt deploys the smart AC unit and a smart domestic water heater (but no battery) for solar plus. Solar plus increases system NPV by about 80% by increasing PV self-use REopt deploys the smart AC unit and a smart domestic water heater (but no battery) for solar plus. Solar plus increases NPV by about 60% by increasing PV self-use and performing grid arbitrage REopt deploys a smart AC unit, a 0.3-kWh battery, and smart domestic water heater for solar plus. Solar plus increases system NPV by about a factor of 8, primarily through demand charge reduction

Residential demand charge: The Arizona demand tariff includes a monthly demand charge based on the customer’s maximum demand during peak hours (weekdays 12 pm–7 pm)

Peak period: 12 pm-7 pm; off-peak rate: $0.06/kWh; winter (May-Oct) peak rate: $0.20/kWh; summer peak rate: $0.24/kWh; super peak (3pm-6 pm, Jun-Aug): $0.47/kWh; net metering: $0.03/kWh Peak period: 12 pm-7 pm; off-peak rate: $0.04/kWh, winter (May-Oct) peak rate: $0.06/kWh; summer peak rate: $0.09/kWh; winter demand charge: $9.3/kW; summer demand charge: $13.5/kW; net metering: $0.03/kWh

and then deploy them at optimal capacities. We find that load control, rather than battery storage, provides a more cost-effective approach for near term solar plus applications. However, falling battery costs and supportive policies may ensure a growing role for batteries in solar plus systems. Our results suggest that the solar plus and other creative approaches to PV optimization could support the residential PV value proposition in evolving rate environments.

incremental value of solar plus is highest in some of the most challenging PV rate environments, including lower grid export rates, non-coincident TOU peak periods, and demand charge structures. Our optimization model deployed the smart domestic water heater and smart AC unit under all rate structure scenarios and in all case studies. In contrast, the model only deployed batteries in certain contexts with either relatively high demand charges or high retail rates coupled with no grid export compensation (Hawaii case study). These results are consistent with previous studies [14,16,24,25,44], in which lower-cost load-control devices are deployed first and more often than batteries. Lithium-ion batteries remain a relatively costly technology. Our analysis assumes battery costs of $1060/kWh, equating to over $3000 for 3 kWh of storage capacity. In contrast, the smart domestic water heater and smart AC upgrades together cost $450, though these devices are much less flexible in terms of load shifting than batteries. The REopt analysis indicates that low-cost upgrades to existing home technologies may take primacy over batteries in near-term solar plus systems. However falling battery costs and supportive state and national policies may ensure a more prominent role for batteries in future solar plus applications [7,41–43,45]. Our analysis may under-state the value of solar plus due to the focus of our study on the value of solar plus from electricity cost reduction. Particularly in the case of batteries, PV customers may derive additional benefits such as backup power. Further, solar plus technologies can provide myriad grid-level benefits as well. By aggregating solar plus homes, grid operators can perform more effective demand side management and use solar plus technologies to provide grid-level ancillary services [7,46]. The solar plus approach may therefore facilitate largescale PV deployment by mitigating grid integration issues. At the same time, our analysis may over-state the value of solar plus for at least two reasons. First, the REopt model optimally dispatches all technologies with perfect foresight of climatic conditions, a condition that is clearly untenable for applied technologies. Second, some customers may be unwilling to change energy use patterns in order to maximize the value of solar plus systems. For instance, customers that are typically at home during peak PV hours may be less willing to use the pre-cooling capacity of smart AC units, which would reduce the potential value of the smart AC unit for PV system optimization. Therefore the value of solar plus varies by customer according to the degree to which customers are willing and able to shift load profiles. To conclude, we find that solar plus – a more integrated approach to PV optimization using batteries and load control devices – improves customer economics relative to standalone solar. We build on a growing body of literature by showing that the economics of solar plus depend on grid export rates as well as other rate structure components. We find that the solar plus approach is well suited to address some of the rate structure challenges facing future PV deployment. We provide a new method for evaluating, selecting, and sizing solar plus technologies, allowing our model to choose amongst a suite of candidate technologies

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