Replacement policy of residential lighting optimized for cost, energy, and greenhouse gas emissions

When making purchase decisions, consumers are encouraged to look past LEDs' high initial cost to the energy savings over their long life, and to consider financial assessment tools such as rate of return (ROR), return on investment (ROI), and payback period to illustrate all the benefits and costs. Alstone et al found that the energy 'debts' based on light output per unit of embodied energy plus energy consumption for off-grid LED lighting systems are paid back in just 20–50 days and have an energy ROI of 10–40 times [7]. Many studies have also demonstrated the competitive cost savings and environmental benefits of LEDs compared to incumbent lighting from a life cycle perspective [8–14]. However, without considering the timing of replacement, these methods alone cannot maximize the cost and environmental benefits of replacement.

Although equipment replacement with optimization has been widely researched, particularly for industrial equipment undergoing rapid technological change, many of the studies only focused on cost–benefit analysis [15–18]. A subset of replacement studies focused on automobiles, refrigerators, and other consumer products considers both cost and environmental benefits of replacement under technological progression but has not considered the social cost of carbon and variable electrical grid fuel mixes [19–26]. As the US moves toward low-carbon power generation driven in part by the Renewable Portfolio Standards [27, 28], the long-term benefits of energy efficiency gain will be lower due to an impact reduction in upstream energy and material production [29]. With electricity accounting for most of the life cycle impacts of lighting [8, 13, 14], it is imperative to consider changes to electricity fuel mix in lighting replacement decisions.

To the best of the authors' knowledge, there are only two studies that optimize the decision and/or timing of lighting replacement, but neither of the studies considered the environmental tradeoffs in replacement. Balachandra and Shekar [30] explored the replacement of residential IL with various fluorescent lamp types in India by comparing the relative annual ROR and investment risk of each alternative. However, this study was limited to fluorescent lighting and cost benefit considerations only. Ochs et al's study [31] on streetlight replacement on US military bases found that delaying the switchover from high intensity discharge luminaires to LEDs achieves better performance and cost savings from future improved LED technology. However, it did not consider the potential savings from early replacement [32], i.e. from upgrading LED luminaires to newer, more energy-efficient models before they reach the end of their rated lifetime. With a longer service life and a parametric failure mode [33], LED replacement after adoption of the technology becomes less intuitive. A knowledge gap thus remains in understanding how technological changes in solid-state lighting (SSL) and power generation affects future replacement decisions for lighting.

This study aims to conduct a comprehensive replacement analysis for residential lighting by considering several key parameters: environmental loads (primary energy and greenhouse gas (GHG) emissions), initial conditions (e.g. whether a luminaire is pending for replacement at the time of the decision), and technology improvement (to power generation and LED lighting). By studying the replacement of 60 W-equivalent (900 lm)⁴ lamps, which are commonly found in US households, this paper seeks to provide guiding policy for low-cost and low-impact residential lighting replacement across various regions of the US.

Life cycle optimization (LCO) is a method that integrates life cycle assessment (LCA) with optimization analysis for enhancing product sustainability [34] and is used to construct a lighting replacement optimization model. The model draws data from LCA studies that follow ISO 14040 as well as US Energy Information Administration outlook for LED technology [3] and the grid [5]. By considering how a product's life cycle impact profile changes over time with its design, the LCO framework determines an optimal replacement policy (characterized by timing of purchase and duration of use) in which the total life cycle impact (e.g. cost) of the product aggregated over a time horizon is minimized. This LCO framework has been used to study automobiles [22, 25], refrigerators [21, 23], washing machines [19], and air conditioners [20].

LED lamps are expected to reach 150–180 lm W⁻¹ in efficacy by 2020 and 50 000 hours in lifetime by 2025 [3]. Another study has the forecast at 250–300 lm W⁻¹ and 80 000 hours by 2050 [29]. From 2015–2020, LED lamps would decrease by 40% in cost, 33% by electronic mass and proportionally to wattage demand in terms of the heat sink [3]. Based on these projections, logistic models (see supplementary appendix A available at stacks.iop.org/ERL/12/114034/mmedia) are created to describe the future cost, efficacy, and rated lifetime of the LED lamps. Due to the maturity of the technology, the efficacy of CFLs are not expected to change significantly over time, improving at less than 1% annually [35]. It is expected that both IL and HL are being phased out of operation by EISA [6].

For each lamp technology, data for cost, primary energy, and GHG emissions is collected for the production, transportation, use, and end of life (EOL) stages, where all GHG emissions are expressed in AR4 GWP-100. The production stage encompasses all sub-stages from cradle-to-gate per DOE's LCA studies [13, 14, 36] and the production impact for LED is adjusted to reflect the actual LED efficacy improvement rate to-date. The transportation stage represents only the transportation between the original equipment manufacturer suppliers (defined per DOE's study) and the retailer (assumed at the geographical center of the continental US (Kansas). It accounts for LED weight reduction, [3] improved vehicle technology, and lower-carbon fuels, the latter two of which would decrease the life cycle energy factor and GHG emission factor by 57% and 91% respectively for bunker fuel container ships, and 58% and 56% respectively for diesel trucks by 2050 [37].

The use stage accounts for the purchase and installation of a new lamp when the incumbent lamp is ready for retirement and disposal. An average of 3 hours of use (HOU) per day is studied as a baseline condition while 1/7 (1 hour per week), 1.5 (average A19 lamp usage rate in US [6]), and 12 HOU are also explored. Although lamp change-out is typically done by consumers themselves, an opportunity cost [38] equivalent to one third of the US median wage of $17.40 hr⁻¹ [39] is assigned to an estimated 9 min labor time (which includes purchase and installation of the new lamp, and disposal of the old lamp). For lamps that are already in use at the start of the time horizon, both the lamp cost and installation cost are omitted from the calculation.

Between 2015 and 2040, the share of US electricity from natural gas and renewables are expected to increase by 6% and 13%, respectively, while the share from nuclear and coal decrease by 4% and 15%, respectively [5]. These fuel mix data are assumed valid for extrapolation until 2050. Using a bottom-up aggregation approach by generation type and accounting for the upstream impacts of power generation [40–42], the average primary energy factor and average GHG emission factor for the US grid are estimated to be 2.95 (kWh kWh⁻¹) and 0.647 kg CO₂e kWh⁻¹, respectively in 2015, with an annual growth rate of −0.385% and −1.31%, respectively. This study recognizes that the use of average generation factors may underestimate the potential savings from energy efficiency gain [43]. Although marginal generation factors may better capture the time-of-use impacts and savings, their projected changes from grid decarbonization cannot be estimated easily (due to lack of data), or with certainty (due to their temporal variability). To provide some insight on marginal generation impacts, replacement policies for coal, natural gas, and combinations of the two fuels are assessed and discussed in supplementary appendix E.

In the EOL stage, 10% recycling is assumed for IL and HL, 20% for CFL and LED, and 30% for all lamp packaging [13, 14]. Lamp recycling is assumed through mail-back programs (e.g. EasyPak and LampMaster), which offer prepaid recycling kits to send used lamps to recycling centers, at $0.25 lamp⁻¹. Landfill cost is estimated at $45 ton⁻¹ [44] and the same rate is applied to recycling packaging. The life cycle energy is estimated using the EPA Waste Reduction Model [45] data for landfilling various materials, including aluminum, glass, copper, and corrugated containers. The recycled portion is assumed net zero energy given the unknown fate of the recycled materials.

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The technology projections and life cycle impact profiles for all lamp types are summarized in table 1. HL is assumed to have the same non-use life cycle inventories as IL. In addition, this study assumes an annual discount rate of 3% and a social cost of carbon of $47.77 metric ton⁻¹ CO₂ in 2015 with an annual increase of 4.86% [46].

The replacement model is constructed such that an initial lamp undergoes two technology upgrades during a time horizon of 35 years. Between each upgrade, retiring lamps are replaced with new and improved models of the same technology, purchased at the time of replacement. To explore different technology options for the upgrade, lamp type variable l is defined as:

$$\begin{equation} l = \left( {{l_1},{l_2},{l_3}} \right) \end{equation} \tag{ 1 }$$

where l_i∈{LED,CFL,HL,IL}. l₁ is the initial lamp type, and l₂ and l₃ are the lamp type in the first and second upgrades, respectively.

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Decision variables specify the timing of lamp upgrades and replacements during the time horizon, defined as:

$$\begin{equation} x = \left( {{x_1},{x_2}, \ldots ,{x_{n + m}}} \right) \end{equation} \tag{ 2 }$$

where x_i ∈ [0,35] is the number of years since 2015 when the ith lamp replacement occurs. It is assumed that the total lighting service required during the time horizon is fulfilled by, in succeeding order, one initial lamp of type l₁, n incumbent technology lamps of type l₂, and m replacement technology lamps of type l₃. The initial lamp is 'upgraded' to the incumbent technology at x₁ and to the replacement technology at x_n+1. In the case where an initial lamp does not exist, x₁ = 0. Operation of the last lamp is truncated at the end of the time horizon using a terminal value method. It should be noted that, in addition to x_i, n and m are also considered as decision variables in the model. Figure 1 shows the replacement order for an example where n = 3 and m = 2. Note that the first lamp (initial) is operated from 0−x₁, the second lamp from x₁−x₂, and so on.

For a given combination of initial and upgrade technologies l, the optimization problem to find the optimal values of x, n, and m, can be formulated as follows:

$$\begin{equation} \begin{array}{l@{}l@{}l@{}} \mathop {\min }\limits_{x,n,m} f \left( {M,U,W,l,x,n,m} \right)\\ = \mathop {\min }\limits_{n,m} \left\{ {\mathop {\min }\limits_x f\left( {M,U,W,l,x,n,m} \right)} \right\}. \end{array} \end{equation} \tag{ 3 }$$

Subject to

$$\begin{equation} {x_1} \le {\rm LT}\left( {{l_1},0} \right){\kern-2pt}. \end{equation}$$

$$\begin{equation} {x_{i + 1}} - {x_i} \le {\rm LT}\left( {{l_2},{x_i}} \right){\kern-2pt};i \in \left\{ {1, \ldots ,n} \right\} \end{equation}$$

$$\begin{equation} {x_{i + 1}} - {x_i} \le {\rm LT}\left( {{l_3},{x_i}} \right){\kern-2pt};i \in \left\{ {n + 1, \ldots ,n + m - 1} \right\} \end{equation}$$

$$\begin{equation} 35 - {x_i} \le {\rm LT}\left( {{l_3},{x_i}} \right){\kern-2pt};i = n + m \end{equation}$$

$$\begin{equation} 0 \le {x_i} \le 35 \end{equation}$$

$$\begin{equation} n \in \left\{ {0, \ldots ,{n_{\rm max}}} \right\} \end{equation}$$

$$\begin{equation} m \in \left\{ {0, \ldots ,{m_{\rm max}}} \right\} \end{equation}$$

where f is the objective function composed of impact functions M, U, W, which represent the impacts before, during, and after the use-phase of the lamp, respectively. LT (l,x) is the rated lifetime (in years) of the lamp of type l in year x. The objective function f can take the forms of: (1) cost to consumer (abbreviated as Cost), (2) primary energy (abbreviated as Energy), (3) GHG emissions (abbreviated as Emissions), or (4) life cycle cost (LCC), which is defined as the sum of cost to consumer and social cost of carbon. The model is also used to optimize a 'burnout' replacement policy, in which each lamp is replaced explicitly at the end of its rated lifetime. This is done by turning the first four inequality constraints into equality constraints. Detailed definitions of the modeling functions can be found in supplementary appendix A.

Similar to the Wagner–Whitin approach in dynamic programming, this model allows the objective function to depend only on the decision epoch to replace, which determines the optimal useful lifetime of the lamps [15, 48]. Since n and m are the numbers of decision epochs to replace within each technology upgrade, the minimization of f with respect to x, n, and m is separable into a minimization with respect to x, nested within the minimization of n and m, as shown in equation (3). This allows the inner optimization to be solved with respect to x using a nonlinear programming algorithm and repeated n_max × m_max times for all feasible combinations of n and m.

Figure 2 presents the optimized replacement policies for Case 1 at 3 HOU under different objectives: (A) Cost, (B) Energy, (C) Emissions, and (D) LCC. For all objectives, the optimal policies occur under the upgrade scenario where l₂ = CFL and l₃ = LED. Note that the initial lamp type does not affect the results since it is replaced immediately at the start of the time horizon. For comparison, two burnout replacement policies—E1 (an optimized solution where a CFL is purchased and later upgraded to an LED) and E2 (a suboptimal solution where an LED is purchased from the start) are also presented. Figure 3 shows a breakdown of the LCC-optimized policy (D) per individual lamp contribution.

Table 2 provides a summary of the LCC-optimized policies for both Case 1 and Case 2 under different initial lamp types l₁ and HOU rates. To compare across the lamp usage rate, all life cycle impact values in the table are normalized to 1 HOU. Note the optimized policies for both Case 2 with l₁ = IL and Case 2 with l₁ = HL recommend the immediate disposal of the initial lamp and placement policies same as those for Case 1, except for when HOU = 1/7. A complete set of results is available in supplementary appendix F.

Due to differences in the regional grid electricity and transportation in terms of cost, primary energy intensity, and carbon intensity, the policies are expected to vary by region. Table 3 shows the 3 HOU regional results for the District of Colubmia (DC), Texas (TX), and California (CA), which provide a representation for the Eastern, Texas, and Western Interconnections, respectively. Each state's electricity profile (except for cost) is based on the North American Electric Reliability Corporation (NERC) region it is in. Detailed grid profiles and replacement policies for the three regions, as well as for Illinois, Kansas, Wyoming, and Hawaii can be found in supplementary appendices A, D, and F.

Table 4 lists the parameter values used to test the sensitivity of the baseline scenario under the LCC objective. Each of the lower and higher values from the ten categories of parameters were tested one at a time. The sensitivity results, shown in figure 4, are ordered in terms of the changes in the objective value normalized to a unit of change in the parameter, compared to the baseline scenario. Thus, even though the variation from LED Net Price Reduction seems smaller than that from Fixed Installation and EOL Cost in figure 4, the variation per unit of change is greater from the former parameter than from the latter. For reference, the baseline scenario yields a LCC of $40.15. A list of policies per parameter value change is available in supplementary appendix B.

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Figure 2 shows that the policy depends on the objective of replacement. For example, it is optimal to delay the adoption of LED lamps until 2020 by purchasing a CFL first in terms of both Cost (policy A) and Energy (policy B). However, purchasing an LED lamp from the start is recommended from an Emissions perspective (policy C), indicating that the emission saving from using less electricity with the LED lamp outweighs the production emissions of the lamp. Two Pareto curves comparing the tradeoffs between the three objectives are available in supplementary appendix C.

A breakdown of the LCC-optimized policy (D) in figure 3 shows that the CFL contributes the least lumen-hours but the most in Cost, electricity consumption, Energy, and Emissions. However, the CFL provides both energy and cost savings overall by allowing for the adoption of lower cost and more energy-efficient LED lamps later. This is also supported by the comparison of E1 and E2 in figure 2. In addition, it is not recommended to keep any of the lamps to the end of their rated lifetime (burnout), as doing so would increase the total life cycle impacts by 9%–41%. However, given that consumers generally do not replace their lamps until burnout, consumers may still achieve 84%–86% in life cycle impact savings by following E1, compared to using ILs only.

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Table 2 shows that the decision to keep or replace depends on the type of lamp used initially. In the baseline scenario at 3 HOU, if the initial lamp is an IL or HL, immediate disposal is recommended as well as the purchase of new lamps following the same policies as Case 1. If the initial lamp is a CFL, upgrading it to an LED is recommended in 2018 for Emissions and 2 years later for other objectives. If the initial lamp is an LED (assumed with the 2015 efficacy of 78 lm W⁻¹), replacement to a newer model between 2020 and 2021is recommended. In general replacement depends on the lamp usage rate. As shown in table 2, all life cycle impacts decrease on a per HOU basis as the lamp usage rate increases. This is a result of an increase in the utilization of each lamp in the policy, which lowers the per HOU non-use phase impacts. Another factor is increased dominance of the use-phase impacts, which favor rapid replacement and adoption of more energy-efficient lamps, thereby lowering the per HOU use phase impacts.

Replacement policy depends on the fuel mix of the grid, which differs by region. Although DC and TX in table 3 have different total life cycle impacts, their LCC-optimized replacement policies are similar due to their individual tradeoff between Cost and Emissions (e.g. high Cost is balanced by low Emissions in DC and vice versa in TX). Compared to DC and TX, CA benefits from an earlier adoption of LED and more frequent replacements thereafter, driven primarily by its high electricity cost. Although LED upgrade is less urgent for CA in terms of emissions due to its cleaner grid compared to DC and TX, the cost saving from rapid replacement outweighs the emission benefit from delayed replacement for CA under the LCC objective.

Figure 4 shows that the model is most sensitive to the base rates of electricity (e.g. cost and emission factor in 2015) and least sensitive to improvement to the service life of LEDs (due to early replacement). Although the variations in LED cost and efficacy are less significant than the variations in electricity attributes at affecting the objective value, they still led to important changes in the policy. For example, the lower efficacy gain resulted in the purchase of an LED lamp immediately in 2015 due to the reduced benefit from waiting. Overall, 11 out of the 17 parameter value changes led to a shift in policy—four of those (marked by single indicators) have shifted slightly in replacement timing while six (marked by double indicators) have increased in the total number of lamps used.