Demand response programs

DR has a wealth of literature studying the various programs, benefits, and challenges (see [14–20] for review articles). In general, DR can be split into two categories; incentive-based and price-based. Incentive-based programs have customers opt into a program where the utility or aggregator can control a certain amount of their load in exchange for reduced payments or other incentives. Examples of this type of program include direct load control, scheduled load reduction, interruptible loads, or curtailable loads. Price-based programs have customers voluntarily modify their load in response to economic signals (i.e., price changes of energy). Examples of this type of program include Time of Use (TOU) rates, real-time pricing, critical peak pricing, and extreme day pricing.

Incentive- and price-based programs have both been implemented in energy planning models. The state-of-the-art equations used in incentive-based programs are well summarized by Morales-Espana et al. [6]. The authors highlight methods to expand idealized load shifting constraints to include other parameters, such as saturation and load recovery, and provide constraints specific to certain loads, such as EVs. Alternatively, price-based implementations focus on the DR pricing strategy. For example, Miri et al. [21] highlight how Locational Marginal Prices (LMPs) can be used to implement a real time pricing scheme, Dranka et al. [22] use historical spot prices to set seasonal DR rates, or Mallapragada et al. [23] (who build on [24]) showcase a DR strategy that allows load to be shed once different price set-points are exceeded. Regardless of the implementation, studies consistently highlight the importance of including DR in energy planning models.

Measuring the impacts of demand response

Summarized by Nolan and O’Malley [16] (and supplemented by [25,26]), is that the effectiveness of DR programs can be measured against a baseline load profile. This is “the electricity that would have been consumed by a customer in the absence of a demand response event” [16]. To do this, a model is first run without DR to obtain a baseline result. DR is then implemented and the results are compared.

Impacts on load shedding.

To measure the need for load shedding, system demand peaks are measured [30]. Peak net-load measures the maximum hourly system net-load over the year while Peakiness measures the height of system peak net-load about the 100th highest hourly net-load. This is graphically represented in Fig 3. A lower peak load represents a reduced need for short-term load shedding. A lower peakiness value represents a reduced need for consistent load shedding. These metrics are important because the system’s tolerance to load shedding is minimal; with a typical loss of load expectation set at 0.1 days per year in the United States of America (USA) [31].

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Fig 3. Load shed characteristics.

Highlighted is the peak yearly net-load and the peakiness, which represents the difference between the peak net-load and the highest peak net-load. Example net-load data is extracted from the 2022 load in the CAISO region of the USA [32].

https://doi.org/10.1371/journal.pclm.0000918.g003

Impacts on load shifting.

To measure the need for load shifting, net-load ramping characteristics are measured [30]. Routine ramping measures the maximum daily three-hour net-load ramp on demand on the day with the highest ramp. Extreme ramping measures the maximum annual three-hour net-load ramp compared to the highest ramping day. These metrics are shown in Fig 4. A lower extreme ramping represents a reduced need for short-term load shifting, while a lower routine ramping represents a reduced need for consistent load shifting.

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Fig 4. Load shift characteristics.

Plotted is the peak daily absolute 3hr net-load ramp value. The highest value represents the routine ramping requirement. The difference between the peak value and the highest value represent the extreme ramping value. Example net-load data is extracted from the 2022 load in the CAISO region of the USA [32].

https://doi.org/10.1371/journal.pclm.0000918.g004

Multi-sector demand response

Although less prevalent than electrical only DR, there are studies that focus on multi-sector DR. These can range from the study of what loads can participate in DR, to investigating the impact of DR on heavily electrified systems that include fuel switching.

Load participation has been studied by Gils [33] who evaluate the theoretical potential of DR within Europe while considering different energy carriers and energy sectors. Additionally, O’Connell et al. [34] develop a production cost model to study DR on thermo-electric loads. The authors place particular emphasis on implementing saturation and load recovery constraints by tagging individual loads. Both studies highlight the benefits of considering multi-sector DR, but do not evaluate the role of sector-specific DR within a capacity expansion framework.

Understanding how electrical and natural gas networks interact while considering DR has been studied by Shams et al. [35] and Li et al. [36]. These studies develop multi-sector energy optimization models to do day-ahead scheduling problems that incorporate DR. The authors find that system costs are sensitive to bottlenecks in the natural gas network and that multi-sector DR improves energy security margins. Moreover, capturing the variability associated with weather patterns is essential to understand the full impact of DR. While these studies excellently highlight key uncertainties to take into account, the impacts of future energy system development is not studied.

Evaluating the impact multi-sector DR can have on future, heavily electrified, energy systems has been done by Specian et al. [13]. The authors investigate DSM solutions for future winter peaking energy systems in the USA. They show that many DSM solutions can work together to effectively smooth the electrical load profile. Moreover, they highlight that DR will be a key factor in managing peak winter heating loads in increasingly electrified systems. The authors conclude by stating the need for further analysis to capture the interactions between the electrical and natural gas network. Moreover, this work does not highlight how investment decisions interact with DR.

Capacity expansion studies that include multi-sector DR have been conducted by Satchwell et al. [28], Qadrdan et al. [37] and Dominkovic et al [38]. These studies show that space heating, space cooling, and electrical loads can all offer significant cost benefits to the system. This is driven by DR offsetting the need for new peaking natural gas power plants, resulting in lower capital and fixed expenditures on the electrical network. Results are shown to be sensitive to electrical transmission bottlenecks. Due to the coarse time resolutions used in these long-term studies, results could not relate back to net-load characteristics. Furthermore, the impacts of electrical and thermal DR applications are not studied individually.

All of these studies highlight a few key considerations when performing multi-sector DR analysis. First, the need to capture service level thermal demands (space-heating, space-cooling) and EV deployment charging requirements is important. Second, capturing heating peaks due to weather variability is crucial, as these can occur when DR is most beneficial to reduce capital expenditures. Finally, bottlenecks within the electrical and natural gas network may affect DR effectiveness and should be modeled.

Contributions of this paper

Within the literature, there is a gap to study the multi-sector interactions of DR programs in capacity expansion frameworks with high spatial and temporal resolution. We address this gap with the following contributions:

1. We implement a price-based DR program that can be used for any carrier across any energy sector. This implementation remains computationally tractable for a mutli-region and multi-sector energy planning model at hourly resolution.
2. We investigate pricing DR based on the the marginal cost values of each fuel (that is the dual value on each energy balance constraint).
3. We investigate two different DR pricing strategies; a carrier-average and carrier-specific value.

In addition to these contributions, we incorporate two features not often found in capacity expansion DR studies. Firstly, we directly shift end-use loads, rather than the energy consumed from each technology. For example, instead of shifting a HPs load on the electrical network, we directly shift the heating load which can be met through other (non-electric) heating technologies. Secondly, we incorporate metrics to evaluate the impact of DR on the net-load profile. These metrics are often overlooked in the energy planning literature, but can provide valuable insight on the impact of DR that goes beyond the cost and capacity results.

PyPSA-USA

Python for Power System Analysis (PyPSA) is a reputable open-source energy planning framework [39]. It is formulated as a linear cost optimization model and can be used for electricity and energy system capacity expansion planning and economic dispatch studies. PyPSA-USA [40] is an open-source and open-data model that can build configurable energy models of the USA on top of the PyPSA framework. It has full sectoral coverage and supports multiple end-use fuels. The reader is referred to S1 Appendix and PyPSA-USA’s documentation [41] for detailed supplementary information about the model.

In this study we evaluate if multi-sector DR is an effective mechanism to improve future energy systems based on the metrics described in the literature review. To conduct our analysis, we use PyPSA-USA to study future 2030 energy systems. A near-term target is selected as high-resolution load profiles for all energy sectors becomes increasingly uncertain for distant futures. Moreover, a near-term target allows us to capture existing end-use stock (furnaces, heat pumps, etc.) to study tradeoffs associated with replacing these technologies. We restrict investment in transmission lines and natural gas pipelines to highlight the impacts of DR in constrained systems. We run two different regional systems at high-temporal resolution to capture geographic differences and demand and weather variability. Finally, we model multiple end-use fuel demands across multiple energy sectors to understand how energy transition trends in different sectors will impact DR.

Demand response

For this study, we implement a DR module in PyPSA-USA. As discussed, both price-based and incentive-based programs have been implemented in the literature. We implement a price-based program for two reasons:

1. Incentive-based programs benefit from loads that are classified by type. This allows DR specific constraints, such as allowable shift times, to be implemented. Studies, such as in [4,33,47,48], provide methods and data to help complete this process. However, due to the aggregation methods and limitations of the raw load metadata, classifying the loads by individual end-use in PyPSA-USA is not feasible.

2. To retain computationally tractable models at hourly resolution, avoiding inter-temporal (or connectivity) constraints is desirable [49]. Implementing the state-of-the-art incentive-based DR equations often introduces these connectivity constraints through load balancing equations [6].

PyPSA is formulated as a linear program that minimizes system costs according to Equation 1. In general, it states that the objective is to minimize the summed capital costs and operational costs of the system. DR is modeled as a store that allows energy to be shifted from one timestep to another, similar to that done in [22] for only electrical loads. To shift load, the model will incur a cost to store a unit of energy for each hour it is deferred (that is $/MWh/hr), following Equation 2. This represents a willingness-to-pay for DR. Specific PyPSA implementation details are given in S1 Appendix.

(1)

(2)

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https://doi.org/10.1371/journal.pclm.0000918.t002

To price DR we use the annual average marginal price of energy. This is found by first running the model without DR to extract the average annual shadow price for each energy carrier, as shown in Fig 5. This value represents the demand side willingness-to-pay to defer energy loads. We acknowledge that a real-world willingness-to-pay value will have temporal effects that are not captured by a flat DR rate, however, this rate acts as a neutral reference cost. The model will treat any marginal cost above this setpoint as having cost-saving potential. This approach allows us to isolate the benefits of multi-sector DR without conflating the results with the setup of the pricing scheme. Further work to optimize the cost function is described in Future work.

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Fig 5. Demand response pricing strategy.

The residential sector energy carrier marginal costs for the mid natural gas cost scenario in California. The green dashed line represents the carrier-average pricing method. The black dashed lines represent the carrier-specific pricing methods.

https://doi.org/10.1371/journal.pclm.0000918.g005

Two pricing strategies are investigated to evaluate the potential benefits of multi-sector DR. First, we model a carrier-average pricing strategy, where all energy carriers within a sector incur the same cost to shift load. This represents a simplified pricing scheme that aims to remove the complexity of end-users having to optimize their response against competing price signals. Second, we model a carrier-specific pricing strategy, where each energy carrier within each sector has a separate cost to shift load.

Scenario design

A common method to handle uncertainty in energy planning studies is through scenario analysis [50,51]. This section will describe the dimensions used in our scenario design; those being demand response sector, demand response cost, and natural gas cost.

Scenario naming.

For reporting purposes, each model run is given a unique scenario name. An overview of the 39 scenario names for each pricing strategy is given in Table 1. California and New England follow the same naming conventions. All runs are repeated for both the carrier-average and carrier-specific DR pricing methods. This results in 78 runs per region, or 156 runs total.

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Table 1. Scenario Matrix with Scenario Names.

https://doi.org/10.1371/journal.pclm.0000918.t001

System costs

System level net-present value costs for the carrier-average pricing strategy in California and New England are given in Fig 6. These costs include capital expenditures and operating costs across all sectors. Three key trends can be observed from the figure. First, electrical DR does not offer cost savings in any scenario in California. This result is contrary to typical findings, as the literature consistently states that electrical DR is an effective mechanism to reduce costs. Secondly, cost savings can be significant (almost 40%) in some scenarios in New England. Finally, cost savings diminish as the cost of natural gas increases.

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Fig 6. System objective cost results.

Heatmaps show the cost deviation from the reference case of no DR applied to the system. The carrier-average pricing strategy is shown, where each carrier incurs the same cost to shift load. Negative values indicate a cheaper system. (a) California. (b) New England.

https://doi.org/10.1371/journal.pclm.0000918.g006

Before discussing cost results in detail, we note the cost accounting strategy used. To quantify the economic benefit to the grid, we report the realized cost, not the objective cost. This realized cost is calculated by subtracting the cost of DR from the objective cost. We do this as the cost DR incurs is not seen by the system operator, rather it is a penalty to shift load. This strategy amplifies cost trends, however, it can lead to minor artifacts. For example, in Fig 6b the system with only thermal DR (t-high-hgas) shows slightly more savings (0.1%) than the system with thermal and electrical DR (et-high-hgas). This discrepancy is due to similar DR usage between systems and rounding errors (in this case, in the third decimal place). Unadjusted costs are given in S2 Appendix Fig A.

California has existing flexibility measures that economically out-compete electrical DR. These measures primarily consist of electrical imports and significant OCGT capacity backed by ample natural gas pipeline capacity. We demonstrate this by constructing a capacity constrained California system and present its costs in Fig 7. This new system removes the ability to import electricity, removes existing OCGT capacity, and relaxes supply side build constraints. Under these conditions, electrical DR now out competes the existing peaking capacity and acts as a flexibility mechanism to reduce costs and promote VRE integration.

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Fig 7. California capacity constrained system costs.

Heatmaps show the cost deviation from the reference case of no DR applied to the system. The carrier-average pricing strategy is shown, where each carrier incurs the same cost to shift load. Negative values indicate a cheaper system.

https://doi.org/10.1371/journal.pclm.0000918.g007

In contrast, New England’s system is constrained by transmission level capacity bottlenecks in the electrical and gas networks. Coupled with the fact that no new oil furnaces are permitted and that Air Source Heat Pumps (ASHPs) in the winter have a low Coefficient of Performance (COP), electrical DR acts as a flexibility mechanism to reduce costs. This flexibility is primarily within the residential and commercial sectors to shift short-term heating load peaks (further discussed in Capacity results).

Key Result 3.

A higher price of natural gas results in a lower total relative amount of cost savings from DR. It is system dependent if the savings decrease is seen in the investment or operational costs.

Fig 8 shows that pricing DR by carrier (carrier-specific pricing) is more cost effective compared to pricing all DR carriers at the same price (carrier-average pricing). With only minor exceptions (<0.4% difference), the carrier-specific strategy consistently yields greater cost savings. This is primarily due to the price difference between energy carriers; with electricity being significantly more expensive than heating and cooling (see Fig 5). A carrier-average pricing scheme effectively inflates the costs of shifting thermal loads, as it is weighted by the expensive electricity. In these cases, the system will often build capacity to meet consistent peaks within the thermal sector, rather than pay a to defer load where the penalty is weighted by the electrical cost. Since thermal load peaks can offer significant capital investment cost savings (see Capacity results), this generally results in a more expensive system.

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Fig 8. System costs for carrier-average and carrier-specific pricing strategies.

Heatmaps show the cost deviation from the reference case of no DR applied to the system. Negative values indicate a cheaper system. Results for mid natural gas costs are given. The top row is carrier-average pricing, while the bottom row is carrier-specific pricing. (a) California. (b) New England. (c) Capacity constrained California.

https://doi.org/10.1371/journal.pclm.0000918.g008

Capacity

Thermal DR significantly reduces system costs by lowering the end-use heating capacity requirements in the service sector. In all systems, natural gas furnace and HP capacity reduces while still meeting the same heating energy load, as given in Fig 9. Notable is the extreme reduction in total HP capacity in New England (90%+ in some scenarios). While this reduction is amplified by specific structural assumptions, as next described, it effectively highlights the ability of thermal DR to act as a flexibility measure.

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Fig 9. Service sector heat pump and gas furnace capacity.

Heatmaps show the total capacity deviation from the reference case of no DR applied to the system. Negative values indicate less capacity. Results for mid natural gas costs are given. The top row is heat pump capacity, while the bottom row is gas furnace capacity. (a) California. (b) New England. (c) Capacity Constrained California.

https://doi.org/10.1371/journal.pclm.0000918.g009

The significant reduction in HP capacity is driven by the land-use constraints that govern its deployment in PyPSA-USA. While the model can invest in both ASHPs and Ground Source Heat Pumps (GSHPs), GSHP investment is constrained in urbanized areas due to ground-space requirements. This approach follows methodologies seen in similar PyPSA projects [9], with full implementation details provided in S1 Appendix.

Within New England, maximizing resource efficiency is critical to meet its significant heating load in the winter. Due to natural gas pipeline and electrical transmission capacity constraints, combined with the inability to expand heating oil furnaces capacity, meeting this load is challenging. Without DR, the system overbuilds ASHP to satisfy the GSHP capacity constraint, securing access to the stable COP GSHPs offer. The introduction of thermal DR provides a method to shift load to adapt to the variable COP of ASHP, drastically reducing the amount of total HP capacity and reducing costs.

In reality, system planners will not build redundant ASHP capacity just to satisfy a land-use constraint, but this outcome shows the lack of flexibility measures without DR for near term transitions. The alternative to building unused ASHP is simply shedding load, which is also not realistic as consumers need to heat their buildings. Thermal DR reduces system dependence on the stable COP GSHPs offer, and allows for the adaption to the variable ASHP COP to meet the same heating load. Furthermore, load shifting allows the system to work around capacity constraints in the natural gas network and maximize existing natural gas furnace capacity, which does not have a time varying efficiency.

Key Result 6.

The pricing strategy implemented does not hinder or incentivize the deployment of light-duty EV capacity.

Physical batteries and DR, effectively a virtual battery, present an important tradeoff; a physical battery incurs investment costs with minimal operational costs, while DR has no investment cost but consistent operation costs. The base California system does not consider this tradeoff, as existing flexibility measures do not require additional battery capacity and no changes are observed. In contrast, New England shows that DR consistently replaces significant physical battery capacity. Here, DR offers a more economical method to navigate network bottlenecks, often driven by short-term load peaks rather than prolonged storage needs.

The capacity constrained California system, shown in Fig 10, reveals more complex interactions. First, we observe a substitution effect. As DR costs decrease, physical battery capacity declines until a saturation point is reached. Interestingly, in scenarios with high DR costs (e-high- scenarios), the system expands its battery capacity alongside DR. This suggests a complementary relationship where DR and batteries can work together to produce cheaper systems with more flexible capacity. Second, thermal DR can only substitute so much battery capacity, with it never reaching the saturation point (i.e., the currently installed battery capacity). This is consistent with the limitations of thermal DR. That being, it can shift electrified thermal loads (for example heat pumps) but can not address non-thermal electrical loads (for example EVs) which physical batteries can. Therefore, the system must always retain some physical battery capacity if only thermal DR is introduced.

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Fig 10. Capacity constrained California battery capacity.

Heatmaps show the total battery capacity (MWh) deviation from the reference case of no DR applied to the system. Negative values indicate less capacity.

https://doi.org/10.1371/journal.pclm.0000918.g010

Emissions

In the absence of an emission target or price on emissions, DR may or may not drive down emissions, as shown in Fig 11. In both Californian systems, DR offers mild benefits (<4%) in emission reduction. In part, this is driven by California naturally reducing emissions without the help of DR by 2030. Their mild winters provide good opportunity for HP deployment to electrify heating loads, while their excellent natural resources support maximum VRE deployment. In these cases, DR helps manage costs of the system through balancing loads and capital deferral, but is restricted in its ability to further drive down emissions given supply side build constraints.

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Fig 11. Total carbon emissions.

Heatmaps show the emission deviation from the reference case of no DR applied to the system. The carrier-average pricing strategy with mid natural gas costs are shown. Negative values indicate less emissions released. (a) California. (b) New England (c) Capacity constrained California.

https://doi.org/10.1371/journal.pclm.0000918.g011

Conversely, in New England, the introduction of DR can increase emissions by up to almost 10% in some scenarios. This result is primarily driven by the increase in generation from gas and oil furnaces. Through shifting electrical load, fossil fuel furnaces can be run consistently throughout the year. Heating loads can be modulated to work around the poor COP of ASHPs and transmission level bottlenecks. This is favorable for the system as existing oil and natural gas furnaces can be run, instead of generating or importing additional electricity to run through newly invested HPs. Introducing thermal DR can show emission benefits, as load is shifted to eliminate the more expensive heating oil in favour of cheaper, and less emission intense, natural gas.

Peak net-loads

The electrical net-load duration curve highlights the requirement for firm capacity throughout the year. In New England, Fig 12a corroborates our cost findings that maximum benefits are unlocked though the introduction of thermal DR. All multi-sector DR profiles (et- scenarios) overlap with thermal only DR profiles (t- scenarios), indicating electrical DR offers no additional benefits in net-load reduction on top of what is offered by thermal DR. The time-series data given in Fig 13a confirms that the net-load is consistently reduced across all DR runs, reducing the requirement of firm capacity that must be available. However, this does not guarantee ramping is also reduced, as is discussed in the next section.

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Fig 12. Electrical net-load duration curves.

The left frame shows the duration over the full year. The right frame is the top 100 hours of the year, given by the red rectangle. Results are given for the mid natural gas scenario with carrier-average pricing. (a) New England. (b) Capacity constrained California.

https://doi.org/10.1371/journal.pclm.0000918.g012

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Fig 13. Electrical net-load timeseries.

The net-load time series for the week containing the peak net-load over the year. Results are given for the mid natural gas scenario with carrier-average pricing. (a) New England. (b) Capacity constrained California.

https://doi.org/10.1371/journal.pclm.0000918.g013

In contrast, the capacity constrained California system has differing economic and physical outcomes when introducing DR. From a net-load perspective, Fig 12b shows electrical DR can reduce peak net-load by up to 16%, while, thermal DR does little to improve the peak net-load, and in some cases raises it by up to 2%. However, from a economic and system planning perspective, pairing the net-load reduction from electrical DR with the cost savings of thermal DR (the et- scenarios) results in a 14% cheaper system (see Fig 7) with a net-load reduction of up to 10%. Unlike New England, this system relies less on aggressive load shifting, as shown in Fig 13b. This is largely due to the interactions between the various electrical and non-electrical end-use heating technologies providing energy services.

Demand response metrics

As discussed in the literature review, peakiness, routine ramping, and extreme ramping metrics can provide further insight into the impact of DR. However, PyPSA-USA optimizes based on a simplified economic dispatch model to remain computationally tractable and does not capture system inefficiencies. This led to no consistent patterns being identified across any scenario dimensions for these metrics.

PyPSA-USA minimizes the total cost of the system by sizing the capacity to the maximum load and then acting economically rationally to dispatch generators. Although we run at hourly resolution, we do not capture full operational details. For example, we do not track generator status to perform Unit Commitment (UC) studies and capture startup and shutdown costs. Moreover, PyPSA-USA, as configured for this study, runs with perfect-foresight. This means that the model knows the weather patterns and demand profiles for the full year and does not have to account for additional flexibility. Without more rigid operational constraints, even high temporal capacity expansion studies (up to 1 hour) do not have the fidelity to capture DR specific metrics.

Sensitivity analysis

A core limitation with many energy system optimization models, including PyPSA-USA, is the assumption of economically rational behavior. This implies that all consumers will shift load when it makes economic sense, ignoring the behavior of real people. To account for this, we perform a sensitivity analysis constraining the maximum percentage of load that can be met through shifting. This analysis was applied to the mid natural gas cost scenario with the very-low DR costs (the et-vlow-mgas scenario) for all three systems.

Fig 14a shows the system cost response to increasing DR participation limits. While costs improve with higher participation limits, the marginal benefits continually reduce. This occurs as the initial introduction of DR targets the most expensive peak events. Once these peak events have been managed, additional DR applies to periods of lower volatility. Fig 14b shows the emission response to increasing DR participation limits. In the Californian systems, emissions generally decrease with more DR participation, with the exception between to adoption rates. In New England, emissions increase upon introduction of DR (see the Emissions results) and steadily decrease with more DR participation. In all three systems, emissions are less sensitive to DR participation limits compared to costs.

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Fig 14. Sensitivity to allowable contribution of DR.

System metrics are given for different levels of allowable DR contribution to meeting the load. Results for the et-vlow-mgas are given. The left pane shows carrier-average pricing, while the right pane shows carrier-specific pricing. (a) System costs. (b) System emissions.

https://doi.org/10.1371/journal.pclm.0000918.g014

The continual reduction in marginal cost benefits have an important policy implication. It suggests that significant cost savings can be unlocked with low adoption rates (<20%) of DR. From a near-term energy transition perspective, this is important as DR adoption of is a realistic goal in the near-term in some jurisdictions [31].

Policy insights

Three key policy insights are found from this work. The system benefits of multi-sector DR, suggestions on how to price DR programs, and the importance of thermal DR for near-term energy transitions.

Methodological insights

Three key methodological insights are found from this work. Using the marginal cost of energy to price DR, the short-term load shifting that this implementation prioritizes, and evaluating DR specific metrics in high temporal capacity expansion studies.

Future work

We highlight three directions which this work can be built upon. First, incorporating social aspects of DR. Second, exploring different cost functions in this DR implementation. And finally, improving the economic dispatch analysis of this study.