Understanding the Role and Design Space of Demand Sinks in Low-carbon Power Systems

As the availability of weather-dependent, zero marginal cost resources such as wind and solar power increases, a variety of flexible electricity loads, or `demand sinks', could be deployed to use intermittently available low-cost electricity to produce valuable outputs. This study provides a general framework to evaluate any potential demand sink technology and understand its viability to be deployed cost-effectively in low-carbon power systems. We use an electricity system optimization model to assess 98 discrete combinations of capital costs and output values that collectively span the range of feasible characteristics of potential demand sink technologies. We find that candidates like hydrogen electrolysis, direct air capture, and flexible electric heating can all achieve significant installed capacity (>10% of system peak load) if lower capital costs are reached in the future. Demand sink technologies significantly increase installed wind and solar capacity while not significantly affecting battery storage, firm generating capacity, or the average cost of electricity.


Summary of Findings
(Provided for benefit of reviewers; will be removed from final manuscript as per journal format requirements) 1. Demand sink technologies with high potential include, but are not limited to: hydrogen electrolysis, direct air capture, and flexible resistive heating. To become a 'significant' (installed capacity >10% of system peak load) technology in the system, the following specifications are needed for these potential technologies: (a) Electrolysis: $150/KW in capex with a hydrogen market price of $1.40/kg, up till $300/KW in and $2.00/kg (b) DAC: $1200/KW in capex with a carbon market price of $120/metric ton, up till $1500/KW in and $150/metric ton (c) Flexible resistive heating: $150/KW in capex with a heating market price of $7.50 /MMBtu, up till $300/KW in and $13.40/MMBtu 2. Demand sinks generally do not significantly affect the price of electricity. Significant cost reductions (>10%) are achieved only at very high demand sink output market prices, outside of the feasible design space of technologies considered in this study.
3. Including demand sink technologies in the power system leads to significant increases in renewable energy generating capacity, to supply electricity for demand sink production.
In the fully decarbonized power system, for every MW of demand sink capacity built, 0.95-1.15 MW of additional wind and solar capacity gets built in the Northern system, versus 1.0-1.9 MW in the Southern system.
To put the results of this study in perspective, and apply them to real-world technologies 102 and their potential future developments, Eq. 2 was used to convert the output product value 103 parameter to physical products associated with potential demand sink technologies. The 104 results of these conversions and their supporting assumptions can be found in Table 1 Values that span the currently or future feasible design space have been highlighted based on existing research cited in Table 3. The values in this table are for illustrative and interpretative purposes only. a : Assuming 80% electrolyzer efficiency, $1/MWh variable cost, and 130 MJ/kg H 2 heating value [15,16]. b : Assuming $25/t CO2 variable cost, and that it takes 1.316 MWh to capture 1 metric ton of CO 2 [17,18,19]. c : Assuming 95% heater efficiency [20] d : Using 2020 data to determine electricity consumption: 0.46M BTC mined with 80TWh electricity [21,22]. e : Assuming 3.2kWh/m 3 , with a variable cost (non-electricity) of $0.50/m 3 [23,24]. These values are illustrative, as desalination parameters are highly sensitive to geography. Installed demand sink capacity in the system plotted as a fraction of the system's peak load. The top row shows the results in the Northern system, the bottom row the Southern system. From left to right, the stringency of the carbon dioxide emissions limit increases. The red line indicates the crossover to a 'significant' (>10% of system peak load) capacity. The rectangular boxes with potential demand sink technologies stretch both the current and future feasible design spaces of those technologies.
• DAC: $1200/KW in capex with a carbon market price of $120/metric ton, up till Change in system cost as compared to the reference scenario. The top row shows the results in the Northern system, the bottom row the Southern system. From left to right, the stringency of the carbon dioxide emissions limit increases. The red line indicates the crossover to a 'significant' (>10%) cost reduction. The rectangular boxes with potential demand sink technologies stretch both the current and future feasible design spaces of those technologies.
We find that even in scenarios with substantial demand sink deployment, demand sinks 135 generally do not have a significant impact on average electricity prices. In line with the results 136 found for the installed capacity, the demand sink impact is relatively greater in the Southern 137 system than in the Northern one. The stringency of the emissions limit has virtually no effect 138 on the results. On the limit of the future feasible design spaces for the three example demand 139 sinks considered in this study, including demand sinks in the power system can result in a 140 cost reduction in the Southern system of at most 3% in the case of hydrogen electrolysis, 4% 141 in the case of resistive heating, and 17% for DAC (versus 1%, 2% and 10% in the Northern 142 system, respectively). In none of the scenarios considered did the demand sinks increase the 143 average price of electricity. 144 Moreover, we find that while average costs do not change appreciably, the presence of demand sinks can alter the distribution of prices throughout the year. In particular, in 146 scenarios with low capital cost demand sinks (<$500/KW in ), electricity prices are more 147 stable throughout the year and periods of very low electricity prices become less frequent, 148 as shown in Figure A.1. In higher demand sink capex scenarios, we observe little change 149 in the electricity price duration curves in the system. We also find that the average price 150 of electricity used for demand sink production is about half of the average output product 151 value in magnitude (44-56%, see Table B.2), with the difference representing the gross margin 152 required to compensate the capital costs of the demand sink capacity. We also find that the  can be found in Figure 3.

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Including demand sink technologies in the power system leads to significant increases in 163 renewable energy generating capacity, to supply electricity for demand sink production. In

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The main difference in results between the Northern and the Southern system is that we 169 observe very little to no additional wind capacity in the Northern system ( Figure 3). The

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LCOE of wind resources in the Northern system is significantly higher, which explains this 171 difference. To compensate for this, we observe slightly higher increases in solar capacity in 172 the Northern system. 173 Figure 3: Demand Sink Impact on Installed Capacity of Other Resources. Change in installed capacity as a fraction of system peak load, as compared to the reference scenarios. The top row shows the results in the Northern system, the bottom row the Southern system. From left to right, the stringency of the carbon dioxide emissions limit increases. Results are grouped by both the demand sink output product value and the demand sink capital cost. operates.

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The results can be found in Figure 4, Across the various scenarios, we observe that demand sinks in the Northern system operate 199 at a slightly higher utilization rate than in the Southern system. Moreover, the more stringent 200 the emissions limit is, the higher the demand sink utilization is in any given scenario. These 201 effects are directly related to the cost of electricity; A higher cost of electricity results in a 202 higher utilization rate for demand sinks than in a scenario with a lower cost of electricity, 203 generally. One might expect that given a fixed demand sink capacity, higher electricity prices 204 would lead to lower demand sink utilization rates. However, higher prices of electricity lead 205 to lower demand sink capacity, and lower (higher) demand sink capacity leads to higher 206 (lower) demand sink utilization rates, as what is built can take advantage of overgeneration 207 on the margin more (less) frequently.

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A full year of demand sink operations for certain representative scenarios can be found  Table 2. At periods of high net 214 load we observe lower demand sink production. Since these periods would correspond to 215 Figure 4: Demand Sink Capacity Factors. The top row shows the results in the Northern system, the bottom row the Southern system. From left to right, the stringency of the carbon dioxide emissions limit increases.
higher prices of electricity, this result is in line with expectations.

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Additionally, Table 2   The main sensitivity analysis in this study is inherent to the comparison in results be-277 tween the Northern and the Southern system, in which we find that with higher renewable 278 generation potential and lower average prices of electricity, demand sinks are more favorable 279 in the Southern system. At the same demand sink capital cost and output product value, 280 we will find higher installed capacity and total annual production in the Southern system 281 than in the Northern system across all cases. In addition to that, we observe the effect of an 282 increasingly stringent emissions limit, which effectively raises the average price of electricity 283 and thus makes demand sinks less favorable. However, between the 90%, 95% and 100% CO 2 284 emissions reductions modeled, the effects on demand sink results are minimal.

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To further evaluate the robustness of this study's results, we apply a variety of additional 286 scenarios to the case most sensitive to changes: The Northern system with a 0g CO 2 /kWh All corresponding cost assumptions can be found in Table C The three scenarios involving low resource costs all have a similar effect: They increase 303 the total annual demand sink production. Since those scenarios effectively reduce the average 304 Figure 5: Change in Demand Sink Annual Production Across Sensitivity Scenarios.
Results are grouped by four levels of demand sink output product values and three levels of demand sink capital cost. The change in demand sink annual production is measured as an absolute change in TWh of production as compared to the same demand sink scenario without the sensitivity applied.
cost of electricity, it becomes more favorable to use demand sinks at lower output product 305 values. Low renewable resource costs increase the installed demand sink capacity across 306 all scenarios, accompanied by a slight decrease in utilization rates. In these scenarios, the 307 demand sinks are more closely tied to renewable energy availability, resulting in more flexible 308 operations and thus lower demand sink capacity factors. However, total annual production 309 increased in all scenarios. 310 We find that low-cost battery storage systems affect low capital cost (<$500/KW in ) de-311 mand sinks, resulting in higher installed capacity and increased annual production as com-312 pared to the scenario with mid-range battery storage costs. This shows that rather than com- Low-cost firm generation resources result in higher installed capacities for demand sinks 319 with capital costs >$500/KW in . In low capital cost demand sink scenarios, cheaper firm 320 resources significantly reduce installed demand sink capacity, a change accompanied by in-321 creased utilization rates, as these technologies are now less tightly coupled with renewable 322 generation. These low-cost firm generation scenarios allow for demand sink production from 323 electricity directly from firm resources, which together with lower average prices of electricity 324 will increase the total annual demand sink production as well. This indicates that if capable 325 of producing electricity with a sufficiently low levelized cost, firm low-carbon resources offer 326 a potential alternative or complement to variable renewables to fuel demand sinks.

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Lastly, a lower price elasticity of demand (-0.6 instead of -0.8) was tested to observe its 328 effects on demand sink results. Since a lower price elasticity of demand effectively causes de-329 mand to fall more slowly with increasing prices, demand sinks become slightly more favorable 330 in this scenario, with overall increases in annual production across all cases. This sensitiv-331 ity shows an important directionality; should one consider a demand sink with an output 332 product that has a higher (or lower) price elasticity of demand instead, it would decrease (or 333 increase) total annual demand sink production, all else equal.

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This study demonstrates that for an impactful level of demand sink capacity to be cost-  Rather, we find that the magnitude of firm capacity reductions is only a small fraction of the demand sink capacity, where this reduction is mostly enabled through the additional 348 renewable generation available during periods of highest net load, when demand sinks halt 349 production. The value of the flexibility that demand sinks can offer the power system is 350 visible in various other outcomes presented in this study; this includes that demand sinks 351 with a <$800/KW in capex have the potential to reduce the cycling of thermal plants by 352 5-50%, and that <$400/KW in capex demand sinks can decrease renewable curtailment (as a 353 percentage of total potential renewable generating capacity) by 10-75%. When considering 354 demand sinks with higher capital costs, these effects disappear, as those technologies will 355 operate less flexibly overall.

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When we consider demand sink output products, there is an inherent assumption of 357 the existence of product demand in this study, which will be required for any demand sink 358 technology to be viable. There needs to be a sufficiently large market for the output product 359 produced, with consistent and preferably flexible demand. In this study, we assume an 360 identical, constant-slope price elasticity of demand between all scenarios, and we show that 361 a lower (higher) elasticity will result in a higher (lower) total demand sink production. We 362 note that we abstract away any level of potential seasonality in the demand for the output 363 product, which has the potential to impact real-world demand sink operations. 364 We find that low capex demand sinks (<$500/KW in ) ideally operate at a 30-40% utiliza-365 tion rate, with the possibility of prolonged periods of reduced production (as seen in Figure   366 A.3). While high capex demand sinks (>$900/KW in ) ideally operate at a 75-95% utilization 367 rate, there can still be several days of reduced production in a given year, during periods of 368 high load and low renewable generation. This inherent intermittency in production, closely 369 tied to renewable generation intermittency, reinforces the requirements for demand sinks to 370 be flexible, for operations to be highly automated, and for the output product to be flexibly 371 consumable and/or easily storable. If a technology does not meet these requirements, it will 372 be challenging for it to effectively operate as a demand sink, as it will most likely be unable 373 to efficiently respond to changes in electricity market prices.

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The specific characteristics of infrastructure required to transport and store demand sink 375 products will also affect the viability of candidate technologies. Each demand sink technology 376 will require some level of supporting infrastructure and/or storage for its output product.
This additional cost has been abstracted away in this study, partly because it is not im-378 mediately clear who that cost would fall on (see Limitations). Since many demand sink 379 technologies create connections between the power system and other sectors, the costs for 380 these technologies, as well as the revenue of their output products, will likely be shared across 381 sectors as well.

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Each demand sink technology is also associated with output-specific market conditions 383 as well, which are different for each technology: desalination, which were both briefly discussed as well, there is a broad range of other po-414 tential technologies that could operate as a demand sink in the low-carbon power system.

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Other possible technologies that could be considered as demand sinks include, but are not

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• Nuclear enrichment of fuels or spent nuclear fuel processing: This is a highly energy-431 intensive process, but the level of flexibility is unclear.

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Regardless of the specificity of certain technologies, one of the main advantages of this 433 study is that the generic modeling strategy allows for any potential demand sink technology 434 that falls within the requirements laid out in the Introduction to be evaluated using the 435 presented results. Any such evaluation can provide valuable insights into the technology's 436 potential impact on the power system and its operations within that system, as well as help   The various demand sink output product value scenarios were constructed using a constant-455 slope price elasticity of demand. This slope was calculated based on an elasticity of demand 456 of -0.8 in the vicinity of a starting value of $50/MWh in and a level of demand equal to 20% of 457 the total annual system load. We approximate this slope with a step-wise function using fixed 458 supply segment sizes that are each 1% of the total annual system load, resulting in a change 459 in price of $3.125 between each segment. We use the same slope, bound to an artificially 460 imposed supply limit, in each scenario modeled to normalize between them. We define each 461 scenario by a base starting price from which we use this constant slope to generate supply 462 segments: we generate lower-value segments until the product value falls to zero, and we each scenario (5, 2, and 0 g CO 2 /kWh), corresponding roughly to a 90%, 95% and 100% 483 reduction in emissions [36]. Altogether this results in 98*3*2 = 588 cases.

484
Furthermore, we run each of the 6 region-emissions limit scenarios without the option to 485 build demand sinks as reference cases, of which the results are shown in resources, but not for nuclear and natural gas with CCS. Therefore, we implement a low-508 cost firm generation scenario by imposing a 50% fixed cost reduction for nuclear and a 25% 509 fixed cost reduction for natural gas with CCS as compared to the ATB. Since we place 510 emphasis on the directionality of the outcome rather than the absolute change in demand 511 sink production, the magnitude of the cost reduction itself is of secondary importance, given 512 that it is sufficiently large to observe a change in the model results. The corresponding 513 low-cost assumptions for these sensitivity scenarios can be found in Table C This model is described in detail in [14], but an overview is provided in Appendix F and its 519 configuration for this study is described in more detail in Appendix E, with a setup similar to 520 the one used in [4]. In its application in this study, the model considered detailed operating  Demand sink production in zone z during hour h in sub-period w y DS z Demand sink capacity installed in zone z x supply q Total demand sink production in market segment q Maximum demand sink production in market segment q x value q Demand sink output product value in market segment q The original GenX objective function in Eq. F.1 must be modified to include new invest-543 ment and revenue variables associated with the demand sinks. It is therefore updated with 544 additional terms to account for the total cost of demand sink related capacity investments 545 (y DS z · c DS ) and the total revenue of demands sink production (x supply New investment and production decisions require additional constraints to the problem 547 described in the previous section. While the installed demand sink capacity is not lim-548 ited, production is limited in each market segment by the maximum supply in that segment 549 through Eq. 4a. Moreover, the total annual supply is limited by the total annual production 550 across all zones in Eq. 4b. Lastly, demand sink production is limited by the installed capacity 551 in each zone in Eq. 4c.

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x supply Limitations 553 We note several limitations of this work. First, we make several abstractions to enable the 554 evaluation of demand sinks as a generic class of resource across a wide potential design space.

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Each potential demand sink technology will require some level of supporting infrastructure and/or storage for its output product. This additional cost has been abstracted away in this 557 study, partly because it is not immediately clear who that cost would fall on. Since many 558 demand sink technologies create connections between the power system and other sectors, 559 the costs for these technologies, as well as the revenue of their output products, will likely be 560 shared across sectors as well. This paper can form a basis for future work that could focus  Capacity is plotted as a fraction of the system's peak load, where the change in capacity is considered for 4 resource groups: solar, wind, firm (nuclear and natural gas with CCS), and Li-ion battery storage systems. The top row shows the results in the Northern system, the bottom row the Southern system. From left to right, the stringency of the carbon dioxide emissions limit increases.     Results are grouped by four levels of demand sink output product values and three levels of demand sink capital cost. The change in demand sink capacity is measured as a fraction of the system peak load as compared to the same demand sink scenario without the sensitivity applied.    Non-thermal resources like wind, solar and Li-ion batteries were all modeled as continuous resources (no fixed plant size), with a 0% minimum stable output, and a 100% hourly ramp rate. Li-ion batteries were modeled with an up-down efficiency of 92/92%. In Table C

Appendix D. Variable Renewable and Demand Assumptions
For both wind and solar profiles we use the open-source software tool PowerGenome [38]. The year of 2012 was chosen as base weather year used for the renewable resource availability data (e.g. hourly capacity factors). PowerGenome uses electric utility data from Public Utility Data Liberation (PUDL) database [39], which collates a relational database using public data from the U.S. Energy Information Administration, Federal Energy Regulatory Commission, and Environmental Protection Agency. PowerGenome also uses wind and solar availability profiles (at 13-km resolution) from Vibrant Clean Energy [40,41] using the NOAA RUC assimilation model data, and distributed generation profiles from Renewable Ninja web platform [42].
With this data, PowerGenome generates several hourly PV profiles grouped by the LCOE of the solar resources in each region with an associated maximum capacity in each cluster, such that we have 9 solar clusters in the Northern system and 5 solar clusters in the Southern system. The duration curves of all these clusters are nearly identical and are therefore represented as a single curve in Figure D  The left plot shows the duration curves in the Northern system, the right plot those in the Southern system. Only one representative curve is shown for solar, as the duration curves of the various solar curves in each system are nearly identical. Wind duration curves are classified by 'Wind (zone number) (cluster number)'.
As noted elsewhere, we are modeling hypothetical systems, not specific regional power systems. Our intention in this study is to capture differences in temporal profiles of renewable energy (and demand) that might commonly be encountered at different latitudes and test the impact on the value/role of energy storage, rather than to capture planning challenges particular to the actual ISO New England or ERCOT power systems. We thus do not consider variation in transmission interconnection or spur line costs for the wind clusters, as these costs are idiosyncratic and location specific.
The base electricity demand profile uses real demand data from each region in 2012, to match the year used in the wind and solar profiles. To account for load growth, the demand in each hour is scaled up to 2050 assuming a 1% growth rate each year. Additionally, a high electrification profile with electrification of transportation, space and water heating energy demands was generated by adding these electrified, partially time-shiftable loads to the base load. We allow the model to delay 90% of EV-loads by a maximum of 5 hours, 25% of water heating loads by 4 hours, and 30% of space heating loads by 2 hours, for use as a Demand Response (DR) resource. The electrified loads used were taken from the Electrification Futures Study Load Profiles from the National Renewable Energy Laboratory for the year 2050 [3]. The reference scenarios in this research use the high electrification and moderate technology advancement scenario, whereas the low electrification sensitivity analysis uses the low electrification scenario from the study. As shown in Figure D.2, electrification greatly increases the system peak and average demand. Moreover, electrification adds a strong seasonal component due to electrification of heating while at the same time it increases the short-time frequency due to the electrification of transportation among others.

Appendix E. GenX Configuration
The GenX electricity resource planning model [14] developed at MIT was used in this study to model a "greenfield" capacity plan -i.e., everything is built from scratch. The previous assumption is justified given the lifetime of existing generation assets (less than 30 years) and the explored year 2050. Arguably, the electricity generation resources operating in 2050 will have to be built in the decades to come and most current resources will not be in operation. In addition, we are not performing a planning study for a specific region. Instead, we use two "test systems" with differing climates as a way to explore the general impact of different demand profiles and VRE availability on outcomes of interest.
We model a time interval of one full year, divided into discrete one-hour periods and representing a future year (e.g., 2050). In this sense, the formulation produces a static longrun equilibrium outcome, because its objective is not to determine when investments should take place over time, but rather to produce a snapshot of the minimum-cost generation capacity mix under some pre-specified future conditions.
The model uses a linear relaxation of integer unit commitment constraints for thermal power plants. Integer unit commitment as developed in [43] and [44] is included in GenX. Linearization is accomplished by replacing the integer unit commitment and capacity addition variables with continuous variables, but subject to the same set of constraints. The integer unit commitment approach helps reducing the number of integer variables in a full binary unit commitment formulation (one binary variable for each thermal generator) to a more tractable formulation that uses integer variables to represent a set of resources of the same type in a cluster [44]. The linear relaxation of the unit commitment constraints set offers an additional significant improvement computational tractability while the increased abstraction error is kept below 1% as shown in [45].
We assume that transmission networks within each zone in both regional power systems are unconstrained with multiple VRE generation clusters within each zone. That is, each of the three zones in each system is represented as a "single node" without considering transmission losses or congestions between generators and demand. In principle, significant transmission reinforcements and expansions could take place in these systems by the year 2050 that would allow dispersed renewable resources, storage systems, and new generators to be accommodated. However, explicit consideration of transmission losses, congestions, and expansion decisions significantly increases model solution time. In addition, transmission networks typically represent a relatively modest share (around 5% [46]) of total power system costs. In the interest of computational tractability, explicit transmission power flows and expansion decisions are not considered within each system zone. However, transmission power flows, network capacity constraints and capacity expansion decisions are explicitly modeled (as simplified transport flows) for the transmission network paths between the three zones in each of the two systems.
The model is fully deterministic and assumes perfect foresight in planning and operational decisions. The model is capable of modeling day-ahead commitment of frequency regulation and operating reserves, which are employed by system operators to deal with errors in renewable energy or demand forecasts or unanticipated failures of generators or transmission lines. However, we considered regulation and reserve requirements in several preliminary analyses and found that these requirements did not have a significant effect on outcomes. In the interest of computational tractability and the ability to model a greater number of total cases, we therefore do not consider regulation or reserve requirements in the cases reported.

Appendix F. GenX Overview
Existing decision-making tools and technology valuation metrics are mainly cost-based and focus on the individual technology. The Levelised Cost of Electricity (LCOE) is an intuitive metric for technology-specific production cost, aggregating the investment and operational cost per unit of energy generated in $/MWh. This metric was practical in a 20 st century electricity system, containing exclusively dispatchable power plants. Today however, the LCOE has lost its meaning as it does not account for asset operability, prices and production variability, nor the impact that a plant's operation has on the electricity system in terms of reliability and operability as a whole (e.g., necessary back-up capacity, balancing and inertial services, reduced utilisation factors/increased emissions for other power plants). It is becoming clear that such services and technology features provide value to the power system but are not captured by existing valuation tools purely based on cost.
Rather than comparing different resources to one another based on cost (LCOE), the 'Value-Cost Model' compares the marginal cost of each resource to the marginal value that the same resource provides to the system if is deployed. Technologies that might look promising from a purely cost-based perspective might present short-lived value in the system with 'optimal' penetrations below expectations, and the other way around. The challenge is that although cost can be exogenously approximated, ultimately the incremental system value of a technology is a function of the prevalent system design and constraints and must be endogenously determined. Therefore, a centrepiece of value-based technology assessment methods are electricity system models which account for system integration effects and interrelated technology behaviour. The degree to which system requirements, environmental targets, and technical variety and detail are present in the model formulation must then be adequate for the decision-making or policy question.
For decarbonization and increasing penetration of variable renewable generation and battery storage it is essential to include enough operational detail in the model formulation. The reason for this is the need to capture challenges like the variable nature of wind and solar power, the different value sources of energy storage (energy, capacity deferral, network deferral, etc), the technical constraints of thermal plants (cycling, ramping limits, etc) and the synergies between different resources at the operational level. Systems value technical characteristics (flexibility, location, uncertainty, ability to provide services, etc) differently depending on the system's characteristics, consumption profiles and policies in place (CO 2 target, Clean Energy Standard or Renewable Standard).
Below we provide a summary of GenX, an electric power system investment and operations model described in detail elsewhere [14]. where h denotes an hour and H is the set of hours in a sub-period w. w ∈ W where w denotes a sub-period and W is the set of sub-period within the year. z ∈ Z where z denotes a zone/node and Z is the set of zones/buses in the network. l ∈ L where l denotes a line and L is the set of transmission lines in the network. g ∈ G where g denotes a technology cluster and G is the set of available resources. s ∈ S where s denotes a segment of consumers and S is the set of all consumers segments.

Indices and Sets
where R is the subset of resources subject to ramping limitations. U C ⊆ G where U C is the subset of resources subject to Unit Commitment requirements.
where O is the subset of resources subject to energy balance requirements.
where G z is the subset of resources in zone z . Notation Description y P + g new power investments on resource cluster g. y P − g retired power investments on resource cluster g. y P Σ g total available power capacity in cluster g. y F + l new investments on transmission capacity line l. y F Σ l total available transmission capacity line l.

Decision Variables
x inj g,h,w power injection from resource cluster g during hour h in sub-period w.
x wdw g,h,w power withdrawals from resource cluster g during hour h in sub-period w.
x lvl g,h,w energy balance level on resource cluster g during hour h in sub-period w.
x nse s,h,w,z curtailed demand segment s during hour h in sub-period w at zone z.
x f low l,h,w power flow in line l during hour h in sub-period w.
x commit g,h,w commit state cluster g during hour h in sub-period w.
x start g,h,w start events cluster g during hour h in sub-period w.
x shut g,h,w shutdown events cluster g during hour h in sub-period w.    Hourly capacity factor in hour h for cluster g. ρ ∨ g Minimum stable output for units in cluster g. η 0 g Self discharge rate for units in cluster g for energy balance.

Parameters
Continued on next page Ratio energy to power (duration) investments in cluster g. κ + g Maximum ramp-up rate for units in cluster g as % power capacity κ − g Maximum ramp-down rate for units in cluster g as % power capacity τ +

ST D i,z
Policy standard energy requirement (% total energy) for policy i in zone z.

Objective Function
The Objective Function in Eq. (F.1) minimizes over 3 components that are jointly cooptimized.
x nse s,h,w,z · n slope s + (F.1c) w∈W h∈H g∈U C x start g,h,w · c st g (F.1d) As shown in (F.1a) the method consist of minimizing the total system cost (or maximizing social welfare) with respect to investments variables y (e.g., new investments in power capacity y P + g ) and operational variables x (e.g., power injections x inj g,h,w ) over a one year period with W sub-periods and H hours per sub-period. The first component, Eq. (F.1b), of the objective function corresponds to the capacity expansion element of the problem. New investments in power (y P + g ) and transmission capacity (y F + l ) can be made at their respective investment costs c P i g and c F i l . Additionally, the total available power capacity (y P Σ g ) is subject to the fixed operation and maintenance cost (c P om g ). The second term of the objective function, Eq. (F.1c), corresponds to the economic dispatch element of the problem. Power injections (x inj g,h,w ) can be made at a cost equal to the variable operation and maintenance cost (c P o g ) plus the fuel cost (c f g ) from each resource cluster g ∈ G. Some resource clusters g ∈ O have the ability to make power withdrawals (x wdw g,h,w ) at their variable operation and maintenance cost (c P o g ) (e.g., energy storage). Additionally, non-served demand (x nse s,h,w,z ) from different consumer segments s ∈ S might be necessary in some of the nodes of the system z ∈ Z with a cost of unserved energy (n slope s ) per segment s. The last component of the objective function, Eq. (F.1d), corresponds to the unit commitment element of the problem. Some resource clusters g ∈ U C are subject to unit commitment constraints. These resources incur cycling costs (c st g ) every time a startup event (x start g,h,w ) is necessary.

Constraints
The optimization function defined in Eq. (F.1) is subject to different sets of constraints that define the feasible space for solutions to the variable sets y and x. Without constraints like the Demand Balance constraints the solution to our problem would be no investments nor production and the objective value would be zero.
Demand Balance Constraints . The Demand Balance constraints, Eq. (F.2), are among the main sets of constraints driving the optimization. For each hour h ∈ H, sub-period w ∈ W and zone z ∈ Z a constraint forces the electricity demand (d h,w,z ) to be equal to: (i) the power injections (x inj g,h,w ) from resource clusters g ∈ G z belonging to zone z, (ii) minus power withdrawals (x wdw g,h,w ) from resource clusters that can withdraw energy g ∈ O and belong to zone z, g ∈ G z , (iii) plus unserved energy (x nse s,h,w,z ) across all consumer segments s ∈ S, and (iv) the net effect of power flows (x f low l,h,w ) across lines l ∈ L that are connected to zone z.
Policy Constraints. Central to the motivation of this work are the policy constraints (e.g., clean or renewable energy mandates and CO 2 emission limits). These are sets of constraints that can broadly affect the feasible region for variable sets y and x. Moreover, these constraints in most cases greatly increase the complexity of the problem by linking a great number of operational variables x from different resource clusters g across all sub-periods w ∈ W , all hours h ∈ H, and in some cases all regions z ∈ Z. There are two main types of policies considered in this methodology. The first type, Eq. (F.3), are the 'direct decarbonization' policies that set a limit on the system's CO 2 emissions rate over the year. These policies can be implemented in two different ways Eq. (F.3a) and Eq. (F.3b). For Eq. (F.3a) the constraint is implemented for each zone z ∈ Z independently. The total CO 2 generation at each zone z is the product of the power injections (x inj g,h,w ) and the emissions rate ( CO2 g ) across all clusters in the zone g ∈ G z summed over all sub-periods w ∈ W and hours h ∈ H. The total CO 2 generation at each zone z must be less or equal than the total CO 2 allowance for that zone, calculated as the total zonal demand times the maximum emissions rate ( max z ) for that zone. Total zonal demand is calculated as the sum over all sub-periods w ∈ W and hours h ∈ H of the electricity demand of the zone (d h,w,z ) and the net energy losses (x wdw g,h,w − x inj g,h,w ) across resources that can withdraw energy in the zone (g ∈ (O ∩ G z )). For Eq. (F.3b) the 'direct decarbonization' policy constraint is implemented for the system as a whole. The change can be understood as if zones were pooling their CO 2 allowances together in order to reduce total system cost by improving the CO 2 allocation while ensuring that the total emissions in the system are kept to the same level. The change in going from Eq. (F.3a) to Eq. (F.3b) requires summing over all zones z ∈ Z on both sides of the constraint. w∈W h∈H g∈Gz z∈Z w∈W h∈H g∈Gz The second type of policy, Eq. (F.4), are the 'indirect decarbonization' policies or 'energy standards' like renewable portfolio or clean energy standards or a combination of both. In this case we do not set a limit or allowance but instead set a minimum requirement ( ST D i,z ) on the fraction of total demand (electricity demand plus net energy losses) that must to be served by resources that qualify g ∈ ST D i for each standard i ∈ I. As with Eq. (F.3) the implementation of these policies can be done in two ways Eq. (F.4a) and Eq. (F.4b). First, by zone as in Eq.(F.4a), power injections (x inj g,h,w ) are summed over all sub-periods w ∈ W and hours h ∈ H for all resources that are in each zone g ∈ G z and that qualify for the specific standard g ∈ ST D i for each standard i. These total injections must be greater than or equal to the minimum energy requirement set be the standard i. The minimum energy requirement set by the standard i is calculated as the total zonal demand times the policy standard energy requirement ( ST D i,z ) for that zone. Total zonal demand, as was the case for Eq. (F.3), is calculated as the sum over all sub-periods w ∈ W and hours h ∈ H of the electricity demand of the zone (d h,w,z ) and the net energy losses (x wdw g,h,w − x inj g,h,w ) across resources that can withdraw energy in the zone (g ∈ (O ∩ G z )). For Eq. (F.4b) each standard i ∈ I is implemented for the system as a whole. The change can be understood as if zones were pooling their total requirements together in order to reduce total system cost by improving the allocation while ensuring that the total quotas in the system are kept to the same minimum level. The change in going from Eq. (F.4a) to Eq. (F.4b) requires summing over all zones z ∈ Z on both sides of the constraint. Investment Related Constraints . Different constraints must be imposed on the investment related variables as shown in Eq. (F.5). First, for all resource clusters g ∈ G power investment retirements (y P − g ) times their unit size (ȳ P ∆ g ) must be less than the initial existing or brownfield investments (ȳ P ∨ g ) in the cluster, Eq. (F.5a). Second, for all resource clusters g ∈ G new power investment (y P + g ) times their unit size (ȳ P ∆ g ) must be less than the maximum deployable power investments (ȳ P ∧ g ) in the cluster, Eq. (F.5b). Finally, for all resource clusters g ∈ G the total available power capacity (y P Σ g ) is equal to the sum of the initial existing or brownfield investments (ȳ P ∨ g ), plus the unit size (ȳ P ∆ g ) times the net result of new investment (y P + g ) and investment retirements (y P − g ), Eq. (F.5c).
Additionally, investment related constraints for power lines between model zones must be imposed, Eq. (F.6). For all power lines l ∈ L network reinforcements (y F + l ) must be less or equal than the maximum deployable line reinforcements (ȳ F ∧ l ) in the line, Eq. (F.6a). For all lines, total available transmission capacity (y F Σ l ) is equal to the sum of the initial existing or brownfield transmission capacity (ȳ F ∨ l ), plus the network reinforcements (y F + l ), Eq. (F.6b).

Economic Dispatch Constraints.
A key component of this methodology compared to costbased approaches is the inclusion of technical constraints on the Economic Dispatch Problem. Basic micro-economic analysis that intersects demand with the supply curves for each hour falls short in that all technologies are assumed to have similar (if any) limitations on chronological changes in demand and available supply (e.g., variable renewable energy). In the absence of these types of constraints the solution to the economic dispatch problem is simply the generation from lowest marginal cost resources in ascending order in the system, i.e., purely cost-based. However, when including operational constraints and hours are chronologically coupled the result is that resources are differentiated not only on the basis of their costs, and that technical characteristics such as location, flexibility, and the ability to provide a range of services also provide value -and that in different power systems these characteristics are valued differently. The first group of constraints, Eq. (F.7), corresponds to the ramping, minimum stable output and maximum production limits. Ramping constraints are imposed in both directions. Ramp-down constraints, Eq. (F.7a), are set as the negative difference in power injections between consecutive hours (x inj g,h−1,w − x inj g,h,w ) for each hour h ∈ H in all sub-periods w ∈ W for all resource clusters subject to ramping limits but not to unit commitment requirements g ∈ (R − U C). For these resources the negative difference in power injections must be less than or equal to total available power capacity in the cluster (y P Σ g ) times the maximum ramp-down rate (κ − g ) of the cluster. Similarly, ramp-up constraints, Eq. (F.7b), are set as the difference in power injections between consecutive hours (x inj g,h−1,w − x inj g,h,w ) for each hour h ∈ H in all sub-periods w ∈ W for all resource clusters subject to ramping limits but not to unit commitment requirements g ∈ (R − U C). For these resources the difference in power injections must be less than or equal to total available power capacity in the cluster (y P Σ g ) times the maximum ramp-up rate (κ + g ) of the cluster.
Minimum stable output limits, Eq. (F.7c), are also imposed on all resource clusters that are not subject to unit commitment requirements g ∈ (G − U C). For each hour h ∈ H in all subperiods w ∈ W power injections (x inj g,h,w ) must remain above the minimum level determined by the total available power capacity in the cluster (y P Σ g ) times the stable output rate (ρ ∨ g ) for the cluster. Note that this minimum output level (ρ ∨ g ) may be 0 for some resources (e.g. solar PV, wind, Li-ion batteries). Maximum power output, Eq. (F.7d), limits are imposed to all resource clusters that are not subject to unit commitment requirements g ∈ (G − U C), including energy storage resources. For each hour h ∈ H in all sub-periods w ∈ W power injections (x inj g,h,w ) must remain below the maximum production level determined by the total available power capacity in the cluster (y P Σ g ) times the hourly capacity factor (ρ ∧ g,h ) for the cluster. The hourly capacity factor, ρ ∧ g,h , varies in each hour for weather-dependent variable renewable resources (to reflect variations in e.g. wind speeds or solar insolation or stream flows) and is 1.0 in all periods for all other resources. For resources with the ability to withdraw energy g ∈ O, including Li-ion battery energy storage, Eq. (F.7e) imposes a limit on maximum withdraw at each hour h ∈ H in all sub-periods w ∈ W to be less than or equal to the power capacity of the resource.
The second group of constraints, Eq. (F.8), corresponds to the energy balance and operation requirements for resource clusters that can carry an energy balance g ∈ O across time periods for all hours h ∈ H and sub-periods w ∈ W , such as Li-ion batteries modeled in this study. The energy balance constraint, Eq. (F.8a) enforces that the energy balance difference between one hour and the next one (x lvl g,h+1,w − x lvl g,h,w ) must be equal to increments minus reductions in energy stored. Energy is increased via energy withdrawals (x wdw g,h,w ) multiplied by the corresponding efficiency (η + g ) to account for losses. Energy is reduced via energy injections (x inj g,h,w ) divided by the corresponding efficiency (η − g ) to account for losses; and via internal losses calculated as the product between the energy balance (x lvl g,h,w ) during that hour and the self discharge rate (η 0 g ). Different operation limits must be imposed on these resource clusters. Eq. (F.8b) sets a limit on the maximum energy balance (x lvl g,h,w ) to be always less or equal than total available power capacity in the cluster (y P Σ g ) times the duration or energy-to-power ration (δ g ). Eq. (F.8c) sets a limit on the injections (x inj g,h,w ) to be less than or equal to the energy balance (x lvl g,h,w ) times the injection efficiency (η − g ). Eq. (F.8d) sets a limit on the withdrawals (x wdw g,h,w ) to be less than the remaining energy capacity. This remaining capacity is determined by taking the difference between the energy capacity (y P Σ g · δ g ) and the energy balance (x lvl g,h,w ).Finally, Eq (F.8e) limits the simultaneous operation of the injections (x inj g,h,w ) and withdrawals (x wdw g,h,w ) of the cluster to be less than or equal to the total available power capacity (y P Σ g ). Note that simultaneous charging and discharging of a storage resource is possible because we are modeling an aggregation of many discrete storage units. Some storage units may be charging while others charging in a given time period. In practice, this occurs very rarely, as any positive marginal cost of energy in a given time period will encourage the model to only charge or discharge so as to avoid incurring additional costs associated with round-trip storage losses. Simultaneous charging and discharging only improves the objective function during rare periods when ramp down constraints or minimum stable output constraints along with minimum up/down time constraints on thermal generators would create a negative marginal energy prince at a time period in the absence of storage, indicating that increasing consumption would reduce the objective function or improve total costs by avoiding a thermal unit shut-down and later start-up costs upon restart of that unit. In these rare periods, the model may choose to charge and discharge at the same time to incur round-trip storage losses and reduce system costs. Eq. (F.8e) ensures that in these rare moments, the sum total of charging and discharging does not exceed installed storage power capacity and thus remains physically feasible. Note also that Eq. (F.8c) and (F.8d) are generally redundant with the combination of constraints in Eq. (F.8a)-(F.8b) and the non-negativity constraint on x lvl g,h,w . However, during periods of simultaneous charging and discharging (which may occur during negative price periods as discussed above), these constraints limit the maximum charge and discharge in each period to physically feasible values considering the available current storage state of charge and maximum capacity. In cases where the remaining storage capacity (considering charge losses), (y P Σ g · δ g ) − x lvl g,h,w , is ≤ the charge power capacity y P Σ g , then the charge (or withdrawl) power in that time step, x wdw g,h,w , will be constrained by Eq. (F.8d). Similarly, when the available energy for discharge (considering discharge losses), x lvl g,h,w ·η − g , is ≤ the storage discharge power capacity, y P Σ g , then Eq. F.8c will be constraining on discharge power (or injection).
x inj g,h,w + x wdw g,h,w ≤ y P Σ g ∀g ∈ O, h ∈ H, w ∈ W (F.8e) The final group of economic dispatch constraints correspond to transmission constraints, Eq. (F.9). Constraints Eq. (F.9a) and (F.9b) impose the requirements that for all hours h ∈ H and sub-periods w ∈ W the power flow (x f low l,h,w ) in either direction must be less than or equal to the total available transmission capacity (y F Σ l ) for every line l ∈ L.

Unit Commitment Constraints.
Another key component of this methodology that contrasts with to cost-based approaches is the inclusion of technical constraints associated with the Unit Commitment (UC) Problem. Unit commitment refers to the scheduling of resources to be available to operate ahead of time. Including UC details is important to reflect the increasing need for cycling as variable renewable energy is further increased in the system. Additionally, UC helps model increased flexibility by including startup and shutdown decisions that, if not included, would require all resources to always operate between their minimum stable output and their maximum output, without any ability to take resources offline and bring them back online later. The first of these constraints, Eq. (F.10), imposes limitations on the number of committed units (x commit g,h,w ), startup events (x start g,h,w ), and shutdown events (x shut g,h,w ) for all resource clusters subject to UC constraints g ∈ U C for all hours h ∈ H and all sub-periods w ∈ W to be less than or equal to the number of units in the cluster. The number of units is calculated as the total available power capacity (y P Σ g ) divided by the unit size in the cluster (ȳ P ∆ g ).
x commit g,h,w ≤ y P Σ g /ȳ P ∆ g ∀g ∈ U C, h ∈ H, w ∈ W (F.10a) x start g,h,w ≤ y P Σ g /ȳ P ∆ g ∀g ∈ U C, h ∈ H, w ∈ W (F.10b) x shut g,h,w ≤ y P Σ g /ȳ P ∆ g ∀g ∈ U C, h ∈ H, w ∈ W (F.10c) Ramping, minimum stable output and maximum operation limits for clusters with UC requirements can be seen in Eq. (F.11) versus the same set of operating requirements for clusters without UC in Eq. (F.7). Ramp-down constraints are shown in Eq. (F.11a). The negative difference in power injections between consecutive hours (x inj g,h−1,w − x inj g,h,w ) for each hour h ∈ H in all sub-periods w ∈ W for all resource clusters subject to UC g ∈ U C must be less than or equal to the ramping down capacity of the committed units accounting for any start-up and shut-down events. Ramping capacity is calculated as the number of committed units that were not started-up in the same time period (x commit g,h,w − x start g,h,w ) times the cluster's unit size (ȳ P ∆ g ) times the maximum ramping rate (κ − g ). The ramping down capacity is reduced by the number of start-up events in the cluster during the same period (x start g,h,w ) since these units must operate above their minimum stable output (ρ ∨ g ) for units of size (ȳ P ∆ g ). Ramping down capacity is increased by units that are shut down during the time period allowing a larger change in the cluster's output. Thus, the minimum between the maximum output (ρ ∧ g,h ) and the maximum between the minimum stable output (ρ ∨ g ) or the maximum ramp-down rate (κ − g ), times the cluster's unit size (ȳ P ∆ g ) for all units shut down (x shut g,h,w ) are added to the ramp-down capacity. In other words, an individual unit shutting down can result in a change in aggregate output for the cluster equal to the greater of either. Similarly, for ramp-up constraints, Eq. (F.11b), the difference in power injections between consecutive hours (x inj g,h,w − x inj g,h−1,w ) for each hour h ∈ H in all sub-periods w ∈ W for all resource clusters subject to UC g ∈ U C must be less than or equal to the ramping up capacity of the committed units accounting for any start-up and shut-down events. Ramping up capacity is calculated as the number of committed units that were not started up in the same time period (x commit g,h,w − x start g,h,w ) times the cluster's unit size (ȳ P ∆ g ) times the maximum ramping rate (κ + g ). The ramping up capacity is increased by the number of start-up events in the cluster during the same period (x start g,h,w ). Newly started units increase output up to the minimum between their maximum output (ρ ∧ g,h )and the minimum between their minimum stable output (ρ ∨ g ) and the ramp-up rate (κ + g ), times the cluster's unit size (ȳ P ∆ g ) for started units (x start g,h,w ). Units shut down reduce the ramping up capacity by the total number of shutdown units (x shut g,h,w ) times the minimum stable output of this units (ρ ∨ g ) and the unit's size (ȳ P ∆ g ).
x inj g,h−1,w − x inj g,h,w ≤ (x commit g,h,w − x start g,h,w )κ − g ·ȳ P ∆ g − x start g,h,w ·ȳ P ∆ g · ρ ∨ g + x shut g,h,w ·ȳ P ∆ g · min(ρ ∧ g,h , max(ρ ∨ g , κ − g )) ∀g ∈ U C, h ∈ H, w ∈ W (F.11a) x inj g,h,w − x inj g,h−1,w ≤ (x commit g,h,w − x start g,h,w )κ + g ·ȳ P ∆ g + x start g,h,w ·ȳ P ∆ g · min(ρ ∧ g,h , max(ρ ∨ g , κ + g )) − x shut g,h,w ·ȳ P ∆ g · ρ ∨ g ∀g ∈ U C, h ∈ H, w ∈ W (F.11b) x inj g,h,w ≥ x commit g,h,w ·ȳ P ∆ g · ρ ∨ g ∀g ∈ U C, h ∈ H, w ∈ W (F.11c) x inj g,h,w ≤ x commit g,h,w ·ȳ P ∆ g · ρ ∧ g,h ∀g ∈ U C, h ∈ H, w ∈ W (F.11d) Minimum stable output, Eq. (F.11c), for clusters g ∈ U C is sets for power injections (x inj g,h,w ) to be greater than or equal to the number of units committed in the cluster (x commit g,h,w ) times the cluster's unit size (ȳ P ∆ g ) and the minimum stable output rate (ρ ∨ g ). Similarly, maximum operation limits, Eq. (F.11d) are set for power injections (x inj g,h,w ) to be less or equal than the number of units committed in the cluster (x commit g,h,w ) times the cluster's unit size (ȳ P ∆ g ) and the maximum output rate (ρ ∧ g,h ). Finally, constraints on the UC states and limitations accounting for minimum Up and Down Times must be included. Eq. (F.12a) sets the relationship for commitment state changes between consecutive hours (x commit g,h,w − x commit g,h−1,w ) to be equal to the net change in startup and shut-down events (x start g,h,w − x shut g,h,w ) in the cluster g ∈ U C for all hours h ∈ H and sub-periods w ∈ W . Minimum down-time requirements are imposed in Eq. (F.12b) setting the number of units offline (y P Σ g /ȳ P ∆ g − x commit g,h,w ) to be greater than or equal to the total number of shut-down events (x shut g,h,w ) during the preceding hours (h − τ − g ) and the current hour (h), where τ − g is the minimum down-time for units in cluster g. Minimum up-time requirements are imposed in Eq. (F.12c) setting the number of committed units (x commit g,h,w ) to be greater than or equal to the total number of start-ups (x start g,h,w ) during the preceding hours (h − τ + g ) and the current hour (h), where τ + g is the minimum up-time for units in cluster g.

Time Wrapping and Coupling
Our modeling approach does not assumes exogenous initial conditions for any of the time related components (e.g. unit commitment, ramping, energy storage balance, etc). Instead, we wrap-up initial and final conditions by setting the previous hour to the first hour of the first sub-period (h − 1, w|h = 1, w = 1) to be equal to the last hour of the last subperiod (h, w|h = H, w = W ) in the time horizon -e.g. the storage level at the end of the planning horizon is equal to the initial condition for the first hour of the planning horizon. Additionally, our methodology keeps the chronological coupling across different sub-periods w (e.g. weeks) ensuring the operation is consistent and optimized simultaneously for the full year. This is done by setting the previous hour to the first hour of each sub-period (h − 1, w|h = 1, w ∈ {2, .., W }) to be equal to the last hour of the previous sub-period (h, w − 1|h = H, w ∈ {2, .., W }) -e.g. the commitment state at the end of a sub-period is the initial commitment state for the next sub-period.