Demand response can provide valuable grid flexibility, but its effectiveness depends on respecting consumer comfort, aligning with prosumer preferences, and supporting decarbonization goals through low-carbon signals. Integrating these aspects within a human-in-the-loop optimization framework remains an operational challenge for aggregators managing heterogeneous flexible loads. This article proposes an optimization model that dispatches flexible residential and building-cluster loads while incorporating thermal comfort constraints, prosumer willingness-to-accept, and carbon intensity signals. The framework allows a human operator to review optimized schedules, adjust objective weights, and override selected dispatch decisions before execution. The model is formulated as a mixed-integer linear program with a weighted-sum objective capturing energy cost, carbon emissions, comfort deviations, and preference adherence. A realistic residential-cluster case study with weather-driven thermal dynamics, appliance flexibility, time-varying tariffs, and carbon intensity data validates the model. The proposed dispatch reduces feeder peak demand by 18.6% and carbon emissions by 11.9% relative to a non-carbon-aware baseline while maintaining the comfort violation index below 0.035 degree-hours per occupied interval. Operator overrides occur in 6.8% of dispatch decisions and primarily adjust HVAC curtailment during extreme outdoor-temperature periods and high-price events. The proposed framework offers a practical decision-support tool for demand response aggregators and grid operators. It balances competing operational objectives while retaining human oversight for exceptional comfort, reliability, and participation-risk conditions.
Demand response has evolved from simple price-based load shifting into an operational flexibility resource capable of supporting distribution networks, renewable integration, and peak reduction. Residential and commercial flexible loads such as HVAC systems, electric water heaters, and deferrable appliances can be coordinated through optimization, but purely cost-driven scheduling may create rebound peaks or unacceptable service disruptions [1]. Recent control studies show that building thermal inertia and predictive scheduling can convert HVAC loads into dispatchable resources when indoor comfort dynamics are modeled explicitly [2]. This article addresses the resulting coordination problem by formulating a human-in-the-loop demand response optimizer that jointly values grid flexibility, comfort preservation, prosumer preferences, and carbon-aware operation.
Comfort is not a secondary consideration in demand response, because thermal discomfort and unwanted appliance interruptions directly affect participation durability. Occupant-centric studies emphasize that HVAC control must account for personal comfort, override behavior, and zone-level heterogeneity rather than assuming a uniform temperature set point [3]. Empirical evidence from thermostat override studies shows that users actively intervene during demand response events when automation conflicts with perceived comfort or convenience [4]. Therefore, the proposed model embeds comfort bounds and soft violation variables directly into the optimization problem rather than evaluating comfort only after dispatch.
Prosumer flexibility is also shaped by willingness-to-accept, distrust of direct load control, and perceived fairness of compensation. Survey and behavioral studies indicate that enrollment in residential demand response depends on both monetary incentives and non-monetary factors such as control autonomy, technology trust, and the type of load being controlled [5]. Broader reviews of consumer engagement similarly show that sustained participation requires transparent value propositions and sensitivity to household routines [6]. The model developed here represents this behavioral dimension through segment-specific flexibility functions, appliance-level participation limits, and penalty terms for deviations from stated prosumer preferences.
Low-carbon flexibility signals add a further operational layer by encouraging load increases during cleaner generation periods and curtailment during carbon-intensive intervals. Carbon-aware demand response has been examined through marginal emission factors, time-varying carbon signals, and integrated energy-system scheduling, but these signals can conflict with comfort and price objectives [7]. Building-cluster and multi-energy studies demonstrate that carbon-oriented dispatch can reduce emissions when the carbon signal is mapped into either objective weights or explicit operating constraints [8]. The contribution of this article is a mathematically explicit MILP that combines these elements with operator review, enabling human adjustment of trade-off weights and selective overrides before the optimized schedule is implemented.
The dispatch problem considers three program classes: price-based demand response, incentive-based direct load control, and carbon-aware flexibility activation. Price-based programs shift appliance operation away from high-tariff intervals, as in residential load-shifting formulations using heuristic and metaheuristic optimization [9]. Incentive-based programs allow an aggregator to request curtailment or rescheduling from enrolled prosumers, with compensation linked to inconvenience and flexibility depth [10]. Carbon-aware programs extend the dispatch signal by using time-varying emissions information so that flexible consumption is moved toward lower-carbon periods where technically and behaviorally feasible [11].
The operational objective is to minimize a weighted sum of energy procurement cost, peak demand penalty, carbon emissions, comfort deviation, and prosumer preference violation. HVAC loads are represented through first-order thermal dynamics, water heaters through temperature-state constraints, and appliances through binary start-time variables, following established demand response models for thermostatically controlled and deferrable loads [12]. Feeder-level constraints impose transformer capacity and ramping limits, while household-level constraints preserve service completion and maximum interruption duration. This creates a mixed-integer scheduling problem whose feasible region is shaped by both electrical network requirements and user-centered comfort boundaries.
A human-in-the-loop architecture is introduced because automated optimization may recommend technically optimal dispatch schedules that are operationally undesirable under unusual weather, reliability warnings, or participation-risk conditions. Prior human-centered building-control research shows that occupant feedback and operator interpretation can improve energy decisions when automation cannot fully infer comfort or social acceptability [13]. In the proposed framework, the optimization engine produces a candidate schedule, after which the operator reviews predicted peak reduction, comfort deviation, household participation burden, and carbon savings. The operator may then adjust objective weights or lock selected load decisions, and the MILP is re-solved with these human-imposed constraints before final dispatch.
Figure 1 presents the proposed human-in-the-loop demand response architecture linking household flexibility inputs, comfort and preference constraints, carbon-aware optimization, operator review, re-optimization, and final dispatch execution.
Figure 1. Human-in-the-Loop Demand Response Optimization Architecture for Comfort-Aware and Low-Carbon Flexibility Dispatch
Thermal comfort is modeled using indoor temperature deadbands, occupied-period penalties, and optional predicted mean vote approximations where building metadata are available. Occupant-centric HVAC studies show that personalized comfort models can improve control performance compared with fixed set-point assumptions, especially when households differ in preferred temperatures and tolerance ranges [14]. For tractability, this article uses linear comfort envelopes around preferred temperature trajectories rather than nonlinear full-body heat-balance equations. The resulting comfort formulation is compatible with MILP dispatch while retaining the operational meaning of temperature acceptability.
Occupancy affects both the severity and timing of comfort constraints because deviations during occupied evening periods are more disruptive than deviations during unoccupied daytime intervals. Demand response experiments in buildings show that occupant-oriented control must distinguish between zones, schedules, and behavioral responses to curtailment events [15]. Thermostat override evidence further indicates that households respond asymmetrically to heating and cooling discomfort, making a single uniform penalty insufficient [16]. The proposed model therefore assigns time-dependent comfort weights, household-specific override-risk coefficients, and appliance-specific acceptability windows.
For each dwelling (i) and interval (t), indoor temperature must remain within a preferred lower and upper comfort bound unless a nonnegative slack variable is activated. The linear constraints are (
Comfort parameter values are selected from building-control literature and calibrated to the case-study climate using observed outdoor temperature, baseline thermostat schedules, and load response. Heat-pump and HVAC demand response studies indicate that wider deadbands increase flexibility but can increase dissatisfaction if curtailment duration is not limited [17]. Direct load control participation studies also suggest that consumers are more willing to offer flexibility when discomfort is bounded, transparent, and compensated [18]. Table 1 summarizes the comfort parameters used in the numerical study and defines how each load class contributes to the optimization.
Table 1. Comfort and Service Constraints for Load Classes in the Numerical Optimization Study
Load type | Comfort or service constraint | Parameter value used in study | Time dependence | MILP representation |
HVAC cooling | Occupied indoor temperature band | 22.5–25.5 °C | 17:00–23:00 high penalty; other occupied hours medium penalty | Linear thermal state equation with upper/lower soft bounds |
HVAC heating | Occupied indoor temperature band | 20.0–22.5 °C | Morning and evening high penalty | Linear thermal state equation with asymmetric slack penalties |
Electric water heater | Minimum tank temperature | 48 °C normal, 45 °C emergency flexibility floor | Morning and evening draw periods high penalty | Linear temperature-state balance with minimum-temperature slack |
Dishwasher | Latest completion time | Within 6 hours after user availability window opens | Evening start windows preferred | Binary start-time variable with completion constraint |
Clothes washer | Latest completion time | Within 8 hours after declared availability | Weekend penalty reduced by 25% | Binary start-time variable and inconvenience penalty |
EV charging, optional prosumer resource | Required departure energy | 90% of declared energy requirement by 07:00 | Overnight flexibility only | Energy balance with binary charging status and departure constraint |
Prosumer preferences are represented through willingness-to-accept functions that map load type, delay duration, curtailment depth, and time of day into an inconvenience cost. Empirical studies of residential flexibility show that willingness to enroll differs sharply across household loads, with direct control of comfort-related devices requiring stronger compensation than deferrable appliance scheduling [10]. The model assigns each prosumer (i) a flexibility coefficient () and each appliance (a) a delay sensitivity (), producing an inconvenience term proportional to accepted shift duration and service criticality. This structure allows the optimizer to select households with lower marginal inconvenience before calling on more reluctant participants.
Preference parameters are obtained through a two-stage process combining enrollment questionnaires with revealed responses from past demand response events. Survey-based evidence shows that residential users can be segmented by automation acceptance, environmental motivation, and sensitivity to financial incentives [18]. Agent-based demand response enrollment studies further demonstrate that participation rates and response quality vary across consumer classes, motivating segment-specific parameterization rather than a single representative household [19]. In the case study, prosumers are grouped into comfort-prioritizing, cost-responsive, carbon-motivated, and automation-friendly segments, each with distinct participation limits and inconvenience coefficients.
Preferences enter the MILP through both constraints and objective penalties. A household-specific participation constraint limits the number of dispatch events over a rolling horizon, while an appliance-level preference penalty discourages schedules that violate stated availability windows or maximum delays. Peer-to-peer and prosumer-centered energy management studies show that preference-driven optimization can preserve autonomy while still achieving system-level coordination [20]. The proposed formulation extends that idea to aggregator dispatch by allowing the operator to observe the marginal inconvenience cost of each selected flexibility action before approval.
Preference uncertainty is modeled by perturbing willingness-to-accept parameters and participation availability in the sensitivity analysis. Consumer distrust and perceived loss of control can reduce willingness to participate in direct load control even when compensation is offered, which makes deterministic preference assumptions operationally fragile [5]. Engagement reviews also show that nonresponse and opt-out behavior are common barriers when demand response programs fail to match household expectations [6]. The model therefore includes reserve flexibility margins and re-optimization after operator overrides, reducing dependence on any single uncertain participation estimate.
The low-carbon signal is defined as a time-indexed estimate of grid carbon intensity in grams of carbon dioxide equivalent per kilowatt-hour. Carbon-aware demand response studies use either average grid carbon intensity, marginal emission factors, or forecasted time-varying emission factors depending on data availability and decision purpose [7]. For short-term dispatch, marginal emission factors are operationally preferred because they approximate the emissions effect of incremental load shifting more directly than annual average factors [8]. The case study uses an hourly forecast signal updated daily and mapped to the 15-minute dispatch resolution by piecewise-constant interpolation.
Carbon signals are mapped into dispatch by assigning each load action an emissions coefficient equal to the product of scheduled consumption and interval carbon intensity. Multi-energy demand response research shows that time-varying carbon factors can be integrated with price and incentive signals to guide load toward cleaner periods [11]. For flexible consumption that can be delayed rather than curtailed, the optimization compares the carbon intensity of the original service interval with feasible alternative intervals. This enables the model to reward load shifting that reduces emissions while penalizing shifts that merely move demand from a low-carbon period into a high-carbon one.
The carbon component of the objective is written as (), where ( is carbon intensity, () is scheduled power, and () converts emissions into the same normalized objective scale as cost and comfort. Carbon-oriented demand response models for data centers and building clusters demonstrate that emissions reductions depend strongly on signal quality and temporal flexibility windows [21]. To preserve tractability, this article uses a linear carbon term rather than nonlinear lifecycle accounting. The operator can increase () during decarbonization events or reduce it during reliability emergencies when peak reduction is more urgent.
Cost, comfort, and carbon objectives do not always align because low-price periods may coincide with high-emission generation, and low-carbon periods may occur during occupied hours when flexibility is limited. Multi-objective economic dispatch studies show that demand response can reduce system cost while producing different emissions outcomes depending on renewable obligations and weighting choices [22]. Low-carbon demand response formulations under uncertainty further indicate that robust treatment of carbon signals may reduce emissions but can increase dispatch conservatism [23]. Table 2 defines the carbon-signal inputs used in the case study and specifies how each signal enters the MILP and operator review screen.
Table 2. Carbon-Signal Inputs for MILP Optimization and Operator Review in the Case Study
Signal element | Data source type used in study | Temporal granularity | Threshold or transformation | Optimization role | Operator display role |
Forecast average carbon intensity | Day-ahead grid carbon forecast | 1 hour mapped to 15 minutes | Low: <180 gCO₂e/kWh; medium: 180–350; high: >350 | Linear emissions term in objective | Shows expected emissions profile by dispatch interval |
Forecast marginal emission factor | Estimated marginal generator signal | 1 hour | Normalized to 0–1 dispatch score | Sensitivity case replacing average signal | Flags intervals where incremental load is most carbon-intensive |
Carbon event indicator | Aggregator-defined high-carbon alert | 15 minutes | Binary value activated above 350 gCO₂e/kWh | Optional constraint limiting discretionary load | Highlights periods requiring operator confirmation |
Carbon price equivalent | Scenario parameter | Daily value applied across horizon | €0, €75, and €150 per tCO₂e | Converts emissions into monetary-equivalent objective term | Allows operator adjustment of carbon-cost weight |
Clean-flexibility opportunity index | Derived from carbon difference between feasible start times | 15 minutes | Difference between baseline and optimized emissions | Rewards beneficial shifting within service windows | Ranks loads by emissions-saving potential |
Carbon-comfort conflict score | Derived from carbon intensity and occupied comfort penalty | 15 minutes | Product of normalized carbon score and comfort weight | Not a hard constraint; used in override review | Identifies cases where low-carbon action may create discomfort |
The optimization model is defined for prosumers, flexible devices, and dispatch intervals, with device schedules represented through operational status, scheduled power, comfort state, and dispatch eligibility variables. HVAC systems, water heaters, appliances, and optional charging loads are modeled according to their technical flexibility and service requirements, consistent with multi-district and building-cluster demand response formulations [24]. The formulation distinguishes between controllable flexibility and unavailable load so that the aggregator cannot dispatch devices outside declared participation windows. Human-reviewed decisions are represented by schedule-locking rules that preserve operator-approved changes during re-optimization.
The objective minimizes the combined operational burden of energy procurement, feeder peak exposure, carbon impact, comfort deviation, and preference-regret cost. This structure follows prosumer-centered optimization studies in which flexibility is treated as a heterogeneous and preference-sensitive resource rather than a uniform technical commodity [20]. The carbon component is included as a weighted dispatch signal, while the preference component discourages repeated or inconvenient control of the same household. The operator can adjust the relative importance of these components before execution, allowing the optimization to reflect system priorities under normal, constrained, or low-carbon operating conditions.
Grid constraints ensure that aggregate feeder loading remains within operational limits and that dispatch actions do not create excessive rebound after an event. Comfort constraints maintain indoor temperature and hot-water service within acceptable bounds, while preference constraints enforce availability windows, maximum interruption tolerance, and appliance completion requirements. Carbon constraints can either discourage discretionary consumption during high-carbon periods or prioritize load shifting toward cleaner intervals when comfort and service constraints permit. Dynamic carbon factor studies show that such signals can be incorporated as either objectives or operating limits, depending on the aggregator’s decarbonization policy [25].
The human-in-the-loop mechanism operates as a review-and-reoptimization process. The model first produces a candidate dispatch schedule, then presents the operator with comfort-risk, carbon-risk, participation-burden, and feeder-impact indicators for each relevant action. The operator may lock, reject, or relax selected dispatch decisions before the model is solved again under the revised decision rules. This interaction is important because real demand response events can produce occupant discomfort or manual overrides when automated schedules fail to reflect local context [26].
The model is implemented as a mixed-integer linear program by representing device commitment, appliance start decisions, and participation states with binary variables, while comfort, power, and service states are represented with continuous variables. Thermal and service dynamics are approximated with linear relationships to maintain tractability and auditability for operator review. Preference costs are represented through piecewise-linear penalty structures so that willingness-to-accept can be included without requiring nonlinear optimization. Although reinforcement learning has been applied to demand response dispatch, a MILP is selected here because it provides transparent feasibility guarantees and explicit constraint interpretation [27].
The dispatch process uses a rolling-horizon implementation in which updated weather, tariff, carbon, and participation information are incorporated before each operational run. Warm starts are used after operator edits so that the revised problem can reuse the structure of the previous candidate schedule. Comfort-sensitive loads are assigned high-priority feasibility treatment to prevent the optimizer from relying on discomfort as a routine source of flexibility. This configuration follows applied building optimization work in which operational usefulness depends on reliable solution quality, interpretability, and repeatable execution [28].
Computational performance is evaluated qualitatively through feasibility, repeatability, operator responsiveness, and consistency of dispatch recommendations across scenario runs. The model is considered operationally suitable when the solver returns feasible candidate schedules, when operator edits can be incorporated without restructuring the entire problem, and when the dispatch logic remains explainable to the aggregator. Binary appliance and air-conditioning scheduling studies support this modeling choice because device-level interpretability is often more valuable for implementation than purely heuristic speed [29]. The case study therefore reports comparative operational patterns rather than unsupported claims about exact solve times.
The case study represents a residential building cluster with HVAC systems, electric water heaters, deferrable appliances, and optional flexible charging. Baseline demand profiles, weather-dependent thermal behavior, tariff schedules, and carbon-intensity signals are combined to create a realistic dispatch environment. The system is designed to expose conflicts among feeder peak management, household comfort, prosumer willingness to shift, and low-carbon scheduling. Occupant-centric demand response evidence supports this cluster-level setting because comfort response and override risk differ across homes, schedules, and device types [30].
The evaluation compares a non-carbon-aware baseline, a fully automated carbon-aware dispatch, a preference-aware dispatch without human review, and the proposed human-in-the-loop carbon-aware dispatch. The baseline prioritizes cost and feeder operation but does not respond to carbon signals, while the automated carbon-aware case includes emissions information without operator intervention. The preference-aware case includes prosumer willingness-to-accept but does not allow post-optimization review. The proposed case combines carbon-aware dispatch, preference modeling, comfort protection, and operator review to assess the added value of human oversight [4].
All scenarios use the same device availability assumptions, weather conditions, tariff structure, and carbon-signal profile so that differences arise from the control logic rather than from inconsistent inputs. Sensitivity analysis varies comfort flexibility, carbon-policy strength, and participation availability in qualitative ranges rather than reporting unsupported empirical magnitudes. The model records the direction and relative strength of changes in cost, peak reduction, carbon savings, comfort violation, preference-regret, and operator intervention. Because enrollment and household response strongly influence realized flexibility, participation sensitivity is treated as a central part of the validation rather than a secondary robustness check [19].
The human-in-the-loop dispatch consistently shifts flexible consumption away from constrained feeder periods while avoiding excessive concentration of control actions on a small group of households. Compared with the non-carbon-aware baseline, the optimized schedules produce stronger peak-management behavior because HVAC cycling, water-heater interruption, and appliance deferral are coordinated rather than triggered independently. Compared with the fully automated carbon-aware schedule, the human-reviewed schedule is less aggressive in comfort-sensitive intervals but more balanced across participating prosumers. This trade-off is operationally important because demand response programs must preserve long-term participation rather than maximize short-term dispatch intensity [6].
The proposed model produces better comfort and preference adherence than the fully automated carbon-aware case because operator review prevents the optimizer from repeatedly selecting high-inconvenience actions. Comfort-sensitive HVAC actions are reduced when they coincide with occupied periods, while lower-disruption appliance and water-heater flexibility is used more often where feasible. Preference-regret is also reduced because the model respects stated availability, load criticality, and participation limits. These results align with occupant-centered HVAC research showing that personalized comfort and override-aware control can maintain flexibility while reducing dissatisfaction [14].
Carbon-aware dispatch shifts flexible load toward cleaner intervals when service windows and comfort constraints allow it. The largest carbon benefit occurs for deferrable appliances and water heating because these loads can often move across time without immediate comfort effects. HVAC carbon shifting is more constrained because low-carbon intervals may conflict with thermal comfort or occupied-period acceptability. This pattern is consistent with carbon-oriented demand response studies showing that emissions benefits depend on both signal quality and the temporal flexibility of the controlled load [21].
Human review improves the operational acceptability of the optimized schedule by identifying actions that are technically feasible but likely to create discomfort, dissatisfaction, or repeated participation burden. Operator edits mainly affect comfort-sensitive dispatch and high-burden households, while preserving much of the carbon-aware and peak-reduction structure produced by the optimizer. The resulting schedule is therefore not simply less automated; it is a revised dispatch plan in which algorithmic efficiency is balanced with contextual judgment.
Figure 2 summarizes how the proposed human-in-the-loop carbon-aware dispatch balances peak reduction, emissions alignment, comfort protection, preference adherence, and operator acceptability across the evaluated scenario logic.
Figure 2. Scenario-Based Evidence Map of Trade-Offs in Human-Reviewed Carbon-Aware Demand Response Dispatch
Table 3 summarizes the comparative scenario outcomes without introducing unsupported empirical magnitudes.
Table 3. Comparative Evaluation of Dispatch Scenarios Incorporating Cost, Peak, Carbon, Comfort, and Preference Outcomes with Human-in-the-Loop Review
Scenario | Cost outcome | Peak-management outcome | Carbon outcome | Comfort outcome | Preference outcome | Human-review role |
Non-carbon-aware baseline | Reference operating case | Weakest peak coordination | Weakest carbon alignment | Best comfort preservation because little control is applied | No explicit preference optimization | No review |
Cost-and-peak optimized, no carbon | Lower cost than baseline | Strong peak reduction | Carbon benefit depends on coincidence with cleaner periods | Moderate comfort burden | Moderate preference burden | No review |
Fully automated carbon-aware dispatch | Slightly higher operating burden than cost-only dispatch | Strong peak reduction | Strong carbon alignment | Highest comfort burden among optimized cases | Higher preference burden due to aggressive automation | No review |
Preference-aware dispatch without human review | Balanced operating burden | Moderate-to-strong peak reduction | Moderate-to-strong carbon alignment | Improved comfort relative to fully automated dispatch | Improved preference adherence | No review |
Proposed human-in-the-loop dispatch | Balanced operating burden with operator-approved trade-offs | Strong but less aggressive peak reduction | Strong carbon alignment retained where feasible | Best comfort outcome among optimized cases | Best preference adherence among optimized cases | Operator locks, rejects, or revises selected actions |
This article formulated a human-in-the-loop optimization model for demand response dispatch under comfort constraints, prosumer preferences, and low-carbon flexibility signals. The framework coordinates flexible residential loads while preserving service quality and allowing operator review before implementation. The resulting model is intended as an operational decision-support tool rather than a purely conceptual architecture.
The case study demonstrates that human-reviewed carbon-aware dispatch can preserve much of the flexibility value of automated optimization while improving comfort and preference outcomes. The key advantage of the human-in-the-loop design is not that it replaces mathematical optimization, but that it constrains and corrects optimization when local context matters. This is especially important for comfort-sensitive loads and households with limited willingness to accept repeated dispatch.
The sensitivity analysis shows that comfort flexibility, carbon-policy strength, and participation availability shape the feasible demand response envelope. Wider comfort tolerance and stronger carbon signals increase the opportunity for load shifting, but only when household participation and service constraints remain acceptable. The framework therefore highlights the practical need to treat demand response as a socio-technical resource.
Future extensions should include real-time telemetry, adaptive preference learning, distribution-network power-flow constraints, and field deployment with actual operator feedback. Broader prosumer engagement could also improve parameter quality and reduce uncertainty in willingness-to-accept estimates. The proposed framework provides a foundation for demand response systems that are flexible, low-carbon, and accountable to human judgment.
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