Feature request: Capacity tariff

[snauwaertc]

There is a capacity tariff in the region where I live (e.g., yearly average of peak 15mins kWh per month is used to calculate net use cost). Could we include this in the price calculation?

[thibaultmol]

I'll try and word exactly how it works.. cause it's a bit messy. (I made the text using AI with a few modifications; cause it can just make a more overviewable thing than I can), but I have fully read it and it matches with my understanding of the capacity tariff:

Quarter-hour Power Calculation

The foundation of the capacity tariff is the "kwartiervermogen" (quarter-hour power):

Quarter-hour Power (kW) = Quarterly Consumption (kWh) × 4

Your digital meter records your consumption for each 15-minute period throughout the day (96 quarters per day).

For example, if you consumed 1.5 kWh during a specific 15-minute period, your quarter-hour power for that period would be:

Quarter-hour Power = 1.5 kWh × 4 = 6 kW

Monthly Peak Determination

Monthly Peak = MAX(Quarter-hour Power) for all 15-minute periods in a month

This uses the highest quarter-hour power measurement recorded during any 15-minute interval in that month.

Billing Peak Calculation

For annual billing (with digital meter):

Billing Peak = AVG(Monthly Peaks from last 12 months)

If fewer than 12 months of data are available (e.g., you recently got a digital meter), only the available months are used in the calculation. Only monthly peaks measured after January 1, 2023 count toward this average.

Capacity Tariff Formula

For digital meters:

Capacity Component = MAX(Billing Peak, 2.5 kW) × Cost per kW

Where in 2025, Cost per kW is approximately:

• 42.33 euros (including VAT) annually
• 3.53 euros (including VAT) monthly

The minimum capacity charge corresponds to 2.5 kW (so tbc, even if you only had a peak of 1kW... you'd pay the same as if you had 2.5kW peak. Because that's the minimum), resulting in a minimum annual payment of approximately 107.06 euros (including VAT).

Example Calculation

If your monthly peaks over the past 12 months were: 4.2 kW, 3.8 kW, 4.0 kW, etc., with an average of 3.9 kW:

Capacity Component = 3.9 kW × 42.33 euros/kW = 165.09 euros annually

This would be your capacity component of the network costs, which represents approximately 7% of a typical household's electricity bill.

For households with a social tariff, the capacity tariff doesn't apply.

[snauwaertc]

Thanks for that clarification. That's indeed what was meant.

Here's already some output for an implementation approach (to be discussed). I also understood that the capacity tariff may become dynamic in the future (in line with energy pricing), but still work with an AVG(MAX(...)) approach. We may want to factor that in as well.

Optimizing for Capacity Tariffs (Demand Charges) in EMHASS

This document outlines a proposed approach to enhance EMHASS to consider capacity tariffs (often referred to as demand charges) in its optimization process. These tariffs are typically based on the peak power consumption (e.g., highest average kW over a 15-minute interval) within a billing period (e.g., monthly).

1. Rationale and Benefits

Capacity tariffs can form a significant portion of an electricity bill. Optimizing for them involves not just reducing total energy consumption (kWh) but also managing and reducing the peak power demand (kW).

• Cost Reduction: Directly targets a potentially large cost component of the electricity bill.
• Improved Load Shaping: Encourages smoother load profiles by avoiding high, short-duration peaks.
• Enhanced Grid Friendliness: Helps reduce stress on the electricity grid during peak times.

2. Understanding Capacity Tariffs

Typical characteristics:

• Peak Measurement: Based on the highest average power demand over a specified interval (e.g., 15 minutes, 30 minutes, 1 hour) within a billing cycle (usually a month).
• Billing Cycle: The peak for the current month sets the charge for that month.
• Tariff Rate: A cost per unit of peak power (e.g., €/kW/month).
• Longer-Term Averaging (Optional): Some tariffs might be based on an average of monthly peaks over a longer period (e.g., a year). This proposal primarily focuses on managing the current month's peak, which is the most direct control point.

3. Proposed Modeling Approach within EMHASS

This involves tracking the current month's peak demand and incorporating a cost for exceeding it into the optimization.

3.1. Persistent State Tracking:

EMHASS needs to store and retrieve the peak demand achieved so far within the current billing month.

• State Variable (Persistent):
  • Current_Month_Peak_Power_kW: The highest average power demand (over the defined tariff interval, e.g., 15 minutes) recorded in the current billing month up to the last optimization run. This value must be saved by EMHASS and reloaded for each new optimization.
  • This variable is reset at the beginning of each new billing month.

3.2. Optimization Horizon Variables and Constraints:

Within each optimization run (e.g., for the next 24-48 hours):

• Input (Calculated per Tariff Interval i):
  • Total_Load_kW[i]: The sum of all forecasted and scheduled loads (grid import) for each tariff-relevant interval i (e.g., each 15-minute block) within the optimization window. This is derived from the optimizer's scheduling of individual appliances, EV, heating, battery, etc.
• Decision Variable (for the current optimization run):
  • Prospective_Horizon_Peak_Power_kW: A variable representing the maximum Total_Load_kW[i] that will occur across all intervals i within the current optimization horizon.
• Constraint Linking Prospective_Horizon_Peak_Power_kW to Total_Load_kW[i]:
  • Prospective_Horizon_Peak_Power_kW >= Total_Load_kW[i] for all relevant intervals i.
    (The optimizer, aiming to minimize costs, will effectively set Prospective_Horizon_Peak_Power_kW to the actual peak during the horizon if that peak influences costs.)

3.3. Cost Calculation in Objective Function:

The core of the capacity tariff optimization is adding a cost component that penalizes the creation of a new, higher monthly peak.

• Capacity Tariff Rate Parameter:

  • Capacity_Tariff_Rate_per_kW_per_Month: The cost per kW of peak demand for the month (e.g., €2.50 / kW / month).

• Objective Function Component for Incremental Capacity Cost:
  Let Peak_Increase_kW be an auxiliary variable.
  The incremental cost term added to the objective function to be minimized is:
  Incremental_Capacity_Cost_Term = Peak_Increase_kW * Capacity_Tariff_Rate_per_kW_per_Month

  With the following constraints to define Peak_Increase_kW (linearizing the max(0, ...) logic):

  1. Peak_Increase_kW >= Prospective_Horizon_Peak_Power_kW - Current_Month_Peak_Power_kW
  2. Peak_Increase_kW >= 0

  This formulation ensures that a cost is only incurred if the Prospective_Horizon_Peak_Power_kW (the peak planned for the upcoming optimization window) exceeds the Current_Month_Peak_Power_kW (the peak already set for the month). The optimizer will try to keep Peak_Increase_kW at 0 if possible.

3.4. Post-Optimization Update:

• After an optimization run, EMHASS determines the actual highest scheduled Total_Load_kW[i] from its plan.
• The persistent Current_Month_Peak_Power_kW is updated:
  Current_Month_Peak_Power_kW = max(Current_Month_Peak_Power_kW, Actual_Scheduled_Peak_this_Run_kW)

3.5. Handling Longer-Term (e.g., Yearly) Averaging:

Directly optimizing a yearly average of monthly peaks in each short-term run is complex. Practical strategies include:

• Monthly Peak Targeting: Users can define a Target_Monthly_Peak_kW parameter for EMHASS. The cost calculation would then penalize exceeding max(Current_Month_Peak_Power_kW, Target_Monthly_Peak_kW). This allows users to work towards a yearly average by setting conservative monthly targets.
• Manual/External Adjustment: Users can monitor their evolving yearly average and adjust their monthly targets or operational strategies accordingly.
• Focus on Current Month: Often, minimizing the current month's peak provides the most significant and actionable savings.

4. Configuration Parameters Needed for EMHASS

• enable_capacity_tariff_optimization: Boolean (e.g., true/false).
• capacity_tariff_rate_cost_per_kw: The monetary rate for the tariff (e.g., 2.50 if currency is defined elsewhere or implied).
• capacity_tariff_interval_minutes: The interval over which the peak is measured (e.g., 15, 30, 60). EMHASS will need to aggregate its internal shorter timesteps to these intervals for peak calculation.
• capacity_tariff_billing_day_of_month: (Optional, for automating reset) The day of the month when the billing cycle resets and Current_Month_Peak_Power_kW should be reset (e.g., 1).
• persistent_state_path: Path to a file where Current_Month_Peak_Power_kW and its last update timestamp/month can be stored.
• target_monthly_peak_kw (Optional): A user-defined target monthly peak in kW.

5. Problem Type and Solver Impact

• The addition of these variables and linearized constraints should keep the problem as a Mixed-Integer Linear Program (MILP) if the base EMHASS model is already MILP.
• The increase in model size is relatively small, and performance impact on modern solvers should be manageable.
• The main implementation complexity lies in the persistent state management and the logic for aggregating loads to the tariff interval.

6. Conclusion

Incorporating capacity tariff optimization into EMHASS would allow it to make more economically sound decisions by managing peak power demand alongside energy consumption. This feature is crucial for users in regions with demand charges, providing a more comprehensive approach to home energy cost minimization. Careful management of the persistent peak state and clear configuration options for the user will be key to a successful implementation.

[purcell-lab]

Thanks for your consideration of this capability enhancement.

In Australia we call this demand tarrifs and it calculated by considering the highest 30 minute average power level for the month over a daily demand window which maybe 4pm-8pm. So similar in structure but a bit different so some flexibility in parameters would be welcome.

IMHO these are difficult for consumers to understand and are not cost reflective on behalf of the networks which seem akin to an unfair revenue generation strategy in behalf of the networks. They are very difficult to optimize for without the type of approach proposed here.

Currently in Australia some folks have taken to adjusting the load_cost_forcast during the demand window with +$1/ kWh, which doesn't optimize but does avoid consumption at this time.

I'll post a link to this issue to our AU forum so hopefully we can get some extra perspectives here.

[snauwaertc]

Hi all,
I gave it some more thought: The original approach, where the full monthly capacity charge for an increase is applied to the day that sets the new peak, could heavily penalize that specific day's optimization. This might lead to overly conservative behavior early in the month or on days where a slightly higher peak might be economically justified over the entire month.

Therefore, I created a 2-stage approach with a "model day" in a specific month. Let me know what you think.

Optimizing for Capacity Tariffs (Demand Charges) in EMHASS

This document outlines a proposed approach to enhance EMHASS to consider capacity tariffs (often referred to as demand charges) in its optimization process. These tariffs are typically based on the peak power consumption (e.g., highest average kW over a 15-minute interval) within a billing period (e.g., monthly).

1. Rationale and Benefits

Capacity tariffs can form a significant portion of an electricity bill. Optimizing for them involves not just reducing total energy consumption (kWh) but also managing and reducing the peak power demand (kW).

• Cost Reduction: Directly targets a potentially large cost component of the electricity bill.
• Improved Load Shaping: Encourages smoother load profiles by avoiding high, short-duration peaks.
• Enhanced Grid Friendliness: Helps reduce stress on the electricity grid during peak times.

2. Understanding Capacity Tariffs

Typical characteristics:

• Peak Measurement: Based on the highest average power demand over a specified interval (e.g., 15 minutes, 30 minutes, 1 hour) within a billing cycle (usually a month).
• Billing Cycle: The peak for the current month sets the charge for that month.
• Tariff Rate: A cost per unit of peak power (e.g., €/kW/month).
• Longer-Term Averaging (Optional): Some tariffs might be based on an average of monthly peaks over a longer period (e.g., a year). This proposal primarily focuses on managing the current month's peak, which is the most direct control point.

3. Proposed Modeling Approach within EMHASS

The proposed approach utilizes a two-stage optimization strategy to balance daily operational costs with monthly capacity charges. The first stage establishes a planned monthly peak, and the second stage performs daily optimizations guided by this plan.

3.A. Stage 1: Monthly Planning Optimization (Establish Planned Monthly Peak)

This stage is typically run once at the beginning of each billing month.

• Objective: To determine an economically optimal Planned_Monthly_Peak_kW for the current billing month.
• Methodology:
  1. Define a "Model Day": Construct a representative load and generation profile for a typical day in the billing month. This can be based on historical averages (e.g., temperature-driven loads, typical appliance usage patterns for the season), user-defined profiles, or other forecasting methods available to EMHASS.
  2. Amortized Cost Calculation: Perform an optimization for this "Model Day." The capacity charge component in the objective function uses an amortized rate:
     • Amortized_Capacity_Cost = Prospective_Peak_kW_for_Model_Day * (Capacity_Tariff_Rate_per_kW_per_Month / N_days_in_billing_month)
     • Prospective_Peak_kW_for_Model_Day is a decision variable representing the peak demand on the model day.
     • N_days_in_billing_month is the number of days in the current billing cycle.
  3. Output:
     • Planned_Monthly_Peak_kW: The peak demand resulting from the model day optimization. This value is stored (e.g., in the persistent_state_path) and used by the daily operational optimizer throughout the month.
     • This variable is reset/recalculated at the beginning of each new billing month.

3.B. Stage 2: Daily Operational Optimization

This stage runs regularly (e.g., daily or intra-day) to manage energy for the upcoming horizon (e.g., 24-48 hours).

• Persistent State Variable (Tracked Continuously):

  • Actual_Current_Month_Peak_Power_kW: The highest average power demand (over the defined tariff interval) recorded in the current billing month up to the last optimization run. This value must be saved by EMHASS (e.g., in persistent_state_path) and reloaded. It is reset at the beginning of each new billing month.

• Inputs for Daily Optimization:

  • Planned_Monthly_Peak_kW (from Stage 1).
  • Actual_Current_Month_Peak_Power_kW.
  • Capacity_Tariff_Rate_per_kW_per_Month.

• Optimization Horizon Variables and Constraints (within each daily run):

  • Input (Calculated per Tariff Interval i):
    • Total_Load_kW[i]: The sum of all forecasted and scheduled loads (grid import) for each tariff-relevant interval i (e.g., each 15-minute block) within the optimization window.
  • Decision Variable (for the current optimization run):
    • Prospective_Horizon_Peak_Power_kW: A variable representing the maximum Total_Load_kW[i] that will occur across all intervals i within the current daily optimization horizon.
  • Constraint Linking Prospective_Horizon_Peak_Power_kW to Total_Load_kW[i]:
    • Prospective_Horizon_Peak_Power_kW >= Total_Load_kW[i] for all relevant intervals i.

• Cost Calculation in Daily Objective Function:
  The capacity cost component penalizes exceeding the higher of the actual peak already set or the planned monthly peak.
  Let P_horizon = Prospective_Horizon_Peak_Power_kW.
  Let P_actual = Actual_Current_Month_Peak_Power_kW.
  Let P_plan = Planned_Monthly_Peak_kW.

  An auxiliary variable Peak_Increase_For_Full_Charge_kW is used:

  1. Peak_Increase_For_Full_Charge_kW >= P_horizon - max(P_actual, P_plan)
  2. Peak_Increase_For_Full_Charge_kW >= 0
     (Note: max(P_actual, P_plan) would be implemented using intermediate variables or linearized if the solver requires strict linearity, e.g., Baseline_Peak >= P_actual, Baseline_Peak >= P_plan, then Peak_Increase_For_Full_Charge_kW >= P_horizon - Baseline_Peak.)

  The incremental cost term added to the daily objective function to be minimized is:
  Incremental_Capacity_Cost_Term = Peak_Increase_For_Full_Charge_kW * Capacity_Tariff_Rate_per_kW_per_Month

  This formulation ensures that a cost is only incurred if P_horizon (the peak planned for the upcoming optimization window) significantly exceeds both the peak already achieved this month and the planned peak for the month. The optimizer will try to keep Peak_Increase_For_Full_Charge_kW at 0 if possible.

• Post-Optimization Update (Daily):

  • After a daily optimization run, EMHASS determines the actual highest scheduled Total_Load_kW[i] from its plan for that run (Actual_Scheduled_Peak_this_Run_kW).
  • The persistent Actual_Current_Month_Peak_Power_kW is updated:
    Actual_Current_Month_Peak_Power_kW = max(Actual_Current_Month_Peak_Power_kW, Actual_Scheduled_Peak_this_Run_kW)

3.C. Handling Longer-Term Averaging and User-Defined Targets

Directly optimizing a yearly average of monthly peaks in each short-term run remains complex. The two-stage approach offers better monthly handling. For longer-term strategies:

• Guided Monthly Planning (Stage 1): Users can define a Target_Monthly_Peak_kW parameter (see Section 4). The Stage 1 (Monthly Planning Optimization) can use this Target_Monthly_Peak_kW as an additional constraint (e.g., Planned_Monthly_Peak_kW <= Target_Monthly_Peak_kW) or as a soft target in its objective function to guide the determination of Planned_Monthly_Peak_kW.
• Manual/External Adjustment: Users can monitor their evolving yearly average and adjust their monthly targets (Target_Monthly_Peak_kW) or operational strategies accordingly.
• Focus on Informed Monthly Peaks: The Planned_Monthly_Peak_kW derived from Stage 1 provides a more economically sound basis for the month than a simple reactive approach, which indirectly supports better longer-term outcomes.

4. Configuration Parameters Needed for EMHASS

• enable_capacity_tariff_optimization: Boolean (e.g., true/false).
• capacity_tariff_rate_cost_per_kw: The monetary rate for the tariff (e.g., 2.50 if currency is defined elsewhere or implied).
• capacity_tariff_interval_minutes: The interval over which the peak is measured (e.g., 15, 30, 60). EMHASS will need to aggregate its internal shorter timesteps to these intervals for peak calculation.
• capacity_tariff_billing_day_of_month: (Optional, for automating reset) The day of the month when the billing cycle resets and Current_Month_Peak_Power_kW should be reset (e.g., 1).
• persistent_state_path: Path to a file where Current_Month_Peak_Power_kW and its last update timestamp/month can be stored.
• target_monthly_peak_kw (Optional): A user-defined target for the monthly peak in kW. This can be used as an input to Stage 1 (Monthly Planning Optimization) to guide or constrain the calculation of Planned_Monthly_Peak_kW.

5. Problem Type and Solver Impact

• The addition of these variables and linearized constraints should keep the problem as a Mixed-Integer Linear Program (MILP) if the base EMHASS model is already MILP.
• The increase in model size is relatively small, and performance impact on modern solvers should be manageable.
• The main implementation complexity lies in the persistent state management and the logic for aggregating loads to the tariff interval.

6. Conclusion

Incorporating capacity tariff optimization into EMHASS would allow it to make more economically sound decisions by managing peak power demand alongside energy consumption. This feature is crucial for users in regions with demand charges, providing a more comprehensive approach to home energy cost minimization. Careful management of the persistent peak state and clear configuration options for the user will be key to a successful implementation.