A Better Approach on Billing for Electricity

• Introduction
  • Why variability is expensive
• Current Payment Models for Households
• Proposed Billing Model
  • Optional Higher-Order Penalty
  • The Total Bill
  • Discrete Implementation
• Conclusion
• Appendix: How to Reduce Your Load Variation in Practice
  • Avoid Sudden Large Load Steps
  • Use Smart Scheduling for Flexible Loads
  • Decouple Consumption from Instantaneous Demand (Buffering)
  • Limit High-Frequency Switching
  • Coordinate Loads Within the Household
  • Monitoring
  • Shift Thinking from Total Energy to Smooth Power
• References

Introduction

Electric power systems are not monolithic. They are a layered composition of generation assets, each optimized for a different role in time and variability.

Baseload plants such as run of river, nuclear and coal power plants are designed to operate continuously at or near their nominal output. Their economics are dominated by high capital expenditure and very low marginal costs. These plants achieve their lowest levelized cost of electricity when running steadily. Any deviation like ramping up and down, partial loading or cycling reduces thermodynamic efficiency, increases mechanical stress and raises effective cost per kWh.

Load following plants like combined cycle gas turbines and reservoire hydro can adjust output on timescales of minutes to hours. They fill the gap between baseload and fast-response resources. Their marginal costs are higher than baseload but they are far more flexible

Peaking and balancing resources like open cycle gas turbines, pumped hydro storage and batteries are designed for rapid response on time scales of seconds to minutes (this cannot be achieved by load following- or baseload plants). They are essential for:

• Frequency regulation
• Contingency reserves (i.e. responding to sudden outages or sudden demands)
• Intra day balancing

These resources have the highest marginal cost and often low utilization. Their costs must be covered by fewer operating hours which means they are the most expensive resources on the grid, but they cannot be replaced by baseload or load following plants.

The timescales the grid operates on can be separated into four categories, which can roughly be separated into technical requirement (primary and secondary) and a economic stage (tertiary and day-head or intraday markets):

• The primary control happens on the scale of seconds. This is automatic frequency response and requires extremly fast ramping resources (network capacity, open cycle gas turbines, batteries)
• The secondary control happens on the scale of tens of seconds to minutes. Here centralized control happens to restore frequency and balancing areas. This still requires fast ramping resources (open cycle gas turbines, batteries and partially already combines cycle gas turbines and reservoire hydro).
• Tertiary control happens on the scale of minutes to hours and handles economic dispatch and reserve replacement.
• Day-ahead and intraday markets operating on the scale of hours to days. Here generation is sheduled and planned via economic rules (compareable to a stock market).

Why variability is expensive

For many people energy cost is only given by the amount of total energy (in kWh) consumed. But even more important is the shape of the load curve. A perfectly constant load can be served almost entirely by baseload generation. A highly variable load on the other hand requires more reserved held online, more ramping of thermal units, increased cycling (and thus wear and maintaneance costs) as well as higher reliance on fast response (expensive) assets. Rapid househols level switching aggregates across millions of users into steep net-load ramps. This leads to transformer and distribution stress (wear and infrastructure cost), voltage deviations and increased reserve requirements. These integration and balancing costs add up massively at higher variability levels[1]. The same total energy volume can cost a retailer far more[2] if the load shape is spiky/variable due to hedging costs, peak procurement and lost opportunities to use low-cost periods.

Frequency regulation markets see price spikes with higher variability or renewable penetration. For example increasing wind from low to 30% can raise regulation prices by 32% and doubling regulation requirements can increase them by 84%. Flexible resources (hydro, batteries) help mitigate this but the baseline cost of fast response is clearly elevated compared to steady operation[3]. Soothing of shifting load (i.e. the opposite of rapid switching) lowers system costs by reducing peak demand, deferring infrastructure and dampening price volatility. This can cut operational expenses, improve reliability and avoid billions in distribution upgrades[4].

Variable residential profiles are far more expensive to serve than steady commercial and industrial ones. In addition the injected variability by renewabeles like solar and wind also injects the same kind of cost, being the dominant cause of load variations at this point in time. Load variability also compresses grid margins through tighter reserves and more cycling of equipment[2].

Current Payment Models for Households

Today, most residential billing is based almost exclusively on total energy consumption:

[ \begin{aligned} E = \int_0^T P(t) \mathrm{d}t \end{aligned} ]

This model assumes implicitly that all kWh are equal, regardless of when or how they are consumed. In reality on the other hand a kWh drawn during a stable low-demand period can be extremly cheap due to the very low marginal cost of baseload energy. The real system cost for households id increasing variability they inject (sudden powering on or off of an EV charger, a heat pump, an air conditioner, of induction stoves, plugged or unplugged chargers, switching on and off of devices, etc.), which forces the grid operator to deploy fast response resources (like gas peaking supply, hydro pump storage, hydrogen storage and batteries) that are far more expensive per kWh than baseload.

Some tariffs already introduce demans charges

[ P_\mathrm{max} = \max_{t} P(t) ]

However this only captures the maximum level, not the dynamics that cause the real massive costs.

Modern smart meters already sample power at intervals between 1 and 60 seconds (while only reporting on timescales of around 15 minutes). Therefore, the temporal structure of the consumption is already observable without changes to infrastructure, it is just not used in billing.

Proposed Billing Model

In the following section we extend the billing model to include not only total energy but also the temporal variation of the load.

Let

• $P(t)$: instantaneous power (kW)
• $T$: billing interval (for example $T=720h$ for one month)

Then the model includes two key quantities:

As in the traditional model the energy consumption, which can be kept very small or even zero reflecting the very low marginal cost of steady generation:

[ E = \int_0^T P(t) \mathrm{d}t ]

The second term is the load variation:

[ V = \int_0^T \mid \frac{\mathrm{d}P}{\mathrm{d}t} \mid \mathrm{d}t ]

This is the total variation of $P(t)$. Every time one turns a 2 kW load on and off again, $V$ increases by $4 kW$, regardless of how long it was on. Rapid cycling drives $V$ up dramatically, steady load barely moves it. This term is independent of duration and reflects how agressively the grid is stressed.

A even more physical but slightly more complicated model would incorporate the frequency response of the system (i.e. provide frequency cost):

[ V_\mathrm{phys} = \int_0^T \mid \mathfrak{H}(\omega) P(\omega) \mid^2 \mathrm{d} \omega ]

Optional Higher-Order Penalty

To penalize rapid fluctuations even more the implementation of high pass filtering and the square of the derivative can be used:

[ V = \int_0^T \left( \frac{\mathrm{d}P}{\mathrm{d}t} \right)^2 \mathrm{d}t ]

Such a term would in particular hit high frequency switching devices without proper filtering.

The Total Bill

The monthly total bill $B$ is given by

[ B = c_E E + c_V V + c_D \max_{t} P(t) + F ]

The factors are given by:

• $c_E$: The energy price, which could be set very low (even in the range of 1 Cent per kWh).
• $c_V$ which is the variation rate measuring the load swings. This layer would recover the balancing and infrastructure costs and has to be tuned so the utility recovers its fixed and control costs.
• $c_D$ is an optional demand rate charging for the maximum available power. I personally would not introduce this.
• $F$ is a fixed customer charge handling the provisioning of metering infrastructure, the paperwork and support availability.

Discrete Implementation

Due to the discrete sampling of the smart meters in units of $\Delta t$ the real implementation would of course be discrete:

[ V \propto \sum_{i=1}^N \mid P_i - P_{i-1} \mid \frac{\Delta t}{3600} ]

Conclusion

This system could be implemented easily with existing smart-meter infrastructure available in many parts of Europe and would give the customer a clear financial incentive to smooth their load. Such a system would provide behavioural incentives reflecting the real cost structure:

• Encouraged behaviour:
  • Slow ramping of loads (soft starting, not switching larger loads, etc.)
  • Buffering via Batteries or thermal storage
  • Sheduling of flexible loads
• Discouraged behaviour:
  • Rapid on/off cycling of loads
  • Synchronized switching across households
  • High frequency load fluctuations
  • Non conforming devices leaking high frequency switching noise towards the grid

Industrial consumers already face complex tariffs reflecting demand peaks, power factor and time-of-use. Residential users currently do not, despite contributing significantly to variability. This model aligns individual cost with system impact, making pricing more economically efficient and fair. Importantly this model is immediately implementable using existing infrastructure.

Appendix: How to Reduce Your Load Variation in Practice

If billing starts to reflect not only how much energy is consumed but also how it is consumed, then reducing load variation becomes both economically and technically meaningful. Fortunately, many strategies are already available with relatively simple tools.

Avoid Sudden Large Load Steps

The main driver of load variation is not energy usage itself, but rapid changes in power. Typical problematic patterns include:

• Switching high-power devices abruptly (like EV chargers, heaters, induction stoves, etc.)
• Multiple devices turining on simultaneously
• Thermostatic systems oscillating between full on and off

Whenever possible:

• Prefer devices with soft-start or ramping behaviour
• Avoid manually switching multiple high loads at once
• Stagger the activation of large consumers by a few seconds

Even small delays between devices can significantly reduce aggregated grid stress.

Use Smart Scheduling for Flexible Loads

Here it gets more interesting and technical. Some loads are inherently flexible in time:

• EV charging
• Dishwashers
• Washing machines
• Water heating

Instead of starting them immediately, shift them to periods where your total load is already stable. A simple strategy is:

• Only start new loads when current consumption is low and stable
• Avoid starting devices during existing ramps (e.g. while heating systems are activating)

Home automation systems can implement this with simple rules.

Decouple Consumption from Instantaneous Demand (Buffering)

This could be done in various ways:

• Electrical buffering: Small home batteries can absorb rapid changes, even modest capacities (1-5 kWh) are sufficient to smooth short spikes. Charging and discharging can be controlled to keep grid-facing power nearly constant.
• Thermal buffering: Heat pumps and buffer tanks and water boilers storing thermal energy. These systems can run at constant power and store energy for later use, transforming spiky load into a smooth baseline.

Limit High-Frequency Switching

Many modern devices (especially cheap power electronics) introduce rapid fluctuations. These include poorly filtered switching power supplies, fast PWM-controlled heaters and cheap motor controllers. While individually small, these effects can accumulate. To mitigate those effects prefer higher quality devices with proper filtering, add input filtering (LC filters) where applicable and avoid unnecessary rapid on/off control loops. In a billing model sensitive to variation, these small fluctuations may become economically visible.

Coordinate Loads Within the Household

A household is not a single device but a combination of dynamic systems. With coordination the total load variation can reduced by ramping devices up and down in a coordinated fashion, keeping the total power approximately constant. Especially coordinating devices like EV charging, heating or washing can drastically reduce load variations.

Monitoring

Without monitoring one does never know what to optimize - or if there is something to optimize. Optimization can be done very easily via

• Digitally readable smart meters providing time resolved readings
• Energy monitors providing the total consumed energy
• Logging systems based on digitally readable smart meters and switch status of home automation systems.

This allows to visualize the load profile $P(t)$ and the rate of load changes $\Delta P(t)$. When looking at the data inefficiencies often become immediately obvious.

Shift Thinking from Total Energy to Smooth Power

This is most likely the hardest one since most of us learnt at school to turn of unneeded devices to conserve power. The useful mental model is that the grid prefers a constant request over multiple small bursty ones. This shift in thinking would lead to fewer peaks, less cycling and lower system cost.

References

• [1] From baseload to peak: Renewables provide a reliable solution
• [2] Volume and Shape: Understanding the cost of electricity and the value of flexibility
• [3] Prices in Frequency Regulation Markets: Impacts of Natural Gas Prices and Variable Renewable Energy
• [4] Demand response can play a vital role in ensuring grid reliability and dampening price volatility in wholesale electricity markets

This article is tagged: Opinion, Basics, Power grid, Finance