energies

Article
Design and Impact of Grid Tariffs
Christian Winzer * and Patrick Hensler-Ludwig

ZHAW School of Management and Law, Center for Energy and Environment, 8400 Winterthur, Switzerland
* Correspondence: christian.winzer@zhaw.ch

Abstract: We propose a novel grid tariff design proportional to grid load and analyze its performance
in comparison to other grid tariff designs with regards to (i) effectiveness, (ii) efficiency, (iii) profitabil-
ity of technologies and (iv) equity. In the case of a large share of automated loads, time-of-use tariffs
and critical peak prices create problematic new rebound peaks. Direct load control and capacity prices
can reduce grid load without rebound peaks but are less effective at reducing both grid and energy
costs. The novel tariff design proportional to the grid load can reduce both grid and energy costs
but needs to be designed appropriately to avoid rebound peaks. Tariff impacts on the profitability of
different technologies are more pronounced than equity impacts because households from all income
brackets may be equipped with PV and flexible technologies.

Keywords: grid tariff; demand response; automatic load-control

1. Introduction
The switch to decentralized renewable energies and the increasing electrification of
various economic sectors (e.g., mobility, heating) call for expansion in many power grids.
The need for additional grid capacity depends heavily on installed technologies and user
behavior which, in turn, is influenced by the incentives resulting from grid tariffs. However,
the development of demand response (DR) as an alternative to grid expansion is currently
limited due to the chicken-egg problem explained in [1]. As current levels of DR are low,
grid operators tend to over-size the grid to prevent bottlenecks. This, in turn, means that
Citation: Winzer, C.; there is a limited need to develop DR beyond today’s levels. Efficient grid tariffs that
Hensler-Ludwig, P. Design and minimize the sum of dispatch and investment costs for the total system, including the grid
Impact of Grid Tariffs. Energies 2024, and flexibility options, could resolve this problem. By ensuring that the grid tariffs that
17, 1364. https://doi.org/10.3390/ prosumers pay correspond to the grid costs that result from their consumption behavior,
en17061364 efficient grid tariffs could incentivize the development of local flexibilities.
Most electricity consumers pay a regulated tariff for their electricity consumption. As
Academic Editors: Grzegorz Mentel,
Sebastian Majewski and Xin Zhao
illustrated in Figure 1, the electricity bill of households in Europe includes costs, ranging
from the cost of electricity production (“Energy”), transmission and distribution grids
Received: 14 February 2024 (“Network”), cost of renewables (“RES”) and different types of taxes (“Taxes” and “VAT”).
Revised: 28 February 2024 Within this paper, we focus on the efficient design of tariffs for the recovery of grid
Accepted: 1 March 2024 costs. However, as we will discuss the same principles could also be applied to other
Published: 12 March 2024
cost components.
The three main tariff approaches that are used are lump sum payments (per time
period), energy charges (per kWh) and capacity charges (per kW and time period). As
Copyright: © 2024 by the authors.
illustrated in Figure 2, a variety of different combinations of these charges are used in
Licensee MDPI, Basel, Switzerland. EU countries. In addition to that, the share of costs that are allocated to each compo-
This article is an open access article nent, and the detailed design for each of these charging components vary greatly among
distributed under the terms and different countries.
conditions of the Creative Commons The great variety in approaches and designs raises the question regarding optimal
Attribution (CC BY) license (https:// tariff design. As a result of the increasing electrification of transport and heat sectors,
creativecommons.org/licenses/by/ short-term elasticity of demand is rapidly growing. At the same time, the rollout of smart
4.0/). meters is providing new opportunities for the smart control of these devices. Future-proof

Energies 2024, 17, 1364. https://doi.org/10.3390/en17061364 https://www.mdpi.com/journal/energies

Energies 2024, 17, 1364 2 of 23

tariffs should thus be designed in a way that leverages these opportunities to send optimal
dispatch and investment signals.

Figure 1. Composition of household electricity prices in Europe. Source: [2].

Figure 2. Number of countries using different tariff structures in the EU. Based on: [3].

Analyses of grid tariff designs are often limited to the tariff impact on grid peak load
and the resulting grid investment need. Within this paper, we include an assessment of
additional criteria such as the tariff impact on electricity generation cost, profitability of
different technologies and cost-redistribution between households from different income
brackets, which are also relevant for the choice between different tariff approaches.
The structure of this paper is as follows. In Section 2, we summarize the approaches
that were suggested and the main relevant findings from the literature on optimal tariff
design. In Section 3, we describe the tariff scenarios and in Section 4 the data used in the
analyses for this paper. The results of our analysis are reported in Section 5 and discussed
in Section 6. In Section 8 we describe our conclusions and policy implications.

2. Literature
To date, a substantial body of literature has explored different optimization strate-
gies for home energy management systems (HEMS), particularly for appliance scheduling.
Many decentralized approaches use linear optimization to determine households’ responses
to external price signals. Ref. [4] uses mixed-integer linear programming (MILP) to min-
imize household electricity costs by adjusting appliance load profiles in a time-dynamic
pricing scheme. They model prosumer households with various adaptable appliances and
Energies 2024, 17, 1364 3 of 23

devices such as EVs, ESS, thermal storage systems, and household appliances. Ref. [5]
minimizes electricity bills over a multi-day time horizon, incorporating a penalty term into
the objective function to account for the prosumers’ comfort. In addition to time-dynamic
electricity tariffs, [6] employ MILP to investigate prosumers’ short-term adaption under
five distinct electricity tariffs, which include a capacity tariff and multiple bidirectional
tariffs. They find that these two concepts significantly reduce grid interaction. Ref. [7]
introduces a multi-objective optimization problem to study the balance between minimiz-
ing electricity costs and enhancing households’ comfort under two different power-based
electricity contracts.
Taking into account that individual optimal appliance scheduling is not necessarily
beneficial to the grid operation, several studies propose frameworks that coordinate DR.
Ref. [8] uses a bi-level optimization problem to investigate coordinated DR. At the lower
level, they optimize the electricity bills of households, while in the upper level, they
minimize the overall system load. Ref. [9] proposes an optimization approach at the
neighborhood level to coordinate DR.
One of the main findings from this literature is that with increasing levels of automa-
tion, discontinuous price signals, such as time-of-use tariffs and critical peak prices could
not reduce the peak load, and lead to an even higher rebound peak at the beginning of
low-price periods. The solutions proposed to this problem include the introduction of a
protection period after the high-tariff hours [10], the introduction of different price signals
for different consumer groups [11] and the imposition of binding power limits during
scarcity [4,9,12]. However, while the resulting dispatch may be effective in achieving a
lower peak demand, these studies do not distinguish between the tariff approaches for
recovering energy cost, grid cost or residual cost, and do not analyze how the suggested
proposals affect other tariff design criteria, such as cost-recovery, welfare, equity and other
dimensions of acceptability (i.e., fairness, transparency) [13–15]. In addition to that, only
two of the studies assess the suitability of capacity tariffs [6,7], and none of them evaluate
the impact of using a continuous tariff signal, instead of a discrete step-function.
In our paper, we will fill this gap, by exploring the impact of both a capacity tariff and
a novel continuous tariff signal proportional to grid load and compare their performance
to the performance of other approaches for avoiding rebound peaks along all the above-
mentioned tariff design criteria and calculate the overall efficiency of tariffs including
impacts on grid peak-load, grid and energy cost, technology profitability and equity.

3. Methodology
To simulate the behavior of consumers and prosumers in response to dynamic electric-
ity prices and to analyze the effects of the resulting load profiles on the grid infrastructure
and consequently grid costs, we use a linear optimization model. An overview of the model
structure is provided in Figure 3. The inputs for this model include the “infrastructure
scenario” and the “tariff scenario”.

Figure 3. Structure of the simulation model.

Energies 2024, 17, 1364 4 of 23

The “infrastructure scenario” outlines the number, types, and equipment of house-
holds being simulated. We define 13 distinct consumer and prosumer types based on
variations in asset equipment and household characteristics. Consumers can have different
combinations of heat pumps (HP), electric vehicles (EV), or neither of these assets, while
prosumers are additionally equipped with photovoltaic (PV) systems and potentially Bat-
tery Electric Storage Systems (BESS). We model BESS, EVs and HPs as shiftable in time
since these devices offer the required flexibility and are likely to be the largest contributors
to demand peaks by 2035 [16]. Other household loads, such as wet goods, stoves, consumer
electronics, etc., are considered inflexible in the model.
We will analyze the effects of nine different “tariff scenarios” by comparing two
distinct incentive mechanisms: capacity tariffs (type 2) and time-differentiated tariffs (tariff
type 3–8) which are price-based mechanisms, along with a “direct load control” scheme
(tariff type 9) which operated as an incentive-based mechanism.
1. flat: constant price per kWh during all hours
2. capacity: constant price per kW individual annual consumption peak
3. tou: time-of-use tariff, with a daily high- and low tariff period
4. cpp-h: critical-peak-price tariff, with a high tariff during those hours when load
reaches its annual maximum and a low tariff otherwise
5. cpp-d: critical-peak-price tariff, with a high tariff during all high-tariff hours of the
tou tariff on days, when load reaches its annual maximum and a low tariff otherwise
6. grid load: a tariff that is proportional to the projected grid load prior to load shifting
7. spot: a tariff that is proportional to spot prices
8. grid load and spot: a combination of 5 and 6.
9. dlc: direct load control tariff
The simulation model consists of three stages. In the first stage, system costs are
calculated based on the exogenous infrastructure scenario. The electricity tariff levels are
calibrated following the cost recovery principle which ensures that grid, energy and residual
costs are fully recovered by each tariff scheme. The second stage models households’
operational decisions on the electricity tariffs using a linear optimization model. After
calculating the optimal household dispatch, the third and last stage of the model adjusts
tariff levels according to the optimized load profiles to ensure grid cost recovery. Re-
calibrated tariff levels are then used as input for calculating the impact metrics. The
mathematical notation and further details regarding the dispatch model, the method for
tariff calibration and calculation of the impact metrics are provided in the Appendices A–E.

4. Data
The model was utilized to simulate a synthetic subset of a distribution grid, encompass-
ing a single transformer station that serves 300 households. These households exhibit varia-
tions in terms of device equipment and consumption patterns. The simulation is conducted
for two distinct years, 2020 and 2050, with an hourly resolution. Synthetic load profiles
were employed for households, electric vehicles, heat pumps, and photovoltaic systems.
The simulation model is calibrated for a case study in the canton of Aargau, Switzer-
land. Within the model, two complete years are simulated with hourly resolution, differing
in the distribution of flexible electrical appliances and installations. The electricity tariffs are
aligned with the average electricity cost proportions from the year 2021, corresponding to
an electricity cost of 20.01 Rp./kWh. Between the two simulated years, household appliance
equipment varied based on survey data and forecasts. For the 2020 appliance equipment,
data from the Swiss Household Energy Demand Survey (SHEDS) conducted from 2016 to
2020 were utilized. The survey encompassed 5000 Swiss households and gathered informa-
tion about their appliance equipment and consumption behavior. Appliance equipment
estimation for the year 2050 was performed using forecasts from the Swiss Federal Office
of Energy [17]. These forecasts expect that by 2050 around 68% of all households will have
a heat pump, 78% an EV, 47% a BESS and 67% a PV module. Household counts were
estimated by adjusting household counts for each type from 2020 in a way that achieves
Energies 2024, 17, 1364 5 of 23

this marginal diffusion of the different technologies while minimizing the sum of squared
deviations between the household share in 2020 and the household share in 2050.
The resulting number of household types for each scenario year and node is presented
in Table 1. We differentiate between 12 different types of households, depending on whether
the household is equipped with HP, EV, BESS or PV. For example, for 2020 we assume that
1 of the 300 households (0.3%) which we simulate is equipped with HP, EV and PV (type9),
while during 2050 we assume that this number rises to 60 households (20%).

Table 1. Overview of household types and technologies.

Household Features Household Count Household Share

HH-Type HP EV BESS PV 2020 2050 2020 2050
type1 0 0 0 0 211 66 70.3% 22.0%
type2 1 0 0 0 57 0 19.0% 0.0%
type3 0 1 0 0 5 29 1.7% 9.7%
type4 0 0 0 1 4 0 1.3% 0.0%
type5 1 1 0 0 3 4 1.0% 1.3%
type6 1 0 0 1 3 0 1.0% 0.0%
type7 0 1 0 1 0 1 0.0% 0.3%
type8 0 0 1 1 8 0 2.7% 0.0%
type9 1 1 0 1 1 60 0.3% 20.0%
type10 1 0 1 1 6 0 2.0% 0.0%
type11 0 1 1 1 1 0 0.3% 0.0%
type12 1 1 1 1 1 140 0.3% 46.7%
Total 300 300 100% 100%

We assume that only the load from HPs, EVs or BESSs responds to flexibility incen-
tives. The remaining portion of residential load and PV system generation is considered
non-flexible.
Simulations were based on synthetic load profiles from the LoadProfileGenerator
(LPG) [18]. PV production profiles and heat pump load profiles were calculated based
on building-level data from a distribution grid operator in the canton of Aargau. Further
details on the load profiles can be found in the Appendix F.

5. Results
This section presents the findings of the case study. First, in Section 5.1, we display
the model results for the current scenario, where 28% of households possess one of the
flexible technologies. Additionally, 8% of households in this scenario are equipped with a
PV system. Moving on to the 2050 future scenario, the share of prosumers in the grid area
rises to 67%, while the share of households with flexible technologies increases to 78%. The
outcomes of this scenario are elaborated upon in Section 5.2.

5.1. Scenario 2020

5.1.1. Effectivity
We assess the effectiveness of the tariffs based on the change in peak load incentivized
by each tariff compared to the load under a flat tariff (Status Quo—SQ) within the consid-
ered network area. Figure 4 illustrates the change in load at the time when the peak load
occurred in the SQ scenario (blue) as well as the change in the overall peak load (red).
The time-variable tariffs with two distinct price levels (TOU, CPP_h, and CPP_d)
effectively decrease the load at the time of the peak load in SQ, but they result in a new
peak load occurring at a different time, which is even higher than the original peak load.
Energies 2024, 17, 1364 6 of 23

The effect of increased peak loads due to new tariff structures is recognized in the existing
literature as a “rebound peak” [11,12]. This effect stems from the step-like nature of price
signals in time-varying tariffs with fixed, predefined price levels. This leads to a cumulative
shift in flexible loads from high-tariff periods to the first subsequent low-tariff time slot. As
these subsequent times often exhibit high load levels in comparison to the daily average,
the shifted load can result in a peak load surpassing the original magnitude (Figure 5a).

Figure 4. Change of system peak load compared to the SQ scenario in 2020.

Figure 5. Transformer load in SQ scenario (blue line) compared to grid tariff (grey line) and corre-
sponding transformer load (red line) under (a) TOU and (b) grid-load tariff.

Capacity tariffs (capacity) and direct load control (DLC) can avoid the rebound peak.
However, the capacity tariff only achieves very small peak-load reductions of a few percent-
ages, as the peaks of individual customers often do not coincide with the peak load of the
total grid. The DLC tariff obtains the strongest peak-load reduction, as it assumes a central
optimization with the objective of minimizing the peak load. In the 2020 scenario, the DLC
tariff achieves a peak load reduction of around 20%. However, because of unbundling
restrictions, DLC typically does not account for the energy costs as part of the optimization.
Conceptually, it is, therefore, less suitable for minimizing the sum of grid and energy costs
(see next section).
The tariff signal proportional to total load (grid load) achieves a lower peak-load
reduction than DLC. However, in the 2020 scenario, it can avoid rebound peaks as it
prompts flexible loads to shift to a period when the system load is comparatively lower
(Figure 5b). Compared to capacity tariffs and DLC, an important advantage of the grid-
Energies 2024, 17, 1364 7 of 23

load tariff is, that it may be combined with an energy component that is proportional
to spotprices (gridload_spot). We, therefore, expect that if the grid and energy tariff
components are calibrated appropriately, this tariff should, therefore, minimize the sum of
grid and energy costs (see next section below).

5.1.2. Efficiency
Figure 6 shows the sum of grid, energy and residual cost which result under each tariff
for the 2020 scenario. Across the board, the price impacts of all tariffs remain relatively
modest, ranging from a reduction of −3.2% to an increase of +1.6%. The two main reasons
for this are the small number of households that are equipped with flexible technology, and
the assumption, that only 30% of grid costs depend on peak load.

Figure 6. Grid, energy, and residual cost in the Scenario 2020.

As expected, the trend in network costs closely mirrors the outcomes of the effective-
ness analysis, with DLC and grid-load tariffs reducing grid costs most strongly (by 6.46%
and 2.05%, respectively).
Regarding the impact on energy cost, as expected, most tariffs hardly reduce the energy
cost because of the high tariff periods for time variable tariffs (TOU, CPP_h, and CPP_d)
cover hours with a high grid load, which may not be the hours with the highest spot prices
and capacity tariffs (capacity) and direct load-control does not target a reduction in energy
cost. Tariffs proportional to the spot price (spot), therefore, achieve the strongest reduction
in energy cost (by 2.89%), followed by the combined tariff where the grid component is
proportional to the total load, and the energy component is proportional to spot prices
(gridload_spot).
However, the result regarding the sum of all cost components is different from ex-
pected. Even though the combined gridload_spot tariff is the only one that explicitly
considers both cost components, the total cost reduction achieved by this tariff (1.42%) is
lower than the total cost reduction achieved by direct load control (3.16%) or the grid-load
tariff (1.6%). We assume that this is due to a sub-optimal design of the grid-load tariff
signal, which puts too much weight on a reduction in grid-load during hours when the
grid is not congested. This will be further discussed in Section 6.

5.1.3. Profitability
Figure 7 displays the average electricity costs for households with different appliances
under the baseline scenario with a constant price per kWh.
Figure 8 illustrates how electricity costs for households equipped with different devices
and appliances change under different tariff scenarios compared to the baseline scenario
with a constant price per kWh. With capacity pricing, electricity costs rise for households
lacking flexible technology. The most significant increase occurs in households with PV
systems. This is due to different approaches to allocating variable grid costs. In the baseline
Energies 2024, 17, 1364 8 of 23

tariff, variable grid costs are evenly distributed across total energy consumption. Since
households with PV systems exhibit lower grid consumption due to self-consumption, they
bear only a minor share of variable grid costs under a fixed tariff. However, under the
capacity tariff, variable grid costs are allocated solely to individual peak loads, resulting
in higher electricity costs for PV-equipped households. The introduction of additional
flexibilities can mitigate this cost increase to some extent, but the flexibility of EVs and BESS
is not enough to completely offset the rise in costs, resulting in higher electricity expenses
for households with these device combinations as well.

Figure 7. Electricity cost in case of a constant price per kWh in the Scenario 2020.

Figure 8. Difference in electricity costs [CHF/year] compared to baseline tariff in 2020.

This phenomenon is also observed under TOU, CPP-h, and CPP-d. These tariffs spread
variable network costs over a limited number of hours, mainly in the morning or evening
when PV generation is lower. Conversely, households with high electricity consumption,
which bear a significant portion of variable grid costs in the baseline scenario, can benefit
Energies 2024, 17, 1364 9 of 23

from these tariffs by reducing their peak load or shifting consumption away from high-tariff
periods. HPs are particularly advantageous as they can offer flexibility throughout the cold
season. EVs, due to their limited stationary time, exhibit less flexibility, and therefore, have
a smaller impact on load shifting.
Similarly, the spot tariff leads to increased annual electricity costs for prosumers and
non-flexible households. For non-flexible households, this is primarily due to the low
efficiency of the spot tariff, leading to an overall cost increase. In the case of prosumers,
the strong negative correlation between spot prices and the PV generation profile results
in lower savings from self-consumption during midday hours in the summer. Since this
effect is more pronounced in the summer months, additional flexibility in the form of
HPs has a modest cost-reducing effect. EVs, on the other hand, provide a stronger cost-
reducing impact for prosumers under this tariff. In the gridload_spot tariff, the negative
correlation between PV generation and price signal persists, causing prosumers without
additional flexibilities to fare worse under this tariff compared to the baseline. Inflexible
consumers, however, benefit from the tariff’s efficiency, resulting in only minor additional
costs, typically less than 1 CHF per year.
Under the grid-load tariff, the additional costs for prosumers and households without
flexibility are notably diminished. Only households with PV systems experience a slight
uptick in electricity costs. This phenomenon can be attributed to both the effectiveness and
efficiency of the grid-load tariff in the 2020 scenario, which lowers the costs for allocation.
Furthermore, variable grid costs are still assigned to the total annual energy consumption,
albeit with grid load-dependent weighting. Consequently, the cost increase for prosumers
is less pronounced compared to time-variable or capacity tariffs.
Remarkably, the DLC tariff is the sole tariff resulting in decreased annual costs across
all household types. This is due to the substantial reduction in total costs, which persist
despite the fixed allocation to energy purchases.

5.1.4. Equity
Results in the previous section demonstrated that households equipped with multiple
flexible appliances tend to profit more from dynamic tariffs than households with less
flexibility. In order to verify, to what extent this effect will lead to a cost redistribution from
richer to poorer households, Figure 9 shows the average electricity price for households
from different income brackets under each of the electricity tariffs.

Figure 9. Electricity costs per Household income group 2020.

Contrary to our expectations, the main impact of the tariffs is a parallel shift of the
average cost across most income brackets. The reason for this is, that in 2020 heatpumps
are the only flexible technology which is available to a larger number of households, and
the share of households from different income brackets in Table 1 is roughly the same in
Energies 2024, 17, 1364 10 of 23

the case of “type 2” (with heatpump) and “type 1” (without flexibility). Surprisingly, the
households with the lowest income in this case study exhibit the lowest electricity costs
under all tariff scenarios. This is due to the fact, that there are quite a few households from
the lowest income group which are equipped with PV panels, e.g., because they are tenants
of a landlord that chose to install PV.

5.2. Scenario 2050

5.2.1. Effectivity
In the 2050 scenario, the peak load rises from 492 MW in the 2020 scenario to 919 MW
in the 2050 scenario because of electrification. However, many of the new loads are flexible,
so the share of households with flexible technology increases to 78% and 67% of the
households are assumed to have PV. The impact of the different tariffs on peak load is
illustrated in Figure 10.

Figure 10. Change of system peak load compared to the SQ scenario in 2050.

As a result of the higher share of flexible loads, the rebound peak which is created by
time-varying tariffs (TOU, CPP_h, and CPP_d) increases sharply from between 5% and
15% in 2020 to more than 40% in 2050.
Capacity tariffs and DLC can effectively avoid rebound peaks, and reduce grid peak
load by about 10% (in the case of capacity tariffs) and more than 40% (in the case of DLC).
However, even this load reduction is inadequate to bring the total peak load down to the
levels observed in the 2020 scenario, necessitating grid expansion to accommodate the
increased demand.
By contrast to the 2020 scenario where the grid-load tariff contributed to a reduction in
the peak load, it can no longer avoid rebound peaks in the 2050 scenario. Surprisingly, the
rebound peak, which is caused by grid-load tariffs, even exceeds that which is caused by
time-varying tariffs, causing the peak load to more than double compared to the baseline
tariff. This phenomenon is a result of the shape of the price function associated with the
grid-load tariff. Specifically, there is one single time step per day featuring a minimum price.
Consequently, the entire flexible load around this time step is shifted to the moment with
the lowest price. Given that these low-price periods usually occur during nighttime hours
when a substantial number of EVs are available for charging (as depicted in Figure 11), the
charging load of multiple EVs is concentrated into a single time frame. This concentration
of load results in significant rebound peaks. Suggestions for avoiding these rebound peaks
will be discussed in Section 6. In contrast to grid-load tariffs, the timing of the high tariff
periods for the other time-varying tariffs (TOU, CPP_h, and CPP_d) occurs during morning
or late afternoon hours. During these times, the proportion of available EVs is relatively
limited (Figure 11), which explains the lower rebound peaks.
Energies 2024, 17, 1364 11 of 23

Figure 11. Histogramm of EVs at home.

5.2.2. Efficiency
Regarding grid costs, the same as for the 2020 scenario, the trend in network costs in
Figure 12 closely mirrors the outcomes of the effectiveness analysis. While time-varying
tariffs (TOU, CPP_h, and CPP_d, and in 2050 also the grid-load tariff) increase grid costs
due to rebound peaks, capacity tariffs and DLC can reduce the grid cost by 3.6% and
11.32%, respectively.

Figure 12. Grid, energy, and residual cost in the scenario 2050.

With regards to energy cost, as expected spot tariffs achieve the largest reduction in
energy cost of about 9%, followed by the gridload_spot tariff, which reduces energy cost by
about 8%.
Looking at the sum of all cost components, the impact of rebound peaks on grid costs
clearly outweighs the beneficial impact of the grid load and spot tariffs on energy costs.
Among the tariff designs that were investigated in this study, direct load control, therefore,
achieves the largest cost reduction of about 12%, even though it does not significantly
reduce energy costs. However, as we will describe in Section 6, we assume that further
improvements to the gridload_spot tariff design could lower the total cost even further.

5.2.3. Profitability
The substantial rise in total costs associated with time-variable tariffs has a significant
impact on a considerable proportion of households. As shown in Figure 13, time-varying
tariffs increase annual electricity cost for most households. Only prosumers with PV &
battery storage are partially shielded from escalating bills through potential reductions in
their electricity consumption during peak periods, particularly with TOU and CPP tariffs.
This is achieved by using their battery storage to offset demand during high-tariff periods,
effectively mitigating the pronounced upswing in variable grid costs.
A noteworthy observation is that households equipped solely with an EV experience
cost increases under the capacity tariff in the 2050 scenario, a contrast to the benefit they
gained in the 2020 scenario due to decreasing prices in that tariff. While these households
can curtail their peak load in the 2050 scenario, reducing it by an average of 29% from
13.4 kW to 9.5 kW, most households in the 2050 scenario possess multiple flexible appliances.
Energies 2024, 17, 1364 12 of 23

These households exhibit even greater peak load reductions, averaging at 58%, from
13.3 kW to 5.5 kW. As a result, they bear only a minor portion of the variable grid costs
under the capacity tariff, leaving the less flexible households to shoulder a larger portion
of these costs. In the 2050 scenario, this includes households with an EV or a PV system
along with an EV, leading to a less favorable outcome for them compared to the baseline
tariff. In contrast, the DLC tariff significantly diminishes variable grid costs, contributing
to a reduction in electricity costs for all types of households.

Figure 13. Difference in electricity costs [CHF/year] compared to baseline tariff in 2050.

5.2.4. Equity
Although we assumed that the income distribution within household types remains
unchanged between 2020 and 2050, the impact of the tariffs on average electricity cost in
2050 (Figure 14) changes in two important ways compared to 2020.

Figure 14. Electricity costs per Household income group 2050.

Energies 2024, 17, 1364 13 of 23

First, the overall magnitude of the changes in electricity prices increases sharply. This
is caused by the fact that the larger share of households with flexible devices in 2020 versus
2050 (see Table 1) results in a much larger tariff impact on grid peak load (Figure 10) and as
a result, a larger impact on grid cost (Figure 12).
Second, while the main impact of most tariffs is still a parallel shift, costs for poorer
households increase significantly more than the cost for richer households in the case of
capacity, TOU and CPP tariffs.

6. Discussion
The results from our simulations confirm the occurrence of rebound peaks in the case
of time-varying tariffs in combination with automatic load control [11,12]. Direct load
control and capacity-based tariffs can effectively avoid rebound peaks. However, due to
the legal unbundling between grid and energy companies, direct load control is typically
either used by grid operators to minimize grid costs or by energy suppliers, to minimize
energy procurement costs.
Novel grid charges which are proportional to the grid load could overcome this
problem. If customers are charged a gridload tariff (for their grid usage) and an energy tariff
proportional to the spot price (for their energy consumption), they could ask independent
aggregators to dispatch their loads in a way that minimizes the sum of grid and energy
costs, which should minimize the sum of the total system cost.
While the performance of conventional direct load control (DLC) and capacity tariffs
is similar in 2020 and 2050, the performance of the novel grid-load tariffs depends on the
simulation year. Grid-load tariffs achieve the second biggest reduction in system peak load
(Figure 4) and system cost (Figure 6) during 2020 when there are few flexible loads. This
changes dramatically during 2050, when grid-load tariffs attract a much larger volume of
flexible loads, resulting in rebound peaks of more than 100% (Figure 10) and increasing
system cost (Figure 12). We believe that the failure of grid-load tariffs to minimize system
cost, especially during years with a high share of flexible loads is due to the following two
main reasons:
First, the tariff levels of the grid-load tariff were fixed in advance so that all flexible
loads maximized consumption during the few time periods with the lowest tariff level.
This could be avoided if tariff levels were fixed ex-post, based on the actual grid load which
results after load-shifting and grid-load measurements were communicated close to real-
time [19]. This would mean that the incentive to shift towards a certain time period would
be reduced as more loads start to shift towards that time period. Creating such a feedback
loop between actual grid load and tariff levels could effectively mitigate rebound peaks.
Second, the grid load tariff which we have currently tested created incentives to
reduce load even during such periods, when the grid was not congested. While this may
be desirable from a grid perspective, it may reduce the incentive to minimize energy costs.
To avoid this, grid tariffs should only send incentives for load-shifting, when the grid
is constrained. During all other time periods, the grid tariff should not incentivize load-
shifting, so that flexibility has an incentive to dispatch in a way that minimizes energy cost.
We have summarized our ideas for designing a grid tariff that complies with these
criteria in the following research note [20]. However, due to the complexity of modeling
real-time tariffs, we have so far not been able to assess the impact of these proposals.

7. Limitations
When interpreting the results, it is important to note that certain simplifications and
assumptions were made in this model.
First, we assume automatic load control of all flexible loads in response to electricity
prices. This assumption is clearly not met today. However, as the costs for automation fall,
we expect that more and more households will be equipped with automatic load control.
Second, the determination of grid costs is based on historical data and greatly simplifies
the grid-cost impact that will occur in a real grid. In particular, we assume a linear
Energies 2024, 17, 1364 14 of 23

dependency between grid peak load and grid costs, whereas in practice, the impact will
follow a step-function.
Third, our model simulates only a single electricity tariff within each grid area. In a
liberalized electricity market, households have the freedom to choose their tariff. Therefore,
the extreme scenario of a single tariff will be unlikely to occur in a distribution grid.
Fourth, it was so far not possible to model the tariff designs suggested in [20]. Our
current model either calculates the optimal dispatch of each household independently of
each other or as part of a central optimization problem (see Appendix C). By contrast, the
calculation of an ex-post grid tariff with near real-time load forecasts would require an
iterative calculation of decentral optimizations by each household, which are linked to each
other through their impact on the total grid load.
Fifth, in our current paper, we have simulated the impact of tariff designs for a single
grid node. This could be generalized in subsequent papers by modeling tariff impacts on a
system with several nodes and calculating nodal versions of the proposed tariff designs
based on estimations of the system state [21].
Last but not least we assume exogenous wholesale prices in our model, implying
no feedback effect of behavioral changes in the grid area on wholesale prices. While this
assumption might hold true when new tariff schemes are introduced in a limited number
of distribution grids, it may not remain valid in the case of a large-scale rollout.

8. Conclusions
The increasing penetration of electric vehicles, heat pumps, and energy storage, along
with the rollout of smart metering technology, is expected to significantly increase the
potential for residential demand response. Leveraging this potential is a critical challenge
in future electricity markets. Price-based demand response strategies have the potential
to play a pivotal role by providing incentives for households to adjust their electricity
consumption patterns in a cost-effective manner. However, since loads are controlled by
households, or aggregators who provide the load control as a service rather than the grid
operator, price incentives need to be carefully crafted to ensure that the decentralized load
adjustments reduce the need for grid expansion.
This research aims to contribute to the discussion on electricity tariff design by inves-
tigating the impacts of various tariff structures on the decisions of households equipped
with different combinations of photovoltaics, batteries, electric vehicles, and heat pumps.
The study employs four evaluation metrics: (i) effectiveness, (ii) efficiency, (iii) profitability
of technologies and (iv) equity.
The first finding of our research is the importance of including appropriate impact
metrics. For example, we find that equity impacts on households tend to be smaller than
the impacts on the profitability of different technologies, because a non-negligible share
of poor households may live in houses with PV production or flexible loads. Impacts
on households with and without flexible technologies may thus not be a good proxy for
the distributional implications of different policies. Likewise, an exclusive evaluation of
the impact of grid tariffs on grid load may be misleading, as grid tariffs that achieve a
lower reduction in grid load may still be preferable as they perform better at reducing total
system cost.
Regarding grid tariff design, our findings confirm that time-varying network tariffs
such as time-of-use (TOU) tariffs or critical peak prices (CPP) can lead to rebound peaks
that surpass the original load peak by a significant margin.
Dynamic load control (DLC) by grid operators can avoid rebound peaks and reduce
grid load by up to 43%. Capacity tariffs can also avoid rebound peaks but reduce the
grid load to a much smaller extent (up to 3.6%), as individual consumption peaks do not
correlate well with total grid consumption.
Due to unbundling regulations, grid operators in Switzerland and the European Union
may not use direct load control to minimize energy procurement costs. Direct load control
Energies 2024, 17, 1364 15 of 23

by grid operators is, therefore, not a suitable option for reducing the sum of grid and energy
costs in these countries, while it might be a viable option in other jurisdictions.
A novel grid tariff that depends on grid load could overcome both problems. If it
is appropriately designed, it could incentivize customers to reduce grid load and avoid
rebound peaks. At the same time, customers who are exposed to a grid load tariff (for their
grid usage) and an energy tariff (for their energy consumption) should have an incentive to
minimize total system cost.
To avoid rebound peaks, the grid-load tariff should depend on real-time grid load
instead of ex-ante projections of grid-load. At the same time, the grid-load tariff should
avoid load-shifting incentives when the grid is not constrained, so that flexibility can be
used to minimize energy procurement costs.

Author Contributions: Conceptualization, methodology, validation, formal analysis, investigation,

resources, project administration: P.H.-L. and C.W.; software, data curation, visualization, writing—
original draft preparation: P.H.-L.; writing—review and editing, supervision, funding acquisition:
C.W. All authors have read and agreed to the published version of the manuscript.
Funding: Most of this research was funded by the Swiss Federal Office of Energy (SFOE), Project
Number: SI/501899-01. During article finalization and submission, Christian Winzer received funding
by the Swiss Federal Office of Energy’s SWEET programme as part of the project PATHFNDR. Open
access funding provided by ZHAW Zurich University of Applied Sciences.
Data Availability Statement: Dataset available on request from the authors.
Acknowledgments: We want to thank our colleague Ingmar Schlecht, as well as our SFOE contact
Wolfgang Elsenbast and other members of the advisory group for their helpful comments and the
fruitful discussions during the NETFLEX and PATHFNDR projects.
Conflicts of Interest: The authors declare no conflicts of interest. The work was financed by the SFOE
but the authors are solely responsible for the content and conclusions.

Appendix A. System Cost Calculation

As the subject of investigation in our model is a synthetic grid infrastructure, estimat-
ing the total system costs becomes necessary. We quantify the initial system costs by valuing
the load characteristics of the infrastructure scenarios using the price components of Swiss
electricity prices in 2021 (the data were obtained from the Swiss regulator, which pub-
lishes an overview of Swiss electricity prices once a year on https://www.elcom.admin.ch/
elcom/de/home/themen/strompreise/tarif-rohdaten-verteilnetzbetreiber.html). The sum
of household loads l_(n,a) over one year is multiplied by the electricity price components:

N  
Csystem = ∑ ln,a ∗ pe + pg + pt (A1)
n=1

where the electricity price is composed of an energy component p_e, a grid component p_g,
and a residual component containing taxes and subsidies p_t. The values of these price
components are displayed in Table A1.

Table A1. Median of Swiss household electricity prices for 2021 (Source: ElCom).

Grid Energy Taxes, etc. Total

Household type H4 [Rp./kWh] 9.47 7.73 3.17 20.37

We assume that residual costs are independent of consumers’ and prosumers’ load pro-
files and should, therefore, be allocated via lump sum or a fixed electricity price component
per connection point, following economic literature [22,23].
Regarding grid costs, we assume that 30% of the total grid costs depend on the
grid peak load, and therefore, on consumers’ load profiles, while 70% of the total grid
Energies 2024, 17, 1364 16 of 23

costs are driven by structural grid characteristics such as grid area, terrain, and topology,
making them independent from consumers’ load profiles [24]. The variable grid cost can
be expressed as: !
N
Cg,var = 0.3∗max ∑ ln,t ∗ Cg (A2)
n

This is indeed a simplification. Due to the lumpiness of investment decisions, the

actual cost function is more likely to resemble a step function, where the total cost remains
constant until peak demand surpasses capacity limits and necessitates capacity expansion.
However, as elucidated in [25], the cost estimates are heavily influenced by the method used
to model long-term marginal costs. Since the precise positioning and magnitude of cost
steps are subjective, we assume the aforementioned linear function as an approximation
for the genuine network costs.
Regarding energy costs, we assume that the marginal cost of energy production follows
a pattern similar to the European spot price in 2018. We calculate the total cost of the energy
that is needed to serve load ln,t for household n at time t as the product of the European
spot price and the demand.
T
Ce = ∑ ln,t ∗ pspot,t (A3)
t

By employing this formula, we assume that infra-marginal rents, which producers

receive whenever the price exceeds their marginal cost, serve as a reasonable proxy for their
fixed production costs. As demonstrated by [26], in the context of an optimal production
portfolio this assumption should hold true in the equilibrium situation.

Appendix B. Tariff Calibration

We calibrate a separate tariff for each cost component (energy, grid, residual cost) to
ensure the recovery of the respective total costs. We allocate the costs that are not directly
influenced by the load profile of consumers as a fixed price per consumption unit. This
includes residual costs such as renewable energy subsidies and taxes, as well as the fixed
cost of the grid. Alongside this fixed price, we incorporate the costs directly influenced by
consumers’ load profiles (variable costs) in the form of marginal costs, according to the
tariff approach. The variable costs contain the variable grid costs as well as energy costs. In
the subsequent subsections, we outline the calibration function for each of the approaches
that we integrated into our model.

Appendix B.1. Flat Tariff

In the case of a flat tariff, the total cost that needs to be recovered is distributed equally
over the load l during all hours t = 1 . . . T of the year. The resulting tariff levels tariffflat,t at
each time-step t can, therefore, be calculated as:

Csystem
tariffflat,t = (A4)
∑Tt lt

Appendix B.2. Time-of-Use Tariff (tou)

In the case of a time-of-use tariff, the variable cost that needs to be recovered is
distributed equally over the load l during all peak price periods t ∈ THTtou of the year. The
fixed costs are allocated in the form of a fixed price across the total load throughout the
year. The resulting tariff levels tarifftou,t at each time-step t can be calculated as:
Cg,fix C


∑ t ∈ T lt
+ ∑ g,var lt , t ∈ THTtou
t∈THT
tarifftou, t = Ct +Ce +Cg,fix
tou (A5)

∑ t ∈ T lt
, t∈
/ THTtou
Energies 2024, 17, 1364 17 of 23

Appendix B.3. Critical-Peak-Price during Selected Hours (cpp_h) and Selected Days (cpp_d)
For critical peak pricing we differentiate between an hourly CPP-tariff and a CPP
during selected days. In the hourly CPP-tariff, the peak price is only enforced during hours
with the highest demand. The total cost that needs to be recovered is distributed equally
across the load l during all high-tariff hours t ∈ THTcpp of the year. The daily CPP is applied
during fixed hours of the day on the days with the highest demand. As to the TOU tariff,
the fixed costs are allocated in the form of a fixed price across the total load throughout a
year. The resulting tariff levels tarifftou,t at each time-step t can be calculated as:
 Cg,fix C

∑t∈T lt
+ ∑ g,var lt , t ∈ THTcpp
t∈THTcpp
tariffcpp, t = Ct +Ce +Cg,fix
(A6)
, t∈
/ THTcpp

∑t∈T lt

Tariff that is proportional to gridload (gridload)

The grid-load tariff allocates the variable grid costs proportionally to the grid load.
As in the other tariffs the fixed costs are allocated in the form of a fixed component per
consumption unit. The tariff level tariffgridload,t is calculated as the sum of the fixed
component and the grid load lt at time t multiplied by a constant proportionality factor:

Cg,fix Cg,var
tariffgridload, t = + lt · 2
(A7)
∑Tt lt ∑Tt lt

Appendix B.4. Spot Price (Spot)

While all previous tariffs allocated a flexible grid component to the consumer, the
spot tariff assigns a flexible energy cost component to the consumer that is proportional
to the spot price. The tariff level tariffspot,t is calculated as the spot price pspot,t at time t
multiplied by a constant proportionality factor:

Ce
tariffspot, , t = pspot,t · T
(A8)
∑t pspot,t ∗lt

Appendix B.5. Capacity Price

Additionally, alongside the volumetric tariff approaches, we examine capacity tariffs
as another scheme that researchers have analyzed [6,7] for the purpose of recovering grid
costs in accordance with the cost reflectivity principle. The capacity tariff allocates the grid
costs over the sum of the maximum load of each household n as follows:
Cg
tariffcapacity = N
, t∈T (A9)
∑n max(lt,n )

Appendix B.6. Direct Load Control (loadcontrol)

In the case of direct load control, we assume that the consumers receive a flat tariff, as
there is no need to incentivize load-shifting through price changes.

Appendix C. Optimization Problem

We model the demand response of consumers and prosumers to price-based and
incentive-based tariff mechanisms using an optimization approach. For price-based tariffs,
we introduce dynamic grid and/or energy components with the goal of reducing grid
congestion. By altering tariff settings, we create incentives for load shifting, prompting
households to respond by minimizing their electricity costs. This is simulated through a
decentralized optimization model, assuming households respond rationally to exogenous
tariff signals. In contrast, for incentive-based tariff mechanisms, a central optimization prob-
lem has been formulated to minimize congestion at transformer stations. Both approaches
will be described in separate sections below.
Energies 2024, 17, 1364 18 of 23

Appendix C.1. Decentral Optimization—Household Optimization Problem

The decentralized optimization model calculates the load profiles for each household
which result from an optimal dispatch under a given exogenous tariff scenario. The model
is formulated as a linear optimization program (LP) that determines the cost-minimal
operation of a prosumer’s storage devices (A10). To address potential dissatisfaction
caused by device scheduling, a penalty term is introduced into the objective function. In
the case of heat pumps, this penalty term corresponds to a deviation from the desired ideal
indoor temperature (A11). For electric vehicles, it corresponds to a deviation from the
maximal state of charge that would have been achievable without flexibility provision at
the departure time (A12). For a single household, this is expressed by:

T
∑(lt,n ∗ ∆T ∗ pt
buy EV, HPPen
minCn = − iPV sell
t ∗ ∆T ∗ pt + C t ) + max(lt,n ) ∗ ppower (A10)
t

HPPenalty
= ∆SOCHP
Ct,n HP
t,n ∗PLS ∀t (A11)
EVPenatly
  
EV,departure
Ct,n = SOCEV
max,t − SOCEV
t,n ∗ ut,n ∗ PEV
LS ∀t (A12)

with:
lt,n load from household n at time t
it,n injection from household n at time t
∆T Simulation time interval (1 h)
buy, sell
pt electricity price at time t/injection few at time t
ppower capacity price-at time t
CLS Dissatisfaction term for load shifting
This objective function is subject to power balance constraints. The power consump-
tion for a household at time t is described by (A13). Equation (A14) ensures that the amount
of generated power from the PV plant is either consumed by the household or injected into
the grid.
lt,n = lfix EV,ch
t,n + lt,n + lHP,SQ
t,n + lHP PV,used
t,n − lt,n + lBESS
t,n ∀t, n (A13)
PV,used
gPV
t,n = it,n + lt,n ∀t, n ∈ NPV (A14)
with:
lfix
t,n Not shiftable part of the load for household n at time t
lEV,
t,n
ch
Power demand to charge EV/BESS for household n at time t
HP
lt,n Power demand of the heat pump for household n at time t
gPV
t,n generation from PV for household n at time t
lPV/BESS,
t,n
used
Power consumed from PV/BESS for household n at time t
it,n Power injected to grid from PV for household n at time t
The objective function is subject to various device-specific constraints that define the
operation of flexible assets, namely BESS, EV, and HP. The operating limits of a BESS
are defined by Equations (A15)–(A17), ensuring that the BESS operates within its state of
charge (SOC) and power limits. Additionally, these equations ensure that the BESS is solely
charged by the PV plant. The charging and discharging logic of a BESS is stipulated by
Equation (A18). Electric vehicles are equipped with battery electric storage systems that are
discharged while driving and available for charging, thereby providing flexibility during
parking times. Consequently, the constraints for BESS and EV share many characteristics.
In addition to the constraints describing the BESS operation, the EV model incorporates
an extra variable ensuring that an EV is only charged when plugged in, Equations (A19)
and (A20). Furthermore, our model does not account for Vehicle-to-Grid services. Hence,
we assume that an electric vehicle’s battery is solely discharged during driving (A21).
Energies 2024, 17, 1364 19 of 23

This assumption implies that electric vehicles in our model offer flexibility primarily by
deferring the charging process.

−lBESS BESS
max ≤ lt,n ≤ lBESS
max , ∀n ∈ NBESS (A15)

lBESS
t,n ≤ lPV,used
t,n , ∀n ∈ NBESS (A16)

0 ≤ SOCBESS
t,n ≤ SOCBESS
max , ∀n ∈ NBESS (A17)
 
SOCBESS
t+1,n = SOCBESS
t,n ∗ 1 − η
BESS
+ lBESS
t,n ∗ ∆T, ∀n ∈ NBESS (A18)

0 ≤ lEV,ch
t,n ≤ lEV,ch EV,home
max ∗ ut,n , ∀n ∈ NEV (A19)

0 ≤ SOCEV EV
t,n ≤ SOCmax , ∀n ∈ NEV (A20)
EV ,ch
SOCEV EV
t+1,n = SOCt,n + lt,n ∗ ∆T − lEV,drive
t,n ∗ ∆T, ∀n ∈ NEV (A21)
with:
BESS|EV ,ch
lmax Maximum charging and discharging rate of the BESS/EV
BESS|EV
SOCmax Maximum BESS/EV capacity
EV
ut,n home Binary variable that indicates that the EV is pluged in at time t
BESS|EV
SOCt,n Energy capacity of the BESS/EV at t (kWh)
η BESS Efficiency the BESS (implemented as standing losses)
In our model, we represent heat pumps as thermal storage devices with a certain
degree of inertia, which is defined by constraints (A22)–(A24). A synthetic heat pump
profile depicts the required electrical power to fulfill the household’s heat demand. We posit
that a deviation from this profile beyond a defined dead band triggers a temperature change,
consequently causing charging or discharging of the thermal storage (A24). Equation (A23)
outlines the SOC limits of the thermal storage, thereby determining the heat pump’s load-
shifting potential. Equation (A22) guarantees that the heat pump’s electrical power limits
are not breached.
−lHP,SQ
t,n ≤ lHP HP HP,SQ
t,n ≤ lmax,n − lt,n , ∀n ∈ NHP (A22)

0 ≤ SOCHP HP
t,n ≤ SOCmax,n , ∀ n ∈ NHP (A23)
HP
SOCHP HP
t+1,n = SOCt,n + lt,n ∗ ∆T, ∀ n ∈ NHP (A24)
with:
lHP
t,n Power that adjusts the set point of the heat pump
lHP,SQ
t,n Power demand of the heat pump to ensure the set room temperature
SOCHP t,n Capacity of the thermal storage

Appendix C.2. Central Optimization—Transformer Optimization Problem

To simulate a direct-load-control tariff l, we employ a slightly different optimization
problem. The objective of DLC is to alleviate grid congestion by directly manipulating the
operation points of flexible assets. This is achieved by minimizing transformer overloads.
Similar to the decentralized optimization model, we include a penalty term in the objective
function to minimize household discomfort through load restrictions (A25). In addition,
we add a term that includes the electricity costs and the revenues from PV injection to the
grid to include self-consumption on the grid level. Additionally, we incorporate a term
that accounts for electricity costs and revenues from PV injection to the grid to include self-
Energies 2024, 17, 1364 20 of 23

consumption at the grid level. The operation of flexible assets and the penalty terms mirror
the definition of the decentralized model and are represented by Equations (A14)–(A24).

T  
min∑Max ltrafo
t − ltrafo
max ∗ p
VOLL
t
T N (A25)
+∑ ∑ln,t ∗ pt
buy
− in,t ∗ psell
t
t n
EV,HOPen
+ ∑Tt ∑N
n Ct,n , ∀t, n

N
ltrafo
t = ∑ ln,t − in,t (A26)
n

Appendix D. Grid Cost Recovery

In a post-optimization calculation, we adjust the tariff levels that were calculated
during the initial calibration to achieve cost recovery. The device scheduling optimiza-
tion alters the system’s load profile, leading to adjustments in variable grid and energy
costs. These revised costs are computed utilizing post-optimization load statistics, as
outlined in Equations (A2) and (A3). Subsequently, the tariffs are recalibrated with the
updated variable network costs and energy costs, following the same formulas as during
the initial calibration.

Appendix E. Impact Measures

We assess the impact of various tariff designs across the following four dimensions:
1. Effectiveness: We determine how much each tariff reduces the peak load at each
node, as well as the peak load of the overall system.
2. Efficiency: We calculate the extent to which each tariff changes the total system cost,
encompassing energy costs, grid costs, and residual costs.
3. Impact on Profitability of New Technologies: We compute the cost difference be-
tween households equipped with and without heat pumps, electric vehicles, PV
systems, or batteries across various tariff scenarios. This assessment focuses exclu-
sively on the electricity cost implications resulting from a tariff scheme, excluding
investment cost considerations. To quantify the variations in electricity costs among
households with distinct appliance equipment, we employ a multiple linear regression
model featuring interaction terms. Initially, we ascertain the impacts of appliance
equipment on household electricity bills under a single tariff. This is achieved through
Equation (A27). To evaluate changes in profitability, we extend this calculation with a
dummy variable for the new tariff. The parameter estimates of this dummy variable
reflect the electricity cost disparities arising from the new tariff. In simpler terms, this
relationship can also be represented by the difference in the average electricity cost
tariff
of all households with a particular equipment level e under a new tariff Chh,e and
the average electricity cost of households with the same equipment level under the
SQ
existing tariff Chh,e (Equation (A28)).

Chh = α + β1 EV + β2 HP + β3 PV + β4 PV ∗ BESS + β5 PV ∗ EV + β6 PV ∗ HP + β7 PV ∗ EV ∗ HP + β8 HP ∗
(A27)
EV + β9 PV ∗ HP + β10 PV ∗ HP + β11 PV ∗ BESS ∗ EV ∗ HP + ϵhh

tariff SQ
∆Chh,e = Chh,e − Chh,e , ∀e in E (A28)
4. Equity: We assess how much each tariff influences consumer bills across different
income brackets. This measure is obtained by multiplying the bill impact for each
household type by the proportion of consumers from each income bracket belonging
to that household type. We base this allocation on survey findings from the Swiss
Household Energy Demand Survey (SHEDS) described in [27] (see Table A2). Due
Energies 2024, 17, 1364 21 of 23

to the substantial variability in electricity costs among households with varying

appliance equipment, we standardize electricity costs to one consumption unit (kWh).
By evaluating these dimensions, we can gain a comprehensive understanding of the
effects of diverse tariff strategies on various facets of the energy system, economic outcomes,
and fairness considerations.

Table A2. Share of SHEDS respondents from different income brackets per household type.

Household Features Income Class CHF per Month

HH-Type HP EV BESS PV 3000–4499 3000–4499 4500–5999 6000–8999 9000–12,000 >12,000
type1 0 0 0 0 4% 9% 19% 31% 20% 16%
type2 1 0 0 0 3% 5% 13% 27% 29% 24%
type3 0 1 0 0 2% 4% 8% 22% 32% 32%
type4 0 0 0 1 10% 5% 15% 32% 21% 17%
type5 1 1 0 0 4% 0% 8% 23% 27% 38%
type6 1 0 0 1 2% 10% 11% 22% 21% 33%
type7 0 1 0 1 0% 0% 10% 10% 40% 40%
type8 0 0 1 1 10% 5% 15% 32% 21% 17%
type9 1 1 0 1 0% 5% 5% 16% 21% 53%
type10 1 0 1 1 2% 10% 11% 22% 21% 33%
type11 0 1 1 1 0% 0% 10% 10% 40% 40%
type12 1 1 1 1 0% 5% 5% 16% 21% 53%

Appendix F. Load Profiles

For the diverse appliances, synthetic load profiles were generated. To capture the
diversity of households’ behaviors, an ensemble of 100 synthetic load profiles was initially
created, from which 300 load profiles were selected for the simulation. In the subsequent
part of this section, the process of generating synthetic profiles for each simulated appliance
is detailed.
Regarding the non-flexible household load, an ensemble of 100 synthetic load profiles
was generated using the LoadProfileGenerator (LPG) [18]. These profiles were scaled to
match the average measured electricity consumption of households within the grid area of
a distribution grid operator in the canton of Aargau in 2018, amounting to 4873 kWh per
household. This procedure results in 100 diverse household load profiles, each representing
the non-flexible electricity consumption of households, in a one-hour resolution.
The synthetic load profiles for electric vehicle charging were also generated using the
LPG. A matching electric vehicle charging profile was assigned to each household load
profile. We assumed a charging power of 11 kW, an average vehicle battery capacity of
50 kWh, and an average consumption of 16 kWh per 100 km. We also assumed that load
shifting for EV charging would not compromise households’ comfort if the EV was fully
charged at the desired departure time.
The load profile for HP was generated by determining the relative heating demand
for each hour of the year and scaling it by the thermal energy demand of households. The
latter was estimated using the measured gas consumption of households within the grid
area of a distribution grid operator in the canton of Aargau in 2018. The resulting mean
max
load of the heat pump profiles is lt,hp = 2.75 kW. To simulate the flexibility operation of
the heat pump, it was assumed that a load shift of 2 h would only marginally impact the
perceived room temperature, and therefore, would not affect the household’s comfort.
For PV profiles, more than 300 standard generation profiles with varying module
orientation and slope were calculated. The distribution of module orientation and slope
Energies 2024, 17, 1364 22 of 23

was assigned based on realized PV plants in the considered distribution grid. This approach
introduces heterogeneity in the generation patterns to the simulation model. The synthetic
generation profiles were then allocated to households and sized according to the realized
PV plants in a specific distribution grid area in Switzerland. The peak power of the PV
plants was adjusted to cover the household load.
Only households that were already equipped with PV could be additionally equipped
with a BESS. To simulate the operation of a BESS, the following assumptions were made:
the battery capacity is sized with a factor of 1.5 relative to the PV peak power, the maximum
charging power was assumed to be 3 kW, and the roundtrip efficiency was set at 0.9.

Figure A1. Synthetic load profiles for one household over one week in (a) winter and (b) summer.

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