# Balancing DSO interests and PV system economics with alternative tariffs

Alejandro Pena-Bello  Photovoltaics and thin film electronics laboratory (PV-
LAB), École Polytechnique Fédérale de Lausanne (EPFL), Institute of Electrical
and Microengineering (IEM), Neuchâtel, Switzerland  Robin Junod  Christophe
Ballif  Nicolas Wyrsch

###### Abstract

Distributed rooftop photovoltaics (PV) is one of the pillars of the energy
transition. However, the massive integration of distributed PV systems
challenges the existing grid, with high amounts of PV injection possibly
leading to over-voltage and reverse power flow, with line and transformer
overloading, among other issues. Moreover, the increase in PV self-consumption
and consequently the reduction of imported electricity poses a problem in
recovering Transmission System Operators (TSOs) and Distribution System
Operators (DSOs) grid costs, that until now have been directly linked to the
amount of electricity consumed due to the volumetric nature of traditional
tariffs. To investigate whether alternative tariffs could mitigate PV impacts
at the distribution level without hampering PV development, we assess five
electricity tariffs that could help the DSOs to recover the costs of
maintaining the distribution grid. Additionally, we evaluate how such tariffs
may affect private investment in storage and their impact on three types of
low-voltage networks (i.e., urban, semi-urban, and rural). We found that
tariffs with a capacity-based component promote further adoption of PV and
storage. At the same time, they allow the DSOs to recover the grid cost
without incurring relevant economic differences for the customer. However, all
assessed tariffs were found to have a limited role in mitigating PV impacts at
the distribution level.

###### keywords:

PV , energy storage , battery , electricity tariffs

††journal: Applied Energy

[table]capposition=top

PV | Photovoltaic | FiT | Feed-in Tariff
---|---|---|---
SC | Self-consumption | SS | Self-sufficiency
FT | Flat tariff | DT | Double tariff
CT | Capacity-based tariff | LV | Low-voltage
TOU | time of use | MV | Medium-voltage
EV | Electric vehicle | HP | Heat pump
CAPEX | capital expenditure | OPEX | Operational expenditure
TSO | Transmission system operator | DSO | Distribution system operator
SIA | Swiss Society of Engineers and Architects | IQR | Interquartile range
RegBL | Registre fédéral des bâtiments et des logements | MILP | Mixed Integer Linear Programming
IRENA | International Renewable Energy Agency |  |

List of abbreviations.

##  1 Introduction

The massive integration of distributed photovoltaics (PV) poses several
challenges at the distribution level. For instance, PV injection can lead to
over-voltage, line, and transformer overloading, and reverse power flow, among
other issues [1]. This is mainly because the distribution grid infrastructure
was dimensioned for consumption only and without upstream flow.

From the transmission system operator (TSO) and the distribution system
operator (DSO) perspective, there is a need to recover the costs of the
transmission and distribution grid (i.e., grid costs), to ensure the adequate
maintenance of the infrastructure and the reliability and stability of the
grid [2]. Until now small consumers are charged for their share of grid costs
based on their energy consumption [3]. Therefore, the recovery of such costs
is being offset by the prosumers due to the increased amount of PV self-
consumption and it is expected to be hindered since typical electricity
tariffs are mainly volumetric (i.e. the final bill corresponds to the amount
of electricity consumed, in €/kWh) in many regions including Switzerland [4],
UK [5], and Europe, in general, [6, 7]. However, using volumetric network
charges is driving inefficiencies not previously seen in the electricity
industry [8, 9]. Although an increase in demand from new devices such as
electric vehicles (EVs) and heat pumps (HPs) is anticipated, the increased PV
penetration, together with distributed energy storage and energy efficiency
measures are expected to eventually reduce the final amount of electricity
sold to the final user (in kWh) and volumetric contribution to grid costs.

Existing studies have looked at the effects of volumetric tariffs on prosumer
behavior and incentives for residential buildings and households in
particular. Günther, Schill, and Zerrahn [10], considered the impact of three
retail tariffs on prosumer behavior in Germany. The authors explored a flat
volumetric tariff, a double tariff, and a real-time pricing tariff and further
consider different feed-in tariff (FiTs) rates. The results show a reduction
in the optimal PV and battery capacities under a double tariff, leading to
reduced self-generation while requiring prosumers to contribute more to fixed
power sector costs. Al Arrouqi et al. [11], considered flat, double, and
dynamic tariffs and analyzed their impact on PV profitability in Australia.
They found the dynamic tariff to be more economically beneficial for the
utility company in comparison to a flat rate tariff, the latter being the
tariff that provides the best internal rate of return for the homeowners.
Fett, Fraunholz, and Keles [12], looked at the long-term impacts of
residential PV and battery diffusion on the electricity market taking into
account an electricity market simulation, and different scenarios, including
different types of tariffs, comprising the use of volumetric and fixed grid
charges, as well as the use of FiTs and dynamic export prices (i.e., depending
on the electricity market price), and feed-in limitations. The authors found
that restrictive measures (fixed grid charges, and feed-in limitations) lead
to substantially smaller photovoltaic and storage systems in the medium term,
but this effect is smaller in the long term, mainly due to the lower cost of
the PV and storage system and higher retail prices in the future.

Conversely, it has been argued that tariffs with a capacity-based component
(i.e. tariffs that are completely or partially based on the maximum measured
power demand during a billing period, in €/kW) will be able to produce a more
efficient and more equitable price signal [8]. This type of tariff has been
widely analyzed in the literature, for instance, Avau, Govaerts, and Delarue
[13], compared the impacts of different retail tariffs, including a pure
capacity-based tariff that charges the user depending on the maximum annual
power capacity measured every hour. They found that prosumers are very
sensitive to capacity tariffs and that the price of the capacity tariff is
hardly relevant. Schittekatte, Momber, and Meeus [2], looked into volumetric,
capacity-based, and fixed grid costs tariffs, and detected that capacity-based
charges (over) incentivized investment in PV and batteries, which severely
distort the investment decisions of consumers. On the contrary, Bloch et al.
[14], benchmarked five retail tariffs, including one with a capacity-based
component depending on the monthly maximum power exchanged with the grid (for
both, import and export), and analyzed the trade-offs between the economic
viability of privately owned energy systems and their grid usage intensity.
The authors found that the capacity-based tariff did not encourage investment
in the battery system, since the cost is dominated by the PV injection power,
which can be simply curtailed. Finally, these tariffs were found to create
more value for residential batteries when combining different applications
[15].

While some studies take both perspectives, the private investor and the DSO
perspective [10, 14], the impact of the tariffs and PV and battery scheduling
on the network operation is usually out of the scope of the studies. Only very
little research has considered the technical impacts of retail tariffs on the
low-voltage (LV) network. Pimm, Cockerill, and Taylor [16], analyzed Time-of-
Use (TOU) tariffs’ impact on import and export peaks at the low voltage level
but only took into account the reduction in maximum demand at the aggregated
level. Azuatalam, Chapman, and Verbič [17], used a probabilistic assessment
for two volumetric tariffs and two tariffs with a volumetric and a capacity-
based component. The authors concluded that flat tariffs perform better than
ToU tariffs for mitigating voltage and alleviating line congestion problems,
and the addition of a capacity-based component to such flat tariffs helps to
reduce network peaks further. The assessment was done for a single LV network
and for predefined PV capacities. Schreck et al. [18], considered a local
energy market and determined the impact of energy-based grid tariffs with
constant, dependent on the network (urban, semi-urban, and rural), and time-
variable cost components and power-based tariffs. The results indicate a high
potential of power-based tariffs for peak reduction. However, the authors used
pre-defined PV and storage capacities.

The previously mentioned studies deal with the analysis of different
volumetric and/or capacity-based tariffs in LV networks. What is missing,
however, is a comprehensive analysis that, considering the Energy Transition
context, the DSO perspective, and the prosumer’s investment profitability,
integrates the effects of different tariffs on the optimum size and operation
of PV and battery systems, comparing these effects in different LV networks.

Against this background, we aim to assess alternative electricity tariffs that
help to mitigate the impact of distributed energy resources on the grid,
without hampering PV development. This study builds on the related work of
Holweger et al. [4]. We use a MILP optimization of the PV and battery sizing
and operation from the consumer’s point of view at the building level,
following a purely economic rationale. Here we include different types of
tariffs and two additional types of LV networks, as well as a new evaluation
of the results of the power flow analysis, based on statistical analysis, to
assess the following three research questions:

  * 1.

What is the impact of alternative electricity tariffs on the adoption and
operation of distributed PV-coupled battery systems?

  * 2.

How does the operation of distributed PV-coupled battery systems under
alternative electricity tariffs affect the LV network operation?

  * 3.

How does the impact of the tariffs differ depending on the LV network
typology?

We contribute to the existing literature by shedding light on the effects of
alternative tariffs and alternative tariff structures on the adoption of
distributed PV-coupled battery systems, preventing undesired outcomes of
tariffs. Moreover, the integration of the three perspectives (i.e. from the
national Energy Transition goals, the DSO, and the prosumer), provides a
comprehensive view of the outcomes of the study, which would prove to be
valuable also for policy-makers and regulators in the path towards a
decarbonized economy.

Bearing these questions and contributions in mind, we design five alternative
retail tariffs. We use three volumetric tariffs and two tariffs that mix a
volumetric and a capacity-based component, developed in collaboration with a
Swiss DSO. The volumetric tariffs include two Time-of-Use (TOU) tariffs, and a
dynamic volumetric tariff based on historical data at the transformer station
to replicate the stress at the transformer level and give a price signal to
the consumer to reduce their consumption. Whereas the two tariffs with a
capacity-based component have different billing horizons, namely monthly and
daily. These five tariffs are compared to two reference tariffs that are
currently used, a flat and a double tariff.

Subsequently, these retail tariffs are tested in three typical Swiss LV
networks (urban, semi-urban, and rural), using power flow analysis to evaluate
the power exchanges at the transformer station, as well as line overloading,
and voltage violations. We look at the year 2025, using the expected cost of
the PV and battery systems for such year [19], that are assumed to be
installed at once for all buildings, one full year of demand data with a
15-minute resolution collected back in 2015 [20, 21], that is then adjusted to
the transformer present-day load at the transformer level [22]. The proposed
method allows us to provide technical and regulatory recommendations which are
important for DSOs, regulators, and policy-makers to design new electricity
retail tariffs that help to mitigate the impact of large amounts of
distributed energy resources at the LV level without hampering PV development
and contribute to recover network costs. With a relatively low density and a
small number of residents, the Swiss context allows the derivation of insights
into the effects of retail tariffs in residential areas.

The remaining parts of the paper are structured as follows. In Section 2, the
input data, as well as the methodology of the paper are introduced. In Section
3, the results are presented. Section 4 is a discussion of the implications of
our results; limitations and possibilities for future work are also summarised
here. Lastly, a conclusion is formulated.

##  2 Materials and methods

Five electricity tariffs are defined in collaboration with a Swiss DSO,
Romande Energie, with a forward-looking perspective based on the expected
costs of PV and batteries in the year 2025. These tariffs are tested in three
real LV networks (urban, semi-urban, and rural), that are representative of
the Romande Energie electric distribution grid network. In the first step, we
use an optimization framework to assess the impact of the electricity tariffs
on the consumer’s decision to install PV and batteries at the building level,
as well as its operation, using a purely economic rationale. Then, we run a
power flow analysis to evaluate the impact of the electricity tariffs on the
LV network. It is worth mentioning that EVs and HPs are out of the scope of
this study, and therefore, their associated electricity profile is not
considered here.

###  2.1 Input data

####  2.1.1 Demand and PV data

Demand data measurements are not available for the selected LV networks,
therefore an estimation of the building demand is needed. Data from three
sources are used to estimate the load curves for each building within each
zone. First, we recover data from the Registre fédéral des bâtiments et des
logements (RegBL), such as building date of construction or renovation,
building/local categories, building surface, dwellings surface, and the number
of floors. Second, we use data from the Swiss Society of Engineers and
Architects (SIA) norms, such as electrical consumption per building type and
age. Third, smart-meter measurements from the Swiss French-speaking area
collected in the framework of the Flexi projects, with 15-min resolution for
different building categories (i.e., apartment, house, and not residential)
[22, 20, 21] are used as a proxy variable. Finally, we utilize the real load
curve at the transformer station provided by Romande Energie to match the sum
of individual building loads at the aggregated level.

Additionally, for the three LV networks, information on the roof surface area,
azimuth, and tilt for every building inside the selected LV network is
extracted using the RegBL. To model the PV generation, monitored environmental
variables including outdoor temperature and horizontal solar irradiance of the
MeteoSwiss weather station situated in Pully, Vaud are used. These data are
combined with data from the Sandia PV module database for the SunPower
SPR-315E-WHT PV modules, to calculate the current and voltage performance per
module, which are then aggregated depending on the roof orientation.

Finally, The PV and battery price levels have been set according to the
reference year 2025. The price projections have been extracted from the IRENA
report [19] and calibrated for the Swiss price levels provided in a recent
market study [23] using the empirical model presented by Bloch et al. [14].
The resulting PV and battery cost function is decomposed into a fixed (e.g.
administrative procedures and fixed installation costs) and a linear component
(relative to the installation capacity) [23]. These linear cost functions are
annualized and used along with the PV yearly maintenance cost and battery
lifetime in Eq. 1. Table 1 displays the main techno-economic parameters of
this study.

Parameter | Value | Reference
---|---|---
System lifetime | 25 years | [19]
Discount rate | 3% | Own assumption
PV fixed cost | 10 049 € | [19, 23]
PV specific costs | 1.05 €/W | [19, 23]
Battery fixed cost | 0 € | [19, 23]
Battery specific costs | 229 €/kWh | [19, 23]
Table 1: Techno-economic parameters used in this study.

####  2.1.2 Low-voltage network data

Romande Energie provided for each LV network the transformer, cables, and line
characteristics (e.g. capacity, line length, impedance…), as well as the
federal building identifier (EGID) of each customer linked to each injection
point and the measured load charge of the transformer station, including a
correction for the existing PV capacity. The three LV networks were chosen to
represent rural, semi-urban, and urban LV networks (see Figure 1). Table 2
presents the main characteristics of each LV network.

(a)  Urban LV network. (b) Semi-urban LV network.

(c)  Rural LV network.

Fig. 1: Illustration of the LV networks used in this study.

LV network type |  Transformer capacity [kVA] |  Virtual Transformer Capacity [kVA] |  Number of loads |  Number of buildings |  Number of injection points |  Max power [kW] |  PV correction max [kW] |  Total consumption [MWh]
---|---|---|---|---|---|---|---|---
Urban | 2x 630 | 1000 | 287 | 65 | 33 | 419.8 | - | 1671.2
Semiurban | 2x 400 | 1000 | 174 | 71 | 37 | 508.6 | - | 2065.6
Rural | 1x 630 | 630 | 48 | 32 | 24 | 75.9 | 59.7 | 204.3

Table 2: Main characteristics of the low-voltage networks.

###  2.2 Tariffs

Five alternative tariffs aiming to limit the impact of PV at the distribution
level are assessed. We aim to avoid hampering the economic attractiveness of
potential rooftop PV installations in order to reach the national PV targets.
Moreover, the five tariffs are assessed and compared to two references from
Romande Energie (flat and double tariff) [24]. These alternative tariffs have
two different structures, three are purely volumetric tariffs (i.e. the final
bill corresponds to the amount of electricity consumed, in €/kWh), and two are
mixed tariffs with a volumetric and a capacity-based part (i.e. the tariffs
are partially based on the maximum measured power demand during a billing
period, in €/kW):

  1. 1.

A volumetric DT that seeks to promote consumption when PV production is
substantial (i.e., DT solar) with an off-peak time during half of the year
(i.e., from April to September) every day before 18 h, and during winter the
tariff is the same as the reference DT.

  2. 2.

A volumetric double tariff during winter, equal to the reference DT, with a
flat tariff during summer (i.e., DT summer flat). This tariff seeks to promote
lower consumption during peak hours in winter and to encourage self-
consumption in summer.

  3. 3.

A purely volumetric dynamic tariff that is proportional to the aggregated
expected load curve of Romande Energie for 2025 including projections for PV
integration, with peaks at the same time when demand peaks at the aggregated
level (for instance, the dynamic tariff is higher in the afternoon than the
rest of the day, as well as it is higher in winter than in summer, see Figure
A1 in Supplementary Material).

  4. 4.

A tariff with a capacity component with a monthly billing horizon (i.e.,
€/$kW_{month-i}$). With this tariff, the idea is to limit the maximum monthly
power drawn from the grid and limit the impact of demand on the grid.

  5. 5.

A tariff with a capacity component with a daily billing horizon (i.e.,
€/$kW_{day-j}$). As in the case of the monthly tariff, the rationale is to
limit the daily maximum power drawn from the grid and limit the impact of
demand on the grid.

The tariffs with the capacity component are a mix of volumetric and capacity-
based tariffs, accounting for the volumetric nature of energy procurement and
taxes, whereas the capacity component aims to replace the grid cost (see Table
3). These distribution and transmission costs are designed to match the
average of the distribution and transmission costs of the two reference
tariffs. For all the tariffs, the taxes (including federal and cantonal duties
as well as feed-in remunerations) are maintained volumetric and constant and
account for 2.92 ¢/kWh (please note that taxes are maintained constant across
different municipalities for comparability reasons). Finally, the export
tariff (i.e., the mandatory take-back/feed-in tariff) is kept constant across
tariffs at 9.5 ¢/kWh, whereas the fixed part of the tariff (subscription, in
€/month) is set to zero in order to do a fair comparison among the seven
tariffs. Table 3 presents the main components of each tariff.

A calibration of these tariffs was performed aiming at keeping the DSO revenue
(from selling energy minus the cost of buying exported power) of each network
as close as possible to the net profit of the reference scenario, under the
hypothesis that all buildings will behave exactly the same way as under the
reference scenario. This process was done empirically through the adjustment
of the energy costs and the grid costs in the case of purely volumetric
tariffs. Whereas in the case of tariffs with a capacity component, the
adjustment was done on the energy costs and the import power cost (see Table
3).

Please note that the taxes and the export tariff are kept constant across the
different tariffs. In the case of the dynamic tariff, the energy cost and the
grid cost are considered to be equal (i.e., 50/50 distribution after the
subtraction of taxes). Finally, the average of the results for the three grid
networks was used for the final results presented in this report, to avoid
local pricing and enable fair comparisons between the networks.

Tariff | Seasona | Peak |  Energy cost [¢/kWh] |  Grid cost [¢/kWh] |  Tax [¢/kWh] |  Total cost [¢kWh] |  FiT [¢/kWh] |  Fixed Fee [ €/month] |  Import power cost [ €/kW] |  Export power cost [ €/kW]
---|---|---|---|---|---|---|---|---|---|---
Reference FT | - | - | 7.98 | 8.45 | 2.92 | 19.35 | 9.5 | 0 | - | -
Reference DT | - | Peak (M-F 6-22) | 9.17 | 9.86 | 2.92 | 21.95 | 9.5 | 0 | - | -
Off-Peak | 5.87 | 5.26 | 2.92 | 14.05 | 9.5 | 0 | - | -
DT solar | Summer | Peak (18-00)b | 9.17 | 9.86 | 2.92 | 21.95 | 9.5 | 0 | - | -
Off-Peak | 5.87 | 5.26 | 2.92 | 14.05 | 9.5 | 0 | - | -
Winter | Peak (M-F 6-22) | 9.17 | 9.86 | 2.92 | 21.95 | 9.5 | 0 | - | -
Off-Peak | 5.87 | 5.26 | 2.92 | 14.05 | 9.5 | 0 | - | -
DT summer flat | Summer | FT | 7.98 | 8.45 | 2.92 | 19.35 | 9.5 | 0 | - | -
Winter | Peak (M-F 6-22) | 9.17 | 9.86 | 2.92 | 21.95 | 9.5 | 0 | - | -
Off-Peak | 5.87 | 5.26 | 2.92 | 14.05 | 9.5 | 0 | - | -
Dynamic | - | - | 10.76c | 10.76c | 2.92 | 24.44c | 9.5 | 0 | - | -
CT Monthly | - | - | 7.98 | - | 2.92 | 10.9 | 9.5 | 0 | 16.4 | 0
CT Daily | Summer | - | 7.98 | - | 2.92 | 10.9 | 9.5 | 0 | 0.5312 | 0
Fall/Spring | - | 7.98 | - | 2.92 | 10.9 | 9.5 | 0 | 0.9296 | 0
Winter | - | 7.98 | - | 2.92 | 10.9 | 9.5 | 0 | 1.3280 | 0

  * a

When the year is divided into two seasons. The summer runs from the $1^{st}$
April to the $30^{th}$ September.

  * b

The on-peak tariff applies every day of the week.

  * c

The values of the dynamic tariff are variable throughout the year, here we
present the median values for the energy cost and the grid cost, whereas the
taxes are constant throughout the year.

Table 3: Electricity tariff components depending on the tariff used in this
study. See Section 2.2 for details on the calibration process followed to
obtain the coefficients presented in this table.

###  2.3 Modeling

The modeling is done in three stages. First, the demand allocation for each LV
network, followed by the optimization from the consumer perspective, based on
a purely economic rationale, and finally, the power flow analysis for each LV
network is carried out.

####  2.3.1 Demand allocation

The methodology for demand allocation was developed by Holweger et al.[22],
and it relies on a two-stage Mixed-integer linear programming (MILP)
optimization. The allocation process is separated into three steps. First, the
annual energy consumption of each building within each predefined zone is
estimated using the RegBL data and SIA norms, describing the load category of
each building (e.g., apartment, house, not-residential) [22, 20, 21]. Then,
the first stage of the optimization is to allocate and scale a load curve to
each building depending on its category and annual consumption. For this, a
minimization of the difference between the annual energy consumption for each
building and the reference load curves from real smart-meter data is carried
out. Finally, the second stage of the optimization minimizes the difference
between the sum of all building load curves and the measured transformer load
curve, while the changes done to every building load curve are also minimized
(see Supplementary Information Section 3 for the model validation).

####  2.3.2 Design and battery scheduling optimization

Building upon previous work [14, 4], the PV and battery sizing and operation
for each building are optimized, minimizing the total cost of ownership, i.e.,
the sum of the annualized investment, maintenance, and operational cost (see
Eq. 1), subject to power balance constraints (see Refs. [14, 4], Supplementary
Information Section 2 for further information on modeling, and Supplementary
Information Section 3 for the model validation). In this work, battery
charging from the grid and battery export are forbidden, according to existing
Swiss regulations for behind-the-meter storage systems. Therefore, the battery
can uniquely be used to charge from the PV system and to cover the building’s
electricity needs. Perfect forecasting is used for both PV generation and
electrical demand.

$minimize\leavevmode\nobreak\
(\textsc{capex}(P_{CAP}^{PV},E_{CAP}^{BAT})+\textsc{opex}(P_{t}^{IMP},P_{t}^{EXP}))$
(1)

where capex is a function of the installed PV capacity ($P_{CAP}^{PV}$) and
the battery size $(E_{CAP}^{BAT})$, opex are a function of the grid exchange
power ($P_{t}^{IMP}$,$P_{t}^{EXP}$). The objective function is subject to
battery constraints and power balance constraints (for the load, the grid, and
the PV system). The operational costs are the cost of exchanging energy with
the grid (maintenance costs are not taken into account). We consider
volumetric and capacity-based tariffs (Eqs. 3a and 3b).

$\textsc{OPEX}=\textsc{ox}_{\text{ge}}^{\text{vol}}+\textsc{ox}_{\text{ge}}^{\text{pow}}\\\
$ (2) Volumetric tariff $\displaystyle\textsc{ox}_{\text{ge}}^{\text{vol}}$
$\displaystyle=\sum_{t=1}^{T}\left[P^{\textsc{imp}}_{t}\cdot
t^{\textsc{imp}}_{t}-P^{\textsc{exp}}_{t}\cdot
t^{\textsc{exp}}_{t}\right]\cdot\textsc{ts}_{t}$ (3a) Capacity-based tariff
$\displaystyle\textsc{ox}_{\text{ge}}^{\text{pow}}$
$\displaystyle=\sum_{k=1}^{K}P^{\textsc{max}}_{k}\cdot t^{\textsc{max}}_{k}$
(3b)

where $t^{\textsc{imp}}_{t}$ and $t^{\textsc{exp}}_{t}$ are the volumetric
import and export tariff respectively (in €/kWh), and $\textsc{ts}_{t}$ is the
simulation time-step. For the capacity-based tariff, the maximum power of the
billing period k, $P^{\textsc{max}}_{k}$ and $t^{\textsc{max}}_{k}$, is the
maximum import power per billing period k. Two of the tariffs assessed in this
study include a capacity-based component (namely tariffs CT monthly and CT
daily), but they also count with a volumetric component, therefore, the opex
is the sum of both, volumetric and capacity-based tariff components (see Eq.
2).

####  2.3.3 Power flow analysis

Taking as input the results of the PV-coupled battery system scheduling
optimization, and the LV network characteristics, a graph of the grid network
is defined using python packages Networkx and pandapower. We use the per-unit
(p.u.) system for voltage at every network node and for current flowing
through every line.

Line loading level is used as a metric for grid congestion, given the lines’
properties, in particular, the maximum allowable current. The line loading
level is the ratio between the current and the maximum nominal current of the
line; we consider an overloaded line when the line loading level is higher
than 100%. Moreover, we consider the situation separately when the bus voltage
at an injection point is above 1 p.u. and when it is below 1 p.u., and use the
$95^{th}$ percentile of the bus voltage deviation, to distinguish when there
is a local excess of energy from when there is a local deficit of energy. We
consider voltage violations to be higher than 1.1 p.u. and lower than 0.9 p.u.
[25].

Finally, we use load duration curves to assess the violations of the
transformer power capacity for reverse power flow from LV towards upstream
medium-voltage (MV) networks, as well as the transformer permissible overload
for different periods of time.

###  2.4 Key performance indicators

We use four technical indicators to evaluate the five considered tariffs’
performance. First, PV self-consumption, which is the share of on-site PV
generation that is used to cover the local electricity demand, and self-
sufficiency (SS), which is the share of local demand that is covered by the
on-site PV generation as shown in Eqs. 4 and 5. Moreover, we present the
results of the total amount of PV and storage installed per grid network.

$SC={\frac{\sum_{t}{(P^{\textsc{pv}-\textsc{load}}_{t}+P^{\textsc{pv}-\textsc{batt}}_{t})}}{\sum_{t}{P^{\textsc{pv}}_{t}}}}$
(4)
$SS={\frac{\sum_{t}{(P^{\textsc{pv}-\textsc{load}}_{t}+P^{\textsc{batt}-\textsc{load}}_{t})}}{\sum_{t}{P^{\textsc{load}}_{t}}}}$
(5)

where $P^{\textsc{pv}-\textsc{load}}_{t}$ is the share of PV generation that
directly meets local electricity demand; $P^{\textsc{pv}-\textsc{batt}}_{t}$
is the share of PV generation that is charged into the battery;
$P^{\textsc{PV}}_{t}$ is the total PV generation;
$P^{\textsc{batt}-\textsc{load}}_{t}$ is the amount of electricity discharged
from the battery to cover local electricity demand ($P^{\textsc{load}}_{t}$).

We analyze the PV hosting capacity of the LV network, i.e. the maximum amount
of PV that can be accommodated in a power grid within current regulations
without requiring reinforcement, taking into account not only the transformer
capacity but also the permissible overload for different timespans. Finally,
we calculate two economic indicators, the total cost of the bill per building
and aggregated per zone, and the portion corresponding to the sum of
distribution and transmission costs, to evaluate the grid cost recovery.

##  3 Results

The results are presented in three sections: Firstly, the impact of tariffs on
investment decisions (i.e. PV and battery investment) and energy imports and
exports. Secondly, the impact on the grid, covering the load duration curve at
the transformer as well as the permissible overload for varying periods of
time, voltage deviation and line loading levels and grid usage, and finally,
the impact on the grid cost recovery is examined.

###  3.1 Tariff’s impact on investment decisions and energy consumption

We compare the electricity tariffs first in terms of PV and storage capacity
installed, as well as differences in energy import and export, and secondly in
terms of self-consumption and self-sufficiency.

Table 4 presents the differences per electricity tariff for PV and battery
capacity installed, as well as yearly energy imports and exports as a result
of the optimization from the building perspective. In terms of PV capacity,
the tariffs with a capacity-based component (i.e. CT daily and CT monthly)
allow more PV installations to be operated within the three studied zones (1
to 5 additional percentage points more than in the reference cases). However,
the differences in total PV capacity are smaller than 5% and most of the
potential is exploited. All simple and double tariffs reach similar results,
with very similar PV and storage capacity installed. As a response to variable
prices in the case of dynamic tariffs and to the capacity component of CT
daily and CT monthly tariffs, the rational prosumer will install energy
storage. As a result of battery installations, energy imports decline up to
64%, 39%, and 37% for rural, semi-urban, and urban, respectively, for the CT
monthly tariff, compared to the FT reference.

Conversely, energy exports are slightly affected in the rural zone, with a
reduction of 2%, when comparing CT monthly with the FT reference. In the cases
of semi-urban and urban zones, the maximum differences are 16%, and 28%,
respectively. Despite the relatively small difference in installed PV capacity
in the reference FT and CT monthly cases (i.e., an additional 52, 12, and 66
kW for the rural, semi-urban, and urban zones, respectively), the increase in
the aggregated annual yield of the PV systems (i.e., equivalent to 970
kWh/kW), together with the increase in self-consumption due to the differences
in the installed battery capacity, account for the differences in annual
import and export energy. At the building level, among all volumetric tariffs,
the differences in the amount of energy imported are not statistically
significant (p-values$>$0.1 when compared to the two references). Energy
export differences are not statistically significant for either type of tariff
(p-values$>$0.1 when compared to the two references).

Network | Tariff | PV Capacity | PV penetration | Battery Capacity | Energy Import | Energy Export
---|---|---|---|---|---|---
kW | % | kWh | MWh p.a. | MWh p.a.
Rural | FT reference | 1085 | 94 | 1 | 108 | 1006
DT reference | 1085 | 94 | 1 | 107 | 1006
DT summer flat | 1085 | 94 | 1 | 107 | 1006
DT solar | 1084 | 94 | 1 | 108 | 1005
Dynamic | 1111 | 96 | 112 | 76 | 999
CT daily | 1125 | 98 | 229 | 55 | 992
| CT monthly | 1137 | 99 | 399 | 39 | 987
Semi-urban | FT reference | 1384 | 92 | 6 | 520 | 1274
DT reference | 1384 | 92 | 15 | 517 | 1271
DT summer flat | 1384 | 92 | 10 | 519 | 1273
DT solar | 1360 | 91 | 16 | 521 | 1248
Dynamic | 1384 | 92 | 396 | 424 | 1173
| CT daily | 1396 | 93 | 888 | 341 | 1097
| CT monthly | 1396 | 93 | 1160 | 316 | 1072
Urban | FT reference | 1711 | 95 | 69 | 1113 | 1295
DT reference | 1711 | 95 | 79 | 1110 | 1291
DT summer flat | 1711 | 95 | 83 | 1107 | 1289
DT solar | 1703 | 95 | 52 | 1121 | 1298
Dynamic | 1741 | 97 | 621 | 967 | 1172
CT daily | 1777 | 99 | 2092 | 754 | 985
| CT monthly | 1777 | 99 | 3338 | 701 | 930

Table 4: Cumulative installed capacities and energy imports and exports per
low-voltage network and per tariff.

Figure 2 presents the energy matching chart, with the self-consumption and
self-sufficiency at the building level for each network. The points in the
diagonal line represent net-zero buildings on yearly basis (i.e., buildings
that produce as much energy as they consume), whereas points above the
diagonal line are net producers and those below are net consumers on yearly
basis. In the three networks analyzed and regardless of the electricity tariff
used, most buildings are net producers. Moreover, as a result of the storage
installed, tariffs with a capacity-based component increase self-sufficiency
up to 45, 29, and 28 percentage points for the rural, semi-urban, and urban
zones, respectively.

Fig. 2: Energy matching chart to analyze self-consumption (SC) and self-
sufficiency (SS) per network. Please note that each point represents one
building under the considered electricity tariff, which is represented by the
color scale

###  3.2 Tariff’s impact on the grid

Figure 3 presents the violations of the transformer power capacity, where
values over the transformer capacity (indicated with dashed lines in the
figure) indicate reverse power flow from the LV network towards the MV
network. In the case of the rural zone, the maximum PV potential exceeds the
capacity of the local transformer (630 kVA), however, the transformer is
overloaded only between 177 and 261 hours p.a. (depending on the electricity
tariff). In the semi-urban zone, the situation is similar, and the transformer
is overloaded between 223 and 260 hours p.a. In the case of the urban zone,
however, the transformer is overloaded only for 1.75 hours. In general, the
transformers of the three zones are overloaded less than 3% of the hours per
year. Finally, the tariff CT monthly is the tariff that reduces the most the
peaks of demand. When the maximum peak demand results from the tariff CT
monthly are compared to the FT reference, the peak is reduced from 81 to 56 kW
(i.e. 30.9%) in the rural zone, in the case of the semi-urban zone the
reduction is from 302.7 to 199 kW (i.e. 34.2%), and in the case of the urban
network from 426 to 363 kW (i.e. 14.8%).

Transformers may be operated above average continuous temperatures, typically
above 95 ∘C for transformers rated at 55 ∘C and 110 ∘C for transformers rated
at 65 ∘C, for short times without affecting the normal life expectancy if most
of the time they are operated at lower temperatures [26]. Figure 4 presents
the number of events where the transformer is overloaded (mainly due to PV
injection) depending on the tariff applied. The permissible overload for
different periods of time, where the transformer is operated without affecting
the normal life expectancy, are below the red (based on [26]) and blue (based
on [27]) curves. The main hypotheses behind the curves are an ambient
temperature of 30°C and an initial load factor of 80%, which may be an extreme
case (if the initial load factor is lower, the curve is displaced to the
right). Based on the results, there are only a few moments throughout the year
when the transformers of the rural and semi-urban networks are overloaded
beyond the points of safe operation (i.e. affecting the normal life expectancy
of the transformer). However, the provision of flexibility services to the
DSO, PV curtailment, or capacity-based restrictions on the export could
further alleviate the PV injection and admit a full deployment of PV within
the two zones without the need for grid reinforcement. In the case of the
urban network, no measure is needed since the transformer can manage the
limited overloads without reducing its normal life expectancy.

Fig. 3: Load duration curve at the transformer. Dots on the vertical axis
indicate the total installed PV capacity per scenario. Negative values
indicate power flow from the high-voltage toward the low-voltage side Fig. 4:
Permissible overload for varying periods of time, based on [26] (in red) and
[27] (in blue).

The results of the current of the lines and voltage magnitude at the node
level are presented in Figures 5 and 6. The rural network presents a median
line loading level of 23.9%, and only three data points are above the 100%
line loading level, regardless of the tariff used. For the semi-urban zone,
the maximum line loading level is 64%, with a median value of 20%. In the
urban zone, the median line loading level reaches 22% but the maximum line
loading level is 173% for all tariffs except for the two references FT and DT,
which reach 172% and 83%, respectively. The line overloading occurs mainly
during the winter months (primarily, November, December, and February), and
affects ten lines (out of 93). It is therefore not related with PV excess
injection.

Positive voltage deviations are critical in the rural network, where there are
up to 18420 data points above the (rather soft) limit of 1.1 p.u., violating
current European and Swiss regulations [25]. In the case of semi-urban and
urban networks, there are no voltage violations due to PV injection. No
evidence of voltage violations due to demand in the studied zones was found.
However, the use of the dynamic tariff and tariffs with a capacity-based
component present statistically significant differences with the reference
tariffs (p-value $\leq$ 2e-16), resulting in median values for voltage
deviation closer to 1, meaning that the use of such tariffs most probably will
result in lower voltage deviations.

Fig. 5: Line loading level distribution ($95^{th}$ percentile); Box plots show
the median (horizontal line) and the IQR (box outline). The whiskers extend
from the hinge to the highest and lowest values that are within 1.5 × IQR of
the hinge, and the points represent the outliers. Fig. 6: Voltage deviation
distribution ($95^{th}$ percentile); Box plots show the median (horizontal
line) and the IQR (box outline). The whiskers extend from the hinge to the
highest and lowest values that are within 1.5 × IQR of the hinge, and the
points represent the outliers.

###  3.3 Tariff’s impact on the grid cost recovery

Table 5 presents the grid cost recovery per network. For the aggregated
results the volumetric tariffs (i.e., summer flat, solar, and dynamic) are
slightly above the reference DT, surpassing the total grid cost recovery by
0.9%, 0.3%, and 0.3%, respectively. In the cases of the two tariffs with a
capacity-based component (i.e. CT monthly, and CT daily), the grid cost
recovery falls behind the level of the DT reference by 5 and 1%, respectively.
These values can be further improved to match the required grid cost recovery
levels, nevertheless, what is worth mentioning is that with a CT monthly of
16.4 €/kW and a CT daily between 0.53 and 1.33 €/kW, the DSO can recover the
grid costs.

The total bill cost per building per year is presented in Figure 7. The total
bill cost per building does not present statistically significant differences
even when tariffs with a capacity-based component are used (p-values$>$0.1
when compared to the two references). This result indicates that when changing
the reference tariff for another one of the five proposed in this study, the
total bill cost per building remains similar. The only exception is the rural
LV network under a CT daily when compared to the FT reference, where there is
a significant difference (p-value=0.039), and therefore, a lower bill cost
should be expected. Nevertheless, when the same comparison is done regardless
of the network, there is no statistically significant difference between the
two cases, which indicates that at the aggregated level there are no
differences in the total bill per building. We acknowledge that the absence of
statistically significant differences among the studied tariffs is true under
a scenario with high penetration of PV and storage.

Network | FT reference | DT reference | DT summer flat | DT solar | Dynamic | CT daily | CT monthly
---|---|---|---|---|---|---|---
Rural | 9093 | 10581 | 10586 | 10606 | 8957 | 8811 | 10948
Semiurban | 43979 | 51005 | 51174 | 51358 | 50704 | 48945 | 53106
Urban | 94049 | 109411 | 109195 | 110543 | 111932 | 104523 | 105333
Total | 147121 | 170997 | 170955 | 172507 | 171593 | 162279 | 169387

Table 5: Grid cost recovery per network and tariff, in € per year. Fig. 7: Box
plot of the annual cost for each building depending on the network; Box plots
show the median (horizontal line) and the IQR (box outline). The whiskers
extend from the hinge to the highest and lowest values that are within 1.5 ×
IQR of the hinge, and the points represent the outliers. The individual
p-values of the two-sided Wilcoxon tests with the Holm procedure to control
the family-wise error rate are reported in the figure.

##  4 Discussion

Our study, bridging real LV network data with robust energy modeling,
indicates that alternative tariffs can drive the adoption of storage, and
recover the grid costs without causing relevant economic differences for the
customers in LV networks. However, they only marginally mitigate the impact of
PV on the network. Our findings have four key implications for DSOs, policy-
makers, and academics.

First, we found that all the assessed tariffs in this study perform similarly
or better than the two references in terms of driving the adoption of PV and
storage. In the case of the two more traditional volumetric tariffs (DT summer
flat and DT solar), they do not provide further incentives to increase the
amount of PV or battery capacity within the LV networks. This result calls for
complementary incentives to increase the share of storage such as financial
rebates if the electricity tariff structure cannot be drastically modified for
economic or social reasons. On the contrary, the Dynamic tariff, based on the
expected aggregated load curve of the DSO, drives the adoption of additional
capacity of PV and storage in the three LV networks, helping to reduce the
energy imports but only marginally reducing the energy exports. Finally, the
tariffs with a capacity-based component are the tariffs that help the most to
increase the installation of PV and storage, being particularly important the
effect of the tariff with a billing horizon of one month. Moreover, under this
same tariff (i.e. CT monthly), in the three LV networks, the energy imports
and exports are reduced the most, with respect to the reference tariffs. In
terms of self-consumption and self-sufficiency, most of the buildings are net
producers across the three LV networks, which points towards a reduction in
energy needs in the future. The tariffs with a capacity-based component were
found to increase both indicators when compared to the references, mainly due
to the higher penetration of batteries.

Second, we found that in general, the assessed tariffs display a similar
impact of PV on the LV network in terms of PV hosting capacity, i.e. the
maximum amount of PV that can be accommodated in a power grid within current
regulations without requiring reinforcement. Regardless of the tariff, the
three analyzed LV networks are reaching the limits of their PV hosting
capacity, the rural and semi-urban networks are the networks with higher
overload. However, the three analyzed transformers would mostly operate within
the permissible zones, without affecting their normal life expectancy and
therefore without the need for reinforcement. Despite the PV penetration for
the three zones being over 90% and therefore close to the technical maximum,
the theoretical maximum PV penetration used in this study only takes into
account the maximum rooftop potential, neglecting further facade PV additions
that could then contribute to exceeding the networks’ PV hosting capacity. In
such a case, the provision of flexibility services to the DSO, PV curtailment,
or capacity-based restrictions on the export could alleviate further the PV
injection and admit a higher deployment of PV within the three zones without
the need for grid reinforcement. The use of tariffs with a capacity-based
component was found to result in lower voltage deviations above 1 p.u., when
compared to the volumetric tariffs, in the rural setup. These results, are in
line with the findings of Hartvigsson et al. [25], for Sweden, Germany, and
the UK, where voltage increase is the main factor limiting the PV hosting
capacity. This result is more noticeable when a more stringent limit for the
voltage limits (e.g. a 5% deviation) is used since for most of the $95^{t}h$
percentile voltage distribution, it is violated in all three networks when PV
electricity is exported and in the Urban setting when electricity is drawn
from the grid. Similarly, we found that most problems stem from the rural
networks, where lines are longer, the available area for PV is higher and the
demand is lower than in the urban networks [28, 25].

Third, the mixed tariffs with volumetric and capacity-based components allow
the DSOs to recover the grid cost, without incurring in statistically relevant
differences for the customer in a scenario with high PV penetration and with
some storage. However, we acknowledge that socio-economical differences, as
highlighted by Azarova et al. [29], should be taken into account at the moment
of proposing a change of tariffs to the clients. Moreover, the tariffs
assessed in this study concern only the demand side, since as explained by
Bloch et al. [14], a capacity-based tariff for both, import and export does
not encourage investment in battery systems, since the cost is dominated by
the PV injection power, which can be simply curtailed. Additionally, this
tariff would charge twice the user for the use of the grid, once when
consuming electricity from the grid, and the second when injecting PV
electricity into the grid.

Fourth, in the Swiss context, rooftop PV plays a paramount role in the energy
transition. Only a reduced amount of land is available for solar farms due to
scarcity, citizen opposition, and/or law mandates. Our results highlight the
problems that DSO may encounter, mainly in rural areas. This study emphasizes
the need to act on the export side to help to mitigate the impact of PV.

While we have considered as reference cases three low-voltage networks
representative of Switzerland, further case studies including other regions
and countries could lead to conclusions that could be generalized. We
considered an optimization following an economic rational behavior for all
buildings and considered PV and battery installations to be done at once,
whereas in reality, most probably not every building will be able to install
PV on the rooftop either for economic or non-economic reasons hindering the
national objectives towards PV deployment. Moreover, this process is done
progressively leaving some time for DSOs to adjust their decisions in terms of
tariff design and low-voltage system operation. We assumed perfect foresight
of the demand; however, the longer the period over which the peak demand is
observed, the higher the incertitude of the peak demand would be. Our research
can also be a starting point for future research considering the grid-friendly
operation of low-voltage networks considering other distributed energy
resources such as EVs and HPs that could help to increase the PV hosting
capacity. Moreover, since most of the problems arise from the export side, the
exploration of capacity tariffs to the export or variable export prices could
give a better idea of how to mitigate such problems at the distribution level.
Finally, curtailment or curtailment incitation (e.g., higher export tariffs if
the DSO can control PV curtailment or pays for curtailed energy) could lead to
more cost-efficient results and have higher social acceptance than capacity-
based tariffs.

##  5 Conclusions

In this study, we did a comprehensive analysis that integrates the effects of
five tariffs on the optimum size and operation of PV and battery systems, as
well as on different typical LV networks, namely, rural, semi-urban and urban
in Switzerland. The considered tariffs include two traditional (volumetric)
double tariffs that seek to promote PV self-consumption (DT solar and DT
summer flat), as well as a volumetric dynamic tariff proportional to the
aggregated expected load curve of the DSO for 2025. Moreover, we analyze two
mixed tariffs including a volumetric and a capacity-based component (in €/kW),
with two billing horizons, one monthly (CT monthly) and one daily (CT daily).
These five tariffs are compared to two reference tariffs (flat and double
tariff) that are currently used by the DSO.

The results show that traditional volumetric tariffs perform similarly to the
two reference tariffs (flat and double tariff) without adding any benefit, in
terms of the adoption and operation of distributed PV-coupled battery systems.
Only alternative tariffs, such as dynamic tariffs (based on the aggregated
expected load of the DSO, in this study) and tariffs with a capacity-based
component, were found to induce a higher adoption of PV and storage.

In line with the literature, we found the major issues to arise mainly in
rural grids, and to involve voltage violations and reverse power flow.
Additionally, the maximum amount of PV that can be accommodated in a power
grid without requiring reinforcement was found to be higher than the maximum
capacity of the transformer, given that the overloading events of the
transformer are short in timespan. In this sense, and since the main problems
for the distribution grid, in general, stem from PV injection, the
electrification of the heating and transport sector may relieve such problems
if additional demand occurs during surplus times. Otherwise, solutions
involving the management of the PV export should be considered. For instance,
considering PV curtailment, capacity-based tariffs to the contracted capacity,
capacity-based tariffs to the export, or local flexibility to mitigate the
crucial hours of the year and in this way help to relieve transformer
overloading.

##  6 Acknowledgements

This research project was financially supported by Romande Energy. The funding
source had no involvement in the preparation of the article, in the study
design, the collection, analysis, and interpretation of data, nor in the
writing of the manuscript. Furthermore, we thank Arnoud Bifrare, Stéphanie
Weiler, and Maret Julien for their insights and comments on this study.

##  7 Declaration of competing interest

The authors declare that they have no known competing financial interests or
personal relationships that could have appeared to influence the work reported
in this paper.

##  8 CRediT authorship contribution statement

Alejandro Pena-Bello: Conceptualization, Data curation, Methodology,
Validation, Investigation, Formal analysis, Writing - original draft,
Visualization. Robin Junod: Software and Investigation. Christophe Ballif:
Writing - review & editing, Funding acquisition. Nicolas Wyrsch:
Conceptualization, Supervision, Writing - review & editing, Funding
acquisition, Project administration.

##  9 Data Availability

The model will be made available on reasonable request. The LV network data is
subject to a confidentiality agreement.

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# Comparative Analysis of THz Signal Emission from SiO2/CoFeB/Metal
Heterostructures: Wideband and High-Frequency THz Signal Advantage of PtBi-
based Emitter

Tristan Joachim Winkel<EMAIL_ADDRESS>Institut für Physik,
Universität Greifswald, Greifswald, Germany  Tahereh Sadat Parvini
<EMAIL_ADDRESS>Institut für Physik, Universität Greifswald,
Greifswald, Germany  Finn-Frederik Stiewe  Institut für Physik, Universität
Greifswald, Greifswald, Germany  Jakob Walowski  Institut für Physik,
Universität Greifswald, Greifswald, Germany  Farshad Moradi  ICELab, Aarhus
University, Denmark  Markus Münzenberg  Institut für Physik, Universität
Greifswald, Greifswald, Germany

###### Abstract

Spintronic THz emitters have attracted much attention due to their desirable
properties, such as affordability, ultra-wideband capability, high efficiency,
and tunable polarization. In this study, we investigate the characteristics of
THz signals, including their frequency, bandwidth, and amplitude, emitted from
a series of heterostructures with ferromagnetic (FM) and nonmagnetic (NM)
materials. The FM layer consists of a wedge-shaped CoFeB layer with a
thickness of 0 to 5 nm, while the NM materials include various metals such as
Pt, Au, W, Ru, Pt%92Bi%8, and Ag%90Bi%10 alloys. Our experiments show that the
emitter with Pt-NM layer has the highest amplitude of the emitted THz signal.
However, the PtBi-based emitter exhibits a higher central THz peak and wider
bandwidth, making it a promising candidate for broadband THz emitters. These
results pave the way for further exploration of the specific compositions of
Pt1-xBix for THz emitter design, especially with the goal of generating higher
frequency and wider bandwidth THz signals. These advances hold significant
potential for applications in various fields such as high-resolution imaging,
spectroscopy, communications, medical diagnostics, and more.

##  I Introduction

The Hall effect, discovered in 1879 Hall (1880), is a crucial technique in
modern measurement technology, allowing for the determination of magnetic
field strength and charge carrier type, density, and mobility. The spin Hall
effect (SHE), which is the quantum mechanical analogue of the Magnus effect,
was predicted in 1971 D’Yakonov and Perel (1971) and later experimentally
confirmed in the early 2000s Murakami  _et al._ (2003); Kato  _et al._ (2004);
Sinova  _et al._ (2004). The SHE arises from the interplay between the
electron’s spin and motion in the presence of spin-orbit coupling, and has
significant implications for spintronics and related technologies such as the
generation of terahertz (THz) radiation, high-speed data processing, and
quantum information processing Demidov  _et al._ (2014); Sinova  _et al._
(2015); Jungwirth  _et al._ (2012). THz waves have potential applications in
materials science, biology, and medicine, and further research could broaden
their use in spectroscopy, imaging, and communication Tonouchi (2007); Cheon
_et al._ (2019); Pawar  _et al._ (2013); Gowen  _et al._ (2012); Henriksen
_et al._ (2022); Wang  _et al._ (2014); Seifert  _et al._ (2016). Typical THz
emitters are made up of ferromagnetic (FM)/nonmagnetic (NM) heterostructures
where the FM layer is pumped using a femtosecond laser to generate a spin-
dependent excitation of electrons. The inverse spin Hall effect (ISHE) in the
NM layer converts the longitudinal spin-polarized current ($\mathbf{J}_{s}$)
into a transient transverse current ($\mathbf{J}_{c}$) according to
$\mathbf{J}_{c}=\theta_{SH}\mathbf{J}_{s}\times\frac{\mathbf{M}}{|\mathbf{M}|}$,
resulting in the emission of terahertz radiation Kampfrath  _et al._ (2013);
Battiato  _et al._ (2010); Zhukov  _et al._ (2006); Gradhand  _et al._ (2010).
$\theta_{SH}$ is the spin Hall angle that characterizes the efficiency of the
spin Hall effect and can be enhanced through various means such as selecting
materials with large spin-orbit coupling, optimizing material properties
including crystal structure, impurity level, and thickness, as well as
controlling experimental conditions. By precisely determining the materials
and thickness in THz emitters, it becomes possible to optimize the amplitude,
frequency, and bandwidth of the THz field.

In this study, we fabricated a series of FM/NM heterostructures to conduct a
comparative study on the characteristics of the emitted THz signal. The FM
layer consists of a wedge layer of Co40Fe40B20 with a thickness ranging from 0
to 5 nm. Meanwhile, the NM layer comprised a diverse range of materials,
including Pt (2, 3, and 4 nm), W (2 nm), Au (2 nm), Ru (4 nm), as well as the
alloys Pt%92Bi%8 (2 nm) and Ag%90Bi%10 (2 nm). Our investigation focused on
evaluating the amplitude, central frequency, and bandwidth of the THz signal
emitted from all samples. Furthermore, we analyzed the determining factors
that influenced our observations.

##  II Materials and Methods

In this study, we adopted a conventional approach of employing the
substrate/FM/NM layer configuration for the fabrication of THz emitters.
Initially, a magnetic layer consisting of Co40Fe40B20 (CoFeB) was deposited
onto a fused silica substrate using magnetron-sputtering technique. To explore
the influence of FM-layer thickness on the characteristics of the emitted THz
signal, we designed the layer in a wedge shape, allowing for a variable
thickness ranging from 0 to 5 nm. To investigate the contribution of the NM-
layer material to the terahertz signal, we examined various pure heavy metals
such as Pt, W, Au, Ru , as well as alloys Pt%92Bi%8 and Ag%90Bi%10 as NM-
layers. Furthermore, We fabricated a series of heterostructures with varying
thicknesses of pure Pt layers to study the impact of Pt layer thickness on the
emitted THz signal. The NM-layers were deposited on the CoFeB using electron
beam (e-beam) evaporation. The alloys are formed through a controlled combined
deposition of both constituent materials. The ratio between the alloyed
materials is determined by adjusting the deposition rates, monitored using
quartz crystal monitoring. The required ratio of the deposition rates
($v_{a}/v_{b}$) can be calculated using the following formula

$\frac{v_{a}}{v_{b}}=\frac{M_{a}\times\rho_{b}}{M_{b}\times\rho_{a}}.r,$ (1)

where $\rho$ represents the density, $M$ denotes the molar mass, and $r$
signifies the desired molar ratio of the alloyed materials. Due to the high
sensitivity of spin currents to interface contaminations or oxidation, we
implemented strict precautions during sample fabrication. This involved
conducting the fabrication process and transferring the samples between
chambers under high vacuum conditions, ensuring the preservation of interface
integrity without any modifications.

##  III Results and Discussion

Our previous publication Stiewe  _et al._ (2022a) have provided a detailed
description of our experimental setup for generating and detecting THz signals
from spintronic emitters. Fig. 1 provides a simple schematic of our THz
emitters and the corresponding mechanism for THz generation. We generate THz
radiation in heterostructures by employing femtosecond laser pulses with
central wavelengths of $\sim$810 nm, pulse durations of 40 fs, and repetition
rates of 80 MHz. The detection of THz signals is carried out using commercial
low-temperature grown-GaAs (LT-GaAs) Auston switches with a bandwidth greater
than 4 THz. To obtain a temporal THz spectrum at each position of the sample,
we utilized a two dimensional scanning technique with motorized stages. A
comprehensive description of the methodology can be found in Stiewe  _et al._
(2022b). Additionally, the samples were subjected to scanning using a magneto-
optic Kerr effect setup to investigate the relationship between the position
and the thickness of the CoFeB layer. The obtained data was fitted using an
error function and combined with the data acquired from the THz setup. This
integration allowed us to determine the THz emission corresponding to each
sample as a function of the CoFeB layer thickness.

Figure 1: Side view of a FM/NN bilayer consisting of a ferro-magnetic metal
layer (FM) and an adjacent nonmagnetic metal layer (NM). A femtosecond laser
pulse excites the metal stack from the substrate side.

Figure 2: THz signal amplitude as a function of CoFeB layer thickness and
pump-probe delay time for stacks with Pt and PtBi NM layer. (a) 2nm Pt, (b)
3nm Pt, (c) 4nm Pt, and (d) 2nm PtBi alloy. The pump fluence is
0.8$\pm$0.2$mJ/cm^{2}$.

Under the illumination of ultrafast femtosecond (fs) laser pulses, spin-
polarized electrons ($j_{s}$) within the FM layer get excited and diffuse into
the NM layer, forming a spin current. The inverse spin Hall effect (ISHE)
comes into play, converting this spin current into a transient transverse
charge current ($j_{c}$) within the NM layer, ultimately leading to the
emission of terahertz (THz) radiation. In the plane-wave approximation, the
amplitude of the electric field of the emitted THz signal reads Seifert  _et
al._ (2022)

$E_{THz}=\frac{AF}{d_{NM}+d_{FM}}.j_{s}^{0}t_{\frac{FM}{NM}}\lambda_{NM}tanh\frac{d_{NM}}{\lambda_{NM}}.\theta_{SH}.eZ(\omega),$
(2)

where the terms respectively represent pump-pulse absorption, spin-current
generation, spin-to-charge current conversion, and charge-current-to-electric-
field conversion. The parameters A, $j_{s}^{0}$, $t_{\frac{FM}{NM}}$,
$\lambda_{NM}$, and $\theta_{SH}$ represent the absorbed fraction of the
incident pump-pulse fluence ($F$), the generated spin-current density per
pump-pulse excitation density, the interfacial spin-current transmission
amplitude between the FM and NM layers, the spin-current relaxation length in
the NM layer, and the spin Hall angle specific to the NM material,
respectively. The frequency-dependent impedance of the emitter, denoted as
$Z(\omega)$, is given by $Z(\omega)=\frac{Z_{0}}{n_{1}+n_{2}+Z_{0}G}$, where
$Z_{0}\approx 377\Omega$ represents the free-space impedance, and
$n_{1}(\omega)$ and $n_{2}(\omega)$ are the refractive indices of air and the
substrate, respectively, and $G(\omega)$ represents the THz sheet conductance.
Consequently, by meticulously controlling the parameters in Eq. 2, it is
possible to achieve the desired signal. Subsequently, we proceed to
investigate the role of these parameters in the emitted THz signal from our
fabricated emitters.
Dependence of THz Signal Amplitude, Central Frequency, and Bandwidth on
Heterostructure Thickness and NM Materials: Fig. 2 illustrates the emitted THz
signal as a function of delay time and laser spot position for distinct
samples. Accordingly, irrespective of the type of metal layers, no THz
emission is detected at the thin end of the wedge, where the CoFeB thickness
is 0 nm. As the thickness of the CoFeB layer increases, the amplitude of the
emitted THz signal exhibits growth, peaking at around 2 nm of CoFeB thickness.
It is noteworthy that beyond this critical point, further increases in CoFeB
thickness do not have a significant impact on the amplitude of the THz signal.
This behavior can be attributed to the progressive diffusion of an increasing
number of electrons into the NM layer as the CoFeB layer thickness increases
up to 2 nm. The influx of electrons enhances the induced spin current, thereby
generating stronger THz radiation. However, beyond a 2 nm thickness of the
CoFeB layer, the presence of heightened structural defects, electron
scattering, and resistance within the magnetic layer hinders further
amplification of the THz signal amplitude. As a result, the THz signal reaches
a plateau beyond this critical thickness. Furthermore, the results indicate
that the maximum THz amplitude is attained when utilizing a 2 nm Pt layer as
the heavy metal component of the emitter. The decrease in THz amplitude with
increasing Pt thickness can be attributed to the absorption and attenuation of
THz waves by the Pt layer, which will be discussed in the subsequent section.

Figure 3: (a) The amplitude of the THz signal at a frequency of 1 THz as a function of CoFeB-layer thicknesses for stacks containing different NM layers and varying thicknesses. The amplitude is measured in attovolt-seconds. (b) A magnified scale of the THz signal for stacks comprising NM layers Ru, Au, and AgBi. (c) The amplitude of the emitted THz signal as a function of frequency for emitters with a constant CoFeB thickness of 2 nm. (d) The THz bandwidth as a function of CoFeB-layer thicknesses.  Table 1: Saturated THz amplitude and central frequency of the THz pulse emitted from heterostructures CoFeB (2nm)/NM. NM Layer |  | 2nm Pt |  | 3nm Pt |  | 4nm Pt |  | 2nm PtBi |  | 2nm W |  | 4nm Ru |  | 2nm Au |  | 2nm AgBi
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
Amplitude [aVs] |  | 46.35 |  | 36.02 |  | 30.83 |  | 22.90 |  | -13.27 |  | 2.21 |  | 2.15 |  | 1.32
Frequency [THz] |  | 0.75 |  | 0.73 |  | 0.71 |  | 1.04 |  | 0.84 |  | — |  | — |  | —

To gain deeper insights into the fabricated THz emitters, we analyzed the
correlation between the amplitude of the emitted THz field at 1 THz and the
varying thicknesses of the CoFeB layer in stacks with specified NM layers, see
Fig. 3 (a) and (b). The THz emitters composed of pure Pt layers demonstrate
the highest THz amplitude among the emitters. Specifically, the stack with a 2
nm Pt layer exhibits a THz signal amplitude that is twice as high as the stack
with a 2 nm PtBi layer. However, the emitter with PtBi, as shown in Figs. 3
(c) and (d), exhibits a wider bandwidth of approximately 0.35 THz compared to
other stacks, along with a higher central frequency of the THz signal.
Interestingly, it demonstrates a significant central frequency shift of
approximately 0.3 THz when compared to the emitter with 2 nm Pt. These
findings highlight the crucial role of the NM layer material in influencing
THz characteristics and suggest the potential advantages of the PtBi stack for
applications requiring broader bandwidth and higher frequencies, despite a
lower THz amplitude. When evaluating the trade-off between THz signal strength
and bandwidth, it is crucial to consider the specific requirements of the
intended application, as different applications may prioritize either a higher
THz signal strength or a broader bandwidth based on their unique needs and
constraints. This observation suggests potential advantages in applications
that benefit from higher frequency THz signals, including high-resolution
imaging, spectroscopy, communications, medical diagnostics, and etc. The
values of the saturated THz amplitudes and THz peak position measured for
different emitters are presented in Table LABEL:table1.

Figure 4: Real (solid line) and imaginary (dashed-dotted line) parts of (a)
conductivity, $\sigma(\omega)$, and (b) impedance, Z($\omega$), of different
heavy metal thin films obtained via THz-TDS.

Exploring Conductance of NM Layers through Terahertz Time-Domain Spectroscopy
(THz-TDS): The conductance of the NM layer, as indicated by Eq.2, is a
significant factor affecting the THz signal amplitude. To determine the
conductance value of each NM layer, we direct the THz transient signal onto
both the bare substrate and the substrate coated with a thin metal film. By
measuring the THz transmission through the sample ($T_{s}(\omega)$) relative
to that through the bare substrate ($T_{\text{sub}}(\omega)$), we can infer
the conductance of the metal at THz frequencies using Tinkham’s formulas
Grüner and Dahl (1998); Kamboj  _et al._ (2017); Seifert  _et al._ (2018);
Tinkham (1956):

$\frac{T_{s}(\omega)}{T_{sub}(\omega)}=\frac{E_{s}(\omega)}{E_{sub}(\omega)}=\frac{1+n_{sub}}{1+n_{sub}+Z_{0}G(\omega)},$
(3)

here, $E_{s}(\omega)$ and $E_{sub}(\omega)$ are the Fourier Transforms of the
time-dependent THz electric field waveforms transmitted through the sample and
substrate, respectively. The refractive index of the substrate is obtained
using the formula $n_{\text{sub}}=\frac{c\Delta\phi}{d_{\text{sub}}\omega}+1$,
where $\Delta\phi$ is the phase difference of the pulsed THz radiation
incident upon the substrate ($E_{i}$) and transmitted through the substrate
($E_{\text{sub}}$). For a SiO2 substrate with a thickness of
$d_{\text{sub}}=500\mu$m, applying this method yields
$n_{\text{sub}}\approx$1.98.

Fig. 4(a) shows the real and imaginary parts of the optical conductivity for
different NM thin films, obtained through the formula
$G(\omega)=\sigma(\omega)\cdot d_{\text{NM}}$. The observed inequality
$\left|\sigma_{Pt(2)}\right|<\left|\sigma_{Pt(3)}\right|<\left|\sigma_{Pt(4)}\right|$
demonstrates a positive correlation between film thickness and conductivity.
Increasing the film thickness improves conductivity due to factors such as an
increased number of charge carriers, reduced interfacial scattering, improved
crystallinity, and decreased surface roughness. The Drude model Jackson (2021)
was utilized to fit the conductivity of the Pt layers, enabling the
determination of plasma frequency
($\omega_{p}=\sqrt{Ne^{2}/m\varepsilon_{0}}$, where N, e, m, $\varepsilon_{0}$
are the carrier electron density, electron charge, electron effective mass,
and vacuum permittivity, respectively) and scattering time ($\tau$). The
findings demonstrate a clear trend of increasing $\omega_{p}$ with film
thickness, indicating a proportional rise in carrier density
($\omega_{p,\text{Pt}(2)}=0.19\times 10^{16}\text{ Hz}$,
$\omega_{p,\text{Pt}(3)}=0.3\times 10^{16}\text{ Hz}$,
$\omega_{p,\text{Pt}(4)}=0.36\times 10^{16}\text{ Hz}$). Additionally, as the
film thickness increases, the scattering time decreases
($\tau_{\text{Pt}(2)}=52f$s, $\tau_{\text{Pt}(3)}=32f$s,
$\tau_{\text{Pt}(4)}=23f$s), resulting in a decrease in electron mobility
($\mu\propto\tau$). The impedance analysis in Fig. 4(b) confirms that thicker
Pt layers exhibit lower impedance compared to the thinner layers, with a clear
trend of
$\left|Z_{Pt(2)}\right|>\left|Z_{Pt(3)}\right|>\left|Z_{Pt(4)}\right|$. This
finding directly corresponds to a reduction in the emitted THz signal from
thicker NM layer, as supported by Eq. 2 and proved in Fig. 2. W exhibits
greater impedance compared to other metals, but one contributing factor to its
smaller THz amplitude is its relatively diminished spin Hall angle.
Remarkably, PtBi (2nm) exhibits a real component of conductivity that is
comparable to that of Pt (2nm). However, what sets it apart is its surpassing
imaginary component, which not only exceeds that of Pt but also bears a
negative value (Im$[\sigma_{PtBi}]=-a\omega$, where $a$ is a constant). This
can not be explained by simple Drude model Kang  _et al._ (2009) and suggests
a distinctive behavior in PtBi that warrants deeper exploration and
investigation. Experimental evidence has demonstrated that the spin-charge
conversion efficiency of PtBi is twice that of pure Pt Hong  _et al._ (2018).
However, due to the influence of other factors such as reduced impedance or
interfacial spin-current transmission, the THz signal amplitude of PtBi is
comparatively smaller than that of pure Pt. Here, our main focus was to
perform a comparative analysis of THz emission from emitters fabricated with
different materials. The investigation of emitters with distinct compositions
of Pt1-xBix will be addressed in a separate study.

##  IV Conclusion

To optimize spintronic THz emitters performance, we conducted a comparative
study on SiO2/CoFeB/NM heterostructures, where the CoFeB layer thickness
varied from 0 to 5nm, and different heavy metals (Pt, W, Au) and alloys
(Pt%92Bi%8 and Ag%90Bi%10) served as the NM layer. Our investigation revealed
a critical threshold at 2nm thickness for the CoFeB layer, beyond which the
emitted THz signal amplitude saturated. Furthermore, the heterostructure with
2nm CoFeB and 2nm Pt exhibited the highest THz signal amplitude. Surprisingly,
despite the Pt%92Bi%8 (2nm) emitter exhibiting only half the THz amplitude
compared to the Pt (2nm) emitter, it demonstrated a higher central THz
frequency and the largest THz bandwidth among all the emitters investigated in
our study. This study provide a solid foundation for future studies on
different compositions of Pt1-xBix alloy aimed at achieving even higher
wideband and frequency capabilities in THz emitters. To gain a deeper
understanding of the behavior exhibited by the different emitters, we
conducted time-domain THz spectroscopy to analyze their conductivity and
impedance characteristics. Our findings demonstrate that thicker NM layers
exhibit higher electron concentration and lower mobility, resulting in lower
impedance and subsequently lower THz amplitude. The anomalous behavior of
PtBi, characterized by a negative imaginary part of conductivity according to
our applied model, highlights the need for in-depth investigations and
potential modifications of the model to better comprehend and explain the
unique properties exhibited by this material.

###  IV.1 Acknowledgement

This project has received funding from the European Union’s Horizon 2020
research and innovation program under grant agreement No 899559 (SpinAge).

###  IV.2 Availability of data

The data that supports the findings of this study are available within the
article.

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