${\cal A}(w)={\cal C}(w)$. For ${\mathsf{Val}}={\mathsf{LimSup}}$, recall that
every run of ${\cal B}$ yields a nonincreasing weight sequence. In particular,
there exists $k\in\mathbb{N}$ such that $\gamma(\rho_{\cal
B}[k])=\gamma(\rho_{\cal B}(\ell))={\cal B}(w)$ for all $\ell\geq k$. Then, we
exhibit an infinite sequence of positions $\\{y_{i}\\}_{i\in\mathbb{N}}$ such
that $\gamma(\rho_{A}[y_{i}])={\cal B}(\gamma(\rho_{\cal B}[y_{i}]))={\cal
B}(w)$ and $\gamma(\rho_{\cal C}[y_{i}])=\top$ for all $i\in\mathbb{N}$.
Consequently, ${\cal C}(w)=\top$ and ${\cal A}(w)={\cal B}(w)$.

In either case, ${\cal A}(w)=\min({\cal B}(w),{\cal C}(w))$.

Next, we show that ${\cal C}$ is live using the same argument as in the proof
of Theorem 5.10: On the one hand, every word $w$ for which ${\cal A}(w)={\cal
B}(w)$ trivially satisfies the liveness condition as it implies ${\cal
C}(w)=\top$. On the other hand, by Proposition 2.2 every word $w$ for which
${\cal A}(w)<{\cal B}(w)$ is such that each finite prefix $uw$ admits a
continuation $w^{\prime}$ satisfying ${\cal A}(uw^{\prime})={\cal
B}(uw^{\prime})$. Hence, $\sup_{w^{\prime}}{\cal C}(uw^{\prime})=\top$ for all
$uw$, implying the liveness condition.


# On the economic viability of solar energy when upgrading cellular networks

Zineb Garroussi12, Abdoul Wassi Badirou12, Mathieu D’amours12, André Girard12,
Brunilde Sansò12

{zineb.garroussi, abdoul-wassi.badirou, mathieu.damours, andre.girard,
<EMAIL_ADDRESS>1Electrical Engineering Department
Polytechnique Montréal, Québec, Canada  2 LORLAB and Research Group in
Decision Analysis (GERAD)

###### Abstract

The massive increase of data traffic, the widespread proliferation of wireless
applications and the full-scale deployment of 5G and the IoT, imply a steep
increase in cellular networks energy use, resulting in a significant carbon
footprint. This paper presents a comprehensive model to show the interaction
between the networking and energy features of the problem and study the
economical and technical viability of green networking. Solar equipment, cell
zooming, energy management and dynamic user allocation are considered in the
upgrading network planning process. We propose a mixed-integer optimization
model to minimize long-term capital costs and operational energy expenditures
in a heterogeneous on-grid cellular network with different types of base
station, including solar. Based on eight scenarios where realistic costs of
solar panels, batteries, and inverters were considered, we first found that
solar base stations are currently not economically interesting for cellular
operators. We next studied the impact of a significant and progressive carbon
tax on reducing greenhouse gas emissions (GHG). We found that, at current
energy and equipment prices, a carbon tax ten-fold the current value is the
only element that could make green base stations economically viable.

###### Index Terms:

Solar base station, cellular networks, green energy, greenhouse gas emissions,
CAPEX, OPEX, cell zooming, carbon tax, network upgrade, network planning,
energy management.

##  I Introduction

Cellular operators are facing traffic growth due to the increasing use of
mobile applications [1] and the rapid development of wireless access
technologies such as 5G and beyond. To meet this demand, new base stations
(BSs) are being added or upgraded to the next generation technologies [2].

We claim that this current and future upgrading of cellular systems provides a
great opportunity for operators to reduce their environmental impact. The
COP21 Paris agreement has set a target limit of 2°C for the global warming. In
that context, the Information and Communication Technologies sector has a role
to play given that it accounts for about 4% of the global energy use [3] and
has generated approximately between 1.8% to 2.8% of the global GHG emissions
in 2020 [4]. A significant part of this is produced by cellular networks [5]
which generate the equivalent of 220 MtCO2, which represents 0.4% of global
emissions [6]. It is estimated [7] that the full deployment of 5G could have
an environmental impact up to 2 to 3 times larger. Moving to the millimeter
wavebands [1] will reduce the range of the new 5G antennas. This in turn will
require a much more dense radio infrastructure [8] with the ensuing large
increase in energy use.

One solution is to wait for the grid to use energy sources that don’t emit
CO2. This is a major undertaking that will take years to be implemented. In
this paper, we look at a different approach to reduce the emissions of the
wireless networks. We posit that it is possible to reduce both OPEX and CO2
emissions by carefully integrating the energy management features within the
planning process while taking into account the CAPEX cost.

The idea is to make use of technology that is either currently available or
that will become more common with 5G full deployment: sleep mode, cell
zooming, user allocation and solar power. These can be implemented gradually
as the need arises and do not depend on the general greening of the power
grid. More specifically, we want to see if this evolution can be driven by
market economics where the savings provided by the reduction in grid costs are
sufficient to cover the additional capital cost of the equipment. In cases
where this is not possible, we want to see to what extent a carbon tax can
drive the process.

For this, we propose a model to evaluate the combined technical and economic
viability of future green cellular networks. This is done by a detailed
modeling of energy, communication and demand features and by an in-depth study
on how the issues of energy management, solar energy, CO2 emission, CAPEX and
OPEX are interrelated.

##  II Literature Review

The literature relevant to this work is very large, encompassing the use of
solar equipment, energy management, dynamic user assignment and green
planning. In what follows, we go through a quick technological and literature
survey of each one of those areas.

###  II-A Solar Equipment

Solar panels have been obvious candidates for green networks for more than 10
years (See references in [9]). The main advantage of solar energy is the fact
that the cost per kW has been decreasing steadily over the last 10 years and
is currently the lowest of the more frequently used green sources [10]. Solar
panels are particularly useful and coveted for power stations in remote areas
not covered by the power grid and that use non-renewable resources. An extreme
case is off-grid rural areas where base stations are just diesel powered.

For instance, the technique proposed in [11] decreases both OPEX and
greenhouse gas emissions for remote rural base stations in Malaysia using
solar photovoltaic/diesel generator hybrid power systems. The economical and
environmental viability of PV/diesel/battery hybrid system configuration for a
BS in Nigeria was examined in [12]. Due to the large amount of solar energy
available, this system offers an alternative power source for a BS by reducing
operational costs and emissions of greenhouse gases. A solar PV/Fuel cell
hybrid system under the software HOMER is proposed in [13] to power a remote
base station in Ghana. The objective is to reduce both greenhouse gas
emissions and lower the levelized cost of electricity (LCOE). In this hybrid
system, the LCOE is reduced by 67% compared to diesel power. Similarly, the
authors of [14] use the HOMER software to simulate PV-battery-diesel to power
a BS during 24 hours under South African climate. They minimize operation
costs, emissions, and power use. The potential of photovoltaic to power BS is
studied in [15] for Kuwait where the HOMER software is used to determine the
number of PV, batteries, and converters for an off-grid solar PV system with
diesel generator while minimizing the net present cost in order to power a
cellular BSs.

There have also been some urban implementations. The work of [16] studies a
case in urban areas of South Korea where both on- and off-grid sites use
standalone solar batteries to power a macro LTE cellular base station. A
multi-objective optimization algorithm is proposed in [17] for the optimal
sizing of a standalone PV/battery to power a BS under the climate of Sydney.
The objective is the minimum annual total life cost. An optimal decision of
demand-side power management for a green wireless base station is proposed in
[18] to minimize the power cost and provide flexibility under traffic load,
grid power price, and renewable source uncertainties.

These studies, rural or urban, all have something in common: they refer to a
single base station and, in most cases, they lack accounting for the
replacement, degradation and installation costs for the solar equipment.

###  II-B Energy Management and Dynamic User Assignment

Given that 80% of the energy used by a cellular network comes from the radio
infrastructure [19], radio energy management must become an integral part of
the base station operation. Even though the existing management tools are
performance-oriented, they make it possible to design management strategies
that can also be used to reduce energy use, based on the fact that real-world
data shows that most base stations are underutilized during low traffic
periods [20].

In fact, it has already been shown that dynamic management may potentially
save between 20% to 30% of energy [21] in cellular networks if the system is
planned from the start with enough base stations. These savings are obtained
either by completely turning off some base stations or by reducing their power
during key times of the day. Even though these methods are nothing new, they
will be more easily implemented in 5G networks and beyond using the notion of
_cell zooming_.

The actual operation of cell zooming can be viewed in two ways. In [22], the
total available power can be reassigned arbitrarily among radio blocks which
in turn can be allocated to different down-link transmissions. It is also
stated in [23, 24] that a cell can extend its range through zooming. An
extreme case of cell zooming is putting some base stations in sleep mode [25,
26, 27, 28], or even turning them off completely whenever user demand is
lower. Different objective metrics have been used such as coverage [29], user
demand [30] or the actual power usage [31]. A multi-criteria model is
presented in [32] to minimize both the energy use and the user drop
probability.

A nonlinear model to minimize energy use subject to quality of service
constraints is proposed in [33]. The technique described in [34] uses solar
power and on-off operation to minimize energy cost by assigning users to
different base stations and choosing solar or grid power during the day.

One consequence of sleep mode or cell zooming is that one must re-assign users
to different base stations during the day whenever a user can no longer be
served by its base station due to a power reduction. This has been examined in
detail in [35, 36, 37]. The conclusion was that dynamic user assignment can
reduce the network cost significantly when it is integrated into the long-term
planning model. These results will not be repeated here in order to conserve
space.

###  II-C Green Planning

The techniques described above can be viewed as network management and operate
on a short-term horizon of minutes or hours. Network planning, on the other
hand, where one has to decide on the installation of base stations and the
equipment to go with it, works on a time scale of many years. This is by
itself a complex procedure since one needs to combine cells of different
sizes, including macro, micro, pico, and femto cells. The size of base
stations depends on several factors, including the site location and the
antenna position. Small stations serve areas with high traffic density using a
lower amount of energy [38, 39] but need to be combined with larger base
stations for lower-density areas.

Because of the large difference in time scales, the process was often split
into two independent parts: plan the equipment upgrades every year and manage
the resulting network on a shorter scale using the equipment available.

Unfortunately, network planning and network management are tightly coupled
because one cannot use a network management technique, such as solar cells, if
the equipment has not been installed. In fact, it has been shown that
integrating the technology choice with the long-term planning process produces
networks significantly cheaper than a two-step procedure [35, 36, 37]. There
is thus a definite need for an _integrated_ model that takes into account the
effect of short-term management techniques when deciding on equipment
upgrades.

The problem of minimizing the total CAPEX and OPEX cost over a 10-year horizon
has been examined, albeit for a single base station, in [40]. They make a
detailed model of the energy interactions and study the trade-off between
solar panels, a diesel generator or grid power. A similar energy approach was
presented in [34] when minimizing the energy cost of a given network. The
variables are the allocation of users to base stations and the energy source
used by each base station during each one of a given number of time intervals.
Even though both [40] and [34] study the energy planning of the network,
neither treats the networking planning problem, in particular the decision of
where and when to locate new green base stations over the planning horizon.

Some limited work has been done on related topics. The allocation of users
over a single day to maximize the network operator’s revenue has been examined
in [41].

The work of [42] explores the long-term network planning with green energy
harvesting of solar or wind sources. The problem is to select a subset of
candidate BSs and to assign users to the available base stations subject to a
minimum SINR requirement in order to minimize the base station installation
and the user connection costs and the cost of electric grid.

The first attempt at integrating the short-term benefits of solar energy and
network planning has been presented in our previous work [37]. The goal was to
minimize the total operating plus capital cost of the network. The users can
be re-assigned and the base station antennas can be switched off depending on
the demand at different times of day.

Some work has also considered a marketing-oriented approach. A financial
analysis of network upgrade is described in [43] to optimize the trade-off
between the generated revenue produced by the upgrade and its cost. A dynamic
programming model is proposed and a fast heuristic solution is used to compute
solutions. A similar approach is used in [44] where a case study is presented
to evaluate the impact of energy trading either between base stations or
through an energy broker and also with spectrum sharing between operators.

###  II-D Our contribution

Differently from the above body of work, this paper proposes a comprehensive
approach to study not just the technical or the economic viability of using
solar equipment to update cellular networks, but the interaction between the
two. The strength of our contribution to the state of the art comes from a
detailed model of energy management and networking planning. It is precisely
this level of detail what allows us to clarify the technical and economic
features of network upgrade.

  1. 1.

We integrate the short-term network and energy management with the long-term
network expansion over many years into a single model to provide a more
realistic view of how the planning and operation are inter-related.

  2. 2.

The planning determines decisions on different base stations sizes and types,
including solar panels, that are needed to update an existing network in an
urban area.

  3. 3.

The modeling of network and energy operation is very detailed and includes
sleep mode, cell zooming, user re-allocation, solar, batteries, inverters,
controllers to reduce the energy use of cellular networks

  4. 4.

Very detailed and realistic costs are considered for solar equipment and
battery purchase and replacement. We also model the degradation of the
efficiency of batteries and solar equipment while taking into account the time
value of money.

  5. 5.

Realistic evolution of user demand, energy usage and illumination profiles are
considered as well as regulatory or environmental constraints on base station
installations.

  6. 6.

Co2 emissions and possible taxes are integrated into the model.

We want to use this model to answer some specific questions such as:

  * •

How large is the cost reduction provided by allowing installations over the
whole horizon as opposed to a model where the installation decisions can be
taken only at the beginning of the planning horizon?

  * •

Are the OPEX savings provided by solar energy large enough to justify the
added CAPEX?

  * •

Does cell zooming make solar energy more economical?

  * •

Do the benefits of cell zooming add up to those of solar?

  * •

Is it possible to use cell zooming to reduce the CAPEX by delaying the
installation of base stations?

  * •

What is the impact of a carbon tax on the reduction of greenhouse gases?

##  III Mathematical Model

As can be seen from the previous discussion, planning a network is a complex
task, from long-term market considerations to technological choices and real-
time network management.

In this work, we want to see how prices and taxes can be used to reduce carbon
emission using different energy-saving techniques. For this, we need to
_compare_ the effect of these techno-economic options to some base case. If
this is to be meaningful, problems have to be solved to optimality. Therefore,
the model’s complexity should not prevent us from finding optimal solutions.
As a result, in the model presented below, we have just kept enough level of
detail for the study to be meaningful. The approximations and assumptions will
be clearly introduced as the model description progresses.

###  III-A Assumptions

We now briefly review some of the more important simplifications and
assumptions that were made and explain to what extent they are realistic.

####  III-A1 Network Structure

In our model, the users are aggregated into so-called _test points_ which can
be viewed as real concentrators or simply as a collection of users close
together. We are given a set of available test points for the whole planning
horizon, some of which may be currently inactive.

The choice of technology is not modeled by separate decision variables.
Instead, we introduce the notion of a base station _type_ which contains a
description of the technical features of the base station, e.g., whether it
has solar panels or not, its size, e.g., pico, micro, etc. The test cases can
then be run with a small set of given types.

####  III-A2 Demand

Network growth is driven by the increasing number of users and new
applications and services and the quality of service they require. This
involves economic issues such as market forecasting and technical issues such
as power or bandwidth management. Because our focus is on energy, we assume
that these different kinds of demands are converted in an energy requirement
from each test point. This can be done by the engineering or the traffic
department of the operator and is outside the scope of this paper. A simple
example of such a procedure is given in the Appendix.

Demand growth is modeled by activating these test points at some future time
and computing their energy requirement as given by the demand forecast.

####  III-A3 Forecasting

In practice, the results of a long-term planning model depend of the growth
forecast provided by the marketing department. Because the forecast accuracy
decreases for later years, one can use the model’s results for the coming year
to decide whether to install new equipment for that year only. The model can
then be run each year with new forecasts and technology options. This approach
is more realistic than doing a one-year planning since it does take into
account the future demands and technology as they are known at the time when a
decision has to be made.

####  III-A4 Solar Energy Model

Figure 1: Solar Equipment

An important feature of solar power is that the energy production can vary
widely over short periods of the order of an hour or less and these variations
are unpredictable. A minimum amount of solar equipment is thus required to
power a green base station. The main components are the solar panels and the
battery bank. We also model the charge controllers needed to protect the
batteries from overflowing and increase their lifetime. Finally, an AC-DC
converter is also required to power the base station with DC current from its
battery bank. Figure 1 shows the storage of solar energy into electrical
energy as a back-up energy source to the electrical grid.

We use a solar profile to estimate the amount of electricity produced during
the day since replacing the daily variation of sunlight by a single average
value for the whole planning horizon would leave out the daily changes in
sunlight. This profile is computed for an _average day_ and assume that this
is representative of the operation for the whole year.

This is clearly an over-simplification since the sunlight available can depend
strongly on the season in regions far from the equator. First note that the
illumination profile is defined for a year and that the actual length of a
“year” is a parameter. The model can then easily be used to take into account
the seasonal variations by taking a “year” as an actual season with the
corresponding profile. The downside is that this makes the optimization
problem larger and severely limits the size of networks that can be calculated
by an IP solver.

What we have done instead was to use a single profile corresponding from a
region in southern Morocco with abundant sunlight. Because one of our goals is
to see if solar equipment proves in based on economics alone, this can be
viewed as a most favorable case for solar. Since we found that using solar
equipment is not economically justified with this optimistic profile, the same
conclusion would hold under a more realistic profile.

####  III-A5 Cell Zooming

Cell zooming is a power control technique by which a base station can change
its transmission power to match certain conditions. Decreasing the power of a
given base station will decrease its coverage area but may increase that of
neighboring ones by decreasing their SINR. Increasing the power has the
opposite effect of increasing the coverage of the base station and potentially
decreasing the QoS, and hence the coverage of neighbors. Implementing cell
zooming is a complex issue that requires coordination between base stations
and a knowledge of user demands. This is clearly outside of the scope of this
paper.

Here, we assume that the network can operate within some specified bounds on
the user coverage and QoS when all base stations transmit at their maximum
power. This is the current mode of operation for networks that don’t use power
management. Under this assumption, cell zooming can be modeled by introducing
a state variable for the base stations. We assume that a given base station
type has a certain number of power levels that it can use to transmit. The
state variable indicates which of these levels is used at a given time. We
also define a coverage variable that indicates whether a test point is covered
by a base station in some state and add some constraints to make sure the
coverage is logically consistent. The model then computes the best power
levels and the corresponding coverage.

####  III-A6 Costs

The objective of the optimization model is to minimize the sum of capital and
operating costs over the planning horizon. While it is true that an operator
would be concerned by the net revenue produced by the network, in the present
case, we assume that the network will always be able to meet the demand,
independently of the decision to use solar energy or cell zooming. In other
words, the revenue is independent of the choice of technology and can be
ignored.

###  III-B Sets

Network management has to do with short-term decisions related to solar power,
cell zooming and dynamic user assignment. These decisions are taken every day
on a much shorter time scale than the planning decisions, typically a few
hours. In this paper, we will use the term _time_ to denote them.

The decisions to install base stations is taken on a much larger time scale,
typically a year, and we will use the term _year_ to denote these instants.
The sets used in our model are defined in Table I.

$\mathcal{B}$ |  The set of base stations installed at the beginning of year 1. This is indexed by $j$.
---|---
$\mathcal{C}$ |  Set of candidate sites where new base stations can be installed. We can install at most one base station per candidate site. This is indexed by $j$.
$\mathcal{I}$ |  Set of test points. A test point represents the aggregated demand of a set of users, present or future. This is indexed by $i$.
$\mathcal{L}$ |  Set of base station types. This is indexed by $l$. Type $l=0$ corresponds to the base stations in $\mathcal{B}$.
$\mathcal{Q}$ |  The set of years that defines the planning horizon. This is indexed by $q=1\dots Q$. The traffic demand is defined at the beginning of each year and the planning decisions are made at that time.
$\mathcal{S}_{l}$ |  Set of states for base stations of type $l$. This is currently defined by the transmission power but the states could be used to model other operating conditions of the base stations. This is indexed by $s=0\dots S_{l}$.
$\mathcal{T}$ |  The time instants used to model the daily variation of traffic. This is indexed by $t=1\dots T$.

TABLE I: Sets

###  III-C Parameters Values

$B_{l,q^{\prime},q}^{+(-)}$ |  Maximum (minimum) amount of energy that can be stored in the battery of a base station of type $l$ installed in year $q^{\prime}$ and used in year $q>q^{\prime}$.
---|---
$C_{l,q}$ |  The installation cost of a base station of type $l\geq 1$ in year $q$. This is the undiscounted, nominal cost. This is made up of the construction cost, upkeep and software license costs. If the base station has solar equipment, this includes the cost of the system used for converting solar to electrical energy: solar panels, batteries, converters, inverters, etc.
$C^{G}_{j,q,t}$ |  Grid unit energy cost. This is the total charge per energy unit charged by the utilities company but excludes any emission cost that may be imposed by the regulators. We assume in the most general case that this can depend both on the time period, e.g., time-based grid rates, the base station, if the supplier of grid power has different rates in different regions and that it can change from one year to the next.
$E^{T}_{i,j,q,t}$ |  The energy needed by the station in site $j\in\mathcal{B}\cup\mathcal{C}$ to serve test point $i$ in period $t$ of year $q$.
$e_{l,q^{\prime},q,t}^{S}$ |  Amount of electrical energy produced by the solar panels in a base station of type $l$ during period $\Delta_{t}$ of year $q$ when these were installed in year $q^{\prime}<q$.
$k_{i,j,l,s,q,t}$ |  Indicator function for coverage. When set to 1, indicates that test point $i$ is in the coverage radius of base station of type $l$ installed on site $j\in\mathcal{B}\cup\mathcal{C}$ and using power level $W_{s},s\in S_{l}$ during period $\Delta_{t}$ of year $q$.
$m$ |  Number of installation periods per year.
$M_{l,j}$ |  Indicator function for base station installation. When set to 1, this indicates that a base station of type $l$ may be installed on candidate site $j$. By definition, $M_{0,j\in\mathcal{C}}=0$.
$q_{i}^{\ast}$ |  The first year when test point $i$ becomes active. This is used to model the growth of demand.
$r$ |  Discount rate.
$U_{l}$ |  Indicator function of solar equipment. When set to 1, this indicates that a base station of type $l$ has solar equipment. By definition, $U_{0}=0$.
$W_{l,s}$ |  Total power available to a base station of type $l$ in state $s$. By convention, for base stations that use cell zooming, $W_{l,0}$ is the power used when idle. For base stations that don’t use cell zooming, this is the given maximum used power. This includes the power used for serving the test points.
$W_{l,s}^{x}$ |  Transmission power used by a base station of type $l$ in state $s$. By convention, for base stations that use cell zooming, $W_{l,0}^{x}=0$. For base stations that don’t use cell zooming, this is the given maximum transmission power.
$\phi$ |  The number of days in an installation period.
$\Delta_{t}$ |  Length of the interval between time instants $t$ and $t-1$.
$\lambda_{k,q}$ |  Amount of greenhouse gasses emitted per unit energy produced, e.g., Mt/kWh, emitted by a source of type $k$, e.g., coal, gas, oil, etc.
$\pi_{q}$ |  Unit price per amount of greenhouse gasses emitted, e.g, $/Mt, in year $q$.
$\nu_{i,q}$ |  Indicator function for test point use. When set to 1, indicates that test point $i$ starts to be used. This is defined by  $\nu_{i,q}=\begin{cases}0&\text{ if $q<q^{\ast}_{i}$}\\\ 1&\text{otherwise.}\end{cases}$

TABLE II: Parameters

The parameters are defined in Table II. Note that we need the two year indices
$q$ et $q^{\prime}$ to describe the use of solar equipments. For an equipment
installed in year $q^{\prime}$, the energy production and storage capacity
decrease over time so that they become less efficient as they grow older.

###  III-D Variables

In Table III we describe the decision variables, i.e., the quantities that are
computed by the model. First, a number of decision variables that are set to 1
when the stated conditions hold.

$h_{i,j,q,t}$ |  Test point $i$ is assigned to site $j\in\mathcal{B}\cup\mathcal{C}$ in period $t$ of year $q$.
---|---
$u_{j,q,t}$ |  Solar batteries are used at site $j\in\mathcal{C}$ in period $t$ of year $q$.
$v_{l,s,j,q,t}$ |  The base station of type $l$ on site $j\in\mathcal{C}$ is in state $s$ in period $t$ of year $q$.
$z_{l,j,q}$ |  A base station of type $l$ is installed on candidate site $j\in\mathcal{C}$ in year $q$.

TABLE III: Decision variables

We also define some intermediate variables that can be computed from the
parameters and decision variables. These will allow us to simplify the
presentation of the optimization model and they also have a direct physical
interpretation. They are presented in Table IV

$D_{j,q,t}$ |  The total amount of energy needed in a base station $j\in\mathcal{B}\cup\mathcal{C}$ in period $t$ of year $q$ by all test points currently served by the base station.
---|---
$\overline{E}_{j,q,t}^{P}$ |  Total amount of energy used by base station $j\in\mathcal{B}\cup\mathcal{C}$ during period $\Delta_{t}$ of year $q$ when operating from batteries.
$\overline{E}_{j,q,t}^{G}$ |  Total amount of energy used by base station $j\in\mathcal{B}\cup\mathcal{C}$ during period $\Delta_{t}$ of year $q$ when operating from the grid.
$E_{j,q,t}^{B}$ |  Energy available from the batteries of base station $j\in\mathcal{C}$ at the beginning of period $t$ of year $q$.
$E_{j,q,t}^{S}$ |  Energy produced by the solar panels of base station $j\in\mathcal{C}$ during period $t$ of year $q$.
$L_{j,q,t}$ |  Solar energy lost at base station $j\in\mathcal{C}$ during period $t$ of year $q$.
$w_{l,j,q}$ |  Indicator variable set to 1 if a base station of type $l$ is currently installed on site $j\in\mathcal{B}\cup\mathcal{C}$ in year $q$. This can be seen as the indicator of the state of site $j\in\mathcal{B}\cup\mathcal{C}$ in year $q$.

TABLE IV: Intermediate variables 1

We also need some intermediate variables to take into account the nonlinear
terms that will show up in the model, they are defined in Table V.

$x_{l,s,j,q,t}$ |  Binary variable set to 1 if the base station of type $l$ that is installed at site $j\in\mathcal{C}$ operates in state $s$ using the batteries during period $t$ of year $q$. These variables are given by $x_{l,s,j,q,t}=v_{l,s,j,q,t}u_{j,q,t}$.
---|---

TABLE V: Intermediate variables 2

###  III-E Objective Function

The capital cost depends on the type of installed base stations and the
installation year. Operating cost come from the grid cost for operating the
base stations and the emission costs. Installing solar equipment can then
allow a reduction in the operating cost, as well as a reduction of greenhouse
gases, but at the expense of an increase in the capital cost. The objective
function can then be written as:

$\displaystyle\tiny
Z=\sum_{q\in\mathcal{Q}}(1+r)^{-q}\sum_{j\in\mathcal{C}}\sum_{l\in\mathcal{L}}C_{l,j,q}z_{l,j,q}$
$\displaystyle+\sum_{q\in\mathcal{Q}}(1+r)^{-q}m\phi\sum_{j\in\mathcal{B}\cup\mathcal{C}}\sum_{t\in\mathcal{T}}\left\\{C^{G}_{j,t}+\pi_{q}\lambda_{k,q}\right\\}\overline{E}^{G}_{j,q,t}.$
(1)

###  III-F Installation of Base Stations

We now describe the various constraints that may limit the installation of
certain base stations in some sites.

First, some base station types might not be allowed on some sites because of
physical or environmental conditions. This yield the constraint

$\sum_{q\in\mathcal{Q}}z_{l,j,q}\leq M_{l,j}\qquad\forall
l\in\mathcal{L},j\in\mathcal{C}.$ (2)

Given that $M_{0,j\in\mathcal{C}}=0$, then if follows that
$z_{0,j,q}=0\quad\forall j\in\mathcal{C},q\in\mathcal{Q}$. There is no
replacement of base stations during the planning horizon so that a base
station can be installed on a given site at most once, which yields the
constraint

$\sum_{l\in\mathcal{L},q\in\mathcal{Q}}z_{l,j,q}\leq 1\qquad\forall
j\in\mathcal{C}.$ (3)

If a base station is currently installed on some site at a given time, it must
have been installed first at some previous time, so that

$\displaystyle w_{l,j,q}=\sum_{q^{\prime}\leq
q}z_{l,j,q^{\prime}}\qquad\forall
l\in\mathcal{L},j\in\mathcal{C},q\in\mathcal{Q}.$ (4)

In order for a base station to use solar energy, the type must have solar
capability

$u_{j,q,t}\leq\sum_{l\in\mathcal{L}}w_{l,j,q}U_{l}\qquad\forall
j\in\mathcal{C},q\in\mathcal{Q},t\in\mathcal{T}.$ (5)

###  III-G Test Point Assignment

All currently used test points must be assigned to a site:

$\sum_{j\in\mathcal{B}\cup\mathcal{C}}h_{i,j,q,t}=\nu_{i,q}\qquad\forall
i\in\mathcal{I},q\in\mathcal{Q},t\in\mathcal{T}.$ (6)

The assignment is possible only if the coverage radius of the base station is
large enough so that

$\displaystyle h_{i,j,q,t}$
$\displaystyle\leq\sum_{\begin{subarray}{c}l\in\mathcal{L}\geq 1\\\
s\in\mathcal{S}_{l}\end{subarray}}v_{l,s,j,q,t}k_{i,j,l,s,q,t}$
$\displaystyle\forall
i\in\mathcal{I},j\in\mathcal{C},q\in\mathcal{Q},t\in\mathcal{T}$ (7)
$\displaystyle h_{i,j,q,t}$
$\displaystyle\leq\sum_{\begin{subarray}{c}l\in\mathcal{L}\\\
s\in\mathcal{S}_{l}\end{subarray}}k_{i,j,l,s,q,t}$ $\displaystyle\forall
i\in\mathcal{I},j\in\mathcal{B}\cup\mathcal{C},q\in\mathcal{Q},t\in\mathcal{T}.$
(8)

###  III-H Energy Storage

The amount of energy available in a base station must be large enough to meet
the demand for the test points that it serves

$\displaystyle D_{j,q,t}$
$\displaystyle=\sum_{i\in\mathcal{I}}E_{i,j,q,t}^{T}h_{i,j,q,t}$
$\displaystyle\forall
j\in\mathcal{B}\cup\mathcal{C},q\in\mathcal{Q},t\in\mathcal{T}$ (9)
$\displaystyle D_{j,q,t}$ $\displaystyle\leq\Delta_{t}W_{0,0}^{x}$
$\displaystyle\forall j\in\mathcal{B},q\in\mathcal{Q},t\in\mathcal{T}$ (10)
$\displaystyle D_{j,q,t}$
$\displaystyle\leq\Delta_{t}\sum_{l\in\mathcal{L}\geq
1,s\in\mathcal{S}_{l}}v_{l,s,j,q,t}W_{l,s}^{x}$ $\displaystyle\forall
j\in\mathcal{C},q\in\mathcal{Q},t\in\mathcal{T}.$ (11)

###  III-I Energy Production Model

The base station installed on some site $j$ must be in a single state for
every period $t$ of year $q$. This is modelled by variable $w_{l,j,q}$. If a
station of type $l$ has not yet been installed on site $j$ in year $q$, then
$w_{l,j,q}=0\Rightarrow v_{l,s,j,q,t}=0\quad\forall s\in\mathcal{S}_{l}$. On
the other hand, if type $l$ has already been installed, then $w_{l,j,q}=1$
which forces the selection of a single transmission power.

$\sum_{s\in\mathcal{S}_{l}}v_{l,s,j,q,t}=w_{l,j,q}\qquad\forall
l\in\mathcal{L},j\in\mathcal{C},q\in\mathcal{Q},t\in\mathcal{T}.$ (12)

A base station must operate either in battery or grid mode but not both. This
makes the model somewhat more complex. If we power the antennas from the
batteries, we have to meet two conditons: the base station type that is
currently installed must be of the right type and we must have decided to use
battery power during that time. This yields:

$\displaystyle\overline{E}_{j,q,t}^{P}$
$\displaystyle=\Delta_{t}\sum_{l\in\mathcal{L}\geq
1,s\in\mathcal{S}_{l}}W_{l,s}v_{l,s,j,q,t}u_{j,q,t}$
$\displaystyle=\Delta_{t}\sum_{l\in\mathcal{L}\geq
1,s\in\mathcal{S}_{l}}W_{l,s}x_{l,s,j,q,t}~{}~{}~{}\forall
j\in\mathcal{C},q\in\mathcal{Q},t\in\mathcal{T}$ (13)
$\displaystyle\overline{E}_{j,q,t}^{P}$ $\displaystyle=0~{}~{}~{}\forall
j\in\mathcal{B},q\in\mathcal{Q},t\in\mathcal{T}$ . (14)

If we power from the grid, the conditions are that the right type of base
station is installed and we have decided not to use battery power, i.e.,

$\displaystyle\overline{E}^{G}_{j,q,t}$
$\displaystyle=\Delta_{t}\sum_{l\in\mathcal{L}\geq
1,s\in\mathcal{S}_{l}}W_{l,s}v_{l,s,j,q,t}(1-u_{j,q,t})$
$\displaystyle=\Delta_{t}\sum_{l\in\mathcal{L}\geq
1,s\in\mathcal{S}_{l}}W_{l,s}(v_{l,s,j,q,t}-x_{l,s,j,q,t})$
$\displaystyle\forall j\in\mathcal{C},q\in\mathcal{Q},t\in\mathcal{T}$ (15)
$\displaystyle\overline{E}_{j,q,t}^{G}$ $\displaystyle=\Delta_{t}W_{0,0}$
$\displaystyle~{}~{}\forall j\in\mathcal{B},q\in\mathcal{Q},t\in\mathcal{T}.$
(16)

Note that both (13) and (16) introduce nonlinear terms in the model. This is
taken care of in section III-J.

The energy produced by the solar equipments is defined by:

${E}^{S}_{j,q,t}=\sum_{l\in\mathcal{L},q^{\prime}\in\mathcal{Q}}e_{l,q^{\prime},q,t}^{S}z_{l,j,q^{\prime}}\qquad\\\
~{}~{}~{}\forall j\in\mathcal{C},q\in\mathcal{Q},t\in\mathcal{T}.$

The energy available at the beginning of period $t$ is given by:

$\displaystyle E^{B}_{j,q,t}$
$\displaystyle=E^{B}_{j,q,t-1}+E^{S}_{j,q,t-1}-L_{j,q,t-1}-\overline{E}^{P}_{j,q,t-1}$
$\displaystyle~{}~{}~{}\forall
j\in\mathcal{C},q\in\mathcal{Q},t\in\mathcal{T}\geq 2$ (17) $\displaystyle
E^{B}_{j,q,1}$
$\displaystyle=E^{B}_{j,q,T}+E^{S}_{j,q,T}-L_{j,q,T}-\overline{E}^{P}_{j,q,T}$
$\displaystyle~{}~{}~{}\forall j\in\mathcal{C},q\in\mathcal{Q}$ (18)

The storage capacity of batteries is bounded above and below by:

$\displaystyle\sum_{l\in\mathcal{L},q^{\prime}\in\mathcal{Q}}z_{l,j,q^{\prime}}B^{-}_{l,q^{\prime},q}\leq
E^{B}_{j,q,t}\leq\sum_{l\in\mathcal{L},q^{\prime}\in\mathcal{Q}}z_{l,j,q^{\prime}}B_{l,q^{\prime},q}^{+}\qquad$
$\displaystyle~{}~{}~{}\forall
j\in\mathcal{C},q\in\mathcal{Q},t\in\mathcal{T}$ (19)

In a given period, a base station with solar equipment cannot lose more than
the solar energy produced by the panels during this period:

$0\leq L_{j,q,t}\leq E^{S}_{j,q,t}\qquad\forall
j\in\mathcal{C},q\in\mathcal{Q},t\in\mathcal{T}$ (20)

###  III-J Linearization

As written, the model contains nonlinear constraints due to the presence of
the term $v_{l,s,j,q,t}u_{j,q,t}$ in (13) and (16). We can make the
constraints linear by adding a set of independent variables
$x_{l,s,j,q,t}=v_{l,s,j,q,t}u_{j,q,t}$ and adding the constraints:

$\displaystyle x_{l,s,j,q,t}$ $\displaystyle\leq v_{l,s,j,q,t}$ (21)
$\displaystyle x_{l,s,j,q,t}$ $\displaystyle\leq u_{j,q,t}$ (22)
$\displaystyle x_{l,s,j,q,t}$ $\displaystyle\geq v_{l,s,j,q,t}+u_{j,q,t}-1$
(23) $\displaystyle\forall l\in\mathcal{L},s\in\mathcal{S}_{l},j$
$\displaystyle\in\mathcal{C},q\in\mathcal{Q},t\in\mathcal{T}$

##  IV Data Sets

In order for the results to be meaningful, we tried as best as possible to use
realistic data for the costs and other technical parameters. The cost of a
base station is made up of the building and installation cost in addition to
the cost of the solar equipment. This is given by:

$\displaystyle C_{l,q}=C^{B}_{l}+C^{S}_{q}$ (24)

where

$C^{B}_{l}$ Construction and installation cost of a base station of type $l$
[45],

$C^{S}_{q}$ Purchase and installation cost of the solar equipment. This
depends of the maximum power that can be generated and the battery storage
cost. According to [46], a realistic value is 3$/W. This cost is indexed by
year to model the expected decrease of the cost of solar generation.

Figure 2: Traffic profile Figure 3: Illumination profile

The numerical results were computed for two small networks P1 and P2 with
different peak traffic profiles. The parameters common to all cases are shown
in Table VI. We have split the day into eight different periods to get a more
accurate view of the changes in the user demands. These are shown on Figure 2.
They correspond to a workday profile in an inner core cell [47].

The initial peak user rate for P1 is 10Mbps and grows at a 20% yearly rate so
that user demand doubles every four years. The peak user rate for P2 is
12Mbps. We have used a 12% discount rate and a 2.64% inflation rate which
reduces by half the value of a capital expenditure after 6 years. A unit cost
of $0.20/kWh is representtive of the power rates in many countries. In Canada,
for instance, this varies [48] from $0.07/kWh to $0.38/kWh for residential
users. The cost of solar equipment is critical for the introduction of solar
energy in networks. In northern countries, a realistic value [49] of $3/W is a
threshold for having profitable solar power. In the numerical work, we have
used the same cost over the whole planning horizon.

An antenna gain of 3 is typical for current antennas. The propagation
coefficient and the channel noise are typical values for urban networks.
Figure 3 shows the illumination profile for a city in southern Morocco [50].
The peak illumination is set to 800 $W/m^{2}$.

Parameter | Value
---|---
No periods | 8
Discount rate | 0.12
Inflation rate | 0.0264
Annual demand growth rate | 0.20
Unit cost of grid energy($/kWh) | 0.20
Unit cost of solar equipment ($/w) | 3
Antenna gain | 3
TABLE VI: Common parameters for all networks Pb No | No years | No Macro BS | No CS | No TP | Maximum initial user rate (Mbps) | Channel noise | Propagation coefficient
---|---|---|---|---|---|---|---
P1 | 10 | 1 | 8 | 18 | 10 | $10^{-5}$ | 3
P2 | 10 | 1 | 14 | 30 | 12 | $1.5e-5$ | 2
TABLE VII: Specific network parameters
BS: Base Station, CS: Candidate Sites, TP: Test Points

The parameters that vary for each network are shown on Table VII. They define
the size of each problem. All cases are for a 10-year horizon. This value was
chosen as a compromise between having a problem size small enough to be able
to solve it in reasonable time and having a large enough horizon to allow
significant discounting and installation delays.

The macro base stations are the ones currently in the operator’s network. We
use only one of these so that the candidate sites will be needed to meet the
demand. We limit the study to small networks because we want to compare the
total cost for different scenarios. For this to be meaningful, we need to
compute optimal solutions or at least solutions with a small gap. This can be
done in a reasonable execution time only for small networks.

##  V Scenarios

The options that are compared are summarized in a number of scenarios.

#####  B: Base Network

This is the reference network. It has no solar equipment, no cell zooming and
no dynamic management. It corresponds to most of the base stations currently
used in 4G networks.

#####  S: Solar Power

In this scenario, only solar is enabled so that we can quantify the savings
from solar power. One goal is to try to determine a relationship between the
unit cost of solar power on the one hand and the capital cost of the solar
equipment and the grid cost on the other. We also want to see, in the case
where the unit cost of solar is smaller than the grid cost, whether the best
solution is to install solar equipment everywhere.

#####  O: On-OFF

In this scenario, only the BS sleeping mode is enabled, when a base station
can be put on idle power during a low traffic period. This is a special case
of cell zooming.

#####  Z: Cell Zooming

Here, only cell zooming is enabled. With cell zooming, we can increase the
reach of base stations in a given direction while reducing it elsewhere. We
can then evaluate the impact of cell zooming on the network cost. This will be
reflected by a reduction of the operating costs and may have an impact on the
capital cost.

#####  S+O: Solar and On-off

This is a combination between scenario S and scenario On-OFF where both
technologies are used at the same time. This will allow us to see whether the
benefits of the two technologies add up.

#####  S+Z: Solar and Cell Zooming

In this scenario, both solar and cell zooming are available. This is the most
important one, because it optimizes the dynamic management and the use of the
solar together to achieve a truly optimal solution.

##### S + Z0

Here, both solar and cell zooming are available but can be installed only in
the first year. This corresponds to a planning technique that does not
consider the time evolution of the network, as was done in [37].

##### FS + Z

This scenario is used to compare a solution where we force the installation of
solar equipment on all BS. That case is interesting to know if a purely solar
solution gives reduced costs and if not, how sub-optimal it is.

These scenarios are implemented in the model by fixing different variables at
zero while leaving the others free. This is summarized in Table V. For
simplicity and brevity, we only illustrate solutions to the peak period the
last year which corresponds to the peak of demand for TP on the planning
horizon. Any feasible solution at this time is also feasible for all other
periods.

Scnr | S | O | Z | $z$ | $v$ | $u$ | $h$
---|---|---|---|---|---|---|---
B | no | no | no | F | 0 | 0 | F
S | yes | no | no | F | 0 | F | F
O | no | yes | no | F | *** | 0 | F
Z | no | yes | yes | F | 0 | 0 | F
S+O | yes | yes | no | F | *** | F | F
S+Z | yes | yes | yes | F | 0 | F | F
S+Z0 | yes | yes | yes | * | 0 | F | F
FS+Z | yes | yes | yes | ** | F | F | F

TABLE VIII: State of variables for each Scenario: *: Free in first year only
**: Only solar types allowed ***: Two states only. F: variable is free

##  VI Numerical Results

In this part, we analyze the results from the optimization model with and
without GHG taxes. We use two small networks, P1 and P2, generated from the
same data except for channel noise, propagation coefficient and the demand
with low values for network P1 and high for P2.

In order to produce optimal solutions, the problem and its variants are
modeled by AMPL and solved using CPLEX with the default options. AMPL
integrates pre-solving mechanisms which allow certain variables and
constraints to be eliminated before calling on the solver. We used a standard
IP solver because we must have an exact solution for all scenarios in order to
compare the costs of solar and sleep modes. Larger networks will require
heuristic techniques specifically adapted to the optimization model. The
algorithms were executed on Intel(R) Core(TM) i7-8700 CPU $@$ 3.20GHz with 12
cores running at 3.5 GHz and 65 GBs RAM.

Tables V and V give various costs and amounts of energy for the two networks
without GHG taxes. The column titles represent

$Z$

Total network cost. This is the sum of $Z_{c}$ and $Z_{op}$

$\Delta$

Change in $Z$ relative to the cost of scenario B

$Z_{c}$

Total capital cost including solar equipment

$Z_{s}$

Capital cost of solar equipment

$Z_{op}$

Operating cost

$Z_{g}$

Cost of grid energy

$Z_{CO_{2}}$

Cost of greenhouse taxes

$Z_{s}$/kWh

Production cost of solar energy = $Z_{s}$/(Total energy produced by the
panels)

$Z_{s}^{\ast}$/kWh

Production cost for the energy used. This is $Z_{s}$/(Total energy used by the
network)

The second set of tables V and V shows energy information where all energy
values are in MWh. The column labels are defined as

$E_{N}$

This is the total amount of energy that the network needs

$E_{G}$

The amount of energy coming from the grid

CO2

The number of tons of CO2 produced by the network

$E_{si}$

The amount of energy produced by the installed solar equipment

$E_{su}$

This is the amount of solar energy effectively used

The difference $E_{si}-E_{su}$ is the energy lost due to the limited capacity
of batteries. The $Z_{s}$/kWh column gives the cost in dollars per kilowatt-
hour of solar based on the amount of solar energy actually used. This is
simply the value of the CAPEX column divided by the solar energy used. The
$Z_{s}^{\ast}$/kWh column is the energy lost due to the limited capacity
batteries. Solar losses are the ratio $(E_{si}-E_{su})/E_{si}$. This ratio
clearly shows that installing too much solar equipment will increase losses
and installing larger batteries is too expensive.

Figure 4: Network P1 (Without taxes and Scenario S+Z) Figure 5: Network P2
(Without taxes and Scenario S+Z)

###  VI-A Without taxes

In this part, we do not consider emissions taxes. Our objective is to see if
free market economics can drive the introduction of solar BSs to reduce GHG
emissions. Figures 4 and 5 show the base station installation planning for the
S+Z scenario for P1 and P2 without taxes. One can also see the assignment of
each of the TPs to BSs every year. The growing demand over the years requires
the installation of new stations. It turns out that the optimal solution is
_not_ to install solar base stations both for low and high traffic. This is
due to the current high costs of solar equipment and also to the cost of
batteries replacement. Batteries for green micro BSs have a lifetime of 7
years and 5 years for green pico BSs. This is less than the planning horizon
so that the batteries have to be replaced. It then turns out that with the
current grid prices, the traditional BSs system is less expensive so that even
over a 10-year horizon, the installation of stations that run on solar energy
is not justified.

This can be seen by comparing the results of Table V for the scenarios S+Z and
FS+Z. In the second case, we force the installation of solar equipment on all
base stations. For P1, this reduces the operating cost $Z_{o}$ from 17.2 to
16.3 with a saving of 0.9 while the capital cost of solar equipment $Z_{s}$
increases from 21.16 to 23.8 for an added expense of 2.64, larger than the
savings on the operating cost. The same results can be found for P2, where the
savings is 5.7 and the added cost, 7.4. The corresponding results of Table V
also show that forcing the use of solar will have a significant impact on CO2
emissions.

It should be noted that while solar stations do not emit CO2, there is still
some amount of CO2 emissions in the Full S + Z scenario. We assumed that the
system already includes non-solar macro stations BSs that still produce
emissions because of their large energy use.

If we consider only GHG emissions, PV-Battery BSs, which produce no GHG, are
very attractive as compared with traditional BSs. When we take into account
realistic cost data, as we do here, the investment in solar equipment is not
profitable for cellular operators. The size of the batteries and PV needed to
reduce the GHG emissions is such that this increases the price of the solar
equipment and thus the total CAPEX above that for non-solar networks.

Even if solar base stations are not viable, we can also see from scenario Z
that cell zooming by itself can reduce the CO2 emissions and the operating
cost, with a net saving on the total cost. Thus cell zooming is a good
compromise compared with the Full S+Z scenario.

TABLE IX: Results without taxes (Costs)

TABLE X: Results without taxes (Energy).

###  VI-B With taxes

In this section, we study how a GHG tax can improve the the environmental
impact of the network. A GHG tax on fuels is set at a price of $50 per ton of
ECO2 in the first year and increased by $50 each year until it reaches $500 in
the 10th year. We consider that coal is the source of electricity and that 1
kWh of coal-produced electricity emits 1 kg ECO2.

We arrived at the tax growth formula by a trial-and-error procedure. We
started with a constant value of $50, the carbon tax for 2022 [51] in Canada.
Initial results showed that this was not large enough to yield solutions with
green BSs. We then tried small progressive increases from this value, without
success. We finally found that the carbon tax had to increase by a factor of
ten over the planning horizon to produce solutions with green BSs, which is an
important finding of this project.

TABLE XI: Results with taxes (Costs)

TABLE XII: Results with taxes (Energy)

Table V and V list the cost and energy when GHG taxes are considered. We can
see that the total costs are increased both for P1 and P2 due to the rise of
the OPEX. In most scenarios, when solar is enabled, it is used in the
planning. We can also notice a reduction of 47 tons of C02 emissions for P1
and 118 tons for P2.

Figure 6: Network P2(With taxes and Scenario S)

Figure 7: Network P2(With taxes and Scenario S+Z)

As we have seen from the cost tables, the largest part of the total capital
cost comes from the installation of the base stations themselves while the
operating cost is only a small fraction of this total. We can see an important
result from Figures 6 and 7. Both scenarios produce basically the same
sequence of base station installations with the single exception of base
station 9 in year 6. In the S scenario with only the solar option, the optimal
solution is to install a _solar_ micro base station. If we allow cell zooming,
however, we need only to install a _non-solar_ micro base station. Because the
solar cost is relatively large, this produces a significant decrease in the
capital cost of solar equipment, from 8.1 to 5.1. In other words, the
introduction of cell zooming can reducee not only the operating cost, as
expected, but also the _capital_ cost, in the present case by choosing a less
expensive equipment. It is quite conceivable that in other cases, this might
lead to actually postponing a capital expense with a large reduction in the
total cost.

Figure 8: Network P2(With taxes and Scenario S + Z + Z free at year 0 )

We can also see why a static model like S+Z0, where the decision is taken only
at the beginning of the study period, can produce such costly solutions. From
Figure 8, we see that a large number of base stations are installed at period
0 but are not used until (much) later.

Figure 9: Network P1(With taxes and Scenario Full S + Z)

We can also see from Figure 9 why scenario FS+Z, where solar is installed
everywhere in network P2, is more expensive. All the non-solar base stations
that were installed in the S+Z scenario are now forced to be solar which is
where the cost increase comes from.

###  VI-C Daily Assignment of TPs to BS

We can examine in some detail the TP assignment to the BS for P1 and the S+Z
scenario. We see that the dynamic assignment of test points to base stations
uses sleep mode in an optimal way in each period to reduce both the OPEX and
CAPEX.

Figure 10: Assignment of TPs at 10:00

Figure 10 shows the dynamics of the network with the peak traffic demand at
period 10:00.

Figure 11: Assignment of TPs at 13:00

We see on Figure 11 that base stations 3 and 5 are in standby mode at 13:00.

Figure 12: Assignment of TPs at 15:00

At 15:00, BS 3 is in standby mode in Figure 12.

##  VII Conclusions

With the advent of 5G and beyond, there will be a significant increase in
energy use and green gas emissions in cellular networks. A potential solution
is to use solar-powered base stations in the access in addition to other
energy management techniques.

In this article, we propose a comprehensive optimization model that not only
shows the technical integration of solar power with other management features,
but also allows an in-depth study of its economics. The objective is to reduce
the total cost, including CAPEX and OPEX, over a ten-year horizon and under
constraints that reflect the inter-relation between networking and energy. Our
aim is to study the viability of green networks in reducing costs and GHGs. We
use data that is as realistic as possible to study the technical and economic
interactions.

We found that cellular zooming offers an effective solution for reducing
planning and operating costs in a cellular network. We also found that cell
zooming can not only reduce operating costs but also capital costs by avoiding
the installation of expensive solar stations. However, in terms of greening
future networks, we found that current energy and solar-related equipment
prices are such that green base stations are not economically viable for
cellular operators.

We then added a high and progressive carbon tax to the model. This produced
networks where the CO2 emissions were drastically reduced as green base
stations were added into the planning. A conclusion is that unless there is a
significant reduction in the cost of solar equipment, some form of carbon tax
will be needed and that that tax has to be significantly higher than current
values.

##  Appendix A Demand Model

The main requirement from users is generally expressed in terms of the bit
rate of a connection. In our model, demand is expressed in terms of
$E^{T}_{i,j,q,t}$, the energy required by the base station to serve a user so
that the demand in bit rate needs to be converted into an energy demand.

This in turn is related to the notion of coverage. In current networks, where
base stations are always turned on at a fixed power, we can define a fixed
coverage radius for a given bit rate to the users. With cell zooming and the
ensuing dynamic user allocation, the coverage radius is no longer a fixed base
station parameter but now depends on the transmission power of the base
station at some instant.

In this section, we provide a simple model for this extended coverage radius
concept and also a transformation rule from a demand in bit rates into an
energy demand. This model is more realistic than the one used in [37] where
these values were generated randomly.

###  A-A Coverage

In order to model the coverage, we assume and additive, white noise channel.
This could easily extended to more complex models if needed. In that case, the
maximum bit rate $\overline{\rho}_{i,j,l,s}$ that a test point $i$ can receive
from a base station $j$ of type $l$ transmitting at the power level of state
$s$ is given by

$\overline{\rho}_{i,j,l,s}=B_{l}\log_{2}\left(1+\frac{W^{r}_{i,j,l,s}}{N}\right)$
(25)

where

$B_{l}$ The bandwidth of the channels used by a base station of type $l$

$W^{r}_{i,j,l,s}$ The power received by the test point

$N$ The channel noise.

A base station can meet a required bit rate $\rho_{i,q,t}$ from a test point
$i$ at time $t$ from year $q$ if $\rho_{i,q,t}\leq\overline{\rho}_{i,j,l,s}$.
From this, we can define the generalized coverage parameter ${\mathbf{k}}$ for
each time instant by the condition.

$\displaystyle k_{i,j,l,s,q,t}$ $\displaystyle=\begin{cases}1&\text{if
$\rho_{i,q,t}\leq\overline{\rho}_{i,j,l,s}$}\\\ 0&\text{otherwise}\end{cases}$
(26) $\displaystyle\forall\,i\in\mathcal{I},\ $ $\displaystyle\
j\in\mathcal{B\cup C},\ l\in\mathcal{L},\ s\in\mathcal{S}_{l},\
q\in\mathcal{Q},\ t\in\mathcal{T}.$

####  A-A1 Channel Gain

The signal power received by a test point from a base station transmitting at
a given power is given by

$\displaystyle W^{r}_{i,j,l,s}$ $\displaystyle=W^{x}_{l,s}\gamma_{i,j}$ (27)
$\displaystyle\gamma_{i,j}$ $\displaystyle=\frac{\alpha}{d_{i,j}^{n}}$ (28)

where

$W^{x}_{i,j,l,s}$

is the base station transmission power

$W^{r}_{i,j,l,s}$

is the power received at the test point

$d_{i,j}$

the distance between $i$ and $j$

$n$

the propagation coefficient.

$\alpha$

the antenna gain

####  A-A2 Energy Demand

We can now compute the power required from a base station by a test point by
replacing (27) and (28) into (25) and solving for $W^{x}_{i,j,q,t}$ to get

$W^{x}_{i,j,q,t}=\frac{Nd_{i,j}^{n}}{\alpha}\left(2^{\rho_{i,q,t}/B_{j}}-1\right)$
(29)

so that the energy requirement during period $(q,t)$ is given by

$E^{T}_{i,j,q,t}=\Delta tW^{x}_{i,j,q,t}$ (30)

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