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Optimal Direct Load Control of Renewable Powered Small Cells:

Performance Evaluation and Bounds

Nicola Piovesan, Marco Miozzo, Paolo Dini

CTTC/CERCA, Av. Carl Friedrich Gauss, 7, 08860, Castelldefels, Barcelona, Spain

{npiovesan, mmiozzo, pdini}@cttc.es

Abstract—In this paper, we propose an optimal direct load

control of renewable powered small base stations based on

Dynamic Programming. The optimization is represented using

Graph Theory and the problem is stated as a Shortest Path

problem. The proposed optimal algorithm is able to adapt to

the varying conditions of renewable energy sources and trafﬁc

demands. We analyze the optimal ON/OFF policies considering

different energy and trafﬁc scenarios. Then, we evaluate network

performance in terms of system drop rate and grid energy

consumption. The obtained results are compared with a greedy

approach. This study allows to elaborate on the behavior and

performance bounds of the system and gives a guidance for

approximated policy search methods.

Index Terms—Mobile Networks, Energy Sustainability, Opti-

mal Control, Demand Response, Dynamic Programming, Direct

Load Control

I. INTRODUCTION

Recently, cellular networks have witnessed an impressive

increase in mobile user demand. This is due to the introduction

of new services that require reliable and fast connectivity,

as well as the increase in the number of connected devices,

including machines. In fact, the data trafﬁc is augmenting at

a rate of approximately 1.5 to 2 times per year, while the

emergence of machine-type communication and IoT will lead

to 29 billion connected devices in 2022 [1]. Therefore, the ﬁfth

generation mobile network (5G) is expected to support 1000

times more data volume per unit area, 100 more user data rate,

1000 more connected devices, 10 times longer battery life and

5 times reduced end-to-end latency than 4G [2].

A new architecture and new network deployments are, thus,

necessary to meet those requirements. Massive deployment

of small base stations (SBSs) represents the most promising

architecture to meet the high capacity demand of mobile

networks. However, the deployment of such network elements

will lead to an increase in the energy consumption of the

network that will cause negative economic and environmental

impacts. Predictions conﬁrm that, if no actions are taken, the

greenhouse gas (GHG) emissions per capita for Information

and Communication Technology (ICT) will increase from 100

kg in 2007 to 130 kg in 2020, globally [3]. Moreover, the

high energy consumption of the cellular network forces the

operators to pay high bills, which constitute half of their

operating expenditures (OPEX) [4]. Total global energy con-

sumption by all mobile networks was approximately 120 TWh

in 2010, resulting in energy costs of $13 billion [5]. Although

this is not a recent estimate, it represents a lower bound

for the actual values due to the increasing price of energy.

Therefore, there is a need for controlling and mitigating the

energy consumption in the next generation cellular networks.

The reduced energy requirements of small base stations

encourage the use of renewable energy sources (RES) as

distributed power suppliers. The adoption of renewable energy

in modern mobile networks will lead to (i) a reduction of

the grid energy consumption, (ii) a reduction of the carbon

footprint of ICT and (iii) savings on the energy bills from the

network operators [6].

The introduction of RES entails an intermittent and erratic

energy budget for the communication operations of the SBSs.

Therefore, Demand Response (DR) is fundamental to properly

manage energy inﬂow and spending, based on the trafﬁc

demand. Considering the high number of SBSs in the system,

distributed self-organizing techniques represents a viable so-

lution that can enable intelligent energy management policies,

such as Direct Load Control [7]. An optimal switch ON-OFF

problem has been solved in [8] by using a two-stage DP

algorithm. In particular, the BSs’ on-off states are optimized in

the ﬁrst stage, and the active BSs’ resource blocks are allocated

iteratively in the second stage. However, the problem has been

stated for a single-tier architecture.

In our previous work [9], a two-tier architecture with

hybrid power suppliers is introduced: macro base stations

(MBSs) reside in the ﬁrst tier to provide baseline coverage and

capacity and are powered by the electrical grid, whereas SBSs

operate in the second tier to provide capacity enhancement

and are supplied by solar panels plus batteries. The data

trafﬁc ofﬂoaded by the SBSs has higher spectral efﬁciency

and allows a reduction of the energy drained from the grid. An

optimal direct load control of renewable powered SBSs based

on dynamic programming, is proposed. The DP optimization

is represented using Graph Theory and the problem is stated as

a shortest-path search. The Label Correcting Method is used to

explore the graph and ﬁnd the optimal ON/OFF policy for the

SBSs. DP has the key property of applying optimal control as

a trade-off between the present and the future costs. This is a

fundamental feature in our scenario, to prevent SBSs blackout

during periods with low renewable energy arrivals and high

trafﬁc demands. In this paper, we extend our previous work

by analyzing the optimal policies considering different energy

harvesting and trafﬁc conditions. The obtained policies are

also compared with a greedy approach. Finally, we evaluate

c

2018 IEEE

the network performance in terms of system drop rate and grid

energy consumption.

The remainder of the paper is organized as follows. In Sec-

tion II we present the system model, whereas the optimization

problem is formulated in Section III. In Section IV we analyze

the optimal policies for different energy harvesting and trafﬁc

scenarios and we discuss some performance results. Finally,

in Section V we draw our conclusions.

II. SY ST EM MO DE L

The Radio Access Network (RAN) is represented as a

set of clusters. Each of them is composed of 1 macro base

station (MBS) and Csmall base stations (SBSs). Each SBS

is powered by a solar panel and it can store energy into a

battery. On the contrary, the MBS is connected to the electrical

grid. The SBSs implement an intelligent energy management

system that decides their operative state. The two feasible

operative states are: (i) ON, where the SBS serves the users

in its coverage area, and (ii) OFF, where the SBS is in an

energy saving mode and its users are handed over to the MBS.

The state of all the CSBSs at time tis described by the

vector St= [S(1)

t, S(2)

t, ..., S(C)

t]. Each element S(i)

t, with

i= 1, ..., C, is deﬁned as follows:

S(i)

t=(0,if i-th SBS is OFF

1,if i-th SBS is ON (1)

The energy harvested by the SBSs at time tis indicated by

the vector Et= [E(1)

t, E(2)

t, ..., E(C)

t], while the amount of

energy stored in the SBSs batteries at time tis indicated by

the vector Bt= [B(1)

t, B(2)

t, ..., B(C)

t].

The energy consumption of the BS is approximated by the

linear function P=P0+βρ, where P0is the baseline power

consumption and ρ∈[0,1] is the normalized trafﬁc load.

The typical values of these parameters are PMBS

0= 750W,

βMBS = 600 for MBSs and PSBS

0= 105.6W,βSBS = 39

for SBSs. This model is supported by real measurements and

closely matches the real power proﬁle of BSs [10].

We consider a LTE RAN with a transmission bandwidth

BW divided into Rresource blocks (RBs) of 1msec per

180 kHz each [11]. The trafﬁc level of the SBSs at time tis

indicated by the trafﬁc load vector ρt= [ρ(1)

t, ρ(2)

t, ..., ρ(C)

t].

If the SBS iis OFF at time t, its users are managed by the

MBS and we assume that the SBS can be entirely switched

OFF (e.g., P= 0). However, the MBS may have reached its

capacity limit at that time instant (i.e. cannot allocate any RB

to users) and may drop part of the handed over users. This

situation is deﬁned as system outage.

III. OPTIMIZATION PROB LE M

The periodicity of the trafﬁc demand and the energy arrivals

leads to a cyclic evolution of the system. At every cycle t, a

centralized controller computes the optimal state conﬁguration

of the SBSs in the cluster.

This sequential decision making process is modeled as a

DP optimization problem. The objective is to minimize the

grid energy consumed by the MBS and the trafﬁc drop rate of

the system. Since there is a linear relation between the energy

consumption and the BS load, the objective is converted into

the minimization of the MBS load over a given time horizon,

by ofﬂoading the trafﬁc to the renewable powered SBSs.

Furthermore, a threshold Bth on the battery level is introduced

to prevent damages to the storage devices [12].

The optimization problem is formulated as follows:

min

{St}t=1,...,K

K

X

t=1

f(St, t)

B(i)

t> Bth ∀i.

(2)

where Kis deﬁned as time horizon of the optimization and

corresponds to the number of times the control is applied.

Furthermore, the cost function f(St, t)is deﬁned as follows:

f(St, t) = 1

2[w1·L(St, t) + w2·D(St, t)] (3)

where

•L(St, t), is the normalized load of the MBS given the

SBSs states and the time instant t.

•D(St, t)is the trafﬁc drop rate of the system, given the

state of the SBSs and the time instant t. Its value ranges

from 0 (when all the trafﬁc is served by the system) to 1

(when all the trafﬁc is dropped by the system).

The two weights must always sum to one, i.e., w1+w2= 1.

The battery levels of the SBSs are updated at each decision

instant t, according to the following formula:

Bt+1 = min(Bt+Et−((PSBS

0+βSBSρt)∆t, Bcap )) (4)

where Bcap is the maximum battery capacity. The amount of

energy exceeding the battery capacity cannot be stored and it

is wasted.

The complexity of this optimization problem increases

quasi-exponentially with the number of SBSs in the cluster

and with the time horizon. In order to solve it in an efﬁcient

way, this problem has been graphically represented and subse-

quently transposed to a graph theory shortest-path problem in

[9]. The proposed algorithm based on the Label Correcting

Method has been used to obtain the results shown in the

following section.

IV. RES ULTS ANALYSIS

A. Simulation Scenario

We consider a square area with a side of 1 km. The MBS

is located at the center of the area and 3 SBSs are randomly

positioned. The SBSs have a transmission power of 38 dBm,

which corresponds to a coverage radius of 50 m. The coverage

areas of the SBSs do not overlap. The base stations have

a transmission bandwidth of 5 MHz. Aggregated downlink

trafﬁc has been generated based on the trafﬁc proﬁles deﬁned

in [13]. In particular, we consider three different weekly trafﬁc

proﬁles: Resident, Transport and Ofﬁce. User trafﬁc is based

0 12 24 36 48 60 72 84 96 108 120 132 144 156

Hour of the week [h]

0

1

2

3

Traffic [Mbps]

104

0

0.5

1

Energy [kWh]

January July

(a) Resident trafﬁc proﬁle

0 12 24 36 48 60 72 84 96 108 120 132 144 156

Hour of the week [h]

0

1

2

Traffic [Mbps]

104

0

0.5

1

Energy [kWh]

(b) Ofﬁce trafﬁc proﬁle

0 12 24 36 48 60 72 84 96 108 120 132 144 156

Hour of the week [h]

0

1

2

Traffic [Mbps]

104

0

0.5

1

Energy [kWh]

(c) Transport trafﬁc proﬁle

Fig. 1. Example of temporal variation of the trafﬁc and energy harvesting process in a week of January and July. Scenario with 90 UEs per SBS with 50%

of heavy users.

on the classiﬁcation proposed in [10]. Heavy users have a

data volume of 900 MB/h, whereas ordinary users have a

data volume of 112.5 MB/h. We underline that, with the

considered approach, the trafﬁc is described both in time

(temporal variation during the week) and in space (spacial

distribution in the area).

As for the RES system, we consider the Panasonic N235B

solar modules, which have single cell efﬁciencies of about

21% delivering about 186 W/m2. Each SBS is equipped with

an array of 16 ×16 solar cells (i.e. 4.48 m2). The battery

size is 2 kWh (panel and battery sizes have been chosen

so that SBS batteries can be replenished in a full winter

day). Realistic energy harvesting traces are obtained using the

SolarStat tool [14], considering the city of Los Angeles. All

the simulations have been performed considering a generic

week of January and July, in order to highlight the differences

between a generic winter (low energy arrivals) and a sum-

mer month (high energy arrivals). Moreover, the coordinator

takes actions with a time step of 1 hour, considering a time

horizon of 21 hours, as described in [9]. In the analysis here

presented, we have assigned the same importance to the energy

consumption and the system drop rate, when computing the

optimal policy. Therefore, the weights in equation (3) have

been set to w1=w2= 0.5.

The optimal approach is compared with a greedy algorithm

that operates by turning OFF the SBSs when their battery

levels go below the threshold and turning them ON when the

level is above it.

B. Optimal policies

An example of the temporal variation of the trafﬁc and the

harvested energy arrival processes during a week is shown in

Fig. 1. The trafﬁc requests in considered areas differ both in

terms of temporal distribution and magnitude. In particular,

the Resident area is the most demanding, with a weekly

aggregated trafﬁc of 2.17 TB. The lowest trafﬁc demand is

experienced in the Transport area, with a weekly aggregated

trafﬁc of 0.41 TB. The three trafﬁc proﬁles and the two energy

arrival processes are not always time correlated. In fact, in the

case of Resident trafﬁc, the peak of the demand is at 10 pm.

In the case of Ofﬁce trafﬁc, it is at 11 am on the weekdays

and at midday on the weekends. Finally, in the Transport

case we have two peaks during the weekdays, at 8 am and

6 pm, while on the weekends there is a single peak at 5 pm.

From the energy side, the peak of energy arrivals is always

between midday and 1 pm for the two considered months.

This conﬁrms the necessity of taking into account present and

future costs when the optimal control is applied.

The daily average switch OFF rate of the SBSs for the

optimal and the greedy policy is reported in Fig. 2 and Fig.

3, respectively. The three trafﬁc proﬁles and the months of

January and July are depicted. We consider a high-trafﬁc

intensity involving 90 UEs (50% heavy) represented by solid

lines, and a low-trafﬁc intensity with 10 UEs (20% heavy)

indicated with dashed lines.

In Fig. 2 we observe that the number of SBSs in OFF is

generally higher during night hours. This fact is due to the

scarce availability of the energy and the low trafﬁc demand

during the night. More in detail, we can notice that high-trafﬁc

intensity and low energy arrivals (January) result in longer and

more intensive switch OFF periods during the night. For the

Resident proﬁle (Fig. 2a) the switch OFF rate in a typical

week of July is intensive between 3 am and 6 am (low-trafﬁc

low traffic - Jan high traffic - Jan low traffic - Jul high traffic - Jul Avg. traffic profile..

0 5 10 15 20

Hour [h]

0

0.2

0.4

0.6

0.8

1

Switch OFF rate

(a) Resident trafﬁc

0 5 10 15 20

Hour [h]

0

0.2

0.4

0.6

0.8

1

Switch OFF rate

(b) Ofﬁce trafﬁc

0 5 10 15 20

Hour [h]

0

0.2

0.4

0.6

0.8

1

Switch OFF rate

(c) Transport trafﬁc

Fig. 2. Daily average switch OFF rate for the optimal algorithm. Simulations on the Resident, Ofﬁce and Transport trafﬁc proﬁle for a week of January and

July. The scenario with 10 UEs (20% heavy) is indicated as low trafﬁc, whereas the scenario with 90 UEs (50% heavy) is indicated as high trafﬁc.

low traffic - Jan high traffic - Jan low traffic - Jul high traffic - Jul Avg. traffic profile..

0 5 10 15 20

Hour [h]

0

0.2

0.4

0.6

0.8

1

Switch OFF rate

(a) Resident trafﬁc

0 5 10 15 20

Hour [h]

0

0.2

0.4

0.6

0.8

1

Switch OFF rate

(b) Ofﬁce trafﬁc

0 5 10 15 20

Hour [h]

0

0.2

0.4

0.6

0.8

1

Switch OFF rate

(c) Transport trafﬁc

Fig. 3. Daily average switch OFF rate for the greedy algorithm. Simulations on the Resident, Ofﬁce and Transport trafﬁc proﬁle for a week of January and

July. The scenario with 10 UEs (20% heavy) is indicated as low trafﬁc, whereas the scenario with 90 UEs (50% heavy) is indicated as high trafﬁc.

case) and from 2 am to 8 am (high-trafﬁc case). In a week of

January, the switch OFF rate is intensive from 1 am to 10 am

(low-trafﬁc case). In the case of Ofﬁce (Fig. 2b) and Transport

(Fig. 2c) proﬁles, these intensive night OFF periods are less

inﬂuenced by the total number of UEs served by the SBSs.

This is due to the low magnitude of the total trafﬁc demand

experienced in these areas.

In Fig. 3 we observe that the switch OFF rate is intensive

also in periods of high trafﬁc demand. The greedy algorithm

takes immediate decisions without considering any future evo-

lution of the trafﬁc and energy arrival processes. In this way, a

SBS always consumes the available energy and then it remains

in an OFF state until the harvested energy is sufﬁcient to return

operative. On the contrary, the optimal policy turns OFF a

SBS in an intelligent way, by considering future evolutions

of the trafﬁc and energy arrivals. Therefore, it saves energy

during low trafﬁc periods (e.g. night hours) to maintain ON

the SBS during high trafﬁc peaks, which may correspond to

scarce energy arrivals. For instance, let’s consider the Resident

proﬁle with high-trafﬁc intensity in January, where the peak of

the trafﬁc demand is at 10 pm. The greedy algorithm switch

OFF rate is 0.5at 10 pm (Fig. 3a), whereas it is zero during

the daytime (i.e., from 11 am to 7 pm). In fact, the SBSs

are immediately using the available energy during the day,

and then switching OFF in the evening due to scarce energy

availability. On the contrary, the optimal switch OFF rate

(Fig. 2a) is almost zero during the trafﬁc peak hours and it is

not null during the daytime. This behavior indicates that some

SBSs are switched OFF during the day to save the necessary

energy to satisfy the trafﬁc peak in the evening.

C. System outage

In this section, we analyze the system outage measured as

the percentage of the trafﬁc dropped in the system. We present

the case of Resident proﬁle only, since the others have similar

performance. The percentage of the trafﬁc dropped in a week

is reported in Fig. 4 for a number of UEs ranging from 10 to

90 (50% of them are heavy users).

The optimal policy succeeds in delivering all the trafﬁc

requested and the system does not experience any outage

in almost every studied situation. In January, however, some

trafﬁc is dropped starting from 60 UEs per SBS, reaching the

maximum of 0.9% for 90 UEs. The greedy approach, on the

other hand, always performs worse than the optimal policy. In

particular, in January the trafﬁc dropped is reaching 10% in

the case of 90 UEs per SBS.

This phenomenon is conﬁrmed in Fig. 5, where the average

hourly trafﬁc dropped is shown for a scenario with 90 UEs

per SBS with 50% of heavy users. As for the optimal policy,

the outage is concentrated in the morning (from 7 am to 10

am), afternoon (5 pm) and night, with values that reach the

10 20 30 40 50 60 70 80 90

UEs per SBS

0

2

4

6

8

10

12

Traffic drop [%]

Optimal - Jan

Optimal - Jul

Greedy - Jan

Greedy - Jul

Fig. 4. Percentage of weekly trafﬁc request not serviced for both the greedy

and optimal algorithm in January and July. The 50% of the UEs are heavy

users.

0 5 10 15 20

Hour [h]

0

5

10

15

20

25

30

35

40

45

Avg. traffic drop [%]

Optimal - Jan

Optimal - Jul

Greedy - Jan

Greedy - Jul

Avg. traffic profile

Fig. 5. Average hourly trafﬁc drop for the optimal and the greedy algorithms

in January and July. The trafﬁc proﬁle is Resident and every SBS has 90 UEs

in its coverage area; 50% of them are heavy users.

maximum value of 5% at midnight. The greedy approach,

instead, causes system outage for longer periods and with

higher values of the dropped trafﬁc, which is reaching a

maximum of 44% at 11 pm.

D. Energy consumption

The amount of the grid energy consumed by the MBS is

shown is Fig. 6, varying the number of UEs in the coverage

area of the SBSs. We consider two cases: a scenario with 20%

and 50% of heavy users, respectively. In both scenarios, the

grid energy consumption increases linearly with the number

of UEs. The slope of the curves is higher for the scenario

20 40 60 80 100 120

UEs per SBS

125

130

135

140

145

150

155

160

165

Grid energy [kWh]

Optimal - Jan

Optimal - Jul

Greedy - Jan

Greedy - Jul

50% heavy users

Fig. 6. Grid energy consumption for the optimal and the greedy algorithms

in January and July, while increasing the number of UEs in the SBS area.

with 50% of heavy users since the trafﬁc is increasing faster

with the number of UEs. Grid energy consumption is higher

during the winter months since the scarce availability of the

renewable energy turns out into longer SBS sleeping periods

and higher MBS operation.

The greedy approach presents higher values of the grid

energy consumption than the optimal policy. However, in the

case of January and with 50% of heavy users, we observe that

the greedy approach has lower energy consumption for more

than 70 UEs per SBS. This behavior is due to the fact that the

system is heavily in outage and loses a considerable amount

of trafﬁc, as described in the previous subsection.

Finally, Fig. 7 reports the grid energy consumption for a

week of July of different architecture scenarios. We compare

a solution where MBS and SBSs are connected to the grid

(also referred to as grid-only) with our scenario where SBSs

are solely powered by solar panel plus battery (also referred

to as EH SBS). The grid-only scenario consumes 190.3 kWh

in a week; deploying renewable powered SBSs saves 28%

of the grid energy. Moreover, since the RES systems have

been dimensioned for winter, the harvested energy may be

abundant during summer and be discarded by the SBSs, i.e.,

it can neither be used for transmission nor stored in the battery.

This redundant energy is concentrated during the peak hours

of the energy arrival process (i.e., between midday and 2

pm). Considering that the SBSs may be connected through a

power micro-grid, the excess energy can be used for ancillary

services (e.g., light system) or shared to support the MBS

operation, thus reducing its grid energy consumption. In fact,

a grid energy saving of 38% is achieved, in case the MBS

instantly uses the energy shared by the SBSs (also referred to

as EH SBSs + energy sharing). However, the MBS might not

be able to instantly consume the whole amount of the received

energy, which would create instability in the micro-grid. For

Grid energy consumption [kWh]

Fig. 7. Grid energy consumption for different deployment architectures during

a week of July. The trafﬁc proﬁle is Resident and every SBS has 90 UEs in

its coverage area; 50% of them are heavy users.

this reason, we consider the option of deploying a storage

device at the MBS site (also referred to as EH SBSs + energy

sharing + MBS battery). As a result, the MBS uses the shared

energy when needed and saves 46% of the grid energy.

V. CONCLUSIONS

In this paper, we have introduced an optimal direct load

control of renewable powered SBS in a two-tier mobile

network. We have analyzed the optimal policies and their

dependence on the trafﬁc and the energy arrival process. We

have compared the optimal approach with a greedy algorithm

and analyzed the network performance in different scenarios.

We have also introduced a new possibility of energy sharing

among the network elements to reduce the dependence on the

power grid and increase the energy savings.

From this analysis, we can draw the following conclusions.

The different temporal behavior of the trafﬁc and energy

arrival processes highlights the necessity of deploying storage

devices along with solar panels. Moreover, it is fundamental

to properly manage the storage to maintain good network

performance. The comparison between the optimal and the

greedy approach shows that grid energy savings and trafﬁc

drop limitations are possible only if the control algorithm is

able to forecast the evolution of the two processes. Finally, the

analysis of the redundant energy shows that sharing energy

among base stations may lead to considerable amount of grid

energy savings.

ACKNOWLEDGMENT

This work has received funding from the European Union

Horizon 2020 research and innovation programme under

the Marie Sklodowska-Curie grant agreement No 675891

(SCAVENGE) and by the Spanish Government under project

TEC2017-88373-R.

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