ArticlePDF Available

Abstract and Figures

The dimensioning of photovoltaic (PV) panel and battery sizes is one of the major issues regarding the design of solar powered cellular base stations (BSs). This letter proposes a multistate Markov model for the hourly harvested solar energy to determine the cost optimal PV panel and battery dimensions for a given tolerable outage probability at a cellular BS.
Content may be subject to copyright.
A Multistate Markov Model for Dimensioning Solar Powered
Cellular Base Stations
Vinay Chamola and Biplab Sikdar, Senior Member, IEEE
Abstract—The dimensioning of photovoltaic (PV) panel and
battery sizes is one of the major issues regarding the design of
solar powered cellular base stations (BSs). This letter proposes a
multistate Markov model for the hourly harvested solar energy to
determine the cost optimal PV panel and battery dimensions for a
given tolerable outage probability at a cellular BS.
Index Terms—Green communications, solar energy.
SOLAR POWERED, offgrid cellular base stations (BSs)
provide a communication infrastructure in places without
reliable grid power. This letter presents a Markov model for
hourly solar energy and applies it to dimensioning offgrid cel-
lular BSs. Existing Markov models for solar energy lack the
day-level weather correlations that are critical for dimensioning
high-reliability systems [1], [2]. Thus, we propose a model that
combines hourly and daily transitions in the weather conditions.
This letter considers a long-term valuation (LTE) cellular BS
whose power consumption at time tis given by [3]
PBS(t)=Ntrx (P0
where Ntrx is the number of transceivers, P0is the power con-
sumption at no load (zero traffic), Δpis a BS specific constant,
Pmax is the output of the power amplifier at the maximum traffic,
and Kis the normalized traffic at the given time.
To model the traffic, Poisson distributed call arrivals with
time-of-day dependent rates, and exponentially distributed call
durations with mean 2 min are used [4]. Kis obtained by nor-
malizing the instantaneous traffic by the maximum number of
calls that the BS can support at any time. We assume that lead
acid batteries are used. The battery lifetime is calculated by
counting the charge/discharge cycles for each range of depth
of discharge (DoD) for a year and is given by [5]
LBat =1
where Ziis the number of cycles with DoD in region i, and
CTFiis the cycles to failure corresponding to region i.Given
nPV photovoltaic (PV) panels each with dc rating Epanel, and nb
Manuscript received August 26, 2014; revised April 09, 2015 and May 25,
2015; accepted May 29, 2015. Date of publication August 05, 2015; date of
current version September 16, 2015. Paper no. PESL-00132-2014.
The authors are with the Department of Electrical and Computer
Engineering, National University of Singapore, Singapore (e-mail: vinay.;
Digital Object Identifier 10.1109/TSTE.2015.2454434
Fig. 1. (a) Transition between good and bad days. (b) Hourly transition in a
good day. For clarity, only the transitions from state G(i,1) are marked.
batteries, each with capacity Ebat, the overall PV panel dc rating
is PVw=nPV Epanel, and the battery bank capacity is Bcap =
nbEbat. This letter uses solar irradiance data made available by
National Renewable Energy Laboratory (NREL), USA [6].
To develop the solar energy model, for any site, solar irra-
diance data of 10 years are fed into NREL’s System Advisor
Model tool [6] to calculate the hourly energy generated by a
PV panel with 1-kW dc rating. This data is then parsed on a
monthly basis. The solar energy output for each day in a given
month is computed and the days are sorted based on this energy.
β% of the days with the lowest energy are termed “bad,” and
the rest, “good” days. The probability of transition from one
day type to another is calculated from the data. This is modeled
as a Markov process [Fig. 1(a)] with transition matrix
T=pgg pgb
pbg pbb (3)
where pgg (pbb, respectively) is the transition probability from
good to good (bad to bad), and pgb =1pgg (pbg =1pbb ,
respectively) is the transition probability from good to bad (bad
to good) day.
Within a day, the harvested solar energy varies with time. We
model these variations on a hourly basis as a Markov process.
For each day type (good/bad), the minimum and maximum PV
panel output for each hour of the day are calculated. The region
between the minimum and maximum values is divided uni-
formly into four regions, as shown in Fig. 2. Each of these
regions, along with the day type, represents a “state” of the
harvested solar energy. The state at time tis denoted by
1949-3029 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See for more information.
This letter proposed a multistate Markov model for charac-
terizing the hourly solar irradiation. The model was used for
dimensioning solar powered cellular BSs in terms of the cost
optimal PV panel and battery bank size.
[1] R. Weissbach and J. King, “Estimating energy costs using a Markov
model for a midwest off-grid residence,” in Proc. IEEE Green Technol.
Conf., Apr. 2013, pp. 430–434.
[2] Kakimoto et al., “Two-state Markov model of solar radiation and con-
sideration on storage size,” IEEE Trans. Sustain. Energy, vol. 5, no. 1,
pp. 171–181, Jan. 2014.
[3] Auer et al., “Cellular energy efficiency evaluation framework,” in Proc.
IEEE Veh. Technol. Conf. (VTC Spring), Yokohama, Japan, May 2011,
pp. 1–6.
[4] Mutlu et al., “Spot pricing of secondary spectrum access in wireless cel-
lular networks,” IEEE/ACM Trans. Netw., vol. 17, no. 6, pp. 1794–1804,
Dec. 2009.
[5] Dufo-Lpez et al., “Comparison of different lead-acid battery lifetime pre-
diction models for use in simulation of stand-alone photovoltaic systems,
Appl. Energy, vol. 115, pp. 242–253, Feb. 2014.
[6] National Renewable Energy Laboratory, (2015, Mar. 18) [Online].
... Energy efficiency [34]- [36] and EH [37] are two ways to attain green communications [38], [39]. Different energy sources can be utilized, which can supply us with ambient renewable energy sources such as wind, solar [40], [41], motion, electromagnetic (EM) waves, water [42], [43]. In the past few years, there has been a lot of research on ambient EH [44]- [48]. ...
... It is possible to integrate two or more of these renewable energy resources to harvest more energy [40] at a larger scale, depending on the application and requirements. For instance, a cellular network could use a hybrid solar and wind base station (BS) [41], [53] to serve its subscribers or mobile users. If the energy harvested by a BS is below a certain threshold, the BS could switch to an alternate nonrenewable energy source. ...
Full-text available
Energy harvesting (EH) and spectrum harvesting (SH) are two promising and useful green communication and networking mechanisms for the next-generation wireless networks. While the former techniques exploit ambient energy sources to scavenge energy, the latter exploit the unused or moderately used electromagnetic spectrum. With the advent of cyber-physical systems and the Internet-of-Things (IoT), the presence of tens of billions of low power sensor devices would soon be a reality. These small sensing devices would be present in many systems around us, such as home appliances, telecommunication devices, medical electronics, transport systems, etc. These miniaturized, low-power consuming devices may exploit EH and SH techniques for energy storage and communication. These EH-SH-enabled sensors or low-power nodes need to consume very little energy for sensing and communicating opportunistically. However, several theoretical problems and practical challenges exist in EH-SH communications. In this comprehensive survey paper, we first present the historical background of EH, and SH techniques, and their development over several decades. Specifically, we focus on EH-SH communication technologies and protocols for a wide range of systems and networks. We present a detailed survey of the various harvesting techniques and protocols from recent literature. Finally, we describe exciting open, intra-disciplinary, and inter-disciplinary challenges for further research on EH-SH communication technologies.
... Indeed, this new scenario is very attractive since it is a promising alternative to make the networks more sustainable and self-sufficient, while reducing also the electricity bill [6]- [9]. Various papers address the critical issue of properly dimension RE generation systems to power mobile networks [10], [11]. The sizing process entails trading off self-sustainability, cost and feasibility constraints due to the installation of a RE generation system. ...
... The sizing process entails trading off self-sustainability, cost and feasibility constraints due to the installation of a RE generation system. In [10], the problem of a proper dimension of the PV panels is investigated via simulation, whereas authors in [11] deploy models to derive the optimal RE system dimension for powering a BS. In this work, we investigate the impact on mobile communication services of the occurrence of outages of the electric grid; the scenario is quite common in countries where the electric grid is not reliable but are expected to occur the more and more frequently also in other regions in which the power infrastructure is more reliable by effect of the power demand increase. ...
... Here, a discrete time-variant Markov model is used for estimating the hourly clear index and generating the daily shape of solar radiation on a monthly basis. The proposed Markov model is a simplified version of that in [25]. We leverage the nature of solar radiation (i.e., an average rising behavior in the morning, an average falling behavior in the afternoon, and a smooth behavior around noon) to extract a time-variant TM for estimating the radiation in transition between states for a 24-h time horizon (N = 24). ...
... In order to obtain the TM for the solar energy generation, the generated energy (Wh/m 2 ) is discretized in n states each representing a region of occurrence, i.e., (25) where E max PV is the maximum hourly radiation level, and the number of states, n, is determined based on E max PV . From a set of historical hourly solar radiation data in one month, the frequency of transitions from state to λ, f ,λ , is found. ...
Full-text available
Islanded nanogrids (NGs) are autonomous systems consisting of small-scale generation units including renewable energy sources and traditional fuel generators and energy storage systems (ESS) that typically serve few buildings or loads. This work aims at developing and validating a new optimal energy management (EM) algorithm for an islanded NG. To minimize the generator's operating cost and maximize battery availability at each operating cycle, dynamic programming (DP) framework is employed to solve the underlying optimization problem. The goal of the proposed approach is to ensure the use of maximum available solar power and to achieve optimal battery state of charge (SOC). To meet that goal, the management of the ESS is formulated as a stochastic optimal control problem, where nonlinearities in the battery discharging process are considered. A Markov model is constructed for predicting the probability distribution of the solar production used in the stochastic DP formulation. Simulation results are given to illustrate the efficacy of the proposed DP-based approach compared to a rule-based algorithm. Finally, a hardware-in-the-loop system is used to evaluate the real-time operation of the proposed EM algorithm.
... However, with an increase in the ultra-dense and heterogeneous class of networks, resource provisioning and management poses a potential challenge in maintaining Quality of Service (QoS) and reliable ultra-low latency services in green cellular networks. In such scenarios, the existing frameworks lack intelligent resource optimization and management for green cellular base stations [5]. Furthermore, the existing frameworks have inadequate provision for prediction based resource distribution within the macro base station (MBS) layer consisting of the set of small cell base stations (SCBS) [6], [7]. ...
Full-text available
Optimal resource provisioning and management of the next generation communication networks are crucial for attaining a seamless Quality of Service with reduced environmental impact. Considering the ecological assessment, urban and rural telecommunication infrastructure is moving towards deploying green cellular base stations to cater to the needs of the ever-growing traffic demands of heterogeneous networks. In such scenarios , the existing learning-based renewable resource provision-ing methods lack intelligent and optimal resource management at the Small Cell Base Stations (SCBS). Therefore, in this article, we present a novel machine learning-based framework for intelligent resource provisioning mechanisms for micro-grid connected green SCBSs with a completely modified ring parametric distribution method. In addition, an algorithmic implementation is proposed for prediction-based renewable resource redistribution with Energy Flow Control Unit (EFCU) mechanism for grid-connected SCBS, eliminating the need for centralised hardware. Moreover, this modeling enables the prediction mechanism to estimate the future on-demand traffic provisioning capability of SCBS. Furthermore, we present the numerical analysis of the proposed framework showcasing the systems' ability to attain a balanced energy convergence level of all the SCBS at the end of the periodic cycle, signifying our model's merits.
... Rapid developments in the next-generation networks have enabled the telecommunication industry to provide adaptive user-centric services through resource dimensioning and software-defined networking approaches [1]- [4]. However, the need for optimal spectrum allocation among the users is still an addressable issue with the available network resource [5]- [7]. ...
Full-text available
Optimal allocation of the available spectrum is a crucial requirement of 5G and Beyond (B5G) for achieving higher Quality of Service (QoS) and low-latency. However, in 5G and Beyond, this requirement presents a potential need for dimension-ing and managing the spectral resource in the cellular services. In this article, we address the issues of spectral distribution using DAG and Vickrey Clarke Groves (VCG) mechanisms by evaluating with a derived parameter for sustainable revenue and social welfare of the entire network. In particular, we modelled a framework to optimize social welfare of the users and the revenue of the cellular operator by proposing an efficient spectral allocation and pricing mechanism.
... The widely used model with fixed relation between the energy consumption and the traffic is very simple and facilitates the development of green systems as it provides a static feedback to any planning systems such as the work in [12], [21], [22] or for energy efficient radio resource management ...
Conference Paper
Full-text available
Global warming is becoming a paramount concern in the world. One way to decrease the effect of global warming is by decreasing carbon emission and using renewable energy. In particular, there are many works on using renewable energy technologies in mobile communication systems. In order to enable such technologies in mobile communication systems, we should be able to estimate the required energy. Most of research was focusing on techniques to be used to exploit renewable energy sources assuming that the required energy to run the base stations is known. Only few works were focusing on the estimation of the energy based on transmitted energy, and fewer relating the former to traffic. In this paper, we present a regression-based power consumption estimation method based on voice and data traffic provided by base stations with 2G and 3G capabilities. Our results show that the power consumption of different base stations as a function of the provided traffic can have different patterns. Furthermore, the same base stations can have different energy consumption models at different period of time. Therefore, we advocate the use of machine learning algorithms inside each base station to learn its specific pattern. © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
... A green BS is envisaged as having one or more renewable energy source in addition to the conventional grid and the generator. Renewable energy sources (RESs) such as solar and wind have been modeled for a BS from different perspectives by the researchers [5,[16][17][18]. Since these sources can be unpredictable or unavailable at times, a battery bank is invariably used to regulate the harvested energy. ...
Full-text available
In this paper, an energy cost minimization framework is presented for a green cellular network. The proposed novel energy cooperation scheme ensures optimal energy cooperation among grid-connected green cellular base stations (BSs). The framework is both economical and environment-friendly where the energy is saved by cutting down on the grid energy and sharing surplus green energy among the BSs. The intended scenario requires knowledge of harvested energy as well as traffic awareness to determine energy demand of a BS and inter-BS connectivity for incorporating energy transfer. A realistic utility function is developed to minimize energy cost under various constraints which entail energy borrowing from neighboring BSs (offering their surplus energy which is cheaper than grid and diesel generator), thereby reducing the overall energy cost of the network. The proposed framework for energy cooperation has bilinear non-convex structure. We use McCormick envelopes to convexify the optimization problem and transform the bilinear non-convex optimization into a linear optimization problem. The numerical results verify the effectiveness of the proposed traffic aware sustainable and environmental friendly BS operation through energy cooperation.
A massive increase in the amount of data traffic over mobile wireless communication has been observed in recent years, while further rapid growth is expected in the years ahead. The current fourth-generation (4G) mobile networks are evolving to the fifth-generation (5G) networks to fulfill the demand for high data rates and broad network coverage. The advent of the ultra-dense 5G network and a vast number of connected devices will bring about the obvious issues of significantly increased system energy consumption, operational expenses, and carbon dioxide emissions. Renewable energy is considered a viable and practical approach to power the small cell base station in an ultra-dense 5G network infrastructure to reduce the energy provisions from the electric grid and carbon dioxide emissions. In this paper, we discuss the role of renewable energy in the design of sustainable, eco-friendly, and cost-effective 5G mobile networks and provide a comprehensive survey on the state-of-art of renewable energy management techniques aiming to promote the sustainability and cost reduction of the large-scale mobile wireless infrastructures. This survey specifically covers a variety of energy efficiency techniques, the utilization of renewable energy sources, interaction with the smart grid (SG), and the renewable energy powered base stations. It also highlights the outstanding technical challenges and future perspectives to enable future sustainable 5G network infrastructure.
The use of base station (BS) sleep modes is one of the most studied approaches for the reduction of the energy consumption of radio access networks (RANs). Many papers have shown that the potential energy saving of sleep modes is huge, provided the future behavior of the RAN traffic load is known. This paper investigates the effectiveness of sleep modes combined with machine learning (ML) approaches for traffic forecast. A portion of a RAN is considered, comprising one macro BS and a few small cell BSs. Each BS is powered by a photovoltaic (PV) panel, equipped with energy storage units, and a connection to the power grid. The PV panel and battery provide green energy, while the power grid provides brown energy. Our study examines the impacts of different prediction models on the consumed energy mix and on QoS. Numerical results show that the considered ML algorithms succeed in achieving effective trade-offs between energy consumption and QoS. Results also show that energy savings strongly depend on traffic patterns that are typical of the considered area. This implies that a widespread implementation of these energy saving strategies without the support of ML would require a careful tuning that cannot be performed autonomously and that needs continuous updates to follow traffic pattern variations. On the contrary, ML approaches provide a versatile framework for the implementation of the desired trade-off that naturally adapts the network operation to the traffic characteristics typical of each area and to its evolution.
Conference Paper
Full-text available
In order to quantify the energy savings in wireless networks, the power consumption of the entire system needs to be captured and an appropriate energy efficiency evaluation framework must be defined. In this paper, the necessary enhancements over existing performance evaluation frameworks are discussed, such that the energy efficiency of the entire network comprising component, node and network level contributions can be quantified. The most important addendums over existing frameworks include a sophisticated power model for various base station (BS) types, which maps the RF output power radiated at the antenna elements to the total supply power of a BS site. We also consider an approach to quantify the energy efficiency of large geographical areas by using the existing small scale deployment models along with long term traffic models. Finally, the proposed evaluation framework is applied to quantify the energy efficiency of the downlink of a 3GPP LTE radio access network.
Conference Paper
The use of energy storage in conjunction with renewable energy sources such as wind and solar is receiving more attention to help mitigate the effects of the intermittent nature of these sources at off-grid residences. One wishes to maximize the probability that there will be enough energy available to meet the residential load demand while minimizing the cost of both the renewable energy sources as well as the energy storage device(s). In this paper, the energy storage required to ensure high reliability of supply to an off-grid residence in the Midwest is determined iteratively based on the amount of installed solar power. A Markov model is employed consisting of 288 state transition matrices to generate synthetic solar data for analysis. By accounting for the costs of both the photovoltaic system and the energy required energy storage, an optimal cost solution is provided.
This paper proposes a two-state Markov model to determine the storage size of a photovoltaic system. The system is usually connected to a distribution grid, but once a large disaster occurs, it becomes the main source of supply. Daily solar radiation changes due to the weather, and it could become lower than a specified supply level for a sequence of days. Transition probabilities are determined from meteorological data on the solar radiation. The Markov model shows that its frequency exponentially decreases as the sequence becomes long. One or two days of storage is adequate to reduce the number of insufficient supply days to an acceptable level, and the value of adding the storage exponentially decreases, too. Some simulations and experiments are executed to verify these facts.
Lifetime estimation of lead–acid batteries in stand-alone photovoltaic (PV) systems is a complex task because it depends on the operating conditions of the batteries. In many research simulations and optimisations, the estimation of battery lifetime is error-prone, thus producing values that differ substantially from the real ones. This error can indicate that the “optimal” system selected by the optimisation tool will not be optimal. In this paper, all of the components of a PV system have been considered simultaneously to simulate the behaviour of the system. One of these important components is the battery charge controller, which significantly affects the lifetime of batteries. The results of the simulations have allowed a comparison of the most common methods of battery lifetime prediction used by simulation and/or optimisation tools with a weighted Ah-throughput method developed a few years ago. The results show that this recent method provides more accurate lifetime values. In a simulation of a real off-grid household PV system where the real battery lifetime was 6.2 years, the weighted Ah-throughput model predicted a lifetime of 5.8 years; however, the other methods obtained lifetimes of more than 15 years. In a simulation of another PV system designed to supply the load of an alarm where the real batteries lifetime was 5.1 years, the weighted Ah-throughput model predicted a lifetime of 4.4 years; however, the other methods obtained lifetimes of more than nine years.
Recent deregulation initiatives enable cellular providers to sell excess spectrum for secondary usage. In this paper, we investigate the problem of optimal spot pricing of spectrum by a provider in the presence of both non-elastic primary users, with long-term commitments, and opportunistic, elastic secondary users. We first show that optimal pricing can be formulated as an infinite horizon average reward problem and solved using stochastic dynamic programming. Next, we investigate the design of efficient single pricing policies. We provide numerical and analytical evidences that static pricing policies do not perform well in such settings (in sharp contrast to settings where all the users are elastic). On the other hand, we prove that deterministic threshold pricing achieves optimal profit amongst all single-price policies and performs close to global optimal pricing. We characterize the profit regions of different pricing policies, as a function of the arrival rate of primary users. Under certain reasonable assumptions on the demand function, we prove that the profit region of threshold pricing is optimal and independent of the specific form of the demand function, and that it includes the profit region of static pricing. In addition, we show that the profit function of threshold pricing is unimodal in price. We determine a restricted interval in which the optimal threshold lies. These properties enable very efficient computation of the optimal threshold policy, which is far faster than that of the global optimal policy.