Battery agingaware energy management of green small cells powered by the smart grid
 Mouhcine Mendil^{1, 2}Email authorView ORCID ID profile,
 Antonio De Domenico^{1},
 Vincent Heiries^{1},
 Raphael Caire^{2} and
 Nouredine Hadjsaid^{2}
https://doi.org/10.1186/s1363801709134
© The Author(s) 2017
Received: 11 November 2016
Accepted: 6 July 2017
Published: 18 July 2017
Abstract
Mobile operators are deploying energyharvesting heterogeneous networks due to their foreseen advantages such as selfsustainable capability and reduced operating expenditure, which cannot be offered by conventional grid powered communications. However, the used energy storage is subject to irreversible aging mechanisms, requiring intelligent management that considers both the energy cost and battery life cycle. In this paper, we propose a cognitive energy management strategy for small cell base stations powered by local renewable energy, a battery, and the smart grid to simultaneously minimize electricity expenditures of the mobile operators and enhance the life span of the storage device. Nonlinear battery models and aging processes are considered to formulate the energy cost optimization problem. Simulation results in different configurations show that a degradationaware policy significantly improves the battery lifetime, while achieving considerable cost savings.
Keywords
Cognitive energy management Green communication Energy harvesting Small cell Battery Smart grid1 Introduction
In the last decades, mobile user density and data traffic volume have exponentially increased all over the world. To respond to this trend, the mobile network operators (MNOs) have deployed small cell base stations (SBSs) to enhance their network service capabilities [1]. According to [2], this solution results in a significant energy demand augmentation essentially generated by the base station power consumption that represents 75 to 80% of the entire mobile network. Based on this, the deployment of heterogeneous cellular networks (HetNets) requires an efficient energy management to ensure their economic and environmental sustainability.
A multitude of concepts have recently been proposed to improve the energy efficiency in wireless communications, addressing network planning, protocols, and equipments [3]. In addition, renewable energy (RE) usage in cellular networks has drawn attention for its numerous benefits such as decreasing carbon emissions, enabling longterm cost savings thanks to reduced operating expenditure (opex) [4], and feeding offgrid base stations where the connection to the power grid is expensive or impossible [5]. In this context, cognitive techniques have been explored to improve energyharvesting communications [6]. More specifically, the cognitive radio offers the ability to sense the conditions of the wireless communication networks and interact with the environment to adjust some parameters such as the transmission power, frequency band, and modulation mode [7].
The current energyharvesting technologies require local energy storage to absorb the production fluctuation and ensure a continuous equilibrium between energy offer and demand. However, the typical used energy storage, i.e., electric battery, generates expensive investment cost and is subject to irreversible degradations. Such phenomenon, called battery aging, has been intensively studied and been classified into two categories: cycle aging, which is due to the energy exchanges with the battery, and calendar aging that appears when the battery is on rest [8]. In this context, Barre et al. [9] have presented a comprehensive review of techniques, models, and algorithms used for Liion battery aging estimation.
The presence of energy storage requires intelligent energy management policies to optimize the energy cost of gridconnected base stations (BSs) with energy harvesting. Some studies in the literature have addressed this problem by using either offline or online optimization approaches. The first category assumes perfect knowledge of the stochastic energy variables [10–12]. In [11] for example, the power consumption of a HetNet powered by RE and equipped with an infinitecapacity battery has been optimized by supervising the BS transmit power and the battery usage. In particular, nonlinear model predictive control theory has been used to manage the stored energy considering the average electricity price and power production. Zhang et al. [12] have proposed an energyaware traffic offloading for a HetNet with multiple SBSs. They have used queuing theory to model the energy production and consumption and deduced an efficient power control according to the statistical information of energy arrival and traffic load. Online policies have also been proposed by assuming a casual knowledge of the environment. In this context, stochastic optimization has been implemented by assuming that the statistics of the energy processes are known and that past observations can correct the energy forecasts [13–15]. The authors in [13] have investigated an online stochastic approach based on multiperiod recourse. Mao et al. [15] have considered a hybrid energy supply for the HetNet and formulated the energy cost minimization problem as a discrete Markov decision process. The monotony properties of the optimal policy have been inferred to simplify and solve the optimization problem using the backward induction algorithm. In [16], we have proposed an energy controller that uses reinforcement learning techniques to elaborate an optimal energy flow policy without prior knowledge of the environment stochastic behavior.
These works have focused on maximizing the energy saving, and none has integrated both calendar and cycle battery agings in the energy management framework. As a matter of fact, the maximal use of the battery flexibility enables large cost savings but can lead to rapid battery life loss. However, the battery is an expensive investment of the system, and enhancing its life span is vital for an efficient return on investment. Consequently, there is a tradeoff between pure costefficient and battery agingaware strategies that has not been evaluated so far. This motivated us to investigate the design of a cognitive energy controller that optimizes the operating energy cost while using the battery in the most effective way to avoid accelerated cycle and calendar agings. The current study extends our work [17] by introducing the battery aging models and formulating the energy cost problem such that the battery degradation factors are reduced while the optimal cost saving is still achieved. Additionally, the battery life evolution is studied to show the impact of the proposed energy strategies on the aging process.
1.1 Contributions and organization

Different from existing works, we propose a cognitive energy flow management framework for gridconnected energyharvesting SBSs to jointly optimize the energy opex and the battery life cycle. The cognitive decision architecture is centered around the battery and uses realistic models to capture the nonlinear battery behavior and aging mechanisms. Without loss of generality, the present framework is implemented in the offline case, in which we consider noncasual information about the environment variables. System simulations show that the proposed controller achieves considerable cost reduction compared to simpler strategies.

The tradeoff between pure energy cost optimization and battery agingaware policies is explored. The energy cost and battery aging are evaluated in different configurations. Simulation results show that the proposed energy management allows considerable battery life extension such that the battery lasts five times longer compared to a pure energy cost optimization strategy. In exchange, the opex is slightly increased but this additional expense remains negligible with respect to the current battery replacement cost.
The paper is structured as follows. Section 2 introduces our proposed architecture and the associated system models. Section 3 provides a formulation of the joint cost minimization and battery life preservation problem for a green small cell. Section 4 presents the simulation results. The paper is concluded and perspectives are discussed in Section 5.
2 System architecture

The SBS: wireless communication station covering a small area (10 m to 1 km), used to offer high data rate services to mobile users.

The photovoltaic (PV) system: equipment harvesting solar energy to produce electricity. It is one of the two energy sources of the system.

The twoway link to the smart grid (SG): the SG is the second energy source of the system. The twoway energy connection enables to buy or sell electricity to the power grid.

The battery: storage device that offers flexibility in the energy utilization. It can store the electricity coming from the SG and the PV system to feed the SBS or sell the energy back to the SG.

The cognitive energy supervision system (ESS): controller that schedules the energy flows to reduce the electricity bill and improve the battery life span.
In the following, we present the chosen model for each component of the system.
2.1 Small cell base station power consumption model
where P _{0} is the power consumption at the minimum nonzero output power, Δ _{p} is the slope of the inputoutput power consumption, P _{max} is the maximum output power, and P _{sleep} is the power consumed in sleep mode.
2.2 Energy storage model
We choose a Lithiumion battery as the power storage device in our architecture for its several advantages such as high energy density and low selfdischarge. The battery can store the electricity provided by the PV system and the SG and discharge the stored energy to feed the SBS and sell it back to the SG. In this paper, the battery state is jointly described by its state of charge (SOC) and its state of health (SOH), which both depend on the (dis)charge power. The SOC is an expression of the battery momentary storage level as a percentage of its nominal capacity C _{N}[Ah], which corresponds to the battery capacity at the beginning of life, and the SOH is a metric that reflects the general condition of a battery and its ability to deliver the specified performance compared with a new battery.
2.2.1 State of charge model
where z(t) is the SOC at time t, Δ t represents the time step between two SOC estimations, and η is the battery Coulombic efficiency, equals to η _{dis} when discharging and η _{chg} when charging.
2.2.2 Battery power model
where n is a natural number and (a _{ j })_{ j=1..n } are the polynomial coefficients calculated from the experimental OCVSOC dependency function.
2.2.3 State of health models
where C _{ref}(t) is the reference capacity defined as the battery maximum storage capacity at time t. The degradation of the battery reference capacity can be caused by two aging situations: during use (cycle aging) and on storage (calendar aging) [8]. In the following, these two aging mechanisms are considered independent and thus additive.
2.2.3.1 Cycle aging:
where χ is a scalar strictly greater than one.
2.2.3.2 Calendar aging:
For simplicity, the heat generation and temperature within the battery are assumed to be uniformly distributed. The singlecell thermal model is thus supposed to represent the overall internal battery temperature.
where T _{0} and V _{0} are reference temperature and voltage, Δ T and Δ V are reference temperature and voltage variation, and c _{a}, c _{V}, and c _{T} are fitting parameters based on accelerated calendar aging test data. Given this model, we can conclude that high voltages, and therefore high SOCs (Eq. (4)), contribute to an accelerated battery degradation during rest. Also, the calendar aging grows exponentially with the temperature. Knowing the relation between the current intensity and the heat generated within the battery (Eq. (12)), it is clear that a high current rate increases the internal temperature and therefore leads to faster calendar aging.
2.2.4 Battery aging constraints

We restrict the battery usage on the specific range of the SOC Δ _{soc}=[20%,90%]. As discussed earlier, operating the battery outside this range accelerates the cycle aging by factor χ. In addition, the calendar aging is amplified when the battery voltage is high, which corresponds to a high SOC.

We avoid using high (dis)charge currents that cause accelerated cycle aging (due to deep cycling) and calendar aging (due to heat generation). The current restriction can be reformulated as a limitation of the SOC variation in each decision period:$$ \forall t, \Delta \textup{SOC}_{\text{min}}\le z(t+\Delta t)z(t)\le \Delta \text{SOC}_{\text{max}} $$(14)
where ΔSOC_{max} ≥0 (resp. ΔSOC_{min} ≤0) is the maximum variation of the SOC during charge (resp. discharge).

We prevent the battery from long resting to lower the calendar aging impact. It is possible to completely avoid rest periods and force the battery into permanent cycling. However, according to some researches [29, 30], providing batteries with a rest period after (dis)charging might be essential for relaxation of gradients generated due to the passage of current and could enable capacity recovery. Such phenomenon is not included in our models, but we can take it into consideration by allowing at most one time step rest between charges and discharges. Equation 15 expresses this constraint by imposing a minimum variation of the SOC (be it positive or negative) over any two consecutive time steps:$$ {} \forall t, \left[z(t+2\Delta t)z(t+\Delta t)\right]^{2} + \left[(z(t+\Delta t)z(t)\right]^{2} \ge \epsilon, $$(15)
where ε is strictly positive.
2.3 Harvested energy model
Our architecture uses solar panels to capture solar energy and convert it into electricity via the photovoltaic (PV) effect. The solar radiation I _{g} [W/m ^{2}] depends on several factors including geographical location and time of the day.
where η _{PV} is the energy conversion efficiency of the solar panel and S [m^{2}] is the panel surface.
2.4 Energy price model
In the SG, reducing the peak to average consumption ratio is one of the main keys to maintain a smooth balance between the power consumption and production. To this purpose, dynamic pricing can be adopted to adapt consumption profiles to the energy availability.
In this paper, we consider a stochastic dynamic energy price. Let p(t) [$/kWh ] be the random variable corresponding to the buying price (i.e., the cost of energy from the SG) at hour t. The vector (p(1),…,p(24)) of daily energy buying price is supposed to follow a multivariate Gaussian distribution GP(μ _{price},Σ _{price}), where μ _{price} is a vector of size 1×24 composed of the hourly average buying price of the day and Σ _{price} is the covariance matrix 24×24. We compute μ _{price} and Σ _{price} as the mean and the covariance of successive realizations related to historical data of electricity pricing for residential customers during 5 years [33]. Moreover, we consider that the price of energy sold to the SG is proportional to the buying price such that p _{sell}=κ·p, where κ is the price factor.
3 Cognitive energy supervision system
 1.
The high level controller (HLC) schedules the consecutive battery SOCs during the optimization horizon. The obtained energy strategy minimizes the energy cost and reduces the battery aging.
 2.
The low level controller (LLC) implements the HLC’s energy strategy by controlling the power flow between each subsystem in real time such that the energy balance is respected.
where (z(1),…,z(N+1)) is the decision vector that represents the battery SOCs over the optimization horizon and E _{ b }≥0 (resp. E _{ s }≤0) is the amount of energy bought from (resp. sold to) the SG. The objective function of P _{ 1 } corresponds to the longterm cost due to power transactions with the electrical grid. At all time steps, the balance between the power supply and demand is illustrated by the constraints (Eqs. (17) and (18)). Note that the battery can be either an energy source (when P _{Batt}(z(t),z(t+1))≤0) or a load (when P _{Batt}(z(t),z(t+1))≥0). When the energy consumed is greater than the energy provided by the PV/battery system (i.e., P _{BS}(t)+P _{Batt}(z(t),z(t+1))−P _{PV}≥0), the controller perceives a cost p(t)·E _{ b }(t)≥0 corresponding to the energy bought from the SG. In contrast, when the energy available is superior to the energy consumption (i.e., P _{BS}(t)+P _{Batt}(z(t),z(t+1))−P _{PV}≤0), the controller receives a negative cost κ p(t)·E _{ s }(t)≤0 (that can be seen as a reward) associated with the energy sold to the SG. The aim of the HLC is to jointly minimize the cumulative positive costs and maximize the cumulative rewards, which corresponds to minimize the negative costs. In addition, during all the decision periods, Eqs. (19), (20), and (21) represent the constraints on the SOC that have to be respected to improve the battery life span (see Section. 2.2.4).
4 Results and discussion
Simulation parameters
Parameter  Value  Parameter  Value  

SBS  P _{0}  13.6 W  Δ _{p}  4 
P _{max}  0.13 W  P _{sleep}  8.6 W  
Battery  n _{s}  5  C _{N}  7 Ah 
∀k R _{ k }  50 m Ω  η _{chg}  96%  
η _{dis}  100%  z _{0}  30%  
ΔSOC_{min}  −30%  ΔSOC_{max}  30%  
ε  10^{−4}  
Solar panel  η _{PV}  14%  S  0.25 m^{2} 
Energy price  κ  100% 
 1.
\(\mathcal {C}_{1}=\{\)Eqs. (17) and (18) }. The decisionmaking does not take into consideration the battery life span preservation.
 2.
\(\mathcal {C}_{2}=\{\)Eqs. (17) to (20) }. The power flow strategy includes as constraints the recommended battery operating SOC interval and maximum (dis)charge rate.
 3.
\(\mathcal {C}_{3}=\{\)Eqs. (17) to (21) }. In addition to the recommended battery operating SOC interval and maximum (dis)charge rate, the power flow strategy includes the battery rest time limitation.
The results obtained for each 24 h are averaged and presented in the following subsections.
4.1 Power flow management
4.2 Battery aging
In this section, we investigate the impact of each power scheduling policy on the battery aging. As mentioned before, such aging phenomenon can be dissociated into two parts: the cycle aging and the calendar one.
Finally, by summing the cycle and calendar aging effects, we conclude that the respect of the SOC constraints enables considerable reduction of the battery degradation rate. This allows in average 51% (resp. 30%) of the battery SOH preservation per year when operating under \(\mathcal {C}_{3}\) (resp. \(\mathcal {C}_{2}\)) compared to the unconstrained case \(\mathcal {C}_{1}\).
4.3 Economic performance
 1.
The reference strategy that systematically buys all the energy needed to feed the SBS from the SG. The battery and the PV system are not used.
 2.
The naive strategy is a greedy strategy that aims to decrease the immediate energy cost, regardless of any longterm cost saving opportunity. At each decision period, the PV production is first dedicated to cover the SBS consumption. In case the production exceeds the consumption, the surplus is sold to the SG. Otherwise, the missing energy is purchased from the SG. Consequently, the battery is never used.
Normalized average opex for the ideal (with and without SOC constraints), naive, and reference strategies
Strategy  Ideal under \(\mathcal {C}_{1}\)  Ideal under \(\mathcal {C}_{2}\)  Ideal under \(\mathcal {C}_{3}\)  Naive  Reference 

Cost  −0.45  −0.332  −0.329  −0.11  1 
It is clear that an efficient use of the battery enables more flexibility in the energy trading. In fact, the ESS can exploit the price variation to buy energy at low cost, not only to match an imminent energy demand but also to store it in prevision of future consumption that can generate heavy expenditures from the SG. Also, the RE energy can be saved in the battery until interesting selling prices are offered by the SG. However, there is a tradeoff between how much the battery can be used to realize cost savings and the aging issues. In fact, when the battery aging constraints (\(\mathcal {C}_{2}\) and \(\mathcal {C}_{3}\)) are respected, the cost saving is reduced by about ten points, which corresponds to a loss of $1.6 in 1 year. At the same time, 30% (resp. 51%) of the battery initial SOH is preserved per year, equivalent to $13 (resp. $20) cost saving each year under \(\mathcal {C}_{2}\) (resp. \(\mathcal {C}_{3}\)), which is by far more profitable given the current battery cost. In other words, it means that the implementation of the ideal energy strategy requires the battery replacement after 1.5 years under \(\mathcal {C}_{1}\), 3 years under \(\mathcal {C}_{2}\), and 7 years under \(\mathcal {C}_{3}\).
5 Conclusions
In this paper, we have presented a cognitive energy controller for a small cell base station connected to the smart grid and equipped with a battery and renewable production. This architecture had for purpose to jointly optimize the energy cost and reduce the battery aging effects. Obtained simulation results have shown that the energy supervision system achieves very large cost reduction compared to basic strategies while enhancing the storage life span. In particular, the battery aging constraints allows to considerably reduce the calendar and cycle degradation (up to 51% in average of the initial state of health preserved per year). Furthermore, the respect of these constraints resulted in only ten points decrease of the average opex cost saving, which is negligible considering current battery costs. As future work, we plan to study the proposed cognitive energy supervision framework considering casual information about the environment energy variable. We also aim to realize a demonstrator of the proposed solution to assess its performances in reallife conditions.
Declarations
Funding
The research leading to these results is funded by the French Agence Nationale de la Recherche in the framework of the SOGREEN project (ANR14CE29002501).
Authors’ contributions
MM, ADeD, VH, RC, and NH substantially contributed to the conception or design of the work or the acquisition, analysis, or interpretation of data for the work. MM, ADeD, and VH drafted the work and revised it critically for important intellectual content. MM, ADeD, VH, RC, and NH agreed to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. MM, ADeD, VH, RC, and NH contributed to the final approval of the version to be published.
Competing interests
The authors declare that they have no competing interests.
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References
 Small Cells Deployment Market Status 2015 Report. http://scf.io. Accessed 20 Feb 2016.
 HAH Hassan, L Nuaymi, A Pelov, in Online Conference on Green Communications (GreenCom), 2013 IEEE. Renewable energy in cellular networks: a survey (IEEE, 2013), pp. 1–7.Google Scholar
 A De Domenico, E Calvanese Strinati, A Capone, Enabling green cellular networks: a survey and outlook. Comput. Commun. 37:, 5–24 (2014).View ArticleGoogle Scholar
 G Piro, M Miozzo, G Forte, N Baldo, LA Grieco, G Boggia, P Dini, HetNets powered by renewable energy sources: sustainable nextgeneration cellular networks. IEEE. Internet Comput.17(1), 32–39 (2013).View ArticleGoogle Scholar
 H Wang, H Li, C Tang, L Ye, X Chen, H Tang, S Ci, Modeling, metrics, and optimal design for solar energypowered base station system. EURASIP J. Wirel. Commun. Netw. 2015(1), 39 (2015).View ArticleGoogle Scholar
 J Palicot, in Proceedings of the 2009 International Conference on Wireless Communications and Mobile Computing: Connecting the World Wirelessly. Cognitive radio: an enabling technology for the green radio communications concept (ACM, 2009), pp. 489–494.Google Scholar
 S Jin, X Ma, W Yue, Energysaving strategy for green cognitive radio networks with an LTEadvanced structure. J. Commun. Netw. 18(4), 610–618 (2016).Google Scholar
 M Broussely, P Biensan, F Bonhomme, P Blanchard, S Herreyre, K Nechev, RJ Staniewicz, Main aging mechanisms in liion batteries. J. Power Sources. 146(12), 90–96 (2005).View ArticleGoogle Scholar
 A Barré, B Deguilhem, S Grolleau, M Gérard, F Suard, D Riu, A review on lithiumion battery ageing mechanisms and estimations for automotive applications. J. Power Sources. 241:, 680–689 (2013).View ArticleGoogle Scholar
 N Michelusi, L Badia, R Carli, L Corradini, M Zorzi, Energy management policies for harvestingbased wireless sensor devices with battery degradation. IEEE Trans. Commun. 61:, 4934–4947 (2013).View ArticleGoogle Scholar
 C Liu, B Natarajan, Power management in heterogeneous networks with energy harvesting base stations. Phys. Commun. 16(C), 14–24 (2015).View ArticleGoogle Scholar
 S Zhang, N Zhang, S Zhou, J Gong, Z Niu, X Shen, Energyaware traffic offloading for green heterogeneous networks. IEEE J. Selected Areas Commun. 34(5), 1116–1129 (2016).View ArticleGoogle Scholar
 R Kaewpuang, D Niyato, P Wang, Decomposition of stochastic power management for wireless base station in smart grid. IEEE Wirel. Commun. Lett. 1(2), 97–100 (2012).View ArticleGoogle Scholar
 J Leithon, TJ Lim, S Sun, in Smart Grid Communications (SmartGridComm), 2013 IEEE International Conference on. Online energy management strategies for base stations powered by the smart grid (IEEE, 2013), pp. 199–204.Google Scholar
 Y Mao, J Zhang, KB Letaief, Grid energy consumption and QoS tradeoff in hybrid energy supply wireless networks. IEEE Trans. Wirel. Commun. 15(5), 3573–3586 (2016).View ArticleGoogle Scholar
 M Mendil, A De Domenico, V Heiries, R Caire, N Hadjsaid, in Personal, Indoor, and Mobile Radio Communications (PIMRC), 2016 IEEE 27th Annual International Symposium on. Fuzzy Qlearning based energy management of small cells powered by the smart grid (IEEE, 2016), pp. 1–6.Google Scholar
 M Mendil, A De Domenico, V Heiries, R Caire, N Hadjsaid, in International Conference on Cognitive Radio Oriented Wireless Networks. Energy management of green small cells powered by the smart grid (Springer, 2016), pp. 642–653.Google Scholar
 G Auer, V Giannini, C Desset, EA Godor, How much energy is needed to run a wireless network?IEEE Wirel. Commun. 18(5), 40–49 (2011).View ArticleGoogle Scholar
 L Lu, X Han, J Li, J Hua, M Ouyang, A review on the key issues for lithiumion battery management in electric vehicles. J. Power Sources. 226:, 272–288 (2013).View ArticleGoogle Scholar
 R Restaino, W Zamboni, in IECON 201238th Annual Conference on IEEE Industrial Electronics Society. Comparing particle filter and extended kalman filter for battery stateofcharge estimation (IEEE, 2012), pp. 4018–4023.Google Scholar
 A Barre, F Suard, M Gérard, M Montaru, D Riu, Statistical analysis for understanding and predicting battery degradations in reallife electric vehicle use. J. Power Sources. 245:, 846–856 (2014).View ArticleGoogle Scholar
 WY Chang, The state of charge estimating methods for battery: a review. ISRN Appl. Math. 2013:, 1–7 (2013).View ArticleMATHGoogle Scholar
 C Weng, J Sun, H Peng, in ASME 2013 dynamic systems and control conference. An opencircuitvoltage model of lithiumion batteries for effective incremental capacity analysis (American Society of Mechanical Engineers, 2013), pp. V001T05A002–V001T05A002.Google Scholar
 Y Riffonneau, S Bacha, F Barruel, S Ploix, Optimal power flow management for grid connected PV systems with batteries. IEEE Trans. Sustainable Energy. 2(3), 309–320 (2011).View ArticleGoogle Scholar
 E LemairePotteau, F Mattera, A Delaille, P Malbranche, in 23rd European Photovoltaic Solar Energy Conference (Valencia, Spain, 2008). Assessment of storage ageing in different types of PV systems: technical and economical aspects (Valencia, 2008), pp. 2765–2769.Google Scholar
 Lithium battery failures. http://www.mpoweruk.com/lithium_failures.htm. Accessed 20 Feb 2016.
 A CordobaArenas, S Onori, G Rizzoni, A controloriented lithiumion battery pack model for plugin hybrid electric vehicle cyclelife studies and system design with consideration of health management. J. Power Sources. 279:, 791–808 (2015).View ArticleGoogle Scholar
 M Ecker, JB Gerschler, J Vogel, S Käbitz, F Hust, P Dechent, DU Sauer, Development of a lifetime prediction model for lithiumion batteries based on extended accelerated aging test data. J. Power Sources. 215:, 248–257 (2012).View ArticleGoogle Scholar
 A Eddahech, O Briat, JM Vinassa, Lithiumion battery performance improvement based on capacity recovery exploitation. Electrochimica Acta. 114:, 750–757 (2013).View ArticleGoogle Scholar
 M Rashid, A Gupta, Effect of relaxation periods over cycling performance of a liion battery. J. Electrochem. Soc. 162(2), 3145–3153 (2015).View ArticleGoogle Scholar
 G SOLAR, Solar radiation time series. http://geomodelsolar.eu/data/fulltimeseries. Accessed 20 Feb 2016.
 G Rami, T TranQuoc, N Hadjsaid, JL Mertz, in Power Engineering Society General Meeting, 2004. IEEE. Energy supply for remote base transceiver stations of telecommunication (IEEE, 2004), pp. 1916–1921.Google Scholar
 Ameren: Ameren price database. https://www2.ameren.com/RetailEnergy/rtpDownload. Accessed 20 Feb 2016.
 A Forsgren, PE Gill, MH Wright, Interior methods for nonlinear optimization. SIAM Rev. 44(4), 525–597 (2002).MathSciNetView ArticleMATHGoogle Scholar
 K Uddin, A Picarelli, C Lyness, N Taylor, J Marco, An acausal liion battery pack model for automotive applications. Energies. 7(9), 5675–5700 (2014).View ArticleGoogle Scholar
 G Auer, O Blume, V Giannini, I Godor, M Imran, Y Jading, E Katranaras, M Olsson, D Sabella, P Skillermark, et al, D2. 3: Energy efficiency analysis of the reference systems, areas of improvements and target breakdown. EARTH. 20(10) (2010).Google Scholar