Methods and apparatus for battery-augmented network planning

Abstract

Methods, apparatuses, and systems for selecng a batery capacity for a base staon system comprising base staon circuitry and at least two electricity sources for powering the base staon circuitry, the at least two electricity sources comprising a batery system and one or more renewable energy sources. An example method comprises modeling (1410) energy supply versus me for each of the one or more renewable energy sources, based on a locaon for the base staon system, and modeling (1420) energy demand versus me for the base staon system. The example method further comprises esmang (1430) an opmal inial capacity for the batery system, based on the modeled energy supply for each of the one or more renewable energy sources, the modeled energy demand versus me for the base staon system, a batery management funcon that takes into account a capacity degradaon model of the batery system, and several other parameters.

Description

[0001] METHODS AND APPARATUS FOR BATTERY-AUGMENTED NETWORK PLANNING

[0002] TECHNICAL FIELD

[0003] The present disclosure is generally related to base station systems using renewable energy sources and battery systems for power and is more particularly related to techniques and systems for selecting a battery capacity for such systems.

[0004] BACKGROUND

[0005] Base stations in wireless communication systems are typically connected to the electrical power grid. In some areas, the power grids may be very unreliable (e.g., in India, down-times average about 20% per day). Even more generally, power grids are less reliable than might be imagined. For example, in the U.S., power grid reliability is only 98.6%.

[0006] One approach to addressing this problem is the adoption of distributed storage solutions, such as batteries close to each base station. However, this is rare.

[0007] A great deal of scientific research has focused on battery technology and renewable energy in general, e.g., on the modeling of lithium-ion battery degradation or on increasing the efficiency of photovoltaic panels. In addition, it has been previously suggested to complement access points with energy harvesting devices, e.g., photovoltaic panels. One example is International Patent Application Publication No. WO 2011 / 071425, filed 8 December 2009, which describes techniques for energy balancing among multiple base stations powered by any of a variety of power sources, including wind power, solar power, diesel-generation power, and the electrical grid.

[0008] Most renewable energy sources are intermittent, with their outputs and reliability being location dependent. Renewable energy sources may be complemented with battery systems, to provide power when the renewable power is unavailable, and / or when a connected grid is out of service. Combining a battery system with renewable energy sources for powering a wireless network raises new issues regarding how to manage the battery usage, to optimize battery life without unduly sacrificing base station services or performance. These combinations also raise issues regarding how to properly select battery capacity for these systems. SUMMARY

[0009] The techniques described herein address these issues by providing a planning tool that can be used to dimension the initial capacity of the battery in a system that is either disconnected from the grid (completely off-grid solution) or connected to a (possibly unreliable) grid.

[0010] Embodiments of this planning tool described herein include an example method for selecting a battery capacity for a base station system comprising base station circuitry for communicating with one or more wireless devices and other components of a wireless network and further comprising at least two electricity sources for powering the base station circuitry, where the at least two electricity sources comprise a battery system and one or more renewable energy sources. The example method comprises modeling energy supply versus time for each of the one or more renewable energy sources, based on a location for the base station system, and modeling energy demand versus time for the base station system. The example method further comprises estimating an optimal initial capacity for the battery system, based on the modeled energy supply versus time for each of the one or more renewable energy sources, the modeled energy demand versus time for the base station system, one or more parameters indicating maximum allowed downtime for the base station circuitry, a replacement threshold parameter indicating a level of degradation at which the battery system should be replaced, and a battery management function that takes into account an initial capacity of the battery system and a capacity degradation model of the battery system.

[0011] Other embodiments include corresponding battery-capacity selection circuitry for use in selecting a battery capacity for a base station system that, again, comprises base station circuitry, a battery system, and one or more renewable electricity sources. The battery-capacity selection circuitry, which may comprise processing circuitry and a memory storing program instructions for execution by the processing circuitry, is configured to estimate an optimal initial capacity for the battery system, based on a modeled energy supply versus time for each of the one or more renewable energy sources, a modeled energy demand versus time for the base station system, one or more parameters indicating maximum allowed downtime for the base station circuitry, a replacement threshold parameter indicating a level of degradation at which the battery system should be replaced, and a battery management function that takes into account an initial capacity of the battery system and a capacity degradation model of the battery system. Variants of the above-summarized embodiments are detailed below, as are other objects, advantages, and novel features of the presently disclosed invention.

[0012] BRIEF DESCRIPTION OF THE FIGURES

[0013] Figure 1 is an example base station system according to some embodiments.

[0014] Figure 2 is another view of an example base station system.

[0015] Figure 3 is a process flow diagram illustrating example techniques according to some embodiments.

[0016] Figure 4 is still another view of an example base station system.

[0017] Figure 5 is a process flow diagram illustrating an example method, according to some embodiments.

[0018] Figure 6 shows an example of variability in solar energy availability on a seasonal basis.

[0019] Figure 7 shows an example of variability in solar energy availability on an intra-day basis.

[0020] Figure 8 shows an example of internet traffic variability on a seasonal basis.

[0021] Figure 9 illustrates an example of intra-day variability in internet traffic.

[0022] Figure 10 illustrates a modeling of solar energy availability.

[0023] Figure 11 shows a modeling of wind speed.

[0024] Figure 12 illustrates an optimization of initial battery capacity selection, for a first example scenario.

[0025] Figure 13 shows an optimization of initial battery capacity selection, for a second example scenario.

[0026] Figure 14 is a process flow diagram illustrating an example method, according to some embodiments.

[0027] Figure 15 is a block diagram illustrating an example battery-capacity selection circuitry, according to some embodiments.

[0028] DETAILED DESCRIPTION

[0029] The present solutions are described herein in terms of methods and arrangements for use in or with a communication system, which may be put into practice in the embodiments described below. The present solutions may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the present solution. It should be understood that there is no intent to limit the present methods, and / or arrangements to any of the particular forms disclosed, but on the contrary, the present methods and arrangements are to cover all modifications, equivalents, and alternatives falling within the scope of the present solution as defined by the claims.

[0030] The present solutions may, of course, be carried out in other ways than those specifically set forth herein without departing from essential characteristics of the solution. The present embodiments are to be considered in all respects as illustrative and not restrictive, and all changes coming within the meaning and equivalency range of the appended claims are intended to be embraced therein.

[0031] As noted above, most renewable energy or electricity sources are intermittent and location dependent. In the context of supplying power to a base station, this problem can be addressed, at least in part, by providing the base station with a battery system, e.g., an arrangement of lithium-ion cells configured to store surplus power generated by the renewable energy sources and to power the base station when the power generated by the renewable energy sources is inadequate, or completely unavailable.

[0032] One problem with such a solution is how to properly manage the battery system to maximize its lifetime. As is well-known, the storage capacity of a battery system will degrade with use. With lithium- ion-based systems, for example, the storage capacity of the cells will gradually decrease, as a function of charge-discharge cycles, until they reach a critical point, after which the degradation in capacity becomes severe enough that the battery system may be considered unusable. This problem becomes particularly acute when a base station has no connection at all to the electrical power grid, or when the electrical grid is unreliable or only intermittently available.

[0033] This problem can be addressed by equipping a base station, which may or may not be connected to a power grid, with an energy storage device, e.g., a lithium-ion battery system, and one or more renewable energy harvesting devices, e.g., a solar panel and a wind turbine, together with an algorithm or algorithms to facilitate managing the charging process in real time. Such a system could be completely off-grid or semi-off-grid, in various embodiments, with the latter including a situation where a power grid is available but where the system draws energy from the grid only in limited circumstances, e.g., to replenish the battery at night, or to draw energy in the event of unexpected low renewable energy supply. Such a system might also supply energy to the grid in certain circumstances, e.g., to sell excess energy obtained from a solar system during the day.

[0034] It will be appreciated that at least some renewable energy sources, such as solar power systems or wind energy systems, may be considered to be intermittent or unreliable sources of power since, for example, solar power is unavailable at night and prevailing winds may vary over time. In some cases, the base station may be connected to an electrical grid that is considered to be an intermittent or unreliable source of power, as well. A well-designed battery management system can take any or all of this into account when determining how to best manage the use of the battery system.

[0035] Figure 1 thus illustrates an example system in which some or all of the techniques described herein may be employed. The illustrated system includes a base station 110, as well as several power sources or power generators, including solar panels 120, wind turbine 130, and power grid 140. While Figure 1 illustrates base station 110 separately, the entire system might together be considered a "base station system." It will be understood that other power sources might be available as well, and that various systems may only contain one or a few of these sources.

[0036] The system shown in Figure 1 also includes a battery system 150, which may be, for example, a bank of lithium-ion battery cells with appropriate charging and power conversion circuitry. A batterymanagement system 160, which includes battery-management controller circuitry that will be described in more detail below, monitors and controls the energy state and usage of the battery system 150 and, as will be discussed below, may also adapt one or more operational modes and / or operational parameters of the base station 110, based upon, inter alia, the state of the battery system 150, which includes its energy state , or charge level, as well as its current capacity, current demand for or supply of energy from / to the rest of the system, etc.

[0037] Implementations of the battery management system 160 may include an algorithm, or battery management function, that defines the charging and discharging processes for the battery system 150, based on the demand of the base station and the supply from the renewable electricity sources. The battery management system 160 may take into account all or some of the following parameters, models, etc., which may be stored in database 180:

[0038] — Initial battery capacity;

[0039] — A capacity degradation model for the battery system; — Historical prices of power per kWh depending on day and time if an open energy market is available and a variable energy contract is adopted, otherwise fixed price per kWh;

[0040] — Current prices of power;

[0041] — Historical data traffic patterns;

[0042] — Historical seasonal patterns of energy supplied by the chosen renewable electricity sources;

[0043] — Daily weather forecast.

[0044] The algorithm may optimize one, several, or a combination of the following objectives, e.g., weighted together in one objective referred to as reward:

[0045] — Maximum remaining battery lifetime, e.g., defined as the number of days before the capacity of the battery is a fraction of the initial capacity. As an example, this might be defined as the time before the fully-charged capacity of the battery is expected to reach 70% of the initial capacity, due to repeated charges and discharges);

[0046] — Minimum downtime for the base station (e.g., in the case the system is completely off-grid or where there is a known likelihood of grid outages, the system might at least sometimes be completely dependent on the battery system, which may be unable to maintain 100% availability - in such a scenario, the energy state of the battery may be optimized at least in part to minimize downtime, in view of predicted grid outages); one of the objective functions could be the downtime of the base station (due to lack of power) and the optimization problem could be to minimize such downtime. This impacts the choices for energy storage and potentially battery lifetime because the algorithm may 1) require a larger battery, and 2) use the battery at levels that degrade it faster than at other levels (e.g., use the battery when the charge is 10% is worse than using it when the charge is at 50%, but the algorithm may be forced to use the battery when the level is 10% because otherwise the base station would be turned off).

[0047] — Maximum revenues in terms of price paid for electricity pushed into the power grid minus cost of electricity drawn from the power grid. This applies in cases where the system is connected to the power grid. Without renewable energy or electricity sources, such a revenue would be negative. With renewables and battery, such a revenue may be positive or negative.

[0048] Some of the above objectives can be merged, with each other or with other objectives / costs. For example, the revenue streams during the battery lifetime and the capital costs (often referred to as capital expenditures, or CAPEX) of the system can be all merged to provide a complete picture of the cost / benefit of building and running the system.

[0049] The operation of the algorithm for managing the battery system 150, i.e., the battery management function, may be characterized as utilizing feedback from various components of the overall system. A detailed example follows.

[0050] For simplicity, assume that time is discretized: t = 0, 1, 2, ... . Let the initial capacity of the battery be Co, which is measured in joules, or kWh (thousand watts x hour). The energy supply and demand at any given discrete time step can be normalized to Co, in which case these quantities are dimensionless. For example, if the energy supplied at time 0 is So= 0.05, it means that, if there is no demand and all energy supplied is stored (ideal case), then at time 1 the energy stored is 5% higher than at time 0 (unless, of course, the battery stored more than 95% of its capacity, in which case it would reach full capacity and some of the available energy would be wasted, unless it can be supplied to the grid).

[0051] Next, the computation that is needed to end up with dimensionless energy supply and demand in a realistic scenario is detailed.

[0052] Suppose, for example, that a wind turbine generates 10 kWh with wind blowing at 3 m / s (10.8 km / h), and suppose that the time step in the algorithm is 1 minute, during which interval is assumed that the wind speed is almost constant, with average 3 m / s. Thus, the energy supplied in that minute is 10 kWh / 60 ~ 166 Wh.

[0053] Suppose further that the battery capacity is 6 kWh. Then So0.0276 or 2.76% of the initial battery capacity. If this energy is actually stored in the battery, the battery charge level goes up by 2.76%. But, the battery capacity for time step 1 is reduced, over that interval, due to battery degradation, by a small but nonzero amount, say AC0, that is, = Co— AC0. Note that the specifics of this degradation are technology-specific, and also depend on the usage patterns and state of the battery system - all of these may be captured in a capacity degradation model of the battery system, which may be, for example, empirically derived by the manufacturer or supplier of the battery system and which uses, as inputs, the energy state and usage of the battery over time.

[0054] In general, at time t, the typical operation of the system may proceed as follows: The renewable energy sources (e.g., wind and solar) supply some energy, say St(whether or not this energy is stored, in the case it exceeds demand, is a choice that will be made by the algorithm described here). The base station demands some power, say Dt(the base station requires a baseline level of power even when idle, and additional power is needed depending on traffic and other parameters). If connected to a properly functioning power grid, let the price of one normalized unit of power (equal to Cojoules or equivalent in kWh) be Pt. The battery management system takes as inputs St, Dt, Pt, and all the historical patterns, including possibly the energy price and weather forecasts, to come up with a choice on i) whether or not to store the excess energy Xt= St— Dtif it is positive, and ii) whether or not to fully or partially satisfy the demand. Note that if demand is not satisfied, then the base station may go down, or services may be curtailed in some way. In extreme situations, e.g., in scenarios where there is no grid power available, it may be a desirable outcome for the base station to become fully inoperative, but in general it may be assumed that it is preferable for the base station's demand to be always satisfied.

[0055] The two choices may be represented by two variables, <jtE {0,1}, which represents the action of not storing (crt= 0) or storing (crt= 1) excess energy, and 6tE {0,1}, which represents the action of not satisfying (<5t= 0) or satisfying (<5t= 1) the base station's demand. Note that limiting the choices for <5tto 0 and 1 suggests that the latter choice is limited to either fully satisfying the base station's demand or not satisfying it at all. In some embodiments, it may be possible to partially satisfy the base station's demand by altering or adapting an operational mode or operational parameter, e.g., limiting transmission power, turning off one or more services, etc. This may be modeled by either allowing Dtto take on a variety of values, depending on the operational modes and / or parameters applicable to a given interval or by allowing 6tto take on intermediate values between 0 and 1. In either case, the energy available to be stored for the interval in which the base station's demand is satisfied (if any) is limited to the difference between the total energy supplied by all sources and the energy consumed by the base station,.

[0056] Note also that it may be undesirable to store or satisfy demand at every interval possible. The reason for this is that every time the battery is used, its capacity degrades. Consequently, here is thus an optimal strategy that can be adopted. One way to find this optimal strategy is by using a learning algorithm, e.g., a deep Q-learning. However, this is not the only way to proceed - it is simply one possible implementation. Other machine-learning algorithms such as a trained random forest might be used, as might a decision tree or even simpler set of rules.

[0057] 5. The energy stored in the battery is updated accordingly. Let Etbe the energy stored at time t normalized as usual to Co. Then, at time t = 1, the energy will be equal to

[0058] Et+i=Et+ t > provided that demand is satisfied (as it usually is), the excess energy Xtis stored, and 0 < Et+1The last inequality indicates that the energy in the battery is always nonnegative Co and at most it is equal to the (degraded) capacity (normalized to Co). In fact, as operations go on, Ctdecreases because the energy storage capability of the battery deteriorates. In total generality, the energy at the following time step is given by:

[0059] Note that excess energy may be sold, rather than being stored. In this case, of course, the equations above should be modified to account for excess generated energy that is sold and not used to charge the battery system. Likewise, in a grid-connected system, it is also possible to pull energy from the grid and add it to the battery - this likewise will require straightforward modifications to the above equations.

[0060] 6. The battery is degraded by a quantity equal to ACt> 0 and thus Ct+1= Ct— ACt.

[0061] 7. All quantities above are recorded in the database and become part of historical data used in step 4.

[0062] 8. The time step is updated, t «- t + 1, and the process continues (go to step 1).

[0063] This process continues until the capacity drops below a certain pre-determined level. For example, for lithium-ion batteries, there is a fairly linear degradation for a few thousand cycles, until the capacity degrades to about 70% of the initial capacity. Beyond the 70% level or thereabouts, the degradation accelerates. Therefore, the process detailed above should continue until the capacity approaches a point close to the nonlinear part of the degradation. At that point, further use of the battery system may be regarded as infeasible, and maintenance actions may be taken. There are multiple choices for the algorithm to be used in step 4. One such choice is to base the algorithm on deep Q-learning. Other reinforcement learning algorithms would work, and also nonlearning algorithms may be suited in case there is no database available. A benefit of a learning algorithm though is that it becomes tailored to the specific location and specific products used, i.e., the specific battery, solar panels, and wind turbines. Such a learning algorithm can run locally, on one or more processors co-located with the base station, or in the cloud, if internet access is available. It does not require special hardware accelerators (like GPUs), although if present they can be leveraged.

[0064] The block diagram of Figure 2 illustrates basic components of a system. Arrows represent messages about power requested or supplied. As seen in the figure, several energy sources 210 supply power for the operation of a base station 220. These energy sources 210 include at least one renewable energy generator (e.g., solar panels and / or wind turbine), such that some or all of these sources have available energy outputs that vary with time. The hardware also includes a battery system, illustrated as energy storage unit 230. The battery management system 240, which includes a compute unit 245, which may be regarded as an example implementation of the battery-management controller circuitry described elsewhere herein, takes as inputs energy measurements, historical data, and current data, including possibly weather forecasts, to determine when and how to serve the demand of the base station and when to store energy in the battery system.

[0065] The dashed boxes correspond to storage of a historical database 250, e.g., for historical data regarding the outputs of the energy sources and historical operation of the battery management system 240. This historical data may be stored in and / or retrieved from the cloud, in some instances. While the availability of this historical data is not essential for the operation of the system, if present, it offers the possibility of more accurate prediction and better overall decisions.

[0066] Figure 3 is a process flow diagram illustrating the main loop of operation of an example algorithm carried out by, for example, battery-management control circuitry 245 in battery management system 240. Note that this example assumes a connection to the electrical grid, as well as access to a database of historical information. In various embodiments, one or both of these might not be present.

[0067] 300: Time is initialized to zero when the energy storage system or battery system, which might be referred to as simply a battery, is new and the full initial capacity is available. Each time step thereafter corresponds conceptually to a time interval, which can be measured for the sake of simplicity in seconds or minutes.

[0068] 310-320: As shown at block 310, the current energy storage capacity of the battery is checked, to determine whether it is less than an end-of-life value. This may be done, for example, by computing the ratio of the current capacity of the battery to its initial, or nominal, capacity, e.g., to obtain a percentage value, which can be compared to a threshold value. If the current capacity of the battery has degraded below a certain threshold, then maintenance or replacement of the battery must be performed, as shown at block 320, after which the battery management algorithm may be re-started.

[0069] 330-360: As shown at block 330, at the current time step, the battery management system receives a measurement of the average supply of energy during the interval from all the renewable sources. As shown at block 340, for systems with a connection to the electrical grid, a measurement of the current price of energy from the power grid is obtained / received. Note that this may a historical average price, in some cases, or a contracted price or dynamic price offered by the grid in others. As shown at block 350, the system may check to confirm that the grid is available to supply power, or "up." Finally, as shown at block 360, the system may receive a weather forecast, or an indication of current weather conditions, or both.

[0070] 370: As shown at block 370, the battery management system then applies an algorithm on the basis of information in a historical database, shown at block 365, and measurements from blocks 330, 340, 350, 360, using a battery-management model or, more generally, an energy-management model, which is discussed in more detail below. A decision on satisfying demand (5) and storing energy (a) is taken here.

[0071] 380: The decision taken at block 370 is satisfied at block 380. This decision may be to satisfy the power demand of the base station, i.e., to provide energy to the base station from one or more of the resources and / or the battery system, and / or to store energy in the battery system. Note that this satisfying of the base station's energy demands may be full or partial, in various situations and / or embodiments, and may comprise, for any given interval, supply all or a portion of the energy needed by the base station from the battery, when inadequate energy is available from the other energy sources. As discussed above, it may be possible to partially satisfy the base station's demand by altering or adapting an operational mode or operational parameter of the base station, e.g., limiting transmission power, turning off one or more services, etc. This may be modeled, for example, by allowing 6tto take on intermediate values between 0 and 1.

[0072] The decision taken at block 370 may instead or also be to store energy. In some cases, this may be a decision to store energy supplied by the energy resources over and above the demand of the base station. In other, more extreme cases, this may be a decision that complements a decision to turn off the base station, i.e., to store whatever energy is supplied by the energy resources instead of satisfying base station demand.

[0073] To the extent that any of the demand is supplied from the battery or any energy is stored in the battery, the impact of that supply on the battery's energy storage status, or energy state, is updated. The battery's energy storage status may be tracked in units of energy, or as a percentage of nominal or current capacity, for example. Note that managing a battery system that requires multiple cells or multiple sets of cells may include selecting, from among the multiple cells or sets of cells, one or more cells or sets of cells to charge or discharge at a given time, e.g., to level out the degradation or to otherwise optimize the battery system's life and / or performance.

[0074] 390: As shown at block 390, the battery's capacity is updated, using a capacity degradation model for the battery system that uses, as input, the battery's energy state and usage over time. Other factors, such as age and temperature might also be included in the capacity degradation model.

[0075] 395: Finally, as shown at block 395, updates to the battery capacity are stored. Usage information for the battery, whether per-interval usage or usage statistics, may also be stored, for use by the energymanagement model in making future decisions. Likewise, any or all of the most recent data for energy available from the energy resources, grid pricing, weather conditions, etc., may be stored, again for use by the energy-management model in subsequent decisions. The time step is updated, and control passes back to the beginning of the algorithmic loop.

[0076] Figure 4 is another view of an example base station system, including an example of the battery management system described herein. The base station system comprises base station circuitry 410, which in turn comprises transceiver circuitry 414 and controller circuitry 418 operatively coupled to the transceiver circuitry 414 and configured to control operation of the transceiver circuitry 414. The base station system further comprises at least two electricity sources, the at least two electricity sources comprising a battery system 420 and one or more renewable electricity source(s) 430, such as a solar power generation system or a wind power generation system.

[0077] The base station system further comprises battery-management controller circuitry 440, operatively coupled to the at least two electricity sources and to the base station circuitry 410. The batterymanagement controller circuitry 440, which may comprise, in various embodiments, one or more processors, memory storing program instructions by the one or more processors, digital hardware / logic, analog switches and other analog circuitry, such as current / voltage sensors, etc., is configured to carry out one or more of the techniques described above. Namely, the batterymanagement controller circuitry 440 is configured to monitor and control the energy state and usage of the battery system 420 and to adapt one or more operational modes and / or operational parameters of the base station circuitry 410 to adjust power consumption of the base station circuitry 410. Adapting an operational mode of the base station circuitry 410 may comprise selectively activating and / or deactivating all or portions of the base station's functionality, in various embodiments or instances. Adapting operational parameters may comprise adjusting or setting / resetting any parameters that impact the energy consumption of the base station circuitry 410. Examples include, for instance, a transmit power parameter, or a parameter controlling a number of transmit beams.

[0078] The adapting of the operational mode(s) and / or operational parameter(s) of the base station circuitry 410 by battery-management controller circuitry 440 may be based on an energy-management model 442 that takes into account (i) an initial capacity of the battery system, (ii) a capacity degradation model 444 of the battery system 420, and (iii) historical energy production data and / or an energy production model of seasonal energy production for each of the one or more renewable energy or electricity sources 430. In some embodiments, the energy-management model 442 may further take into account a historical data traffic pattern for traffic data flowing through the base station system. Note that the term "energy-management model" is used here to reflect that the model utilizes input from and is used to control energy usage throughout the system, even as its most basic function may be to control charge and discharge of the battery system 420. This model might alternatively be referred to as, for instance, a battery-management model.

[0079] In some embodiments, the base station system further comprises an electrical interface for connection to an electrical grid, in which case the energy-management model may further take into account one or more of: a current cost for power supplied by the electrical grid, a current price paid for power supplied to the electrical grid from renewable sources, historical data or a model representing cost over time for energy supplied by the electrical grid, and historical data or a model representing price paid for power supplied to the electrical grid from renewable sources.

[0080] In various embodiments or instances, the battery-management controller circuitry 440 is configured to adapt the one or more operational modes and / or operational parameters of the base station circuitry 410 using an algorithm that optimizes a weighted combination of at least (iv) a remaining useful lifetime of the battery system and (v) on-time for each of one or more base station operational modes or for the base station circuitry 410 as a whole. In embodiments where the base station system has an electrical interface for connection to an electrical grid, the weighted combination optimized by the algorithm may further include (vi) a parameter corresponding to a net cost of energy supplied to and received from the grid. The algorithm may be a reinforcement-learning algorithm, in some embodiments, such as a deep-Q. learning algorithm.

[0081] In various embodiments or instances, the battery-management controller circuitry 440 may be configured to adapt the one or more operational modes and / or operational parameters of the base station circuitry to adjust power consumption of the base station circuitry by selectively turning on and / or off one or more communication services provided to users by the base station system. In some embodiments or instances, the battery-management controller circuitry 440 may be configured to adapt the one or more operational modes and / or operational parameters of the base station circuitry 410 to adjust power consumption of the base station circuitry 410, for example by adjusting transmission power of one or more signals transmitted by the base station circuitry 410.

[0082] Portions of the battery-management controller circuitry 440 executing software may be implemented using processing circuitry local to the base station system or remotely, e.g., in the "cloud," or some combination thereof, in various embodiments.

[0083] Figure 5 is a process flow diagram illustrating an example method for operating a base station system that comprises base station circuitry, a battery system, battery-management controller circuitry, and one or more renewable electricity sources. This method is intended to be a generalization of and to include the techniques described above - thus, where terminology here differs from similar or related terminology used above, the terminology used to describe Figure 5 should be understood to at least encompass the related terms used above. As shown at block 510, the method comprises monitoring and controlling the energy state and usage of the battery system. This comprises measuring and tracking energy supplied from and supplied to the battery system. The method further comprises, as shown at block 520, adapting one or more operational modes and / or operational parameters of the base station circuitry to adjust power consumption of the base station circuitry, based on an energy-management model that takes into account (i) an initial capacity of the battery system, (ii) a capacity degradation model of the battery system, and (iii) historical energy production data and / or an energy production model of seasonal energy production for each of the one or more renewable energy or electricity sources. In some embodiments or instances, the energy-management model further takes into account a historical data traffic pattern for traffic data flowing through the base station system. In some embodiments, the base station system may comprise an electrical interface for connection to an electrical grid, in which case the energy-management model may further take into account one or more of: a current cost for power supplied by the electrical grid, a current price paid for power supplied to the electrical grid from renewable sources, historical data or a model representing cost over time for energy supplied by the electrical grid, and historical data or a model representing price paid for power supplied to the electrical grid from renewable sources.

[0084] In various embodiments or instances, adapting the one or more operational modes and / or operational parameters of the base station circuitry may comprise using an algorithm that optimizes a weighted combination of at least (iv) a remaining useful lifetime of the battery system and (v) on-time for each of one or more base station operational modes or for the base station circuitry as a whole. In some embodiments where the base station system comprises an electrical interface for connection to an electrical grid, the weighted combination optimized by the algorithm may further comprise a parameter corresponding to a net cost of energy supplied to and received from the grid.

[0085] In various embodiments, the algorithm may be a reinforcement-learning algorithm, such as a deep-Q. learning algorithm.

[0086] In some embodiments or instances, adapting the one or more operational modes and / or operational parameters of the base station circuitry comprises selectively turning on and / or off one or more communication services provided to users by the base station system. In some of these and in other embodiments or instances, adapting the one or more operational modes and / or operational parameters of the base station circuitry may comprise adjusting transmission power of one or more signals transmitted by the base station circuitry.

[0087] Thus, the techniques, circuits, and systems described above comprise a tool that operates a base station system and determines when the energy storage should be increased or used and by what amount, and when the power demand needs to be satisfied. This management tool increases or decreases energy storage in order to maximize a battery's lifetime or to minimize the downtime of the equipment, or to optimize a cost function comprising a weighted combination of several parameters, such as battery lifetime, service downtime, etc.

[0088] This tool may utilize a simple theoretical model underpinning the battery capacity degradation in a reinforcement learning framework (e.g., using deep Q-learning techniques) to optimize battery life while trying to satisfy the traffic demand. The tool may employ an algorithm that also takes into account the energy price when optimizing the battery charging and discharging processes.

[0089] While the techniques, circuits, and systems described herein may be advantageously employed in base station systems that have a connection to the electrical grid, a completely off-grid base station is also possible, providing the potential for increased coverage in rural areas since the location of the base station is mostly free. With such an off-grid solution, a mast or pole can be erected almost everywhere.

[0090] Other non-technical advantages include 1) a reduced reliance on the power grid, which implies a potential reduction of energy to be supplied, and 2) reduced operational expenditures (OPEX) for operators that quickly compensate the increased CAPEX incurred to equip base stations with the necessary hardware and software to make them independent or semi-independent of the power grid.

[0091] The methods and apparatuses described above may be used to optimize the behavior of a battery- equipped base station system given a maximum capacity of the battery and various other energy- related constraints on the problem. What is not discussed above is a method to dimension the system, e.g., how to find an optimal initial battery capacity given cost constraints.

[0092] It will be appreciated that a key parameter of the systems and techniques described above is the initial capacity of the battery 420. Left unaddressed above is how that initial capacity should be determined, or selected. Without cost constraints, the larger the battery, the more reliable the system, all else being equal. However, in practice there are two costs associated to deploying batteries: The initial cost of the battery (to store energy) and energy capture systems (to collect energy from renewable sources), which are accounted for in the CAPEX of the battery-augmented system; and the cost of operating the system, or OPEX, if the system is connected to the grid.

[0093] The battery undergoes degradation every time it is used. This process depends on the management function and the initial capacity, with the most important factor determining the lifetime of the battery being the charge and discharge path as a function of time. For example, a lithium-ion battery will last for a shorter time if it is completely charged and discharged, and for a longer time if the energy stored is always between 20% and 80% of the capacity. This, in turn, depends on the energy patterns and the battery management function used to control the use of the battery.

[0094] Below is described a planning tool that can be used to minimize the cost of the battery per unit time (capex per unit time) plus the cost of operating the battery per unit time (opex per unit time). There are several inputs that are used by the planning tool to optimize the initial battery capacity:

[0095] 1. Battery degradation function: This is the function that determines the capacity of the battery as a function of battery level path. The battery level path can be thought of as the energy stored in the battery as a function of time.

[0096] 2. Minimum battery capacity threshold: This is the threshold below which the battery should be replaced. It can be expressed as a percentage of the initial capacity. This threshold may be selected, according to the battery technology, to give an indication that battery deterioration is likely to accelerate soon. This is generally selected so that it is not a hard threshold in the sense that the battery stops working immediately, but rather a warning that action should be taken soon.

[0097] 3. Energy supply and demand processes: These are the probabilistic processes that define the energy supplied to the battery and the demand requested by the load.

[0098] 4. Battery management function: This is the function that determines how much energy to store when available and how much energy to provide when requested. Examples of this function were described in detail above.

[0099] 5. Spot energy price process: This is the probabilistic process that defines the energy spot price on the energy market. 6. Maximum allowed downtime: This is the maximum fraction of time that the base station system is allowed to fail. Failure is defined by a request for an energy that is not supplied to the load. It can be expressed as a probability or in percentage.

[0100] Inputs 1-4 are necessary for determining the capex per unit time. Input 5 is necessary for determining operating expenses (OPEX), which is only needed if the system is connected to the electrical power grid.

[0101] Some of the above inputs can be trivialized, if unknown. For example, the battery management function could be as complex as a reinforcement learning algorithm that is trained offline on historical data and refined online during the system operation, or as simple as a decision tree with just a few options, e.g., the battery is charged whenever the level dips below 20% of capacity and stops charging whenever it rises above 80% of capacity. As another example, the spot energy price model could be as complex as a stochastic pricing model that is time- and space-dependent and takes into account the futures contract market, or as simple as the average price observed in the past.

[0102] The planning tool finds the battery capacity that optimizes the capex plus opex per unit time.

[0103] In some embodiments, the core of the algorithm is a Monte Carlo simulator that finds the initial capacity that minimizes capex per unit time only by sweeping a possible range of capacities. This is worth applying in two cases: i) only capex is considered; and ii) capex and opex are considered, but the system can only draw energy from the grid (in other words, it can buy energy, but cannot sell energy).

[0104] In other embodiments, e.g., in which the system is connected to the grid, the core of the algorithm is a reinforcement learning algorithm that finds the initial capacity that minimizes capex plus opex per unit time by taking decisions about buying and selling energy. This is worth applying in two further cases: i) the system buys and sells energy as a background activity, namely, the main operational purpose of the system is different than buying and selling energy (for example, the system is a base station whose purpose is to provide connectivity, and it performs the buying and selling as a secondary activity); and ii) the sole purpose of the system is to buy and sell energy, thereby balancing the grid.

[0105] Referring back to the inputs to the planning algorithm, the battery degradation function that determines the capacity degradation as a function of battery level path 7. The battery level path is defined by the energy stored in the battery as a function of time: 7 — (■®'t)t>o. This is the most general approach that captures the whole complexity of the battery degradation process. Battery degradation is a complex phenomenon that that does not only depend on the number of cycles— complete charge and discharge of the battery— but also on the levels visited— for some battery technologies, such as lithium-ion, it is detrimental to exceed some levels, customarily 20% on the downside and 80% on the upside.

[0106] Another input to the planning algorithm is the minimum battery capacity threshold Cmin, which is the threshold in-use capacity below which the battery should be replaced. It can be expressed as a percentage of the initial capacity. For example, for lithium-ion batteries, it is known that when the battery capacity Ct at time t degrades below about 75% of the initial capacity Co, the degradation accelerates; therefore, it would be reasonable to set Cmin = 0.75or evenCmin= 0.810keepSOme margin of safety.

[0107] Further inputs briefly mentioned above are the energy supply and demand processes (denoted ^Es and ED, respectively). These are the probabilistic processes that define the energy supplied to the battery and the demand requested by the load. These energy supply and demand processes are complex because i) they are location specific, and ii) they have to take into account seasonality at several time scales.

[0108] The first point, i.e., the location-specific nature of these processes, is obvious when considering that different locations experience different weather patterns and are embedded in different climates, which affect the renewable energy capture. The second point, the seasonal aspect of these processes, refers to the superposition of seasonal effects in both supply and demand. For example, the supply of solar energy is characterized by yearly seasonality and daily seasonality, and the demand of energy can be seasonal as well depending on the system to be served (for a base station, seasonality depends, in part, on data traffic, and as such, there is daily seasonality (day vs night), weekly seasonality (weekdays vs weekends), and yearly seasonality (holidays). Moreover, these processes include a random component that is difficult to predict. This is the reason to adopt a probabilistic model for each of these processes.

[0109] Figures 6-9 illustrate these features of the energy supply and energy demand processes. Figure 6 illustrates the seasonality of incident shortwave (visible plus ultraviolet) per square meter in the Stockholm metropolitan area. The data takes into account the length of the day, the elevation of the Sun on the horizon, and the absorption of clouds. Figure 7 shows the variation in solar energy supply on a daily basis, for a specific day, in this case 21 June. Together, these figures illustrate the seasonal and daily variations of the energy supply, for a particular region.

[0110] The energy demand of the base station system, which is at least partially proportional to the traffic carried by the system, is also a probabilistic process with seasonal and intraday features. An example of seasonality in Internet traffic is shown in Figure 8, which shows daily average internet traffic in the Stockholm metropolitan area. Figure 9 shows intraday internet traffic for the same location. Again, these figures illustrate seasonal and daily variations, but in this case for internet traffic, which may be regarded as a proxy for the energy demands of the system.

[0111] Another input to the planning algorithm is the battery management function f, which is the function that determines how much energy to store when available and how much energy to provide when requested. The battery management function acts as a constraint on the planning tool, namely, the planning tool seeks to minimize capex plus opex for a given battery management function. Optimization of the battery management function, examples of which were described in detail above, can be performed separately from the planning algorithm or, in some embodiments, can be performed jointly with the selection of the initial battery capacity.

[0112] Another possible input to the planning algorithm is the spot energy price process t)t>otwhich is the probabilistic process that defines the energy spot price on the energy market. The probabilistic model of the process, denoted can be very complex, taking into account derivatives markets, or very simple, assuming that the price of energy is constant or stochastic (constant plus noise). The planning tool may take a model of the process as an input.

[0113] Maximum allowed downtime £ is another input to the planning algorithm. This is the maximum fraction of time that the base station system is allowed to fail. Failure is defined by a request for energy that is not supplied to the load. It can be expressed as a probability, or in percentage terms. For example, if it is reasonable to expect that a base station is down for 1 hour per year (there are 8760 hours in 1 year), then£= 1 / 8760 = 1.14 x 10“4

[0114] Notice that the planning tool takes into account the maximum allowed downtime of the base station system for a given battery management function, which implies that a not-well-optimized battery management function will be coupled with a larger battery, and vice-versa, a well-optimized battery management function will allow the system to run with a smaller battery, all else being equal. Directly from data, power sources in a particular location can be modeled. For example, Figure 10 and Figure 11 illustrate models for the shortwave incident radiation and wind speed, respectively, in San Diego.

[0115] For a given set of parameters and battery management system, the latter of which includes the battery management function and accounts for the specific battery technology or technologies in use and their degradation processes, the energy level, capacity degradation, and downtimes can be simulated for extended periods of time. These simulations can be used by a planning tool to optimize the selection of an initial battery capacity, e.g., using an optimization problem that consists of the minimization of the overall cost (capex plus opex) in terms of the initial battery capacity: min costc(Co, Cmin, PES, PEV, f) + costo(PK) Co

[0116] In this example optimization function, the first term is capital expenditure (capex) and the second term is operational expenditure (opex). Capex can be assumed to be proportional to , where T = T CQ, Cmin, PEa, PED, f) is the lifetime of the battery, which depends on all the inputs. The reason why capex is proportional to the initial capacity is that a battery can be made of many small units and the price of the final battery is generally linear as a function of the number of small units. The reason why the initial capacity is divided by the lifetime of the battery is that the battery must be changed with period equal to the lifetime, and capex is incurred again with the same frequency.

[0117] Figure 12 illustrates the optimization solution for the first of two example cases. In this example, the system is completely off-grid. The probability of downtime, which is shown as a solid line in Figure 12, with values mapped on the right side of the graph, decreases, as expected, as the initial battery capacity increases. In this example scenario, the probability of downtime approaches a minimum of about .03, as the initial battery capacity Coincreases. However, capex ^o / -^ ,which is represented in Figure 12 by the dashed curve and which has values mapped to the left side of the graph, has a minimum value as a function of initial battery capacity: A small battery is degraded faster because it will visit more often the extreme levels; a large battery lasts longer because its levels can be better managed but it also costs more. The planning tool can therefore choose the sweet spot, an initial battery capacity equal to 29 kWh in this case. To do so, it can run several Monte Carlo iterations corresponding to different possible weather situations and increasingly large batteries. The optimal battery capacity may be selected from the several battery capacities used in the Monte Carlo simulation, or interpolated from those capacities. Figure 13 illustrates results for a second scenario, where the grid is present but unreliable - in the illustrated example, the probability of the grid being operative is equal to 80%. As can be seen there is still an optimum battery capacity that minimizes the capex. The probability of downtime, which again is shown as a solid line in Figure 13, with values mapped on the right side of the graph, decreases as the initial battery capacity increases. Capex ,wich is represented in Figure 13 by the dashed curve and which has values mapped to the left side of the graph, again has a minimum value as a function of initial battery capacity.

[0118] In some embodiments, then, the planning algorithm performs a series of Monte Carlo simulations, using the parameters and modeled processes discussed above. This approach allows the simulation of many possible evolutions of the system (random supply and demand of energy, battery degradation, etc.) and finds an initial battery capacity that minimizes the total cost. In some embodiments or implementations, the algorithm may include a sensitivity analysis to check the resiliency of the system to external supply or demand shocks. Further, while the selection of the optimal initial battery capacity can be carried out using a given battery management function, the planning algorithm described here can in some cases be implemented so as to jointly optimize the initial battery capacity selection with one or more parameters of the battery management function.

[0119] Various embodiments or instances of the planning tools and planning algorithms described here can be understood as embodying or incorporating a method for selecting a battery capacity for a base station system that comprises base station circuitry, for communicating with one or more wireless devices and other components of a wireless network, and further comprises at least two electricity sources for powering the base station circuitry, where the at least two electricity sources include a battery system and one or more renewable energy sources, such as a solar power generation system and / or a wind power generation system. Figure 14 is a process flow diagram illustrating a generalization of such methods - as such, the illustrated method is intended to encompass the detailed techniques described above. Accordingly, where there are differences in terminology used in Figure 14 and its discussion below, compared to terminology used above, the terminology used with respect to Figure 14 should be understood to at least encompass the similar terms used above.

[0120] As shown at block 1410 in Figure 14, the illustrated method includes the step of modeling energy supply versus time for each of the one or more renewable energy sources, based on at least a location for the base station system. As shown at block 1420, the method further comprises modeling energy demand versus time for the base station system.

[0121] As shown at block 1430, the method still further comprises estimating an optimal initial capacity for the battery system, based on the modeled energy supply versus time for each of the one or more renewable energy sources, the modeled energy demand versus time for the base station system, and one or more parameters indicating maximum allowed downtime for the base station circuitry. This estimating may be further based on a replacement threshold parameter indicating a level of degradation at which the battery system should be replaced and a battery management function that takes into account an initial capacity of the battery system and a capacity degradation model of the battery system.

[0122] In some embodiments or instances, the estimating shown at block 1430 may be further based on historical data and / or a model representing cost over time for energy supply at the location from an electrical grid. In some of these or other embodiments or instances, the battery management function may further take into account historical data and / or a model representing cost over time for energy supply by the electrical grid at the location, in addition to the initial capacity of the battery system and the capacity degradation model.

[0123] In some embodiments, the estimating shown at block 1430 of Figure 4 may comprise performing a Monte Carlo simulation using the modeled energy supply versus time for each of the one or more renewable energy sources and the modeled energy demand versus time for the base station system, for each of a plurality of initial battery capacities from which a capacity may be selected or interpolated. In some other embodiments, the base station system is connected to the electrical grid and the estimating shown at block 1430 comprises running a reinforcement learning algorithm that minimizes a sum of battery system cost and base station system operating cost over time, by incorporating decisions to buy and sell electricity via an attachment to the electrical grid.

[0124] In some embodiments or instances, the estimating shown at block 1430 may be performed jointly with an optimization of one or more parameters of the battery management function.

[0125] Figure 15 illustrates example battery-capacity selection circuitry 1500, for use in selecting an initial battery capacity for a base station system like those described above, e.g., a base station system like the one illustrated in Figure 4, comprising comprises base station circuitry 410, a battery system 420, and one or more renewable electricity sources 430, such as a solar power generation system, or a wind power generation system, or a solar generation system and a wind power generation system.

[0126] The battery-capacity selection circuitry 1500 may comprise processing circuitry 1510 and memory 1520 storing program instructions for execution by the processing circuitry 1510, in various embodiments, and may be implemented in any of a variety of physical nodes or combinations of physical nodes.

[0127] The battery-capacity selection circuitry 1500 is configured, e.g., with appropriate program instructions stored in a computer-readable medium like the memory 1520, to estimate an optimal initial capacity for the battery system 420, based on a modeled energy supply versus time for each of the one or more renewable energy sources 430, a modeled energy demand versus time for the base station system, one or more parameters indicating maximum allowed downtime for the base station circuitry 410, a replacement threshold parameter indicating a level of degradation at which the battery system 420 should be replaced, and a battery management function that takes into account an initial capacity of the battery system 420 and a capacity degradation model of the battery system 420. The battery-capacity selection circuitry 1500 may be further configured to model the energy supply versus time for each of the one or more renewable energy sources 430, based on a location for the base station system, and model the energy demand versus time for the base station system, in various embodiments or instances, or may be simply supplied with one or both of these models.

[0128] In some embodiments or instances, the battery-capacity selection circuitry 1500 is configured to perform said estimating based further on historical data and / or a model representing cost over time for energy supply at the location from an electrical grid. In some of these or in other embodiments or instances, the battery management function may further take into account historical data and / or a model representing cost over time for energy supply by the electrical grid at the location, in addition to the initial capacity of the battery system and the capacity degradation model.

[0129] In some embodiments or instances, the battery-capacity selection circuitry 1500 is configured to perform the estimating by performing a Monte Carlo simulation using the modeled energy supply versus time for each of the one or more renewable energy sources 430 and the modeled energy demand versus time for the base station system, for each of a plurality of initial battery capacities, from which an initial battery capacity may be selected or interpolated, and estimating the optimal initial battery capacity based on the Monte Carlo simulation. In other embodiments or instances, e.g., where the base station system is connected to the electrical grid, the battery-capacity selection circuitry 1500 may be configured to perform the estimating by running a reinforcement learning algorithm that minimizes a sum of battery system cost and base station system operating cost over time, by incorporating decisions to buy and sell electricity via an attachment to the electrical grid. The battery-capacity selection circuitry 1500 may be configured to perform the estimating jointly with an optimization of one or more parameters of the battery management function.

[0130] The planning tool and algorithms described herein seek to minimize the cost of the battery per unit time (capex per unit time) plus the cost of operating the battery per unit time (opex per unit time). The planning tool and algorithms can be applied to a variety of systems and in a variety of scenarios, since they take as inputs several processes and variables that may be technology-, time-, and location-specific. The cost of deploying and operating the system is minimized under a minimum operational quality constraint (defined by the maximum allowed downtime).

Claims

CLAIMSWhat is claimed is:

1. A method for selecting a battery capacity for a base station system comprising base station circuitry for communicating with one or more wireless devices and other components of a wireless network and further comprising at least two electricity sources for powering the base station circuitry, the at least two electricity sources comprising a battery system and one or more renewable energy sources, the method comprising: modeling (1410) energy supply versus time for each of the one or more renewable energy sources, based on a location for the base station system; modeling (1420) energy demand versus time for the base station system; and estimating (1430) an optimal initial capacity for the battery system, based on the modeled energy supply versus time for each of the one or more renewable energy sources, the modeled energy demand versus time for the base station system, one or more parameters indicating maximum allowed downtime for the base station circuitry, a replacement threshold parameter indicating a level of degradation at which the battery system should be replaced, and a battery management function that takes into account an initial capacity of the battery system and a capacity degradation model of the battery system.

2. The method of claim 1, wherein said estimating (1430) is further based on historical data and / or a model representing cost over time for energy supply at the location from an electrical grid.

3. The method of claim 1 or 2, wherein the battery management function further takes into account historical data and / or a model representing cost over time for energy supply by an electrical grid at the location.

4. The method of any one of claims 1-3, wherein the one or more renewable electricity sources comprises one or more of any of the following: a solar power generation system; and a wind power generation system.

5. The method of any one of claims 1-4, wherein said estimating (1430) comprises performing a Monte Carlo simulation using the modeled energy supply versus time for each of the one or more renewable energy sources and the modeled energy demand versus time for the base station system, for each of a plurality of initial battery capacities.

6. The method of any one of claims 1-4, wherein said estimating (1430) comprises running a reinforcement learning algorithm that minimizes a sum of battery system cost and base station system operating cost over time.

7. The method of claim 6, wherein the base station system is connected to an electrical grid and wherein the reinforcement learning algorithm incorporates decisions to buy and sell electricity via an attachment to the electrical grid.

8. The method of any one of claims 1-7, wherein said estimating (1430) is performed jointly with an optimization of one or more parameters of the battery management function.

9. Battery-capacity selection circuitry (1500) for use in selecting a battery capacity for a base station system that comprises base station circuitry (410), a battery system (420), and one or more renewable electricity sources (430), wherein the battery-capacity selection circuitry (1500) is configured to: estimate an optimal initial capacity for the battery system (420), based on a modeled energy supply versus time for each of the one or more renewable energy sources (430), a modeled energy demand versus time for the base station system, one or more parameters indicating maximum allowed downtime for the base station circuitry (410), a replacement threshold parameter indicating a level of degradation at which the battery system (420) should be replaced, and a battery management function that takes into account an initial capacity of the battery system (420) and a capacity degradation model of the battery system (420).

10. The battery-capacity selection circuitry (1500) of claim 9, being further configured to: model the energy supply versus time for each of the one or more renewable energy sources(430), based on a location for the base station system; and model the energy demand versus time for the base station system.

11. The battery-capacity selection circuitry (1500) of claim 9 or 10, wherein the battery-capacity selection circuitry (1500) is configured to perform said estimating based further on historical data and / or a model representing cost over time for energy supply at the location from an electrical grid.

12. The battery-capacity selection circuitry (1500) of any one of claims 9-11, wherein the battery management function further takes into account historical data and / or a model representing cost over time for energy supply by an electrical grid at the location.

13. The battery-capacity selection circuitry (1500) of any one of claims 9-12, wherein the one or more renewable electricity sources (430) comprises a solar power generation system, or a wind power generation system, or a solar generation system and a wind power generation system.

14. The battery-capacity selection circuitry (1500) of any one of claims 9-13, wherein the batterycapacity selection circuitry (1500) is configured to perform said estimating by performing a Monte Carlo simulation using the modeled energy supply versus time for each of the one or more renewable energy sources (430) and the modeled energy demand versus time for the base station system, for each of a plurality of initial battery capacities, and estimating the optimal initial battery capacity based on the Monte Carlo simulation.

15. The battery-capacity selection circuitry (1500) of any one of claims 9-13, wherein the batterycapacity selection circuitry (1500) is configured to perform said estimating by running a reinforcement learning algorithm that minimizes a sum of battery system cost and base station system operating cost over time.

16. The battery-capacity selection circuitry (1500) of claim 15, wherein the reinforcement learning algorithm is configured to incorporate decisions to buy and sell electricity via an attachment to the electrical grid when the base station system is connected to an electrical grid.

17. The battery-capacity selection circuitry (1500) of any one of claims 9-16, wherein the batterycapacity selection circuitry (1500) is configured to perform said estimating jointly with an optimization of one or more parameters of the battery management function.

18. The battery-capacity selection circuitry (1500) of any one of claims 9-17, comprising processing circuitry (1510) and memory (1520) storing program instructions for execution by the processing circuitry (1510), the program instructions being configured to cause the battery-capacity selection circuitry (1500) to perform said estimating.

19. A computer-program product comprising program instructions configured to cause processing circuitry (1510) to carry out a method according to any one of claims 1-8.

20. A computer-readable medium comprising the computer-program product of claim 19.

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