FIELD OF THE INVENTION

The present invention relates to a controller for a photovoltaic generation and energy storage system.

BACKGROUND TO THE INVENTION

The significant cost reduction in photovoltaic (PV) systems residential-scale photovoltaic (PV) systems coupled with the gradually falling prices of residential-scale battery energy storage (BES) systems is shaping the way for a future in which consumers could locally supply most of their energy needs, thus reducing their carbon emissions and energy grid dependence (i.e. , reducing grid imports). Consumers with residential-scale BES systems will be able to store the excess of their PV generation (i.e., generation minus demand) during the day and use it later at night, cutting down electricity bills.

Commercially available residential BES systems also have technical capabilities that allow them to implement control strategies such as load following and tariff arbitrage. Currently these control strategies are designed from the perspective of what is perceived to be good for the consumer. As a result, such systems, hereafter referred to as off-the-shelf (OTS) BES systems, might not charge during times of high PV generation. That is because consumer-led control strategies prioritize storing as much excess PV generation as possible, it is likely that a full state of charge (SOC) of the BES is reached even before peak PV generation periods. Whilst beneficial to the consumer, reverse power flows from multiple sites can potentially result in technical issues, such as overvoltage and thermal congestion, on low voltage (LV), (e.g., <400V line-to-line in Europe and most of the world and <208V line-to-line in North America) and medium voltage (MV) networks (e.g., >1 kV). However, there is an opportunity to adopt different control strategies that could allow BES systems to significantly reduce or even eliminate reverse power flows and, hence, the corresponding network issues. This has the potential to avoid infrastructure work to reinforce the network. As the cost of reinforcing the network is ultimately passed on to the consumer, power control schemes that take into account the impact on the network are of benefit both to consumers and network providers.

Although the use of residential-scale BES systems is a relatively new concept, a few papers have tried to address the aforementioned issues by proposing control schemes to manage technical problems in distribution networks. Most proposed solutions have focused primarily on voltage management; one of the dominant constraints in LV networks. For instance, the paper H. Sugihara, K. Yokoyama, O. Saeki, K. Tsuji, and T. Funaki, "Economic and Efficient Voltage Management Using Consumer-Owned Energy Storage Systems in a Distribution Network With High Penetration of Photovoltaic Systems," IEEE Transactions on Power Systems, vol. 28, no. 1 , pp. 102-11 1 , 2013 proposes an optimization-based control scheme that allows Distribution Network Operators (DNOs) (also known as Distribution Network Service Providers) to manage voltage issues by providing reactive compensation through the BES systems of consumers. However, it is shown that BES systems have to reduce their charging power rate during periods with voltage issues so that the inverter can absorb reactive power; hence, limiting the amount of energy that can be stored.

S. Hashemi, J. 0stergaard, and G. Yang, "A Scenario-Based Approach for Energy Storage Capacity Determination in LV Grids With High PV Penetration," IEEE Transactions on Smart Grid.pp. 1514-1522, 201 ; and F. Marra, G. Yang, C. Traeholt, J. 0stergaard, and E. Larsen, "A Decentralized Storage Strategy for Residential Feeders With Photovoltaics," IEEE Transactions on Smart Grid, pp. 974-981 , 2014, propose control methods that force BES systems to start charging only once a predefined PV generation threshold is reached. One of the main issues, however, is that the BES system would have unused capacity during low PV generation days. Furthermore, these studies did not quantify the stored energy and, therefore it is unclear to what extent the approaches still benefit consumers. Despite the effectiveness of the above studies, the use of off-line optimization techniques to find the corresponding settings requires extensive network information (e.g., topology) that most Distribution Network Operators (DNOs) might not have readily available.

More recently, and in the context of investigating more practical and scalable BES control schemes, M. N. Kabir, Y. Mishra, G. Ledwich, Z. Y. Dong, and K. P. Wong, "Coordinated Control of Grid-Connected Photovoltaic Reactive Power and Battery Energy Storage Systems to Improve the Voltage Profile of a Residential Distribution Feeder," IEEE Transactions on Industrial Informatics, vol. 10, no. 2, pp. 967-977, 2014; and [1 1] M. Zeraati, M. E. H. Golshan, and J. Guerrero, "Distributed Control of Battery Energy Storage Systems for Voltage Regulation in Distribution Networks with High PV Penetration," IEEE Transactions on Smart Grid, vol. PP, no. 99, pp. 1-1 , 2016 propose the adoption of local droop-based control methods to define the operation of residential-scale BES systems to manage voltage issues in LV networks. Such schemes, however, require off-line voltage sensitivity analyses to define the corresponding droop settings. This, unfortunately, limits their scalability given that the corresponding droop curves have to be tailored to each of the thousands of LV networks in a given region. Additionally, the adoption of droop-based control approaches to manage voltage issues might lead to unfair cases where BES systems connected at the end of the feeder might be participating more often in the voltage management compared to other BES systems.

In the majority of prior approaches, the reduction of grid imports by the consumer, which is the primary goal of residential-scale BES systems, is not fully addressed and in some cases not even considered. The inventors have realized that this, in practice, creates challenges as consumers are unlikely to be willing to have their BES systems managed for the benefit of the networks.

There is a need for a control strategy for BES systems to reduce voltage and thermal issues whilst still benefiting consumers.

SUMMARY

Described embodiments provide a control technique that mitigates against high PV exports (the cause of network issues) by adapting the BES charging power proportionally to the PV generation. In some embodiments, the power charging and discharging rates are constantly calculated throughout the day based on data indicative of clear-sky irradiance, PV generation, demand, and state of charge; significantly reducing reverse power flows and ensuring adequate storage capacity the next morning.

An embodiment of the invention provides a controller for an energy storage and photovoltaic generation system comprising a photovoltaic generator and a battery, the controller configured to:

control the battery, during a first time period beginning after the photovoltaic generator stops generating energy, to gradually export energy in excess of demand to a distribution network so that the battery reaches a defined minimum stored energy by the beginning of an energy storage period;

control relative proportions of energy generated by the photovoltaic generator in excess of demand that are a) stored by the battery and b) exported to the distribution network during the energy storage period by: determining a desired charging profile that (i) has a gradient that follows the gradient of an estimated clear-sky photovoltaic generation profile of the photovoltaic generator, and (ii) if followed will result in the battery reaching a defined maximum stored energy by the end of the energy storage period; and

controlling storage of energy in the battery in accordance with the desired charging profile.

In an embodiment, the controller determines the desired charging profile by modifying the estimated generation profile until the area under the curve of the estimated generation profile corresponds to the amount of energy required for the battery to reach the defined maximum stored energy from the defined minimum stored energy and setting the modified generation profile as the desired charging profile.

In an embodiment, the controller periodically updates the desired charging profile based on the state of charge of the battery.

In an embodiment, the estimated generation profile is a clear-sky generation profile.

In an embodiment, the estimated generation profile is a forecast generation profile.

In an embodiment, the controller is further configured to control the battery to supply energy during the charging period when demand exceeds photovoltaic generation.

In an embodiment, the defined maximum stored energy corresponds to a full state of charge of the battery.

In an embodiment, the defined minimum stored energy corresponds to an allowable minimum state of charge of the battery.

In an embodiment, the first time period starts when estimated photovoltaic generation stops and ends after estimated photovoltaic generation begins.

In an embodiment, the first time period ends at the beginning of the desired charging profile. Another embodiment provides an inverter comprising the controller.

Another embodiment provides an energy storage and photovoltaic generation system comprising the controller.

Another embodiment provides a method of controlling an energy storage and photovoltaic generation system comprising a photovoltaic generator and a battery, method comprising to: controlling the battery, during a first time period after the photovoltaic generator stops generating energy, to gradually export energy in excess of demand to a distribution network so that the battery reaches a defined minimum stored energy by the beginning of an energy storage period;

controlling relative proportions of energy generated by the photovoltaic generator in excess of demand that are a) stored by the battery and b) exported to the distribution network during the energy storage period by:

determining a desired charging profile that (i) has a gradient that follows the gradient of an estimated photovoltaic generation profile of the photovoltaic generator, and (ii) if followed will result in the battery reaching a defined maximum stored energy by the end of the energy storage period; and

controlling storage of energy in the battery in accordance with the desired charging profile.

In an embodiment, the method comprises determining the desired charging profile by modifying the estimated generation profile until the area under the curve of the estimated generation profile corresponds to the amount of energy required for the battery to reach the defined maximum stored energy from the defined minimum stored energy and setting the modified generation profile as the desired charging profile.

In an embodiment, the method comprises periodically updating the desired charging profile based on the state of charge of the battery.

In an embodiment, the estimated generation profile is a clear-sky generation profile.

In an embodiment, the estimated generation profile is a forecast generation profile. In an embodiment, the method comprises controlling the battery to supply energy during the charging period when demand exceeds photovoltaic generation.

In an embodiment, the defined maximum stored energy corresponds to a full state of charge of the battery.

In an embodiment, the defined minimum stored energy corresponds to an allowable minimum state of charge of the battery.

In an embodiment, the first time period starts when estimated photovoltaic generation stop and ends after estimated photovoltaic generation begins.

In an embodiment, the first time period ends at the beginning of the desired charging profile.

Another embodiment provides computer program code comprising instructions which when executed by a processor implements the above method.

Another embodiment provides a non-transitory computer readable medium comprising the computer program code.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described in relation to the accompanying drawings in which:

FIG. 1A illustrates an example of desired charging and discharging profiles.

FIG. 1 B illustrates an example of how desired charging and discharging profiles are updated responsive to changes in conditions.

FIGs. 2A-2C provide comparative household level operation data for different controllers.

FIG. 3 is an example medium voltage feeder topology.

FIGs. 4A-4C illustrate comparative voltage profile performance for different controllers.

FIGs. 5A-5C illustrate comparative utilization level performance for different controllers.

FIG. 6 illustrates average household net profiles for different controllers.

FIG.7 contains comparative grid dependency index data for different controllers.

FIG. 8 illustrates an example PV generation and battery storage system.

FIG. 9 illustrates an example inverter. FIGs. 10 to 12 illustrate further example PV generation and battery storage systems.

DETAILED DESCRIPTION

Embodiments of the invention provide a controller for systems that combine photovoltaic generation, one or more loads and battery storage. Embodiments of the invention are described in relation to residential-scale systems but the controller of the embodiment can be used in other implementations where it is desirable to control energy inputs and PV exports. Embodiments of the invention reduce high magnitude PV exports by adapting the BES charging power proportionally to the PV generation, and ensuring available capacity by at least partially discharging the battery overnight.

The combination of these techniques allows a similar total PV export to existing consumer centric strategies while resulting in a more gradual rate of PV exports where the peak magnitudes of PV exports are reduced relative to prior control strategies. As a result, the proposed controller mitigates against power exports being too high for the network to which it is connected and against thermal and voltage problems arising in the network from such power exports.

To achieve this, the controller employs an estimate of maximum PV generation. In one example, the daily maximum PV generation is estimated by computing ideal clear-sky generation profiles and then, for example, storing the estimated profile in the PV device so that the PV device can retrieve it. The estimated profiles can be stored elsewhere, for example in the PV inverter, or the BES inverter or the controller or any other device that can store data. As mentioned below, the profiles can also be stored somewhere remotely and accessed by the controller through communication links (i.e., wired, wireless). It is advantageous to store the profiles in the proposed controller so that access to the profiles is direct and not reliant on a communication link.

In one example, the estimated profile can be stored during configuration of the device, for example, by a technician downloading estimated profile data localized to the installation or by a configuration routine that contacts a server over a data network to retrieve configuration data specific to an input location. Depending on the amount of data that can be stored in the device, the estimated profiles can be individual daily profiles for each day of the year, or one daily profile representing each month or one daily profile representing each season, etc. The controller employs a desired charging profile that follows the bell-shape of the maximum PV generation with an area that matches the BES capacity, in this example, an ideal charging profile. This directly tackles reverse power flows as the BES will charge with higher power rates during critical times, reducing the amount of energy exported at these times.

FIG. 1A is a graph showing of active power 104 over a 24 hour time period 102 and shows an example of a desired charging profile 120 and an ideal clear-sky generation profile 1 10 to produce store a desired amount of energy, in this example 10kWh (which is the area under the curve 120).

Fig. 1 B illustrates that in practice, at any given time, surplus PV generation can be below that expected by the ideal charging profile. In this example, there is a gap 140 in power generation. That is before the gap, a first portion 122A of the charging profile matches the desired charging profile 120 shown in FIG. 1A but after the gap the corresponding power charging rate is re calculated by the controller using actual measurements (PV generation and demand) to produce an updated desired charging profile 122B to deliver storage of the desired amount of energy (again 10kWh) over the two charging profiles 122A.122B. While the embodiment, uses ideal clear-sky generation profiles, other embodiments could use forecast data (for example, forecast radiance obtained over a data connection) or recent measured PV generation in order to obtain an estimated generation profile). Using forecasting can enhance the ability of the controller to cater for uncertainties such as cloud-effects, and changes in demand.

The above charging technique is enhanced by ensuring the BES has an adequate available capacity at the beginning of the charging period. To achieve this, a baseline discharging power rate 130A.130B is calculated by the controller 820 taking into account the time at the end of the maximum PV generation profile, the corresponding SOC, and the time at the beginning of the charging period next day by which a defined SOC should be achieved. The controller 820 controls the battery to gradually export energy in excess of demand from loads to the distribution network to ensure that the consumer makes the most of the BES system. As shown in FIG. 1 B the discharging power rate is updated by the controller 820 whenever demand exceeds the baseline value. For example, following greater than average discharge of the battery in section 132A, energy is discharged more gradually. See section 132B as an illustrative example for a case where FIG. 1 B shows a repeating cycle). That is, as necessary to gradually export energy to reach the defined SOC at the beginning of the charging period, the baseline discharging power is updated by the controller.

Referring to FIG. 8 there is shown an embodiment of a PV generation and battery storage system 800. The system 800 employs a hybrid DC coupled inverter connection where a controller 820 is imbedded within the inverter 810. The inverter 810 is connected to the PV generation 830, a BES 850, and a distribution board 840. The distribution board is connected to household loads 860 and the electricity grid 870. A sensor 880 measures energy imported and/or exported to the grid 870 and is connected to the controller 820A via communications link 825.

As shown in FIG. 9, an example inverter 810 has a DC to DC converter 814 with Maximum Power Point Tracking (MPPT) control, connected via DC links 940, 942 to PV generation 830 and BES 850. The DC to DC converter 814 is connected to DC to AC converter inverter 816 which, in turn, is connected via AC link 950 to the power distribution board. Both DC to DC converter 814 and DC to AC converter inverter 816 are under control of microcontroller 812. In this respect, while controller 820A is shown as separate to microcontroller 812 in Figure 9 (and it can be implemented as a separate controller) controller 820A can also be implemented by microcontroller 812. Indeed, depending on the capabilities of existing controllers, controller 820A can be implemented by upgrading the firmware of an existing controller. As a result, persons skilled in the art will appreciate that controller 820 can be implemented by any appropriate processing device based on computer program instructions stored in an associated memory.

FIG. 10 shows an alternative embodiment of a PV generation and battery storage system 1000, where instead of being embedded in the inverter, the controller is provided as an external controller 820B connected to inverter 1010 and sensor 880 via communications link 1025.

FIG. 11 shows an alternative embodiment of a PV generation and battery storage system 1 100. In this embodiment, a first inverter 1 15 is connected between the PV generation 830 and the distribution board 1140. A second inverter is connected between distribution board 1 140 and BES 850. In this example, an external controller 820C is connected to the second inverter 1 100 in order to implement the control technique. External controller 820C is connected via communication link 1 125 to sensor 880.

FIG. 12 is a variant system 1200 on FIG.1 1 where controller 820D is embedded in inverter 1210 and connected to sensor 880 via communications link 1225.

Desired Charging Power Profile

In the embodiment, the desired charging power profile is calculated by the controller 820 at each sampling interval, At (minutes). From the current instant i to the time at which PV generation ends, b, this profile is defined by a set of charging power values, C _t (kW), where t E [ϊ, b] in steps of At. In the embodiment, this is calculated by the controller 820 iteratively reducing the corresponding clear-sky generation profile (a set of maximum PV power generation values, CS _t , where t E [ϊ, b] in steps of At), so that the resulting area (i.e. , energy to be stored) is less or equal to the energy required to achieve full SOC, as in (1). That is, the clear-sky generation profile is adjusted

where E ^s , E and h ⁺ are the rated capacity (kWh), stored energy (kWh), and the charging efficiency, respectively.

In example embodiments, the clear-sky power generation profile is calculated beforehand considering the position of the Earth with respect to the Sun (changing every day, every hour) as well the characteristics of the PV installation(s) (e.g.., geographical location, panel tilt, azimuth) as shown in the example BES charging profile of Figs. 1 (a) 1 (b). As the control strategy is adaptive, the clear-sky power generation profile does not need to be perfect, as the controller 820 will adjust the rate at which it charges the battery as discussed below. It will be apparent that as a result, the desired charging profile follows the gradient of the estimated clear-sky PV generation profile. As a result, the charging profile tends to keep the maximum power export to the grid during any time period to a minimum, and if followed will ensure the battery will be fully charged before the end of photovoltaic generation (assuming normal operation). It also has the result of reducing the corresponding voltage at the connection point of the load, PV system and battery.

Models found in G. M. Masters, Renewable and efficient electric power systems. Hoboken, NJ: John Wiley & Sons, 2004, p. 654 or readily available tools such as the one in Richardson and M. Thomson, “Integrated simulation of Photovoltaic Micro-Generation and Domestic Electricity Demand: A one minute resolution open source model”, United Kingdom: Loughborough University, 201 1. Available: https://goo.gl/igXxrdcan be utilized to produce these daily clear-sky profiles.

Based on the above, the desired charging power profile for a particular day and PV installation can be produced using Algorithm 1 , where n is an arbitrarily small number (a fraction of the peak clear-sky PV power generation). The adequate definition of this number is a trade-off between n computational efficiency (larger n) and accuracy (smaller n).

Baseline Discharging Power Value

The baseline discharging power value, D (kW), is defined, at the current instant t , to ensure that the BES system will adequately discharge at the start of the next charging period, a (time at which PV generation starts). This is given by (2).

Ef - E min

D = h (2)

(a - 0/60

where (a - t) is the remaining period (minutes) until the start of the next charging period, rf is the discharging efficiency and E ^mm (kWh) is a pre-defined minimum energy that should always be stored (manufacturer or user preference) - i.e. a base state of charge.

Start (a) and End (b) of the Charging Period

A variable definition of a and b is employed, as different times of the year, as well as different PV and BES system configurations (i.e., size, tilt, orientation etc.) result in different start and end of the charging period.

The start (a) and end (/?) of the charging period, shown in in FIGs. 1A and 1 B, are defined at the beginning of each day (i.e., t= 1 as shown in A3-3). The start of the charging period is defined based on A2-2 and A2-3, where the reduced clear-sky profile, i.e., the ideal charging profile C _t , calculated in Algorithm 1 is passed to Algorithm 2 (A2-2). Then, the value a is defined as the first period where the C _t is larger than zero (i.e., BES starts to charge, shown in A2-3). The end of the charging period b, on the other hand, is calculated based on the clear-sky profile, CS _t . It is defined as the last period where CS _t is larger than zero (i.e., PV generation stops, shown in A2-1).

Daily Operation of BES System

Based on the desired charging profile and baseline discharging value at instant t, the daily operation of the BES system (split into a number of discrete P periods), is implemented by the controller 820 using Algorithm 3, where P and P are the demand and PV generation (kW), respectively. The BES system power output, Pf, and energy stored in the BES system are constrained as shown in (3) and (4), respectively.

R? e [E1,R*] (3)

Ef E \EP x ( 100 - DOD)/ 100 , EP ] (4)

where P _ and P ^s are the minimum (discharging) and maximum (charging) power ratings (kW), respectively, and DoD is the maximum permitted depth of discharge (%).

In the embodiment, Algorithm 3 is designed to maximize benefits to consumers. As such, during the charging period [a, b], any time there is a positive net demand, i - Pf > 0, the available energy stored will be used (lines A3-12, A3-13). Similarly, outside the charging period, the battery will help meeting the demand if larger than the baseline discharging power rate (A3-8, A3-9). That is energy is gradually discharged but the rate of discharge is adjusted based on actual demand.

Algorithm 1 : Ideal Charging Power Profile

A1-1 : Let

A1-2: while (1) = False do

A1-3: for t = i to b do

A1-4: C _t <- C _t - n

A1-5: end for

A1-6: C _t [C _t < 0] <- 0

A1-7: end while

A 1-8: return C _t

Algorithm 2: Defining a and b

A2-1 : b <- CS _t [CS _t > 0]_ _x

A2-2: C _tfº[ i _,G] <- Algorithm 1

A2-4: return a, b

Algorithm 3 Daily operation of the BES system

A3-1 : for t = 1 to P do

A3-2: if t = 1 do

A3-3: a, b <- Algorithm 2

A3-4: end if

A3-5: Measure E , P ·, P

A3-6: if (t < a or t > b) do A3-7: if Ef ³ E ^min do

A3-8: D <- (2)

A3-9: Pf <- - ma x(D, Pf - P )

A3-10: end if

A3-1 1 : else

A3-12: e _[i, / _?] <- Algorithm 1

A3-13: Pf <- min(Ci, Pf - P )

A3-14: end if

A3-15: end for

EXAMPLE

In an example, three performance metrics are used to quantify the performance of the control approaches with respect to the network and BES owners.

Utilization Level. This metric is the maximum apparent power of a transformer or current flowing in a line divided by its corresponding rated capacity (calculated at every At).

Percentage of consumers with voltage problems. This metric takes the daily voltage profile at each consumer connection point and checks compliance with the corresponding standard.

Grid Dependency Index (GDI). Using equations (5)-(6), this metric calculates the percentage of a household’s energy consumption that originated from the grid. This is done for the horizon of interest (e.g., a month) split into discrete Y periods.

Without PV generation (and BES), the GDI value is 100%. Therefore, the lower the GDI, the more beneficial for the consumers as it leads to lower electricity bills.

In this example, the controller 820 is referred to as an adaptive decentralized (AD) controller 820 as the algorithm is adaptive and not subject to centralized control. In the example, the performance of the AD controller 820 is assessed and compared against the OTS control considering household and network level analyses. For the latter, a real Australian MV feeder with realistically modelled LV networks is considered. The yearly effects on BES owners are also quantified. For completeness, simulations are also performed for the case where consumers do not have a BES system installed (“PV only” case). In the example, the distribution system analysis software package OpenDSS described in R. C. Dugan and T. E. McDermott, "An open source platform for collaborating on smart grid research," in Power and Energy Society General Meeting, 201 1 IEEE, 2011 , pp. 1-7, and Python are used to run the time-series, three-phase four-wire power flows as well as the control approaches.

A real 22kV MV feeder 300 with 79 residential, underground LV networks from Victoria, Australia, owned and operated by the DNO AusNet Services, is used in the example. The MV feeder, shown in FIG. 3, is one of multiple feeders supplied by a 2x33MVA, 66kV/22kV primary substation 325. For simplicity, the voltage at the head of the MV feeder is considered to be constant at 22kV (1 0pu) which corresponds to the voltage target setting used by the on-load tap changers (OLTCs) at the substation. Each LV network is supplied by a 22kV/0.433kV distribution transformer (natural boost of 8%) with off-load tap position number 1 (reducing 5%), i.e. , effectively transforming to 411V. Distribution transformers (i.e., secondary transformer) are shown as circles in Fig. 3. Their rated capacities can be identified using the color map 310.

The total number of consumers in each LV network is assumed to be equal to the distribution transformer rated capacity divided by 4kVA (typical after diversity maximum demand for residential consumers in this area). Consequently, the total number of (single-phase connected) residential consumers in the MV feeder is estimated to be 4,626. Based on the number of consumers, the LV networks are realistically modeled considering electrical distribution substation standards and design manuals used in Australia. The resulting total number of LV feeders is 175 with a median of 1 feeder per transformer and an average main path length of 500m. The total conductor length of the integrated MV-LV network amounts to 165km.

A pool of 30-min resolution, year-long (i.e., 17,520 points), anonymized smart meter demand data, collected from 342 individual residential customers in the year of 2014, as well as, a 30-min resolution, year-long normalized PV generation profile (also recorded in 2014) are used for the analyses. Using this data, the yearly-long demand and generation profiles were broken down into daily profiles, i.e., a pool of ~30,000 daily demand profiles and 90 daily PV generation profiles per season. Moreover, 30-min resolution, ideal clear-sky PV generation profiles are created for each day of the year using the tool developed in I. Richardson and M. Thomson. (201 1). Integrated domestic electricity demand and PV micro-generation model, and considering PV panels with tilt angle of 37°, azimuth of 0° (north facing), and Melbourne, Victoria, Australia (latitude: -37.81 , longitude: 144.96) as the geographical location. This tool, once the day of year and the configuration information of the installed PV panel (i.e., geographical location, panel tilt, azimuth) are provided, high resolution (i.e., 1-min) clear-sky irradiation profiles can be produced.

Household Level Analysis

To demonstrate the operation of the two BES controllers (i.e., OTS and AD), a household with a 5.5kWp PV system and a 5kW/13.5kWh BES system (100% depth of discharge and 88% round- trip efficiency) is investigated using a summer day. To adopt a realistic SOC at the beginning of the day of interest, the prior day is also considered in which the BES system starts from empty.

FIG. 2A presents the behavior of the household’s net demand 231 when only the PV system is installed. A large amount of the household’s demand 220 is supplied by the PV generation 210. More specifically, 49% of the daily household demand is supplied by the PV system. It is important, however, to highlight that due to the high PV generation and low demand around midday, the household’s net profile results in significant exports. If multiple neighboring consumers have the same behavior, then, the resulting reverse power flows can lead to voltage rise and congestion issues in the network.

From the perspective of the consumer, the installation of a BES system with an OTS control brings major benefits, as shown in FIG. 2B. In this case, the net demand 232 is never positive; all the demand is supplied by the PV and BES systems, i.e., the consumers have become self-sufficient.

However, from the perspective of the network, the OTS controller is unable to reduce the PV exports during midday (>4kW). This, as explained above, is because the BES system does not fully discharge overnight and, hence, starts charging 251 all the excess of PV generation with a relatively high SOC 241 (50% around 7:30am). Therefore, the full SOC is reached before midday. PV exports are not reduced after that point.

The AD controller 820 of the embodiments overcomes all the limitations of the OTS controller while still making the householder self-sufficient. As shown in FIG. 2C, the AD controller 820 follows the early morning demand, achieving full discharge by 8am ensuring that the full storage capacity is available throughout daylight. Note in some embodiments, the BES may not be fully discharged, for example, to leave a defined buffer of stored energy (E ^min ). From time a=8:30am (defined using Algorithm 2), the BES system starts to adaptively charge with the power rate specified by the AD controller 820. The charging profile 252 resembles the shape of clear-sky PV generation, allowing a progressive increase in the SOC 242. This, in turn, significantly reduces exports (<2kW). Around 5pm, full SOC is reached. Between this time and time /?=8pm, PV generation is smaller than demand, therefore the BES systems discharges enough to avoid grid imports. After 10pm, when the PV system stops generating, the household demand is higher than the baseline discharging power value (0.85kW), hence the BES system is discharging with a power rate equal to the demand. Thereafter, once the demand 233 becomes lower than the baseline, the BES system continues discharging with the baseline discharging power (i.e. , the SOC 242 progressively reduces). While this results in power exports, the values are significantly smaller than those found by the OTS and, therefore, unlikely to lead to network issues. More importantly, this ensures that the specified storage capacity (in this case, full capacity, i.e., E ^min = 0), will be available for the next charging period.

This analysis demonstrates that the performance of the controller 820 can significantly enhance the BES system operation in a way that is beneficial to the network with limited (or no) impact on consumers, despite the limited information considered (only clear sky generation profile).

Table I: Summary of Technical Issues in MV-LV Network

PV Only OTS AD

Consumers with Voltage Issues (%) 18 10 0

Max Utilization of Transformers (%) 125 125 68

Max Utilization of MV Lines (%) Ϊ86 171 82

Max Utilization of LV Lines (%) TΪ0 105 50

MV-LV Network Analysis

The performance of the controller 820 as well as the OTS controllers was also assessed using a real Australian integrated MV-LV network considering 100% of PV penetration (i.e., 100% of LV consumers with PV systems). Real demand and PV generation data recorded on the 7th and 8th January (summer, high solar irradiance) are used. The size of the PV systems is based on new installation statistics from 2016 onwards where the proportion of PV installations with 2.5, 3.5, 5.5 and 8kWp is 10, 30, 50 and 10%, respectively. The storage systems used for the analysis have a capacity of 5kWp/13.5kWh (100% depth of discharge and 88% round-trip efficiency). This BES system is currently available in the Australian market and is popular with residential consumers. In this, example, the value of parameter n (shown in Algorithm 1) is set to be equal to 0.001. This value was selected as it results to an ideal charging profile with an area being very close to the energy storage capacity. For example, considering a battery with a capacity of 13.5kWh, the resulted area of the ideal charging profile (using n=0.001) will be equal to the 13.499kWh, corresponding to a mean square error of 2.5e-5. Through a trial-and-error approach we have concluded that this value results in a good trade-off between accuracy and computational efficiency, as larger values would result in higher error, while smaller values would result in higher computational times.

The percentage of consumers with voltage problems is quantified based on the Australian Electricity Distribution Code , which states that a consumer is non-compliant if the steady-state voltage (>1 minute) exceeds the 10% of the nominal 230V line-to-neutral voltage.

Voltage Issues

FIGs. 4A to 4C show the daily 402 30-min voltage 404 profiles 408 of all 4,626 LV consumers for the case where households do not have BES systems installed (PV only - FIG. 4A) and the cases where BES systems are installed and controlled for both OTS controllers (FIG. 4B) and the AD controller 820 (FIG. 4C).

FIG. 4A shows that without a BES system, many consumers experience voltages above a statutory limit 406 (i.e., 1.1 p.u.) during the peak generation period. As shown in Table I, almost a fifth of the consumers were found to be non-compliant with the voltage statutory limit. When adopting the BES systems with OTS controller, shown in FIG. 4B, voltage rise issues are reduced slightly. As a result, the number of non-compliant consumers goes down to 10%. On the other hand, the AD controller 820, FIG. 4C, succeeds in mitigating all voltage issues.

The behavior seen in these voltage profiles can be explained considering the average net profiles of all consumers presented in FIG. 6, for each case. For the OTS controller, despite the reductions in exports (8am - 1 pm) compared to the PV-only case, the net demand profile continues as if no BES system was installed; resulting in similar voltage profiles 61 1 , 612. With the AD controller 820, exports are significantly reduced and, hence, the voltage profile 613. It is also important to highlight that the small exports seen in morning hours do result, as expected, in higher voltages than the PV only 61 1 and OTS 612 cases. However, these values are far from the statutory limit. Thermal Issues

For the PV only case, assets in both MV and LV networks are affected. As shown from utilization profiles 508A in FIG. 5A - 5C, the daily 50 2utilization level 504 of MV lines can rise above 180%. For LV transformers and feeders, as presented in Table I (summary of technical issues in LV networks), the daily maximum utilization level goes up to 125 and 110%, respectively.

In line with the voltage analysis, the adoption of BES systems with OTS control, does not mitigate thermal issues. The maximum utilization level of LV transformers remains approximately the same as the PV only case (125%) while for the LV feeders the value reduces slightly to 105%. For MV lines, as shown by the profiles 508B in FIG. 5B, despite a minor reduction, their maximum utilization remains well above their limits (175%).

Consumer Impacts - Year analysis of GDI level results in substantial network benefits as all thermal issues are mitigated for both MV and LV assets. As shown in Table I, the maximum utilization level of LV transformers and LV feeders is reduced to 68 and 58%, respectively. The utilization profiles 508C shown in FIG. 5C also highlight that the daily utilization level of MV lines remains below their limits as a result of using the AD controller 820. he asset utilization behavior described above can also be explained using FIG. 6. The similarities between the OTS controller and the PV-only case result, unavoidably, in almost the same reverse power flows and, therefore, the same utilization. On the other hand, the AD controller 820 significantly reduces exports and, hence, asset utilization during the day as shown in FIG. 5C. During the night however, small exports occur, resulting in slightly higher utilization than the PV-only and OTS cases.

The above results highlight the need to consider thermal aspects when assessing PV impacts; a consideration of limited coverage in the literature as most works focus on voltage issues. Furthermore, the integrated network modelling of multiple voltage levels becomes crucial to adequately quantify thermal and voltage issues across large geographical regions.

Effects on BES Owners

To assess the extent to which the AD controller 820 affects BES owners in their ability to reduce their grid imports, the metric GDI (section III. C) is calculated for a whole year for each of the 4,626 consumers. This allows to capture changes due to the seasonality and demand behavior. The GDI is statistically presented in FIG. 7 for each season, using a boxplot. For comparison purposes, the GDIs for the other two cases (PV only, OTS) are also quantified and presented. Considering that the OTS control is currently available to consumers and is designed for the sole benefit of the consumer, results are compared against its performance.

Considering the case without residential-scale BES systems, results show that the consumer’s median GDI during spring and summer (i.e. , sunny, high irradiance days) is 57 and 49%, respectively. On the other hand, during autumn and winter, where cloudy and low irradiance days exist, the GDI increases to 63 and 73%, respectively. These results, demonstrate that only using PV systems consumers can potentially achieve an annual median GDI of 60%, i.e., a 40% reduction on their annual electricity bill.

Crucially, when residential-scale BES systems are adopted, with either control method, the corresponding seasonal GDI indexes reduce even more. Taking for example the performance of the OTS controller, the median GDI level of the consumers drops significantly down to 1 and 2% during spring and summer, respectively. Similarly, during autumn and winter, the median GDI reduces to 9 and 23%, respectively. Consequently, with the OTS controller consumers can potentially achieve an annual median GDI of 10%, i.e., a 90% reduction on their annual electricity bill. However, despite the significant benefits this control offers to the owners, network benefits are minimal.

On the other hand, the proposed AD controller 820 not only provides significant benefits to the network (as discussed in the previous section) but also significantly reduces consumer grid imports. Indeed, as shown in FIG. 7the proposed AD controller 820 brings almost as much benefits to consumers as the benchmark OTS, resulting in annual median GDI of 14%, i.e., a reduction of 86% on electricity bills. It was found that this slightly higher GDI, compared with the OTS, is because of sunny days followed by a cloudy day. In such cases, once the PV generation stops in the sunny day, the AD controller 820 will fully discharge the battery by the morning of the next day (cloudy). However, due to the cloudy day (low PV generation), the BES system will not adequately charge, hence will not be able to support the local demand on that day.

Although results show that consumers with the AD controller 820 might have slightly higher grid imports than with the OTS control, the corresponding expense might be considerably lower than the capital investments required to provide the same network benefits with asset-intensive solutions, such as network reinforcements. Computational Performance

Daily, 30-min time-series power flow analysis on the MV-LV network with 100% of PV penetration (i.e., 9947 nodes and 4626 loads, PV and BES systems) required a total of 1 12s and 145s for the AD and OPT cases, respectively. Each power flow (considering both controllers) took in average 2.7s out of which 0.7s correspond to the control of all (4626) BES systems and the rest (2s) to the power flow and collection of results. More importantly, the actual time required for the control of each individual BES systems was in average 150ps. This demonstrates the implementability of the proposed control scheme, as the control of BES systems is performed in just a fraction of a millisecond. All simulations are carried out using a standard Windows OS machine with Intel Core i7-7500U processor at 2.7 GHz and 16GB of DDR3 RAM.

Conclusions

Embodiments of the invention provide a controller 820 that implements an adaptive decentralized (AD) control strategy for residential-scale BES systems to reduce voltage and thermal issues whilst still benefiting consumers. With this strategy, the power charging and discharging rates constantly adapt throughout the day based on clear-sky irradiance, PV generation, demand, and state of charge; significantly reducing reverse power flows and ensuring adequate storage capacity the next morning.

Results demonstrate that the AD controller 820 overcomes the limitations of the OTS control and allows mitigating all voltage and thermal issues. In terms of the benefits to consumers, the AD controller 820 was found to achieve almost the same performance of the benchmark OTS.

Considering the significant simultaneous network and consumer benefits brought by the AD controller 820, regulators and/or DNOs could require residential BES system manufacturers to incorporate such an algorithm in a similar way that certain PV inverter functions (e.g., Volt-Watt) are required in some parts of the world.

Persons skilled in the art will also appreciate that the method could be embodied in program code. The program code could be supplied in a number of ways, for example on a tangible computer readable storage medium, such as a disc or a memory (for example, that could replace part of memory of an existing controller) or as a data signal (for example, by transmitting it from a server). Persons skilled in the art, will appreciate that program code provides a series of instructions executable by a processor.

It will be understood to persons skilled in the art of the invention that many modifications may be made without departing from the spirit and scope of the invention, in particular it will be apparent that certain features of embodiments of the invention can be employed to form further embodiments.

In the claims which follow and in the preceding description of the invention, except where the context requires otherwise due to express language or necessary implication, the word“comprise” or variations such as“comprises” or“comprising” is used in an inclusive sense, i.e. to specify the presence of the stated features but not to preclude the presence or addition of further features in various embodiments of the invention.

It is to be understood that, if any prior art publication is referred to herein, such reference does not constitute an admission that the publication forms a part of the common general knowledge in the art, in Australia or any other country.