Residential micro-grid load management through artificial neural networks

Journal of Energy Storage 17 (2018) 287–298

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Journal of Energy Storage journal homepage: www.elsevier.com/locate/est

Residential micro-grid load management through artificial neural networks a,⁎

a

b

L. Barelli , G. Bidini , F. Bonucci , A. Ottaviano a b

T

a

Department of Engineering, University of Perugia, Via G. Duranti 1/A4, Perugia 06125, Italy VGA s.r.l., Via dell'Innovazione snc, Deruta, PG, 06053, Italy

A R T I C LE I N FO

A B S T R A C T

Keywords: Load management Residential micro-grid Battery ANN

This paper presents an innovative load management tool for a micro-grid composed by a photovoltaic (PV) system and an energy storage device installed at a residential user. The objective is to develop a suitable residential load management to maximize the PV plant exploitation through the storage system in order to achieve a greater energy independence of the micro-grid (MG) from the electric grid. For this purpose a MG dynamic model was developed in Matlab Simulink environment useful to analyse and optimize the MG energy performance. On the modelling results, through artificial neural networks (ANN) technique, a hierarchy load management that takes into account of the load demand, battery state of charge and weather forecast was defined. Specifically the aim of the ANN model here proposed is to predict the scheduling of programmable loads considering the weather conditions relative to the current day and the previous one, beyond that on the weather forecast for the day after. The obtained results, considering the relatively small dataset, are to be considered strongly encouraging. Greater performance is expected in the case the data set is enlarged.

1. Introduction Nowadays, the substantial increase in Renewable Energy Sources (RES) exploitation makes necessary to control and regulate the events of renewable energy over-production or sub-production [1,2]. RES are nonprogrammable sources because of their intermittent and fluctuating intrinsic character [3] (e.g. wind, solar energy). As consequence, globally, systems powered by non-programmable RES negatively affect grid safety and stability and force the thermal power plants, with particular reference to combined cycles fed by natural gas, to a continuous power up to compensate their variations and to avoid network imbalance [4–8]. Anyway the interest in this issue arises from the need to fully exploit the energy produced by non-programmable RES. Integration of RES electric production into the power grid, even at national level, is therefore a crucial and critical issue which requires research and development efforts to maximize the exploitation of these plants. The way to achieve the effective management of fluctuations and intermittent behaviour of RES is based on the availability of smartly controlled intelligent networks and infrastructures, capable of managing power streams innovatively by optimizing the whole electric system. To drastically reduce the RES variability and uncertainty, there are various possibilities. An efficient opportunity to synchronize RES working operation with electric grid can be the adoption of storage systems [9,10].

⁎

In [11–13] are shown overviews about the relevance of energy storage penetration in future power networks. Specifically, in [12,13] different energy storage technologies and their possible time-variable operation modes are analysed. Also in [14] several ways to store energy, with a range of more or less developed commercial and pilot technologies, are presented. Summarizing, an Energy Storage Systems (ESS) can be used to store energy surplus, due to overproduction contextual to low power demand, and to allow its post-usage when required. So, specifically, the use of ESS can lead to the three following situations: a) Storage makes possible the deferred use of the produced energy in the complete or partial absence of a concurrent energy demand. b) Storage allows to the user to exploit power at a different power level than that at which it is available during production. c) Storage system must be reversible (not in thermodynamic sense), i.e. it must allow the deferred use of almost all accumulated energy according to its energy efficiency. In technical literature several studies propose various optimization tools for residential demand response (DR). Moreover, in the presence of PV plant, the batteries utilization to increase the exploitation of PV self-consumption and reduce the cost due to electricity withdraw are analysed [15–17]. In [16] an interesting comparison between batteries

Corresponding author. E-mail address: [email protected] (L. Barelli).

https://doi.org/10.1016/j.est.2018.03.011 Received 4 December 2017; Received in revised form 5 February 2018; Accepted 19 March 2018 2352-152X/ © 2018 Elsevier Ltd. All rights reserved.

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production exploitation at the same time as the optimization of storage system operation, in order to make MG as autonomous as possible from the grid, is observed. In this context, the present study, according to an innovative approach, focused the attention on a residential micro-grid (residential user, PV plant, storage batteries) connected to the grid. Specifically, the purpose of this work was the development of a suitable loads management to realize, thanks also to the adopted storage integration, the maximization of the PV plant exploitation with a greater energy independence of the micro-grid (MG) in terms of:

and hydrogen storage performance is presented. It results that battery technology is more suitable than hydrogen to perform PV self-consumption thanks to higher round-trip efficiency and negligible selfdischarge. In [18] an economic optimization, based on genetic algorithm, of a residential battery operation with a PV system is presented. The study concerns both PV self-consumption and demand-load shifting. Their results show that, for a household which already invested in a PV system, the addition of a battery storage is not yet economically viable due to tariff structure and battery capacity. In literature, the topic of DR optimization is often dealt separately with respect to energy storage or RES production issues. Specifically, it is easy to identify research works in which the system optimization is aimed at minimizing costs due to network withdrawals rather than improving system efficiency or self-sufficiency. For example in [19], each residential load is classified into different categories according to different demand response capabilities in order to reduce the peak load and peak-valley difference. This optimization addressed to an electricity pricing strategy. Furthermore, in [20,21] the residential loads curves are analysed and changed in order to ameliorate the DR, while [22] introduces a control strategy for all controllable loads in a single house based on TOU tariffs. In [23] a DR control model for heating, ventilating and air conditioning (HVAC) system of one house is developed. In [24] it is shown a scheduling model for shiftable loads of household. Also the thermal storage system is considered in DR model for single house in [25,26]. Several papers [27–32] are focused on Home Energy Management (HEM) modelling and formulations in order to reduce the energy cost for the customer as well as the household’s peak load. In [33–35] the priority for controllable appliances along with the associated thermal and operational constraints is set to determine which appliances can be turned off in the case of DR implementation. In [36] a Mixed Integer Linear Programming (MILP) is shown to plan and allocate residential load for consumption in order to conserve the user priority. In [37] the operation of a PV-battery backup system under intermittent grid electricity supply is optimized. In particular, Nondominated Sorting Genetic Algorithm (NSGA-II) technique and a fuzzylogic decision maker are applied to get closer to the users preferences. It was observed that the back-up installation size can be reduced. A Modified Mild Intrusive Genetic Algorithm (MMIGA) is applied for intelligent load management of PV powered residential building in [38]. For the optimization of the demand response genetic algorithms (GA) are utilized in [39,40], simulated annealing algorithm in [41], minimization and several multi-objective optimization techniques in [42]. As discussed above, in the literature there are numerous studies about DR optimization, characterized by different techniques aimed at minimizing the electricity purchasing cost. No research works characterized by a loads shift optimization, through neural network, are available. Moreover, a lack in the addressing the maximization of PV

- greater self-consumptions with respect to the PV production; - lower electric consumptions with respect to the total energy demand. Moreover, an artificial neural network (ANN) model was developed to estimate the daily programmable loads that can be turned on based on the determined control logic and the weather conditions over three days (the current day, the previous one and forecast for the day after). The study was performed according to the following steps: - analysis of load profile and definition of a standard daily cycle of residential loads (i.e. home appliances); - development, in the Matlab Simulink environment, of the MG dynamic model; - development of a suitable load management strategy in function of the battery state of charge to optimize MG energy performance on daily basis; - development of an upper hierarchy load management which, on the basis of the maximum number of standard load cycles per day according to irradiance level, allows to determine the proper loads sequence for the day (n), known the weather conditions for days (n) and (n − 1) together with the weather forecast for the day after (n + 1). Such a decisional procedure, developed by means of artificial neural networks technique, takes into account both seasonal and weather conditions effects. 2. Micro-grid layout Fig. 1 shows an overview of the modelled system together with the considered power fluxes. It can be fundamentally divided into 3 areas: “Photovoltaic plant”, “Battery storage system” and “Residential load”. As it can be noted, a bidirectional energy exchange was considered in input and output from battery and electric grid and, on the other hand, PV plant and residential load are respectively characterized by an output (RES production) and input (required load) power flux. All converters, with their efficiency and response delay, are not implemented in this dynamic model.

Fig. 1. Power direction in the modelled system. 288

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Fig. 2. Simulink model overview.

3. Load profile analysis and micro-grid dynamic modelling

was provided. As mentioned in the introduction, the model is essentially divided into three areas: “House Loads and PV production”, “Battery model” and “To/From grid”. From the model layout it is possible to observe the interconnections among the different blocks. A fundamental signal useful for the MG analysis is the output of the “House Loads and PV production” block, or rather the difference between PV production and load demand. This time dependent signal is the input of the battery model: a negative value refers to a power demand from the battery while a positive one denotes the possibility of storage. Moreover, the electric grid acts if the delivery/storage must be limited due to the battery constraints (in terms of: SOC, power and energy). In the follow, a brief description of the different sections of the model is reported.

The dynamic model, developed in Simulink environment, has allowed to simulate and, subsequently, optimize the operation of a residential MG. Specifically, thanks to the exploitation of real dataset, the developed model can replicate the functioning of: - renewable energy production system (following production statistical data), - battery storage system, with particular attention to the trend of the state of charge (SOC) and input/output power fluxes, - electric load profile to be optimized, through a suitable load management strategy, minimizing grid withdrawal. Moreover, different control logics were analysed taking into account of: the state of charge of the storage system (see paragraph 4), the seasonal and weather effect and, consequently, the renewable production (see paragraph 5). In Fig. 2 a global overview of the dynamic model

3.1. Electrical load and photovoltaic production The user load demand is based on the experimental dataset presented in [43]. Specifically, the electrical load measurements comprise

Fig. 3. Example of a single house load demand (W) Vs Time (s). 289

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Fig. 4. Single electrical loads.

whole house aggregate loads and nine individual appliance measurements, collected continuously over a period of two years from 20 houses. Specifically, the load measurements were recorded at 8-s intervals per house. In this model, the house load was split between base load due to non-programmable auxiliary devices (e.g. lamps, computers, TVs, etc.) and programmable loads such as washing machine, dishwasher, dryer. The daily count of the electric load takes also into account the cycle of the refrigerator and any appliances used during lunch and dinner hours (i.e. microwave oven). Fig. 3 shows an example of a daily measured

Table 1 Cycles duration and maximum absorbed power.

Cycle time (s) Maximum absorbed power (kW)

Washing machine

Dishwasher

Dryer

7570 (2.1 h) 2.2

6500 (1.8 h) 2.1

3140 (0.87 h) 2.5

Fig. 5. Average daily production of a 6 kW photovoltaic plant. 290

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Fig. 6. Battery model.

Fig. 7. Current and capacity control.

household load. As stated above, it was possible to identify the consumption data of the single appliances (Fig. 4). In particular the attention was placed on the load cycle of the washing machine (light blue), the dishwasher (orange) and the dryer (green) because these programmable appliances can be daily postponed or anticipated (repeating them if necessary) to better exploit the PV production and the stored energy reducing, at the same time, the power withdrawal from electric grid. The daily cycles of the fridge (in black) as well as the microwave (purple) and the kettle (blue) machine were also considered in the daily loads analysis, together with the “Programmable loads” (washing machine, dishwasher and dryer). In Table 1, for the three “Programmable loads”, the operating cycle duration and the maximum required power are reported. Regarding the renewable production, the generation profiles of a PV plant typical of Central-Southern Italy were implemented. Fig. 5 shows the daily production of a 1 kW PV facing south with a tilt of 30° for each month of the year. In the micro grid here analysed, a PV system of 5 kW was adopted.

Fig. 8. Energy balance section. 291

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Table 2 Energy balance in winter and summer day. 100% irradiation

Winter day (January)

Summer day (June)

Night Cycle

SOC > 0.8

SOC > 0.9

SOC > 0.95

Night Cycle

SOC > 0.8

SOC > 0.9

SOC > 0.95

Network withdraw (kWh) Network input (kWh)

10.4 13.0

8.4 9.8

8.1 9.6

8.0 9.5

8.6 32.9

6.6 30.1

6.1 29.6

6.0 29.5

50% irradiation

Winter day (January)

Network withdraw (kWh) Network input (kWh)

Summer day (June)

Night Cycle

SOC > 0.8

SOC > 0.9

SOC > 0.95

Night Cycle

SOC > 0.8

SOC > 0.9

SOC > 0.95

10.5 4.5

10.3 2.6

10.3 2.0

10.2 1.9

9.0 13.7

8.3 11.6

7.9 10.6

7.8 10.5

Fig. 9. Total Load, Solar Production, (Total Load-Solar Production) and SOC Vs Time (s). Test: Winter day, SOC > 0.95, 100% irradiation.

Precisely, the open circuit voltage (Vocv), the change of internal resistance during charging (Rch) or discharging (Rdis) were used to characterize the battery behaviour as follow. Usually battery current (Ibat) and voltage (Vbat) can be characterized by Eq. (1) and (2).

In the PV model, in order to take into account of meteorological conditions, photovoltaic production was multiplied by the following percentages [44]:

• 0%: no production, day with total cloud cover. • 30%: very cloudy with temporary clear up. • 50%: day with variable cloudiness. • 100%: maximum production, clear sky.

Ibat =

This weather rating is crucial for the subsequent daily scheduling of individual programmable loads and consequently on the management loads strategy. What described above was entirely modelled in the “House Loads and PV production” area of Fig. 2 where it was possible to activate the “Programmable loads” individually and to repeat them if necessary.

Vocv −

2 int Vocv − 4Rbat P int 2Rbat

(1)

int Vbat = Vocv − Rbat Ibat

(2)

where P is the power required/deliver to the battery and:

Vocvc = f (SOC )charge ⎫ Vocv = ⎧ ⎨ ⎭ ⎩Vocvd = f (SOC )discharge ⎬

(3)

R ch = f (SOC )charge ⎫ int Rbat =⎧ ⎨ ⎩ Rdis = f (SOC )discharge ⎬ ⎭

(4)

3.2. Battery model In order to implement the most of MG's capabilities, an integrated dynamic model of the storage system was developed to optimize its transient operation. In this model it is also evaluated how much power is possible to store or deliver to the grid. These information are subsequently used as input data in the energy balance block (“To/From grid”). Authors in a previous research works [45] have tuned the model for a Q (Ah) capacity battery with which the state of charge (SOC: state of charge) was estimated taking into account a specific battery datasheet.

The Eqs. (3) and (4) are determined by using look-up tables based on experimental data. In [45] the Vocv trends of the LFP (Lithium iron phosphate) battery together with its internal resistance are shown. SOC determination was carried out as follow:

SOC = SOCini −

292

∫ η QIbat

(5)

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Fig. 10. Total Load, Solar Production, (Total Load-Solar Production) and SOC Vs Time (s). Test: March day, 100% irradiation, No Optimization.

η=

⎧ ηch =

Vocv charge Vocv − Ibat R ch

⎨η = ⎩ dis

Vocv − Ibat Rdis discharge ⎬ Vocv ⎭

network and, vice versa, if SOC is below the minimum battery operating limit, Ibat is provided by the grid.

⎫ (6)

3.3. Models integration where SOCini is the initial value of SOC and Q [Ah] represents the battery capacity. In the MG system object of study, SOCini was set to 1 and the battery capacity was chosen equal to 470 Ah (2 modules in series) with a nominal storage power of about 1.5 kWh. The Simulink battery model is shown in Fig. 6. Specifically in the blocks named Vcharge, Vdischarge, Rcharge and Rdischarge the curves shown in [45] were included. In “Current and capacity control” (Fig.7) block the current demand Ibat (out 4 in Fig. 6) is compared with the maximum charging and discharging current (both set to 100 A) as well as the actual instantaneous SOC. Therefore if Ibat is greater than the maximum charge/discharge current, the exceeding current is delivered/requested to the grid. Then, if battery is charged, Ibat current is addressed to the

The integration of model sections was carried out following the functional scheme previously described and shown in Fig. 2. At the base of modeling there is the comparison between the electric load required by the user (Wload) and the photovoltaic production (Wpv). The difference between these two power terms can represent a power lack or surplus. As expressed in Eq. (7), dividing this difference for the battery operation voltage, it is possible to determine the charging or discharge current (Ibat) which influences the battery SOC (Eq. (5)).

Ibat =

Wpv − Wload Vbat

Fig. 11. Total Load, Solar Production, (Total Load-Solar Production) and SOC Vs Time (s). Test: March day, SOC > 0.95, 100% irradiation. 293

(7)

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It is important to emphasize that the battery operating mode is strictly related to its minimum operating state. Indeed, the electrochemical storage systems (i.e batteries) have a SOC threshold (DoD: depth of discharge) under which it is advised not to work due to system aging sensitive issues. In this model, considering a PV plant life of 30 years, nevertheless the LFP improved duration with respect to lead-acid technology, the battery DoD value was set at 20% to enhance the pack duration. It doesn’t imply negative effect on efficiency, since LFP battery, differently to lead-acid technology, will still achieve 90% efficiency under shallow discharge conditions [46]. Anyway, it is remarked as the present study doesn’t deal with the techno-economic study to optimize the storage size and operating conditions. For completeness in Fig. 8, “To/From grid” model section is presented. Here the energy balance between the MG and the electric grid is performed. Specifically, the amount of energy (kWh) sent or taken from the network is calculated.

Table 3 June loads scheduling. Where DW, WM, DR are Dishwasher, Washing Machine and Dryer. Numbering 1 and 2 is to identify the first or second working cycle. Days with zero PV production are highlighted in bold.

4. Lower hierarchy strategy: loads management in function of battery SOC The main purpose of this study, as anticipated in the introduction, is to optimize the exploitation of PV plant production, using batteries as an energy buffer available in the absence of solar irradiation (night, cloudy day) or in support to PV production if not sufficient. The battery use was constrained above three different threshold SOC values (0.8, 0.9, 0.95) in order to minimize energy withdrawn from the electric network. In other words, each of the three programmable loads is not activated until the battery SOC reaches the minimum operating threshold (always under the same operating conditions, i.e. DoD of 20%). In the preliminary phase of the control logic development, simulations were performed on two test days, one in summer and one in winter with 100% and 50% sun irradiation, to evaluate the impact of the SOC threshold variation on a daily electric withdraw during a basic loads cycle. This latter consists of the activation of the three programmable loads (washing machine, dishwasher, dryer) once a day. From the results shown in Table 2 it can be highlighted that, both for 100% and 50% irradiation, the minimum energy exchanges with the grid were found for a SOC threshold of 0.95. This condition allows, both in January that in June, greater MG autonomy from the grid. Table 2 shows also the results obtained if loads are activated in sequence only at night. It is noted that this condition is the one with the largest energy exchanges with the grid, both in terms of energy provided by/delivered to the grid. For completeness Fig. 9 shows the results of the simulation carried out for January. It's clear from the figure how the difference between the PV production and required load influences SOC daily trend. Another preliminary test was performed by comparing one day using the loads as measured from the user for a specific day of March (without loads management) (Fig. 10), with the case of adoption of the SOC > 0.95 activation strategy (Fig. 11). From the energy point of view, the optimized load control has led to a consumption from the network and an energy surplus sent to the grid equal to 3.26 and 25.2 kWh, with respect to 6.1 and 28.5 kWh. So in this case too, the energy-efficient convenience of controlled load management was verified. 5. Upper hierarchy strategy: ANN-based loads management in function of irradiance level The second step for the development of the control logic is the implementation of the weather conditions. The above cases (Table 2 and Fig. 9) are examples where a single washing machine-dishwasherdryer cycle is provided for daily use, and they can therefore be

294

Test

Production (%)

–

n-1

n

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64

100% 50% 30% 0% 100% 50% 30% 0% 100% 50% 30% 0% 100% 50% 30% 0% 100% 50% 30% 0% 100% 50% 30% 0% 100% 50% 30% 0% 100% 50% 30% 0% 100% 50% 30% 0% 100% 50% 30% 0% 100% 50% 30% 0% 100% 50% 30% 0% 100% 50% 30% 0% 100% 50% 30% 0% 100% 50% 30% 0% 100% 50% 30% 0%

100% 100% 100% 100% 50% 50% 50% 50% 30% 30% 30% 30% 0% 0% 0% 0% 100% 100% 100% 100% 50% 50% 50% 50% 30% 30% 30% 30% 0% 0% 0% 0% 100% 100% 100% 100% 50% 50% 50% 50% 30% 30% 30% 30% 0% 0% 0% 0% 100% 100% 100% 100% 50% 50% 50% 50% 30% 30% 30% 30% 0% 0% 0% 0%

Programmable loads on day (n)

Loads recovery (from n − 1) or anticipation (from n + 1)

n+1

DW1

WM1

DR1

DW2

WM2

DR2

100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 50% 50% 50% 50% 50% 50% 50% 50% 50% 50% 50% 50% 50% 50% 50% 50% 30% 30% 30% 30% 30% 30% 30% 30% 30% 30% 30% 30% 30% 30% 30% 30% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0%

1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1

1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0

1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0

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Fig. 12. Double cycle of daily loads operated at night. Red (in the left side) and green box (in the right side) are the first and the second cycle. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

and their weather conditions, in the months of January, March, June and October. Table 4 shows loads scheduling for the selected months. Table 5 shows the results obtained throughout the simulated weeks. For all the considered months it was observed that in case the automatic loads management is adopted:

considered standard cases in which all three loads, thanks to favourable weather conditions, can be activated. In the real application it depends on weather conditions; moreover, there could be loads to be recovered or anticipated according to the weather conditions of the day before and after. It is emphasized that the maximum number of single loads or standard load cycles (washing machine-dishwasher-dryer) that can be daily activated, was determined performing daily simulations by varying the loads repetition and the PV production conditions. Consequently, the control logic has to take into account how the PV plant production behaves according to the weather on days (n − 1), (n + 1) where (n) denotes today. To clarify this concept we provide some practical examples:

- energy consumptions from the grid are lower with respect to the night cycling. Specifically the reduction is equal to 18%, 43%, 27% and 38% in January, March, June and October. - energy sent to the grid is reduced, specifically of 31%, 17%, 16% and 19% respectively in January, March, June and October. In confirmation of what previously said, these two results confirm that the loads management, here implemented, makes the MG more independent from the electric network optimizing the exploitation of the produced renewable energy. To develop a tool with generalization capability in order to consider all possible irradiance levels according to real weather conditions, ANN technique was chosen. ANNs simulate the biological neural network behaviour; they are non-linear informational processing devices, built on the basis of interconnected elementary calculations (performed in the neurons). They can operate like a black box model, which doesn’t require a complete and rigorous knowledge of the investigated system, but it creates an implicit correlation between inputs and outputs of the phenomenon under study, basing on a representative data set. ANNs are therefore very useful if applied to provide an implicit representation of a complex and generally non-linear phenomenon, also in presence of noise, with a very reduced computational time. To get a sufficient generalization capability, this technique needs of a large amount of data describing the phenomenon to be modelled. The aim of the ANN model here proposed is to predict the scheduling of programmable loads basing on weather conditions relative to day (n) and to one day before (n − 1) and on the weather forecast for the day after (n + 1). In particular, known the dates and the related weather conditions, the corresponding irradiation levels are determined and used as inputs of the ANN model. The data shown in Table 3, together the ones relative to January, March and October, were rearranged in two datasets, to be processed by two separate neural networks (ANN1 and ANN2), grouping:

- Loads Recovery: If due to the weather condition all three loads could not be activated, one or more of these will be recovered the next day (n + 1), as long as the forecasts permit, otherwise you can choose whether to postpone again or activate the loads manually. - Loads Anticipation: in case the forecasts of (n + 1) day are unfavourable and the photovoltaic production will be insufficient to handle the three loads, one or more of these are anticipated on day (n), if weather conditions allow it. If this is not possible, the user will give priority to loads manually. On the basis of these logical rules, a monthly planning table, with which to manage all possible weather combinations (called “Test”), was compiled for January, March, June and October. For example, the June scheduling table (Table 3) is shown. It is underlined that in some particularly unfavourable weather conditions (in bold in the table), characterized by a zero production day (n) and partial production on days (n − 1) and (n + 1), the chosen load is activated without the energetic support of the PV system. In this situation the authors have fixed the dishwasher as a “mandatory” minimum daily load. In order to verify the performance of the above methodology, simulations for the comparison between the operation with or without the developed control logic were performed. In absence of the automatic loads management, the choice to operate loads only in the night time was carried out considering it as the optimal choice for manual load management (for completeness Fig. 12 shows the simulation results for a night cycle). Specifically, a test week was simulated selecting randomly the days 295

6 2 1

0 1 1 49

21

0 18

1 1 1 1

0

1 1

0 1 1 1

1

0 1

0 1 0 1

0

0 1

0 1 0 1

0

0 1

0 0 0 1

0

0 1

WM2

1 1 1 1

0

1 1

DR2

1 1 1 1

1

1 1

DW1

0 1 1 1

1

0 1

WM1

0 1 0 1

0

0 1

DR1

296

5 18 21 6 2 1 49 Total

# test

7.6 10.3 7.6 7.6 9.1 8.0 10.3 60.6

4.0 7.9 4.0 4.0 7.9 9.5 7.9 45.2

7.8 13.9 7.8 7.8 12.7 10.4 13.9 74.2

4.5 13.0 4.5 4.5 13.0 13.0 13.0 65.6

3.7 4.8 3.7 3.7 3.0 3.0 3.8 25.6

W* 12.0 24.6 12.0 12.0 25.3 27.0 23.7 136.7

I*

W*

W*

I*

logic control (kWh)

night cycle (kWh)

logic control (kWh)

I*

March

January

4.7 7.7 4.7 4.7 7.4 5.9 9.3 44.6

W*

0 0 0 1

0

0 1

WM2

14.2 30.4 14.2 14.2 30.4 30.4 30.4 164.2

I*

night cycle (kWh)

0 0 0 1

0

0 0

DW2

1 1 1 1

1

1 1

DW1

7.8 6.0 7.8 7.8 6.0 6.0 6.1 47.5

W*

1 1 1 1

1

1 1

WM1

10.5 29.5 10.5 10.5 29.5 30.5 26.0 146.9

I*

logic control (kWh)

June

1 1 1 1

0

1 1

DR2

0 0 0 1

0

0 0

DW2

9.0 8.6 9.0 9.0 8.6 8.6 12.1 65.0

W*

13.7 32.9 13.7 14.7 32.9 33.9 32.9 174.6

I*

night cycle (kWh)

0 0 0 1

1

0 1

DR1

0 0 0 1

0

0 0

WM2

1 1 1 1

1

1 1

DW1

4.7 4.8 4.7 4.7 3.8 3.8 4.8 31.3

W*

9.1 20.3 9.1 9.1 19.6 21.3 18.7 107.3

I*

logic control (kWh)

October

1 1 1 1

0

1 0

DR2

0 1 1 1

1

0 1

WM1

0 0 0 1

0

0 0

DW2

5.6 8.6 5.6 5.6 8.4 6.7 10.2 50.5

W*

11.2 24.7 11.2 11.2 24.7 24.7 24.7 132.6

I*

0 0 0 1

0

0 1

WM2

Loads recovery or anticipation (from days n − 1 and n + 1)

night cycle (kWh)

0 1 0 1

0

0 1

DR1

DW2

DR1

DW1

WM1

Day (n) programmable loads

Loads recovery or anticipation (from days n − 1 and n + 1)

Day (n) programmable loads

Day (n) programmable loads

Loads recovery or anticipation (from days n − 1 and n + 1)

Day (n) programmable loads

Loads recovery or anticipation (from days n − 1 and n + 1)

October

June

March

January

Table 5 Test week result. (*) W and I are respectively energy consumed and delivered to the grid (kWh).

1

0

1

5

DR2

Test number

Table 4 Test week: loads scheduling for January, March, June, October.

L. Barelli et al.

Journal of Energy Storage 17 (2018) 287–298

Journal of Energy Storage 17 (2018) 287–298

L. Barelli et al.

Table 6 ANN1 training OUTPUT 1.

RMS (θ ) =

Network number

Hidden Layer

Neurons number 1 st hidden layer

Neurons number 2 st hidden layer

RMS error (%)

1 2 3 4 5

1 2 2 2 2

10 10 5 10 5

0 10 5 5 10

26.27 33.85 7.22 6.25 10.21

-

Hidden Layer

Neurons number 1 st hidden layer

Neurons number 2 st hidden layer

RMS error (%)

6 7 8 9 10 11 12 13 14

1 2 2 2 2 2 2 2 2

10 10 5 10 5 18 16 8 18

0 10 5 5 10 12 15 14 14

67.41 13.50 15.73 25.00 27.24 8.07 8.84 10.83 5.10

n no

(8)

Where:θann,i output value calculated by the ANN θexp,i target output value n number of samples in the testing dataset no number of ANN output parameters.

Among the investigated architectures, the best performance of the ANN models, in terms of RMS error value, was obtained for the configuration characterized by 10–5 and 18–14 neurons in the hidden layers, respectively for ANN1 and ANN2. Specifically, a RMS error of 6.25% and 5.1% was exhibited (highlighted in bold in Tables 6 and 7). Results are interesting even if affected by a low samples number. Greater performance is expected in the case the data set is enlarged.

Table 7 ANN2 training OUTPUT 2. Network number

Σin (θann, i − θexp, i )2

6. Conclusions The substantial increase in RES exploitation makes necessary to control and regulate the events of renewable energy over-production or sub-production. Due to RES intermittent and fluctuating intrinsic character, systems powered by non-programmable RES negatively affect grid safety and stability and force the thermal power plants to a continuous cycling. Several possibilities can be found to reduce the RES variability and uncertainty. In the micro-grid analysed in this paper, in order to synchronize RES working operation with electric demand, the adoption of an ESS was considered. Aiming to maximize the PV production exploitation, to optimize the storage system operation and to make MG as autonomous as possible from the network, a load control logic based on artificial neural network technique was developed. The development of this control logic, suitable to estimate the daily programmable loads that can be turned on according to the determined control logic, was preceded by the following working steps:

- irradiation levels for the three days (n − 1, n, n + 1) and parameters “DW1”, “WM1” and “DR1” for ANN1 for a total of 256 samples; - irradiation levels for the three days (n − 1, n, n + 1) and parameters “DW2”, “WM2” and “DR2” for ANN2 for a total of 256 samples. Each dataset was subdivided into three subsets of samples, according to the ratio 7:1.5:1.5. The first is used for the training phase and it is fed to the network algorithm in order to tune the network inner parameters to decrease the error measured on the output. The second is used as validation basis. This is employed to measure the generalization capability of the network and to abort the training process early if the network performance on this set fails to improve. The validation set does not influence the network generalization capabilities. The third data set is the test one, that is used as a further check that the network is well generalizing, but it does not have any effect on training. Both ANN1 and ANN2 have 3 inputs, namely the irradiation levels relative to day (n), to one day before (n − 1) and to the day after (n + 1), and 3 outputs (“DW1”, “WM1” and “DR1” for ANN1; “DW2”, “WM2” and “DR2” for ANN2). Therefore, ANN1 has to predict which loads of the day (n) operate (basic load cycle), while the ANN2 to establish which loads to recover or anticipate from day (n − 1) and (n + 1) respectively. Multi-layer feed forward neural network architectures with two hidden layers were chosen and a Back Propagation learning algorithm based on gradient descent with momentum was considered. This technique allows a network to respond not only to the local gradient, but also to recent trends in the error surface. Acting like a low pass filter, momentum allows the network to ignore small features in the error surface. The model was realized in MATLAB, considering a random initial distribution of weights. For both ANNs, the number of neurons in the input and output layers was equal to the number of input (3) and output (3) parameters respectively. For both ANN1 and ANN2, several artificial network architectures, characterized by different neurons number in the hidden layers, were considered. For each architecture a training-test campaign was carried out. Performances were evaluated by the Root Mean squared Error (RMS, Eq. (8)) on the basis of the gap between each neural network output ((θann,i)) and the experimental data (θexp, i) in the test dataset, sorted under same conditions. Tables 6 and 7 show the ANN configurations investigated and the corresponding values of the RMS error committed in the test phase.

- the analysis of load profile and definition of a standard daily cycle of residential loads (i.e. home appliances), - the development of the MG dynamic model - the development of load controlling strategy in function of the battery state of charge. The ANN model here proposed, on the basis of the monthly loads management maps (as the one provided in Table 3 for June), can suggest the scheduling of programmable loads known weather conditions relative to day (n) and to one day before (n − 1) and the weather forecast for the day after (n + 1). In particular, known the dates and the related weather conditions, the corresponding irradiation levels are determined and used as inputs of the ANN model. According to the performance of the developed ANNs, in terms of the RMS error value, the programmable loads scheduling is provided with an accuracy of about 6% (ANN1) and 5% (ANN2), with respect to the expert’s knowledge base (here represented by authors evaluations based on dynamic simulations of the MG behaviour), for the first and the second load cycle respectively. Specifically, the best multi-layer feed forward neural network architectures, among the investigated ones, are characterized by 2 hidden layers with 10–5 and 18–14 neurons in the hidden layers, respectively for ANN1 and ANN2. It is remarked as in the present study the ANN models were developed only on the basis of the loads management maps relative to 4 months. Therefore, the presented results are interesting even if ANN performances are affected by a low samples number. In future works, in case of higher dataset availability, better performances are expected.

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Acknowledgements [23]

The authors thank UmbraControl S.r.l. and Giorgio Passeri for their help and support.

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