Self-consumption enhancement and peak shaving of residential photovoltaics using storage and curtailment

Energy 112 (2016) 221e231

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Self-consumption enhancement and peak shaving of residential photovoltaics using storage and curtailment
n, Joakim Munkhammar, David Lingfors Rasmus Luthander*, Joakim Wide Built Environment Energy Systems Group, Department of Engineering Sciences, Uppsala University, Sweden

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 February 2016 Received in revised form 18 May 2016 Accepted 7 June 2016

Increasing the self-consumption of photovoltaic (PV) power is an important aspect to integrate more PV power in the power system. The profit for the PV system owner can increase and the stress on the power grid can be reduced. Previous research in the field has focused on either self-consumption of PV power in individual buildings or PV power curtailment for voltage control. In this paper self-consumption of residential PV power in a community of several single-family houses was investigated using highresolution irradiance and power consumption data. Cases with individual or shared battery energy storages for the houses were examined. PV power curtailment was investigated as a method to reduce feed-in power to the grid, i.e. peak shaving. Results indicated that the self-consumption ratio increased when using shared instead of individual storage. Reducing the feed-in power from the community by almost 50% only led to maximum 7% yearly production losses due to curtailment and storage losses. The economics for shared storage are slightly better than for individual ones. These results suggest that residential PV-battery systems should use (i) shared energy storage options if local regulations allow it and (ii) PV power curtailment if there are incentives to lower the feed-in power. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Photovoltaics Self-consumption Battery storage Peak power shaving Curtailment

1. Introduction Subsidy schemes have historically played an important role in making photovoltaic (PV) systems competitive on the electricity market [1]. A common subsidy is Feed-in Tariffs (FiTs) for which the producer is guaranteed a fixed price per kWh of electricity fed in to the grid for an extended period of time [2]. In some markets the FiTs are lower than the buying price of electricity, which makes it more profitable to match periods of high electricity generation with household electricity consumption instead of selling excess electricity and buying it back when the consumption is higher [3]. In situ consumption of PV generated electric energy is often referred to as self-consumption [4]. Increasing the self-consumption may increase the profitability of grid-connected PV systems, which is an important aspect to increase the number of installations. In power grids with a high level of PV penetration, an increase of the selfconsumption can also lower the stress on the grid if the peak feed-in from the PV systems can be reduced. In this paper, there will be a distinction between self-consumption and self-consumption

€ mlaboratoriet, Uppsala University, PO Box 532, * Corresponding author. Ångstro SE-751 21, Uppsala, Sweden. E-mail address: [email protected] (R. Luthander). http://dx.doi.org/10.1016/j.energy.2016.06.039 0360-5442/© 2016 Elsevier Ltd. All rights reserved.

ratio. Self-consumption states the self-consumed electricity in kWh and self-consumption ratio states the share of self-consumed electricity relative to total PV electricity production. There are mainly two ways of increasing the self-consumption ratio, namely energy storage and demand side management (DSM) [4,5]. DSM implies to improve the load pattern, for example to time-shift loads to better match the PV power production [6]. In this study, only storage is considered as a tool to increase the selfconsumption ratio since the potential for DSM in the studied households are less than 4% [7]. There are different kind of storages, for example batteries, fuel cells and thermal energy storage using the thermal mass of the building or hot water storage tanks combined with heat pumps [4,8e10]. There are two aims of this study. The first aim is to investigate how battery storage contributes to increased self-consumption ratio in a community with houses equipped with rooftopmounted PV systems. The second aim is to reduce the maximum power fed into the power grid, also known as peak shaving. This study will not only include one single house with PV systems, instead a whole community of detached houses is studied using high time-resolution data. Previous research on self-consumption of residential PV using energy storage has focused on individual buildings [8,9,11e24]. One

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Nomenclature 4sc c C DSM Efeed-in Elosses Enet Esc Etotal FiT k

self-consumption ratio [%] fraction of battery capacity that holds available charge battery capacity [Wh] demand side management accumulated feed-in power [Wh] storage charging or discharging losses [Wh] PV electricity production excluding storage losses [Wh] self-consumption [Wh] PV electricity production including storage losses [Wh] feed-in tariffs battery rate constant

study by Lopes et al. examined self-consumption of PV electricity production in both single households and a community of five Net Zero Energy Buildings using DSM [10] The results showed that the self-consumption ratio was 14e15% higher on a community level than on a building level without DSM. When a DSM method was implemented the self-consumption ratio was 5e9% higher for the community than for the individual buildings. Previous research on power curtailment of residential PV includes several studies of communities with grid-connected PV [25e29]. The focus of the studies was primarily on voltage control in the distribution grid and not on self-consumption. One of them also included battery storage, either individual or centralized, but did not calculate the self-consumption [27]. The novelty of this study is the combination of optimization of the self-consumption and peak shaving of residential PV power using both battery storage and power curtailment in communities. Curtailment of PV power production is examined as an option to reduce the power delivered to the grid. Cases where the houses either have individual storage systems or share one larger storage are compared. This will be used to investigate the effects on both self-consumption ratio and losses related to a limited feed-in power and storage capacity. When several households share one connection to the power grid, their combined load is subject to random coincidence of the individual loads, which averages stochastic fluctuations [4]. This means that PV power production from a house with excess power production can be consumed in another house with excess consumption. When using batteries to lower the feed-in power, a smaller battery is likely needed when using shared storage for the whole community compared with using batteries at each house [30]. This study extends a study where self-consumption of PV electricity in a community with battery storage and electric vehicle charging was investigated [30]. That study focused on improving the self-consumption ratio, whereas this study examines both selfconsumption ratio and grid management. Home-charging of electric vehicles is excluded in this study since it had a negligible contribution to the self-consumption ratio. This is due to mismatch of home charging of electric vehicles and PV power production [15]. The outline of this paper is as follows: In Section 2 the concept of PV-battery systems in combination with power production curtailment is explained and previous research in the field is summarized. The data and models used for this study plus simulation procedure are described in Section 3. Results from the simulations, including self-consumption ratio, feed-in power, losses and an economic assessment are presented in Section 4. The models and results are discussed in Section 5 and conclusions of the

KiBaM L LiDAR Psc Ptotal PV qmax Rbuy Rsell Rtotal S SOC X

kinetic battery model load [W] light detection and ranging self-consumption [W] PV power production [W] photovoltaic(s) maximum capacity of the battery [Ah] buying price of electricity [V] selling price of electricity [V] revenue [V] storage charging or discharging power [W] state of charge of the battery [%] feed-in power limit [W]

study are presented in Section 6. 2. Background For residential PV systems of a few kW installed power the generation during clear days often exceeds the power demand. The excess electricity is then fed into the power grid and sold to an electricity retailer. A review of studies covering PV selfconsumption showed a spectrum of “natural” self-consumption, i.e. without any energy management or storage, between 15% and 56% of the total PV electricity production [4]. The self-consumption ratio depends on the installed power of the PV system, location of the installation, the yearly power consumption in the household and power consumption profile, both over the day and over the year. In colder regions at high latitudes the electricity consumption is often higher in the winter than in the summer, whereas the production pattern has the opposite profile. Houses with PV systems located in regions with low seasonal fluctuations in solar irradiance and a stable outdoor temperature, often in regions at low latitudes, will therefore have higher “natural” self-consumption ratio in comparison to houses at high latitudes. This holds if the yearly household electricity consumption and PV electricity production are the same. 2.1. Storage and PV There has been extensive research on energy storage combined with distributed generation, often residential PV-battery systems. Mulder et al. developed a method to optimize the storage size for grid-connected residential PV systems to either cover most of the electricity needs or to cover the peak power [31]. In a paper by €vel et al. battery storage was used to both increase the selfMosho consumption from residential PV systems and to lower the peak feed-in power [12]. It was shown that a rather simple forecast method for irradiance had a significantly higher potential to relieve the power grid than a PV-battery system operated solely to increase the self-consumption. Also other types of storages than batteries can be used with residential PV systems. Thygesen and Karlsson compared a PV system with either battery or hot water storage [8]. The conclusion was that the levelized costs for a PV-battery system were twice as high as for the system with hot water storage for Swedish conditions. Munkhammar et al. studied how home-charging of electric vehicles could contribute to increased self-consumption on both individual and aggregate household level [15]. There also exist probability distribution models on self-consumption of PV power

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production, see Ref. [32]. The results indicate that the increase in self-consumption is limited due to low coincidence between PV power production and charging pattern of electric vehicles. The economical aspect of adding battery storage to a PV system is important. A compilation of costs of batteries in 2013 showed a price range from V102 to V2034 per kWh [33]. Lead-acid batteries were the cheapest technology with a mean cost of V171 per kWh. The cost of power conversion system and balance-of-plant was in total V242 per kW, which means that a battery system with a storage capacity of 1 kWh and a power conversion capacity of 1 kW would in this case cost V413 plus yearly maintenance. The extra revenue from adding battery storage to a PV system must therefore be relatively high to make this technique more widespread. With a growing market of PV-battery systems in the world, prices are likely to decrease in the near future. Battery storage systems designed for residential applications, often in combination with PV systems, are offered by a range of suppliers such as Tesla, Sonnenbatterie, Fronius, SMA, Sharp and Panasonic.
n and MunkA previous study from Sweden made by Wide hammar showed a potential for increased revenue of on average no more than V40 per year when adding 5 kWh battery storage to a 5 kWp PV system [7]. This depends heavily on the local electricity prices and there are a few studies from other countries pointing in the other direction; one came to the conclusion that battery storage solutions already in 2013 were economically viable in Germany for small PV systems [34]. Another study of a PV-battery system with 2 kWh lead-acid batteries, also for German conditions, showed a rate of return on the investment of 1.58% per year [17]. The profitability of energy storage depends on desired rate of return, battery and electricity prices and economic incentives. A method for optimizing the battery size for grid-connected PV systems from an economic point of view was developed in Ref. [35]. 2.2. Curtailment of PV power production If the power grid is not able to handle high reverse power flows, this might set a limit for maximum feed-in power from households with PV. The PV power production might therefore need to be curtailed to lower the power fed in to the grid. The power-voltage characteristics of solar cells make it possible to have a lower output than optimum from PV cells by varying the output voltage [36]. This will lead to production losses and the power producer therefore has to have incentives to lower the production. The incentives can either be for the benefit or drawback for the power producer, such as compensation for lost production or a limit on maximum allowed feed-in. Curtailing PV systems must however not lead to high production losses. A Canadian study of 12 net-zero energy houses equipped with large rooftop mounted PV systems connected to a low voltage feeder resulted in a power production loss due to curtailment of approximately 8% over one year [26]. Curtailment might be an interesting option if the benefits for the distribution system operator due to lower feed-in power exceed the compensation to the producer. It can also be of interest if the power producer finds it profitable to install PV even though a limit on feed-in power might affect the profitability. 3. Methodology and data The methodology section describes the different simulation cases, data, methodology and models used for this study. Simulation models were implemented in MATLAB. Self-consumption of PV power, which is an important measure in this study, is defined in Section 3.1. A schematic figure is used in Section 3.2 to illustrate the algorithm of storage and curtailment. Four cases are included in the

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study, which are described in Section 3.3. Descriptions of the collection of electricity consumption data, simulations of the PV electricity production and the battery model used follow in Sections 3.4e3.6. Finally, a brief economic evaluation of PV-battery systems is described in Section 3.7. 3.1. Definition of self-consumption and self-consumption ratio Self-consumption ratio is defined in this study as the share of the PV electricity production consumed in the house on which it is mounted, divided with the total PV electricity production. This is similar to the definition in Ref. [4]. The self-consumption is limited by the lowest value of either the PV power generation, denoted Ptotal(t), or total household load, denoted L(t). The instantaneous self-consumption PSC(t), can therefore be expressed as

Psc ðtÞ ¼ minfLðtÞ; Ptotal ðtÞg:

(1)

Excess PV power production, i.e. when Ptotal(t) > L(t), can either be fed in to the power grid or stored in a residential energy storage for later use. In the case of energy storage in the building, this can be extended to

Psc ðtÞ ¼ minfLðtÞ; Ptotal ðtÞ þ SðtÞg

(2)

where S(t) is the power to and from the storage unit, with S(t) < 0 when charging and S(t) > 0 when discharging. For both cases, the €sc is defined as self-consumption ratio o

Z 4sc ¼ Z

t2

t¼t1 t2 t¼t1

Psc ðtÞdt :

(3)

Ptotal ðtÞdt

How to handle charging and discharging losses as well as other losses related to the storage are important when calculating the self-consumption ratio of a PV-battery system. In this case storage losses will not be considered as self-consumption, otherwise selfconsumption ratio could be increased without any useful energy benefit. Curtailment losses are calculated as a lowering of the total PV power production, which will affect the self-consumption ratio in a positive way. This becomes important when comparing the values. 3.2. Storage and curtailment A schematic figure of the grid interaction in the community, i.e. total power consumption minus total PV power production, and corresponding charge status of the battery system is shown in Fig. 1. A negative grid interaction means feed-in power (electric power from prosumer to grid), whereas positive values mean feed-out (electric power from grid to prosumer). Battery storage is used on the second day to increase self-consumption and batteries plus curtailment are used on day three for peak shaving and increased self-consumption. The batteries start charging when the PV power production exceeds the power consumption. This means that the batteries might be fully charged before peak power production of the day, which normally occurs around noon. This strongly depends on the relationship between PV system size and total battery capacity. The battery storage is in this case mainly used to increase the selfconsumption of the system and a small total capacity might not decrease the maximum feed-in power at all. Curtailment of the PV power is therefore used to reduce the maximum feed-in power. The inverters regulate the PV systems and reduce the production so that no more power is fed in to the power grid than allowed. The

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Power

PV power production

Power consumption

Grid interaction

Battery charging/discharging

Curtailment losses

Day 1

Day 2

Day 3

PV

PV + storage

PV + storage + curtailment

0

Time

Fig. 1. Schematic figure of PV power production, household power consumption, battery charging, curtailment and resulting grid interaction for three days. Negative grid interaction indicates feed-in to and positive feed-out from the power grid.

maximum feed-in power is varied to determine how power production losses are affected by curtailment. The feed-in limit is set for the whole community. Overproduction from one house can therefore be consumed in another house in the community without affecting the feed-in power.

of the battery system is explained in Section 3.6. The following cases are simulated:  Case a (reference scenario): individual power grid connections and meters (Fig. 2a)  Case b: individual battery storages and individual grid connections and meters (Fig. 2b)  Case c: individual battery storages and shared grid connections and meter (Fig. 2c)  Case d: shared battery storage and shared grid connection and meter (Fig. 2d)

3.3. Studied systems Household power consumption data from 21 detached singlefamily houses in Sweden together with simulated PV power production over one year were used for this study. 18 of the houses had a rooftop area suitable for PV systems (cf. Fig. 3 and Table 1), and they were also equipped with battery storages of various sizes. In case of shared storage, total size was the sum of all batteries in the community. The battery capacity in this study was varied between 0 and 2 kWh per installed kWp of PV power. The maximum installed PV power was 11 kWp per system (see Section 3.5), which means that the study includes storage capacities between 0 and 22 kWh per household. Previous studies on PV-battery systems have often studied PV systems with 0.5e1 kWh storage per kWp [4]. Modeling

3.4. Electricity consumption data Household electricity consumption data with a time resolution of 10 min were used for this study. The electricity consumption data was collected by the Swedish Energy Agency during a monitoring campaign between 2005 and 2008. It covers approximately 400 households in Sweden, both apartments and detached singlefamily houses [37]. The location of the houses is not known. The

Table 1 Houses, electricity consumption, orientations and sizes of the rooftop segments and installed PV power. House no.

Consumption house (kWh/yr)

Rooftop azimuth ( )

Rooftop tilt ( )

Rooftop area suitable for PV (m2)

PV system (kWp)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

7297 21,365 11,384 5646 20,824 8189 21,521 12,189 18,610 13,533 16,941 17,485 15,149 9747 31,222 12,384 12,580 9978 4492 22,513 12,281

15 19 15 19 73 75 74 72 e 74 15 17 15 e 19 e 15 16 73 31 76

27 24 32 31 26 32 30 32 e 22 32 26 26 e 32 e 42 42 30 34 27

43.8 87.0 42.5 41.0 32.5 27.0 37.0 21.5 8.5 42.4 44.8 69.5 69.0 0.2 52.6 6.1 24.0 40.4 15.7 71.4 20.3

5.5 11 5.5 5.5 3.3 3.3 5.5 3.3 e 5.5 5.5 11 11 e 7.7 e 3.3 5.5 2.2 11 3.3

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Fig. 2. Schematic illustration of the different cases. Arrows represent power flows.

majority of electricity consumption data series in the data set represent individual household data over the duration of one month. 21 data series are long-term measurements of roughly one year for detached houses. The measurement process and data processing are described in Ref. [37]. The data have been used in several previous studies, including [30,32,38]. This data set is the most extensive and detailed data set for electricity consumption in Swedish households available today. The focus of the study is the relative impact of different connections and storage solutions and not the exact consumption patterns, since they vary strongly for different households. The heating systems used in the houses used in this study are not specified, but the total electricity consumption used for heating represents more than 50% of the total yearly power consumption in 14 of 21 houses included in this study [7]. This indicates that electric heating is used in a majority of all houses. The average consumption of the 21 detached houses is 14,500 kWh per house and year, which can be compared to the average electricity consumption for detached single-family houses in Sweden in 2008 of 15,800 kWh [39]. Since the irradiation data, and thus the PV electricity production data, are measured and simulated on a 1-min basis, the household consumption data was linearly interpolated to minute basis.

implemented in MATLAB described in Ref. [7]. Cloud movement would have a smoothing effect on the aggregate PV electricity production during days with scattered clouds. However, the houses and their PV systems in the community are probably too closely located to have any major effect on aggregate PV power production on minute basis [41]. The same data set of irradiance is therefore used for all houses. With higher time resolution, the smoothing effect due to cloud movements may become significant [41]. A LiDAR image of the housing area with numbered buildings and their annual solar irradiance can be seen in Fig. 3. From the LiDAR data (50 points/m2), tilt and azimuth angles of the rooftops of the houses were computed in the GIS software ArcGIS [30]. Each grid cell represents 0.4  0.4 m. To be able to choose well-suited parts of the rooftops, yearly accumulated global irradiation for each house was calculated in ArcGIS with the built-in tool Area Solar Radiation [42]. In this tool the annual solar irradiance is based on the solar path and the typical clearness of the sky

3.5. Modeling PV power production An example area in Uppsala (59.86 N, 17.61 E) with 21 detached houses, the same number as in the electricity consumption data set, was selected to represent a small community in a Swedish city. The area in Uppsala was chosen because high-resolution LiDAR (Light Detection And Ranging) data was available [40]. This made it possible to determine individual azimuth and tilt angles of the rooftops and areas suitable for PV installations. Calculations of the PV power production are based on measured high-resolution meteorological data from the Swedish Meteorological and Hydrological Institute (SMHI). The data used for this study was measured € ping (58.58 N, in 2008 in a meteorological station in Norrko  16.15 E) with a resolution of 1 min. The weather measurement station is the closest one to Uppsala with high-resolution irradiance data. The PV electricity production was simulated using a model

Fig. 3. Aerial LiDAR image of the studied area showing the yearly solar irradiance on rooftops. The rooftops included in the study are numbered and marked with thick lines.

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at the studied location. The potential area for solar energy installations was identified based on the annual solar irradiance, which was set to minimum 950 kWh/(m2  yr). The simulation procedure and choice of PV system size are described more thoroughly in Ref. [30]. Five different PV system sizes were chosen for the simulations, similar to the turnkey systems offered by the electricity retailer Vattenfall together with Solkompaniet, Sweden's largest installation company of PV systems (status January 2016). The PV system sizes offered are 2.2 kW, 3.3 kW, 5.5 kW, 7.7 kW and 11.0 kW, corresponding to 13 m2, 20 m2, 34 m2, 48 m2 and 68 m2, respectively [43]. The largest PV system possible for each house was used for the simulations. The houses are numbered and details of the PV systems are presented in Table 1. The azimuth angle is defined as [90 ,0 ,90 ] ¼ [east, south,west], the tilt angle as [0 ,90 ] ¼ [horizontal, vertical]. 3.6. Battery model A model for charging and discharging of batteries was implemented in the simulation program MATLAB. The batteries are charged only when there is excess PV power production and with no more power than the difference in instant power production and consumption. Discharging only occurs when the power consumption exceeds the PV power production. The battery storage is therefore not charged from the power grid, and also does not deliver power to the grid. The battery model selected is the kinetic battery model (KiBaM), which was developed by Manwell and McGowan in 1993 for leadacid batteries [44]. Lead-acid batteries storage is a well-known, mature and widespread technology [8]. The relatively low cost of lead-acid batteries are also a reason why this technology was chosen. Maximum charge and discharge power is primarily based on instantaneous power production or consumption surplus. Moreover, the maximum charging and discharging power is dependent on the state-of-charge (SOC) of the battery. The SOC is calculated in a range of 0e100% and specifies how much energy is stored in the battery relative to the maximum storage capacity. The maximum charging power decreases with higher SOC and the maximum discharging power decreases for low SOC. Therefore, it might not be possible to store all excess PV electricity production even though the batteries are not fully charged. In the kinetic battery model used for this study, three input parameters are needed to calculate the maximum charge and discharge current for every time step:  qmax e maximum capacity of the battery in Ah.  c e fraction of battery capacity that may hold available charge.  k e battery rate constant. Manwell and McGowan verified the KiBaM by using a battery with c z 0.40, k z 0.58 and qmax z 200 Ah per cell, and the two first parameter values will also be used in this study [44]. Lead acid batteries have a voltage of approximately 2 V per cell and the capacity of each cell is therefore set to 50 Ah, i.e. 100 Wh, to make the battery system scalable with relatively small steps [44]. The battery storage modelled in this study is only used for daily storage since weekly or seasonal storage would require either much larger battery storages or another storage technology. The maximum capacity of each battery system is varied between 0 and 2 kWh per kWp installed PV power to make it possible to evaluate how this affects the results. Only households with PV panels are equipped with batteries. Several previous studies have included battery storage of 0.5e1 kWh per installed kWp [4]. Due to decreasing battery cost this interval has been slightly extended to

maximum 2 kWh per installed kWp. The number of batteries in a system is rounded towards the closest integer. Frequently low SOC results in large stress of the battery, higher risk of failures and accelerated aging, i.e. the usable battery capacity will fade away faster than if the SOC is kept at higher levels [45]. The minimum SOC is therefore set to 30%, which means that only 70% of the nominal battery capacity can be used as storage. The roundtrip efficiency, i.e. efficiency for charging times efficiency for discharging, is set to 80%. The batteries are assumed to be placed in the basement of each house in case of individual storage or in a tempered location in case of shared storage. Temperature effects are therefore not taken into consideration in this study. Self-discharge and cycle life of the batteries is also not taken into account. These are aspects that could further improve the model. In a study by Jossen et al. the selfdischarge of lead-acid batteries was found to be 3e4% per month [46]. This means that the self-discharge is low when using the batteries for daily storage. The cycle life of lead-acid batteries is rather poor in comparison with lithium-based ones. This is an important aspect for the service life of a residential battery storage system [47]. 3.7. Economic assessment The profitability of adding storage to a PV system is often connected to self-consumption. Without dedicated supporting schemes for PV-storage systems, the extra revenue comes from the difference in buying and selling price of electricity and hourly price fluctuations. Increased self-consumption reduces the need of selling excess electric energy to a lower selling price and buying it back later to a higher price. The price difference must be high enough to compensate for storage losses. Initial costs of the PV system and regular maintenance or replacement costs are not taken into consideration in this assessment. Net present value is often used to evaluate an investment, but is not calculated in this paper. This is due to the uncertainties of future electricity prices, changes in future consumption patterns and rate of return. The latter is up to the producer, if the investment in a PV or PV-battery system is motivated by for example economic or environmental concerns. Furthermore, degradation of the batteries has to be considered to be able to calculate the net present cost, since it would decrease the self-consumption. Also maintenance and replacement costs would have to be taken into consideration. Instead, it is solely based on buying and selling prices of electricity, PV electricity production and curtailment losses. Three scenarios (case b, c and d) are compared to the reference scenario identified as case a. Description of the scenarios can be found in Section 3.3. Power losses due to charging and discharging of the battery storage do not contribute to the revenue from the PV battery system. The first step is therefore to calculate the “useful” PV electricity production Enet as

Enet ðX; CÞ ¼ Etotal ðX; CÞ  Elosses ðX; CÞ

(4)

where Etotal is the total PV electricity production, Elosses are the power losses related to the battery. All parameters are calculated as a function of feed-in limit X and storage capacity C. The selfconsumed PV electricity production Esc is calculated as

Esc ðX; CÞ ¼ 4sc ðX; CÞ  Enet ðX; CÞ

(5)

€sc is the self-consumption ratio in percent, which is calcuwhere o lated as in Equation (3) in Section 3.1. Storage losses do not

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Efeedin ðX; CÞ ¼ ð1  4sc ðX; CÞÞ  Enet ðX; CÞ:

(6)

Self-consumed PV electricity reduces the need of buying electric energy and can therefore be considered to have the same value as when buying the electricity from a retailer. Excess PV electricity production fed in to the power grid is considered to be sold to an electricity retailer. The total revenue Rtotal as a function of feed-in limit X and storage capacity C can therefore be calculated as

Rtotal ðX; CÞ ¼ Esc ðX; CÞ  Rbuy þ Efeedin ðX; CÞ  Rsell

30

Consumption/production [MWh]

€sc. The contribute to the revenue, and is therefore not included in o total feed-in power Efeedin is the remaining PV electricity production that is not self-consumed:

227

Electricity consumption PV electricity production

20

10

(7)

where Rbuy is buying price of electricity and Rsell is the selling price of electricity. The electricity prices for buying and selling can be found in Table 2. The buying and selling prices are based on the mean of monthly spot prices on Nord Pool Spot for grid area SE3 where Uppsala is located. Electricity retailers can add an extra fee on the spot price, but it will not be included in the calculations. Taxes and fees are thereafter added to the buying price. The electricity prices are given in Euro, although some prices are only available in Swedish currency SEK. To convert the prices into Euro an exchange rate of SEK 1 ¼ V0.108 (status January 13th, 2016) is used. The grid fee differs for different locations in Sweden and over time and the value used here is valid for Uppsala in 2016. Producers of renewable energy in Sweden can apply for electricity certificate during the first 15 years of operation. Prices for electricity certificates and spot price are mean values for January 2013 to December 2015 to compensate for price fluctuations. In Sweden there is currently (status February 2016) a “tax rebate” for small-scale electric energy production, supporting electricity fed into the power grid with an additional SEK 0.60 (V 0.065) per kWh [48]. In this study the tax reduction is not taken into consideration. 4. Results In the following subsections, the results of the simulations are presented. Power production and consumption for the PV systems and houses in the community are presented in Section 4.1. In Section 4.2 the production losses due to curtailment are presented as a function of maximum feed-in power and storage capacity. Section 4.3 contains results for self-consumption ratio when combining the PV systems with battery systems of various sizes. The results of the economic assessment are presented in Section 4.4. 4.1. PV power production and household power consumption In Fig. 4 the PV electricity production for each house for the simulated year is shown. No curtailment of the power production is

Table 2 Specification of electricity prices for buying and selling. Price specification

V per kWh

(Mean) price for

Reference

Spot price (sell & buy) Energy tax (buy) Grid fee (buy) Electricity certificate (sell) VAT 25% (buy) Tax reduction (sell) Total (Rbuy) Total (Rsell)

0.031 0.031 0.025 0.020 0.022 0.065 0.109 0.051

2013e2015 Jan 2016 Jan 2016 2013e2015 Jan 2016 Jan 2016

[45] [46] [47] [48] [49] [44]

0

0

5

10

15

20

House no. Fig. 4. Yearly PV electricity production and household electricity consumption in MWh.

included in this step. 18 of 21 houses are equipped with a PV system and the annual total electricity production is 107,000 kWh. The houses without PV panels had a too small surface of the roof segments with a yearly irradiance of at least 950 kWh per m2, cf. Fig. 3 and Table 1. The annual total electricity consumption of the 21 houses over the year was approximately 305,000 kWh and the annual mean electricity consumption per house was 14,500 kWh. The smoothing effect of aggregating power consumption of multiple households can be compared to power consumption and PV power production of one house. House number 13 had a yearly electricity consumption of 15,100 kWh which was closest to the annual mean electricity consumption per house. The power consumption of house 13 is therefore compared to the aggregate power consumption in Fig. 5. The figure shows the smoothing effect of aggregate power consumption pattern of multiple houses during a day (plot a) and over the whole year (plot b). The mean power consumption pattern is smoother for the whole year than for one single day, but the mean aggregate power consumption is still smoother than for house 13. 4.2. Feed-in power and losses The maximum overproduction (power to grid) during the year is 93.7 kW and the maximum overconsumption (power from grid) is 94.3 kW. High power to grid is however not common, as can be seen in Fig. 6. There is a large potential to decrease the maximum power to grid without high production losses. Periods of high net power consumption, i.e. power consumption minus power production, are almost as frequent as high power consumption. This suggests that high power demand is negatively correlated with PV power production. It is likely that the power consumption is high in the winter when there is no or very low PV power production. Since the PV power production is low in the winter in Sweden, adding a battery storage system is not likely to reduce the maximum power consumption unless the battery can be charged from the grid during periods with lower consumption. There are different kind of losses for the cases of curtailment and storage. When using PV power curtailment there is a reduction in power production whereas when using storage there are charging and discharging losses. In this study PV power reduction due to curtailment are regarded as losses. How the curtailment losses, battery losses and total losses depend on battery capacity and feedin limit is shown in Fig. 7. Battery losses (plots c and d) are generally not affected by the feed-in limit, since the batteries are mostly fully

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charged before there is any need of curtailment of the production. Plots e and f show that the total losses are very similar in case of individual or shared storage. The losses are low-under 7% with every battery size on a yearly basis-when using a feed-in power limit of 50 kW, i.e. almost a halving of the original maximum feedin power of 93.7 kW.

to the grid, the whole power production has to be consumed in the households. The self-consumption ratio is thus close to 100% for the whole community when using a shared electricity meter. Losses due to charging and discharging of the battery storage are however not regarded as self-consumed. The calculated ratio is therefore lower than 100% with batteries. In the case with individual storages and individual electricity meters (plot a in Fig. 8) the aggregate selfconsumption ratio will not be 100% even if the feed-in limit is set to 0 kW. One or more houses might have overproduction, i.e. an instantaneous self-consumption ratio below 100%, and one or more houses have overconsumption. In this case, no or low power is fed in to the grid from the community even though the overall selfconsumption ratio is not 100%. Another way to measure the self-consumption ratio in case of individual storages is to use a shared connection point and shared electricity meter (plot b) instead of one per household. This is the same configuration as for the case with shared storage. The difference in self-consumption ratio between shared and individual storage options decreases (plot b and c). The self-consumption ratio is however still slightly higher for the case with shared storage (plot c) than for individual storages (plot b). For a scenario with no PV power production curtailment, i.e. a feed-in limit of 100 kW, and the largest battery storage possible-2 kWh/kWp-is the selfconsumption ratio 61% with individual storage and meters (plot a), 67% with individual storage and shared meter (plot b) and 72% with shared storage and meter (plot c). When no storage is used are the numbers 43%, 58% and 58%. Since the minimum allowed SOC is set to 30% only 70% of the nominal battery capacity is usable as electricity storage.

4.3. Self-consumption ratio The self-consumption ratio is calculated via Equation (3) in Section 3.1 and presented relative to battery capacity and feed-in limit in Fig. 8. It can be seen that the self-consumption ratio is higher with a shared storage than with individual ones. The values of battery capacities are valid for each house. Note that the PV electricity production decreases when there is a lower feed-in limit since the curtailment losses increase. Even if the absolute selfconsumption (in kWh) is the same, the relative self-consumption ratio is larger with partly curtailed power production than with full power production according to Equation (3). In case of a feed-in limit of 0 kW, i.e. no power can be delivered

4.4. Economics of storage and curtailment The yearly revenue for the PV-battery systems is calculated via Equation (7) and with electricity prices from Table 2. The yearly total revenue for the whole community when not using storage or feed-in limit is V7430 for the community where every house is using its own electricity meter. With shared electricity meter the revenue is increased to V9110, an increment of V1680 or 23% only by changing location of the electricity meter. Fig. 9 shows the yearly revenue when using battery storage and applying feed-in power limits. The yearly revenue is highest with a high maximum feed-in

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Fig. 7. Annual electricity losses due to curtailment of the PV power production battery charging and discharging. Results for (a) individual storages and (b) and shared storage. Contour lines show annual electricity losses of 5%, 10%, 20% and 40%.

Fig. 8. Self-consumption ratios for (a) individual storage and electricity meters, (b) individual storage and shared meter and (c) shared storage and meter. Reference scenario with no storage is on the baseline of each figure. Contour lines show annual self-consumption ratio of 50%, 60%, 70% and 80%.

level and a large storage, i.e. in the top-right corner of every graph. Maximum total feed-in power for the community without curtailment is 93.7 kW. For a storage size of 2 kWh per kWp installed PV power is the revenue V8720 for individual electricity meters and storage, V9400 for shared meter and individual storage and V9710 for shared meter and storage. This means an increment in annual revenue of V310 or 3% when changing from individual to shared battery storage in a community which shares grid connection. 5. Discussion In a community of several detached single-family houses with PV systems, a shared battery storage, power grid connection and electricity meter will lead to higher self-consumption ratio compared to a case where every house has its own storage system. This holds regardless if they have individual or shared meters. For a community with individual PV-battery systems, the revenue

increases when using a shared electricity meter compared to using one per household. Without storage the yearly revenue is V1500 higher for the community if they share one electricity meter than if every household has its own. However, this does not decrease the total feed-in to the grid, it only shifts revenue from the power supplier to the community. From an economic point of view, it is likely better to have a larger, shared storage rather than smaller ones if the total battery capacity is the same. Every system needs power electronics and a battery management system, which are probably not linearly scalable with battery capacity. The total maintenance costs relative to battery size may also decrease. One problem is how the extra revenue should be shared among the households in the community, especially since they do not have the same sizes of PV systems. Shared electricity meters and shared battery storage could also be problematic due to regulations. The total production losses due to curtailment are rather low even with large cuts of the maximum feed-in power. A reduction of

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Fig. 9. Yearly aggregate revenue in Euro for the whole community. Revenue for households with (a) individual storages and electricity meters, (b) individual storage and shared meter and (c) shared storage and meter. Reference scenario with no storage is on the baseline of each figure. Contour lines show annual revenues of V6000, V7000, V8000 and V9000.

almost 50% leads to yearly production losses of maximum 7% when no storage is used, and even less for a case with battery storage. Incentives, either “positive” such as compensation or “negative” such as restrictions, are needed to make curtailment a realistic option. From the graphs in Fig. 9 it is possible to determine how large the compensation for power production losses has to be to give the same revenue as without curtailment. An important drawback of using battery storage systems for PV in Sweden is the difference in power demand during summer and winter. The storage is very rarely used in the winter due to higher power consumption and considerably lower PV power production. In regions with more stable solar irradiance over the year, such as in lower latitude regions, use of energy storage would probably be higher and thus increase the yearly revenue. In future research, simulation models using other types of batteries such as lithium-based ones could be used. The efficiency, cycle life and degradation are improved with lithium-ion instead of lead acid batteries. With large hourly fluctuations in electricity prices, it may also be profitable to store cheap electricity and use it when the price is higher. This would require regularly input from the day-ahead market at Nord Pool Spot to know when to charge and discharge and a forecast of power consumption. It would be interesting to apply this model on a real neighborhood or community to verify the model. The measured and validated electricity consumption data comes from a monitoring campaign between 2005 and 2008 performed by the Swedish Energy Agency. The resources for such a large campaign do not exist at the university and there are currently no plans to do a new one in the near future. Verification of the results requires several houses located in a community, where a majority of them are equipped with PV systems. Several storage systems for residential applications would also be needed. However, the monetary resources available do not allow this kind of verification. A shared storage would most probably require a joint electricity contract with a retailer and a shared electricity meter. Thereafter each house has to have an individual meter since the annual electricity consumption differs between the households. How to divide the extra revenue due to the shared storage also has to be decided. A possible solution is to use the extra revenue for expenses in the community such as snow clearance in the winter or maintenance work of shared real estate properties. The PV-battery concept could also be further developed by using

“old” batteries from electric vehicles, since the number of electric and plug-in vehicles is rising rapidly globally. The energy density is much less important for stationary than for mobile applications. Therefore, batteries no longer suitable for vehicles may become accessible for stationary applications at a lower price than for a completely new battery system. 6. Conclusion The main conclusions of this study can be summarized as follows: (i) The self-consumption of residential PV systems on 21 single-family houses in Sweden rises with 15% points when all houses use a shared power grid connection and electricity meter instead of one connection and meter per house. No storage is used in this case. (ii) Batteries of 2 kWh nominal capacity (1.4 kWh usable) per kWp installed PV capacity increase the self-consumption ratio in the community with 9% points when using individual batteries for each house and 14% points when all houses share the batteries. (iii) A nearly 50% reduction in feed-in power leads to losses below 7% due to PV power curtailment. (iv) The yearly revenue increases with shared battery storage and electricity meter. The increment in revenue solely by changing from individual to shared electricity meter in the community is 23%. For a scenario without storage and power curtailment is 23% for shared compared to individual storage and electricity meter. With 2 kWh battery storage per kWp of installed PV power, the revenue increases with 3% by changing from individual to shared storage in a community which uses a shared grid connection. (v) If a large storage unit is cheaper per installed capacity than several smaller ones, shared storage and electricity meter are preferable when regulations allow it. The overall conclusion of this study is that the self-consumption of residential PV-storage systems in a community increases by using a centralized storage unit instead of separate units in the households. Shared storage in combination with power curtailment of the PV systems result losses of a few percent on a yearly basis even if the maximum power from community to grid is halved. Acknowledgement This work was carried out as part of the research project Smallscale solar electricity in buildings-Power for change in energy

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