-
Effects of Electricity Tariffs on Optimal Battery Energy Storage
Sizing in Residential PV /Storage
Systems
Mohsen Gitizadeh, Hamid Fakharzadegan Department of Electrical
and Electronics Engineering
Shiraz University of technology Shiraz, Iran
[email protected] , h. [email protected]
Abstract- In this article, the problem of sizing and dispatch
scheduling of battery energy storage in a grid-connected
photovoltaic system with battery storage backup (PV/Storage system)
is addressed. The goal is to minimize the costs of purchasing
electricity from the grid and the costs associated with battery
aging (cost of battery degradation is modeled in daily
dispatching). Grid-connected photovoltaic system assumed to be
available in the typical residential consumer considered in our
study. Electricity generated from the PV is used to charge the
battery and supply the house's demand. If the consumer is net
metered, any exceeding can be sold back to the grid. PV/Storage
system can reduce costs of purchasing electricity from the grid
through peak shaving and load shifting. The rate structure
determines which application is being used. Load shifting
application is implemented when time-of-use pricing is in effect
and peak shaving application is beneficial when the consumers are
charged for peak of the demand. Optimal sizing and dispatch
scheduling of the battery for both pricing structures are
determined and effectiveness of each application in reducing costs
is evaluated. Mixed Integer Programming (MIP) is implemented to
solve the optimization problem.
Keywords-battery energy storage; sizing; scheduling; solar power
generation; peak demand management
I. INTRODUCTION
Rapid reduction of fossil fuel resources on worldwide,
increasing the electricity demand and the environmental concerns
associated with conventional generators, has led to a worldwide
concern on the development of alternative electric energy
production methods. Renewable energy sources have been regarded as
the solution to the world energy concerns. Among renewable energy
technologies, grid-connected photovoltaic (PV) application has
gained a great attention in research because it appears to be one
of the most efficient and effective solutions to this environmental
problem [1].
However matching the intermittent energy generation of the PV
system with the dynamic power demand is one of the major
challenges, a solution is using storage devices. These dispatchable
storage technologies will bring added benefits to utilities,
homeowners, and commercial customers through greater reliability,
improved power quality, and overall reduced energy costs [2].
978-1-4673-6150-7/13/$31.00 2013 IEEE
Issues primarily related to the distribution grid include:
growing end-use demand, transmission substation limits, and voltage
drop [3] have moved utility companies towards peak demand
management by assessing time-of-use (TOU) energy pricing and demand
charges for industrial and commercial consumers. Recently with
Increased implementation of smart meters and electric vehicles,
some utility companies introduced TOU rate structure and peak
demand charges for residential consumers. Capability of batteries
to supply energy generated at one time to a load at some later
time, can provide financial benefits to the system's owner through
Peak shaving, load shifting, and demand response applications. The
rate structure and interactions between the utility and the
customer determine which application is being addressed [2].
Optimal sizing and dispatching of battery are affected by the
application which is being used. Various studies have been
discussed the problem of battery sizing and dispatching in PV and
wind applications. In [4] the control methodologies for a
battery-based energy storage system in wind power applications are
proposed and the effect of control strategy on proper sizing of
battery is investigated. However, the sizing of the battery is
significantly affected by specific control strategies. In [5] a
methodology for calculation the optimum size of the PV array and a
battery bank for a standalone hybrid Wind/PV system is developed.
In [6] the intensive penetration of PV production into the grid is
addressed by proposing peak shaving service at the lowest cost and
the structure of a power supervisor based on an optimal predictive
power scheduling algorithm is proposed. Paper [7] describes the
optimization method of system installation and operation for a
retail store with PV and storage battery system and an electric
vehicle (EV) quick charger and a control on EV charge is
implemented to extend the battery life. Then a genetic algorithm
(GA) is employed to solve the trade-off problem between the
installation cost and the reduced maximum load power. In [8] a
short-term scheduling of battery in securityconstrained unit
commitment (SCUC) is proposed and analyzes the effect of
grid-connected PV Ibattery system on locational pricing, peak load
shaving, and transmission congestion management but sizing problem
is not considered. Paper [9] studies the problem of the battery
size detennination used in grid-connected PV systems for the
purpose of load shifting and peak shaving, when TOU pricing is in
effect. But the effect of peak shaving on the electric bill is not
considered. Paper [10]
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studied the economic benefits of PV for emergency power supply
and demand charge management applications for typical industrial
customers. However battery sizing is not mentioned. Paper [11]
modeled annual energy bill savings for a PV /Storage system over a
range of battery capacities. An approximate insolation forecast and
a load forecast are used to determine the amount of night time
charging required minimizing the cost of energy purchased by the
customer from the electric utility during the following day. In
[12] a linear programming is implemented to model optimal energy
storage dispatch schedules for peak net load management and demand
charge minimization in a grid-connected PV/Storage system. The
financial benefits of the dispatch strategy are compared with basic
off-peak charging/on-peak discharging and real-time load response
dispatch strategies.
In this paper, we study the effects of electricity tariffs on
optimal battery sizing and dispatch scheduling for residential
customers equipped with PV /Storage systems. Customers of most
utility companies can choose their electricity payment method
according to their usage pattern. Customers with PV /Storage system
which purchase electricity on a time-of-use (TOU) basis can use
excess of PV generation early in the day to support a load later in
the day (i.e. load shifting). Therefore reduce the house's demand
during late-day when the PV generation is low and higher rate times
come. If PV generation was not sufficient to charge the battery,
electricity can be purchased from the grid when the time-of-use
price is low. Electricity purchased from the grid is used to supply
all or part of the load, when peak rates are in effect. For the
propose of peak shaving in a grid-connected PV systems, PV provide
all required power above a specified threshold. If the PV output
was not sufficient, discharging the battery which energized
earlier, reduce the house's demand to desired value. Our objective
is to investigate effects of the most available peak demand
management tariff structures on optimal sizing and dispatching of
battery which minimizes costs of purchasing electricity from the
grid. Charging higher prices at times when it is cost-beneficial to
reduce customer demand and charging lower prices at the other times
(time-varying prices) and charging the customers for the maximum
demand (demand charge) are important types of peak demand
management tariffs. Carolina Power & Light Company [13]
proposes timeof-use (i.e. TOU) and time-of-use with specifying
demand charge (i.e. TOUD) tariffs for residential customers. In a
typical customer, optimal battery sizing and dispatch scheduling
for both cases are calculated and optimum threshold for peak demand
is obtained.
II. SYSTEM MODELING
To determine the optimal sizing and dispatching of the battery,
information on the electricity demand of the residence as well as a
model of the battery and PV is required. Modeling of system's
components shown in Fig.l is described as follows:
A. Battery System This study has been performed with flat plate
lead acid
batteries and the model presented here corresponds to this
technology. This model has already been introduced in [5] and
simplified in [9], thus presentation of calculation in this
paper
is restricted to discrete equations of battery model (1) and
(2). Dynamic equation of battery expresses as follows:
EB (t) (Wh) : Electricity stored in the battery at time t.
PB (t) (W) : Charging/discharging rate of battery.
(1)
The battery is charging if PB(tO and discharging if PB(t)
-
B. P V Generator The PV generator has been modeled by a linear
power
source according to the irradiance level. The model of
electricity generated from PV modules is the simplified model used
in [14]:
Ppv (t) = I (t ) x A x TJ pv
Where:
I (Wm-2) is the global horizontal irradiation;
A (m2) is the total area of PV modules;
llpv is the solar conversion efficiency of PV modules.
(5)
A dc-to-ac inverter with constant conversion efficiency llpv is
used to connect dc output of the PV to ac bus. This modeling of PV
generator is elementary and PV modules temperature effects are not
taken into account but it is appropriate for this application and
significantly representative of the behavior in the range of
operation conditions of the system.
C. Load Load consumption pattern in a single household,
mainly
depends on environmental conditions, set of appliances in the
household, the electrical rating of these appliances and the use of
the appliances. [15]. Therefore, daily usage pattern of each
household is specified by behavior of the occupants which varies
with seasonal changes and weather variations through the year.
Considering seasonal effect and behavior of a single household, the
consumption pattern of the household in each season will be
detennined. In this paper the load at time t is shown as PL
(t).
D. Objective Function The objective function to be minimized is
the expected
daily operation's costs of the system over the entire studied
period. Operation's costs of the system include purchasing
electricity from grid and costs associated to degradation of the
battery.
(0+24 min L Ep(t)PNet(t)
t=IO (6) +K xL'lC(tO+T) +DC x(max(Vet(t))) I
Where
DC: Levelized costs of demand charge
PNet(t): Net power purchased from grid at time t
K: Unit cost for battery capacity loss (K=O.l5 for flooded
leadacid batteries [16])
The summation in the first line is expected costs of purchasing
electricity from grid; the first term in second line corresponds to
demand charge when it is considered; and the second term
corresponds to battery degradation costs. Note
that, demand charge calculates monthly. Thus day with the
highest peak demand of the month is studied and the levelized
demand charged to calculate daily operation costs.
E. Constraints 1) Generated and consumed power at each time
should
satisfy
(7)
2) Stored energy in the battery EB (t) should be less than
battery capacity at each time. Fully discharging of the battery
assumed to be possible but to achieve longer life of the battery,
maximum depth of discharge (DOD) more than 80% of the available
battery capacity, is not allowed. Thus:
(I-0.8)C (t) :s; E B (t):s; C (t) =C If!j -!1C (t) (8)
3) Charging/discharging rate of the battery depends on available
battery capacity C(t) and mlllimum charging/discharging time of the
battery dH which for simplicity assumed to be the same for both
charging and discharging.
(9)
(10)
III. CASE STUDY
To investigate the effects of pricing structure on battery
sizing determination, a typical residential customer is considered.
Two pricing structure proposed by Carolina Power & Light
Company [13] for residential customers, is considered:
A. Time-ofuse
17.037
-
plus 4:00 p.m. through 9:00 p.m. The on-peak demand shall be the
maximum demand used in the on-peak hours of the current month.
To calculate PV output, solar irradiance data in the studied
location for the year 20lO is downloaded from [17]. Output power of
PV is calculated using (5) and solar irradiance data in studied
days. Conversion efficiency of PV modules llpv assumed to be 18%
and area of modules considered to be 20 square meter.
Electricity usage data of a typical residential customer
requested from Carolina Power & Light Company, is used in this
case study. As failure to peak shave on one day can have severe
economic consequences when monthly peak demand charge is taken into
account, day with the highest peak demand in each season is used to
evaluate demand charge management. Demand curves are expressed in
30-min intervals as sampling interval used in this paper
L1t=0.5.
Objective function (6) is function of battery
charging/discharging rate PBac (t), battery capacity Cref Battery
capacity Cref considered as discrete variable with 3 (KWh) steps
and 30 (KWh) upper limits. The proposed Mixed Integer Programming
(MIP) model of battery sizing is solved using the CPLEX solver in
GAMS [18]. For all combination of battery capacity, optimal
dispatching of battery for selected day in each season is
calculated and the best combination which minimizes the objective
function is obtained.
10 12 14 H 18 20 Hours
Figure 2. Demand of a typical customer in a day with the highest
peak demand in summer season (10 August 2010)
WOO 2 -;.----:---,'''0-".--, 20 22 24 Hours
Figure 3. Demand of a typical customer in a day with the highest
peak demand in winter season (17 January 2010)
IV. RESULTS
A. Time-af-use (TOUE) Optimization problem is solved to find
optimal sizing and
dispatching of the battery when time-of-use tariff (TOUE) is in
effect. The primary solution results obtained from the solution of
the optimization problem are the values for the capacity of the
battery storage and the amount of charging/discharging rate (daily
dispatching) of battery. Results from optimal dispatch scheduling
of the battery for a typical value of battery capacity (Cref =
12KWh) in one of the two studied days (17 Jan. 20lO), are shown in
figures (4)-(6).
1000IfM+M------ OJ c:
. 500 -5 III i t L .!: i ii 11 i'/1 i -500 , i , j ; ! ; -5 , r
; 1 i -1 000 L-:'----':---:'- ... 1O:..:..:,121.L..---,16
:..:..:"L82.L.O2L2 ---..J2 Hours
Figure 4. Optimal dispatch scheduling of the battery
3000
2000
1000 0 "-
-1000
-2000 1 0 12 ,. 16 18 20 22 24 Hours
Figure 5. Net load of the customer without using battery system
and when battery system is operating
2.5r-----------==,,"
&> 2 . 1.5 1:i 1 .0
0.5 o
...J 10 12 Hours 16 18 20 22 24
Figure 6. Battery life degradation during system operation
3.5r-------------'-------'----' 3
... -;; 2.5 1iI 8 2 c: .2 1.5 OJ 1 a. o 0.5
0L-0OO60 OO90OO1 2OO01500 018OO0210002400027OOO300 OO
Battery capacity (Wh)
Figure 7. Operation costs of the system (i.e. costs of
electricity purchasing from grid and battery degradation) in two
studied days for different battery capacities
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Charging/discharging rates of the battery is shown in fig.4. The
battery is charged at maximum rate during off-peak hours (0-6 a.m.)
until the battery is fully charged. Battery charge state remains
steady until on-peak hours begin. During 9 a.m.-l p.m. the battery
is discharging, the house's demand is met and excess energy is sold
back to the grid as illustrated in fig.7. During off-peak hours
from 1 p.m.-4 p.m. battery is reenergized to meet the house's
demand. Note that, from 2 p.m. to 3 p.m., net load of the house is
negative, as shown in Fig. 5. Therefore there is surplus PV
generation; however, the surplus generation is stored in the
battery and is not sold back to the grid because currently the
electricity price is not high.
In this case, due to unlimited peak demand of the customer and
high enough margin between on-peak and off-peak prices, it is
profitable to purchase electricity from the grid and charge the
battery in low-price hours (to the maximum battery capacity) and
discharging the battery in high-price hours to meet the house's
demand and selling back the excess energy to the grid. Therefor
higher battery capacities culminate in lower operation costs, as
illustrated in Fig. 7. The optimal battery capacity which minimizes
the operation cost during the studied period was found to be Cref =
30 (KWh). Objective function for this value of battery capacity is
1.238 which has reduced operation costs (without battery system) up
to 154%. For the battery capacity (Cref = 12 KWh), operation costs
reduced about 32%. Fig.6 shows that battery capacity loss during
daily operation was about 2.5 (Wh).
B. Time-ofuse with peak demand charge (TOUD) In this section,
optimal sizing and dispatch scheduling of
the battery is calculated when demand charge is assessed.
Battery scheduling for typical battery capacity (Cref = 12 KWh) in
one of the studied days is shown in figures (8)-(10).
Fig. 8 illustrates that, battery is charged from 4 a.m. to 5
a.m. and 14 p.m. to 16 p.m. The stored energy is used to curtail
net load of the house to targeted peak demand (targeted peak demand
assumed to be PDT=1300 W in this case) during onpeak hours from 7
a.m. to 9 a.m. and 16 p.m. to 21 p.m.
Unlike the previous case, cost of the battery capacity loss
during operations is more than the potential gain expressed as the
margin between on-peak and off-peak prices. Consequently, battery
is not used to sell back electricity to the grid; and discharging
of the battery is restricted to hold peak demand under the targeted
threshold, as illustrated in fig. 9.
Operation costs during the studied period for different battery
capacities is calculated and plotted in fig. 11. The optimal
battery capacity which minimizes the operation cost was found to be
Cref = 6 (KWh) and peak demand target was set to be (PDT=1000 W).
Objective function for this value of battery capacity and peak
demand target is 2.090 which has reduced operation costs (without
battery system) about 17%. According to (10) batteries with higher
capacities have higher discharging rate. Higher discharging rate of
the battery leads to more battery capacity degradation costs, as
expressed by (2). Therefore, for higher battery capacities, costs
of battery degradation grow higher. In this rate structure proposed
by Carolina Power & Light Company, demand charge is not high
enough to compensate costs of battery degradation. As a
sequence, higher battery capacity does not guarantee lower
operation costs (fig. 11). In this case battery capacity loss
during operation is 1.2 (Wh) as shown in fig. 10.
Figure 8. Optimal dispatch scheduling of the battery (case
B)
_. _ .. Without battery system -- With battery system 2500
r-,.J----.-:-........,.-..,.---;.,..'--...---...,...-........,.-..-'"-T---,
2000
'500 'ODD o n. 500
i '
-500 '--'---'----'---"----".Lo ---:-, ':-2 --:-',.'----:":,
6-,.L.---=2.L O --:-'22c........,J2. Hours
Figure 9. Net load of the customer without using battery system
and when battery system is operating (case B)
:E" 1.'
,---.-:-........,.-..,.---...---...,...-........,.---,----, '.2 : 1
'" Q. O.B 0.6 0.4 o 0.2 o
o '--'---'--"----',.LO---:-'':- 2 --:-''''----:": '6---:'8---:2O
--,'2 2c........,J2' Hours Figure I O. Battery life degradation
during system operation (case B)
_ 2.5 2 o u c: 1.5 o :;::; 1 .. Q. 00.5
o 3000 6000 9000 12000 1500018000 21000 24000 2700030000 Battery
capacity (Wh)
Figure 11. Operation costs of the system in two studied days for
different battery capacities (case B)
V. CONCLUSION
PV /Storage systems provide financial benefits to the system's
owner and the utility especially through peak shaving and load
shifting. Interactions between the utility and the
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customer determine which application is being addressed. In this
work, the effects of two pricing structures proposed by Carolina
Power & Light Company, on optimal sizing of battery energy
storage in a residential PV /Storage system was investigated.
Our results illustrate that, financial benefits of battery
energy storage for a customer highly depends on electricity rate
structure and battery aging. In time-of-use pricing, high margin
between on-peak and off-peak prices approve efficiency of battery
energy storage system. When demand charge IS assessed, the margin
is not high enough to cover costs of battery capacity degradation.
Thus, demand charge should cover battery degradation costs and
encourage the customer to use peak shaving application. In our
studied pricing structure, load shifting application with PV
/Storage systems has more financial and environmental benefits to
the system's owner and the utility.
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