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DER optimization to determine optimum BESS charge/discharge schedule using
Linear Programming
Article · July 2016
DOI: 10.1109/PESGM.2016.7741576
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DER Optimization to Determine Optimum BESS
Charge/Discharge Schedule using Linear Programming
Sridhar Chouhan, Deepak Tiwari, Hakan Inan, Sarika Khushalani-Solanki, Ali Feliachi
Advanced Power & Electricity Research Center (APERC)
Lane Department of Computer Science and Electrical Engineering
West Virginia University, Morgantown, WV, USA 26506-6109
Abstract- This paper proposes a novel optimization technique
using Linear Programming (LP) method to solve the optimal
scheduling problem of Distributed Energy Resources (DERs)
including Battery Energy Storage Systems (BESS). The
proposed optimization technique has a dual objective function of
economics and peak-shaving.
Optimization of the BESS
operation is a complex problem as it has special constraints such
as Depth of Discharge (DOD) requirements, State of Charge
(SOC) limitations, Charge and Discharge rates, etc. The
proposed LP method would be a useful tool for distribution
operators to optimally dispatch the distributed resources in their
systems. The derived charge/discharge schedules of BESS ensure
maximum energy arbitrage revenue. The proposed optimization
technique is tested on a taxonomy feeder developed by Pacific
Northwest National Laboratory (PNNL) with a fictitious
microgrid that consists of DERs including a BESS. The
optimization problem is modeled and solved using the Matlab
optimization toolbox with industry standard load and electricity
price data.
Index Terms- Optimal Scheduling, Battery Energy Storage
System (BESS), Distributed Energy Resources (DER), Energy
Arbitrage, Linear Programming (LP).
I.
INTRODUCTION
Distributed energy resources (DER) that are
interconnected to electric distribution systems have been
increasing rapidly in the past few years and this increase is
expected to continue with a growing rate. Integration of DERs
to the traditional distribution system results in various benefits
such as reduced line losses, peak management, voltage
regulation, outage management, ancillary service support, etc.
DERs consist of various assets such as distributed (local)
generation units, energy storage units and controllable loads.
The intelligent tools that will help distribution operators to
monitor, control and manage the operation of DERs, with all
the required functionalities are still evolving. There is a clear
need for an operational and planning tool that can help
manage operation of DERs optimally. The energy storage
systems are used today in the distribution field for so many
applications including renewable capacity firming, renewable
output smoothening, load following, peak shaving, and
ancillary service support. Electric utilities and co-operatives
pursue DERs with BESS to reduce peak demand on their
The first author is a Ph.D. student in Advanced Power & Electricity
Research Center, West Virginia University, Morgantown, WV, USA.
(E-mail: schouhan@mix.wvu.edu).
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system as this helps reduce the demand charges and is
considered to be a direct benefit to the utility.
Recent developments in BESS and power electronics
technologies are making the application of energy storage a
potentially viable solution for various modern power
applications [1]. BESS could present interesting possibilities,
for producers, network operators, and even the large eligible
consumers [2] with respect to technical, economical, and
environmental aspects. The technical aspects include load
peak, unpredictability of renewable energies, faults on the
network, ancillary services, etc. Economical aspect involves
increasing the systems economic efficiency under the
progressing deregulation of the electric market, and the
environmental aspect include regulatory standards on
emissions and renewable mandates.
Some studies have investigated the ways to optimize BESS
in the electricity market and provided impressive results. In
[3] the authors used dynamic programming to optimize ESS
charge scheduling to maximize benefits due to the energy
pricing differences between peak-load and light-load periods.
In [4] a non-linear programming technique is proposed to
optimally schedule cool energy storage system. Authors in [5]
present a multipass iteration particle swarm optimization
approach to solve the optimal operating schedule of a battery
energy storage system (BESS) for an industrial time-of-use
(TOU) rate user with wind turbine generators (WTGs). Lo and
Anderson used dynamic programming algorithms to maximize
fuel-cost savings and optimize battery size [6]. In [7] the
author proposes the LaGrange’s Relaxation method to
determine the spinning reserve requirements, and to achieve
the objective of minimizing the total generation cost. Artificial
and computational intelligence technologies, such as the
Genetic Algorithm (GA), Evolutionary Programming (EP),
and the Simulated Annealing (SA) method, have also been
applied to deal with the scheduling problems of energy storage
systems [8], [9].
Each method differs in the way the optimization problem
is formulated and has its own merits and demerits. In contrast
to the approaches listed above, the proposed LP optimization
approach is a combined optimization technique that not only
deals with the scheduling problem of BESS, but also deals
with the scheduling problem of all other DERs connected to
the distribution system in a single optimization formulation.
The proposed LP optimization has a dual objective of
economics and peak-shaving, i.e., it considers peak shaving
goals by the distribution operator while optimally dispatching
the DERs including BESS. The optimum charge/discharge
schedule of BESS obtained from the optimization maximizes
the revenue out of energy arbitrage.
This paper is laid out as follows. First a short overview of
the BESS model is provided in Section-II. The LP
formulation for DER and storage unit dispatch is presented in
Section-III. The test system and results are presented in
Section-IV and section-V summarizes the conclusions of the
work. Section-VI presents the DER and BESS specifications
used in the test system.
II.
BESS MODEL
A better understanding of the BESS operation is essential
in order to develop the optimization problem that can
determine its charge/discharge schedules. The BESS state
determination is crucial at each stage. The power output of
the BESS can be calculated as the difference between stored
energies of two consecutive stages [2]. In this paper one hour
time difference is used between the consecutive stages.
Energy stored in the energy storage device is expressed as
follows.
When the BESS is charging (
(1 ℎ
When the BESS is discharging (
> 0)
=
−
MATHEMATICAL FORMULATION OF OPTIMIZATION
PROBLEM
The entire problem of determining the optimum DER
schedules including BESS charge/discharge schedules is
divided into two LP problems.
• LP formulation for DER dispatch schedules and
BESS discharge schedule
• LP formulation for BESS charge schedule
A. LP formulation for DER dispatch schedules and BESS
discharge schedule
The main objective function of the proposed LP
optimization formulation is to minimize the total energy cost
( ) to supply a given system load. The objective function of
minimizing ( ) makes sure that at each one-hour time
interval the cheapest available generation is dispatched to
meet the system load. The objective function of minimizing
the total energy costs incurred in operating all the DERs
including BESS, and electric grid over the 24 hour scheduling
horizon is given by:
min(
)=
(
)+
+(
)
= 1,24; = 1, ; = 1,
; (3)
This optimization is subjected to the following system
constraints at every scheduling interval (one-hour).
< 0)
−
=
III.
(1 ℎ
)
(1)
1.
Active power balance in the system.
+∑
+∑
=
2.
DER operational output limits
≤
≤
= 1,24; = 1, ; = 1,
)
(2)
Where,
: Energy storage system efficiency
and
: Energy stored in energy storage system
at hour “t” and hour “ t+1”
: Power transferred to/from the energy storage
system at hour “t”
Following are some important BESS characteristics that are
utilized in the optimization problem formulation.
• State of Charge (SOC): SOC is the indication of
stored energy in the energy storage unit and is
expressed in terms of percentage of total storage
energy capacity in kWh.
• Depth of Discharge (DOD): DOD is the limit to
which an energy storage unit is allowed to be
discharged in a discharge cycle.
• Round Trip Efficiency (RTE): RTE is the ratio of
energy discharge out of an energy storage unit to the
energy charge into the energy storage unit for the
same amount of energy transaction.
978-1-5090-4168-8/16/$31.00 ©2016 IEEE
3.
4.
5.
6.
; (4)
= 1,24; = 1, ; (5)
Feeder peak shaving constraint for not exceeding the
defined feeder or substation transformer limit.
≤
= 1,24; (6)
BESS SOC limit constraint
≤∑
≤
= 1,24; = 1, ; (7)
BESS DOD limit constraint
∑
≤
= 1,24; = 1, ; (8)
BESS discharge-rate limitation
≤
= 1,24; = 1, ; (9)
Where,
: Number of DERs (Distributed Generator and
Responsive Load units) in the system
: Number of BESS in the system
: Real power in kW from electric grid at tth hour
: Real power in kW from the ith DER at tth hour
: Real power discharge in kW from jth BESS at
tth hour
: Operating cost in $/kWh for ith DER
: Operating cost in $/kWh for jth BESS
: Electricity price in $/kWh at tth hour
: System real power demand in kW at tth hour
: Minimum output limit on ith DER
: Maximum output limit on ith DER
: Peak shaving limit specified for distribution
feeder or transformer.
: Lower SOC energy limit in kWh for jth BESS
: Upper SOC energy limit in kWh for jth BESS
: DOD energy limit in kWh for jth BESS
: Discharge rate in kW/hour for jth BESS
The proposed LP formulation determines the optimum
dispatch schedules of distributed generators, responsive load
and optimum discharge schedule of BESS that minimize the
total energy cost satisfying all the constraints listed above.
Also, the formulation achieves the goal of peak shaving
specified for distribution feeder or substation transformer
involved in the system, by making sure that the electric grid
supply doesn’t exceed the limits defined in the peak shaving
constraint. Thus, the optimization has the dual objective of
economics and peak shaving.
B. LP formulation for for BESS charge schedule
Once the BESS discharge schedules and discharge
capacity is determined, the following LP formulation is used
to determine the BESS charge schedule to charge the BESS
with the same amount of energy that has been discharged in
the first LP formulation. The main objective function of this
LP formulation is to minimize the energy cost to charge
) to the given discharge capacity, and is given by.
BESS (
min(
)=
= 1,24;
= 1,
Where,
: Real power discharge in kW for 24-hours
scheduling horizon for jth BESS (as determined
in the first LP)
: Charge efficiency of jth BESS
: Real power charge in kW for jth BESS at tth
hour
: Charge rate in kW/hour for jth BESS
The two proposed LP formulations together will
determine optimum charge and discharge schedules of BESS
) out of all
to maximize the total energy arbitrage value (
BESS present in the system. The derived objective function
can be written as,
(
Where,
∁
∁
IV.
A. Test System
The taxonomy distribution feeder, R1-12.47-2, developed
by PNNL [10] is used as the test system in this paper. This is
a 12.47 kV feeder repressing a moderately populated
suburban and lightly populated rural area. The taxonomy
feeder is modified to contain a fictitious feeder based
microgrid as shown in Fig. 1.The fictitious microgrid
contains 5 fuel-fired distributed generators, one lumped
responsive load, and one storage unit. The operational cost
data and performance constraints of these generation
resources are furnished in Table II. The distribution feeder
thermal loading limit is considered to be 1500 kVA. This is
also the peak shaving limit that can be set by the operator
within the optimization.
Substation
Transformer
138/12.47 kV
33.6 MVA
2.
BESS SOC limitation
≤∑
; (11)
≤
= 1,24;
3.
Taxonomy Feeder
12.47 kV
(R1-12.47-2)
Fictitious
Microgrid
= 1,
= 1,
; (12)
BESS charge-rate limitation
≤
= 1,24;
= 1,
Energy Storage
Unit
ST
Responsive
Load
RL
DG1
Natural Gas
fired Generator
DG2
Diesel
fired Generator
DG3
Natural Gas
fired Generator
DG4
Natural Gas
fired Generator
DG5
Diesel
fired Generator
; (13)
Figure 1: Test System (PNNL Taxonomy Feeder R1-12.47-2)
978-1-5090-4168-8/16/$31.00 ©2016 IEEE
(14)
TEST SYSTEM AND RESULTS
Subject to the following constraints:
1. Equality constraint of meeting the given discharge
capacity
= 1,24;
−∁
: Cost of discharging all BESS units
: Cost of charging all BESS units
; (10)
=
)=∁
A 24-hour load profile for the test system is constructed
based on the dataset developed by National Renewable
Energy Laboratory (NREL)'s distributed energy systems
integration group as part of a study on high penetrations of
distributed solar PV [11]. This dataset consists of hourly load
data for use with the PNNL taxonomy of distribution feeders.
The 8760 load profile data of the taxonomy feeder R1-12.472 is averaged and normalized on an hourly basis to generate
the 24-hour load profile shown in Fig. 2. This data is used as
input to solve the DER optimal scheduling problem using the
proposed optimization technique.
the sense that it minimizes the total cost of supplying the
system load. It is also evident from the obtained dispatching
pattern that the utility electric grid is not committed above the
feeder thermal limit of 1500 kVA to meet the peak shaving
goal. This proves that the proposed LP optimization
formulation provides the optimal dispatch schedules of DERs
that also takes care of the peak-shaving use case.
Figure 4: Optimum DER Dispatch Schedule
Figure 2: 24-hour feeder load forecast
The optimization problem also requires the day-ahead
electricity market forecast data. A random summer day
hourly prices of electricity shown in Fig. 3 are used in this
paper. The price data is constructed from ComEd utility
hourly tariff data based on PJM’s real-time hourly market
prices [12].
Figure 5: Optimum Main Grid Dispatch Schedule
Fig. 6 shows the optimum discharge and charge schedules
of the BESS present on the test feeder. The graphs clearly
indicate that the BESS is getting charged when the grid prices
are at the minimum and getting discharged when the market
prices are high to maximize the arbitrage amount.
Figure 3: 24-hour market forecast for electric grid power
B. Results
The optimization equations are modeled and solved using
the Matlab LP solver. The input data is furnished in the form
of MS-Excel spread sheets. Fig. 4 shows the output of the
Matlab LP solver that shows the optimal dispatch of the
DERs present on the test feeder. Similarly, Fig. 5 shows the
optimal dispatch of the utility electric grid. It is important to
note that the utility electric grid is considered as one of the
generation resources within the optimization problem.
The dispatch pattern provided by solving the optimization
problem shows that the DERs are dispatched especially when
the grid prices are high. This DER dispatch is the optimal in
978-1-5090-4168-8/16/$31.00 ©2016 IEEE
Figure 6: Optimum BESS Charge/Discharge Schedule
Table-I shows the annual arbitrage amount in USD by
scheduling and dispatching the BESS in the test system using
the proposed LP formulation and the input data. The annual
optimization analysis is performed by using the same input
data as shown in Fig. 2 and Fig. 3 for the entire year. The
results of the annual analysis show the efficacy of the
methodology to maximize the arbitrage that can be earned by
the BESS. Distribution operators and engineers can make use
of the proposed analysis to monetize the arbitrage benefit of
the BESS and to run the cost benefit analysis for the
procurement of the BESS.
DG5
RL
ST
Diesel fired Generator
Responsive Load
BESS
MG
Main Grid
Annual cost of discharging
21,111
Annual arbitrage amount
14,176
V.
BESS Specifications
Capacity
Power Rating
SOC Upper Limit
SOC Lower Limit
DOD
Round Trip Efficiency
Terminal Voltage
Charge Rate
Discharge Rate
Charge/Discharge Current limit
CONCLUSIONS
This paper proposes a novel combined optimization
method to solve the optimal scheduling problem of DERs
including the BESS connected to the system. The proposed
method is simple and robust in terms of the optimization
modeling and provides computation rapidity and solution
accuracy as it uses the traditional Liner Programming
technique. The proposed LP formulation determines the
optimal dispatch schedules of DER and charge/discharge
schedule of BESS for minimizing the operational cost and
maximizing the energy storage arbitrage amount. The
proposed LP optimization has a dual optimization objective
of economics and peak-shaving, i.e., the system assets are
dispatched economically that support feeder peak-shaving
application. The optimization problem is tested on a PNNL
taxonomy distribution feeder with a fictitious microgrid
system using the Matlab LP solver. The results are promising
and prove the efficacy of the proposed optimization solution.
VI.
APPENDIX
Table II provides DER operating cost and operational
constraint data. The utility electric grid prices are provided by
the market forecast data shown in Fig. 3.
TABLE II: DER SPECIFICATIONS AND CONSTRAINTS
DER Data
DER
Name
DG1
DG2
DG3
DG4
Type
Natural Gas Fired
Generator
Diesel fired Generator
Natural Gas Fired
Generator
Natural Gas Fired
Generator
Offers
(cents/
kWh)
Min
kW
Max
kW
8.4
100
100
7.9
40
50
9.4
200
200
9.1
150
150
978-1-5090-4168-8/16/$31.00 ©2016 IEEE
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0
200
200
200
150
0
TABLE III: BESS SPECIFICATIONS AND CONSTRAINTS
USD
6,935
200
0
0
Table III provides the BESS specifications including its
constraints such as SOC and DOD limits.
TABLE I: ARBITRAGE OF BESS
Annual cost of charging
8.3
15
12
Market
Data
800kWh
200kW
100% (800kWh)
25% (200kWh)
75% (600kWh)
80%
600V
200 kW/hr
200 kW/hr
500 A
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