Energy and Power Engineering, 2013, 5, 15-21
doi:10.4236/epe.2013.54B003 Published Online July 2013 (http://www.scirp.org/journal/epe)
Short-term Distributed Energy Resource Scheduling for a
DC Microgrid
G. W. Chang, H. J. Lu, H. J. Su
Department of Electrical Engineering, National Chung Cheng University
Email: wchang@ee.ccu.edu.tw
Received September, 2012
ABSTRACT
A microgrid is associated with a low voltage distribution power network and inherits small modular generation systems
and loads that have certain coordinated functions to provide the solution to supply premium power to remote or specific
areas. Similar to conventional power systems, the energy management of distributed generation resources (DERs) is
carried out to minimize the operation cost and maximize benefit of installation of DERS in a microgrid. This paper pre-
sents the process of implementing the short-term DER scheduling function for a dc microgrid. The optimal scheduling
results for two operation modes are then reported.
Keywords: Microgrid; Distributed Generation Resources; PV; Battery
1. Introduction
The microgrid is a group of traditional and/or distributed
generation resources, energy storages, and loads that is
normally connected to a low-voltage power network. The
point of common coupling (PCC) with the connected
power network can be disconnected and the microgrid is
then functioned in islanding mode. The microgrid can
provide the platform for integration of different renew-
able resources with communications [1].
Due to characteristics of distributed energy resources,
modern power systems have functions of changing its
power flow either in one direction or bi-directions. Since
it is a trend that active distributed systems have flexible
and smart control systems to obtain clean energy from
renewable sources, distribution systems have trans-
formed into larger-scale of smarter grids or a smaller
scale of localized microgrids. Microgrids can reduce cost
of investment for installations of renewable sources and
they also provide reactive power compensation and fre-
quency regulation, increase capacity of spinning reserve,
and improve power quality and reliability of customer’s
power system.
Unlike the conventional power system, a microgrid
may include energy-storage devices such as batteries and
becomes a strong coupling system in the time domain
[2-4]. Furthermore, due to uncontrollable characteristics
of DERs, certain operation function such as islanding
mode of the grid and have to be further studied. In this
paper, the short-term DER scheduling that considers the
photovoltaic cell, wind generation, fuel cell, and energy-
storage device (i.e. battery) of a dc microgrid supplying
local loads is presented.
The optimization model is developed for the consid-
ered short-term DER scheduling problem. The objective
is to minimize operational costs while satisfying the mi-
crogrid load demand. All the DER and energy-storage
units must be operated within their lower and upper out-
put limits. The output of the power optimization model
considers the operation limits of the supply options, load
demand, sell/purchase power costs from the connected
grid, and the operating costs of the DERs. Therefore, the
objective function becomes minimizing operational costs
represented by the difference between the profit and the
cost. In the scheduling model, the problem is formulated
as a nonlinear programming problem is solved by an op-
timization toolbox provided by Matlab. To solve the mi-
crogrid DER scheduling problem, a solution algorithm is
proposed and implemented under MATLAB Graphical
User Interface Development Environment (GUIDE).
Results are then presented to show the usefulness of the
proposed algorithm.
2. Problem Formulation
Figure 1 shows the network configuration of the dc mi-
crogrid under study, where the DERs in the system in-
clude a wind turbine with the permanent magnet syn-
chronous generator (PMSG), PV arrays, and a fuel cell.
The energy-storage system is a battery. Two types of
loads are in the system: one is the DC load fed by the DC
bus and the other is the AC load connected to the AC
Copyright © 2013 SciRes. EPE
G. W. CHANG ET AL.
16
grid. Interconnection between the DC microgrid and the
AC grid is through a bi-directional inverter. To ensure a
stable operation, the power generation and consumption
must be balanced to keep the DC bus voltage within an
acceptable range. The inverter and battery are responsi-
ble for DC voltage regulation in the grid-connected and
islanding modes, respectively. In the grid-connected
mode, the battery acts like a constant current source and
can be in charge, discharge, or non-operated mode. In the
islanding mode, the inverter is mainly responsible for
maintaining a stable voltage to the AC loads.
2.1. Photovoltaic Array Model
The single-diode equivalent PV model shown in Figure
2 describes the v-i characteristic of PV arrays. In this
model, the series resistance (RS) and the parallel resis-
tance (RP) represent the effect PV conversion efficiency
[5]. The equation describing the v-i characteristic is
0
()
exp() 1
s
s
PH P
qv iRv iR
ii ikTA R

 


(1)
where i is the output current of the PV, iPH is the current
generated by the incident light, i0 is the reverse saturation
or the leakage current of diodes, q is the electron charge,
v is the output voltage of the PV, k is Boltzmann constant,
Figure 1. A typical configuration of DC microgrid.
Figure 2. Equivalent single-diode PV mode.
T is the temperature in Kelvin, A is the ideal factor of the
PV (A = 1~1.5), RP is the series resistance, and RS is the
parallel resistance. The parameters needed in the equiva-
lent PV model are iPH, i0, RP, RS, and A; they can be ob-
tained from the datasheets and the procedure for calcu-
lating both series and parallel resistances [6, 7].
2.2. Wind Turbine Model
To model the permanent magnet synchronous generator
(PMSG) of the wind turbine, the parameters of the
PMSG are required to establish the detailed wind turbine
models, which include the numbers of poles, dq-axis
inductances, rotor resistance, etc. However, these pa-
rameters are usually not provided by manufactories, the
measurement-based wind turbine models can be obtained
by establishing a look-up table of wind speed versus
output power characteristic curve to represent wind tur-
bine power characteristic [8].
2.3. Models of Fuel Cell and Battery
The fuel cell stack model shown in Figure 3 [9] is com-
monly used and the parameters can be obtained from the
datasheet shown in Figure 4, where Eoc is the open cir-
cuit voltage, i0 is the exchange current, A is the Tafel
slope, N is the number of cells, and Td is the response
Figure 3. A commonly used model for the fuel cell [9].
0
10
20
30
40
50
60
70
020406080100 120 140 160
Current (A)
Voltage (V
)
0
1000
2000
3000
4000
5000
6000
7000
Power (W)
Stack IP Curve
Stack IV Curve
Figure 4. Current-power (i-p) and current-voltage (i-v) cha-
racteristic curves of a 5-kW fuel cell.
Copyright © 2013 SciRes. EPE
G. W. CHANG ET AL. 17
time. The simplified model is based on the equivalent
circuit of a fuel cell stack and represents a particular fuel
cell stack operating at nominal conditions of temperature
and pressure. Battery models in SPS include four prede-
fined types: lead-acid, lithium ion, nickel metal hydride
and nickel cadmium. Parameters of models are battery
types, nominal voltage, rated capacity and initial charge
state.
3. Short-term DER Scheduling of the DC
Microgrid
3.1. Objective Function and Constraints
The short-term DER scheduling of the dc microgrid is to
achieve its minimum operation cost. If the microgrid
includes N controllable DERs over a study period of T
time steps, the objective function to be minimized under
grid-connected and islanding modes can be expressed by
(2) and (3), respectively.
,,
11
[(( ))()()]
TN
nn tgridgridtbattbattt
tn
CFPFPFP


 ,
,
,
(2)
,
11
[(( ))()]
TN
nn tbattbatt t
tn
CFPFP


 (3)
where Pn,t is the output power of the nth DER in the t-th
time step. Pgrid,t and Pbatt,t are the output power of the
connected grid (i.e. electric utility) and the energy-stor-
age device, respectively. Fn, Fgrid, and Fbatt are cost func-
tions associated with the nth DER, power sell or purchase
of the electric utility, and energy-storage device, respec-
tively. The constraints must be met at each time step are
listed in (4)-(8).
,,, ,
1
N
ntgrid tbatt tload tunctrl t
n
PP P P P

(4)
min max
,nntn
PPP (5)
min max
,
g
ridgridtgrid
PP P (6)
min max
arg ,argch ebatttdische
PPP (7)
min 1maxtt
SOCSOCSOC SOC
 (8)
In (4)-(8), (4) is the power balance requirement during
the t-th time step, which ensures a stable operation.
Punctrl,t is output power of uncontrollable DERs (i.e., wind
generation and PV arrays) during the t-th time step, and
Pload,t is total active power of dc and ac loads; (5) is gen-
eration limits for the n-th DER, where and
are minimum and maximum generation, respectively.
Equation (6) is inequality constrain of power from utility,
and
min
n
Pmax
n
P
min
g
rid
P and max
g
rid
P are minimum and maximum power
limitation. Equation (7) is associated with the charging
and discharging power limits of the battery. In (8), the
state-of-charge (SOC) of the battery must meet its nor-
mal operation constraints, where SOCmin and SOCmax are
the lower and upper energy storage limits for the battery.
ΔSOCt is the change of SOC during the t-th time step.
3.2. Proposed Solution Procedure for the DER
Scheduling Problem
To solve the described short-term DER scheduling prob-
lem for the micro grid in both islanding and grid-con-
nected modes, it is assumed that, at each time step, the
forecasts of power generation from uncontrollable DERs
(i.e. PV and wind generator), the utility electricity price,
the load consumption, the initial value of battery SOC
and the microgrid operation mode are provided. In the
grid-connected mode, the scheduling problem of (2)-(7)
will be solved and the battery output and the power pur-
chase from the connected utility grid at each time step
will be determined at the minimum microgrid operation
cost. In the islanding mode, the microgrid is discon-
nected form the utility grid. Consequently, the problem is
without considering the Pgird terms in the objective func-
tion and constraints and is then solved. For both opera-
tion modes, the scheduling problems are solved by the
Matlab Optimization toolbox (quadratic programming
solver) implemented with MATLAB GUIDE. Figure 5
illustrates the flowchart of the proposed solution proce-
dure for both microgrid operation modes.
4. Case Study
In this study, the simulations for an actual dc microgrid
with grid-connected and islanding modes for 48 time
steps (each time step spans over 15 minutes) are per-
formed to show the scheduling results. The associated
cost functions and constraints are listed in (9)-(17).
2
() 0.774.9419.36
FC FCFCFC
FPP P (9)
0.5 5
FC
kW PkW
(10)
_()3
g
rid ingridgrid
F
PP (11)
_()5
rid outgridgrid
F
PP (12)
5
grid
kW PkW5
 (13)
_arg
()1.5
batt chebattbatt
F
P P (14)
_arg
()1.6
batt dischebattbatt
F
PP (15)
10 10
batt
kW PkW
 (16)
1
85% 90%
tt
SOC SOC
 (17)
where (9) and (10) are the fuel cell cost function and as-
sociated generation limits. In (11)-(16), positive value of
Pgrid and Pbatt implies that the electric power flows into
the microgrid.
Copyright © 2013 SciRes. EPE
G. W. CHANG ET AL.
Copyright © 2013 SciRes. EPE
18
4.1. Case 1: Grid-Connected Mode 4.2. Case 2: Islanding Mode
Figure 6 shows the forecasting curves of load demands
and uncontrollable DERs for input to the problem.
Figures 7 and 8 show the connected utility grid power
purchase/sell (indicated by Taipower), DER generation
and battery output with and without optimization, respec-
tively. Table 1 indicates that optimal operation cost can
be achieved by selling and purchasing power to/from the
connected utility at different time steps based on the fo-
recasted input. The cost saving without optimization is
about 13% more than that with optimization.
In this case, the load forecasting curve is shown in Fig-
ure 9 and the generation forecasts of uncontrollable
DERs are the same those of Case 1. Figures 10 and 11
show the connected utility grid power purchase/sell (in-
dicated by Taipower), DER generation and battery output
with and without optimization, respectively. By observ-
ing Table 2, the cost saving with optimization is much
less than that of Case 1. This is because that the islanding
operation is without power purchase and sold to the util-
ity grid.



N
ntbattbatttgridgridtnn
T
t
PFPFPF
1
,,,
1
)]()())(([min

N
ntunctrltloadtbatttgridtn
PPPPP
1
,,,,,
max
,
minntnn
PPP 
max
,
min gridtgridgrid
PPP 
max
arg,
min
arg edischtbattech PPP 
max1min
SOCSOCSOCSOC
tt



N
ntbattbatttnn
T
t
PFPF
1
,,
1
)]())(([min

N
ntunctrltloadtbatttn PPPP
1
,,,,
max
,
min ntnn
PPP 
max
arg,
min
arg edi schtbattech
PPP 
max1min
SOCSOCSOCSOC
tt
Figure 5. Flowchart of scheduling optimization program for grid-connected and islanding operations of the dc microgrid.
0
2
4
6
8
10
15913 17 2125 29 33374145
Time Step
kW
0
2
4
6
159 131721252933374145
Time Step
kW
WT
PV
(a) (b)
Figure 6. Forecasts of (a) load demand, and (b) uncontrollable DERs.
G. W. CHANG ET AL. 19
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8 910111213141516171819202122232425262728293031323334353637 3839 4041 42 43 4445 4647 48
time step
kW
Taip ower
Discharge
Charge
FC
PV
Wind
Figure 7. Power purchase/sell (Taipower), DER generations and battery output with optimization (Case 1).
0
1
2
3
4
5
6
7
8
9
10
12345678910 11 1213 14 15 16 17 18 1920 21 22 23 2425 26 27 2829 30 31 32 33 34 3536 37 38 39 40 41 42 43 44 4546 47 48
time step
kW
Battery
FC
PV
Wind
Figure 8. DER generations and battery output without optimization (Case 1).
Table 1. Comparison of operation cost ($) w/o and with optimization.
Fuel Cell Battery Sell Purchase Cost
w/o optimization 706.50 30.94 0.00 0.00 737.43
With optimization 694.00 8.33 60.33 1.55 642.00
0
2
4
6
8
10
159 131721252933374145
Time Step
kW
Figure 9. Load forecast for case 2.
Copyright © 2013 SciRes. EPE
G. W. CHANG ET AL.
Copyright © 2013 SciRes. EPE
20
0
1
2
3
4
5
6
7
8
9
10
1 2 34 5 6 7 8 910111213141516171819202122232425262728293031323334353637 38 39 4041 42 43 4445 46 47 48
time step
kW
Discharge
Charge
FC
PV
Wind
Figure 10. DER generations and battery output with optimization (Case 2).
0
1
2
3
4
5
6
7
8
9
10
12345678910 11 12 13 14 15 16 17 18 19 2021 2223 24 25 26 27 28 2930 31 3233 34 353637 3839 40 41 4243 4445 46 4748
time step
kW
Battery
FC
PV
Win d
Figure 11. DER generations and battery output without optimization (Case 2).
Table 2. Comparison of operation Cost ($) with and w/o Optimization
Fuel Cell Battery Cost
w/o optimization 663.88 10.96 674.84
With optimization 641.43 24.41 665.84
5. Conclusions
This paper has presented the aspect of short-term sched-
uling of DERs for an actual dc microgrid operated in
both grid-connected and islanding modes. Results of two
study cases were illustrated the usefulness of the pro-
posed solution procedure to minimize the microgrid op-
eration costs while satisfying all operation constraints.
The schedules results were then input the time-domain
simulation model to ensure a stable operation of micro-
grid with maintaining near fixed dc bus voltage under
both grid-connected and islanding operations.
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