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
,
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
rid
P and max
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
rid ingridgrid
PP (11)
_()5
rid outgridgrid
PP (12)
5
grid
kW PkW5
(13)
_arg
()1.5
batt chebattbatt
P P (14)
_arg
()1.6
batt dischebattbatt
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.
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