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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