Short-term Distributed Energy Resource Scheduling for a DC Microgrid

doi:10.4236/epe.2013.54B003

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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: [email protected]

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

G. W. CHANG ET AL.

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

()

exp() 1

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].

020406080100 120 140 160

Current (A)

Voltage (V

)

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.

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.

[(( ))()()]

nn tgridgridtbattbattt

CFPFPFP





 ,

(2)

[(( ))()]

nn tbattbatt t

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).

,,, ,

ntgrid tbatt tload tunctrl t

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

Pmax

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).

() 0.774.9419.36

FC FCFCFC

FPP P (9)

0.5 5

kW PkW



 (10)

_()3

rid ingridgrid

PP (11)

_()5

rid outgridgrid

PP (12)

grid

kW PkW5



 (13)

_arg

()1.5

batt chebattbatt

P P (14)

_arg

()1.6

batt dischebattbatt

PP (15)

10 10

batt

kW PkW



 (16)

85% 90%

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.

G. W. CHANG ET AL.

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.







ntbattbatttgridgridtnn

PFPFPF

,,,

)]()())(([min







ntunctrltloadtbatttgridtn

PPPPP

,,,,,

max

minntnn

PPP 

max

min gridtgridgrid

PPP 

max

arg,

min

arg edischtbattech PPP 

max1min

SOCSOCSOCSOC















ntbattbatttnn

PFPF

)]())(([min







ntunctrltloadtbatttn PPPP

,,,,

max

min ntnn

PPP 

max

arg,

min

arg edi schtbattech

PPP 

max1min

SOCSOCSOCSOC











Figure 5. Flowchart of scheduling optimization program for grid-connected and islanding operations of the dc microgrid.

15913 17 2125 29 33374145

Time Step

159 131721252933374145

Time Step

(a) (b)

Figure 6. Forecasts of (a) load demand, and (b) uncontrollable DERs.

G. W. CHANG ET AL. 19

1 2 3 4 5 6 7 8 910111213141516171819202122232425262728293031323334353637 3839 4041 42 43 4445 4647 48

time step

Taip ower

Discharge

Charge

Wind

Figure 7. Power purchase/sell (Taipower), DER generations and battery output with optimization (Case 1).

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

Battery

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

159 131721252933374145

Time Step

Figure 9. Load forecast for case 2.

G. W. CHANG ET AL.

1 2 34 5 6 7 8 910111213141516171819202122232425262728293031323334353637 38 39 4041 42 43 4445 46 47 48

time step

Discharge

Charge

Wind

Figure 10. DER generations and battery output with optimization (Case 2).

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

Battery

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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