Economic Power Dispatch of Distributed Generators in A Grid-Connected Microgrid
Economic Power Dispatch of Distributed Generators in A Grid-Connected Microgrid
Economic Power Dispatch of Distributed Generators in A Grid-Connected Microgrid
Abstract—Grid-connected microgrids with storage sys- [8]. For instance, the minimization of the energy cost
tems are reliable configurations for critical loads which can and maximization of batteries lifetime in a microgrid is
not tolerate interruptions of energy supply. In such cases, proposed in [9] and a battery management system of a
some of the energy resources should be scheduled in order microgrid for both grid-connected and autonomous modes
to coordinate optimally the power generation according to a is presented in [10]. Likewise, an energy management
defined objective function. This paper defines a generation-
strategy is proposed in [11] for operating PV power
side power scheduling and economic dispatch of a grid-
connected microgrid that supplies a fixed load and then, plants with ESS in order to endow them with a constant
the scheduling is enhanced by including penalties in order production that can be controlled. In that work, the ESS
to increase the use of the renewable energy sources and behaves like a system load, recharging the ESS from the
guarantee a high state of charge in the storage system for grid to achieve a desired state of charge (SoC) value
the next day. Linear models are proposed for the scheduling before starting operation the next day i.e. minimizing the
which are implemented in GAMS. The microgrid model SOC deviation with regard to a SOC reference value.
is obtained deploying MATLAB/Simulink toolbox and then Similar approach has been proposed in [12] where a
downloaded into dSPACE 1006 platform based on real-time constant power generation for PV systems is implemented
simulation to test the economic dispatch. A compromise and a certain percentage of the energy is cut off in a long-
between cost and use of renewable energy is achieved.
term operation when the output power reaches a certain
Keywords—Economic dispatch, generation-side schedul- level so, it is expected that the power reference for RES
ing, microgrids, energy management system. is defined by an optimal value in accordance with the
power capability of each RES.
I. I NTRODUCTION
Moreover, hierarchical control is structured to deal
A microgrid (MG) is composed of distributed gene- with the behavior of the microgrids at different band-
rators (DG), energy storage systems (ESS) and loads, width. Upper level controls deal with optimal operation
that can operate interconnected to the main grid or in is- and power flow management whereas lower levels are re-
landed mode [1]. Particularly, grid-connected microgrids sponsible of power quality control and regulation of local
are commonly used as reliable configurations for critical variables [13]. At the primary level of control, the RES
loads which must be uninterruptedly fed [2]. However, are regulated in order to follow a local maximum power
when there are several resources available to supply the point tracking (MPPT) algorithm or the power reference
demand, they should be scheduled to get an optimal given by an energy management system which schedules
dispatch regarding specific objectives such as economical, the operation of DG in accordance to an optimization
technical and environmental aspects [2], [3]. algorithm, then, DG work under constant current control
Regarding economical issues and from the point of inner loops. Meanwhile, ESS is charged or discharged
view of the owner of the microgrid, the main objective is based on the power unbalance between the generated and
to minimize the operating cost [3], and additional topics consumed power. Normally, when the ESS is completely
on the optimization process have been included refer to charged and the load requests less power than available,
the full use of renewable energy sources (RES) due to the control mode of the DG changes in order to share
their intermittent nature, as well as the prolongation of equally between DG the power that the load requests
the life time of the ESS [4], [5]. As illustration, [6] [14]. Apart from that, banks of lead-acid batteries are
and [7] present energy management systems performed commonly used in microgrids [2], [15]. In this sense, at
to maximize power generation of a hybrid active power least a two-stage charge procedure should be considered
generator for a grid-connected microgrid based on wind in order to ensure adequate life-time for batteries [15].
turbine (WT) generator (WT+ESS) and a photovoltaic
In this paper, some strategies of economic dispatch
(PV) generator (PV+ESS) respectively.
are considered minimizing the operating cost, which aim
In addition, when an ESS is included in the MG, its to reduce the energy consumption of the grid power, the
behavior should be taken into account in the scheduling SoC of the ESS and maximizing the use of the RES to
2015 KIPE
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supply permanently a constant load. The MG consists in the AC grid assumes the responsibility of voltage bus
two RES (a wind turbine (WT) and a photovoltaic (PV) regulation, operating under VCM. In ligh of this, any
panel), a battery, and a critical load connected to the grid power unbalance between the generated and consumed
by means of a AC/AC converter (Fig. 1). power will be assumed by the AC grid, ensuring reliable
operation at the common bus of the microgrid.
Connecting the grid through a converter can be used to
mitigate harmonics and other disturbances as referenced
in [16]. The main grid will be assumed as a dispatchable III. P ROPOSED O PTIMIZATION M ODEL
unit and the ESS will support the fluctuations of gener- This problem has been developed as a linear program-
ation. To be more precise, different stages for charging ming (LP) problem where the data are considered as the
a bank of batteries are presented, as well as, how those mean value for each elementary interval of scheduling.
stages interact with the operation of the microgrid. The
paper is organized as follows: Section II describes the A. Parameters and variables
operation of the microgrid considered as study case,
Section III presents the proposed optimization model, The parameters used in this model are presented in
Section IV includes the simulation results and the Section table I while the variables are included in table II.
V concludes the paper. TABLE I. PARAMETERS OF THE MODEL
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Power Scheduling
Grid Converter
RES Primary EES Primary Control
Primary Control RES Primary
Pgrid Control
Pw Control
PControl Ppv Constant Voltage
PControl AC DC Charger DC
PControl
(VCM) Control AC AC AC
MPPT (VCM) Control
MPPT
AC
AC AC common bus
Main Grid
Critical
Load
storage system represents the relation between the cur- In the case of RES, Pgmax is a set of variable data defined
rent capacity (in [Ah]) and the nominal capacity and is by a 24-h-ahead power predictor for each t.
presented in percentage as a function of the current [18].
2) Energy Storage: The SoC(k, t) in the k − th
Assuming that the voltage of the storage system is con-
storage system of the microgrid can be represented in
stant (V batnom (k)) in Δt, the current can be represented
Pbat (k,t)
terms of its power as:
in terms of power Ibat (k, t) = V battk nom (k)
, and the
SoC(k, t) = SoC(k, t − 1) − (4)
SoC(k) can be defined as:
ϕbat (k) ∗ [Pbat (k, t)Δt] , ∀k, t
SoC(k, t) = SoC(k, t − 1) − (1)
1 considering that at t = 1, SoC(k, t − 1) is replaced by
Cbat (k)∗V batnom (k) ∗ [Pbat (k, t)Δt] , ∀k, t the given initial condition SoC(k, 0).
In this particular case, the considered system storage is
Apart from that, the SoC(k, t) at each t is bounded
an electric battery whose coefficient ϕbat (k) is obtained
in the range:
(out of the optimization model) assuming a nominal
voltage value V batnom (k) for the interval Δt. The ϕbatk SoCmin (k) ≤ SoC(k, t) ≤ SoCmax (k), ∀k, t (5)
coefficient is related to the energy capacity and the SoC The values of SoCmin (k) and SoCmax (k) are defined
as is shown in (1). following the recommendation of the IEEE1561-2007
1 standard [20].
ϕbat (k) = , ∀k (2)
Cbat (k) ∗ V batnom (k)
Additionally, the global balance of the SoC is assured
Likewise, SoCmax (k) is selected to allow the battery by establishing the condition:
to be fully charged without overcharging (SoCmax (k) = T
−1
100%) and SoCmin is chosen to limit the depth of SoC(k, t + 1) − SoC(k, t) ≥ 0, ∀k (6)
discharge (DoD) accordingly with the recommendation of t=1
the IEEE1561-2007 standard [20] (SoCmin (k) = 50%).
3) Energy Balance: The demand must be supplied by
Regarding the proposed penalties, ceasing using the the sources and the storage system.
power available in the i − th RES is penalized the cost ng nk
ξ(i), and in the same way, having the k − th ESS fully Pg (i, t)Δt + Pbat (k, t)Δt = (7)
charged at t = T is rewarded with χ(k). i=1 k=1
where Pg (i, t) correspond to the estimated power PL (t)Δt + Plosses , ∀t, k, i
of the sources, COST is whole cost paid by the user Should be noted that, when Pbat is positive, the storage
(including penalties), and Pbat (k, t) and SOC(t) are the system gives energy to the load (it is being discharged)
power and the SoC of the ESS, respectively. and when is negative, it takes energy from the sources (it
is being charged).
B. Optimization Formulation
4) Objective Function: The objective is to minimize
The optimization problem to be solved is the LP operating costs that the user must pay for the energy
presented below: provided by the sources.
1) Energy Sources: As a general approach, Pg (i, t) is ng T
the power of the sources i = 1, 2, ..., ng at each t, and it COST = [Pg (i, t)Δt] ∗ C(i, t), ∀i, t (8)
is a positive variable delimited by the maximum power i=1 t=1
that can be provided, Pgmax (i, t).
The main grid (i = 1) has a cost C(1, t) that varies each t
0 ≤ Pg (i, t) ≤ Pgmax (i, t), ∀i, t (3) while production costs of the renewable sources are zero.
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5) Proposed penalties: Two penalties are proposed to Power for PV by GAMS
3000
be incorporated in the objective function and compare the
Power (W)
performance of the resources in the MG by combining the 2000
0
a) Penalty 1: This penalty takes into account 0 2 4 6 8 10 12
time (h)
14 16 18 20 22 23
Power (W)
2000
ng
T
1000
Cost (DKK)
6
5
b) Penalty 2: Additionally, a reward for having
charged the ESS at the last t is set as a global condition. 4
0 2 4 6 8 10 12 14 16 18 20 22
time (h)
and simulated: the basic cost function and the ones that Strategy 3
Power (W)
Strategy 1
2000
result for adding the previously defined penalties into Strategy 2
Strategy 4
Strategy 1
No penalty 1 With penalty 1 2000
Strategy 3
Strategy 4
No penalty 2 Strategy 1 Strategy 3
1000
With penalty 2 Strategy 2 Strategy 4
0
0 2 4 6 8 10 12 14 16 18 20 22
time (h)
Power for the grid by GAM S
3000
To compare the strategies, the function fitness is Strategy 2
Strategy 1
Power (W)
2000
defined by adding the strategies: Strategy 3
Strategy 4
1000
ng T
0
Fitness = [Pg (i, t)Δt] ∗ C(i, t)+ 0 2 4 6 8 10 12
time (h)
14 16 18 20 22
i=1 t=1
ng T
ξ(i) ∗ [Pgmax (i, t)Δt − Pg (i, t)Δt] + Fig. 3. Scheduled power for each strategy. Top down: PV scheduled
power, WT scheduled power and scheduled power for the grid.
i=1 t=1
χ(k) ∗ [SoC(k, T ) − SoC(k, 1)] (11) SoC by GAMS
100
90
70
60
Strategy 4
The scheduling process is performed by using real 40 Strategy 1
Strategy 2
data of wind speed and solar irradiance of a winter day Strategy 3
30
and using proper models for the WT and PV 24-h-ahead
PV and WT power prediction. The input data of the 20
0 2 4 6 8 10 12 14 16 18 20 22
time (h)
obtained RES power and the elementary cost of using
the energy from the grid are presented in Fig. 2.
Fig. 4. Expected SoC by GAMS for each strategy.
Along with, a constant initial condition of SoC(k, 0)
(SoC(k, 0) = 75%) is set for performing the simulations.
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A. Generation scheduling grid and the battery switch between CCM and VCM) is
simulated by using a Simulink model. The simulation of
The optimization problem is included in the algebraic
the SOC are presented in Fig. 5. In this case, the energy
model language GAMS and the solver CPLEX is used for
from the RES are not used to charge the storage system
obtained the scheduling data. The results are presented in
since it is not fully charged at any time during the day.
Fig. 3 whereas the SoC that is expected in this model is
shown in Fig. 4.
SoC without scheduling
100
It can be seen that all the strategies make the SoC of
95
the ESS stay in the boundaries and also be charged for
90
a while during the day. Moreover, the strategies 1 and 3
85
(which do not include the second penalty) use the power
SoC (%)
80
of the grid at the same times and in turn, for less time
75
than the strategies 2 and 4, as expected in order to charge
70
the ESS at the last interval of time.
65
penalties) uses the grid for a short time but, it cuts off the 55
0 2 4 6 8 10 12 14 16 18 20 22
available power of the RES when the ESS is not charged Time (h)
Strategy 1 11.6513
0
Strategy 2 21.6778 2 4 6 8 10 12 14 16 18 20 22 24
Time (h)
Strategy 3 2.3658
Strategy 4 21.6811
Fig. 6. Cost summary for the implemented strategies
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3000 100
Power (W)
2000 90
1000
80
00
0 200 400 600 800 1000 1200 70
time (min)
60
2500
2000 50
Power (W)
1500
1000 #1:1 40 0
0 200 400 600 800 1000 1200
500 Time (min)
00
0 200 400 600 800 1000 1200
time (min)
Fig. 8. SoC of the ESS using strategy 1.
2000
750
Power (W)
1500 Vr
Voltage (V)
1000 740
500
Vbat
#1:1 730
#1:2
00
0 200 400 600 800 1000 1200 720
time (min)
710
700
2000
0 200 400 600 800 1000 1200
#1:1
1000 time (min)
Power (W)
2000
1000
Fig. 7. Power of the devices using strategy 1. Top down: Power of #1:1
and the ESS. The power of the generators follows the ref-
2500
erence defined by the scheduling and the ESS is charged 2000
or discharged in accordance to the generated/consumed
Power (W)
1500
power unbalance. The process of charge and discharge is 1000 #1:1
1500
is bigger because of the granularity of the optimization 1000
model. At this case, detailed model of the battery as 500
#1:1
0
time (Fig. 15).
-1000
-2000
0
V. CONCLUSIONS AND FUTURE WORK 0 200 400 600 800 1000 1200
time (min)
The optimization problem of minimizing operating
costs has been established and it has been enhanced by
adding two penalties in order to improve the behavior Fig. 10. Power of the devices using strategy 2. Top down: Power of
of the system. From the economic dispatch results, it PV, Power of WT, Power of the grid, Power of the ESS
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110 110
100 100
90 90
80 #1:1 80 #1:1
State of Charge (%)
60 60
50 50
40 40
30 30
20 20
10 10
00 00
0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200
Time (min) Time (min)
Fig. 11. SoC of the ESS using strategy 2. Fig. 14. SoC of the ESS using strategy 3.
750 750
Vr Vr
Voltage (V)
Voltage (V)
740 740
Vbat Vbat
730 730
#1:2 #1:2
720 720
710 710
700 700
0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200
Time (min) Time (min)
Fig. 12. Voltage of the battery using strategy 2. Fig. 15. Voltage of the battery using strategy 3.
3000 3000
Power (W)
Power (W)
2000 2000
1000 1000
#1:1 #1:1
00 00
0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200
time (min) time (min)
2500 2500
2000 2000
Power (W)
Power (W)
1500 1500
500 500
00 00
0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200
time (min) time (min)
2500 2500
2000 2000
Power (W)
Power (W)
1500 1500
1000 1000
500 500
#1:1 #1:1
00 00
0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200
time (min) time (min)
2000 2000
#1:1 #1:1
1000 1000
Power (W)
Power (W)
0 0
-1000 -1000
-2000 -2000
0 0
0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200
time (min) time (min)
Fig. 13. Power of the devices using strategy 3. Top down: Power of Fig. 16. Power of the devices using strategy 4. Top down: Power of
PV, Power of WT, Power of the grid, Power of the ESS PV, Power of WT, Power of the grid, Power of the ESS
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110
[4] Wang, Chengshan ; Mengxuan Liu; Li Guo, ”Cooperative op-
100 eration and optimal design for islanded microgrid,” Innovative
90 Smart Grid Technologies (ISGT), 2012 IEEE PES , vol., no.,
80 #1:1
pp.1,8, 16-20 Jan. 2012
State of Charge (%)
70 [5] Marra, F.; Guangya Yang; Traeholt, C.; Ostergaard, J.; Larsen, E.,
60 ”A Decentralized Storage Strategy for Residential Feeders With
50 Photovoltaics,” Smart Grid, IEEE Transactions on , vol.5, no.2,
40
pp.974,981, March 2014
30
[6] Kanchev, H.; Di Lu; Colas, F.; Lazarov, V.; Francois, B., ”Energy
20
Management and Operational Planning of a Microgrid With a PV-
Based Active Generator for Smart Grid Applications,” Industrial
10
Electronics, IEEE Transactions on , vol.58, no.10, pp.4583,4592,
00
0 200 400 600 800 1000 1200
Oct. 2011
Time (min) [7] Kanchev, H.; Lazarov, V.; Francois, B., ”Environmental and eco-
nomical optimization of microgrid long term operational planning
Fig. 17. SoC of the ESS using strategy 4. including PV-based active generators,” Power Electronics and
Motion Control Conference (EPE/PEMC), 2012 15th Interna-
tional , vol., no., pp.LS4b-2.1-1,LS4b-2.1-8, 4-6 Sept. 2012
760 #1:1
[8] Malysz, P.; Sirouspour, S.; Emadi, A., ”MILP-based rolling
750
horizon control for microgrids with battery storage,” Industrial
Vr Electronics Society, IECON 2013 - 39th Annual Conference of
Voltage (V)
1168