Real-Time Energy Management of an Islanded
Microgrid Using Multi-Objective Particle
Swarm Optimization
A. J. Litchy, Member, IEEE and M.H. Nehrir, Life Fellow IEEE
Abstract—While minimizing cost has always been a primary
objective in energy management, because of increasing concerns
over emissions, minimization of this objective has been brought
to the forefront of energy management as well. Minimization of
cost and emission are two conflicting objectives. Moreover, the
optimization problem becomes more complex with the addition of
renewable technologies that have varying power generation
energy storage. This paper presents a multi-objective, multiconstraint energy management optimization problem for an
islanded microgrid solved in real time using a modified Multiobjective Particle Swarm Optimization (MOPSO) algorithm.
Simulation results show the benefits of real-time optimization
and the freedom of choice users make to meet their energy
demands. Furthermore, the simulation results from the MOPSObased algorithm are compared with those from the Multiobjective Genetic Algorithm (MOGA)-based optimization
package available in the Matlab optimization toolbox. The
results show that the proposed MOPSO-based algorithm used for
a 24-hour period energy management simulation performs much
faster than the MOGA-based optimization package.
Index Terms—Microgrid, real-time energy management,
particle swarm optimization, genetic algorithm.
I. INTRODUCTION
The Increased interest in emission-free power generation
has resulted in increasing utilization of renewable - wind,
photovoltaic (PV) – power generation during the last decade,
and this trend is expected to continue even at a faster paste.
However, because of the time varying nature of the above
power generation sources, for improved reliability, they need
to operate in a hybrid manner, along with a dispatchable
generation and/or an energy storage (ES) system. In general,
dispatchable sources produce undesired emissions, and the
addition of ES results in increased cost. Ideally, it is desired to
minimize both of the above objectives. However, these
objectives are competing; i.e., the minimization of one
objective results in an increase in the other objective.
In this paper the hybrid combination of solar PV and solidoxide fuel cell (SOFC)-electrolyzer distributed energy
resources (DERs) along with an internal combustion engine
(ICE) and battery ES are used in an islanded microgrid (MG)
setting to provide the energy needs of a medium-size college
in San Francisco, California. Fig. 1 shows the different load
demand profile for a typical summer day of the college
campus [1], [2].
This work was supported by the DOE Award DE-FG02-11ER46817 and
by Montana State University.
A.J. Litchy (email: ajlitchy@gmail.com) and M.H. Nehrir (email:
hnehrir@ece.montana.edu) are with the Electrical & Computer Engineering
Dept., Montana State University, Bozeman, MT 59717 USA.
The MG also has combined heat and power (CHP)
capability (for increased energy efficiency) to supply the
thermal loads of the building with the exhaust heat from the
FC, ICE, and the heat generated by a boiler. The fuel used for
the FC is hydrogen (H2) and that used for the ICE and boiler is
natural gas (NG).
Fig. 1. Sample load demand profile for a typical summer day of a mediumsized college in San Francisco, CA.
Fig. 2 shows the technologies used in the MG and their
corresponding power capacities to supply the load profiles
shown in Fig. 1. The technology selection and unit sizing have
been obtained using the following software application
programs: 1) the original version of DERCAM (WebOpt),
developed at the Lawrence Berkley Laboratory (LBL) [2], and
2) HOMER, originally developed at the National Renewable
Energy Laboratory (NREL) [3]. These programs provide
optimal selection of technologies and their sizes for any
specific load. The details of technology selection and unit
sizing for this project is reported by the authors in [1]. In this
paper, energy management of the designed MG is presented
using a modified multi-objective particle swarm optimization
(MOPSO) algorithm.
It has been shown in [4] that PSO is a useful technique to
perform real-time optimization of an energy management
system (EMS) for a hybrid wind-microturbine energy system.
The MG used in this paper is more complex than that reported
in [4]. The proposed MOPSO finds the optimal power to be
generated by each source at any time to provide the desired
power to the loads, considering the two objectives of
minimizing cost and emissions over a 24-hour period.
Because the two objectives are non-commensurate and
competing, a Pareto front, i.e. a set of solutions is obtained,
among which a trade-off solution can be picked.
The paper also compares the Pareto front performance of
the modified MOPSO algorithm with that of a multi-objective
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genetic algorithm (MOGA) optimization program available in
the Matlab optimization toolbox. The results show the
modified MOPSO algorithm performs better and faster. The
modified MOPSO is used in the EMS simulations of the MG
over a 24-hour period. The optimization process is carried out
every 30 seconds for two different cases: least cost and least
emissions. Simulation results show the effectiveness of the
proposed MOPSO for real-time energy management of
microgrids.
where FCR is the fuel consumption ratio in m3/s/W, ρng is the
density of natural gas in kg/m3, CC is natural gas’ carbon
content, and MWR is its molecular weight ratio of CO2. The
heat generated by the boiler, QB, is the excess heat that needs
to be generated after waste heat from the ICE (QICE), and FC
(QFC), is recuperated as follows.
4
where Qload is the heating load of the designed MG. The
recoverable heat of the ICE and FC are calculated as in (5) and
(6), respectively.
1
%
5
6
where LHV is the lower heating value of the fuel (45 MJ/kg),
%RH is the percentage of recoverable heat, and RHR is the
recoverable heat ratio.
Fig. 2. Block diagram of the designed AC-coupled microgrid.
II. FORMULATION OF OPTIMIZATION PROBLEM
The multi-objective energy management problem of the
designed MG (Fig. 2) contains two non-commensurate
competing objectives, cost and emissions. This section details
the two objective functions and the constraints of the energy
management system.
A. Cost Objective Function
The cost objective function depends on the cost of five
different energy sources as given by (1)
1
where CE, CFC, CBatt, CICE, and CB (boiler operation cost) are
the total operation cost of the different MG components in Fig.
2 during each optimization time step. The cost of PV is not
included in (1) since the same cost is used during each
simulation. The details of the cost formulation for each
component are given in [5].
B. Emissions Objective Function
Emission is the second objective function which is desired
to be minimized in the energy management optimization
problem. The emissions are produced from the natural gas
used to fuel the ICE and the boiler as shown in (2).
,
,
2
where ton,ICE and ton,B are the time the ICE and boiler are
operating, and EICE and EB are the CO2 production rates for the
ICE and boiler, respectively, calculated as follows.
3
C. Constraints
The energy management optimization problem contains
one equality constraint and two to four inequality constraints
depending on the operating state of the system. During power
demand, Pdemand, the equality constraint ensures the sum of the
power generated/absorbed from the different sources equals
the amount of power that is needed in addition to the available
PV power to supply the load, as given by (7). When the
available PV power is more than what is needed by the load,
then the excess available power, Pava, will be used by the
electrolyzer (PE) to generate hydrogen and to charge the
battery, (PBatt), given in (8).
7
8
The inequality constraints are simple operating ranges allowed
for each energy source, generally given by (9).
9
When excess power is available and either the battery or
hydrogen tank or both are fully charged, the excess power will
automatically be consumed by the device that isn’t fully
charged. In the rare case that the electrolyzer and the battery
are fully charged, the excess power will be consumed by a
dump load, Pdump. No optimization run is needed during the
above states.
III. INTELLIGENT OPTIMIZATION ALGORITHMS
A modified multi-objective PSO algorithm was developed
to solve the energy management problem. The descriptions of
each method and a summary on Pareto front are given in this
section.
A. Pareto Front
In the case a multi-objective optimization problem has
competing and non-commensurate objectives, it is not possible
to obtain an optimal operating point; instead a Pareto front of
the viable solutions can be created to help the system
operator/owner make a proper decision. A Pareto front is a
collection of many non-dominated solutions to the
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optimization problem and displays the true trade-offs between
multiple objectives, as shown in Fig. 3, where it is desired that
the two functions f1(x), f2(x) be minimized [6]. Population
based optimization techniques, such as PSO, work well with
this type of multi-objective optimization problem due to the
simultaneous generation of multiple solutions.
earlier. The detailed formulation of the algorithm is given in
[5].
C. Genetic Algorithm
GA is another powerful optimization tool that has been
around since its development in the 1960s [12]. MOGA has
also been extensively used in the literature. In this paper the
MOGA optimization tool available in the Matlab optimization
toolbox was used to compare the MOPSO results to.
IV. SIMULATION RESULTS
Numerous energy management cases were simulated to
obtain the Pareto fronts shown in Fig. 4. Two extreme cases
are discussed below: 1) the optimization case with the
cheapest solution on the Pareto front, and 2) the optimization
case that produced the least amount of emission. An analysis
of each of the energy management cases is given.
A. Pareto Front Comparison
Fig. 4 shows the comparison of Pareto front results
between the MOPSO algorithm and the MOGA algorithm.
B. Particle Swarm Optimization
PSO started as an attempt at simulating the flight of a flock
of birds and transformed into an optimization tool that started
with its original version in [6] and progressed to a multiobjective version in [7]-[10].
Like other evolutionary
algorithms, PSO starts with a randomly initialized set of
solutions and evolves towards the optimal solution through a
series of updated generations. The updated generations are
produced from previous generation information.
The traditional PSO updates its particles as in (10) and (11)
,
,
,
10
,
,
,,
,
,
2.2
2.0
PSO: 1089 solutions 26.9 sec
GA2: 250 solutions 145.5 sec
GA: 150 solutions 38.2 sec
1.8
Cost ($ / 30 sec)
Fig. 3. Pareto front example [6].
1.6
1.4
1.2
1.0
0.8
0.6
0.4
,
11
where Xi,d is the particle’s position of the d dimension variable
and Vi,d is the velocity of the particle. The velocity of the
particle depends on the previous velocity value, the particle’s
personal best position, Pbest,i,d, and the swarm’s global best
position, Gbest,d. The previous velocity value is multiplied by
an inertia weight, w, and the personal and global best distances
from the current particle position are multiplied by the social
learning factors C1 and C2, as well as the random numbers R1
and R2, which have a value between 0 and 1. The global best
value can be replaced by a neighborhood best value, Nbest,d,
which is determined from a defined neighborhood that stays
constant throughout the optimization.
When using PSO in multi-objective optimization problems
the same equations are used to update the particles positions as
in the traditional case, however, since there is no true global or
local optimum, a dynamic neighborhood with extended
memory is selected based on calculated distances between
solutions. The personal best solution in the equation is now
updated only if it is dominated by a new solution [9].
The MOPSO algorithm used in this paper has similar
attributes to that in [11] but is tailored to handle the constraints
of the energy management optimization problem described
0.2
0.6
0.7
0.8
0.9
1.0
1.1
1.2
Emissions (kg / 30 sec)
Fig. 4. Comparison of Pareto fronts for the different optimization algorithms.
Initially, the power demand was set to 250 kW, the battery
state of charge (SOC) was set to 50%, and the hydrogen tank
was set to 50% full as well. As shown in Fig. 4, the Pareto
front for the MOPSO and MOGA cases are on top of each
other which shows the two optimization algorithms give
similar results. However, the MOPSO algorithm proved to be
faster than the MOGA with 150 solutions and over five times
faster than the MOGA case with 250 solutions while also
producing 1089 solutions. The much higher speed of the
proposed MOPSO in reaching a series of solutions shows its
suitability for real-time applications. It should be noted that
the Pareto front shape and values change for each different set
of the initial operating states, but in each case the MOPSO
algorithm was faster and produced a denser Pareto front than
the MOGA optimization case. The MOPSO algorithm was
used to run the simulations.
B. Twenty-Four Hour Energy Management Simulation
Figs. 5 shows the simulation results when the objective is
to minimize the operation cost. Fig. 5(a) shows the power
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from the different generation sources shown in Fig. 2, the
power flow to/from the battery, and to the electrolyzer, and
Fig. 5(b) shows the SOC of the battery and hydrogen tank for
the 24-hr simulation period.
Fig. 6 shows the same quantities shown in Fig. 5 when the
objective is to minimize emission. Each case starts out with
the battery SOC at 50% and the hydrogen tank at
approximately 48% full. Each state uses all of the PV power
that is available and updates the operating points of its sources
every 30 seconds after the optimization is complete. The ICE
power output is allowed to freely change after its new
operating point has been set in order to ensure the equality
constraint is met due to fluctuations in load and PV power
over the 30 second interval.
600
500
Power (kW)
700
600
500
Power (kW)
700
the low multiplicative cost factor for the battery when its SOC
is lower than 70%. Once the battery SOC reaches 70%, it
stops charging. After that point it is cheapest to power either
the electrolyzer or charge the battery alone and not both at the
same time. Since there is more power available than what can
be absorbed by the battery the optimization process chooses
the electrolyzer in order to satisfy the constraints. Once the
available power falls below what is needed to meet the
demand, it is then more cost-effective to operate (discharge)
the battery, since its SOC is above 70%.
400
300
200
400
100
300
0
200
-100
0
2
4
6
8
100
10
12
14
16
18
20
16
18
20
22
24
Time (hrs)
0
-100
0
2
4
6
8
10
12
14
16
18
20
22
24
Time (hrs)
(a)
100
80
State of Charge (%)
(a)
100
State of Charge (%)
80
60
40
60
20
40
0
20
0
2
4
6
8
10
12
14
22
24
Time (hrs)
0
0
2
4
6
8
10
12
14
16
18
20
22
24
Time (hrs)
(b)
Fig. 5. Power from each source for the least cost case (a) and the state of
charge of the battery and hydrogen tank (b).
When the objective is to minimize cost (Fig. 5), the ICE is
the only power-producing source during the time when PV
power is not sufficient to meet the demand. During the period
when excess PV power is available, the battery is charged and
the electrolyzer is powered to produce hydrogen.
In Fig. 5, at the beginning of the period when power is
available (around hour 6), the battery starts charging and the
electrolyzer operating and producing hydrogen. This is due to
(b)
Fig. 6. Power from each source for the least emission case (a) and the state of
charge of the battery and hydrogen tank (b).
The second optimization case chose the solution that would
produce the least amount of emissions over the optimization
time step of 30 seconds (Fig. 6). At the beginning of the
simulation, since PV power is not available the FC and battery
are used along with the ICE to supply the load. When PV
power is available, the same process occurs as during the least
cost case. In the least emission case, the battery discharged
more than the least cost case and therefore charges for a longer
period of time until it reaches around 70% again.
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Around hour 14, the PV power falls below that demanded
by the load and the battery SOC is not sufficient to supply the
additional power demanded by the load. Because the
objective is to minimize the amount of emission produced, the
FC is turned on to provide the remainder of the power
demanded by the load. The FC also provides power to charge
the battery. This is because of the objective being to minimize
emission. The exhaust heat from the FC is used to supply the
heating loads, and the emission-producing boiler is not turned
on until the hydrogen tank eventually runs out of hydrogen.
Then, the battery and the ICE power are used to meet the
demand.
The total cost and emission calculated over the 24-hour
simulation period for the two optimization cases discussed
above are shown in Table I. It is clear from the table that the
two objectives, least cost and least emissions are conflicting,
i.e. cost is minimized, emission is high and for least emission,
cost is high.
TABLE I
Total Cost and Emissions Values over the 24 Hour Period
Run
Least Cost
Least
Emissions
Total Cost ($)
781
1767
Total Emissions (kg)
2857
2680
V. CONCLUSION
Real-time energy management of an islanded microgrid
using MOPSO was presented in this paper. A description of
the modified MOPSO used was presented, and its performance
was compared with the MOGA optimization tool available in
the Matlab optimization toolbox. The faster simulation time
and denser Pareto front showed the MOPSO algorithm to be
superior and was therefore used in the 24-hour energy
management simulations.
The results of the energy
management simulations show the trade-off between least cost
and least emissions. This information can be helpful to the
MG operators/owners to make informed decision regarding
the operation of their MGs.
ACKNOWLEDGEMENT
The authors acknowledge the use of the application
programs, WebOpt, developed at Lawrence Berkley
Laboratory (LBL), and HOMER, originally developed the
National Renewable Energy Laboratory (NREL). They also
acknowledge HOMER Energy, LLC for providing them a
commercial version of the HOMER software.
VI. REFERENCES
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Microgrid:
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