Aalborg Universitet
Analysis and distributed control of power flow in DC microgrids to improve system
efficiency
Chen, Fang; Burgos, Rolando; Boroyevich, Dushan; Diaz, Enrique Rodriguez; Meng, Lexuan;
Quintero, Juan Carlos Vasquez; Guerrero, Josep M.
Published in:
Proceedings of IEEE 2016 4th International Symposium on Environment Friendly Energies and Applications
(EFEA)
DOI (link to publication from Publisher):
10.1109/EFEA.2016.7748774
Publication date:
2016
Document Version
Early version, also known as pre-print
Link to publication from Aalborg University
Citation for published version (APA):
Chen, F., Burgos, R., Boroyevich, D., Diaz, E. R., Meng, L., Quintero, J. C. V., & Guerrero, J. M. (2016).
Analysis and distributed control of power flow in DC microgrids to improve system efficiency. In Proceedings of
IEEE 2016 4th International Symposium on Environment Friendly Energies and Applications (EFEA) IEEE
Press. https://doi.org/10.1109/EFEA.2016.7748774
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Power Flow Analysis and Control for DC Microgrid
to Improve System Efficiency
Fang Chen, Rolando Burgos, Dushan Boroyevich
Center for Power Electronics Systems (CPES)
Virginia Polytechnic Institute & State University
Blacksburg, VA, US
fangchen@vt.edu
Enrique Rodriguez-Diaz, Juan C. Vasquez,
Josep M. Guerrero
Department of Energy Technology
Aalborg University, Aalborg, Denmark
www.microgrids.et.aau.dk
Abstract—DC Microgrid attains popularity in integrating
renewable energy sources and batteries. It also has the potential to
achieve higher efficiency than ac power grid under the condition
of optimized power flow. In this paper, a general dc microgrid is
modeled based on a cluster of general dc nodes, which includes
constant power renewables generation, droop-controlled voltage
source and different kinds of load. Then the dc power flow is
solved for optimization. A voltage restoration method based on
consensus communication is used to restore the voltage deviation
from droop characteristic. An enhanced current regulator is
adopted to guarantee the accurate load sharing considering the
impact from sensor error and line resistance. A tie line power flow
control method is proposed to regulate the tie line power and
increase the system efficiency at light load. All the considered
methods only need the local information and the information from
its nearest neighbor thus the system expendability is guaranteed.
Simulation and experiment results are provided to validate the
proposed methods.
Keywords—dc microgrid; power flow; efficiency
I. INTRODUCTION
DC microgrid gains more and more attention because of the
ease to integrate different renewable sources and energy storage,
no frequency issue and the possibility to achieve higher
efficiency [1]. To coordinate multiple sources in a dc grid that
are paralleled to a common bus, droop control is broadly used
[2]–[4]. By introducing a virtual output resistance to each
source, the circulating current is suppressed and load sharing
among sources is realized.
Though the droop principle is used in many applications,
how to analyze and optimize power flow in a dc grid that
consists of multiple power nodes is seldom analyzed. In [5], the
steady-state performance and sensitivity in a dc microgrid are
analyzed. But it only considered the droop-controlled voltage
source and constant current load. In [6], the droop voltage range
design and the cable’s impact on system performance are
analyzed quantitatively, but the analyzed system is small and
only has a limited number of sources. In [7]–[10], different
secondary control methods were proposed to restore the dc bus
voltage deviation from droop control and ensure a proportional
load sharing. However, all of them rely on dedicated
communication links, which reduces system reliability and
expendability. What is more, though these methods improve the
bus voltage regulation and proportional load sharing, the
outcomes and benefits of these improvement is still unclear. In
[11], a hierarchical control structure was used to optimize the
efficiency of a dc microgrid. It was reported that, to improve the
overall system efficiency, uneven load sharing is better at light
load condition while proportional load sharing is better at heavy
load. But the proposed algorithm is very complicate and was
only demonstrated for a two-source system where source
efficiency curves are already known.
To save the dedicated communication link in distributed
control, consensus based control method was introduced to the
field of microgrid from multi-agent systems in [12]–[17]. It
enables the bus voltage restoration and load sharing with
communications between only adjacent nodes. It also enables an
opportunity to achieve other optimization without dedicated
communication.
In this paper, the analytical solution for the power flow in a
general dc grid is derived, which reveals the impact from cable
resistance and voltage sensor error. Then a secondary level
voltage restoration based on consensus communication is
applied. Two power flow control methods are considered and
compared for the sake of efficiency. All the control methods are
based on the nearest nodes communication in which one node
only talks to its nearest neighbors.
II. POWER FLOW ANALYSIS FOR A GENERAL DC GRID
To get a generalized power flow solution for optimization, a
general dc grid needs modeling. Consider a general dc microgrid
as shown in Fig. 1. It can include many dc nodes which have
different structure and are geographically distributed. In the
figure, five nodes are drawn as an example. Every dc node has
its different local power generation (e.g. solar and wind), energy
storage and loads. The nodes can even be another dc or ac
system. All the nodes are connected to a common dc bus through
power converters.
For the modeling, the sources and loads are categorized into
following types.
1) constant power source (CPS), which is usually the
distributed renewable energy generation (photovoltaic and
wind) working at maximum power point tracking (MPPT)
mode. It can be either one source or a combination of multiple
CPSs. This kind of sources inject a constant power no matter the
dc bus voltage.
www.microgrids.et.aau.dk
2) droop controlled voltage regulators (VR), which buffers
the intermittent power from renewable sources and regulates the
dc bus voltage. Battery is a good candidate for this purpose
because of its bidirectional power capability. In some case, it can
be also a bidirectional ac-dc converter interfaced to the ac utility.
The injected power from this source to the dc bus changes with
different bus voltage.
3) constant power load (CPL) and constant resistive load
(CRL). Nowadays, most loads like consumer electronics, LEDs,
microwaves, washing machines are all constant power style. But
some old lighting bulbs and oven can be still resistive.
Consider the span of a real distribution system, the distance
between different nodes cannot be omitted.
Similar to the power flow analysis in ac system, we define
the system to include N power nodes and the corresponding
admittance matrix Y
N×N
. Its elements y
ij
is the line admittance
between node i and node j. The self admittance y
ii
is defined as
the sum of all branch admittance connecting to node i.
Obviously, the admittance matrix is symmetric and usually
sparse.
For certain node i, suppose the total generation of CPS is
P
CPSi
and total CPL consumption is P
CPLi
. The VR follows the
droop output characteristic in (1) to share the load, where v
i
is
the bus voltage of node i and
*
i
v
is the voltage set point of the
droop for node i. r
d
is the droop resistance and i
o
is the output
current of VR.
*
i i d o
v v r i
(1)
Then the injected power from VR is
*
ii
VRi i o i
d
vv
P v i v
r
(2)
The power consumed on CRL is
2
i
CRLi
CRLi
v
P
R
(3)
The power injected into node i is in (4). If there is no
connection between node i and j, then y
ij
equals to zero.
1,
N
INi i j i ij
j j i
P v v v y
(4)
Due to power balance, for every node i, (5) needs to be
satisfied.
0
CPSi VRi CPLi CRLi INi
P P P P P
(5)
If we put it in a matrix form, then the system power
description can be expressed in (6).
In this equation, the node voltage v
1
to v
n
are unknowns. The
P
CPSi
and P
CPLi
are usually unadjustable. But the droop voltage
set point
*
i
v
and droop resistance r
di
are controllable. They can
be finely programmed to control the power flow between
different nodes and enable the optimized power flow. Since the
droop resistance is usually programmed inverse proportional to
the source rating. In the following section, the voltage set point
is used as the control variable to achieve different optimization
targets.
III. POWER FLOW CONTROL AND OPTIMIZATION
In order to maximize the system efficiency, the system loss
needs to be analyzed and minimized. In practical, the system
loss are mainly from the power conversion loss generated by
power converters and transmission loss consumed on power
cables. In this section, two different power control methods are
Node 4
Node 5
Node 3
DC
DC
Solar
Load
AC
DC
Wind
Load
DC
DC
Battery
Load
DC
DC
DC Grid
Load
DC
AC
AC Grid
Load
Node 1
Node 2
y
12
y
23
y
34
y
45
v
2
v
1
v
3
v
4
v
5
y
13
dc power
distribution
Fig. 1. A general dc microgrid.
_________________________________________________________________________________________________________
*
1 1 1
11
*
2 2 2
22
*
1 11 1 1 12 1
2 21 22 2
0 0 0
/
0 0 0
/
0 0 0
0 0 0
/
0 0 0 1/ 1/
0 0 0 1/ 1/
0 0 0
0 0 0
CPS CPL
d
CPS CPL
d
CPSn CPLn n
n dn
d CRL n
d CRL
n
P P v
vr
P P v
vr
P P v
vr
v y r R y y
v y y r R
v
1
2 2 2
12
0
1/ 1/
n
n n nn dn CRLn n
v
yv
y y y r R v
(6)
discussed by using only the communication between nearest
nodes. One is accurate load sharing control among different
nodes according to their power rating. When the load is heavy,
the conversion loss dominates. The proportional load sharing
can minimize the conversion loss by distributing the load.
However, when the load is light, instead of distributing the load,
it is better to let local source provides the local power
consumption. It has two benefits. Firstly, according to [11], at
light load condition, unevenly distributing the load at light load
condition achieves lower overall conversion loss. Secondly,
since the loads are fed by their local sources, the transmission
loss is eliminated. In order to directly control the power flow on
the tie lines, it requires additional measurement to measure the
current on the tie lines. But the cost is considered reasonable to
achieve the direct power flow control target. In this case, under
normal load condition, the tie line current can be controlled to
be zero. The transmission loss on the lines is completely
eliminated. At heavy load condition, the control can switch to
the proportional sharing mode to guarantee the system
availability.
Because of the droop characteristic of VRs, the steady state
bus voltage will be lower than the nominal voltage which can
deteriorate the system performance and lower the system
efficiency. For both control method, a consensus based voltage
restoration is applied to compensate the steady state error.
Again, this only requires the communication between adjacent
nodes.
The controller structure for each node is shown in Fig. 2.
This paper focuses on the secondary level control, which
consists of three paralleled parts: 1) consensus based voltage
restoration. 2) proportional current control and 3) tie line current
control. It is worth mentioning that the communication can be
bidirectional or unidirectional. In this paper, to show the
simpleness of the proposed method, only unidirectional
communication is used. It means the information can only be
passed from node i-1 to node i, and then to node i+1, but not in
the reversed direction.
The function of the voltage restoration controller is to
generate a compensation voltage offset to cancel the voltage
drift caused by the primary droop control. In order to generate
this restoration signal, each node needs to estimate the bus
voltage by comparing the local voltage estimation
i
v
with the
estimation
1i
v
received from the previous node. The error is
passed through a gain of K
v
and an integrator. The result is added
to the current local voltage measurement result v
i
to update the
local estimation
i
v
. The estimation of bus voltage is then
compared with the voltage set point
*
i
v
. The error is
compensated by a PI controller. This part will restore the voltage
deviation caused by droop characteristic and cable voltage drop.
The local bus voltage estimation is also passed to the next node
for its calculation.
The proportional current control part and tie line current
control part are for different load condition. Though the droop
resistance is designed for the proportional load sharing between
different sources without communication, the ratio is never
accurate in real case because of sensor discrepancy and cable
resistance. The proportional current control part is designed for
this. A new term called “pu current” is defined. It is the
percentage of local current compared to its rated current. So
when the local VR current is 0 then the pu current is also 0.
When the local current is maximized at its rating, the pu current
is 1. By such definition, different sources can compare their
output current directly without any transformation. In this part,
the local controller receives the pu current from previous node
and compare it with the local pu current. Based on the
difference, a second adjustment part for local voltage reference
is generated. Because this is a closed loop compensation with an
integrator, the steady state error is eliminated. Accurate load
distribution is achieved for heavy load condition.
At light load condition, it is not preferred to have even load
sharing. In this case, the tie line current control part is used. It
directly senses the current of transmission line which is
connected to the local node and compare it with the reference.
In this case, we want to stop transmitting power from other
nodes, then the current reference is zero. In fact, this reference
can be set to other desired non-zero values to achieve other
optimization target.
It is worth mentioning that the proportional load sharing and
tie line current control can be contradictory with each other, so
it is preferred to choose one for a certain load condition. But the
K
i
+
11
,
pu
ii
vi
1
pu
i
i
+
-
+
i
v
pu
i
i
K
v
1i
v
i
v
-
+
+
+
*
i
v
+
-
PI
1i
v
2i
v
1,ii
i
K
p
+
+
modified voltage
set point for node i
,
pu
ii
vi
-
+
r
i
i
i
voltage
controller
Primary droop control
Consensus based voltage restoration
Proportional current control
Tie line current control
Secondary control
From tertiary control
from the previous node
from the local tie line
current measurement
to the next node
heavy load
light load
mode
selection
Fig. 2. Consensus based optimized power flow controller.
voltage restoration can work with both since it adjusts all the
node voltage in the same manner.
IV. SIMULATION AND EXPERIMENT VERIFICATION
A three-node system is constructed to simulate and validate
the effectiveness of the proposed control strategy. The system
structure and load profile is shown in Fig. 3. Three VR nodes are
connected through two segments of tie lines. Each tie line has
different resistance. There is also sensor discrepancy for
different VRs, i.e. VR
1
has accurate sensing while VR
2
and VR
3
have 0.2% and 0.1% drift. So without compensation, the load
sharing will be inaccurate. The load at each node is expressed as
load 1 to load 3. In the simulation, loads at node 1 and 3 are fixed
at 0.3 pu and 0.7 pu. Load at node 2 steps up at 10 second and
20 second to demonstrate the performance. The communication
is only between the nearest nodes and unidirectional. Node 1
sends its pu current and voltage estimation to node 2. The same
from node 2 to node 3. Each node also senses its local tie line
current for direct power flow control. To make the conclusion
more general, the nominal bus voltage is 1 p.u.. The current
rating for each source is also 1 p.u..
Fig. 3 (b)-(e) show the simulation results. In (b), no
secondary control is enabled. The system can still work with the
primary droop control. But the load is not evenly shared among
sources. Also, the bus voltage drops as the load current increases
at 10 second and 20 second. In (c), the voltage restoration loop
is enabled. The current sharing is the same as in (a). But the
voltage is lifted up. At the heaviest load condition, the load node
voltage is 0.997 p.u., which is much higher than the value of
0.983 p.u. in (b). In (d), both the voltage restoration and current
sharing control are enabled. In this case, the three source current
are always the same, even with the realistic line resistance and
sensor drift. The effectiveness of the current sharing control is
proved. In (e), the tie line current control is enabled. We can
observe the source current of node 1 and node 3 are constant and
equal to their individual fixed load. Current from source 2 tightly
follows the load step at node 2. The current flow through tie lines
are zero.
The proposal was also verified by hardware experiment. Fig.
4 shows a picture of the experiment setup. Three three-phase ac-
dc converters are placed in a cabinet to mimic the operation of
three distributed sources. The converters are connected through
adjustable cable emulator. So the resistance of each cable can be
accurately controlled. A dSpace control system is used to fulfill
the converter control and higher level optimization. It also works
as the monitoring system to observe the interested waveforms in
real time. It makes it convenient to start and stop each control
function so the effect of each control loop can be identified.
Constant resistive and constant power loads are connected along
the bus to typify the distributed load.
node 1 node 2 node 3
tie line tie line
Source 1 Source 2 Source 3
Load 1 Load 2 Load 3
communicatio n
v
s1
v
s2
v
s3
v
L2
Time (s)
voltage
current
i
s1
i
s3
i
s2
(a) (b)
voltage
current
Time (s)
Time (s)
voltage
current
i
s1
i
s3
i
s2
v
s1
v
s3
v
s2
v
L2
v
s1
v
s2
v
s3
i
s2
i
s3
i
s1
Time (s)
voltage
current
v
s1
v
s2
v
s3
v
L2
i
s1
i
s3
i
s2
(c) (d) (e)
Fig. 3. System structure and simulation results.
(a) simulated three-source three-load dc distribution system. (b) voltage and current without secondary control
(c) with voltage restoration (d) with both voltage restoration and current sharing control (e) with tie line current control
