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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2018.2878084, IEEE
Transactions on Power Electronics
differences.
To conclude above discussion and comparison, the existing
secondary control methods in dc MG are summarized in Table
I. It can be concluded that the main objective for most of the
methods is to achieve the accurate current sharing under
different circumstances. Meanwhile, in the voltage control
sense, they are devoted to either restore the PCC voltage or fix
the average voltages at the nominal value.
Nevertheless, converters or load terminal voltages are also of
great importance. It should be noted that if the differences of
line impedances are considerably large, only fixing the average
voltage value at nominal value cannot guarantee that the
individual terminal voltage is kept within the standard limits.
From the perspective of power flow in a dc MG, the terminal
voltage from each converter should exist deviations around the
nominal value, otherwise there is no power flow in the system
[
]. On the other hand, large voltage deviations can cause
stability problems and destroy power quality according to the
standard in [
]. Furthermore, the power quality and
stability margin for local load will be worse than before due to
the voltage deviations. To solve the above-mentioned
challenges, this paper presents a compromised control
conception between current sharing and voltage regulation to
balance the trade-off and satisfy different requirements. The
main contributions of this paper are considered in the following
aspects:
1). Compromised control conception is proposed to achieve
balanced control between voltage regulation and current
sharing among power converters.
2). The containment-based controller is proposed to bound
voltages within a reasonable range and keep necessary voltage
deviations for power flow regulation. Meanwhile, the
consensus-based current controller is implemented to guarantee
current sharing to a certain degree.
3). According to different system requirements and
conditions, the performance including tighter voltage bound or
more accurate current sharing can be compromised between
each other through tuning control weightings.
4). The large signal model including the proposed controller
and the electrical topology of the dc MG is established to
analyse the sensitivity and tuning principles of control
parameters.
5). The experimental results and comparison with existing
literatures are shown to verify the effectiveness of the proposed
method.
The paper is organized as follows. In Section II, the
compromised control conception is proposed by introducing
containment and consensus-based distributed coordination
control strategy. In Section III, the large signal model and its
stability analysis are provided. In Section IV, experimental
results are presented to prove the effectiveness of proposed
controller. Finally, the paper is concluded in Section V.
II. COMPROMISED CONTROLLER IN REVERSE DROOP BASED
DC MG
This section explains proposed compromised controllers
based on the hierarchical control structure for a dc MG. The
reverse droop control is explained in the primary control level.
Furthermore, the proposed containment-based voltage
controller and consensus-based current controller is explained
in detail in the secondary control level to form the compromised
controller.
A. Definitions and Notations
For the control system with n distributed controllers, a
controller is called a leader if it only provides information to its
neighbors and does not receive information. A controller is
called a follower if it can receive/send information from/to one
or more neighbors through communication topology. Let N
i
denote the set of i
th
-controller neighbors chosen from followers,
and R
i
as the set of leaders which can give its information to i
th
-
agent directly. This definition is applied to containment-based
voltage controller, in which the dynamic range is appointed in
charge of setting the lower and upper voltage boundaries
respectively. Meanwhile, the consensus-based current
controller only uses the neighbors’ information without the
reference leaders’ information.
Let C be a set in a real vector space
. The set C is
called convex if, for any x and y in C, the point (1-z)x+zy is in
C for any z∈[0,1]. The convex hull for a set of points
X={x
1
,…,x
q
}in V is the minimal convex set containing all points
in X. Let Co(X) denote the convex hull of X. In particular, when
, Co(X)={x|x∈[min x
i
, max x
i
]}which will be used in this
paper. In addition, define vector Z∈R
n
, then diag(Z)∈R
n×n
as the
diagonal matrix whose diagonal elements are the elements in
vector Z. I
n
is the unit matrix and 0
[n]
is the zero n
×
n matrix. 0
n
and 1
n
are the n-vectors with all 0 and 1 elements.
For the consensus-based current controller, an adjacency
matrix is defined as A=[a
ij
]∈R
n×n
with a
ij
=1 if node i can
receive information from node j otherwise a
ij
=0; The Laplacian
matrix is defined as
. For the containment-based controller, another
adjacency matrix is defined as
with b
il
=1 if
node i can receive information from one of the two reference
leaders otherwise b
il
=0, in which l represents the label of two
reference leaders; Another matrix is defined as
2
11
nn
ii ij il
j l n
l a b
+
= = +
=+
; for other items,
when j<n, l
ij
=-a
ij
, otherwise when j>n, l
ij
=-b
ij
. For
convenience, the matrix
.
The adjacency matrix represents the communication
topology mathematically. From the graph theory viewpoint, for
the consensus-based current controller, since only followers
communicate with their neighbors, the communication
topology needs to be connected graph. For the containment-
based voltage controller, there are several followers and two
leaders in the system, the communication topology among
followers needs to be connected graph which is same as before,
meanwhile the communication topology between followers and
leaders should contain at least a spanning tree to make sure that
all the followers can receive the information from one of the
leaders at least indirectly. For rigorous theoretical proof