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KSII The 5th International Conference on Internet (ICONI) 2013.
C o p y r i g h t ⓒ 2013 K S I I
1
This research was supported by a research grant from GRRC(Geyonggi Regional Research Center) at Kyonggi
University.
An Automated Impedance Estimation by
Cooperative Load Control
Daisuke Kodaira1, Sekyung Han2*, Soohee Han3, Yasuo Hasegawa4, and Hirohisa Aki4
1Department of Science and Engineering, Tokyo Institute of Technology, Japan
[e-mail: d.kodaira@aist.go.jp ]
2Department of Electronics and Control Engineering, Hanbat National University, Korea
[e-mail: sk.han@hanbat.ac.kr ]
3Department of Electrical Engineering, Konkuk University, Seoul, Korea
[e-mail: shhan@konkuk.ac.kr ]
4Energy Technology Research Institute, National Institute of Advanced Industrial Science and
Technology (AIST), Japan
[e-mail: hasegawa.y@aist.go.jp ]
[e-mail: h-aki@aist.go.jp ]
*Corresponding author: Sekyung Han
Abstract
An innovative algorithm for estimating the impedance in between the estimation nodes in the low
voltage distribution network is suggested. This paper proposes a novel method of the automated
impedance estimation based on the practically measurable parameters including voltage, current, and
power at each terminal node. The load at each node is controlled to yield a specific pattern and the
measured data are shared among the node EMS. Based on the gathered data, the unknown impedances
are estimated for the use of voltage control in the distribution network.
Keywords: impedance estimation, DER, reactive power, voltage regulation
1. Nomenclature
All values are expressed by complex numbers.
junction-node voltage at J-Node(i);
line current from J-Node(i) to
J-Node(i+1);
injected power to J-Node(i);
terminal-node voltage at T-Node (i);
line current flowing to T-Node(i) ;
terminal load at T-Node(i);
line loss between J-Node(N-1) and
T-Node N;
line loss between J-Node(i) and
T-Node(i);
impedance between J-Node(i) and
J-Node(i-1);
impedance between J-Node(i) and
T-Node(i);
2. Introduction
It is well known problem that the photovoltaic
(PV) systems connected to the low voltage (LV)
feeder cause an over voltage problem Error!
Reference source not found.. Currently, when a
feeder voltage exceeds the limited value
guaranteed by the law, it first injects the reactive
power to the grid, and then eventually reduces
the active power to lower the node voltage. This
regulation system puts a limit on the achievable
output power of the PV systems.
Installing some reinforcements may solve the
problem. However, considering the scale of low
voltage distribution system, these are expensive.
For this reason, several studies have proposed the
methods of resolving the over voltage problem
utilizing reactive power control without
expensive reinforcements. However, some
challenging issues remain for practical
2 Dongsun Kim and Junchul Chun: An Interactive Method for Volumetric Human Organ Models
implementation: The bus impedances should be
identified automatically and seamlessly without
the human intervention. In this paper, we focus
on the automatic estimation of the bus
impedances.
3. System Configuration
Measureing impedances directly is impractical
since the EMS and the DERs may be installed
after the construction of the residential house. In
this case, the impedance should be estimated
using an indirect method. In this paper, we
calculate the line impedance using the measured
values such as voltage, current, and the power
factor of the each terminal node.
Considering that the typical electric system
operates at 50 Hz or 60 Hz, the node information
such as voltage and current should be measured
simultaneously with a common time source
where the maximum latency should be less than a
millisecond. However, this level of synchronized
measurement is practically impossible without
the support of global positioning system (GPS)
and a sophisticatedly designed hardware kit.
Nevertheless, the measurement can be still
synchronized with the precision of conventional
digital communication scheme. If the node
power can be maintained for such duration, say a
second, the root-mean-square values of the node
voltage and the current can still be incorporated
into the equations. Likewise, the active and the
reactive power as well as power factor are
usable.
4. Formulation
The measured parameters can be shared in the
following form:
(1)
The aim of the formulation is to represent the
whole node information in terms of the line
impedances (pursuing parameters) and the
terminal node data (measurable parameters) in
(1). In Fig. 1, part A can be formulated in two
stages. In the first stage, (N-1)-th junction-node
parameters are represented in terms of the line
impedances and the parameters in (1). , as
follows:
(2)
Similarly, the (N-1)-th junction power
can be represented in terms of the sum of
terminal loads (,) and the power loss
in between the junction node and the terminal
nodes, as follows:
(3)
From (2), can be represented as
following form:
(4)
In a similar way, can be represented
as follows:
(5)
From (3),(4) and (5):
(6)
From (6) and (2), the current flowing into J-Node
(N-1) is:
Fig. 1. Topology of distribution system.
J-Node(N-3)
J-Node(N-2)
J-Node(N-1)
T-Node (N-1)
T-Node N
T-Node (N-2)
T-Node (N-3)
・・・・
J Node(1)
T Node 1
J Node(3)
T Node
J Node(2)
Pole transformer
Part A
Part B
KSII The 5th International Conference on Internet (ICONI) 2013.
C o p y r i g h t ⓒ 2013 K S I I
3
(7)
(2), (6) and (7) indicate that all parameters
involved with the (N-1)-th junction node can be
represented by and the measured
data from T-Node (N) and T-Node (N-1).
In the second stage, we construct the equations
for (N-1)-th terminal-node using the (N-1)-th
junction-node equations. is the sum
of two terminal-nodes current, then, from (7):
(8)
For the terminal-node voltage, the following
equation holds:
(9)
Then, from (2) and (8):
(10)
Where
(11)
Now, is represented in terms of
, and (1). Regarding the terminal
load, the following equation holds:
(12)
Then, from (8) and (10) , can be
represented with the measurable parameters and
impedances, as follows:
(13)
Now we derived two dynamic equations, (10)
and (13) that involve the bus impedances and the
two terminal-nodes parameters. These dynamic
equations should hold regardless of the
terminal-node values, and thus, we can apply
various loads to yield multiple equations. Since
the equation holds two unknown impedances,
each of which possesses resistance and reactance
values. Even with enough number of equations,
however, it is intractable to estimate the
impedances directly owing to the nonlinearity of
the equations. To this end, we define the cost
functions to be minimized using the derived
equations in (10) and (13), as follows:
(14)
(15)
Then, finding and that
minimizes the sum of the above two costs
sufficiently close to zero will yield the solution
to our problem. These can be found using an
iterative numerical method such as the particle
swarm optimization (PSO). Impedance of Part B
in Fig.1 is calculated by the same way as Part A.
References
[1] R. Walling and R. Saint, “Summary of
distributed resources impact on power
delivery systems,” IEEE Trans. Power
Delivery. vol. 23, no. 3, pp. 1636–1644,
July 2008