1
Sandia Frequency Shift Parameter Selection to
Eliminate Non-Detection Zones
H. H. Zeineldin, Member, IEEE, and S. Kennedy, Member IEEE
Abstract—The Sandia Frequency Shift (SFS) method is one of
the active islanding detection methods that posses small Nondetection Zones (NDZ). The effectiveness of the SFS depends to a
great extent on its design parameters (cfo and k). In this letter, a
formula is derived to aid protection engineers in determining the
optimal parameter setting for the SFS islanding detection
method. It is concluded that the parameter (k) has significant
effect on the NDZ and a modified version of the SFS is proposed
that relies only on this parameter.
impedance load and a 100 kW inverter based DG. The DG
interface control model presented in [3] was implemented and
is given in Fig. 2. For the SFS islanding detection method, the
inverter phase angle ( inv) can be expressed as a function of
the island frequency (f), nominal frequency (fn), and the SFS
parameters cfo and k [2].
(cf o + k ( f f n )) / 2 (1)
inv =
Index Terms— Distributed Generation, Sandia Frequency
Shift, Inverter, Islanding.
I
I. INTRODUCTION
SLANDING is a condition in which a part of the utility
system, which contains both load and generation, is isolated
from the rest of the utility system and continues to operate. It
is important to equip a Distributed Generation (DG) with an
efficient islanding detection method, capable of detecting
islanding for all possible loading cases and thus minimizing,
or even eliminating, the Non-Detection Zone (NDZ). The
NDZ could be defined as the loading conditions for which an
islanding detection method would fail. The majority of passive
islanding detection methods, which rely on measuring a
certain system parameter, suffer from large NDZ [1]. Active
methods, on the other hand, are characterized by having
smaller NDZ. Active methods that rely on frequency shifting
include slide-mode frequency shift (SMS) [1], Active
Frequency Drift (AFD) [2], and Sandia Frequency Shift (SFS)
[2]. The SFS method has been proven to have an extremely
narrow NDZ [1]. In [2] and [3], it has been shown that the
performance of the SFS method is dependent on the design
parameters. In this paper, we extend the work conducted in [2]
by deriving a mathematical formula that aids in setting the
SFS design parameters to eliminate the NDZ. A modified
version of the SFS method is proposed and presented that
relies on only one parameter.
II. SYSTEM UNDER STUDY
The system, shown in Fig. 1, consists of a distribution
network represented by a source behind impedance, a constant
This work was supported by the Masdar Institute of Science and
Technology.
H. H. Zeineldin and S. Kennedy are with the Masdar Institute of Science
and Technology, Abu Dhabi, UAE (e-mail: [email protected]).
Fig.1. System under study.
Fig. 2. DG interface control for constant power operation.
III. MODIFIED SANDIA FREQUENCY SHIFT METHOD
The load phase angle can be expressed as a function of
island frequency, the load resonant frequency, fo, and the load
quality factor, Qf [2]
tan 1[Q f ( f o / f f / f o )] (2)
load =
For this system to operate as a steady state island, the two
phase angles in (1) and (2) must be equal, which results in the
following equilibrium condition, or phase criteria [2].
(3)
f o2 + f tan[ (cf o + k ( f f n )) / 2] f o / Q f f 2 = 0
Previous work has shown that the phase criteria for
different islanding detection methods defines the NDZ and can
be used to select appropriate parameters such that the NDZ is
eliminated [2]. An important aspect of this approach, not
emphasized by previous authors, is that the equilibrium point
defined by the phase criterion must be unstable in order to
ensure islanding detection and to eliminate the NDZ.
Furthermore, the stability of the solution to (3) depends upon
the relative magnitudes of the slopes of the phase angle –
frequency curves defined by (1) and (2). This additional
2
“instability” condition can be expressed as:
62
(4)
d load / df < d inv / df
Following the slope criteria of (4), the value of k in (1) can
be chosen to guarantee that the frequency will drift away from
the equilibrium point defined by the phase criteria (outside of
OFP/UFP threshold values). Differentiating the two
expressions for the phase angle in (1) and (2), the instability
condition can be expressed as follows
[1 + Q 2f ( f o / f
f / f o )]
Load Resonant Frequency,f0
(5)
It can be shown that the maximum value of the right-hand
side of (5) occurs at f = fo, and hence this expression can be
reduced to:
(6)
k > 4Q f / f 0
Equation (6) provides a guideline for protection engineers,
which ensures there will be no NDZ for the SFS method. For
example, to design the SFS such that it eliminates the NDZ for
loads with Qf up to 7, fo would be set to 59.3 (minimum UFP
limit) and Qf would be set to 7 in (6), resulting in a value of k
equal to 0.15.
The effect of k on the NDZ, with cf0 = 0, can be seen in the
fo – Qf space shown in Fig. 3. Each pair of curves, for different
values of k, define an envelope within which islanding will not
be detected. As k increases, the envelope moves to the right,
which confirms the result in (6). Figure 4 shows the NDZ for
different values of cfo. It can be seen that k has a much more
profound effect than cfo in constraining a targeted Qf within
the NDZ. Thus, the proposed modified SFS equation would be
(7)
fn ) / 2
inv = k ( f
The paper analyzes the impact of the SFS parameters on
NDZ and proposes a modified SFS method. A simplified, yet
equally effective, SFS is presented that relies on only one
parameter “k” for islanding detection. A formula is derived to
aid protection engineers to optimally set this parameter to
eliminate the NDZ. Simulation results highlight the
effectiveness of the proposed approach and coincide with the
mathematical derivations.
61
60.5
60
59.5
59
58 0
10
1
10
Quality Factor, Q
10
2
f
Figure 3 Dependence of non-detection zone on k.
62
cf = 0,
k=0
0
cf = 0.05, k = 0.1
61.5
0
cf0 = 0.1,
61
k = 0.1
cf = 0.15, k = 0.1
0
60.5
60
59.5
59
58.5
58 0
10
1
10
Quality Factor, Qf
10
2
Figure 4 Dependence of non-detection zone on cfo.
where k is calculated from (6) to guarantee negligible NDZ.
By eliminating cfo, the effect of the SFS on power quality
would be reduced [1].
The proposed islanding detection method was tested on the
system shown in Fig. 1 and using the control circuit in Fig. 2.
An islanding condition is simulated by opening the utility
breaker at t = 3 seconds. Figure 5 show the frequency
waveforms obtained using time domain simulations in the
PSCAD/EMTDC environment for the various Qf values with
loads that resonate at 60 Hz and k set to 0.15. It can be seen
that for loads with Qf values less than 7, the island frequency
becomes unstable. The frequency drifts more slowly as Qf
approaches 7, while timely detection (within 2 seconds) is
possible for loads with Qf values that are less than
approximately 6.5.
IV. CONCLUSIONS
0
0.05
0.1
0.15
58.5
Load Resonant Frequency,f0
k>
2[Q f ( f o / f 2 + 1 / f o )]
k=
k=
k=
k=
61.5
61
60.8
60.6
Q = 7.5 and Q =12.4
f
60.4
f
Q =7
Frequency (Hz)
f
60.2
60
59.8
Q = 5.3
f
Q = 3.5
Q = 6.5
f
f
59.6
59.4
Qf = 1.77
59.2
59
2
2.5
3
3.5
4
Time (s)
4.5
5
5.5
6
Figure 5 Frequency waveform for different load Qf with k set to 0.15.
V. REFERENCES
[1]
[2]
[3]
M. Ropp, and W. Bower, "Evaluation of islanding detection methods for
photovoltaic utility interactive power systems," International Energy
Agency Implementing agreement on Photovoltaic Power Systems, Tech.
Rep. IEA PVPS T5-09, March 2002.
Lopes, L. A. C. and Sun, H. (2006). Performance assessment of active
frequency drifting islanding detection methods. Energy Conversion,
IEEE Transaction on, 21(1):171-180.
X. Wang, W. Freitas, W. Xu, and V. Dinavahi, “Impact of DG Interface
Controls on the Sandia Frequency Shift Antiislanding Method”, IEEE
Trans. Energy Conversion, vol. 22, pp. 792-794, Sept. 2007.