Tracking algorithm for the gain of the phase modulator in closed-l oop optical
voltage sensors
Li Hui, Bi Lan
n
, Li Lijing, Hu Shuling, Feng Xiujuan, Zhang Chunxi
Science and Technology on Inertial Laboratory, School of Instrumentation Science and Opto-electronics Engineering, Beihang University, XueYuan Road No. 37, HaiDian District,
Beijing 100191, China
article info
Article history:
Received 4 May 2012
Received in revised form
25 July 2012
Accepted 24 August 2012
Available online 12 October 2012
Keywords:
Optical voltage sensor
Temperature fluctuation
Phase modulator
abstract
The accuracy and scale factor of the optical voltage sen sor are considerably affected by the gain drift of
the phase modulator induced by temperature fluctuation. In this paper, we present a tracking system
for the gain drift of the phase modulator based on four-state modulation which provides a significant
improvement in the performance of the optical voltage sensor. We analyze the influence of the main
closed-loop error of optical voltage sensor on the tracking system. The analysis results indicate that the
main closed-loop error causes uncertain parameter and external disturbance for the tracking system.
Then the model of the tracking system for the gain of the phase modulator is transformed into a
dynamic system with uncertainty and stochastic disturbance by substitution of variable. The tracking
system is accurately designed considering the main closed-loop error. To insure the tracking system
achieves good transient performance, the closed-loop poles of the tracking system are constrained to
locate in a desired circular region, while the gain error is mean-square exponentially stable via the
robust control. The experiments show that the tracking system realizes precise compensation for the
gain drift of the phase modulator.
& 2012 Elsevier Ltd. All rights reserved.
1. Introduction
Optical voltage sensors (OVSs) have been widely applied to
electrical power transmission and distribution systems with its
high accuracy, wide dynamic range, immunity to electro-magnetic
interference and inherent safety [1–3]. These advantages offer an
attractive alternative to conventional voltage sensors in high-
voltage transmission networks [4]. In recent decades, considerable
research efforts have been focused on the OVS based on Pockels
effect, because it is a precise and reliable method of voltage sensing
with wideband frequency response [5,6]. Although commercial
voltage sensors based on Pockels effect have been emerged, there
are still some problems in practice [7], especially the effect of the
temperature on the sensor. OVSs based on Pockels effect demand
an open optics approach with lenses and polarizing filters due to
the utilizing of bulk Pockels crystals, so they are vulnerable to
signal intensity fluctuations as well as environmental distortions,
e.g., temperature change and vibration [1]. Lee has developed a
compensation method to eliminate the effect of birefringence
induced by environmental perturbations to improve the stability
of the sensor [8]. This scheme has been successfully applied to the
OVS based on Pockels effect, but the method makes the fabrication
complicated [9,10]. The automatic temperature control system and
high precision driven circuit have been adapted to light source of
the OVS to improve the stability of light power and center
wavelength [11,12]. However, the light power fluctuation and
wavelength drift have not been thoroughly eliminated by this way.
Recently, the closed-loop signal processing technology adopted
from fiber gyroscope has been employed to OVSs to overcome these
limit at ion s [13–16]. Zhang et al. proposes a quasi-reciprocal reflec-
tive optical circuit for OVS based on closed-loop signal processing
[16]. The reciprocal configuration makes the sensor largely reject to
environmental perturbation. Meanwhile, the closed-loop signal
processing improves the dynamic range of the OVS and its immunity
to the fluctuation of light intensity. However, the gain of the phase
modulator is subjected to temperature fluctuation, which directly
affects the scale factor stability and linearity of the OVS. So it is of
great significance to compensate the gain drift of the phase
modulator induced by temperature fluctuation.
To solve this problem, the sensor based on a double feedback
loop technique with square wave biasing modulation is proposed,
where the main closed-loop is utilized to obtain the applied
voltage and the second closed-loop is introduced to control the
voltage reset of the feedback ramp so that the gain drift of the
phase modulator is compensated [17]. But this method is less
efficient at low input voltage due to the long reset time. To avoid
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Optics & Laser Technology
0030-3992/$ - see front matter & 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.optlastec.2012.08.027
n
Corresponding author. Tel.: þ 8 6 010 82316547 816; fax: þ86 010 82316547 855.
E-mail address: bilan0508@yahoo.com.cn (B. Lan).
Optics & Laser Technology 47 (2013) 214–220