Smart grids

3rd Renewable Power Generation Conference (RPG™)
24 - 25 September 2014 - Ramada Naples, Naples, Italy
A Nonlinear and Non-Stationary Signal Analysis for
Accurate Power Quality Monitoring in Smart Grids
Silvano Vergura*, Giulio Siracusano+, Mario Carpentieri*,
Giovanni Finocchio+
*Technical University of Bari
+University of Messina
Italy
DIPARTIMENTO DI
ELETTROTECNICA
ED ELETTRONICA

A Nonlinear and Non-Stationary Signal
Analysis for Accurate Power Quality
Monitoring in Smart Grids
Silvano Vergura Ramada Naples, 25/09/2014
silvano.vergura@poliba.it
 Analysis of the power disturbances in an active line, i.e. line which can
either absorb either feed the active power.
 Use of Wavelet Transform (WT)
 Use of Hilbert-Huang Transform (HHT)
 Application to two different scenarios: line fed by large PV plants
(power indicated as PPV) and line with no PV generators (power
indicated as P ).
AIMS
DIPARTIMENTO DI
ELETTROTECNICA
ED ELETTRONICA

ISSUES
DIPARTIMENTO DI
ELETTROTECNICA
ED ELETTRONICA
 Non-uniform spatial distribution of the electrical power gives rise to
multi-modes and intermittent non-stationary solicitations.
 For SGs with high penetration of DGs, a significant amount of
conventional generation is replaced with distributed PV resources with
the result of the lack of reactive power and reduced system inertia.
 Unexpected fluctuations introduce anomalies: short circuit manifests
itself as a high-frequency component, whereas a load variation gives
rise to a low-frequency component.

Comparison of signal processing techniques
DIPARTIMENTO DI
ELETTROTECNICA
ED ELETTRONICA
Fourier STFT HHT
Basis A priori A priori Adaptive
Frequency
Convolution:
global,
uncertainty
Convolution:
regional,
uncertainty
Differentiation:
local, certainty
Presentation
Energy-frequency
Energy-time-frequency
Energy-time-frequency
Nonlinear No No Yes
Nonstationary No Yes Yes
Feature Extraction No Yes Yes
Theoretical Base
Theory
complete
Theory complete Empirical

PROPOSED APPROACH
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1. WT and HHT have been utilized for the detection of non-stationary
behaviour and recognition of anomaly patterns,
specifically on negative active power conditions.
2. WT identifies the time evolution of the modes of the electrical
power.
3. Computations based on HHT is able to separate the time domain
traces related to the harmonics and the steady states.
4. Finally, they allow to detect and locate the irregular operating
conditions.

WAVELET TRANSFORM
DIPARTIMENTO DI
ELETTROTECNICA
ED ELETTRONICA
For a time-domain signal x(t), the continuous wavelet transform is a linear function
given by:
with s and u the scale and translation parameters of the mother wavelet ψ(t) :
We have used the complex Morlet wavelet mother (with fB=30 and fC=1 ):
    * 1
,
t u
W u s x t dt
s s



  
  
  
2
2 /
,
1 C B
t u t u
j f f
s s
u s
B
e e
s f



     
   
    
  ,
1
u s
t u
t
s s
 
  
  
 

HILBERT-HUANG TRANSFORM 1/2
DIPARTIMENTO DI
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ED ELETTRONICA
By HHT, complex sets of nonlinear and non-stationary data can be decomposed into a
finite collection of Intrinsic Mode Functions (IMF), through the Empirical Mode
Decomposition (EMD). The IMFs have well-defined instantaneous frequencies and
represent the intrinsic oscillatory modes embedded in the original signal.
HHT consists of two parts: Hilbert Transform (HT) and EMD.
Given a time-domain function x(t), its HT (with P the Cauchy principal value):
The HT computes the instantaneous power and frequency of a mono-component signal.
A generalization to a multi-component signal is possible by using the EMD method,
applied to decompose non-linear and non-stationary signals.
 
P x s
y t ds
 t s



 

HILBERT-HUANG TRANSFORM 2/2
DIPARTIMENTO DI
ELETTROTECNICA
ED ELETTRONICA
It extracts a series of IMFs from the analyzed signal by means of an iterative process
which is known as sifting and consists in three steps:
1. starting from the original signal x(t), set , extract the local minima and
local maxima from ;
2. interpolate the local minima and local maxima with a cubic spline to form upper and
lower envelopes, respectively;
3. obtain the mean of the upper and lower envelopes and subtract it from to
determine a new ProtoMode Function (PMF)
The above procedure is repeated until satisfies the ending criteria: the number
of maxima and minima and the number of zero-crossings differs only by one and the
local average is zero.
hi t   x t 
  i h t
  i h t
      i 1 i h t h t m t   
  i 1 h t 

DESCRIPTION OF THE SYSTEM UNDER TEST
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 Several passive and active lines located near Bari (Italy).
 Lines feed both residential and commercial users.
 Each line absorbs a peak mean power in the range [50÷350] kW over a length
which varies from 248 to 472 meters.
 We have chosen two power lines: a passive one with a peak power of about 50 kW
and an active one of about 70 kW of absorbed power.
 Power measurements have a sampling period of 10 minutes and have been
captured between September 2013 and February 2014 for a total of 154 days
with 144 samples per day (154x144=22176 events recorded).
 The passive line has no PV plants, whereas the active line has 18 grid-connected
PV plants with a total rated peak power of about 108 kW

NUMERICAL RESULTS 1/3
DIPARTIMENTO DI
ELETTROTECNICA
ED ELETTRONICA
Mean active power signal: line with no DGs (solid red
line) and line fed by large PV plants (solid black line).
P1 is the main mode of the power dynamics of the
two lines; the amplitude of PPV(t) is double with
respect to the P(t) signal.
P2 mode is associated with the alternation between
daytime and can explain its larger amplitude if
compared with no PV line.
P3 mode is mainly related to seasonal events that
cause a change of the energy demands and load
curves of both power lines. P3 mode is substantially
invariant for the two signals of interest.
fP1=11.4μHz≈24h-1 fP2=23.3μHz≈12h-1
fP3=34.7μHz≈8h-1

DIPARTIMENTO DI
ELETTROTECNICA
ED ELETTRONICA
Time-frequency representation for P(t) (a) and
PPV(t) (b) aims us to better evaluate the intermittent
behaviour of the P2 mode.
In (b) we observe a telegraphic signal appearing
and disappearing which suggests an irregular active
power absorption due to the PV power
We performed the HHT on the signal PPV(t) to
extract the independent oscillations and to
investigate the P2 mode deeply. Once extracted by
means of HHT [24], we applied the previous Morlet
wavelet and computed the Wavelet scalogram to
evaluate the dynamics.

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This figure provides evidence of highly non-stationary
behaviour of the P2 mode, as extracted
from the signal PPV(t). Note the strong temporal
coherence between the occurrence of events
wherein no power has been measured (solid white
stars in the upper part of the Fig.) which follows
the nearest local maxima of the P2 mode. This
indicates a possible relationship between the most
of the unexpected faults in the line and the
nonlinear amplitude of this disturbance.

 A combined Wavelet and HHT-based analysis is proposed, which demonstrates
to be a valuable framework to investigate the impact of DG penetration on the
power quality in SGs.
 Both steady state and dynamic behaviour of distribution lines with and without
PV plants contribution are studied and compared to identify the effects of PV
systems on the power line.
 The results of steady state analysis reveal that increasing the amount of power
due to the DGs leads to larger fluctuations of the active power.
 The procedure has shown the ability to study non-stationary power system
waveforms and non-linear dynamical signals.
Conclusions
DIPARTIMENTO DI
ELETTROTECNICA
ED ELETTRONICA

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