Harmonic Source Identification in Distribution System ...

Disclaimer: This is the preprint version of the accepted paper in Transactions of the Institute of Measurement and Control. Permission should be obtained for using any part/whole of the document from the publisher or the author. This work can be cited as: Preeti Jain, Atul Kumar Tiwari, Sachin Kumar Jain “Harmonic source identification in distribution system using estimation of signal parameters via rotational invariance technique-total harmonic power method” Transactions of the Institute of Measurement and Control. DOI: 10.1177/0142331217721316

Harmonic Source Identification in Distribution System using ESPRITTHP Method Abstract: With proliferation of power electronics devices in the distribution system, harmonic distortion has become one of the major power quality (PQ) problems. In evolving liberalized electricity market, it becomes necessary to develop suitable methods to allocate the responsibilities for the harmonic distortion to improve the PQ. This paper presents a new technique for harmonic source identification, which is based on total harmonic power (THP) method using estimation of signal parameters via rotational invariance technique (ESPRIT). Traditionally, harmonic powers for THP method is computed using Fourier transform, which inherits serious drawbacks of the discrete and fast Fourier transform, viz. inaccuracy due to poor spectral resolution, spectral leakage, etc. Simulation results have been presented for different distribution system configurations and conditions, which confirms the improved capabilities of the proposed method in harmonic source identification. Index Terms—Harmonic distortion, Power system, Fourier transform, Power quality, Signal processing.

1. Introduction Power quality (PQ) is one of the primary concerns for electric utility companies in the emerging competitive electric market. With the increased development of semiconductor technology, harmonic distortion has turned to a grave concern for power entities and many research works have been published for monitoring of harmonics (Jain & Singh, 2011), (Jain & Singh, 2013), (Jain, 2015). Power system distribution and transmission utilities need to limit the voltage and current harmonics to predefined threshold values as per prevailing national and international standards (Anon., 1993). In the distribution system, power is supplied by a bus in which various linear and nonlinear loads are connected. Current harmonics are generated by the nonlinear load, but the voltage is a function of current and impedance which results in harmonics in linear loads. Harmonics may be present in both linear and nonlinear loads, but the source of the harmonics is a nonlinear load only. In this situation, it is necessary to identify the source of harmonics to develop penalty based tariff scheme, and to design mitigation equipment and proper placement of these types of mitigation equipment. With distorted supply voltage, the customers without any harmonic sources may be billed for additional energy due to harmonic losses. Harmonic state estimation based technique (Heydt, 1989) was proposed to identify the harmonic sources in the network by estimating energy injection in the system at harmonic frequencies. However, this requires installation of a large number of measuring devices for distributed synchronous measurement, hence, it is not cost effective. The attempts have been made (D'Antona, et al., 2009), (D'Antona, et al., 2011) to use a priori knowledge or pseudo-measurements to minimize the requirement of number of measurements, however, single point measurement-based techniques are gaining popularity due to simplicity, better reliability, easy installation, and less maintenance cost (E. J. Davis & Pileggi, 2000). The direction of harmonic power flow is applied in (Saxena, et al., 2014) to rank the nodes in the system to suspicious and non-suspicious nodes. However, this method also requires availability of harmonic voltage phasor measurements for all the nodes in the system. There are various methods based on single point measurement (Cristaldi & Ferrero, 1995), (Tanaka & Akagi, 1995), (Aiello, et al., 2005), (Omran, et al., 2009), (Thunberg & Soder, 1999), (Xu, et al., 2003), (Barbaro, et al., 2007), (Sinha, et al., 2016) for harmonic source identification. The earlier concept in this category is direction of harmonic power, which states that if a polluted load is present at any node in the system, the direction

of harmonic active power will be from load to the node (Cristaldi & Ferrero, 1995), (Tanaka & Akagi, 1995). The efficacy and consistency of the harmonic power direction concept was challenged in (Emanuel, 1995) and (Xu, et al., 2003), however, it has been then demonstrated and proved by Omran et al. (Omran, et al., 2009) that this concept is well applicable for both radial and nonradial systems with good reliability. A wavelet decomposition based algorithm (Sinha, et al., 2016) uses detail reactive power at the first level to extracting its characterizing harmonics, which in turn identifies the harmonic sources. Need of different sampling frequency for different harmonic level is a serious limitation of this algorithm. The method proposed in (Thunberg & Soder, 1999) used Norton’s equivalent circuit representation of the source and utility and then applied superposition theory for each harmonic component. It requires calculation of Norton’s equivalent circuit for each harmonic order which is very tough and tedious process. Other work based on superposition theorem is reported in (Xu, et al., 2003), in which quantitative harmonic contribution indices are computed to identify the harmonic sources in the system. However, it was shown in (Omran, et al., 2009) that the sign of the harmonic current contribution represents only a part of the mathematical solution and need not lead accurate identification of the harmonic source. There are methods based on non-active power proposed to detect the dominant harmonic source, upstream or downstream to the metering section (Barbaro, et al., 2007). Due to lack of generally acceptable definition of non-active power, this method is still debatable. An observer based algorithm is presented in (Ujile & Ding, 2016), which carry out harmonic estimation for a combination of suspicious nodes, hence it is suitable only for systems with small number of suspicious sources. This algorithm requires prior knowledge of fundamental frequency. The direction of active harmonic power has immerged as the promising solution for harmonic source detection in both radial and nonradial distribution system. There are various methods for calculating harmonic power, like, frequency-domain and time-domain methods. Time domain methods (Tanaka & Akagi, 1995), (Aiello, et al., 2005), (Omran, et al., 2009) use Clark & Park transformation, PLL (Phase locked loop) and orthogonal auxiliary sinusoidal signals for computing active harmonic powers. The first two are only applicable to three phase systems and may have higher inaccuracies due to low pass filter and PLL, while the third one requires precise knowledge of the harmonic frequencies in order to compute harmonic power, which is not possible with pure timedomain approach. A method which uses fast Fourier transform (FFT) is presented in (George & Bones, 1991), but it has many limitations inherited from the FFT, viz. poor frequency resolution, the requirement of a typical number of samples, and spectral leakage. These shortcomings of the FFT with practical signals lead to inaccurate phase angle estimation, which results in false identification of the harmonic sources due to errors in harmonic power calculation. Active and reactive harmonic power flow direction based another algorithm is presented in (Dixit & Kaur, 2016), however, it requires phasor value of harmonic voltages at all buses in the network, which requires harmonic PMUs (Jain, et al., 2017) installation at the selected optimal buses. As the accurate estimation of the amplitudes and phases of all the present harmonic components is the key to calculate the harmonic power, an improved harmonic power algorithm based on high resolution exact model orderestimation of signal parameter via rotational invariance techniques (EMO-ESPRIT) (Jain & Singh, 2012) has been proposed in this paper for identification of harmonic sources. The proposed frequency-domain approach can be applied to both single phase and three phase systems, radial and nonradial systems, synchronously and asynchronously sampled signals, with sufficient accuracy and reliability. This paper is organized as follows: Section 2 and 3 briefly reviews the basic concept of harmonic power concept and EMO-ESPRIT method, respectively. The proposed method is explained in Section 4 and its performance investigation using simulation results is presented in Section 5, followed by concluding remarks in Section 6.

2. The Concept of Active Harmonic Power (AHP) The concept of active harmonic power for harmonic source identification is based on the elementary fundamental network approach, according to which, if a harmonics producing load is connected to a node, it delivers a harmonic current into the node, and hence, the active power associated with each current harmonic component always flows towards the node. Thus, the direction of total active power of the harmonic components

can designate the source of the harmonic power. Usually, a load consumes fundamental power, therefore, harmonic power directions are referred to as the direction of fundamental power. In general, a negative value of harmonic power indicates presence of harmonic producing loads. The basics of total harmonic power (THP) method are demonstrated by considering a simple two node circuit as shown in Fig. 1, where a nonlinear load is connected to a sinusoidal voltage source via distribution line having an impedance Z. The nonlinear load connected to node Q (designated as the point of common coupling (PCC)) injects current harmonics and distorts the voltage at the PCC. The harmonic active power coming from the load will be dissipated in the system impedance Z and will have the direction opposite to that of the fundamental power that is supplied by the utility source. However, if the utility supply is distorted, it will feed the power loss in different parts of the system at the harmonic frequencies presents in it, even if the load is purely linear in nature. In case load is also nonlinear, respective harmonic active powers will have positive and negative directions, and the dominant source of that particular harmonic order will decide the direction of power at the PCC, and will indicate the presence of harmonic source. To further illustrate the concept let us consider the Fourier series representation of the distorted voltage and current signals at the PCC, which can be expressed as:

Utility supply

Z

P

PFundamental PHarmonics

Q PCC

Non-linear load

Fig. 1. A circuit with nonlinear load connected to sinusoidal voltage source

𝑣𝑄 (𝑡) = 𝑉𝑄𝑜 + ∑∞ ℎ=1 √2 𝑉𝑄ℎ sin(2𝜋ℎ𝑓𝑡 + 𝜃𝑄ℎ𝑉 )

(1)

𝑖𝑄 (𝑡) = 𝐼𝑄𝑜 + ∑∞ ℎ=1 √2 𝐼𝑄ℎ sin(2𝜋ℎ𝑓𝑡 + 𝜃𝑄ℎ𝐼 )

(2)

where 𝑣𝑄 (𝑡) and 𝑖𝑄 (𝑡) are instantaneous value of voltage and current, respectively, at node Q, 𝑉𝑄𝑜 and 𝐼𝑄𝑜 denote average (dc component) value of voltage and current respectively, h represents harmonic order, 𝑓 represents fundamental frequency in Hz, 𝑉𝑄ℎ and 𝐼𝐵ℎ represent root mean square (rms) values of voltage and current, respectively, at hth harmonic frequency, and 𝜃𝑄ℎ𝑉 and 𝜃𝑄ℎ𝐼 represent phase angles of voltage and current at a harmonic frequency of order h with respect to an absolute reference. Average value of the active power at node Q can be given as 1

𝑇

𝑃𝑄 = 𝑇 ∫0 𝑝𝑄 (𝑡) 𝑑𝑡 ,

(3)

where T is the fundamental time period of the supply and 𝑝𝑄 (𝑡) is the instantaneous power at node Q, computed by multiplying (1) and (2). Subsequently, the average value of the power can be rewritten as 𝑃𝑄 = 𝑉𝑄𝑜 𝐼𝑄𝑜 + 𝑉𝑄1 𝐼𝑄1 cos 𝜙𝑄1 + ∑∞ ℎ=2 𝑉𝑄ℎ 𝐼𝑄ℎ cos 𝜙𝑄ℎ

(4)

where 𝜙𝑄ℎ = 𝜃𝑄ℎ𝑉 − 𝜃𝑄ℎ𝐼 is the phase difference between voltage and current phasors, 𝑉𝑄ℎ and 𝐼𝐵ℎ . The average power at node Q can be expressed as the sum of power caused by average components of voltage and current PQo, power due to fundamental components PQ1, and power caused by harmonics present in the voltage and current signals, which is termed as the total harmonic power (THP). 𝑃𝑄 = 𝑃𝑄𝑜 + 𝑃𝑄1 + 𝑃𝑄𝐻 .

(5)

In Fig. 1 fundamental power is supplied by the sinusoidal supply voltage connected at node P and has the direction from left to right, as indicated in Fig.1. Nonlinear load connected at node Q injects current harmonics in the circuit, which flows in the circuit and cause power loss in different components. This active power is derived from the total active power consumed by the load and converted to harmonic power. Hence, harmonic power flows from load to the supply, as indicated in the Fig.1. As suggested in (Tanaka & Akagi, 1995), the direction of flow of THP at a particular node determines the harmonic polluting load. The sign of harmonic power at a node in a radial system and sign of harmonic power injected at a bus in case of nonradial system can be used to identify the source of harmonic pollution (Omran, et al., 2009) present in the system. The guidelines for harmonic source identification using the direction of harmonic power flow for radial and nonradial system are presented below. 2.1. For radial system If the fundamental power delivered by supply voltage is considered as positive active power, then the sign of THP can be used as follows for the localization of nonlinear loads in a radial distribution system. i. Positive harmonic power at a node indicates that the source of harmonic pollution is located upstream to the node, and the harmonic power is received from the supply side. ii. If the harmonic powers are negative at a given node, then the source of harmonic pollution is localized downstream to the node, and the harmonic power is received from the load side. 2.2. For nonradial system In nonradial systems, the active power can flow in either direction in the mesh network and there is no clear meaning of upstream or downstream points with respect to any node. Therefore, the sign of injected fundamental active power to the bus under consideration is taken as the reference (Omran, et al., 2009), and sign of the THP determines location of the harmonic source based on following rule: i. Positive harmonic power injection to a bus indicates that the bus is supplying the harmonics to the system. ii. Negative harmonic power injection to the bus under consideration implies that the bus is receiving harmonics from the system and load connected at this bus is being contaminated by the system.

3. EMO-ESPRIT Algorithm (Jain & Singh, 2012) EMO-ESPRIT (Jain & Singh, 2012) is an ESPRIT-based harmonics estimation technique. It provides number of harmonics present in the signal, respective frequencies of the harmonics, and their corresponding amplitudes and phase angles. This parametric method requires relatively lower computational resources and provides faster estimates than a conventional ESPRIT and other parametric methods. Sensitivity of the harmonic estimation can be selected using a sensitivity parameter as defined in (Jain & Singh, 2012). Let us consider that x is the measured signal. This signal can be modelled as a summation of sinusoidal components in addition with Gaussian noise w(n). Accordingly, at the nth sample with the sampling time period Ts, the measured signal can be represented as: 𝑥(𝑛) = ∑𝐾 𝑘=1 𝑎𝑘 cos(2𝜋𝑓𝑘 𝑛𝑇𝑠 + 𝜙𝑘 ) + 𝑤(𝑛)

(6)

where K is the model order (representing the total number of harmonic components present in the signal), 𝑎𝑘 , 𝜙𝑘 and fk are the amplitude, initial phase angle, and frequency of the kth harmonic component, respectively. The values of unknown parameters in the above signal model (6) can be found from the N sampled data sequence of the signal using the EMO-ESPRIT algorithm, which is described briefly as follows: i. Construct the Hankel matrix having order M with the total N data samples of a signal x(n). ii. Find out autocorrelation matrix, carry out eigenvalue decomposition on the autocorrelation matrix, and arrange eigenvalues in descending order. iii. Apply model order algorithm as proposed in (Jain & Singh, 2012).

iv. v. vi. vii.

Segregate the noise subspace and the signal subspace from the autocorrelation matrix. Use suitable selection matrices to get two shifted sub matrices from the signal subspace. Relate shifted sub matrices with the application of shift invariance property. Obtain the frequency components of the signal from above relationship using least squares estimation and its eigenvalues (Jain & Singh, 2012). viii. Obtain the complex amplitudes of the frequency components by solving 2K simultaneous equations for 2K different values of n (Please refer (Jain & Singh, 2012) for detailed description).

4. EMO-ESPRIT-based Harmonic Source Identification It has been found that in most of the practical cases, the amount of harmonic power is very small as compared to the fundamental active power. This is due to one or more of the following reasons: 1. The phase angle between harmonic voltage and current is close to 90o because of inductive type network. 2.

The voltage distortions may not be significant at the node as compared to the distorted current injection due to high capacity of the node (i.e. the system is more robust).

3. The distorted current injection is low as compared to the total load capacity of the system. Therefore, it is utmost important to have precise computation of the harmonic powers for accurate identification of the harmonic sources using the harmonic power flow direction method. There are more chances of inaccuracies with the Fourier transform based method due to its inherent limitations, especially with fundamental frequency deviation and asynchronous sampling. The time-domain based methods reported in the literature use band elimination filters (Tanaka & Akagi, 1995), transformations (Aiello, et al., 2005) and some auxiliary signals (Omran, et al., 2009) for computing harmonic power. These not only have limitations on dynamic response and implementation for real-time applications but also, their performance is greatly influenced by the environmental parameters, such as, operating frequency, order of harmonic, presence of interharmonics, etc. Further, transformation based methods are applicable only for three-phase systems, and it is difficult to implement auxiliary signal based method without prior knowledge of harmonic orders present in the signal. Accurate estimation of harmonic order, their amplitudes and phases is the key to successful implementation of harmonic power direction method. In this section, a model-based parametric technique has been used to compute harmonic power that provides better resolution without any constraint on practical aspects, such as, fundamental frequency deviation, noise, etc. or requirement of typical number of samples. The model-based parametric techniques (Lobos, et al., 2006), (Bracale, et al., 2008), (Chang & Chen, 2010), (Jain, et al., 2013) do not require the knowledge of fundamental frequency, and hence the proposed method provides accurate harmonic power calculation as compared to existing methods. Model order i.e. number of frequencies present in the signal, is a critical parameter in model-based harmonic estimation approaches. The model order affects the estimation accuracy and computational efficiency. Therefore, EMO-ESPRIT-based harmonic source identification algorithm, proposed in (Jain & Singh, 2012), has been used in this work for harmonic power estimation, which provides a reliable and accurate computation of harmonics with reasonable computational complexity. The measured voltage and current signal at a node are sampled with a sampling frequency of at least two times of the maximum harmonic frequency taken under consideration, as suggested by Nyquist sampling theorem. If the measured voltage and current signals at node Q, sampled with a sampling time period Ts, are modelled using the signal model (6), these quantities 𝑣𝑄 (𝑛) and 𝑖𝑄 (𝑛) then can be expressed as 𝑣𝑄 (𝑛) = ∑𝐾 𝑘=0 𝑉𝑄𝑘 cos(2𝜋𝑓𝑘 𝑛𝑇𝑠 + 𝜙𝑉𝑘 ) + 𝑤(𝑛)

(7)

𝑖𝑄 (𝑛) = ∑𝐾 𝑘=0 𝐼𝑄𝑘 cos(2𝜋𝑓𝑘 𝑛𝑇𝑠 + 𝜙𝐼𝑘 ) + 𝑤(𝑛)

(8)

where 𝑉𝑄𝑘 and 𝐼𝑄𝑘 are the voltage and current amplitudes, respectively, of kth frequency component, 𝜙𝑉𝑘 and 𝜙𝐼𝑘 are the phase shifts of the voltage and current of kth frequency component with respect to the reference. The EMO-ESPRIT algorithm is then applied to the sampled voltage and current signals to estimate the voltage and

current. Once the voltage and current amplitudes at different harmonic frequencies are known, the active harmonic power of the kth harmonic order at node Q can be expressed as 𝑃𝑄𝑘 =

𝑉𝑄𝑘 𝐼𝑄𝑘 2

(9)

cos 𝜃𝑘

where 𝜃𝑘 = 𝜙𝑉𝑘 − 𝜙𝐼𝑘 is the phase angle difference between kth harmonic voltage and current phasors 𝑉𝑄𝑘 and 𝐼𝑄𝑘 . The sign of individual harmonic active power can be used to locate harmonic sources for particular harmonic order, whereas, the sign of total harmonic power can be used to get an inclusive idea of presence of harmonic polluting source in the system, irrespective of its order. The total harmonic power PQH can be computed by aggregating all harmonic powers as, 𝑃𝑄𝐻 = ∑𝐾 𝑘=2

𝑉𝑄𝑘 𝐼𝑄𝑘 2

(10)

cos 𝜃𝑘

The power due to dc component of voltage and current, and the fundamental power have been excluded from the total harmonic power. The harmonic power computation is highly sensitive to the phase angle, and harmonic powers are usually small, hence, errors in the direction of individual harmonic power flow may result is incorrect sign of total harmonic power leading to false identification of harmonic sources. The proposed ESPRIT-THP method assures of better results because of well-known high-resolution method for harmonics estimation in practical circumstances. Key steps of the proposed ESPRIT-THP method for harmonic source identification process are summarized in the flow chart shown in Fig. 2. Start Measurement and acquisition of voltage and current signals Apply EMO-ESPRIT Algorithm K, fk, Øk, ak Compute harmonic power using (9) or (10)

Positive

Check the sign of harmonic power at a node ?

-Source of harmonic pollution is upstream to the node (for radial network) -This node has a source of harmonic (for nonradial network)

Negative

-Source of harmonic pollution is downstream to the node (for radial network) -Network is polluting this node (for nonradial network)

Fig. 2. Flow chart of the proposed ESPRIT-THP algorithm for harmonic source identification

5. Simulation results and discussion Various circuit configurations are taken for both radial and nonradial systems to illustrate the effectiveness of the proposed harmonic source identification algorithm. The results obtained by the proposed ESPRIT-THP algorithm are also compared with the results obtained by FFT and time domain algorithm (Omran, et al., 2009) to validate performance of the proposed algorithm as accurate harmonic source identifier. The MATLAB R2014a 32 bit (win32)/Simulink simulation package has been used on Intel (R) Core(TM) i-7 processor at 3.40GHz, with 2GB RAM, 32-bit Windows-7 Professional platform for simulation study. Continuous time voltage and current signals are sampled with a sampling frequency of 1024 Hz. The maximum harmonic component taken under consideration is of the order of five i.e. 250/300 Hz for all cases. 5.1. Radial system: Two different cases for radial system have been considered with different loads in each case. In the first case, one of the loads is linear and the other is nonlinear, whereas, in the second case, both loads are nonlinear type. For the first case, the results of the proposed algorithm and other similar works have been compared with respect to the true value to establish the effectiveness of the proposed method. The true values have been computed analytically using the fundamental network theory and are then verified using simulation tools (MATLAB/ Simulink) under idealized conditions of no fundamental frequency deviation, no noise, number of samples in accordance with the power of two and no time-variation in the signal parameters. It has been found that analytical results have matched reasonably close to the above simulation results. Case 1: In this case, two loads are connected to a 100 V, 50 Hz sinusoidal supply as shown in Fig. 3. The supply has an internal impedance of ZS=1+j6.28 Ω. The value of the line impedance is Zl=2+j12.56 Ω. The nonlinear load is modelled using an AC voltage regulator with two antiparallel SCRs feeding a load impedance of Z1=150+j78.5Ω. Firing angle of AC voltage regulator is taken as 120o. The linear load is connected at node Q with an impedance value of Z2 = 100 + j62.8Ω at the supply frequency. P

Zl

Zl Q

R

ZS AC Supply

Load 1

Load 2

Fig. 3. Radial network having linear and nonlinear loads.

The harmonic powers obtained by different approaches are tabulated in Table 1. Fundamental power is positive in all cases indicating supply source to be upstream of all the nodes, which is correct. Similarly, total harmonic power PH and individual harmonic powers at node P and R are negative, and are positive at node Q, which suggests that harmonic polluting load is downstream to node P and R, and upstream with respect to node Q that suggests the harmonic polluting load is connected at node R. Further, it can be observed that although all the methods give correct identification of the harmonic source, the computed harmonic powers from the proposed ESPRIT-THP algorithm are relatively closer to the true values as compared to the FFT and time-domain based algorithms.

Table 1. Harmonic powers for the system shown in Fig. 3 True Values*

Power (W) Node P

Node Q

Frequency-domain algorithm (FFT) Node R

Node P

Node Q

Node R

Time domain algorithm Proposed in (Omran, et al., 2009) Node P

Node Q

Node R

THP via EMO ESPRIT algorithm Node P

Node Q

Node R

P

61.28

54.28

5.455

61.28

54.28

5.455

61.28

54.28

5.455

61.28

54.28

5.455

P1

61.8103

54.2024

5.6977

60.87

53.9

5.423

61.2652

54.2722

5.4514

61.7954

54.2105

5.7355

P3

-0.0168

0.0482

-0.1721

-0.0081

0.0401

-0.0736

-0.0057

0.0409

-0.0759

-0.0158

0.0471

-0.1663

P5

-0.0005

0.0008

-0.0023

-0.0002

0.0003

-0.0056

-0.0006

0.0003

-0.0007

0

0

-0.0009

-0.0174

0.0494

-0.1757

-0.0081

0.0420

-0.0758

-0.0062

0.0439

-0.0817

-0.0158

0.0471

-0.1673

PH

* The true values have been found using analytical analysis of the circuit and are verified with FFT in idealized operating conditions.

Case 2: In this case, two nonlinear loads of same order are connected to the supply at two different nodes Q and R. Load 1 is an AC voltage regulator connected to an inductive load with an impedance of Z= 150+j78.5 Ω and Load 2 is a phase controlled bridge rectifier connected to a load having an impedance of Z=100+j62.8 Ω, with reference to Fig. 3. The firing angles of Thyristors of AC voltage regulator and bridge rectifier are kept as 120o and 70o, respectively. The computed harmonic powers at node P, Q, and R using different methods have been presented in Table 2. It can be observed from the results that sign of individual harmonic powers computed from the FFT and timedomain methods are not consistent and indicate presence of only one harmonic source based on the total harmonic power, whereas, the proposed method clearly indicates the presence of harmonic sources downstream to all the nodes, i.e. at both the load nodes. This case clearly distinguishes the performance of the proposed algorithm as compared to the existing methods. Table 2. Harmonic powers for the system shown in Fig. 3 having two nonlinear loads P (W)

P P1 P3 P5 PH

Frequency-domain algorithm (FFT) Node P 37.77 37.44 -0.0245 -0.0032 -0.0276

Node Q 5.256 5.196 0.3215 -0.0401 0.2820

Node R 31.03 30.74 -0.3825 0.0282 -0.3564

Time domain algorithm Proposed in (Omran, et al., 2009) Node P Node Q Node R 37.77 5.256 31.03 37.6446 5.22547 30.954 -0.0176 0.3462 -0.4103 -0.0026 -0.0471 0.0338 -0.0231 0.3012 -0.3879

THP via EMO ESPRIT algorithm Node P 37.77 38.9809 -0.4310 -0.1274 -0.5184

Node Q 5.256 5.3696 -0.1003 -0.0499 -0.1318

Node R 31.03 31.3411 -0.3735 -0.0934 -0.4612

5.2. Nonradial system A four bus ring main system has been taken as an example of nonradial system for the study of harmonic source identification. It has a 100V, 50Hz ideal voltage supply connected to bus 1 as shown in Fig. 4. A phase controlled bridge rectifier is connected to bus 2 as Load2. Another phase controlled rectifier is connected to bus 1 as Load1. A linear inductive load with an impedance of Z=150+j78.5Ω is connected at bus 3 as Load3. To consider more comprehensive and realistic representation, a half wave diode rectifier is also connected as Load4 on bus 4, which generates even harmonics. The value of load impedances of Load 1, Load 2 and Load 3 are Z1= 120+j36.1 Ω, Z2=100+j62.8 Ω and Z3=75+j47 Ω respectively. A harmonic filter tuned to the third harmonic is placed parallel to the load 2, as shown in Fig. 4. The value of line impedance is Zl=2+j12.56 Ω, which is identical for all the lines. The firing angles of thyristors of Load1 and Load2 are taken as 120o and 70o respectively. Fundamental and harmonic power injections at all the buses have been calculated by the proposed algorithm as shown in Table 3.

Bus 1

Zl

Bus 2

Filter

AC Supply Load 2

ZS Zl Load 1 Zl

Zl Zl

Bus 3

Bus 4 Load 4

Load 3

Fig. 4. Nonradial distribution system with a filter across load 2.

By observing the powers presented in Table 3 following conclusions can be drawn: i. Fundamental power and third harmonic power injected at bus 1 are positive. It indicates that third harmonic is injected by load connected at bus 1. The sign of even harmonic powers are negative. It implies that the system is responsible for even harmonics pollution at bus 1, not the load 1. ii. The fundamental power and third harmonic power injected at bus 2 are negative. It indicates that the system is responsible for even harmonics pollution at bus 2. iii. The fundamental power and all harmonic powers are negative at bus 3. It indicates that this bus is receiving harmonics from the system, which is consistent with the linear load connected at bus 3. iv. Bus 4 has a half wave diode rectifier, and the results confirm this by providing positive harmonic power values for even harmonics. The fundamental and odd harmonic powers are negative at bus 4, which indicates that this bus is acting as a load bus for fundamental and odd harmonics and as a source for even harmonics. The signs of harmonic powers obtained by proposed EMO-ESPRIT-based algorithm are in accordance with the loads considered in the study. The proposed method provides accurate identification results for even and odd both types of harmonic sources in nonradial system also. Table 3. Harmonic powers for system presented in Fig. 4 P (W) P P0 P1 P2 P3 P4 P5 PH

THP via EMO-ESPRIT algorithm Bus 1 Bus 2 Bus 3 Bus 4 116.78 -37.29 -39.74 -38.13 -0.4431 -0.0061 -0.0072 1.009 116.8023 -37.554 -39.748 -38.1353 -0.0082 0 -0.0215 0.0485 0.1035 -0.0073 -0.0209 -0.0642 0 0 0 0 0 -0.0025 0 0 0.0953 -0.0098 -0.0424 -0.0157

5.3. The IEEE 13 node distribution system To consider a more realistic case, standard IEEE 13 bus distribution system (Abu-Hashim, et al., 1999), approved by the IEEE PES Distribution System Analysis Subcommittee for harmonic studies, has been taken for

performance investigation of the proposed algorithm. This small and relatively highly loaded test network operates at 4.16kV with unbalanced loading. It has overhead and underground lines, shunt capacitors, and an in-line transformer. Fig. 5 shows the single line diagram of the system under consideration, and the detailed parameters/data of the network can be referred from (Abu-Hashim, et al., 1999). This benchmark test network has been implemented on MATLAB/Simulink software platform using the network configuration and assumptions as considered in (Barbaro, et al., 2007). This test network considers three types of load, namely, fluorescent light, adjustable speed drives and composite residential loads. Nonlinear loads have been modelled as current sources and are connected at the nodes 611 and 675, where the load at node 611 is a phase-phase single phase load. For the sake of simplicity and clarity in presentation, only total powers of three phases at different nodes have been reported in the Table 4. 650 646

645

611

684

652

632

671

633

692

634

675

680

Fig. 5. IEEE 13 Node Distribution Test Feeder (Abu-Hashim, et al., 1999).

The network is a radial type distribution feeder and the sign of the harmonic powers at different nodes for this test case indicates following: i. The sign of harmonic powers are negative at nodes 650, 632 and 671, which implies that the harmonic sources are downstream to these nodes. ii. Positive harmonic powers at nodes 646 and 633 suggest that harmonic sources are upstream to these nodes, i.e. harmonic sources are not present at these nodes. iii. The harmonic power at node 652 is positive while it is negative at node 692. This indicates that harmonic source is not present at 652, but it exists downstream of the node 692. iv. Negative harmonic power at the far end nodes 611 and 675 clearly confirms the presence of harmonic sources at both of these nodes. Table 4. Harmonic powers for the IEEE 13 Bus system P (kW)

Node 650

Node 632

Node 646

Node 633

Node 671

Node 652

Node 611

Node 692

Node 675

P

1998.4

1958.3

116.26#

74.218

1767.1

98.612#

130.05$

674.249

149.83

P1

1998.4

1958.3

116.26

74.218

1767.1

98.612

130.05

674.249

149.83

P3

0

0

0.0011

0

0

0.0217

-0.0672

0

0

P5

-0.0013

-0.0107

0.0008

0.0003

-0.726

0.0183

-0.0493

-0.6508

-1.0071

PH

-0.0013

-0.0108

0.0020

0.0003

-0.729

0.0460

-0.1311

-0.6510

-1.0120

#: Single phase load, $: single phase load connected across two phases

6. Conclusion This paper presents a harmonic source identification technique based on for both radial and nonradial type distribution systems. The calculation of harmonic power is sensitive to the phase angle and harmonic amplitudes. In most of the practical applications, the harmonic power magnitude is very small as compared to the fundamental power, therefore, even small errors in harmonic estimation may result in incorrect sign of total harmonic power, which seriously affects the correct decision-making in harmonic source identification. The proposed ESPRIT-THP method computes harmonic estimates very accurately using high-resolution EMO-ESPRIT algorithm, hence it provides more accurate calculation of harmonic powers and thus helps in reliable identification of harmonic sources. The simulation results on three different test networks, including a benchmark IEEE 13 bus feeder, confirm that the harmonic powers calculated by the proposed method are more accurate as compared to the FFT and time domain algorithm. The proposed method is robust against the inaccuracies due to fundamental frequency deviation, measurement noise, and spectral leakage. It can be applied on both single-phase and three-phase networks, balanced or unbalanced systems, radial and nonradial type of distribution system with good accuracy and reliability. Further research is required for improving the identification accuracy in certain cases where two or more than two identical harmonic sources of same order are connected in the system.

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