The Effect of the Ring Mains Units for On-line Partial Discharge Location with Time Reversal in Medium Voltage Networks

The performance of a new on-line partial discharge (PD) location method based on the Electromagnetic Time Reversal (EMTR) theory and the Transmission Line Matrix (TLM) method are investigated for characterization of Medium-Voltage (MV) networks. The distortion of the PD signal during its propagation along a cable connection including network components modelled based on experimental data is reproduced in simulation and the effectiveness of the EMTR-based method to localize the PD source is analyzed. In particular, the effects of the ring main units (RMUs), that behave as a complex impedance, the variation with frequency of the MV cable impedance and the reflection patterns, due to impedance mismatches, are considered and investigated. Simulation results are given showing the performance of the EMTR method in two different networks configurations: the former one with a RMU at the end of a MV cable and the latter one with a second MV cable connected to the RMU of the first configuration having a distribution transformer at its far end. The results show that the EMTR method is able, with only a single observation point, to localize PDs also in the presence of RMU with a relative error, with respect to the line length, of approximately 1%.


I. INTRODUCTION
Partial discharge (PD) events, that are localized electrical discharges starting in discontinuities or defects of the insulation system [1], are often the cause of the power cables insulation degradation in power networks [2]- [3]. The failure of power cables' insulation in power networks leads to severe social and economic consequences producing effects ranging from faults to blackouts and supply interruption. Because statistic indicates that more than 85% of equipment faults are linked to insulation failure [4], PD is widely considered as one of the best 'early warning' indicators of cable failure [2] and, the adoption of on-line PD location is regarded as the most suitable method to monitor the network integrity and improve its resilience and reliability [2]. The on-line PD location methods is, indeed, a desired feature in the protection schemes of the modern power networks to prevent faults and guarantee the electricity security [5]. Currently, the on-line PD location is performed mostly using methods based on reflectometry or traveling wave techniques [6]- [11]. These techniques work on the fact that a PD event produces electromagnetic waves that travel towards the cable ends. Most of the used methods are based on multi-end measurements [6]- [7], simultaneously in two or more observation points (Ops) of the line, of the direct PD wave, coming directly from the PD source, and the reflected waves from the cable ends. The PD source is located evaluating the times of arrival of the measured signals (time of arrival, (ToA), methods). But the need for synchronization makes their practical implementation more costly as communication provisions between the detection ends are required. Furthermore, the accuracy of the reflectometry methods is affected by the distortion of PD signal during its propagation along the line and by the presence of electromagnetic interference (EMI) on power networks [12]. Signal distortions are caused by the impedance mismatches and the variation with the frequency of the impedances of cables and components [13]. Wavelet techniques (WTs) [14]- [15], that are powerful signal processing tools that can be implemented in both time and frequency domains, are often used to solve some of the shortcomings of the classical reflectometry methods, but WTs require a huge amount of computational effort.
A new method for the on-line PD location has been proposed [16]- [19] based on the use of the EMTR (Electromagnetic Time Reversal) theory and the Transmission Line Matrix (TLM) method to describe the EMTR propagation of the PD signals. EMTR theory [20] has been adopted, recently, for the localization of electromagnetic disturbance sources on power systems [21]- [22], showing improved performances with respect to the traditional location techniques, due to the fact that it is possible to apply them in inhomogeneous and complex networks, they need only one observation point to localize the source and are robust against the presence of noise. In [16] the basic design of the new EMTR-based PD location method has been proposed and its effectiveness to locate PDs using only one observation point has been theoretically demonstrated. In [17] its experimental validation is given, showing its effectiveness to locate PDs in real Medium Voltage (MV) homogeneous power cables, and its robustness against the presence of noise has been also analyzed and proved. The EMTR-based PD location method has also been shown to allow a PD location with good accuracy without excessive constraints on the input parameters, requiring only the knowledge of the signal velocity and the cable lengths. Moreover, in [18]- [19] the effectiveness of the method has been verified in simulation also when the PD signal is distorted due to the presence of line impedance mismatches caused by the presence of inhomogeneous cable sections. This paper investigates the effectiveness of EMTR when the waveform is distorted from PD signal attenuation and dispersion during propagation along a transmission line. Power cables on MV grids terminate at ring main units (RMUs) and further distortion occurs, caused by the impedance mismatches due to their presence. The distribution transformer at the RMU together with the cable connecting the transformer to the busbar behaves as a complex impedance. This is a cause of distortion of the PD signal and, consequently, the signal transfer to the measurement sensor is imprecisely known. In addition, other outgoing MV cables may affect the reflection patterns further distorting the PD signal [23]- [24]. In this work the effect of these distortions on the performance of the EMTR PD location method are analysed in two different line configurations. The used models have been developed using experimental measurements [23]- [24] in order to simulate a PD signal distortion close to the real one and to test the effectiveness of the EMTR method in working conditions close to the real behaviour. The paper is organised as follows. In Section II, the EMTRbased method is briefly introduced. Section III the distortion of the PD signal due to the grid components, complex impedance of cables and of RMUs, is described and the adopted models to reproduce it are detailed. In Section IV the performance of the EMTR method is discussed in the two considered line configurations.

II. TIME REVERSAL METHOD FOR PD LOCALIZATION
The PD location method based on EMTR theory is based on the invariance under time reversal of the Telegrapher's Equations for non-dissipative lines [20]. For non-dissipative lines, the telegrapher's equations are given by: where L and C are the per unit length series inductance and shunt capacitance of the line. The propagation speed, u, and a characteristic impedance, Zc, of the line are given by: Applying the time-reversal transformation, equations (1) become: The designed EMTR PD location method uses the Transmission Line Matrix (TLM) numerical method [25] to solve the equations (3) describing the time reversal propagation of the PD signals. In particular, the EMTR simulations are performed using a 1D lossless TLM model of the system under study. The TLM method is a time-domain differential-equation-based method, that discretizes the transmission line, of length L, into a series of N segments, of length Δx, connected as shown in Fig. 1 (a). Each LC section is represented by a transmission line of impedance Zc, given by relation (2), and characterized by a transit time Δt given by: Connecting the N sections, the TLM equivalent model of the line is obtained, as shown in Fig. 1 (b). At each node, the voltage pulses, Vn(k), are scattered as they propagate in the lines, generating incident voltages, VL i n(k) and VR i n(k), and reflected voltages, VL r n(k) and VR r n(k), respectively on the left and on the right-hand side of the node. Replacing the lines to the right and to the left of the node n by their Thevenin equivalent circuits, and applying Millman's theorem, the voltage Vn(k), and the current In(k), at time step k, are evaluated for each node of the network [25]. The basic steps of the EMTR method to locate PDs [16] are shown in Fig. 2 and are the following: 1. Measurement of the PD signal, s(x,t), at one observation point (OP) along the network. 2. Time reversal the measured PD signal.

Definition of guessed PD locations (GPDLs) in nodes
of the 1D TLM model of the network. 4. Simulation of the back-injection of the time-reversed PD signal for different GPDLs. 5. Location of the PD source by finding the GPDL characterized by the maximum energy. For each TR simulation a GPDL is defined in a node of the line where the PD source is guessed to be. The impedance of the GPDL node reproduces the line transversal impedance modified by the presence of a PD event. This is realized by modifying the transversal capacitance of the GPDL node representing the capacitance in the cable insulator modified by the PD event. In [16] a detailed description of the GPDL model in a TLM model is presented. For each TR simulation the energy, En, stored in the transversal impedance of the GPDL is evaluated, normalized with respect to the maximum energy as follows: where _ ( ) is the maximum voltage over all the GPDLs and M the number of the samples.
When the method is used in practice, the first step of the procedure, is carried out experimentally [17]. In this work, the first step is substituted by a direct time (DT) simulation, using a lossy model of the system under study that is able to reproduce the PD signal distortion during propagation in real grids, as described in the Section III.

III. SIGNAL DISTORTION BY GRID COMPONENTS
In the following subsections, the models of each component of the grid that affects the PD signal propagation, distorting the signal, are described. Then, the related reflection patterns are also analysed. It will be assumed that the initial PD pulse duration is short in terms of the bandwidth restrictions of sensors commonly applied in PD diagnostic techniques. The signal distortion by the network together with the detection bandwidth determine the measured PD signal shape.

A. CABLE MODEL
The propagation coefficient of an XLPE cable is modelled by numerically evaluating the harmonic cable impedance Z(ω) and admittance Y(ω) with electromagnetic simulation software (Oersted and Electro from IES [26]). The applied cable geometry and material properties are provided in Table I. The characteristic impedance Zc and the propagation coefficient γ are obtained from:   = � ⁄ and = + j = √ The characteristic impedance, the phase velocity u=ω/β and the per-unit-length attenuation α are shown in Fig. 3 The reflection pattern from a pulse starting from one side in a single cable segment can be modelled by the transfer function: The numerator accounts for the signal propagation up and down the cable with length L1, the reflection coefficient ρ1(ω) at the far end and the transmission coefficient τobs(ω) from the detection impedance at the observation point. The denominator accounts for multiple reflections, which involves, besides ρ1(ω), the reflection coefficient ρobs(ω) at the observation point. It will be assumed that the initial pulse is narrow, meaning that after travelling some distance along the cable its waveform is fully determined by the cable propagation coefficient γ1(ω). Then, the initial pulse can be approximated as a Dirac pulse and the transfer function H(ω) directly represents the reflection pattern in the frequency domain.
The reflection pattern depends on the transition between the cable characteristic impedance Zc1 and the impedance seen at the far end. This can, e.g., be a lumped impedance or the input impedance Zin of a connected cable (length L2, propagation coefficient γ2(ω) and characteristic impedance Zc2): The reflection coefficient ρ2(ω) depends on the load at the end of the second cable. Further cable cascading can be accomplished by substituting the reflection coefficient at the next cable segment here.

B. RMU MODEL
Small RMUs are usually only a few meters in size containing one or a few medium-voltage cables connected to a busbar and a distribution transformer that feeds a local low-voltage grid. A lumped component model is proposed in [23] aiming to describe the influence of an RMU on partial discharge propagation, see Fig. 4. The values of the model parameters were determined by injecting a pulse at the far end of one of the cables and measuring the responses at several locations inside the RMU [24]. The RMU model is subdivided in compartments, each containing a single network component. The cables in compartments 1 and 2 are each modelled with its characteristic impedance and inductances related to loops from the connection to the busbar: -Zc: The characteristic impedance determined by the cable model.  -Ctr, Ltr, Rtr: The transformer behaves mainly capacitively for the main frequency components present in partial discharge signals. It is modelled as a capacitance in series with the inductance and resistance. -Ctcc, Ltcc, Rtcc: The transformer is connected to the busbar through power cables. These cables provide a capacitive load and are modelled together with inductance and resistance. -The connection to the busbar is modelled with Lc and Lbb. Table II provides the parameters for the modelled RMU, which are taken from [23]. They are an average of the values obtained from tests at six RMUs. These parameters are based on best fitting over a frequency range from 200 kHz up to 5 MHz. This frequency range is most relevant for signal propagation along medium-voltage cables ranging from hundreds of meters up to several kilometers. From this model, the impedance of the load at a cable end can be determined. Considering the cable in compartment 1 as the cable to be diagnosed, it is loaded via the impedance from Lc and Lbb to the branches that represent the cable in compartment 2 and the parallel branches of the transformer and its connection in compartment 3. When the RMU is situated at the end of a medium-voltage connection, it is only loaded with the transformer and the contribution of the cable in compartment 2 can be removed. The impedance as seen from the diagnosed cable is shown for both cases in Fig. 5. The inductances, related to the loops formed by the busbar connection, together with the capacitances from the transformer and connecting cables cause resonances in the low megahertz range. These resonances distort the signal waveforms from partial discharge signals as they occur at relevant frequencies for signal propagation along power cables. At lower frequencies either the capacitances dominate the impedance (blue curve) or the characteristic impedance of the second cable (red curve).
Beyond the resonances, the substation impedance increases due to the inductances. Modelling of the reflection pattern from an RMU at the cable termination is accomplished by using the RMU impedance in the calculation of the far end reflection coefficient. When there is a second cable connected that also adds reflections from its far end, it can be modelled using its input impedance Zin rather than its characteristic impedance Zc2 in the scheme of Fig. 4. The parameters in the RMU model were determined accounting for frequencies up to about 5 MHz [24]. For higher frequencies, connection details become important, which are specific for each RMU. In practice for power cable diagnostics, these frequencies hardly contribute due to signal attenuation and the generic model of Fig. 4 provides a representative picture of the influence of RMUs on partial discharge waveforms.

C. REFLECTION PATTERNS
The signal distortion by an RMU can be illustrated by injecting a signal at one end of the cable and simulating its reflections when the cable is terminated by an RMU. For illustration purposes, the near end is terminated with a real valued detection impedance making τobs and ρobs real as well. The applied initial signal is a Dirac pulse and the detection is bandwidth limited (50 kHz -5 MHz). For the two cases, shown in Fig. 6, the reflections due to the RMU impedance are depicted in Fig. 7. The two cases are described in the following:   -CASE 1: The cable length is 1000 m and the RMU only consists of the distribution transformer (blue curve). The pattern shows periodic recurring reflections. The inset shows the peak distortion by the complex RMU impedance. For later reflections, the cable propagation characteristics quench the higher frequencies. For the remaining frequency range, the impedance is high, and the far end reflection coefficient approaches one. This results in less distorted peaks, which broaden and attenuate further because of the cable characteristics. -CASE 2: A second cable is connected to the RMU at the far end with 800 m length having a distribution transformer at its far end (red curve). Cables and distribution transformers are modelled with the parameters in Tables I and II. The first reflection at the RMU is only easily observable for the first reflection. Multiple reflections disappear since for the relatively low remaining frequencies the impedance from the second cable dominates, which closely terminates the first cable characteristically. The far end reflections from the second cable remain contributing since this cable is connected to a transformer only, which behaves like an open circuit for low frequencies. Partial discharges which arise at some position X cause waves running in both directions. The total reflection pattern can be modelled from the sum of the contributing transfer functions: ( ) e − 1 ( ) + 1 ( )e − 1 ( )(2 1 − ) 1 − 1 ( ) ( )e −2 1 ( ) 1 (9)

IV. TIME REVERSAL PD LOCATION FROM SIMULATION
Application of PD locating techniques should not rely on detailed information that is hard to obtain in practice. The analysis can usually be based on general data from the cable specification (such as cable impedance and signal propagation velocity) and on the cable connection topology (such as cable lengths and RMU configuration). Therefore, for pinpointing the PD location, simplified models of the network components need to be adopted and the effectiveness of the methodology must be verified. For application of EMTR, a lossless 1D TLM model of the line has been developed for each case under analysis to perform the time reversal simulations for the PD location, as described in Section II. To define the characteristic of the 1D TLM model of the line the following considerations have been made. When PD signal propagates over distances of 1-2 km, most of the remaining energy is in the frequency range up to 1 MHz or few MHz [19], decreasing further for longer distances. Then, the PD signal, measured at the OP and used to perform the EMTR simulations, is characterised by a frequency content up to a few megahertz. At these low frequencies, the inductances, and capacitances in RMU/substation can be neglected compared with the characteristic impedance of the cable Zc, and the equivalent circuit of the RMU/substation can be approximated by the parallel connections of the characteristic impedances of the N-connected MV cables [23]. With this approximation, in the frequency range of interest, the input impedance of the RMU/substation, seen by the PD signal, ZRMU, and the reflection coefficient at the RMU input, ГRMU, can be evaluated as follows [19]: Hence, for the cases under analysis shown in Fig. 6, in the 1D TLM model the input impedance of the RMU at the line termination, ZRMU_T, is ZRMU_T >> Zc, then the reflection coefficient is equal to ГRMU_T = 1. While when the RMU is in the middle of the line, it has been modelled with a TLM model 3 m long with a characteristic impedance, ZRMU_L, chosen equal to ZRMU = 2·Zc, so with a relative reflection coefficient equal to ГRMU_L = 0.5. This is because, the RMU only causes a distortion mainly for high frequencies. It becomes invisible when the wavelengths associated with the remaining frequencies after signal attenuations are clearly exceeding the RMU size. A similar distortion occurs when modelling the RMU as a short transmission line (TL) with different characteristics. To illustrate this, two cables (1000 m and 800 m) are connected via a short cable length of 3 m with a characteristic impedance double that of the cable. The far end is kept open, and a signal is injected at the observation point.
As shown in Fig. 8, a somewhat less oscillatory response but still quite similar with decaying peaks as in Fig 7 ( For the two analyzed cases the following results have been obtained: -CASE 1: Fig. 9 shows, for example, the collected PD signal at the OP and the time reversed signal when the PD source is 280 m from the OP. In Fig. 10-11 the simulation results, showing the performance of the of the EMTRbased PD location method are shown for cable lengths of respectively 1 km and 2 km. -CASE 2: Fig. 12 shows the collected and time reversed PD signal when the PD source is at 300 m from the OP. The EMTR results are shown in Fig.13 The cable lengths are 1 km and 0.8 km. Figs 9 and 12 show the distortion of the PD signals due to the impedance mismatches of the lines caused by the presence of the RMUs and by the variation with frequency of the impedance of each component of the system. Figures 10-11 and 13 show that the method is able to localize the PD source despite the distortion of the PD signal and the reflections at the impedance's mismatches. Moreover, Fig. 13 shows that also despite the signal distortion from the RMU between the two cable segments, the PD location can be retrieved accurately, independently of whether the PD originates from the 1 km or the 0.8 km cable segment. The accuracy of the localization is summarized in Table III.  Table III summarizes the results for four PD positions (source) together with the located positions (EMTR) and the relative error. The relative error in the localization, evaluated with respect to the line length, is generally below 1%, which is an acceptable error in practical applications. The error increases a little, but remains always ≤ 1.5%, at the terminations in CASE 1 with the line length L=1 km. To locate the PD source, a first scan of the system has been carried out choosing GPDLs 8 m apart from each other. After that, a refined search has been performed, reducing the distance between the GPDLs to 1 m only in the section of the line where the maximum concentration of the energy associated to the time reversed signals propagation has been detected during the first scan. A computational time of about 30 s is necessary for the line 1km long and of about 50 s for the line 2 km long, using a using a 64-bit pc with an Intel® Core™ i7-8700K, CPU at 3.70GHz, 32GB RAM and 1TB disk.

V. CONCLUSION
The performance of the EMTR-based method to locate PD with the presence of ring main units (RMUs) on the grid has been analysed in simulation. A description of the EMTRbased method is given and the models used to simulate the grids components, RMU and power cable, useful to reproduce the PD signal distortion are described. The effectiveness of the EMTR method to localize the PD source has been analyzed in two different configurations: 1). a homogeneous line, both 1 km and 2 km long, with one RMU at the far end and 2). Two cable section with an RMU in between and an RMU at the far end of the second cable section. The simulation results show that the EMTR method is able to localize PDs with a computational time less than a minute. For online monitoring, if this duration would be critical, the technique can be applied when pre-localization, e.g. by threshold discrimination, shows that certain PDs are concentrated or arise near a critical location. More accurate pinpointing of the defect can then be achieved with EMTR. The relative error, with respect to the total cable length, usually is below 1%, except when the PDs arise close to the cable terminations, where the error increases but never exceeded 1.5%. With respect to the big challenge of the EMI on power networks, the authors in a work of under publication, show that noise can be tackled effectively by the EMTR method, allowing the PD localization with errors less than 1% and, in [16], the authors have already shown theoretically that the proposed technique works with an SNR of -7dB using injected white noise.