FIELD

[0001] A method of detecting a power line fault in a multi-phase power distribution system and a power line monitoring system and sensor for use in the system.

BACKGROUND

[0002] It is desirable to detect and respond to power line faults in an electrical power distribution system in a timely manner. If left unresolved, a fault can result in damage to equipment and potentially injuries or even deaths of persons in the vicinity. Faults can be classified as symmetric or asymmetric. Symmetric faults include 3 phase faults and 3 phase-to-earth faults. Typically, symmetric faults represent the most severe power system failures but are comparatively rare. Asymmetric faults include phase-to-phase faults, phase-to-earth faults, and double phase-to-earth faults. These faults are more common than symmetric faults but are less severe. Single phase-to-earth faults, in particular, represent the majority of transmission line faults.

[0003] The design of power system protection involves implementing systems to detect and mitigate power system faults. Accurate detection of a fault is the first and often the most critical step. Once a fault has been detected and its location ascertained, the standard response is to simply operate circuit breakers to isolate the hazardous condition.

[0004] Conventional high-voltage protection solutions tend to react to high fault currents. These solutions generally cannot detect an open circuit high-voltage fault caused by a downed load side conductor being in contact with the ground, as in this kind of fault the faulty line may be back-fed through the high magnetising impedance of the downstream distribution transformers. This may lead to very low fault currents that are hard to measure, even with highly sensitive equipment. SUMMARY

[0005] In a first aspect of the invention, there is provided a method of detecting a high-voltage power line fault in a three-phase power supply system, comprising acquiring voltage data from the low-voltage side of a three-phase distribution transformer; processing the voltage data to determine a voltage imbalance metric and determine a plurality of inter-phase voltage angles; and detecting a power line fault based upon the processed voltage data.

[0006] In a second aspect of the invention, there is provided a power line monitoring system for monitoring downstream power supply lines to detect upstream faults comprising a power distribution system including three-phase power supply lines from an upstream station to a downstream substation; a controller for controlling power supply from the upstream station; a remote low power line voltage line sensor configured to monitor voltages on the high-voltage power lines and detect an upstream power line conductor down fault based on the monitored voltages; and a communication circuit configured to communicate the power line down fault to the controller so that the controller may disconnect power supply to the power lines.

[0007] In a third aspect of the invention, there is provided a remote power line voltage line sensor comprising a sensing circuit for sensing voltages present on the low-voltage side of a three-phase distribution transformer; a signal processor for determining an upstream high-voltage power line conductor down fault condition based on the sensed voltages; and a communication circuit for communicating the fault condition to an upstream controller.

BRIEF DESCRIPTION

[0008] The description is given by way of example with reference to the drawings which show certain examples. However, these drawings are provided for illustration only, and do not exhaustively set out all embodiments. [0009] Figure 1 shows a system for monitoring power lines in a three-phase power distribution system.

[0010] Figure 2 shows a method for detecting a fault in a three-phase power distribution system.

[0011] Figure 3a shows a method for obtaining, evaluating, and selecting a predictor model.

[0012] Figure 3b shows an example confusion matrix.

[0013] Figure 4 shows a power distribution network monitored by a power line monitoring system, wherein the power distribution network is operating normally.

[0014] Figure 5a shows a power distribution network monitored by a power line monitoring system, wherein a source-side downed conductor fault has occurred.

[0015] Figure 5b shows the source-side downed conductor fault of Figure 5a.

[0016] Figure 6a shows a power distribution network monitored by a power line monitoring system, wherein a load-side downed conductor fault has occurred.

[0017] Figure 6b shows the load-side downed conductor fault of Figure 6a.

[0018] Figure 7 shows an example classification tree predictor model.

[0019] Figure 8a shows the test results for a classification tree predictor model in a confusion matrix.

[0020] Figure 8b shows the test results for a random forest predictor model in a confusion matrix.

[0021] Figure 8c shows the test results for a neural network predictor model in a confusion matrix.

SUBSTITUTE SHEETS (RULE 26) DETAILED DESCRIPTION

System

[0022] Figure 1 shows an exemplary system which may be used to implement the aspects of the invention noted above.

[0023] The system 100 is a three-phase power distribution system (network) with power line monitoring and can comprise a remote power line voltage line sensor 102 and an upstream controller 190. The remote power line voltage line sensor 102 can be installed, as a single physical unit, in the three-phase power distribution network at a distribution transformer. In one example, the remote power line voltage line sensor 102 is installed on the low voltage (LV) side of the distribution transformer. For a typical power system in New Zealand, distribution line voltages (high voltages) are either 11 kV or 22 kV and the consumer voltage (low voltage) supplied to most consumers is 230 V Phase to Neutral (400V Phase to Phase). The remote power line voltage line sensor 102 can comprise a measurement module 104, a processor 106, and a communications module 108.

[0024] The measurement module 104 can include a sensing circuit configured to measure and record, substantially in real-time, a number of electrical quantities associated with any one or more of the power lines in the three-phase power distribution network, which can include at least the voltage magnitude and the voltage phase. For a 400 V distribution scheme operating under normal conditions, the line voltages measured will typically be three voltage phasors having equal magnitude of about 230 V evenly displaced by 120 degrees in phase. The measured data can be stored locally at the remote power line voltage line sensor 102.

[0025] The measurement module 104 can additionally include filtering for removing noise in the electrical data measured by the sensing circuit. Having clean measurements will improve the accuracy of results obtained from downstream processes. Conversely, any noise present in the measured data may propagate and deteriorate the quality of the end results. The filtering can comprise multiple stages, implemented as any combination of analogue filtering and digital filtering. The measured data can be filtered before it is stored locally at the remote power line voltage line sensor 102.

[0026] Some processing of the measured and recorded electrical data can occur at the processor 106. This processing can include calculating metrics indicative of the state of operation of the power distribution network. The processing can further include fault detection based on a trained model. The output of the fault detection can be a fault signal, which can include information on one or more of the location of the fault, the time at which the fault occurred, the type of fault, and instructions for how to respond to the fault. More explanation on these processing tasks will be provided hereinafter.

[0027] Additionally, the fault signal can undergo further processing including one or more of fragmentation, compression, encryption, error correction and/or detection encoding at the processor 106. Subsequently, the fault signal can be provided to the communications module 108 for transmission.

[0028] By way of non-limiting examples, the processor 106 can comprise one or more of: a field programmable gate array (FPGA), an application-specific integrated circuit (ASIC), a digital signal processor (DSP), a general purpose computer, or a microcontroller or microprocessor including a central processing unit (CPU). Although not explicitly shown, the processor 106 can include a clock or another means (software or hardware) for tracking real time.

[0029] The communications module 108 can include the necessary software and hardware configured to accommodate at least transmission and optionally reception of data in accordance with a number of communication technologies and/or protocols, including but not limited to the LoRaWAN protocol. In one example, the communications module 108 enables a communications link 110 between the remote power line voltage line sensor 102 and an upstream controller 190. The characteristics of the communications link 110 e.g. whether it is simplex, half duplex, or full duplex, will depend upon the particular protocol employed.

[0030] The communications link 100 can be wired or wireless. In wired embodiments, the communications module 108 comprises hardware and software configured to interface with a suitable physical medium between the remote power line voltage line sensor 102 and the upstream controller 190. In wireless embodiments, the communications module 108 comprises a wireless transmitter and optionally a wireless receiver. In one wireless embodiment, the wireless transmitter is a LoraWAN transmitter.

[0031] Data transmission can occur both periodically and spontaneously. For instance, the communications module 108 can be configured to periodically transmit to the upstream controller 190 the state of operation of the subnetwork corresponding to the particular remote power line voltage line sensor 102. In another instance, the communications module 108 can report, in substantially real-time, to the upstream controller 190 the occurrence of a spontaneous event, such as a detected electrical fault in the subnetwork corresponding to the remote power line voltage line sensor 102.

[0032] To ensure the overall power line monitoring system can respond to spontaneous events in substantially real-time, the total delay imposed by the measurement module 104, the processor 106, and the transmission module 108 may need to satisfy a predetermined constraint. For example, substantially realtime may mean that the total delay between the occurrence of a fault and when the fault signal is received at the upstream controller 190 does not exceed a short period such as three seconds.

[0033] The upstream controller 190 can be configured to communicate with and process information (e.g. a fault signal) received from one or more remote power line voltage line sensors. In this way, the upstream controller 190 can oversee one or more subnetworks corresponding to the one or more remote power line voltage line sensors. Such an arrangement can be configured as an Internet of Things (IOT) network, with each remote power line voltage line sensor being a 'smart' IOT device. The location of each remote power line voltage line sensor in the distribution network can be known to the upstream controller. Each remote power line voltage line sensor can also be aware of its location and the location of any other remote power line voltage line sensor in the network.

[0034] In embodiments where the upstream controller 190 handles multiple remote power line voltage line sensors, the communication and processing tasks can be carried out sequentially as managed by a suitable task scheduler. Additionally or alternatively, some of the tasks can be carried out in parallel.

[0035] In one example, the upstream controller 190 comprises a SCADA (Supervisory Control and Data Acquisition) controller. In an alternative example, the upstream controller comprises a ADMS (Advanced Distribution Management System) controller.

Fault Detection

[0036] At step 202 of the method 200 shown in Figure 2, a processor accesses the measured electrical quantities including at least voltage magnitude data and voltage phase data for each of the three phases. The processor can be the processor 106 of a remote power line voltage line sensor 102. The electrical quantities may have been measured by a sensing circuit in a measurement module 104 of the remote power line voltage line sensor 102.

[0037] A first voltage metric indicative of the relative phase displacements of the three voltage phasors is determined at step 204. Under normal operation, the three phases are spaced substantially evenly apart in a full cycle: phase A is at 0 degrees (the reference), phase B lags byl20 degrees, and phase C is at about 240 degrees (or leads by 120 degrees). Disruptions such as a broken conductor fault can disturb the 120-degree interphase angles, thereby creating a voltage imbalance condition in the three-phase system. [0038] In one example, the three interphase angles are calculated from the three line to ground voltage phasors V _an , V _bn , and V _cn as follows: θ _ab =arg (V _bn ) -arg ( V _an ) θ _bc =arg (V _cn ) -arg (V _bn ) θ _ca ==arg ( V _an ) -arg (V _C J

[0039] The processor can determine both the minimum interphase angle and the maximum interphase angle based on the values θ _ab , θ _bc , and θ _ca - Collectively, the two interphase angles can be regarded as the first voltage metric. This can be regarded as the primary (most significant) voltage metric relative to other voltage metrics described below.

[0040] A second voltage metric can optionally be determined at step 206. The second voltage metric is indicative of the degree of voltage imbalance across the three phases A, B, and C. Under normal operation, the three phases should all have a magnitude of approximately 230 V, which is the nominal single-phase line to neutral voltage in a standard New Zealand mains system. Disruptions such as a broken conductor fault can substantially disturb the voltage balance, thereby creating a voltage imbalance condition in the three-phase system.

[0041] In one example, the second voltage metric is calculated in accordance with the Institute of Electrical and Electronic Engineers (IEEE) definition, also known as the line voltage unbalance rate (PVUR), given by Only voltage magnitudes are considered in this definition; phase information is disregarded.

[0042] The voltage imbalance figure can be regarded as a secondary metric relative to the first voltage metric. In one embodiment, this means that where it is not feasible or not optimal to calculate both the interphase angles and the voltage imbalance, calculation of the interphase angles will take priority.

[0043] A tertiary voltage metric can optionally be determined at step 208. The tertiary voltage metric gives further indication of the degree of voltage imbalance. An unbalanced three phase voltage condition is decomposed into a linear combination of its symmetrical components: the positive sequence components, the negative sequence components, and the zero sequence components. The tertiary voltage metric can be calculated as the ratio of the magnitude of the negative sequence voltages to the magnitude of the positive sequence voltages.

[0044] At least one voltage metric is provided to a predictor model as input. Preferably, this is the primary voltage metric. The secondary voltage metric and the tertiary voltage metric can be provided as additional inputs depending upon the particular prediction model selected and/or the configuration thereof. At step 210, the predictor model determines based on the voltage metric or metrics whether a fault has occurred. The predictor model can further classify the fault (if any) into a particular fault type. Step 210 is performed at a processor, which can be processor 106 of a remote power line voltage line sensor 102. More description for the predictor model is provided hereinafter.

[0045] Step 212 occurs if a fault has been detected at step 210. The fault is then reported to an upstream controller overseeing the section of the distribution system where the fault has allegedly occurred. This can be achieved by the communication module 108 of a remote power line voltage line sensor 102 transmitting a fault signal to an upstream controller 190. In one embodiment, the transmission is wireless and uses the LoRaWAN protocol. The upstream controller can then respond to the reported fault accordingly e.g. by operating a circuit breaker to isolate the fault.

[0046] Should the predictor model determine that no fault has occurred and the distribution network is operating normally, this current iteration of power line monitoring may be regarded as having been completed. The next iteration will occur at a later time using fresh data.

Predictor Model

Obtaining a Predictor Model

[0047] One or more of the voltage metrics described above can be used in the method 300 shown in Figure 3a to yield a predictor model capable of reliably detecting faults in a real-world application according to method 200.

[0048] At step 302, a predictor model is obtained through clustering. Cluster analysis or clustering is a data science method used for identifying data points with similar attributes within a larger dataset and grouping these similar data points as a cluster. Each cluster corresponds to a unique state of operation of the distribution network, thereby differentiating a cluster from another cluster. For example, cluster A might correspond to normal operating conditions, while cluster B corresponds to a source-side downed conductor fault (e.g. that shown in Figures 5 a and 5b) and cluster C a load-side downed conductor fault (e.g. that shown in Figures 6a and 6b). In this way, a predictor model can be obtained from cluster analysis which can be used to differentiate and classify future events.

[0049] In general, a datapoint in cluster analysis can be an n-dimensional vector, where n is the total number of attributes being considered. In one embodiment, the attributes consist of the voltage metrics described hereinbefore, which can be the maximum interphase angle and the minimum interphase angle, the IEEE voltage imbalance figure, and the ratio of negative sequence voltage to the positive sequence voltage. Once a predictor model has been derived, a new data point depicting the state of the power distribution network at a certain time can

SUBSTITUTE SHEETS (RULE 26) then be classified into a predetermined cluster based on its voltage metrics. This is what occurs at step 210 in the fault detection process.

[0050] The clustering process can occur according to a number of different clustering algorithms, each yielding a different predictor model. Broadly speaking, clustering may be implemented as a supervised (machine) learning process or an unsupervised (machine) learning process. The difference between the two lies in the data set being used. Supervised learning uses a data set having preexisting labels associated with them: a program is able to train itself using the labelled data set so that it progressively works towards a function that maps inputs to a desired output or outputs. Contrastingly, unsupervised learning looks for patterns in a data set with no preexisting labels.

[0051] In some embodiments, the data available may not identify what state the distribution network is in for a particular datapoint. A number of unsupervised learning algorithms may be suitable for clustering such a data set. These can include centroid clustering, density clustering, distribution clustering, and connectivity clustering. Due to correlations between the voltage metrics and the state of the distribution network governed by underlying physics, it is expected that successful clustering would identify boundaries that demarcate different operating conditions of the distribution network. In the absence of prior knowledge of what these correlations are, one would need to undertake further experiments to determine the nature of each cluster, that is, whether a cluster corresponds to a phase to ground fault, a phase to phase fault, or a multiphase fault and so on.

[0052] In embodiments where the voltage metrics data is labelled, it may be preferable to use supervised learning. This can be implemented as an artificial neural network with the voltage metrics configured as inputs, which are mapped through a function to a preexisting label (what state is the distribution network in). Through training on a large data set, the artificial neural network would be become capable of classifying a new data point into a preexisting label (effectively equivalent to a cluster). As discussed previously, the voltage metrics can follow a hierarchy. Accordingly, the artificial neural network can be configured to reflect the hierarchy by assigning different weights to the different voltage metrics.

[0053] Alternatively, the supervised learning can be implemented with the random forest method, where a multitude of decision trees are constructed through training based on the training data set. Random forest can be well suited to clustering different operating conditions of the distribution network due to it fundamentally being a classification algorithm. Each decision can be made based on one or more of the voltage metrics provided as inputs.

[0054] Alternatively, the supervised learning can be implemented with the classification tree method. A generic classification tree is shown in Figure 7. The classification tree consists of multiple levels of decision-making. Each decision node (e.g. nodes 701, 702 and 703) resolves whether the inputs (e.g. measured data) satisfy an inequality condition involving a voltage metric. In particular, the classification tree comprises decision nodes concerning the minimum and maximum interphase angles as well as a voltage imbalance metric. The machine learning (training) determines the size and ordering of the tree and the specific inequality conditions for decision nodes. In use, a trained classification tree predictor model predicts a fault scenario corresponding to a leaf node (e.g. nodes 711, 712 and 713) in the tree. As an example, the fault scenario can be characterized by whether or not a fault has occurred and whether there is a downed conductor.

[0055] Irrespective of the type of machine learning employed, additional parameters can be incorporated into the training to yield a predictor model with greater reliability and/or finer classification capabilities. Non-limitingly, these additional parameters can include one or more of network arrangement, load power factor, load balance, and transformer demand. Evaluating the Predictor Model

[0056] A predictor model obtained at step 302 can then be evaluated at step 304. A confusion matrix can be used as a tool to evaluate the reliability of each of the trained predictor models and consequently select the most reliable predictor model. If a predictor model is able to determine the type of fault (including the no fault case) with a high success rate, that predictor model is said to be reliable. Conversely, an unreliable predictor model would have a relatively low success rate.

[0057] In general, the dimensionality of the confusion matrix is n x n (a square matrix) but can be freely scaled depending on the number of different scenarios being considered in the reliability evaluation. Each entry of the matrix is denoted Xrow, column- The matrix compares the predictions against known outcomes, which can be real-world data or simulated data. The total number of test cases is the summation of all the entries from X ₁₁ to X _nn .

[0058] Figure 3b shows an exemplary 3 x 3 confusion matrix X. The rows correspond to the known outcomes while the columns correspond to the predicted outcomes. In this confusion matrix three scenarios are considered: a source-side broken conductor fault (SS), a load-side broken conductor fault (LS), and the no fault case (NF).

[0059] The diagonal entries indicate the number of successful predictions for each scenario. The off-diagonal entries indicate the number of unsuccessful predictions. For example, xi3 shows the number of times the predictor model did not determine a fault when in fact there was a source-side broken conduct fault. A non-optimal predictor model would give various prediction errors. These can be classified as false negative (predicted no fault when in fact a fault did occur), false positive (predicted a fault when in fact a fault did not occur), or inaccurate positive (predicted the occurrence of a fault but determined an incorrect fault scenario).

[0060] In the ideal case, the predictions should match exactly with the known outcomes, that is, the confusion matrix should be a diagonal matrix. For a total of k test cases, an optimally reliable predictor model would successfully determine Xu SS cases, X22 LS cases, and X33 NF cases, where k = X ₁₁ + X ₂₂ + X ₃₃ .

[0061] At step 306, a predictor model is selected from multiple predictor models based on their relative evaluation results. Comparison of different predictor models can be assisted by defining a figure of merit that encapsulates the reliability of each predictor model. For example, a simple figure of merit can be the prediction success rate. A more sophisticated figure of merit, however, can assign different weights to the various prediction errors. A false negative can be given a higher weight than the other errors due to the severity of the potential consequences of not responding to a live fault. The selected predictor model can have the best figure of merit regardless of how the figure of merit is defined.

[0062] The method 300 is performed at a processor, which can be a processor 106 of a remote power line voltage line sensor 102 or a separate computer. In the latter case, the selected predictor model can then be implemented at a processor 106 of a remote power line voltage line sensor 102 to allow the remote power line voltage line sensor 102 to perform power line monitoring and fault detection according to method 200.

Operation

[0063] The operation a power line monitoring system incorporating the aspects described hereinbefore will now be described by referring to three different real- word scenarios shown.

[0064] Figure 4 depicts a section of an exemplary three-phase power distribution network 400. What is shown is simplified and omits devices and complexities that would normally be included in a full representation. The voltages are only one possible configuration and do not limit the invention.

[0065] A 33 kV busbar 402 in the distribution network 400 is receiving power from transmission through a near grid exit point. Upstream distribution transformers 404 step the voltage down from 33 kV to 11 kV, which then energises the busbar 406. Each upstream distribution transformer 404 can be located in an upstream substation. There is provided a central controller 408 for controlling downstream distribution, which can also be physically located in the upstream substation. Downstream distribution transformers 410 reduce the voltage further from 11 kV to 400 V. The 400 V busbar 406 supplies to a load 412. Protection is provided in the form of circuit breakers (CB) throughout the distribution system. Each circuit breaker can comprise or be in communication with a sensitive earth fault detection and mitigation system such as a ground fault neutralizer or a residual earth fault current limiter. A remote power line voltage line sensor 416 is installed on the LV side of distribution transformer 410.

[0066] The remote power line voltage line sensor 416 is monitoring the power lines on the high voltage (HV) side of the distribution transformer 410 according to method 200. Important three-phase electrical quantities are measured including at least the voltage phase and voltage magnitude of each phase using a measurement module 104 comprising a sensing circuit. A processor 106 then performs method 200 using a predictor model selected according to method 300 to process voltage metrics derived from the measurements and determine whether a fault has occurred and the type of fault that occurred (if any).

[0067] In a first scenario shown in Figure 4, there are no faults, and the distribution network is operating under normal conditions. Because the distribution network is operating normally, the maximum and minimum interphase angles (primary metric) may both be approximately 120°. If required by the chosen predictor model, the IEEE voltage imbalance figure (secondary metric) may be found to be approximately 0. If also required by the chosen predictor model, the ratio of positive sequence voltage to negative sequence voltage (tertiary metric) may be found to be a very large number due to the negative and zero sequence components being approximately zero in a balanced system. Having received the voltage metric or metrics as inputs, the predictor model then classifies the scenario into one of the clusters corresponding to different operating conditions. The predictor model determines that the distribution network is operating normally, and the communications module 108 may not immediately transmit to the upstream controller 408 as there is no need to transmit a time-sensitive fault signal.

[0068] In a second scenario shown in Figures 5a and 5b, a fault has occurred at 514, and the fault is a single-line open circuit fault caused by a downed sourceside conductor. Referring to Figure 5b which more clearly shows the nature of the fault, the fault is said to be source-side because the conductor (line) breaks at the distribution transformer 410 end 514. The broken conductor, which may or may not be in contact with ground, remains directly connected to the source side.

[0069] Because a fault has occurred, the values for the voltage metrics are substantially different from those calculated for a distribution network operating under normal conditions. The predictor model recognises that a fault has occurred and classifies the fault into the cluster corresponding to an open circuit fault caused by a downed source-side conductor. As the fault is caused by a downed source-side conductor, the upstream protection is able to detect the fault due to a noticeable increase in fault current and subsequently isolates the fault by triggering the circuit breaker 418. Having determined that the fault occurred on the source-side and knowing it is a fault detectable by upstream protection, the remote power line voltage sensor 416 may not transmit a fault signal to the upstream controller 408. Alternatively, the remote power line voltage sensor 416 may still transmit a fault signal to the upstream controller 408 for extra assurance using a communications module 108. This signal may further be used to trigger alarms to alert a human controller that a potentially hazardous condition exists.

[0070] In a third scenario shown in Figure 6a, a fault has occurred at 614, and the fault is a single-line open circuit fault caused by a broken load-side conductor. Referring to Figure 6b which more clearly shows the nature of the fault, the fault is said to be load-side because the conductor (line) breaks at the circuit breaker 418 end 614. The broken conductor, which may or may not be in contact with ground, is no longer directly connected to the source side but is still directly connected to the distribution transformer 410 (load side).

[0071] Because a fault has occurred, the values for the voltage metrics are substantially different from those calculated for a distribution network operating under normal conditions. The predictor model recognises that a fault has occurred and classifies the fault into the cluster corresponding to an open circuit fault caused by a downed load-side conductor. The predictor model can further distinguish whether the broken load-side conductor is hanging in the air or in contact with the ground. As the fault is caused by a broken load-side conductor, the resultant fault current is too small to prompt a response from the upstream earth fault current detection and mitigation. Having determined that the fault occurred on the load-side and knowing it is a fault undetectable by upstream protection, the remote power line voltage sensor 416 responds in substantially real time by transmitting a fault signal to the upstream controller 408 via the communications module 108. The upstream controller 408 then responds by opening the upstream circuit breaker 418, isolating the hazardous condition. This signal may further be used to trigger alarms to alert a human controller that a potentially hazardous condition exists.

Simulation and Test Results

Simulation

[0072] Different predictor models have been assessed in a simulated environment using the 2021 DlgSILENT PowerFactor™ SP5 software package. An 11 kV distribution network was modelled with the intention to simulate a typical real-world distribution network.

[0073] The 11 kV distribution network was modelled as a series of 3 km radially connected sections, where the customers are evenly distributed. Every 1 km of the line includes 2 single-phase and 1 three-phase transformers, as shown in the table below. The single-phase transformers were connected such that when demand on each of the transformers matches, the total system imbalance is zero, or close to zero. [0074] The overhead distribution lines were modelled assuming the tower geometry and the conductor parameters shown in the two tables below. Notably, to ensure a higher simulation accuracy, all overhead lines were modelled using the distributed parameter system, rather than the lumped parameter (PI) model.

[0075] Additional sensitivity scenarios were undertaken assuming a short 2 km section of underground cable between the main substation transformer and the fault location. The cable was modelled as an 11 kV 300 mm ² AL conductor with earthed outer sheath, where the earth path impedance was varied between 1 and 100 Ω.

[0076] As part of the simulation and testing, the distribution system demand was varied by adjusting the single-phase and three-phase distribution transformer loading; this assumes 20% and 40% loadings. [0077] The single-phase transformer design considers both balanced and imbalanced customer connection options. The unbalanced network was modelled by increasing the load connected between phases B and C by 20% and 40% compared to loads between A-B and C-A phases.

[0078] The power factor conditions tested include 0.8 lagging, 0.8 leading, and unity.

[0079] The fault impedances tested include 1 Ω, 10 Ω, 1 k Ω, 10 k Ω, 50 k Ω.

[0080] The simulation considers four options of neutral point connection to the main substation transformer. The neutral impedance was stepped between 1 and 1 k Ω, assuming the step 1 Ω, 12.5 Ω, 37.5 Ω, 1000 Ω.

Evaluation of Test Results

[0081] A machine learning software package, Orange, was used to analyse a data set of approximately 24000 modelled results for a wide range of simulated distribution network conditions in accordance with the preceding section.

[0082] Three network fault scenarios are considered: first, the faultless scenario (Scenario A); second, one or more open circuit faults with no downed conductor (Scenario B); third, one or more open circuit, downed conductor faults (Scenario C).

[0083] Three predictor models (classification tree, random forest, and neural network) were evaluated using two methods: cross validation with two folds and random sampling.

[0084] The table below shows the performance of the three models based on cross validation with two folds. The performance indicators include Area Under the Curve (AUC), Computational Accuracy (CA), Precision, Recall, and the Fl score (weighted average of Precision and Recall).

[0085] The table below shows the performance of the three models based on random sampling with five repeat tests and a training set size of 70%. The performance indicators include AUC, CA, Precision, Recall, and the Fl score.

[0086] In both cases, the random forest model exhibited marginally better performance than the classification tree model, and the neural network model had the worst performance. Confusion matrices for the classification tree model, the random forest model, and the neural network model are shown in Figures 8a, 8b, and 8c respectively. [0087] Consistent with the performance indicators, the random forest model produced fewest prediction errors. The prediction success rate of the classification tree model is comparable to that of the random forest model. In contrast, the neural network model was proven to have poor performance in regard to differentiating between Scenario B and Scenario C. In other words, the neural network model often incorrectly predicts whether there is a downed conductor fault. Such poor performance is unacceptable as a downed conductor can pose serious health risks.

[0088] It is surprising that the more sophisticated neural network model has worse performance than the elementary classification tree model. This is unexpected since neural network is and has been one of the most researched and trialed machine learning solutions in the field of fault detection.

[0089] While the random forest model exhibits marginally better performance than the classification tree model, it does have the drawback of being more difficult to implement. The classification tree model is simpler to implement but has marginally worse performance. Which of the two models is most suitable will depend upon the application.

[0090] For completeness, the test results affirm the importance of the minimum and maximum interphase angles and the voltage imbalance metric as primary and secondary voltage metrics. Each of these metrics has high information gain, gain ratio, and Gini index value as tabulated below.

INTERPRETATION

[0091] A number of methods have been described above. Any of these methods may be embodied in a series of instructions, which may form a computer program. These instructions, or this computer program, may be stored on a computer readable medium, which may be non-transitory. When executed, these instructions or this program may cause a processor to perform the described methods.

[0092] Where an approach has been described as being implemented by a processor, this may comprise a plurality of processors. That is, at least in the case of processors, the singular should be interpreted as including the plural. Where methods comprise multiple steps, different steps or different parts of a step may be performed by different processors.

[0093] The order of steps within methods may be altered, such that steps are performed out of order or in parallel, except where one step is dependent on another having been performed, or the context otherwise requires.

[0094] The term "comprises" and other grammatical forms is intended to have an inclusive meaning unless otherwise noted. That is, they should be taken to mean an inclusion of the listed components, and possibly of other non-specified components or elements.

[0095] While the present invention has been explained by the description of certain embodiments, the invention is not restricted to these embodiments. It is possible to modify these embodiments without departing from the spirit or scope of the invention.