Chapter -3 ANALYSIS OF HVDC SYSTEM MODEL. Basically the HVDC transmission consists in the basic case of two

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1 Chapter -3 ANALYSIS OF HVDC SYSTEM MODEL Basically the HVDC transmission consists in the basic case of two convertor stations which are connected to each other by a transmission link consisting of an overhead transmission line and/or a cable. Such a HVDC transmission is shown in Figure 3.1. The main parts of the HVDC station comprising of: Two series connected 6 pulse convertors consisting of valves and convertor transformers. The valves provide the conversion from AC to DC and the transformer provide a suitable voltage ratio to achieve the desired direct voltage and galvanic separation of the AC system and the DC system. A smoothing reactor in the DC circuit reduces the harmonic currents in the DC line and possible transient over currents. Filters on the AC side and possibly on the DC side are connected to take care of harmonics generated at the conversion. Shunt capacitors to complement the reactive power generation may be included. 118

2 A control system will give the desired operation performance of the transmission. Figure. 3.1 Main components of the converter station 3.1 OPERATION OF THE TWO WAY 6 PULSE CONVERTOR The two way 6 pulse convertor bridge is shown in Figure 3.2. It consists of 6 thyristor valves. The ability of an HVDC convertor to convert a 3 phase alternating voltage to a direct voltage which can be controlled to any value between a positive and negative value depends on the following properties of the valve. 119

3 1. The valve can conduct current in only one direction, i.e. the forward direction, from the anode to the cathode. In the opposite direction the valve blocks the current, i.e. if a voltage is applied over the valve making the cathode positive relative to the anode the valve will take up the voltage and will block the current. This voltage is called reverse blocking voltage. 2. The valve fires, i.e. starts to conduct current in the forward direction provided that the following two conditions are fulfilled simultaneously. The voltage in the forward direction across a valve is positive. The valve control pulse is sent to the valve. As soon the valve has started to conduct current the magnitude of the current is determined solely by the main circuits outside the valve. A negative grid or gate pulse to a conducting valve cannot influence its state. The flow of current through the valve continues until it decreases by external influence and tries to pass zero. The valve presents this by setting up a negative voltage and the current through the valve is extinguished. 3. In the forward direction the valve sets up a voltage and blocks the current until a control pulse is applied to the gate. This voltage is called Forward blocking voltage. 120

4 During each cycle of the alternating voltage the following states of operation may be identified for a valve: Forward blocking interval Conduction interval Reverse blocking interval The 6 valves forming a bridge connected to an alternating voltage source which is assumed to be represented by an ideally sinusoidal, symmetrical 3 phase emf. The reactance X in each phase is usually determined by the leakage reactance of the convertor transformer The convertor bridge is assumed to be connected to a DC network via an infinitely large inductance. With this assumption the direct current will be completely smoothed. The basic modes of operation will be analyzed in the following steps. Rectifier operation (power flow from AC side to DC side) Operation with uncontrolled valves and X = 0 Operation with controlled valves and X = 0 Operation with uncontrolled valves and X 0 121

5 Inverter operation (power flow from DC side to AC side) with controlled valves and X MODELLING OF HVDC TRANSMISSION SYSTEM HVDC system consists of many components that are common to AC systems, such as transformers, reactors, capacitors, surge arresters and transmission lines. The major equipment that is unique to DC systems is the converter bridge and controller HVDC CONVERTER MODELLING Figure. 3.2 A Converter Bridge 122

6 The converter bridge with its associated transformer Valve winding is shown in Figure 3.2. The valve winding can be modeled as a voltage source (proportional to the voltage at the converter bus) in series with the leakage impedance of the transformer. Thus the converter is decoupled from AC system. The effect of converter on the AC system is to inject current at the converter bus, which are dependent on the current through the valve windings as shown in Figure 3.3. In this approach the transformer magnetizing impedances is a part of AC system. The DC current flows through series connected converter bridges, smothing reactors and the DC line. The system is shown in Figure 3.4, where only two bridges are shown in series with the reactor. This is a modular approach in which AC and DC systems are decoupled using dependent current and voltage sources. The varying topology of the converter circuit due to turning on and off valves in the bridge complicates the analysis. Figure. 3.3 Current injection at the converter bus Figure. 3.4 DC Network 123

7 3.2.2 GENERATION OF CONTROL VOLTAGE The control voltage ec which is the input to the firing controller is obtained as the output from current or extinction angle controllers. These controllers could be of analog or digital type. In either case, they can be described by discrete state equations. In general, the control voltage ec is described by z Fz Gu ( i 1) i i (3.1) e Hz Ku c( i 1) i ( i 1) (3.2) Where ui is the input (say current error) in the i th interval. Zi is the controller state vector corresponding to the i th interval. F,G,H and K are constant matrices. The magnitude of ec may be limited. The current reference is also limited by Voltage Dependent Current Order Limiter (VDCOL). A generic model for VDCOL is shown in Figure 3.5. type G1(S) and G2(S) are represented by simple transfer functions of the G ( S) 1/(1 st ) (3.3) 1 down G ( S) 1/(1 st ) (3.4) 2 up 124

8 Figure. 3.5 Generic model of VDCOL TRANSFORMER MODEL The standard equivalent circuit of a single phase power transformer is shown in Figure 3.6 which contains an ideal transformer. This can be represented by dependent sources as shown in Figure 3.7. Figure. 3.6 Equivalent circuit of a single phase transformer 125

9 Figure. 3.7 Equivalent circuit of a single phase transformer with dependent sources This representation of the converter transformer enables the better interface between the AC, DC systems as shown in Figure 3.8. AC system including filter DC network including smoothing reactors Converter bridges. Figure. 3.8 AC/DC System Diagram 126

10 Figure. 3.9 A Bridge Converter A converter bridge is represented as shown in Figure 3.9 with each transformer secondary winding modeled as a voltage source in series with the corresponding phase leakage impedance (it is assumed that the secondary windings are connected in star). The effect of the two converter bridges (connected in series) is to inject current at the converter buses in the AC system as shown in Figure Figure Current Injection in to AC system 127

11 Figure pulse converter unit showing transformer connections The interface between the converter and the AC system is through the ideal transformers making up the required connection for the twelve pulse unit as shown in Figure MATLAB IMPLEMENTATION OF HVDC SYSTEM Modeling of a high-voltage direct current (HVDC) 12-Pulse transmission link using the Universal Bridge block and the Three-Phase Transformer (Three Windings) block in combination with Simulink blocks is as shown in Figure The electrical part representing the AC network is built using three-phase blocks. The Discrete HVDC control system is a generic control available in the Discrete Control Blocks library of MATLAB. 128

12 3.3.1 DESCRIPTION OF THE HVDC TRANSMISSION SYSTEM A 1000MW (500kV, 2kA) DC interconnection is used to transmit power from a 500kV, 5000MVA, 60Hz network to a 345kV, 10000MVA, 50Hz network. The AC networks are represented by damped L-R equivalents with an angle of 80 0 at fundamental frequency and at the third harmonic. The rectifier and the inverter are 12-pulse converters using two Universal Bridge blocks connected in series. The converters are interconnected through a 300kM line and 0.5H smoothing reactors located on either ends of the transmission line. The converter transformers (Yg/Y/ ) are modeled with Three-Phase Transformer (Three-Winding) blocks. The tap position is rather at a fixed position determined by a multiplication factor applied to the primary nominal voltage of the converter transformers (0.90 on the rectifier side; 0.96 on the inverter side). From the AC point of view, an HVDC converter acts as a source of harmonic currents. From the DC point of view, it is a source of harmonic voltages. The order n of these characteristic harmonics is related to the pulse number p of the converter configuration: n = kp ± 1 for the AC current and n = kp for the direct voltage, k being any integer. As it is a 12-pulse converter the injected harmonics on the AC side are 11, 13, 23, 25, and on the DC side are 12, 24. The specifications of the HVDC system model are given in annexure

13 Figure HVDC System 130

14 AC filters are used to prevent the odd harmonic currents from spreading out on the network. The filters are grouped in two subsystems. These filters also appear as large capacitors at fundamental frequency, thus providing reactive power compensation for the rectifier consumption due to the firing angle α. For α is equal to 30 0, the converter reactive power demand is approximately 60% of the power transmitted at full load. The AC filters subsystem mask contain the high Q (100) tuned filters at the 11th and 13th harmonics and the low Q(3), or damped filter, used to eliminate the higher order harmonics, i.e. 23rd and up. Extra reactive power is also provided by capacitor banks. Two circuit breakers are used to apply faults on the rectifier AC and DC sides. The power system and the control system are both discretised with the same sample time (Ts=1.25e -6 sec). The sampling time is so chosen that the number of samples during a period are as many as possible because the accuracy of the fault location in FFT analysis mainly depends on the sampling rate DESCRIPTION OF THE CONTROL SYSTEM The control systems of the rectifier and of the inverter use the same 12-pulse HVDC control block from the controls library of MATLAB. The block can operate either in rectifier or inverter mode

15 VDCOL FUNCTION The control function which is implemented to change the reference current according to the DC voltage is Voltage Dependent Current Order 132

16 Limiter VDCOL which automatically reduces the reference current (Id_ref) set point when VdL decreases. Reducing the Id reference currents also reduces the reactive power demand on the AC network, helping to recover from fault. The VDCOL parameters of the discrete 12-Pulse HVDC Control block dialog box are explained in Figure Figure VDCOL Characteristic; Id_ref = f(vdl) The Id_ref value starts to decrease when the Vd line voltage falls below a threshold value VdThresh (0.6p.u.). IdMinAbs is the absolute minimum Id_ref value, set at 0.08p.u. When the DC line voltage falls below the VdThresh value, the VDCOL reduces instantaneously to Id_ref. 133

17 However, when the DC voltage recovers, VDCOL limits the Id_ref rise time with a time constant defined by parameter Tup (80ms in the example) SYNCHRONIZATION SYSTEM The Discrete 12-Pulse HVDC Control block uses the primary voltages to synchronize and generate the pulses according to Vd_ref and Id_ref set points. The synchronizing voltages are measured at the Primary side of the converter transformer because the waveforms are less distorted. The firing command pulse generator is synchronized to the fundamental frequency of the AC source. At the zero crossings of the commutating voltages (AB, BC, CA), a ramp is reset. A firing pulse is generated whenever the ramp value becomes equal to the desired delay angle provided by the regulator. In order to improve the commutating voltages used by the pulse generator, the primary voltages (Vabc) are filtered by a low Q second-order band-pass filter centered at the fundamental system frequency. The base system frequency and the filter bandwidth are defined in the block dialog box. The HVDC system is subjected to various operating condition i.e. No fault, DC line fault and AC faults such as single line to ground fault (LG), line to line fault (LL), double line to ground fault (LLG) and symmetrical fault (LLL). The DC line voltage and current at the rectifier terminals are recorded for the analysis of the HVDC system. FFT analysis 134

18 is carried out for the voltage and current signals obtained from the rectifier end of the HVDC system model. The model is as shown in the Figure PROBLEM FORMULATION The detection and fast clearance of faults in HVDC transmission lines is important for a safe operation of the power system. The principle based on travelling wave theory provides the fastest protection for the long HVDC line. The HVDC line is modeled as a distributed parameter line and fault identification technique based on the travelling wave theory is proposed. The objective is to classify different operating conditions of a HVDC system i.e. No fault, DC line fault and AC faults such as single line to ground fault (LG), line to line fault (LL), double line to ground fault (LLG) and symmetrical fault (LLL). According to the travelling wave theory, when a fault occurs on a transmission line, voltage and current travelling waves appear on the line. The travelling waves generated due to the fault contain sufficient information about the fault and the same can be used for the identification and classification of faults. This technique can be adopted for the HVDC transmission line protection. The important requirement of the HVDC line protection is that, different types of faults are identified and a correct decision be made as fast as possible. Different fault 135

19 identification techniques based on FFT, ANN and Wavelet Transforms (WT) were used to analyze various operating conditions of the HVDC system. The Reverse Voltage Travelling Wave (RVTW) observed at the rectifier end is used to identify different types of faults in the HVDC system. The RVTW has been calculated and is used for the fault analysis by FFT, ANN and WT techniques. Comparison has been made among the three analysis tools and most reliable and fast fault identification technique has been proposed. 3.5 HVDC UNDER NORMAL OPERATING CONDITION The HVDC model is discretised at a sampling frequency of 80 khz. The system is designed to reach steady state in less than 0.6sec. The rectifier controls the current and the inverter controls the voltage. Once the steady state is attained the system is designed in such a way that the firing angles are 18 0 and respectively on the rectifier and inverter. During the steady state operations of the DC system, the DC line voltage (VD) is given by Where VDO is the ideal no load DC voltage of a six pulse bridge. (3.5) 136

20 2 V D 3 V C (3.6) Where VC is the line to line RMS commutating voltage i.e. dependent on the AC system voltage and transformer ratio. Rc is the equivalent commutating resistance 3 R C X C (3.7) Where XC is the commutating reactance or transformer reactance referred to the valve side. based on 1200MVA and 22.2KV = 9.874Ω =500+[4.5+1] 2=511KV Figure 3.14(a) and 3.14(b) represents the DC line voltage and current at the rectifier under normal operating condition. It is observed 137

21 that the DC line voltage at the rectifier during the steady state condition is stable and is varying between 0.98p.u to 1.02p.u (500kV base) as shown in Figure 3.14(a). The DC transmission line current at the rectifier end during normal operating condition has been recorded between 0.99p.u to 1.01p.u as shown in Figure 3.14(b). Figure 3.14(c) and 3.14(d) represents the DC terminal voltage and current at the inverter terminal during normal operating condition. It is observed that the DC line voltage is at 0.97 p.u. to 1.01 p.u. as shown in Figure 3.14(c) and the DC line current at the inverter as shown in figure 3.14(d) is observed as stable. Figure 3.14(e) and 3.14(f) are the AC voltage and current waveforms at the input terminals of the rectifier when the HVDC system is running under normal operating condition. Figure 3.14(g) and 3.14(h) are the AC voltage and current waveforms at the AC terminals of the inverter when the HVDC system is running under normal operating condition. The reverse Voltage Travelling wave for various operating conditions of HVDC system (Normal Operation, DC Line fault at 50kM from the rectifier end with a fault resistance of 1Ω and an LG fault on the AC side of the inverter) is given in annexure-ii. 138

22 Figure. 3.14(a) DC line voltage (p.u.) at the rectifier under normal operating condition Figure. 3.14(b). DC line current (p.u.) at the rectifier under normal operating condition Figure. 3.14(c) DC line voltage (p.u.) at the inverter under normal operating condition 139

23 Figure. 3.14(d) DC line current (p.u.) at the inverter under normal operating condition Figure. 3.14(e) AC Voltage (p.u.) at the input terminals of the rectifier under normal operating condition Figure. 3.14(f) AC current (p.u.) at the input terminals of the rectifier under normal operating condition 140

24 Figure. 3.14(g) AC voltage (p.u.) at the input terminals of the inverter during normal operating condition. Figure. 3.14(h) AC current (p.u.) at the input terminals of the inverter under normal operating condition 3.6 HVDC SYSTEM DURING DC FAULT CONDITION The DC transmission line is a distributed parameter line. N-phase distributed parameter transmission line model with lumped losses is used for the simulation. In this model the loss less distributed LC line is characterized by the surge impedance and phase velocity. The surge impedance is given by 141

25 (3.8) The Phase velocity is given by (3.9) The model uses the fact that the quantity e + zi entering one end of the line must arrive unchanged at other end after a time delay of d τ v Where e is the line voltage, i is the line current and d is the line length. The 300kM long HVDC transmission line is subjected to faults at various distances by using a circuit breaker. The various fault resistances have been simulated by changing the breaker resistance. The HVDC system is simulated for DC line faults at 30 different locations with fault resistance at each location of 1Ω, 2Ω, 5Ω, 7Ω, 8Ω, 10Ω, 12Ω, 15Ω, 17Ω, 18Ω, 20Ω, 25Ω, 30Ω and 40Ω. For example the faults at different locations i.e. 50kM, 100kM, 150kM, 200kM and 250kM were presented with fault resistances of 1Ω and 20Ω. The results with other fault data is annexed in annexure-iii. Figure 3.15(a) and 3.15(b) represents the D.C voltage and current waveform of the HVDC 142

26 transmission line when the line is subjected to a DC fault at 50 km from the rectifier end with a fault resistance of 1Ω. The duration of the fault on the transmission line is 0.03sec and the time of occurrence of the fault is 0.6sec i.e. after the voltage and current of the HVDC transmission system reaches steady state. When the HVDC model is simulated for the DC line fault, it is observed that the DC line voltage at the rectifier suffers with large oscillations. The DC line voltage oscillates between p.u. to p.u. as shown in Figure 3.15(a). The DC line current reaches to 2 p.u. in 0.01 sec as shown in Figure 3.15(b). The current starts decreasing due to the increasing firing angle. Figure 3.15(c) and 3.15(d) represents the DC line voltage and current at the inverter during DC line fault with a fault at 50kM from the rectifier end with a fault resistance of 1. The DC line voltage reduces to zero immediately after occurrence of fault and remains zero till the fault has been cleared. The DC line voltage starts oscillating. It can be observed from the Figure 3.15 and Figure 3.20 that the characteristics of the voltage and current do not change much with the variation in the fault resistance. Figure 3.15(e) and 3.15(f) represents AC line voltage and current at the input terminals of the rectifier and Figure 3.15(g) and 3.15(h) represents the AC line voltage and current at AC terminals of the converter during the DC line fault with a fault resistance of 1 at 50 km from the rectifier end. From the Figure 3.15(e) and 3.15(g) it is observed both on AC side of rectifier and inverter the voltage undergo a 143

27 remarkable change and is similar to that of Normal operating condition after 0.03sec i.e. the voltage on the sides of the HVDC system is stable beyond 0.03 seconds. But during the time of fault i.e. from 0.6 sec for a duration of 0.03 sec the voltage on the rectifier side drops by 0.8 p.u. and the voltage on the inverter side raise by 0.1 p.u. But the DC line fault makes a remarkable change in the AC line currents on either side. The AC line currents on the inverter side from Figure 3.15(h) reaches to zero at the instant of the fault itself. The current on the AC side of the rectifier crosses beyond the normal operating condition and reaches to double the normal value in less than 0.01 seconds from the time of occurrence of fault. Due to the control over the firing angle the current has been brought down to zero in less than 0.03sec. the fault duration is so chosen that the number of samples required for the analysis are obtained. Figure. 3.15(a) DC line voltage at the rectifier during DC line fault with a fault resistance of 1 at 50 km from the rectifier end. 144

28 Figure. 3.15(b) DC line current at the rectifier during DC line fault with a fault resistance of 1 at 50 km from the rectifier end. Figure. 3.15(c) DC line voltage at the inverter during DC line fault with a fault resistance of 1 at 50 km from the rectifier end. Figure. 3.15(d) DC line currents at the inverter during DC line fault with a fault resistance of 1 at 50 km from the rectifier end. 145

29 Figure. 3.15(e) AC voltage at the input terminals of the rectifier during DC line fault with a fault resistance of 1 at 50 km from the rectifier end. Figure. 3.15(f) AC current at the input terminals of the rectifier during DC line fault with a fault resistance of 1 at 50 km from the rectifier end. Figure. 3.15(g) AC voltage at the input terminals of the inverter during DC line fault with a fault resistance of 1 at 50 km from the rectifier end. 146

30 Figure. 3.15(h) AC current at the input terminals of the inverter during DC line fault with a fault resistance of 1 at 50 km from the rectifier end Figure 3.16(a) and 3.16(b) represents the D.C voltage and current waveform of the HVDC transmission line when the line is subjected to a DC fault at 100 km from the rectifier end with a fault resistance of 1Ω. The duration of the fault on the transmission line is 0.03sec and the time of occurrence of the fault is 0.6sec. When the HVDC model is simulated for the DC line fault it is observed that the DC line voltage at the rectifier suffer with large oscillations as in case of a DC line fault at 50kM. The DC line voltage oscillates between +1.5 p.u. to -1.5 p.u. as shown in Figure 3.16(a). The DC line current reaches to 2 p.u. in 0.01 sec as shown in Figure 3.16(b). The current starts decreasing due to the increasing firing angle. Figure 3.16(c) and 3.16(d) represents the DC line voltage and current at the inverter during DC line fault with a fault at 100kM from the rectifier end with a fault resistance of 1. The DC line voltage reduced to zero immediately after occurrence of fault and remains zero till the fault has been cleared. The DC line voltage starts oscillating. The characteristics of the voltage and current do not change much with 147

31 the change in the fault resistance. Figure 3.16(e) and 3.16(f) represents AC line voltage and current at the input terminals of the rectifier and Figure 3.16(g) and 3.16(h) represents the AC line voltage and current at AC terminals of the converter during the DC line fault with a fault resistance of 1 at 100kM from the rectifier end. From the Figure 3.16(e) and 3.16(g) it is observed both on AC side of rectifier and inverter the voltage undergoes a remarkable change. During the time of fault i.e. from 0.6sec to 0.63sec the voltage on the rectifier side drops by 0.8p.u. and the voltage on the inverter side rise by 0.1p.u. But the DC line fault makes a remarkable change in the AC line currents on either side. The AC line currents on the inverter side from Figure 3.16(h) reaches to zero at the instant of the fault itself but the current on the AC side of the rectifier crosses beyond the normal operating condition and reaches to double the normal value in less than 0.01 sec from the instant of fault. But due to the control over the firing angle the currents reaches to zero in less than 0.03sec. Figure. 3.16(a) DC line voltage at the rectifier during DC line fault with a fault resistance of 1 at 100 km from the rectifier end. 148

32 Figure. 3.16(b) DC line current at the rectifier during DC line fault with a fault resistance of 1 at 100kM from the rectifier end. Figure. 3.16(c) DC line voltage at the inverter during DC line fault with a fault resistance of 1 at 100kM from the rectifier ends. Figure. 3.16(d) DC line current at the inverter during DC line fault with a fault resistance of 1 at 100kM from the rectifier end. 149

33 Figure. 3.16(e) AC voltage at the input end of the rectifier during DC line fault with a fault resistance of 1 at 100kM from the rectifier end. Figure. 3.16(f) AC current at the input end of the rectifier during DC line fault with a fault resistance of 1 at 100kM from the rectifier end. Figure. 3.16(g) AC voltage at the input end of the inverter during DC line fault with a fault resistance of 1 at 100kM from the rectifier end. 150

34 Figure. 3.16(h) AC current at the input terminals of the inverter during DC line fault with a fault resistance of 1 at 100kM from the rectifier end. Figure 3.17(a) and 3.17(b) represents the D.C voltage and current waveform of the HVDC transmission line when the line is subjected to a DC fault at 150kM from the rectifier end with a fault resistance of 1Ω. The duration of the fault on the transmission line is 0.03sec and the time of occurrence of the fault is 0.6sec. When the HVDC model is simulated for the DC line fault at 150kM from the rectifier end it is observed that the DC line voltage at the rectifier suffers with large oscillations as in case of a DC line fault at 50kM. But it is observed that the frequency of oscillations is decreasing with the increase in the fault location distance from the rectifier end. The DC line voltage oscillates between p.u. to p.u. as shown in Figure 3.17(a). The DC line current reaches to 2p.u. in 0.01sec as shown in Figure 3.17(b). The current starts decreasing due to the increasing firing angle. Figure 3.17(c) and 3.17(d) represents the DC line voltage and current at the inverter during DC line fault with a fault at 150kM from the rectifier end with a fault resistance of 1. The DC line voltage reduces to zero immediately after occurrence 151

35 of fault and remains zero till the fault has been cleared. The DC line voltage starts oscillating. The characteristics of the voltage and current do not change much with the change in the fault resistance. Figure 3.17(e) and 3.17(f) represents AC line voltage and current at the input terminals of the rectifier and Figure 3.17(g) and 3.17(h) represents the AC line voltage and current at AC terminals of the inverter during the DC line fault with a fault resistance of 1 at 150kM from the rectifier end. During the instant of fault i.e. from 0.6sec for the duration of 0.03sec the voltage on the rectifier side drops by 0.8p.u. The DC line fault makes a remarkable impact on the AC line currents on either side i.e. both on inverter side and rectifier side. From Figure 3.17(h) the AC line currents on the inverter side reaches to zero at the instant of the fault itself but the current on the AC side of the rectifier crosses beyond the normal operating condition i.e. double the normal value in less than 0.01sec from the instant of fault. But due to the control over the firing angle the current has been reduced to zero in less than 0.03sec. Figure. 3.17(a) DC line voltage at the rectifier during DC line fault with a fault resistance of 1 at 150kM from the rectifier end. 152

36 Figure. 3.17(b) DC line current at the rectifier during DC line fault with a fault resistance of 1 at 150kM from the rectifier end. Figure. 3.17(c) DC line voltage at the inverter during DC line fault with a fault resistance of 1 at 150kM from the rectifier end. Figure. 3.17(d) DC line current at the inverter during DC line fault with a fault resistance of 1 at 150kM from the rectifier end. 153

37 Figure. 3.17(e) AC voltage at the input terminals of the rectifier during DC line fault with a fault resistance of 1 at 150 km from the rectifier end. Figure. 3.17(f) AC current at the input terminals of the rectifier during DC line fault with a fault resistance of 1 at 150 km from the rectifier end. Figure. 3.17(g) AC voltage at the input terminals of the inverter during DC line fault with a fault resistance of 1 at 150 km from the rectifier end. 154

38 Figure. 3.17(h) AC current at the input terminals of the inverter during DC line fault with a fault resistance of 1 at 150kM from the rectifier end. Figure 3.18(a) and 3.18(b) represents the D.C voltage and current waveform of the HVDC transmission line when the line is subjected to a DC fault at 200kM from the rectifier end with a fault resistance of 1Ω. The duration of the fault on the transmission line is 0.03sec and the time of occurrence of the fault is 0.6sec. When the HVDC model is simulated for the DC line fault at 200kM from the rectifier end it is observed that the DC line voltage at the rectifier oscillates as in case of a DC line fault at other locations, but it is observed that the frequency of oscillations is decreasing with the increase in the fault location when measured from the rectifier end. The DC line voltage oscillates between +2p.u. to -2p.u. as shown in Figure 3.18(a). The DC line current increases above 2p.u. in 0.01sec as shown in Figure 3.18(b). The current starts decreasing due to the increasing firing angle. Figure 3.18(c) and 3.18(d) represents the DC line voltage and current at the inverter during DC line fault with a fault at 200kM from the rectifier end with a fault resistance of 1. The DC line 155

39 voltage reduced to zero immediately after occurrence of fault and remains zero till the fault has been cleared. The DC line voltage starts oscillating. The characteristics of the voltage and current do not change much with the variation of the fault resistance. Figure 3.18(e) and 3.18(f) represents AC line voltage and current at the input terminals of the rectifier and Figure 3.18(g) and 3.18(h) represents the AC line voltage and current at AC terminals of the inverter during the DC line fault at 200kM from the rectifier end with a fault resistance of 1. From the Figure 3.18(e) and 3.18(g) it is observed that both on AC side of rectifier and inverter the voltage undergoes remarkable change. From Figure 3.18(h) the AC line currents on the inverter side reached to zero at the instant of the fault itself but the current on the AC side of the rectifier crossed beyond the normal operating condition and reaches to double the normal value in less than 0.01sec from the instant of fault. Figure. 3.18(a) DC line voltage at the rectifier during DC line fault with a fault resistance of 1 at 200kM from the rectifier end. 156

40 Figure. 3.18(b) DC line current at the rectifier during DC line fault with a fault resistance of 1 at 200kM from the rectifier end. Figure. 3.18(c) DC line voltage at the inverter during DC line fault with a fault resistance of 1 at 200kM from the rectifier end. Figure. 3.18(d) DC line current at the inverter during DC line fault with a fault resistance of 1 at 200kM from the rectifier end. 157

41 Figure. 3.18(e) AC voltage at the input terminals of the rectifier during DC line fault with a fault resistance of 1 at200km from the rectifier end. Figure. 3.18(f) AC current at the input terminals of the rectifier during DC line fault with a fault resistance of 1 at 200kM from the rectifier end. Figure. 3.18(g) AC voltage at the input terminals of the inverter during DC line fault with a fault resistance of 1 at 200kM from the rectifier end. 158

42 Figure. 3.18(h) AC current at the input terminals of the inverter during DC line fault with a fault resistance of 1 at 200kM from the rectifier end. Figure 3.19(a) and 3.19(b) represents the D.C voltage and current waveform of the HVDC transmission line when the line is subjected to a DC fault at 250kM from the rectifier end with a fault resistance of 1Ω. The duration of the fault on the transmission line is 0.03sec and the time of occurrence of the fault is 0.6sec. When the HVDC model is simulated for the DC line fault at 250kM from the rectifier end it is observed that the DC line voltage at the rectifier suffer with large oscillations as in case of a DC line fault at other locations, it is also observed that the frequency of oscillations decreases with the increase in the fault location distance from the rectifier end. The DC line voltage oscillates between +1.6p.u. to - 1.6p.u. as shown in Figure 3.19(a). The DC line current increases above 2p.u. in 0.01sec as shown in Figure 3.19(b). The current starts decreasing due to the increasing firing angle. Figure 3.19(c) and 3.19(d) represents the DC line voltage and current at the inverter during DC line fault with a fault at 250kM from the rectifier end with a fault resistance 159

43 of 1. The DC line voltage reduced to zero immediately after occurrence of fault and maintained zero till the fault has been cleared. The DC line voltage starts oscillating. The characteristics of the voltage and current do not change much with the variation of the fault resistance. Figure 3.19(e) and 3.19(f) represents AC line voltage and current at the input terminals of the rectifier and Figure 3.19(g) and 3.19(h) represents the AC line voltage and current at AC terminals of the inverter during the DC line fault with a fault resistance of 1 at 250kM from the rectifier end. The AC line currents on the inverter side from Figure 3.19(h) reached to zero at the instant of the fault itself but the current on the AC side of the rectifier crossed beyond the normal operating condition and reaches to double the normal value in less than 0.01sec from the instant of fault. Figure. 3.19(a) DC line voltage at the rectifier during DC line fault with a fault resistance of 1 at 250kM from the rectifier end. 160

44 Figure. 3.19(b) DC line current at the rectifier during DC line fault with a fault resistance of 1 at 250kM from the rectifier end. Figure. 3.19(c) DC line voltage at the inverter during DC line fault with a fault resistance of 1 at 250kM from the rectifier end. Figure. 3.19(d) DC line current at the inverter during DC line fault with a fault resistance of 1 at 250kM from the rectifier end. 161

45 Figure. 3.19(e) AC voltage at the input terminals of the rectifier during DC line fault with a fault resistance of 1 at 250kM from the rectifier end. Figure. 3.19(f) AC current at the input terminals of the rectifier during DC line fault with a fault resistance of 1 at 250kM from the rectifier end. Figure. 3.19(g) AC voltage at the input terminals of the inverter during DC line fault with a fault resistance of 1 at 250kM from the rectifier end. 162

46 Figure. 3.19(h) AC current at the input terminals of the rectifier during DC line fault with a fault resistance of 1 at 250 km from the rectifier end HVDC SYSTEM WITH A DC FAULT WITH A FAULT RESISTANCE OF 20 The voltage and current waveform at four measuring locations of the HVDC system i.e. both on DC and AC side of the inverter and rectifier are recorded for different fault locations on the DC transmission line i.e. at 50kM, 100kM, 150kM, 200kM and 250kM from the rectifier end with a fault resistance of 20 are shown in Figure 3.20 to Figure 3.20(a) and 3.20(b) represents the D.C voltage and current waveform of the HVDC transmission line when the line is subjected to a DC fault at 50kM from the rectifier end with a fault resistance of 20Ω. The duration of the fault on the transmission line is 0.03sec and the time of occurrence of the fault is 0.6sec i.e. after the voltage and current of the HVDC transmission system reaches steady state. When the HVDC model is simulated for the DC line fault at 50kM from the rectifier end it is 163

47 observed that the DC line voltage at the rectifier oscillates as in case of a DC line fault at the same location with other fault resistance, it is also observed that the frequency of oscillations is almost same when compared to the fault at the same location with other fault resistances as shown in Figure 3.15(a), but the magnitude of the oscillations is decreasing. The DC line voltage oscillates between 0.8p.u. as shown in Figure 3.20(a). The DC line current reaches to 2p.u. in 0.01 sec as shown in Figure 3.20(b). The current starts decreasing due to the increasing firing angle. Figure 3.20(c) and 3.20(d) represents the DC line voltage and current at the inverter during DC line fault with a fault at 50kM from the rectifier end with a fault resistance of 20. The DC line voltage reduced to zero immediately after occurrence of fault and remains zero till the fault has been cleared. The DC line voltage starts oscillating. The characteristics of the voltage and current do not change much with the variation of the fault resistance. Figure 3.20(e) and 3.20(f) represents AC line voltage and current at the input terminals of the rectifier and Figure 3.20(g) and 3.20(h) represents the AC line voltage and current at AC terminals of the inverter during the DC line fault with a fault resistance of 20 at 50kM from the rectifier end. From the Figure 3.20(e) and 3.20(g) it is observed both on AC side of rectifier and inverter the voltage under go remarkable change and restores to Normal operating stage after 0.03sec i.e. the voltage on the sides of the HVDC system are stable after the fault has been cleared. The AC line currents on the 164

48 inverter side from Figure 3.20(h) reached to zero at the instant of the fault but the current on the AC side of the rectifier crossed beyond the normal operating condition and reaches to double the normal value in less than 0.01sec from the instant of fault. Figure. 3.20(a) DC line voltage at the rectifier during DC line fault with a fault resistance of 20 at 50kM from the rectifier terminals. Figure. 3.20(b) DC line current at the rectifier during DC line fault with a fault resistance of 20 at 50kM from the rectifier end. 165

49 Figure. 3.20(c) DC line voltage at the inverter during DC line fault with a fault resistance of 20 at 50kM from the rectifier end. Figure. 3.20(d) DC line current at the inverter during DC line fault with a fault resistance of 20 at 50kM from the rectifier end. Figure. 3.20(e) AC voltage at the input terminals of the rectifier during DC line fault with a fault resistance of 20 at 50kM from the rectifier end. 166

50 Figure. 3.20(f) AC current at the input terminals of the rectifier during DC line fault with a fault resistance of 20 at 50kM from the rectifier end. Figure. 3.20(g) AC voltage at the input terminals of the inverter during DC line fault with a fault resistance of 20 at 50kM from the rectifier end. Figure. 3.20(h) AC current at the input terminals of the inverter during DC line fault with a fault resistance of 20 at 50kM from the rectifier end 167

51 Figure 3.21(a) and 3.21(b) represents the D.C voltage and current waveform of the HVDC transmission line when the line is subjected to a DC fault at 100kM from the rectifier end with a fault resistance of 20Ω. The duration of the fault on the transmission line is 0.03sec. When the HVDC model is simulated for the DC line fault at 100kM from the rectifier end it is observed that the DC line voltage at the rectifier suffer with large oscillations as in case of a DC line fault at the same location with other fault resistance, it is also observed that the frequency of oscillations is almost same when compared to the fault at the same location with other fault resistances as shown in Figure 3.16(a), but the magnitude of the oscillations is decreasing. The DC line voltage oscillates between 1p.u. as shown in Figure 3.21(a). The DC line current reaches to 2p.u. in 0.01sec as shown in Figure 3.21(b). The current starts decreasing due to the increasing firing angle. Figure 3.21(c) and 3.21(d) represents the DC line voltage and current at the inverter during DC line fault with a fault at 100kM from the rectifier end with a fault resistance of 20. The DC line voltage reduced to zero immediately after occurrence of fault and maintains zero till the fault has been cleared. The DC line voltage starts oscillating. The characteristics of the voltage and current do not change much with the variation of the fault resistance. Figure 3.21(e) and 3.21(f) represents AC line voltage and current at the input terminals of the rectifier and Figure 3.21(g) and 3.21(h) represents the AC line voltage and current at AC terminals of the inverter during the DC 168

52 line fault at 100kM from the rectifier end with a fault resistance of 20. From the Figure 3.21(e) and 3.21(g) it is observed that both on AC side of rectifier and inverter the voltage restores to normal operating voltage level after 0.03sec. From Figure 3.21(h) the AC line currents on the inverter side reached to zero at the instant of the fault but the current on the AC side of the rectifier crossed beyond the normal operating condition. Figure. 3.21(a) DC line voltage at the rectifier during DC line fault with a fault resistance of 20 at 100kM from the rectifier end. Figure. 3.21(b) DC line current at the rectifier during DC line fault with a fault resistance of 20 at 100kM from the rectifier end. 169

53 Figure. 3.21(c) DC line voltage at the inverter during DC line fault with a fault resistance of 20 at 100kM from the rectifier end. Figure. 3.21(d) DC line current at the inverter during DC line fault with a fault resistance of 20 at 100kM from the rectifier end. Figure. 3.21(e) AC voltage at the input terminals of the rectifier during DC line fault with a fault resistance of 20 at 100kM from the rectifier end. 170

54 Figure. 3.21(f) AC current at the input terminals of the rectifier during DC line fault with a fault resistance of 20 at 100kM from the rectifier end. Figure. 3.21(g) AC voltage at the input terminals of the inverter during DC line fault with a fault resistance of 20 at 100kM from the rectifier end. Figure. 3.21(h) AC current at the input terminals of the inverter during DC line fault with a fault resistance of 20 at 100kM from the rectifier end. 171

55 Figure 3.22(a) and 3.22(b) represents the D.C voltage and current waveform of the HVDC transmission line when the line is subjected to a DC fault at 150kM from the rectifier end with a fault resistance of 20Ω. The duration of the fault on the transmission line is 0.03sec and the time of occurrence of the fault is 0.6sec i.e. after the voltage and current of the HVDC transmission system reaches steady state. When the HVDC model is simulated for the DC line fault at 150kM from the rectifier end it is observed that the DC line voltage at the rectifier suffer with large oscillations as in case of a DC line fault at the same location with other fault resistance, it is also observed that the frequency of oscillations is almost same when compared to the fault at the same location with other fault resistances as shown in Figure 3.17(a), but the magnitude of the oscillations is decreasing. The DC line voltage oscillates between 1p.u. as shown in Figure 3.22(a). The DC line current rises to 2p.u. in 0.01sec as shown in Figure 3.22(b). The current starts decreasing due to the increasing firing angle. Figure 3.22(c) and 3.22(d) represents the DC line voltage and current at the inverter during DC line fault at 150kM from the rectifier end with a fault resistance of 20. The DC line voltage reduced to zero immediately after occurrence of fault and maintained zero till the fault has been cleared. The DC line voltage starts oscillating. The characteristics of the voltage and current do not change much with the variation of the fault resistance. Figure 3.22(e) and 3.22(f) represents AC line voltage and current at the input terminals of the rectifier and 172

56 Figure 3.22(g) and 3.22(h) represents the AC line voltage and current at AC terminals of the inverter during the DC line fault at 150kM from the rectifier end with a fault resistance of 20. From the Figure 3.22(e) and 3.22(g) it is observed that both on AC side of rectifier and inverter the voltage restores to normal operating voltage level after 0.03sec i.e. the voltage on the sides of the HVDC system are stable after the fault has been cleared. From Figure 3.22(h) the AC line currents on the inverter side reduces to zero at the instant of the fault but the current on the AC side of the rectifier crossed beyond the normal operating condition. Figure. 3.22(a) DC line voltage at the rectifier during DC line fault with a fault resistance of 20 at 150kM from the rectifier end. Figure. 3.22(b) DC line current at the rectifier during DC line fault with a fault resistance of 20 at 150kM from the rectifier end. 173

57 Figure. 3.22(c) DC line voltage at the inverter during DC line fault with a fault resistance of 20 at 150kM from the rectifier end. Figure. 3.22(d) DC line current at the inverter during DC line fault with a fault resistance of 20 at 150kM from the rectifier end. Figure. 3.22(e) AC voltage at the input end of the rectifier during DC line fault with a fault resistance of 20 at 150kM from the rectifier end. 174

58 Figure. 3.22(f) AC current at the input terminals of the rectifier during DC line fault with a fault resistance of 20 at 150kM from the rectifier end. Figure. 3.22(g) AC voltage at the input terminals of the inverter during DC line fault with a fault resistance of 20 at 150kM from the rectifier end. Figure. 3.22(h) AC current at the input terminals of the inverter during DC line fault with a fault resistance of 20 at150km from the rectifier end. 175

59 Figure 3.23(a) and 3.23(b) represents the D.C voltage and current waveform of the HVDC transmission line when the line is subjected to a DC fault at 200kM from the rectifier end with a fault resistance of 20Ω. The duration of the fault on the transmission line is 0.03sec and the time of occurrence of the fault is 0.6sec. When the HVDC model is simulated for the DC line fault at 200kM from the rectifier end it is observed that the DC line voltage at the rectifier suffer with large oscillations as in case of a DC line fault at the same location with other fault resistance, it is also observed that the frequency of oscillations is almost same when compared to the fault at the same location with other fault resistances as shown in Figure 3.18(a), but the magnitude of the oscillations is decreasing. The DC line voltage oscillates between 1.5p.u. as shown in Figure 3.23(a). The DC line current reaches to 2p.u. in 0.01sec as shown in Figure 3.23(b). The current starts decreasing due to the increasing firing angle. Figure 3.23(c) and 3.23(d) represents the DC line voltage and current at the inverter during DC line fault with a fault at 200kM from the rectifier end with a fault resistance of 20. The DC line voltage decreases to zero immediately after occurrence of fault and maintained zero till the fault has been cleared. The characteristics of the voltage and current do not change much with the variation of the fault resistance. Figure 3.23(e) and 3.23(f) represents AC line voltage and current at the input terminals of the rectifier and Figure 3.23(g) and 3.23(h) represents the AC line voltage and current at AC terminals of the inverter during the 176

60 DC line fault with a fault resistance of 20 at 200kM from the rectifier end. From the Figure 3.23(e) and 3.23(g) it is observed that both on AC side of rectifier and inverter the voltage restores to normal operating voltage level after 0.03sec i.e. the voltage on the sides of the HVDC system are stable after the fault has been cleared. From Figure 3.23(h) the AC line currents on the inverter side reduces to zero at the instant of the fault but the current on the AC side of the rectifier crossed beyond the normal operating condition. Figure. 3.23(a) DC line voltage at the rectifier during DC line fault with a fault resistance of 20 at 200kM from the rectifier end. Figure. 3.23(b) DC line current at the rectifier during DC line fault with a fault resistance of 20 at 200kM from the rectifier end. 177

61 Figure. 3.23(c) DC line voltage at the inverter during DC line fault with a fault resistance of 20 at 200kM from the rectifier end. Figure. 3.23(d) DC line current at the inverter during DC line fault with a fault resistance of 20 at 200kM from the rectifier end. Figure. 3.23(e) AC voltage at the input terminals of the rectifier during DC line fault with a fault resistance of 20 at 200kM from the rectifier end. 178

62 Figure. 3.23(f) AC current at the input terminals of the rectifier during DC line fault with a fault resistance of 20 at 200kM from the rectifier end. Figure. 3.23(g) AC voltage at the input terminals of the inverter during DC line fault with a fault resistance of 20 at 200kM from the rectifier end. Figure. 3.23(h) AC current at the input terminals of the inverter during DC line fault with a fault resistance of 20 at 200kM from the rectifier end. 179

63 Figure 3.24(a) and 3.24(b) represents the D.C voltage and current waveform of the HVDC transmission line when the line is subjected to a DC fault at 250kM from the rectifier end with a fault resistance of 20Ω. The duration of the fault on the transmission line is 0.03sec and the time of occurrence of the fault is 0.6sec. When the HVDC model is simulated for the DC line fault at 250kM from the rectifier end it is observed that the DC line voltage at the rectifier suffer with large oscillations as in case of a DC line fault at the same location with other fault resistance, it is also observed that the frequency of oscillations is almost same when compared to the fault at the same location with other fault resistances as shown in Figure 3.19(a), but the magnitude of the oscillations is decreasing. The DC line voltage oscillates between 1.5p.u. as shown in Figure 3.24(a). The DC line current reaches to 2p.u. in 0.01sec as shown in Figure 3.24(b). The current starts decreasing due to the increasing firing angle. Figure 3.24(c) and 3.24(d) represents the DC line voltage and current at the inverter during DC line fault with a fault at 250kM from the rectifier end with a fault resistance of 20. The DC line voltage decreases to zero immediately after occurrence of fault and maintained zero till the fault has been cleared. The characteristics of the voltage and current do not change much with the variation of the fault resistance. Figure 3.24(e) and 3.24(f) represents AC line voltage and current at the input terminals of the rectifier and Figure 3.24(g) and 3.24(h) represents the AC line voltage and current at AC terminals of the inverter during the 180

64 DC line fault with a fault resistance of 20 at 250kM from the rectifier end. From the Figure 3.24(e) and 3.24(g) it is observed that both on AC side of rectifier and inverter the voltage restores to normal operating voltage level after 0.03sec i.e. the voltage on the sides of the HVDC system are stable after the fault has been cleared. From Figure 3.24(h) the AC line currents on the inverter side reduces to zero at the instant of the fault but the current on the AC side of the rectifier crossed beyond the normal operating condition. Figure. 3.24(a) DC line voltage at the rectifier during DC line fault with a fault resistance of 20 at 250kM from the rectifier end. Figure. 3.24(b) DC line current at the rectifier during DC line fault with a fault resistance of 20 at 250kM from the rectifier end. 181

65 Figure. 3.24(c) DC line voltage at the inverter during DC line fault with a fault resistance of 20 at 250kM from the rectifier end. Figure (d) DC line current at the inverter during DC line fault with a fault resistance of 20 at 250kM from the rectifier end. Figure. 3.24(e) AC voltage at the input terminals of the rectifier during DC line fault with a fault resistance of 20 at 250kM from the rectifier end. 182

66 Figure. 3.24(f) AC current at the input terminals of the rectifier during DC line fault with a fault resistance of 20 at 250kM from the rectifier end. Figure. 3.24(g) AC voltage at the input terminals of the inverter during DC line fault with a fault resistance of 20 at 250kM from the rectifier end. Figure. 3.24(h) AC current at the input terminals of the inverter during DC line fault with a fault resistance of 20 at 250kM from the rectifier end. 183

67 The following are the observations made from the Figures 3.15 to The response of the HVDC system is almost similar for the faults on the DC transmission line irrespective of the location of the fault. It is observed from the DC voltage and current at the rectifier that the frequency of oscillations and the magnitude of voltage during the fault condition are changing when the faults are simulated at various distances. It is observed that the magnitude is decreasing with the fault distances from the rectifier end. From the Figures 3.15(a) and 3.20(a) it is observed that the frequency of oscillations of DC voltage during the DC line fault is almost same but the magnitude of the fault voltage is changing. In case of fault at 50kM with a fault resistance of 1 as shown in the Figure 3.15(a) the voltage starts oscillating during the time of fault and the peak of the voltage crosses beyond 1p.u. But for a fault at 50kM with a fault resistance of 20 as shown in Figure 3.20(a) the DC voltage oscillates and the peak of the oscillations is less than 1p.u. Frequency of oscillations is observed to be same as that of a fault, the DC line current at the rectifier during the time of fault depends upon 184

68 the fault resistance and it is observed that the magnitude of current decreases with increment in the fault resistance. The location of fault on a long DC transmission line is found to be a difficult task just by observing the voltage or the current oscillograms as parameters like fault resistances may influence and causes an error in exact location of the fault. From voltage oscillogram it is observed that frequency based fault location techniques may give more accurate results in location of faults on HVDC transmission line. DC line faults have been created and the data has been recorded for various values of fault resistance to generate the training data for the ANN. 3.7 HVDC SYSTEM DURING AC FAULT CONDITION AC FAULTS ON THE RECTIFIER SIDE AC faults are created using circuit breakers. The following are the faults created on the AC side of the rectifier single line to ground fault (LG), 185

69 line to line fault (LL), double line to ground fault (LLG) and symmetrical fault (LLL). The faults at various instants in a cycle have been created by changing the time of closing of the fault circuit breaker. The faults are created for duration of 0.05sec. It is observed from the Figure 3.25(a) that the DC line voltage at the rectifier crossed 1.5p.u in 0.01sec from the instant of the fault. It is observed that from Figure 3.25(b) that the DC line current reduces below 1p.u. during the AC fault on the rectifier end. The DC line voltage at the inverter is almost similar to that of the voltage at the rectifier. From the Figure 3.25(a) and 3.25(c) it is clear that the DC line voltage reaches 1.5p.u. in 0.01sec from the instant of the fault. And the DC line voltage settles at 1p.u. after the fault has been cleared i.e. after 0.05sec. The AC line voltage at the rectifier end undergoes changes as indicated in Figure 3.25(e), the faulty phase voltage drops to zero at the instant of the fault and maintenance zero till the fault has been cleared. The other phases have a significant impact due to the LG fault on one of the phases on the AC side of the rectifier. The AC side line current also suffers during the fault and has been clearly indicated in Figure 3.25(f). The AC line voltage and current at the 186

70 inverter during the LG fault on AC side of rectifier are as shown in Figure 3.25(g) and 3.25(h). Figure. 3.25(a) DC line voltage at the rectifier during single line to ground fault (LG) on the AC side of the rectifier. Figure. 3.25(b) DC line current at the rectifier during single line to ground fault (LG) on the AC side of the rectifier. Figure. 3.25(c) DC line voltage at the inverter during single line to ground fault (LG) on the AC side of the rectifier. 187

71 Figure. 3.25(d) DC line current at the inverter during single line to ground fault (LG) on the AC side of the rectifier. Figure. 3.25(e) AC voltage at the input terminals of the rectifier during single line to ground fault (LG) on the AC side of the rectifier. Figure. 3.25(f) AC current at the input terminals of the rectifier during single line to ground fault (LG) on the AC side of the rectifier. 188

72 Figure. 3.25(g) AC voltage at the input terminals of the inverter during single line to ground fault (LG) on the AC side of the rectifier. Figure. 3.25(h) AC voltage at the input terminals of the inverter during single line to ground fault (LG) on the AC side of the rectifier. The characteristics of voltage and current at the 4 measuring points on the HVDC model i.e. at the input and output of the rectifier and input and output of the inverter during LL, LLG and symmetrical faults LLL on the AC side of rectifier end are shown in Figure 3.26 to During these fault conditions the power transfer capacity of the transmission line suffers considerably. The DC line voltage and currents 189

73 oscillates between 0 and 1p.u. during the time of fault. The DC line voltage at the rectifier during LL fault on the AC side of the rectifier is as shown in figure 3.26(a). The DC voltage measured at the inverter input terminals is as shown in figure 3.26(c). It is observed that the DC voltage at both rectifier and inverter is similar. Similarly the DC line current at the rectifier is as shown in figure 3.26(b) and the DC current at the inverter is shown in figure 3.26(d). From the comparison of the DC line voltage at the rectifier or at the inverter as shown in figure 3.25(a) and 3.26(a) it is very difficult to discriminate the faults on the AC side of the system. Both voltage and current at the rectifier and inverter undergo similar changes. Figure 3.27 shows the voltage and current at the 4 measuring points on the HVDC model i.e. at the input and output of the rectifier and input and output of the inverter during LLG and on the AC side of rectifier. Figure. 3.26(a) DC line voltage at the rectifier during line to line fault (LL) on the AC side of the rectifier. 190

74 Figure. 3.26(b) DC line current at the rectifier during line to line fault (LL) on the AC side of the rectifier. Figure. 3.26(c) DC line voltage at the inverter during line to line fault (LL) on the AC side of the rectifier. Figure. 3.26(d) DC line current at the inverter during line to line fault (LL) on the AC side of the rectifier. 191

75 Figure. 3.26(e) AC voltage at the input terminals of the rectifier during line to line fault (LL) on the AC side of the rectifier. Figure. 3.26(f) AC current at the input terminals of the rectifier during line to line fault (LL) on the AC side of the rectifier. Figure. 3.26(g) AC voltage at the terminals of the inverter during line to line fault (LL) on the AC side of the rectifier. 192

76 Figure. 3.26(h) AC current at the terminals of the inverter during line to line fault (LL) on the AC side of the rectifier. Figure. 3.27(a) DC line voltage at the rectifier during double line to ground fault (LLG) on the AC side of the rectifier. Figure. 3.27(b) DC line current at the rectifier during double line to ground fault (LLG) on the AC side of the rectifier. 193

77 Figure. 3.27(c) DC line voltage at the inverter during double line to ground fault (LLG) on the AC side of the rectifier. Figure. 3.27(d) DC line current at the inverter during double line to ground fault (LLG) on the AC side of the rectifier. Figure. 3.27(e) AC voltage at the input terminals of the rectifier during double line to ground fault (LLG) on the AC side of the rectifier. 194

78 Figure. 3.27(f) AC current at the input terminals of the rectifier during double line to ground fault (LLG) on the AC side of the rectifier. Figure. 3.27(g) AC voltage at the terminals of the rectifier during double line to ground fault (LLG) on the AC side of the rectifier. Figure. 3.27(h) AC current at the terminals of the inverter during double line to ground fault (LLG) on the AC side of the rectifier. 195

79 Figure. 3.28(a) DC line voltage at the rectifier during symmetrical fault (LLL) on the AC side of the rectifier. Figure. 3.28(b) DC line current at the rectifier during symmetrical fault (LLL) on the AC side of the rectifier. Figure. 3.28(c) DC line voltage at the inverter during symmetrical fault (LLL) on the AC side of the rectifier. 196

80 Figure. 3.28(d) DC line current at the inverter during symmetrical fault (LLL) on the AC side of the rectifier. Figure. 3.28(e) AC voltage at the input terminals of the rectifier during symmetrical fault (LLL) on the AC side of the rectifier. Figure. 3.28(f) AC current at the input terminals of the rectifier during symmetrical fault (LLL) on the AC side of the rectifier. 197

81 Figure. 3.28(g) AC voltage at the terminals of the inverter during symmetrical fault (LLL) on the AC side of the rectifier. Figure. 3.28(h) AC current at the terminals of the inverter during symmetrical fault (LLL) on the AC side of the rectifier AC FAULTS ON THE INVERTER SIDE The DC line voltage at the rectifier during a single line to ground fault on the AC side of inverter is as shown in Figure 3.29(a). From the instant of the fault the DC line voltage reduses from 1p.u. to 0p.u. During this period the DC line current increases from 1p.u. to 2p.u. as shown in Figure 3.29(b). The DC line voltage and current at the input terminals of the inverter are shown in Figure 3.29(c) and 3.29(d). The AC voltage and current at the input terminals of the rectifier are as shown in 198

82 Figure 3.29(e) and 3.29(f). The AC line current increases during the instant of the fault and it drops down to zero and remains zero even after the clearance of the fault. The AC line current starts recovering after 0.02sec after the clearance of the fault. The AC line voltage and current at the output terminals of the inverter is as shown in the Figure 3.29(g) and 3.29(h). From Figure 3.29(g) it is observed that the phase voltage reduces to zero when a LG fault occurs on that phase. From Figure 3.29(h) the three phase currents are in phase during the single line to ground fault and remains zero till the fault has been cleared. Figure (a) DC line voltage at the rectifier during single line to ground fault (LG) on the AC side of the inverter. Figure. 3.29(b) DC line current at the rectifier during single line to ground fault (LG) on the AC side of the inverter. 199

83 Figure. 3.29(c) DC line voltage at the inverter during single line to ground fault (LG) on the AC side of the inverter. Figure. 3.29(d) DC line current at the inverter during single line to ground fault (LG) on the AC side of the inverter. Figure. 3.29(e) AC voltage at the input terminals of the rectifier during single line to ground fault (LG) on the AC side of the inverter. 200

84 Figure. 3.29(f) AC current at the input terminals of the rectifier during single line to ground fault (LG) on the AC side of the inverter. Figure. 3.29(g) AC voltage at the terminals of the rectifier during single line to ground fault (LG) on the AC side of the inverter. Figure. 3.29(h) AC current at the terminals of the inverter during single line to ground fault (LG) on the AC side of the inverter. 201

85 The characteristics of voltage and current at the 4 measuring points on the HVDC model i.e. at the input and output of the rectifier and input and output of the inverter during LL, LLG and symmetrical faults LLL on the AC side of inverter end are shown in Figure 3.30 to During these fault conditions the power transfer capacity of the transmission line suffers considerably. The DC line voltage drops down to 0 and current raise to 2p.u. during the fault. However after the clearance of the fault the voltage starts recovering. Figure 3.30(a) represents the DC line voltage at the rectifier when the HVDC model is subjected to a LL fault on the AC side of the inverter. The DC line voltage oscillates and reduces considerably and maintains low during the fault. After the fault has been cleared the voltage restores back to 1p.u. From Figure 3.30(b) the DC line current rises to 2p.u. in less than 0.01sec. However it starts restoring once the fault has been cleared and the voltage reaches to 1p.u, similar characteristics have been observed when the DC voltage and current has been measured from the inverter end as shown in Figure 3.30(c) and 3.30(d). Figure 3.30(e) and 3.30(f) represents the three phase voltage and current wave forms at the rectifier when the HVDC model is subjected to a LL fault on the AC side of the inverter. Figure 3.30(g) and 3.30(h) represents the three phase voltage and current wave forms at the inverter when the HVDC model is subjected to a LL fault on the AC side of the inverter. 202

86 Figure. 3.30(a) DC line voltage at the rectifier during line to line fault (LL) on the AC side of the inverter. Figure. 3.30(b) DC line current at the rectifier during line to line fault (LL) on the AC side of the inverter. Figure. 3.30(c) DC line voltage at the inverter during line to line fault (LL) on the AC side of the inverter. 203

87 Figure. 3.30(d) DC line inverter at the inverter during line to line fault (LL) on the AC side of the inverter. Figure. 3.30(e) AC voltage at the input terminals of the rectifier during line to line fault (LL) on the AC side of the inverter. Figure. 3.30(f) AC current at the input terminals of the rectifier during line to line fault (LL) on the AC side of the inverter. 204

88 Figure. 3.30(g) AC voltage at the terminals of the inverter during line to line fault (LL) on the AC side of the inverter. Figure. 3.30(h) AC current at the terminals of the inverter during line to line fault (LL) on the AC side of the inverter. Figure 3.31(a) represents the DC line voltage at the rectifier when the HVDC model is subjected to a LLG fault on the AC side of the inverter. The DC line voltage oscillates and falls down considerably and maintains low during the fault as in case of LL fault on the inverter side. After the fault has been cleared the voltage restores back to 1p.u. From Figure 3.31(b) the DC line current rises to 2p.u. in less than 0.01sec. However it starts restoring once the fault has been cleared and the voltage reaches to 1p.u. Similar characteristics have been observed when 205

89 the DC voltage and current has been measured from the inverter end as shown in Figure 3.31(c) and 3.31(d). Figure 3.31(e) and 3.31(f) represents the three phase voltage and current wave forms at the rectifier when the HVDC model is subjected to a LLG fault on the AC side of the inverter. Figure 3.31(g) and 3.31(h) represents the three phase voltage and current wave forms at the inverter when the HVDC model is subjected to a LLG fault on the AC side of the inverter. Figure. 3.31(a) DC line voltage at the rectifier during double line to ground fault (LLG) on the AC side of the inverter. Figure. 3.31(b) DC line current at the rectifier during double line to ground fault (LLG) on the AC side of the inverter. 206

90 Figure. 3.31(c) DC line voltage at the inverter during double line to ground fault (LLG) on the AC side of the inverter. Figure. 3.31(d) DC line current at the inverter during double line to ground fault (LLG) on the AC side of the inverter. Figure. 3.31(e) AC voltage at the input terminals of the rectifier during double line to ground fault (LLG) on the AC side of the inverter. 207

91 Figure. 3.31(f) AC current at the input terminals of the rectifier during double line to ground fault (LLG) on the AC side of the inverter. Figure. 3.31(g) AC voltage at the terminals of the inverter during double line to ground fault (LLG) on the AC side of the inverter. Figure. 3.31(h) AC current at the terminals of the inverter during double line to ground fault (LLG) on the AC side of the inverter. 208

92 Figure 3.32(a) represents the DC line voltage at the rectifier when the HVDC model is subjected to a symmetrical fault i.e. LLL fault on the AC side of the inverter. The DC line voltage oscillates and reduces considerably and remains low during the fault. After the fault has been cleared the voltage recovers back to 1p.u. The DC line current from Figure 3.32(b) rises to 2p.u. in less than 0.01sec. However it starts recovering once the fault has been cleared and the voltage rises to 1p.u. similar characteristics have been observed when the DC voltage and current has been measured from the inverter end as shown in Figure 3.32(c) and 3.32(d). Figure 3.32(e) and 3.32(f) represents the three phase voltage and current wave forms at the rectifier when the HVDC model is subjected to a LLL fault on the AC side of the inverter. Figure 3.32(g) and 3.32(h) represents the three phase voltage and current wave forms at the inverter when the HVDC model is subjected to a LLL fault on the AC side of the inverter. Figure. 3.32(a) DC line voltage at the rectifier during symmetrical fault (LLL) on the AC side of inverter. 209

93 Figure. 3.32(b) DC line current at the rectifier during symmetrical fault (LLL) on the AC side of inverter. Figure. 3.32(c) DC line voltage at the inverter during symmetrical fault (LLL) on the AC side of inverter. Figure. 3.32(d) DC line current at the inverter during symmetrical fault (LLL) on the AC side of inverter. 210

94 Figure. 3.32(e) AC line voltage at the rectifier during symmetrical fault (LLL) on the AC side of inverter. Figure. 3.32(f) AC line current at the rectifier during symmetrical fault (LLL) on the AC side of inverter. Figure. 3.32(g) AC line voltage at the inverter during symmetrical fault (LLL) on the AC side of inverter. 211

95 Figure. 3.32(h) AC line current at the inverter during symmetrical fault (LLL) on the AC side of inverter. The following observations have been made From the Figures 3.25 to From the Figures 3.25(a)and 3.29(a) the DC line voltage at the rectifier during an AC fault on the rectifier side and inverter side it is observed that the voltage falls very fast when a fault is located at the AC side of inverter. However incase of a fault on AC side of rectifier the DC line voltage oscillates and the magnitude of oscillations is positive. The magnitude of oscillation is between 1.5p.u. to 0p.u. The DC line current measured during LG Fault on the AC side of the inverter as shown in Figure 3.29(b) is similar to that of DC line fault. But for an LG fault on the AC side of a rectifier it oscillates between 1p.u. and 0p.u.during the time of fault. 212

96 Hence by observing the waveforms the faults on the AC side of the inverter, LG Faults on the AC side of rectifier and DC line faults can be discriminated. The classification of faults on the AC side of inverter like LG, LL, LLG and LLL may not be done just by observing the DC line voltage. Frequency based techniques may be adopted for more accurate classification of faults on the HVDC system 3.8 CALCULATION OF REVERSE VOLTAGE TRAVELLING WAVE (RVTW) The HVDC line is a distributed parameter line and hence it has the ability to support travelling waves of voltage and current. A circuit with distributed parameters has a finite velocity of electro magnetic field propagations. In such a circuit the change in voltage and current owing to switching lightening or short circuit, do not occur simultaneously in all parts of the circuit but spreads over in the form of travelling ware or surge. The transmission line is represented as LC combinations. The voltage at successive sections builds up gradually. The current wave associated with the voltage wave charges the capacitance travelling from one end to the other end. The current waveform sets up the magnetic field in the surrounding space. At the junctions, these travelling waves undergo reflections and refractions. 213

97 The reverse voltage travelling wave is calculated by (3.10) Where Vdc and Idc are the voltage and current of the DC line respectively and Zc is the surge impedance of the HVDC line. The reverse voltage travelling waves (RVTW) for various operating conditions of the HVDC system are shown in Figure 3.33 to The calculated RVTW has been given in annexure II. Table 3.1 represents the peak magnitude of the absolute reverse voltage travelling wave. From Figure 3.33 it is observed that the absolute maximum value of the reverse voltage travelling wave during the normal operating condition is less than 30. From Figure 3.36 it is clear that the absolute maximum value of the reverse voltage travelling wave for the AC faults on the rectifier side is above 200V and less than 450V. The absolute value of the reverse voltage travelling wave for the faults on the AC side of the inverter is in between 500V to 600V as shown in Figure From the Figure 3.34 and 3.35 it is clear that for the faults on the HVDC transmission line the absolute maximum value of the reverse voltage travelling wave is above 450V. 214

98 Figure Reverse voltage travelling wave at the rectifier under normal operating condition Figure. 3.34(a) Reverse voltage travelling wave at the rectifier during DC line fault with a fault resistance of 1 at 50kM from the rectifier end. Figure. 3.34(b) Reverse voltage travelling wave at the rectifier during DC line fault with a fault resistance of 1 at 100kM from the rectifier end. 215

99 Figure. 3.34(c) Reverse voltage travelling wave at the rectifier during DC line fault with a fault resistance of 1 at 150kM from the rectifier end. Figure. 3.34(d) Reverse voltage travelling wave at the rectifier during DC line fault with a fault resistance of 1 at 200kM from the rectifier end. Figure. 3.34(e) Reverse voltage travelling wave at the rectifier during DC line fault with a fault resistance of 1 at 250kM from the rectifier end. 216

100 Figure. 3.35(a) Reverse voltage travelling wave at the rectifier during DC line fault with a fault resistance of 20 at 50kM from the rectifier end. Figure. 3.35(b) Reverse voltage travelling wave at the rectifier during DC line fault with a fault resistance of 20 at 100kM from the rectifier end. Figure. 3.35(c) Reverse voltage travelling wave at the rectifier during DC line fault with a fault resistance of 20 at 150kM from the rectifier end. 217

101 Figure. 3.35(d) Reverse voltage travelling wave at the rectifier during DC line fault with a fault resistance of 20 at 200kM from the rectifier end. Figure. 3.35(e) Reverse voltage travelling wave at the rectifier during DC line fault with a fault resistance of 20 at 250 km from the rectifier end. Figure. 3.36(a) Reverse voltage travelling wave at the rectifier during single line to ground fault (LG) on the AC side of the rectifier. 218

102 Figure. 3.36(b) Reverse voltage travelling wave at the rectifier during line to line fault (LL) on the AC side of the rectifier. Figure. 3.36(c) Reverse voltage travelling wave at the rectifier during double line to ground fault (LLG) on the AC side of the rectifier. Figure. 3.36(d) Reverse voltage travelling wave at the rectifier during symmetrical fault (LLL) on the AC side of the rectifier. 219

103 Figure. 3.37(a) Reverse voltage travelling wave at the rectifier during single line to ground fault (LG) on the AC side of the inverter. Figure. 3.37(b) Reverse voltage travelling wave at the rectifier during line to line fault (LL) on the AC side of the inverter. Figure. 3.37(c) Reverse voltage travelling wave at the rectifier during double line to ground fault (LLG) on the AC side of the inverter. 220

104 Figure. 3.37(d) Reverse voltage travelling wave at the rectifier during symmetrical fault (LLL) on the AC side of the inverter. The following are the observations made from the waveforms of the Reverse voltage travelling wave during various operating conditions of the HVDC system. The RVTW for the DC line fault at various distances with a fault resistance of 1 are shown in Figures 3.34(a) to 3.34(e). From Figure 3.34(a) to 3.34(e) it is clear that the RVTW is oscillating and the peak of oscillation is almost constant at -800V. The RVTW for the DC line fault at various distances with a fault resistance of 20 are shown in Figures 3.35(a) to 3.35(e). The RVTW is observed to be at -500V peak when the fault resistance is increased to 20. However for both the fault resistances the frequency of oscillations is observed to be almost constant for a DC line fault at a given location. From the Figure 3.34(a) for the DC line fault at 50kM from the rectifier end with a fault resistance of 1 the peak value of the RVTW 221

105 is observed to be V and from the Figure 3.35(a) for a fault at same location with a fault resistance of 20 the peak is observed to be V. The detailed Analysis of RVTW is given in table The Figures 3.36(a) to 3.36(d) represent the RVTW at the rectifier during the AC faults on the rectifier side. For the faults on the AC side of the rectifier the RVTW is observed to be positive and oscillating. But for the faults on AC side of inverter as shown in the Figure 3.37(a) to 3.37(d) the RVTW is observed to be negative during the time of the fault. Therefore by analyzing the RVTW recorded at the rectifier end, based on the frequency domain, the fault classification and location technique of is proposed. 222

106 Table 3.1 Peak magnitude of the absolute reverse voltage travelling wave for various operating conditions of the HVDC system. S.No Details of the operating condition of the HVDC model fault location / Type of fault in km Time at highest magnitude from the time of occurrence of fault in sec Magnitude of Reverse voltage travelling wave In Volts 1 Normal DC Line fault with a fault resistance of DC Line fault with a fault resistance of LG AC fault at the input terminals of rectifier LL LLG LLL LG AC fault at the input terminals of Inverter LL LLG LLL

107 3.9 RESULTS AND DISCUSSIONS FFT ANALYSIS OF REVERSE VOLTAGE TRAVELLING WAVE (RVTW) The HVDC system simulated for various operating conditions has been analyzed using Fast Fourier Transforms. Table 3.2 represents dominance of the harmonic frequencies during various operating conditions. From Table 3.2 and Figure 3.38(a) it is clear that during the normal operating condition the harmonic frequencies are not much predominant. It is observed that from the FFT analysis of the RVTW during the normal operating conditions is much less than in case of fault condition. During the DC faults at various locations on 300kM long transmission line various frequencies are dominant as shown in Figure 3.38(b) and3.38(c). When the fault is at 50kM the frequency 1520Hz is predominant in the DC line when measured from rectifier end. From Figure 3.38(d) it is observed that during the AC faults on the rectifier side 120Hz is the predominant i.e. 2 nd harmonic frequency and from Figure 3.38(c) it is observed that during the AC faults on the inverter side 96Hz,i.e. 2 nd harmonic frequency on the inverter side is predominant. 224

108 Table. 3.2 Dominent frequency for various operating conditions of HVDC system S.No Details of Fault fault location Magnitude (a.u.) 1 Normal Dominant frequency (Hz) DC Line fault with a fault resistance of 1 DC Line fault with a fault resistance of 20 AC fault at the input terminals of rectifier AC fault at the input terminals of Inverter LG LL LLG LLL LG LL LLG LLL

109 Figure. 3.38(a) FFT plot of the reverse voltage travelling wave at the rectifier during normal operating condition Figure. 3.38(b) FFT plot of the reverse voltage travelling wave at the rectifier during DC line fault at various distances from the rectifier end when the fault resistance is 1. Figure. 3.38(c) FFT plot of the reverse voltage travelling wave at the rectifier during DC line fault at various distances from the rectifier end when the fault resistance is

110 Figure. 3.38(d) FFT plot of the reverse voltage travelling wave at the rectifier during various AC fault at the input terminals of the rectifier. Figure. 3.38(e) FFT plot of the reverse voltage travelling wave at the rectifier during various AC fault at the input terminals of the inverter FFT BASED LOCATION OF FAULT ON THE HVDC TRANSMISSION LINE When the RVTW hit the fault point, it is reflected back to the source end of the transmission line [145]. Then it is reflected again from the source end and returns back to the fault point. Since the duration of this complete cycle is 4 (where is the propagation time of the surge from the source end to the fault point) the main components of the 227

111 current signal after the circuit breaker operating has a frequency equal to So that the distance to the fault may be obtained as (3.11) Where D is the distance to the fault location and (3.12) v is the velocity of the travelling wave. Table 3.3 indicates the location of faults on the HVDC transmission line vs the actual location of the fault. Figure 4.39(a) shows the plot between the Absolute percentage error and the location of faults on the HVDC transmission line. From table 3.3 it is clear that the accuracy of the fault location suffers much with the fault moving away from the measuring point i.e. rectifier end. For a fault at 100kM away from the rectifier with a fault resistance of 1 the fault location is located as 95.4kM based on the dominant frequency and for a fault at 250kM away from the rectifier with a fault resistance of I is measured as kM. It is observed that the calculated fault location is not much dependent of fault resistance. 228

112 Table 3.3 Location of fault using FFT analysis Details of Fault DC Line fault with a fault resistance of 1 fault location (km) Dominant frequency (Hz) Location of the fault by FFT (km) DC Line fault with a fault resistance of Figure. 3.39(a) Percentage Error Vs Fault Location. 229

113 3.10 CLASSIFICATION OF FAULTS USING ANN The HVDC system has been simulated for various operating conditions. The calculated Reverse Voltage travelling wave from the recorded voltage and current at the DC end of the rectifier is used for training and testing of ANN. The training data has been developed after taking the local maximum value from every 0.8ms period of the reverse voltage travelling wave. The local maximum values are normalized and are used for training and testing the ANN. The ANN has been trained by using feed forward back propagation algorithm. Out of the data available, 20 sets are used for training and 10 sets of data are used for testing. Figure 3.39(b) shows the mean square error curve during the training of ANN for the classification of faults. ANN has taken 173 epochs to train to attain accuracy of Table 3.4 indicates the test results of ANN for various operating conditions of the HVDC system. It is observed that the ANN based classification is more accurate. From the table 3.4 it is observed that various operating conditions of the HVDC system with an error of 0.03%. 230

114 Table 3.4 Test results of ANN for the classification of faults in HVDC system Test Set No Normal Operation Location/Resistanc e DC Line Faults DCF 1 50 km /1Ω 2 50 km /20Ω 3 70 km /1Ω km /1Ω km /20Ω km /1Ω km /20Ω km /10Ω km /20Ω X km /10Ω Test Set No Fault resistance AC Faults LG LL LLG LLL 1 0.1Ω 2 0.4Ω 3 0.8Ω 4 1.2Ω 5 1.6Ω 6 1.8Ω 7 2.0Ω 8 2.2Ω X 9 5Ω 10 8Ω 231

115 Figure. 3.39(b) Mean square error curve during the training of ANN for the classification of faults in HVDC system LOCATION OF FAULTS IN HVDC SYSTEM USING ANN The DC line voltage and line current data is used to calculate the reverse voltage travelling wave as is in the case of classification of faults. The data has been generated by creating the fault at various locations in the transmission line with various fault resistances. The normalized data is used for the location of the faults. The 300kM long HVDC line is subjected to ground fault at different locations with various fault resistances. Out of the data available, 15 sets of data has been used for training ANN and 5 sets of data is used for testing ANN. Table 3.5 shows 232

116 the exact fault location verses calculated ANN output for various test patterns. Figure 3.39(b) shows the error plot during the training of ANN for the classification of faults. ANN has taken 41 epochs to train to an accuracy of e -13. Table 3.5 Location of fault verses calculated ANN output for various test patterns Fault location on HVDC Line in km Fault resistance

117 The faults on the HVDC transmission line have been analyzed using ANN and the location of fault for various distances has been listed in the table 3.5. It is observed that for a fault simulated at 150kM the location of fault for various fault resistances has been given by Neural Network as 148.6, , and For a fault located at 252kM away from the rectifier the location of fault given by the Neural Network for various fault resistances are 255.6, 257.1, and Therefore the HVDC system fault analysis by generating the training and testing 234

118 patterns from the RVTW can be adopted for the classification and location of faults. However the major drawback of the system is that more amounts of data is required for training the ANN. The accuracy of the results of ANN more depends on the number of training and testing patterns available WAVELET TRANSFORM ANALYSIS OF RVTW The calculated reverse voltage travelling wave has been analyzed using wavelet transform technique. The daubechies4(db4) wavelet has been used as mother wavelet for the analysis of the problem. HVDC system for various operating conditions i.e. normal and fault are analyzed and the energy of the wavelet coefficients for these operating conditions is listed in table 3.6. Figure 3.40 represents the plot of the wavelet coefficients in four levels for the reverse voltage travelling waves during the normal operation. It is observed that the energy of the wavelet coefficients during the normal operating conditions is not much predominant, the energy of the level 1 wavelet coefficients is less than 4. Figure 3.41 shows the detailed wavelet coefficients of the reverse voltage travelling waves during the AC fault on the AC side of the rectifier. Figure 3.41(a) shows the detailed wavelet coefficients during LG fault, Figure 3.41(b) shows the detailed wavelet coefficient during the LL fault, Figure 235

119 3.41(c) shows the detailed wavelet coefficient during the LLG fault, and Figure 3.41(d) shows the detailed wavelet coefficient during the symmetrical fault on the AC side of the rectifier. Similarly Figure 3.42 shows the detailed wavelet coefficients of the reverse voltage travelling waves during the AC fault on the AC side of the inverter. Figure 3.42(a) shows the detailed wavelet coefficients during LG fault, Figure 3.42(b) shows the detailed wavelet coefficient during the LL fault, Figure 3.42(c) shows the detailed wavelet coefficient during the LLG fault, and Figure 3.42(d) shows the detailed wavelet coefficient during the symmetrical fault on the AC side of the inverter. It is observed that during AC faults the energy of the level 1 wavelet coefficients is less than 10. Figure 3.43 shows the detailed wavelet coefficients in 4 levels of the reverse voltage travelling waves during DC line fault at 50kM from the rectifier end with a fault resistance of 1ohm and 20 ohm respectively. It is observed that during the DC line fault the energy of the wavelet coefficient is much higher when compared to that of other operating conditions of the HVDC system. However the energy of the wavelet coefficients decreases with increase in the fault system. Figure 3.44 to 3.47 represents the energy of the wavelet coefficients for the faults at 100, 150, 200 & 250kM respectively. Similar observations have been made for the faults at various distances from the rectifier end when compared to that of the DC line fault at 50kM. In all the above cases the energy of the wavelet coefficients is above 100 and is reducing with 236

120 increase in fault resistance. Hence, various operating conditions of HVDC system can be classified using wavelet transform technique. Table 3.6 The energy of the wavelet coefficients for varying operating conditions of the HVDC system. Details of Fault fault location Wavelet Coefficients A level1 level2 level3 level4 Normal DC Line fault with a fault resistance of 1 DC Line fault with a fault resistance of 20 AC fault at the input terminals of rectifier AC fault at the input terminals of Inverter 50 km km km km km km km km km km LG fault LL fault LLG fault LLL fault LG fault LL fault LLG fault LLL fault

121 Figure Detailed wavelet coefficients in four levels for the reverse voltage travelling wave at the rectifier under normal operating condition Figure (a) Detailed wavelet coefficients in four levels for the RVTW at the rectifier during single line to ground fault (LG) on the AC side of the rectifier. Figure. 3.41(b) Detailed wavelet coefficients in four levels for the RVTW at the rectifier during line to line fault (LL) on the AC side of the rectifier. 238

122 Figure. 3.41(c) Detailed wavelet coefficients in four levels for the RVTW at the rectifier during double line to ground fault (LLG) on the AC side of the rectifier. Figure. 3.41(d) Detailed wavelet coefficients in four levels for the RVTW at the rectifier during symmetrical fault (LLL) on the AC side of the rectifier. Figure. 3.42(a) Detailed wavelet coefficients in four levels for the RVTW at the rectifier during single line to ground fault (LG) on the AC side of the inverter. 239

123 Figure. 3.42(b) Detailed wavelet coefficients in four levels for the RVTW at the rectifier during line to line fault (LL) on the AC side of the inverter. Figure. 3.42(c) Detailed wavelet coefficients in four levels for the RVTW at the rectifier during double line to ground fault (LLG) on the AC side of the inverter. Figure. 3.42(d) Detailed wavelet coefficients in four levels for the RVTW at the rectifier during symmetrical fault (LLL) on the AC side of the inverter. 240

124 Figure. 3.43(a) Detailed wavelet coefficients in four levels for the RVTW at the rectifier during DC line fault with a fault resistance of 1 at 50 km from the rectifier end. Figure. 3.43(b) Detailed wavelet coefficients in four levels for the RVTW at the rectifier during DC line fault with a fault resistance of 20 at 50 km from the rectifier end. Figure. 3.44(a) Detailed wavelet coefficients in four levels for the RVTW at the rectifier during DC line fault with a fault resistance of 1 at 100 km from the rectifier end. 241

125 Figure (b) Detailed wavelet coefficients in four levels for the RVTW at the rectifier during DC line fault with a fault resistance of 20 at 100 km from the rectifier end. Figure. 3.45(a) Detailed wavelet coefficients in four levels for the RVTW at the rectifier during DC line fault with a fault resistance of 1 at 150 km from the rectifier end Figure. 3.45(b) Detailed wavelet coefficients in four levels for the RVTW at the rectifier during DC line fault with a fault resistance of 20 at 150 km from the rectifier end. 242

126 Figure. 3.46(a) Detailed wavelet coefficients in four levels for the RVTW at the rectifier during DC line fault with a fault resistance of 1 at 200 km from the rectifier end. Figure. 3.46(b) Detailed wavelet coefficients in four levels for the RVTW at the rectifier during DC line fault with a fault resistance of 20 at 200 km from the rectifier end. Figure. 3.47(a) Detailed wavelet coefficients in four levels for the RVTW at the rectifier during DC line fault with a fault resistance of 1 at 250 km from the rectifier end. 243

127 Figure. 3.47(b) Detailed wavelet coefficients in four levels for the RVTW at the rectifier during DC line fault with a fault resistance of 20 at 250 km from the rectifier end LOCATION OF FAULTS ON DC TRANSMISSION LINE USING WAVELET TRANSFORM TECHNIQUES When a fault occurs, the fault generated travelling wave propagates along the transmission line. The wave front starts at the measuring location at the time t=t1, again the wave front reaches back the observing location at time t=t2, then the location of the fault can be measured by location (3.13) Where D distance from the fault location to the measuring Velocity of the travelling wave in km/sec t - time delay in sec. (where t t 2 t1 ) 244

128 The level -1 detailed coefficients of the reverse voltage travelling wave during DC line fault at various distances are shown in Figure Figure. 3.48(a) shows the energy of level-1 wavelet coefficient of the reverse voltage travelling waves during DC line fault at 50 km from the rectifier end. From the above equation the t can be calculated as t = = (e) Similarly the fault location is calculated from Figure 3.48(b) to Table 3.7 Fault location using wavelet transform technique S. No Fault location in km T1 T2 t Fault Location using WT in km

129 Table 3.7 indicates the location of faults on the HVDC transmission line vs the actual location of the fault by using the wavelet coefficients. For a fault located at 50 km the calculated fault location from the wavelet analysis of the reverse voltage travelling wave was found to be when the fault is located at 100kM the fault location is observed to be at 99.94kM. Similarly for a fault at 150kM the calculated fault location is kM. Hence it is very clear that the wavelet based fault location technique is most accurate technique in locating the faults on the DC transmission line of the HVDC system. Figure. 3.48(a) Detailed wavelet coefficients (levels-1) for the RVTW at the rectifier during DC line fault at 50 km from the rectifier end. Figure. 3.48(b) Detailed wavelet coefficients (levels-1) for the RVTW at the rectifier during DC line fault at 100 km from the rectifier end. 246

130 Figure. 3.48(c) Detailed wavelet coefficients (levels-1) for the RVTW at the rectifier during DC line fault at 150 km from the rectifier end. Figure. 3.48(d) Detailed wavelet coefficients (levels-1) for the RVTW at the rectifier during DC line fault at 200 km from the rectifier end. Figure. 3.48(e) Detailed wavelet coefficients (levels-1) for the RVTW at the rectifier during DC line fault at 250 km from the rectifier end. 247

131 3.12 COMPARISION OF FFT, WAVELET AND ANN BASED FAULT LOCATION Table 3.8 shows the comparison between above three techniques for the location of fault in HVDC transmission line. From the table 3.8 it is observed that for a fault located at 100kM away from the rectifier end the FFT analysis technique gave the location as 95.8kM, ANN technique gave the location as 98.4kM and from the wavelet analysis technique the location of fault is calculated as 98.4kM. Similarly for a fault located at 200kM away from the rectifier with a fault resistance of 20 the fault location calculated by the FFT analysis technique is where as by using ANN it has been calculated as kM. However the wavelet analysis technique gave most accurate result of kM. Comparing the location of faults using the above three techniques it can be concluded that the wavelet based fault location is most accurate. The accuracy also depends on the sampling frequency and amount of data available. Figure 3.49 shows the comparison of the three methods of the fault location systems. 248

132 Table 3.8 Comparison of the fault location systems with exact fault location Details of Fault DC Line fault with a fault resistance of 1 DC Line fault with a fault resistance of 20 fault location (km) Fault location (km) using FFT using ANN using WT Figure Comparison of the fault location systems with exact fault location 249

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