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DC transmission system corona performance
Journal of Electrostatics, 22 (1989) 279-288
279
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
L A B O R A T O R Y I N V E S T I G A T I O N OF H Y B R I D AC/DC TRANSMISSION SYSTEM CORONA PERFORMANCE
M.R. RAGHUVEER
Department of Electrical Engineering, University of Manitoba, Winnipeg, Manitoba (Canada R3T 2N2) (Received July 12, 1988; accepted in revised form March 19, 1989)
Summary The corona performance of a laboratory model single-phase hybrid ac/dc line has been experimentally investigated. The experimental results presented include the corona current behaviour in the dc line, variation of dc corona injected direct current in the ac line with dc potential and ground level lateral profiles of ionic current density. The dependance of the corona behaviour of the system on ac potential has also been shown.
1. Introduction With the growing demand for electric power and the difficulty of obtaining new right of way, various novel schemes have been proposed to increase the power transmission capacity of an existing transmission corridor. One such scheme entails the conversion of one circuit of a double-circuit three-phase ac line to operate in dc transmission [1 ]. Another scheme, under consideration by a utility, involves the replacement of the two sky wires of a single-circuit three-phase ac line with insulated conductors and operating them in the bipolar dc transmission mode. Both these schemes are a form of ac/dc hybrid transmission and have good potential for increasing power transfer. Because of the close proximity of the ac and dc conductors in a hybrid transmission system, the electric fields due to them will interact and this affects the corona performance of each conductor [1,2]. As in dc transmission, the dc corona current consists of bipolar and unipolar components. The former component flows between the positive and negative poles while the latter, consisting of positive and negative ions emanating from the ionized zones of the positive and negative conductors respectively, is collected by either the ground plane or the ac conductors [2]. Chartier et al. [1] proposed a method of calculating conductor and ground level electric fields in a hybrid system and used their technique to compute radio interference (RI) and audible noise (AN) levels. More recently Maruvada and Drogi [2] have presented an analysis of 0304-3886/89/$03.50
© 1989 Elsevier Science Publishers B.V.
280
the hybrid line ionized field. The resulting nonlinear boundary value problem is solved using a numerical procedure [ 3,4 ] which yields the direct corona current component in the ac conductors and ground level values of ionic current density and electric field intensity. An important assumption made in their analysis is that the ac conductors of the hybrid system may be assumed to be at zero potential. This assumption is justified, in their work, on the basis that the trajectories of ions are practically uninfluenced by the presence of ac conductor sinusoidal potential. In the present paper a single-phase laboratory model hybrid system has been considered. The following sections contain a description of this system and a discussion of the experimental results obtained, which include the corona characteristics of the dc line, the behaviour of the dc current component in the ac line and ground level lateral profiles of ionic current density. The results clearly show the effect that the potential on the ac conductor has on the corona performance of the hybrid system. 2. Description of laboratory model
The hybrid line model system, Fig. 1, consisted of two 3 m long 14 AWG (0.0815 cm radius) bare copper conductors situated horizontally one above the other at heights of 80 and 55 cm. The top conductor was connected to a 120 kV dc supply while the lower conductor could be energized with alternating potential from a 120V/50kV, 3kVA, high voltage transformer. The ground plane was simulated by a conducting mat placed on the floor. For the geometrical configuration of the above system, the ratio of the height to radius of the ac and dc conductors are 981 and 675 respectively. While the above system is not completely representative of an actual hybrid transmission system, it is known [5 ] that trends in the results are more sensitive to the ratio of height to radius than to values of height and conductor radius.
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281 3. E x p e r i m e n t a l
The current in the ac line was measured by monitoring the voltage drop across a 10 kgt resistor inserted at the b o t t o m end of the high voltage winding of the transformer energizing the ac line. This voltage drop was fed to a Data Precision 6000 datalyzer which was programmed to display the waveform in units of current. A H P 7470A plotter connected to the datalyzer was used to obtain plots of waveforms. The corona current in the dc line (I, Fig. 1 ) was monitored by inserting a 10 k ~ resistor in series with the dc line between the dc source and the line. A small-sized battery-operated digital voltmeter was connected across the resistor to read the voltage drop across it. The resistor-voltmeter combination was shielded and the meter display read by means of a telescope. Ground level ionic current density was measured by a probe consisting essentially of a metallic plate 2 cm square in size. The plate which acted as a collector of ionic current, was connected to a preamplifier, the output of which was fed to the datalyzer. The plate was placed horizontally at ground level for measuring ion currents. W h e n both the ac and dc lines are energized and the dc conductor is in corona, the plate current consists of unipolar ionic current and 60 Hz displacement current components. The datalyzer was programmed to average the current intercepted by the plate over one power frequency cycle. This yielded the average ionic current over a duration of one cycle of power frequency and constituted one sample. In addition, the program enabled the monitoring of the trend of this average value over 512 samples. As each sample was procured, the datalyzer provided a graphical display of the computed average values as well as readings of the minimum, maximum and mean values at each step. The mean values over 512 samples were used to draw the profiles of ground level ionic current density. 4. Results and discussion
All tests were conducted with the dc conductor energized at positive polarity. With no potential on the dc conductor, the corona inception voltage of the ac line was 21 kV RMS. In the discussions that follow all ac voltages are R M S values. 4.1. dc line corona current characteristics
Figure 2 shows the variation o f d c line corona current (I, Fig. 1 ) with applied dc line potential obtained with the ac line at zero potential, 10 kV and 25 kV. In each case the dc line corona current increases with dc line potential. For any value of this potential the dc corona current increases as the magnitude of the ac line potential is increased. Figure 2 also shows that the knee of the corona
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characteristic is sharper when the ac line is energized. It is also seen that the dc line corona inception voltage is lowest when the ac line is energized at 25 kV. It is possible to explain the observed decrease in dc line corona onset voltage, in the presence of ac line potential, by examining the unperturbed (i.e. electrostatic) stress on the conductor surfaces. These stresses are calculated by simulating each conductor by an unknown line charge and imaging them with respect to ground. Next, the matrix equation V=PQ is formed in which V a n d Q are column matrices of known potentials and unknown line charge magnitudes respectively and P is the square matrix of Maxwell's potential coefficients. The potential coefficients are known from the geometry of the system. Once the charges are found, the electric field is found by superposition of the contributions of all charges present in the system. From Fig. 2, with the ac line at zero potential, the dc line corona onset voltage is 35 kV. Corresponding to this voltage the maximum stress on the dc conductor, at a point on its surface closest to ground, is found to be 59.81 k V / c m which is the onset gradient. When the ac line is energized at 10 kV (v (t) = 1 0 ~ 2 cos o)t) and the dc line
283 is at zero potential the ac line gradient is below its onset value. As the dc line potential, Vdc, is increased, the time-dependent maximum gradient on the dc conductor increases and is given by the expression (1.71 Vdc- 5.73 cos tot) kV/ cm. Equating the maximum value of this expression, (1.71 Vdc+ 5.73 ), to the onset gradient of the dc conductor one finds the corresponding onset voltage to be 31.62 kV which is in good agreement with experimentally recorded data. Further, calculations show that under these conditions the gradient at the ac conductor is still well below its onset value. When the ac line potential is 25 kV the time-dependent maximum gradient on the dc conductor is given by (1.71 Vdc- 14.32 cos tot) kV/cm. Equating the maximum value of this gradient to the onset gradient, 59.81 kV/cm, the dc line corona onset voltage is found to be 26.6 kV. From Fig. 2 the experimentally observed onset value is close to 10 kV. The reason for this discrepancy is because the calculations ignore the effect of space charge. At an ac line voltage of 25 kV, with the dc line at zero potential, the ac line is already in corona. When the dc line is energized, it introduces a bias on the ac field; the ac field increases during negative swings and decreases during positive swings of the ac line potential. The negative ions produced during the enhanced negative mode of ac corona experience a net motive force directed towards the dc conductor and the dc conductor surface field is increased. This effect increases with dc line potential and dc line corona onset occurs when the maximum gradient at its surface equals the onset gradient due to the combined effects of applied line potentials and space charge. In both cases, when the ac line is energized at 10 or 25 kV, dc line corona activity commences first during the negative half cycle of the ac potential; dc line corona activity during the positive half cycle of ac voltage begins at a higher dc applied potential. 4.2. dc currents injected into the ac line In addition to modifying the corona characteristics of the dc line, the ac conductor also acts as a collector of some of the ions created by the dc corona process occurring around the dc conductor. Irrespective of the value of ac line potential, there always exists a net motive force which acts on some of the ions and directs them towards the ac conductor. This results in a dc current flow in the ac line. The effect of ac potential has been studied in Ref. [2] where the authors state that a non-zero ac potential has the effect of increasing the transit time of ions between the dc and ac conductors. This is equivalent to a decreased ionic mobility. The authors also found that the trajectories of ions are practically independent of ac potential and therefore computed the dc current injected into the ac line by assuming that the ac conductor to be at zero potential. Figure 3 shows the magnitude of the dc injected current as a function of dc applied potential for ac line potentials of 0, 10 and 25 kV. The magnitudes of
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the currents were obtained by recording the waveform across the 10 kg2 resistor in the ac circuit and computing its average value. The curves of Fig. 3 demonstrate that the injected current increases with ac potential for fixed value of dc voltage. This may be attributed to the increased dc line corona activity that accompanies an increase in ac potential. Comparison of Figs. 2 and 3 shows that the dc line corona current and the injected currents in the ac line are almost equal for a set of values of dc and ac potentials. In fact, the injected currents are slightly lower in magnitude and the curves of Fig. 3 lie below the corresponding curves of Fig. 2. For a given condition, the difference between dc line current and the injected current represents the total ionic current flowing to ground. Figure 4 shows three waveforms identified as A, B and C which are the ac line potential, the current in the ac line obtained by measurement across the resistor in the ac circuit, and the direct current flowing in the ac line respectively. These waveforms correspond to the condition when the dc and ac lines are energized at 60 kV and 10 kV respectively. The waveform of direct current
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was obtained in the following manner. First the waveform labelled B (Fig. 4) was obtained by measurement across the dropping resistor employing direct coupling. Next the measurement was repeated employing capacitive coupling. Subtraction of this waveform from waveform B yielded waveform C. The applied voltage was recorded by connection of a voltage divider between the ac bus and ground. Waveform C, Fig. 4, shows slight maxima and minima which occur at some time interval after the minima and maxima of the applied ac voltage, waveform A. When the voltage is a minimum, this condition enhances the dc line corona process and more positive ions are produced. After a time interval corresponding to the time of transit between the dc and ac conductors some of these ions arrive at the ac conductor and account for the observed maximum of current. A similar explanation accounts for the presence of the minimum of the dc current waveform. Waveform B is comprised of three components - a dc injected current, displacement current and ac line corona current components. The dc current component is clearly evident by the fact that waveform B has a positive offset. The average value of waveforms B and C are equal. During the negative half cycle of voltage, waveform B exhibits a hump which peaks prior to the occurrence of the voltage minimum. This hump occurs due to ac line corona which commences when the field at the surface of the ac conductor reaches the onset value due to the combined effect of applied potentials and positive ion space charge. On the other hand ac conductor corona is suppressed during the positive excursion of the ac conductor voltage.
286
Due to the presence of the ac corona related hump in a half cycle, a dc component of current exists in the ac line. This component, which is included in the measurements reported in Section 4.2, is quite small in magnitude for the reported experimental conditions. This is verified by comparing the positive and negative peaks of the capacitively coupled waveform across the dropping resistor. For the experimental conditions corresponding to those of Fig. 4, the maximum and minimum values are 848 and 783 pA respectively. The difference is 65 ~A and this corresponds to an average value of about 1 ~A. The presence of a direct current in the ac line is important from a practical point of view; if relatively large direct currents flow in the ac line they may cause saturation related problems in the transformers connected at the end of the lines [2].
4.3. Ground level lateral profiles of ionic current density Figure 5 shows normalized ground level lateral profiles of ionic current density. The solid curve is obtained when the ac line is removed and the dc line energized at 60 kV. The dashed curve profile corresponds to the case when both lines are present but the ac line is held at zero potential. The values of the current density in the latter case are expressed in per unit using the value obtained under the dc line, with the ac line absent, as the base value. One per unit corresponds to a current density of 1.05 n A / c m 2. From this figure, the shielding effect of the ac line is apparent. The maximum of current density, with both lines present, does not occur below the line but at some distance removed from it. Figure 6 shows similar profiles obtained with both lines present. Here, the dc line is energized at 60 kV and the ac line energized at potentials of 10, 20
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Fig. 6. Ground level lateral profiles of ionic current density with ac line energized at potentials of 0, 10, 20, and 25 kV; dc line at 60 kV in all cases.
and 25 kV. The profile corresponding to the case when the ac line is held at zero potential has been included for comparison. In all cases, as in Fig. 5, the values of current density are expressed in per unit using the same base value. The profiles of Fig. 6 show the influence of ac line potential. At a point on the ground directly below the lines the current density first increases as the ac line potential is increased from 0 to 10 kV; but subsequent increases cause the current density at the same point to decrease. At an ac line potential of 25 kV, the current density is greater than that obtained with the ac line held at zero potential. The profile obtained with the ac line at 10 kV ( 10 kV profile ) lies above that obtained with the ac line at 0 kV (0 kV profile) except for a narrow range straddling the location of the maximum exhibited in the latter case. In contrast, the 20 kV profile lies below the 0 and 10 kV profiles and the 25 kV profile is located below the 20 kV profile throughout the range of lateral distance considered. 5. C o n c l u s i o n s
A single-phase laboratory model hybrid ac/dc system has been considered and experimental results presented which show the existence of a mutual interaction between the dc and ac electric fields. This interaction causes the ac potential to influence dc line corona current characteristics, the dc current
288
component in the ac line and ground level lateral profiles of ionic current density. Similar results may be expected for other geometrical configurations and negative polarity of dc applied potential. Acknowledgement
Financial support from NSERC Canada is gratefully acknowledged. Thanks are also due to Mr. G. Toole for his technical assistance.
References 1 V.L. Chartier, S.H. Sarkinen, R.D. Stearns and A.L. Burns, Investigation of corona and field effects of AC/DC hybrid transmission lines, IEEE Trans. Power Appar. Syst., PAS-100(1 ) (1981) 72-80. 2 P. Sarma Maruvada and S. Drogi, Field and ion interaction of hybrid ac/dc transmission lines, IEEE Trans. Power Delivery, 3 (July 1988) 1165-1172. 3 P. Sarma Maruvada and W. Janischewskyj, Analysis of corona losses on dc transmission lines: Unipolar lines, IEEE Trans. Power Appar. Syst., PAS-88(5) (1969) 718-731. 4 P. Sarma Maruvada and W. Janischewskyj, Analysis of corona losses on dc transmission lines: II Bipolar lines, IEEE Trans. Power Appar. Syst., PAS-88(10) {1969) 1476-1491. 5 W. Janischewskyj, P. Sarma Maruvada and G. Gela, Corona losses and ionized fields of HVDC transmission lines, CIGRE 36.09 ( 1982 ) 10. I
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279
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
L A B O R A T O R Y I N V E S T I G A T I O N OF H Y B R I D AC/DC TRANSMISSION SYSTEM CORONA PERFORMANCE
M.R. RAGHUVEER
Department of Electrical Engineering, University of Manitoba, Winnipeg, Manitoba (Canada R3T 2N2) (Received July 12, 1988; accepted in revised form March 19, 1989)
Summary The corona performance of a laboratory model single-phase hybrid ac/dc line has been experimentally investigated. The experimental results presented include the corona current behaviour in the dc line, variation of dc corona injected direct current in the ac line with dc potential and ground level lateral profiles of ionic current density. The dependance of the corona behaviour of the system on ac potential has also been shown.
1. Introduction With the growing demand for electric power and the difficulty of obtaining new right of way, various novel schemes have been proposed to increase the power transmission capacity of an existing transmission corridor. One such scheme entails the conversion of one circuit of a double-circuit three-phase ac line to operate in dc transmission [1 ]. Another scheme, under consideration by a utility, involves the replacement of the two sky wires of a single-circuit three-phase ac line with insulated conductors and operating them in the bipolar dc transmission mode. Both these schemes are a form of ac/dc hybrid transmission and have good potential for increasing power transfer. Because of the close proximity of the ac and dc conductors in a hybrid transmission system, the electric fields due to them will interact and this affects the corona performance of each conductor [1,2]. As in dc transmission, the dc corona current consists of bipolar and unipolar components. The former component flows between the positive and negative poles while the latter, consisting of positive and negative ions emanating from the ionized zones of the positive and negative conductors respectively, is collected by either the ground plane or the ac conductors [2]. Chartier et al. [1] proposed a method of calculating conductor and ground level electric fields in a hybrid system and used their technique to compute radio interference (RI) and audible noise (AN) levels. More recently Maruvada and Drogi [2] have presented an analysis of 0304-3886/89/$03.50
© 1989 Elsevier Science Publishers B.V.
280
the hybrid line ionized field. The resulting nonlinear boundary value problem is solved using a numerical procedure [ 3,4 ] which yields the direct corona current component in the ac conductors and ground level values of ionic current density and electric field intensity. An important assumption made in their analysis is that the ac conductors of the hybrid system may be assumed to be at zero potential. This assumption is justified, in their work, on the basis that the trajectories of ions are practically uninfluenced by the presence of ac conductor sinusoidal potential. In the present paper a single-phase laboratory model hybrid system has been considered. The following sections contain a description of this system and a discussion of the experimental results obtained, which include the corona characteristics of the dc line, the behaviour of the dc current component in the ac line and ground level lateral profiles of ionic current density. The results clearly show the effect that the potential on the ac conductor has on the corona performance of the hybrid system. 2. Description of laboratory model
The hybrid line model system, Fig. 1, consisted of two 3 m long 14 AWG (0.0815 cm radius) bare copper conductors situated horizontally one above the other at heights of 80 and 55 cm. The top conductor was connected to a 120 kV dc supply while the lower conductor could be energized with alternating potential from a 120V/50kV, 3kVA, high voltage transformer. The ground plane was simulated by a conducting mat placed on the floor. For the geometrical configuration of the above system, the ratio of the height to radius of the ac and dc conductors are 981 and 675 respectively. While the above system is not completely representative of an actual hybrid transmission system, it is known [5 ] that trends in the results are more sensitive to the ratio of height to radius than to values of height and conductor radius.
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Fig. 1. Single-phase hybrid-line laboratory model.
_
281 3. E x p e r i m e n t a l
The current in the ac line was measured by monitoring the voltage drop across a 10 kgt resistor inserted at the b o t t o m end of the high voltage winding of the transformer energizing the ac line. This voltage drop was fed to a Data Precision 6000 datalyzer which was programmed to display the waveform in units of current. A H P 7470A plotter connected to the datalyzer was used to obtain plots of waveforms. The corona current in the dc line (I, Fig. 1 ) was monitored by inserting a 10 k ~ resistor in series with the dc line between the dc source and the line. A small-sized battery-operated digital voltmeter was connected across the resistor to read the voltage drop across it. The resistor-voltmeter combination was shielded and the meter display read by means of a telescope. Ground level ionic current density was measured by a probe consisting essentially of a metallic plate 2 cm square in size. The plate which acted as a collector of ionic current, was connected to a preamplifier, the output of which was fed to the datalyzer. The plate was placed horizontally at ground level for measuring ion currents. W h e n both the ac and dc lines are energized and the dc conductor is in corona, the plate current consists of unipolar ionic current and 60 Hz displacement current components. The datalyzer was programmed to average the current intercepted by the plate over one power frequency cycle. This yielded the average ionic current over a duration of one cycle of power frequency and constituted one sample. In addition, the program enabled the monitoring of the trend of this average value over 512 samples. As each sample was procured, the datalyzer provided a graphical display of the computed average values as well as readings of the minimum, maximum and mean values at each step. The mean values over 512 samples were used to draw the profiles of ground level ionic current density. 4. Results and discussion
All tests were conducted with the dc conductor energized at positive polarity. With no potential on the dc conductor, the corona inception voltage of the ac line was 21 kV RMS. In the discussions that follow all ac voltages are R M S values. 4.1. dc line corona current characteristics
Figure 2 shows the variation o f d c line corona current (I, Fig. 1 ) with applied dc line potential obtained with the ac line at zero potential, 10 kV and 25 kV. In each case the dc line corona current increases with dc line potential. For any value of this potential the dc corona current increases as the magnitude of the ac line potential is increased. Figure 2 also shows that the knee of the corona
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characteristic is sharper when the ac line is energized. It is also seen that the dc line corona inception voltage is lowest when the ac line is energized at 25 kV. It is possible to explain the observed decrease in dc line corona onset voltage, in the presence of ac line potential, by examining the unperturbed (i.e. electrostatic) stress on the conductor surfaces. These stresses are calculated by simulating each conductor by an unknown line charge and imaging them with respect to ground. Next, the matrix equation V=PQ is formed in which V a n d Q are column matrices of known potentials and unknown line charge magnitudes respectively and P is the square matrix of Maxwell's potential coefficients. The potential coefficients are known from the geometry of the system. Once the charges are found, the electric field is found by superposition of the contributions of all charges present in the system. From Fig. 2, with the ac line at zero potential, the dc line corona onset voltage is 35 kV. Corresponding to this voltage the maximum stress on the dc conductor, at a point on its surface closest to ground, is found to be 59.81 k V / c m which is the onset gradient. When the ac line is energized at 10 kV (v (t) = 1 0 ~ 2 cos o)t) and the dc line
283 is at zero potential the ac line gradient is below its onset value. As the dc line potential, Vdc, is increased, the time-dependent maximum gradient on the dc conductor increases and is given by the expression (1.71 Vdc- 5.73 cos tot) kV/ cm. Equating the maximum value of this expression, (1.71 Vdc+ 5.73 ), to the onset gradient of the dc conductor one finds the corresponding onset voltage to be 31.62 kV which is in good agreement with experimentally recorded data. Further, calculations show that under these conditions the gradient at the ac conductor is still well below its onset value. When the ac line potential is 25 kV the time-dependent maximum gradient on the dc conductor is given by (1.71 Vdc- 14.32 cos tot) kV/cm. Equating the maximum value of this gradient to the onset gradient, 59.81 kV/cm, the dc line corona onset voltage is found to be 26.6 kV. From Fig. 2 the experimentally observed onset value is close to 10 kV. The reason for this discrepancy is because the calculations ignore the effect of space charge. At an ac line voltage of 25 kV, with the dc line at zero potential, the ac line is already in corona. When the dc line is energized, it introduces a bias on the ac field; the ac field increases during negative swings and decreases during positive swings of the ac line potential. The negative ions produced during the enhanced negative mode of ac corona experience a net motive force directed towards the dc conductor and the dc conductor surface field is increased. This effect increases with dc line potential and dc line corona onset occurs when the maximum gradient at its surface equals the onset gradient due to the combined effects of applied line potentials and space charge. In both cases, when the ac line is energized at 10 or 25 kV, dc line corona activity commences first during the negative half cycle of the ac potential; dc line corona activity during the positive half cycle of ac voltage begins at a higher dc applied potential. 4.2. dc currents injected into the ac line In addition to modifying the corona characteristics of the dc line, the ac conductor also acts as a collector of some of the ions created by the dc corona process occurring around the dc conductor. Irrespective of the value of ac line potential, there always exists a net motive force which acts on some of the ions and directs them towards the ac conductor. This results in a dc current flow in the ac line. The effect of ac potential has been studied in Ref. [2] where the authors state that a non-zero ac potential has the effect of increasing the transit time of ions between the dc and ac conductors. This is equivalent to a decreased ionic mobility. The authors also found that the trajectories of ions are practically independent of ac potential and therefore computed the dc current injected into the ac line by assuming that the ac conductor to be at zero potential. Figure 3 shows the magnitude of the dc injected current as a function of dc applied potential for ac line potentials of 0, 10 and 25 kV. The magnitudes of
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the currents were obtained by recording the waveform across the 10 kg2 resistor in the ac circuit and computing its average value. The curves of Fig. 3 demonstrate that the injected current increases with ac potential for fixed value of dc voltage. This may be attributed to the increased dc line corona activity that accompanies an increase in ac potential. Comparison of Figs. 2 and 3 shows that the dc line corona current and the injected currents in the ac line are almost equal for a set of values of dc and ac potentials. In fact, the injected currents are slightly lower in magnitude and the curves of Fig. 3 lie below the corresponding curves of Fig. 2. For a given condition, the difference between dc line current and the injected current represents the total ionic current flowing to ground. Figure 4 shows three waveforms identified as A, B and C which are the ac line potential, the current in the ac line obtained by measurement across the resistor in the ac circuit, and the direct current flowing in the ac line respectively. These waveforms correspond to the condition when the dc and ac lines are energized at 60 kV and 10 kV respectively. The waveform of direct current
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was obtained in the following manner. First the waveform labelled B (Fig. 4) was obtained by measurement across the dropping resistor employing direct coupling. Next the measurement was repeated employing capacitive coupling. Subtraction of this waveform from waveform B yielded waveform C. The applied voltage was recorded by connection of a voltage divider between the ac bus and ground. Waveform C, Fig. 4, shows slight maxima and minima which occur at some time interval after the minima and maxima of the applied ac voltage, waveform A. When the voltage is a minimum, this condition enhances the dc line corona process and more positive ions are produced. After a time interval corresponding to the time of transit between the dc and ac conductors some of these ions arrive at the ac conductor and account for the observed maximum of current. A similar explanation accounts for the presence of the minimum of the dc current waveform. Waveform B is comprised of three components - a dc injected current, displacement current and ac line corona current components. The dc current component is clearly evident by the fact that waveform B has a positive offset. The average value of waveforms B and C are equal. During the negative half cycle of voltage, waveform B exhibits a hump which peaks prior to the occurrence of the voltage minimum. This hump occurs due to ac line corona which commences when the field at the surface of the ac conductor reaches the onset value due to the combined effect of applied potentials and positive ion space charge. On the other hand ac conductor corona is suppressed during the positive excursion of the ac conductor voltage.
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Due to the presence of the ac corona related hump in a half cycle, a dc component of current exists in the ac line. This component, which is included in the measurements reported in Section 4.2, is quite small in magnitude for the reported experimental conditions. This is verified by comparing the positive and negative peaks of the capacitively coupled waveform across the dropping resistor. For the experimental conditions corresponding to those of Fig. 4, the maximum and minimum values are 848 and 783 pA respectively. The difference is 65 ~A and this corresponds to an average value of about 1 ~A. The presence of a direct current in the ac line is important from a practical point of view; if relatively large direct currents flow in the ac line they may cause saturation related problems in the transformers connected at the end of the lines [2].
4.3. Ground level lateral profiles of ionic current density Figure 5 shows normalized ground level lateral profiles of ionic current density. The solid curve is obtained when the ac line is removed and the dc line energized at 60 kV. The dashed curve profile corresponds to the case when both lines are present but the ac line is held at zero potential. The values of the current density in the latter case are expressed in per unit using the value obtained under the dc line, with the ac line absent, as the base value. One per unit corresponds to a current density of 1.05 n A / c m 2. From this figure, the shielding effect of the ac line is apparent. The maximum of current density, with both lines present, does not occur below the line but at some distance removed from it. Figure 6 shows similar profiles obtained with both lines present. Here, the dc line is energized at 60 kV and the ac line energized at potentials of 10, 20
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287
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and 25 kV. The profile corresponding to the case when the ac line is held at zero potential has been included for comparison. In all cases, as in Fig. 5, the values of current density are expressed in per unit using the same base value. The profiles of Fig. 6 show the influence of ac line potential. At a point on the ground directly below the lines the current density first increases as the ac line potential is increased from 0 to 10 kV; but subsequent increases cause the current density at the same point to decrease. At an ac line potential of 25 kV, the current density is greater than that obtained with the ac line held at zero potential. The profile obtained with the ac line at 10 kV ( 10 kV profile ) lies above that obtained with the ac line at 0 kV (0 kV profile) except for a narrow range straddling the location of the maximum exhibited in the latter case. In contrast, the 20 kV profile lies below the 0 and 10 kV profiles and the 25 kV profile is located below the 20 kV profile throughout the range of lateral distance considered. 5. C o n c l u s i o n s
A single-phase laboratory model hybrid ac/dc system has been considered and experimental results presented which show the existence of a mutual interaction between the dc and ac electric fields. This interaction causes the ac potential to influence dc line corona current characteristics, the dc current
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component in the ac line and ground level lateral profiles of ionic current density. Similar results may be expected for other geometrical configurations and negative polarity of dc applied potential. Acknowledgement
Financial support from NSERC Canada is gratefully acknowledged. Thanks are also due to Mr. G. Toole for his technical assistance.
References 1 V.L. Chartier, S.H. Sarkinen, R.D. Stearns and A.L. Burns, Investigation of corona and field effects of AC/DC hybrid transmission lines, IEEE Trans. Power Appar. Syst., PAS-100(1 ) (1981) 72-80. 2 P. Sarma Maruvada and S. Drogi, Field and ion interaction of hybrid ac/dc transmission lines, IEEE Trans. Power Delivery, 3 (July 1988) 1165-1172. 3 P. Sarma Maruvada and W. Janischewskyj, Analysis of corona losses on dc transmission lines: Unipolar lines, IEEE Trans. Power Appar. Syst., PAS-88(5) (1969) 718-731. 4 P. Sarma Maruvada and W. Janischewskyj, Analysis of corona losses on dc transmission lines: II Bipolar lines, IEEE Trans. Power Appar. Syst., PAS-88(10) {1969) 1476-1491. 5 W. Janischewskyj, P. Sarma Maruvada and G. Gela, Corona losses and ionized fields of HVDC transmission lines, CIGRE 36.09 ( 1982 ) 10. I
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