00--00 SYSTEM FIGURE 61.8 Monopolar ground return dc system. □ BREAKER FIGURE 61.9 Monopolar metallic return dc system onopolar system will have one conductor, either positive or negative polarity with current returning through either ground or another metallic return conductor. The monopolar ground return current configu- ration, shown in Fig. 61.8, has been used for undersea cable systems, where current returns through the sea. This configuration can also be used for short-term emergency operation for a two-terminal dc line system in the event of a pole outage. However, concerns for corrosion of underground metallic structures and interference with telephone and other utilities will restrict the duration of such operation. The total ampere-hour operation per year is usually the restricting criterion. In a monopolar metallic return system, shown in Fig. 61.9, return current flows through a conductor, thus avoiding problems associated with ground return current. This method is generally used as a contingency mode of operation for a normal bipolar transmission system in the event of a partial converter(one-pole equipment) outage. In the case of outage of a one-pole converter, the conductor of the affected pole will be used as the returning conductor. A metallic return transfer breaker will be opened, diverting the return current from the ground path and into the pole conductor. This conductor will be grounded at one end and will be insulated at the other end. This system can transmit half the power of the normal bipolar system capacity(and can bo increased if overload capacity is available). However, the line losses will be doubled compared to the normal bipolar operation for the same power transmitted. Multiterminal DC Systems There are two basic configurations in which the dc systems can be operated as mu Parallel configuration can be either radial-connected [Fig. 61.10(a)] or mesh-connected [Fig. 61.10(b)]. In a parallel-connected multiterminal dc system, all converters operate at the same nominal dc voltage, similar to ac system interconnections. In this operation, one converter determines the operating voltage, and all other terminals operate in a current-controlling mod c 2000 by CRC Press LLC
© 2000 by CRC Press LLC A monopolar system will have one conductor, either positive or negative polarity with current returning through either ground or another metallic return conductor. The monopolar ground return current configuration, shown in Fig. 61.8, has been used for undersea cable systems, where current returns through the sea. This configuration can also be used for short-term emergency operation for a two-terminal dc line system in the event of a pole outage. However, concerns for corrosion of underground metallic structures and interference with telephone and other utilities will restrict the duration of such operation. The total ampere-hour operation per year is usually the restricting criterion. In a monopolar metallic return system, shown in Fig. 61.9, return current flows through a conductor, thus avoiding problems associated with ground return current. This method is generally used as a contingency mode of operation for a normal bipolar transmission system in the event of a partial converter (one-pole equipment) outage. In the case of outage of a one-pole converter, the conductor of the affected pole will be used as the returning conductor. A metallic return transfer breaker will be opened, diverting the return current from the ground path and into the pole conductor. This conductor will be grounded at one end and will be insulated at the other end. This system can transmit half the power of the normal bipolar system capacity (and can be increased if overload capacity is available). However, the line losses will be doubled compared to the normal bipolar operation for the same power transmitted. Multiterminal DC Systems There are two basic configurations in which the dc systems can be operated as multiterminal systems: 1. Parallel configuration 2. Series configuration Parallel configuration can be either radial-connected [Fig. 61.10(a)] or mesh-connected [Fig. 61.10(b)]. In a parallel-connected multiterminal dc system, all converters operate at the same nominal dc voltage, similar to ac system interconnections. In this operation, one converter determines the operating voltage, and all other terminals operate in a current-controlling mode. FIGURE 61.8 Monopolar ground return dc system. FIGURE 61.9 Monopolar metallic return dc system
CONVERTER I CONVERTER 3 CONVERTER 1 CONVERTER 2 CONVERTER 4 CONVERTER 3 FIGURE 61.10 (a) Parallel-connected radial MTDC system;(b) parallel-connected mesh-type MTDC system FIGURE 61.11 Series-connected MTDC system In a series-connected multiterminal dc system(Fig. 61. 11), all converters operate at the same current. one converter sets the current that will be common to all converters in the system. Except for the converter that sets the current, the remaining converters operate in voltage control mode(constant firing angle or constant extinction angle). The converters operate almost independently without requirement for high-speed ication between them. The power output of a non-current-controlling converter is varied by varying its voltage At all times, the sum of the voltages across the rectifier stations must be larger than the sum of voltages across the inverter stations. Disadvantages of a series-connected system are(1)reduced efficiency because full line insulation is not used at all times and (2)operation at higher firing angles will lead to high converter losses and higher reactive power requirements from the ac system There are now two truly multiterminal dc systems in operation. The Sardinia-Corsica-ltaly three-terminal dc system was originally commissioned as a two-terminal(Sardinia-Italy) system in 1967 with a 200-MW rating. In 1986, the Corsica tap was added and the system was upgraded to a 300-MW rating. The two-terminal Hydro Quebec-New England HVDC interconnection(commissioned in 1985)was extended to a five-terminal system and commissioned in 1990(see Table 61.4). The largest terminal of this system at Radisson station in Quebec is rated at 2250 MW. Two more systems, the Nelson River system in Canada and the Pacific Nw-Sw Intertie in the United States, also operate as multiterminal systems. Each of these systems has two converters each end of the line, but the converters at each end are constrained to operate in the same mode, either ectifier or inverter c 2000 by CRC Press LLC
© 2000 by CRC Press LLC In a series-connected multiterminal dc system (Fig. 61.11), all converters operate at the same current. One converter sets the current that will be common to all converters in the system. Except for the converter that sets the current, the remaining converters operate in voltage control mode (constant firing angle or constant extinction angle). The converters operate almost independently without requirement for high-speed communication between them. The power output of a non-current-controlling converter is varied by varying its voltage. At all times, the sum of the voltages across the rectifier stations must be larger than the sum of voltages across the inverter stations. Disadvantages of a series-connected system are (1) reduced efficiency because full line insulation is not used at all times and (2) operation at higher firing angles will lead to high converter losses and higher reactive power requirements from the ac system. There are now two truly multiterminal dc systems in operation. The Sardinia–Corsica–Italy three-terminal dc system was originally commissioned as a two-terminal (Sardinia–Italy) system in 1967 with a 200-MW rating. In 1986, the Corsica tap was added and the system was upgraded to a 300-MW rating. The two-terminal Hydro Quebec–New England HVDC interconnection (commissioned in 1985) was extended to a five-terminal system and commissioned in 1990 (see Table 61.4). The largest terminal of this system at Radisson station in Quebec is rated at 2250 MW. Two more systems, the Nelson River system in Canada and the Pacific NW-SW Intertie in the United States, also operate as multiterminal systems. Each of these systems has two converters at each end of the line, but the converters at each end are constrained to operate in the same mode, either rectifier or inverter. FIGURE 61.10 (a) Parallel-connected radial MTDC system; (b) parallel-connected mesh-type MTDC system. FIGURE 61.11 Series-connected MTDC system
Economic Comparison of AC and DC Transmission In cases where hvdc is selected on technical consider ations, it may be the only practical option, as in the case of an asynchronous interconnection. However, for long-dis ance power transmission, where both ac and HVDC are practical, the final decision is dependent on total costs of each alternative. Total cost of a transmission system includes the line costs(conductors, insulators, and towers) plus the right-of-way(R-o-W)costs. a dc line with two conductors can carry almost the same amount of power as the three- phase ac line with the same size of line conductors. How ever, dc towers with only two conductors are simpler and cheaper than three-phase ac towers. Hence the per-mile costs of line and R-o-w will be lower for a dc line Power line length IGURE 61.12 Transmission cost as function of losses in the dc line are also lower than for ac for the same power transmitted. However, the HVDC system requires converters at the two ends of the line; hence the terminal costs for dc are higher than for ac. Variation of total costs for ac and dc as a function of line length are shown in Fig. 61. 12. There is a break-even distance above which the total costs of dc option will be lower than the ac transmission option. This is in the range of 500 to 800 km for overhead lines but much shorter for cables. It is between 20 and 50 km for submarine cables and twice as far for underground cables. Principles of Converter Operation Converter circuit Since the generation and most of the transmission and utilization is alternating current, HVDC transmission requires conversion from ac to dc(called rectification)at the sending end and conversion back from dc to ac (called inversion)at the receiving end. In HVDC transmission, the basic device used for conversion from ac to dc and from dc to ac is a three-phase full-wave bridge converter, which is also known as a graetz circuit. This is a three-phase six-pulse converter. A three-phase twelve-pulse converter will be composed of two three phase six-pulse converters, supplied with voltages differing in phase by 30 degrees(Fig. 61. 13). The phase difference of 30 degrees is obtained by supplying one six-pulse bridge with a Y/Y transformer and the other by Relationships between AC and DC Quantities Voltages and currents on ac and dc sides of the converter are related and are functions of several converter parameters including the converter transformer. The following equations are provided here for easy reference Detailed derivations are given in Kimbark[1971 ELL = rms line-to-line voltage of the converter ac bus I =rms value of fundamental frequency component of the converter ac current h= harmonic number a valve firing delay angle( from the instant the valve voltage is positive u= overlap angle(also called commutation angle) o= phase angle between voltage and current cos o= displacement power factor Va= ideal no-load dc voltage (at a=0 and u=0) L commutating circuit inductance B=180 -a= angle of advance for inverter Y=180-(a+ u)=margin angle for inverter c 2000 by CRC Press LLC
© 2000 by CRC Press LLC Economic Comparison of AC and DC Transmission In cases where HVDC is selected on technical considerations, it may be the only practical option, as in the case of an asynchronous interconnection. However, for long-distance power transmission, where both ac and HVDC are practical, the final decision is dependent on total costs of each alternative.Total cost of a transmission system includes the line costs (conductors, insulators, and towers) plus the right-of-way (R-o-W) costs. A dc line with two conductors can carry almost the same amount of power as the threephase ac line with the same size of line conductors. However, dc towers with only two conductors are simpler and cheaper than three-phase ac towers. Hence the per-mile costs of line and R-o-W will be lower for a dc line. Power losses in the dc line are also lower than for ac for the same power transmitted. However, the HVDC system requires converters at the two ends of the line; hence the terminal costs for dc are higher than for ac. Variation of total costs for ac and dc as a function of line length are shown in Fig. 61.12. There is a break-even distance above which the total costs of dc option will be lower than the ac transmission option. This is in the range of 500 to 800 km for overhead lines but much shorter for cables. It is between 20 and 50 km for submarine cables and twice as far for underground cables. Principles of Converter Operation Converter Circuit Since the generation and most of the transmission and utilization is alternating current, HVDC transmission requires conversion from ac to dc (called rectification) at the sending end and conversion back from dc to ac (called inversion) at the receiving end. In HVDC transmission, the basic device used for conversion from ac to dc and from dc to ac is a three-phase full-wave bridge converter, which is also known as a Graetz circuit. This is a three-phase six-pulse converter. A three-phase twelve-pulse converter will be composed of two threephase six-pulse converters, supplied with voltages differing in phase by 30 degrees (Fig. 61.13). The phase difference of 30 degrees is obtained by supplying one six-pulse bridge with a Y/Y transformer and the other by Y/D transformer. Relationships between AC and DC Quantities Voltages and currents on ac and dc sides of the converter are related and are functions of several converter parameters including the converter transformer. The following equations are provided here for easy reference. Detailed derivations are given in Kimbark [1971]. ELL = rms line-to-line voltage of the converter ac bus I1 = rms value of fundamental frequency component of the converter ac current h = harmonic number a = valve firing delay angle (from the instant the valve voltage is positive) u = overlap angle (also called commutation angle) f = phase angle between voltage and current cos f = displacement power factor Vd0 = ideal no-load dc voltage (at a = 0 and u = 0) Lc = commutating circuit inductance b = 180 – a = angle of advance for inverter g = 180 – (a + u) = margin angle for inverter FIGURE 61.12 Transmission cost as function of line length
YIA TRANSFORMER foot FIGURE 61. 13 Basic circuit of a 12-pulse HVDC converter. With a>0. and u=0 cOs C Theoretically a can vary from 0 to 180 degrees(with u=O); hence Va can vary from Vo to-V. Since the valves conduct current in only one direction, variation of dc voltage from Va to-Vao means reversal of power flow direction and the converter mode of operation changing from rectifier to inverter I1 Ix=0.78l (6142) With a>0and0<u>60°, xE.COsα+cos(+u) (61.45)
© 2000 by CRC Press LLC with a = 0, u = 0, (61.40) With a > 0, and u = 0 Vd = Vd0 cos a (61.41) Theoretically a can vary from 0 to 180 degrees (with u = 0); hence Vd can vary from +Vd0 to –Vd0. Since the valves conduct current in only one direction, variation of dc voltage from Vd0 to –Vd0 means reversal of power flow direction and the converter mode of operation changing from rectifier to inverter. (61.42) (61.43) With a > 0 and 0 < u > 60°, (61.44) (61.45) FIGURE 61.13 Basic circuit of a 12-pulse HVDC converter. V EE d LL LL 0 3 2 = = 1 35 p . II I 1 d d 6 = = 0 78 p . cos cos f a = = V V d d 0 V V u d d = + + 0 2 cos cos( ) a a V E u d LL = 3 2 + + p 2 cos cos( ) a a
The error in Eq(61.46)is only 4.3%at u=60 degrees(maximum overlap angle for normal steady-state operation), and it will be even lower(1. 1%)for most practical cases when u is 30 degrees or less. It can be seen from Eqs. (61.45)and(61.46)that the ratio between ac and dc currents is almost fixed, but the ratio between ac and dc voltages varies as a function of a and u. Hence the hVdC converter can be viewed as a variable ratio voltage transformer, with almost fixed current ratio Pac= vald (61.47) P=√-3E -3E1l1cosφ (6148) Substituting for V, and L, in(61. 47)and comparing with(61.48), cos o+cos(o +u) cos o From Eqs. (61.44)and(61.49), Va From egs.(6140),(6144),and(61.49), Va=1.35ELL coS o (61.51) AC Current harmonics The HVDC converter is a harmonic current source on the ac side. Fourier analysis of an ac current waveform shown in Fig. 61. 14, shows that it contains the fundamental and harmonics of the order 5, 7, 11, 13, 17, 19, etc. The current for zero degree overlap angle can be expressed as cos ot --cos 5ot i(t) (61.52) cos llot+—cosl3ot+ (6153) h where Lo and I,o are the fundamental and harmonic currents, respectively, at a=0 and u=0 Equation(6153)indicates that the magnitudes of harmonics are inversely proportional to their order Converter ac current waveform i, for phase a with a Y/A transformer is also shown in Fig. 61. 14. Fourier analysis of this current shows that the fundamental and harmonic components will have the same magnitude c 2000 by CRC Press LLC
© 2000 by CRC Press LLC (61.46) The error in Eq. (61.46) is only 4.3% at u = 60 degrees (maximum overlap angle for normal steady-state operation), and it will be even lower (1.1%) for most practical cases when u is 30 degrees or less. It can be seen from Eqs. (61.45) and (61.46) that the ratio between ac and dc currents is almost fixed, but the ratio between ac and dc voltages varies as a function of a and u. Hence the HVDC converter can be viewed as a variableratio voltage transformer, with almost fixed current ratio. Pdc = VdId (61.47) Pac = ÷–3ELLI1 cos f (61.48) Substituting for Vd and Id in (61.47) and comparing with (61.48), (61.49) From Eqs. (61.44) and (61.49), (61.50) From Eqs. (61.40), (61.44), and (61.49), Vd ª 1.35ELL cos f (61.51) AC Current Harmonics The HVDC converter is a harmonic current source on the ac side. Fourier analysis of an ac current waveform, shown in Fig. 61.14, shows that it contains the fundamental and harmonics of the order 5, 7, 11, 13, 17, 19, etc. The current for zero degree overlap angle can be expressed as (61.52) and (61.53) where I10 and Ih0 are the fundamental and harmonic currents, respectively, at a = 0 and u = 0. Equation (61.53) indicates that the magnitudes of harmonics are inversely proportional to their order. Converter ac current waveform ia¢ for phase a with a Y/D transformer is also shown in Fig. 61.14. Fourier analysis of this current shows that the fundamental and harmonic components will have the same magnitude I I 1 d 6 ª p cos cos cos( ) f a a ª + + u 2 cos f ª V V d d 0 i t I t t t t t d ( ) cos – cos cos – cos cos = + + + ××× Ê Ë Á Á Á ˆ ¯ ˜ ˜ ˜ 2 3 1 5 5 1 7 7 1 11 11 1 13 13 p w w w w w I I h h 0 10 =