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CHAPTER 17
ELECTRIC UTILITY APPLICATIONS
17-1 INTRODUCTIONPow er electronic system s that have unique electric utility applications such as highvoltage dc transm ission, static var com pensators, and the interconnection o f renewable energy sources and energy storage system s to the utility grid are discussed in this chapter. In recent years, as the sem iconductor devices have im proved in their voltage- and current-handling capabilities, new applications o f pow er electronics in pow er system s are being investigated. T w o such exam ples are the flexible ac transm ission systems (FA C TSs), discussed in reference 5 o f C hapter 1, and active filters to im prove power quality. Several universities have added new courses to specifically discuss these high-power applications o f pow er electronics, w here E M TP (discussed in Section 4-6-2 of C hapter 4) is used as the sim ulation tool in reference 1. In keeping with the objective of this book, we have only provided an overview o f these applications.
17-2 HIGH-VOLTAGE dc TRANSMISSIONElectrical plants generate pow er in the form o f ac voltages and currents. T his pow er is transm itted to the load centers on three-phase, ac transm ission lines. H ow ever, under certain circum stances, it becom es desirable to transm it this pow er over dc transm ission lines. T his alternative becom es econom ically attractive where a large am ount o f pow er is to be transm itted over a long distance from a rem ote generating plant to the load center. T his breakeven distance for H V D C overhead transm ission lines usually lies som ew here in a range o f 3 0 0 - 400 m iles and is m uch sm aller for underw ater cables. In addition, many other factors, such as the im proved transient stability and the dynam ic dam ping o f the electrical system oscillations, m ay influence the selection of dc transm ission in preference to the ac transm ission. It is possible to interconnect tw o ac system s, which are at two different frequencies or w hich are not synchronized, by m eans o f an H V D C transm ission line. Figure 17-1 show s a typical one-line diagram of an H V D C transm ission system for interconnecting tw o ac system s (w here each ac system m ay include its ow n generation and load) by an H V D C transm ission line. Pow er flow over the transm ission line can be460
17-2
H IG H -Y O ITA G F. ( k TRANSM ISSION
461
(System*
/ ac'N
Figure 17-1
A typical HVDC transm ission system.
reversed. If w e assum e the pow er flow to be from system A to B , the system A voltage, in the range o f 6 9 - 2 3 0 k V , is transform ed up to the transm ission level and then rectified by m eans o f the converter term inal A and applied to the HVDC transm ission line. At the receiving en d , the dc pow er is inverted by m eans of the converter term inal B, and the voltage is transform ed dow n to m atch the ac voltage o f system B. The pow er received over the H V D C transm ission line is then transm itted over ac transm ission and distribution lines to w herever it is needed in system B. E ach converter term inal in Fig. 17-1 consists o f a positive pole and a negative pole. Each pole consists o f two 6-pulse, line-frequency bridge converters connected through a Y - Y and a A - Y transform er to yield a 12-pulse converter arrangem ent. On the ac side o f the converter, the filters are required to reduce the current harm onics generated by the converters from entering the ac system . M oreover, the pow er factor correction capacitors are included along w ith the ac filter banks to supply the lagging reactive pow er (or the inductive vars) required by the converter in the rectifier as well as in the inverter m ode of operation. O n the dc side o f the converter, the ripple in the dc voltage is prevented from causing excessive ripple in the dc transm ission line current by m eans o f sm oothing inductors Ld and the dc-side filter banks, as shown in Fig. 17-1.
1 7 - 2 -1
T W E L V E -P L L S E L IN E -F R E Q U E N C Y C O N V E R T E R S
The 6-pulse line-frequency controlled converters were discussed in detail in C hapter 6. Because o f high pow er levels associated with the HVDC transm ission application, it is im portant to reduce the current harm onics generated on the ac side and the voltage ripple produced on the dc side o f the converter. T his is accom plished by m eans o f a 12-pulse converter operation, which requires two 6-pulse converters connected through a Y - Y and a A - Y transform er, as is show n in Fig. 17-2. The two 6-pulse converters are connected
462
C H A P TER 17
ELECTRIC UTILITY APPLICATIONS
d> = id
in series o n the dc side and in parallel on the ac side. The series connection o f two 6-pulse converters on the dc side is im portant to m eet the high voltage requirem ent o f an HVDC system . In Fig. 17-2, Vas n leads Vui n by 30. T he voltage and current w aveform s can be draw n by assum ing the current d on the dc side o f the converter to be a pure dc in the p resence o f the large sm oothing inductor L d show n in Fig. 17-2. Initially, for sim plicity, we will assum e that the per-phase ac-side com m utating inductance L , is negligible, thus resulting in rectangular current pulses. In practice, how ever, substantial com m utating inductances are present as a result o f the transform er leakage inductances. The effects of these com m utating inductances on the 12-pulse w aveform are discussed later. W ith the foregoing assum ptions o f L, - 0 and i j t ) d and recognizing that Va, i r leads by 30, we can draw the current waveform s as in Fig. 17-3a. Each 6-pulse converter operates at the sam e delay angle a . The w aveform o f the total per-phase current ia = i, + iaZ clearly show s that it contains fewer harm onics than either iai or ia2 drawn by the 6-pulse converters. In term s o f their Fourier com ponents 2V 3 1 , , I iai = ^ / d(cos 0 j cos 50 + ^ cos 70 - cos 110 + cos 130 . . .) (17-1)02
=
2V 3 , . , , 2 ^ / - ( c o s 8 + - cos 50 j cos 70 cos 110 + -^ cos 130 . . ,) (17-2)
w here 0 = bit and the transform er turns ratio N is indicated in Fig. 17-2. T herefore, the com bined current draw n is
n -2 H IG H -V O LTAG E de TRANSM ISSION
Figure=
17-3
Idealized
w uveform s a.ssumin^
0.
463
464
CH APTER 1 -
I ! M IKK
UTILITY APPLICATIONS
This F ourier analysis show s that the com bined line current has harm onics o f the order h = 12A: 1 (where k = an integer) (17-4)
resulting in a 12-pulse operation, as com pared with a 6-pulse operation w here the ac current harm onics are o f the order 6/t 1 (where k = an integer). The harm onic current am plitudes in E q. 17-3 for a 12-pulse converter are inversely proportional to their har m onic o rd er and the lowest order harm onics are the eleventh and the thirteenth. The currents on the ac side o f the two 6-pulse converters add, confirm ing that the tw o con verters are effectively in parallel on the ac side. On the dc side, the voltage w aveform s vdt and vlf2 for the two 6-pulse converters are show n in Fig. 17-36, T hese tw o voltage w aveform s are shifted by 30 w ith respect to each other. Since the two 6-pulse converters are connected in series on the dc side, the total dc voltage Yd = vrfl + has 12 ripple pulses per fundam ental-frequency ac cycle. This results in the voltage harm onics o f the order h in vd, where h = \2 k (k = an integer) (17-5)
and the tw elfth harm onic is the low est order harm onic. M agnitudes o f the dc-side voltage harm onics vary significantly with the delay angle a . In practice, L t is substantial because o f the leakage inductance o f the transform ers. The presence o f L s does not change the order o f characteristic harm onics produced either on the ac side or on the dc side, provided that the two 6-pulse converters operate under identical conditions. H ow ever, the harm onic m agnitudes depend significantly on L s, delay angle a , and dc current Ij. T he effect o f L s on the ac current w aveform and harm onics was discussed in C hapter 6. B ased on the derivation in C hapter 6, the average dc voltage can be w ritten as Vd 3V 2 3(t)Lj Vdt = Vj2 = = -------V l l cos a ----------- U 2 77 IT (17-6)
w here Vu is the line-to-line rm s voltage applied to each o f the 6-pulse converters and L s is the per-phase leakage inductance o f each o f the transform ers, referred to their converter side. A s w e explained in C hapter 6, a > 90 corresponds to an inverter m ode o f operation w ith a transfer o f pow er from the dc to the ac side o f the converter.
1 7 -2 -2
REACTIVE PO W E R DR A W N BY C O NVERTER S
As w as alluded to earlier, the line-frequency, line-voltage-com m utated converters operate at a lagging pow er factor and, hence, draw reactive pow er from the ac system . Even though the ac-side currents associated w ith the converter contain harm onics in addition to their fundam ental-frequency com ponents, the harm onic currents are absorbed by the ac-side filters, w hose design m ust be based on the m agnitude o f the generated harm onic current m agnitudes, as w e will discuss later. Therefore, only the fundam ental-frequency com ponents o f the ac currents are considered for the real pow er transfer and the reactive pow er draw n. It is necessary to consider only one o f the tw o 6-pulse converters, since the real and the reactive pow er for the 12-pulse converter arrangem ent m aking up a pole are tw ice the per-converter values.
17-2-2-1
R ectifier M ode o f Operation
W ith the initial assum ption that Ls = 0 in Fig. 17-2, Fig. 17-3c show s the phase-to-neutral voltage vaSin] and the current iai (corresponding to converter 1 in Fig. 17-3) w ith id(t) ~
r-2
i i k ; i i - \ o i . i \(.k . 1 r i i w - M i s ^ i o N .
4 (w
I d at a delay angle a . The fundaraental-frequency current com ponent (i ^ shown by the dashed curve lags behind the phase voltage v by the displacem ent pow er factor angle i. where4>i = a (1 7 -7 )
T herefore, the three-phase reactive pow er (lagging) required by the 6-pulse converter because o f the fundam ental-frequency reactive current com ponents, which lag their re spective phase voltages by 90. equals Qi = \ 3 V uXy^.hsin (17-8)
w here V ll is the line-to-line voltage on the ac side of the converter. From the Fourier analysis o f i in Fig. 17-3r, the rms value o f its fundam entalfrequency com ponent is V6 Vai,) l T herefore, from Eqs. 17-8 and 17-9 0 i = V 3 VL V 6, l d sin a = 1 J S V ^ / j s i n a (17-10) Id 0-78 l d (17-9)
The real pow er transfer through each of the 6-pulse converters can be calculated from Eq. 17-6 with Ls = 0 as P j i = VdlI d = l J i V ^ c o s a
(17-11)
F or a desired pow er transfer P di, the reactive pow er dem and Q, should be m inim ized as much as possible. S im ilarly, Id should be kept as small as possible to m inim ize ! 2R losses on the dc transm ission line. T o m inim ize l d and 2 , , noting that VLL is essentially constant in E qs. 17-10 and 17-11. w e should choose a sm all value for the delay a in the rectifier m ode o f operation. F or practical reasons, the m inim um value of a is chosen iri a range of 10-20.
17-2-2-2
Inverter M ode o f O peration
In the inverter m ode, the dc voltage o f the converter acts like a counter-em f in a dc m otor. T herefore, it is convenient to define the dc voltage polarity as shown in Fig. 17-4u, so that the dc voltage is positive w hen written specifically for the inverter mode of operation. In C hapter 6, the extinction angle y for the inverter was defined in terms o f a and u as7
= 180 - (a + u)
(17-12)
where a is the delay angle and u is the com m utation or the overlap angle. The inverter voltage in Fig. 17-4 can be obtained as (see Problem s 17-7) Vd 3(uL, Vji = Vj? = = 1 .3 5 1 ^ cos - y -----------l dLTT
(17-13)
Again with the assum ption that L s = 0 for sim plicity. Fig. 17-46 shows the idealized w aveform s for ' and ias at an a > 90. corresponding to the inverter mode of operation. The fundam ental-frequency com ponent (/, )] o f the phase current is shown by the dashed curve. In the phasor diagram o f Fig. I7-4c. the fundam ental-frequency reac tive current com ponent lags behind the phase-to-neutral voltage, indicating that even in the inverter m ode, where the direction o f pow er flow through the converter has reversed, the converter requires reactive pow er (lagging) from the ac system.
466
C H APTER 17
ELECTRIC IT 1L IT Y APPLICATIONS
Q' (a)
ycsini
J9 0
*1 = are active
(c)
Figure 17-4
In v erter m ode o f o p eratin g (assum ing L , = 0).
W ith L s = 0 , u = 0 in Eq. 17-12 and y = 180 a . T herefore, the expressions for per-converter Q l and P di in E qs. 17-10 and 17-11 can be obtained specifically for the inverter m ode in term s o f -y as Q , = 1 .3 5 V iz ./jsm 7 and P dl = .S S V l l I jcos y (17-15) (17-14)
where the directions o f the reactive pow er (lagging) and the real pow er are as show n in Fig. 17-4a.
1 7 -2
H IG H-V OLTAG E dc TRANSM ISSION
467
In Eqs. 17-14 and 17-15, y should be as small as possible for a given pow er transfer level to m inim ize l 2R losses in the transm ission line due to d and to m inim ize the reactive pow er dem and by the converter. As we discussed in C hapter 6, the m inim um value that y is allow ed to attain is called the m inim um extinction angle 7 rain that is based on allowing sufficient turn-off tim e to the thyristors. I n a l 2-pulse converter arrangem ent, the reactive pow er requirem ent is the sum o f the reactive pow ers required by each o f the two 6-pulse converters. The ac-side filter banks and the po w er factor correction capacitors partially provide the reactive pow er dem and of the converters, as discussed in Section 17-2-4. 1 7 -2 -3 CONTROL OF H VDC CO NVERTER S
It is possible to discuss the control o f converters in an H V D C system on a per-pole basis, since both the positive and the negative poles are operated under identical conditions. Figure 17-5 show s the positive pole, for exam ple, consisting o f the 12-pulse converters A and B. T erm inal A is assum ed to be operating as a rectifier, and its dc voltage is defined as VdA. T erm inal B is assum ed to be operating as an inverter, and its dc voltage VdB is show n w ith a polarity that is specific to the inverter mode o f operation, so that has a positive value. In steady state in Fig. 17 5 /, = (17-16,
is sm all and I d results as a consequence o f a small difference betw een two very large voltages in Eq, 17-16. T herefore, one converter is assigned to control the voltage on the transm ission line and the other to control Ia. Since the inverter should operate at a constant y = "ymin, it is natural to choose the inverter (converter B in Fig. 17-5a) to control Vd. Then, ld and, h ence, the pow er level are controlled by the rectifier (c o n v e rte r^ in Fig. 17-5a). Figure 17-5i> show s the rectifier and the inverter control characteristics in the Vd- I d plane, w here Vd is chosen to be the voltage at the rectifier, that is, ^d ~ VdA- A t the constant extinction angle y = y, the inverter produces a voltage Vd in Fig. 17-5a, w hich is given as 3aaLs1.35V C O S t m i n ----------- I d + R i c hIT
= 2 x 1.35V u,cos -ymin -
- Rdc fid
(17-17)
In v e rte r c n a ra c ie n s u c P o int of o p e ra tio n w ith 1 = /
----- W r = K, VM
R e ctifie r c h a ra c te ristic -^ * . in a c u r r e n t c o n tro l m ode
Rectifier
-i-
inverter
(a) Figure 17-5C ontrol o f HVDC system.
468
C H APTER 1"1
ELECTRIC IT 1L IT Y APPLICATIONS
A ssum ing the quantity w ithin the bracket in Eq. 17-17 to be positive, the constant extinction angle operation o f the inverter results in a Vd~ I d characteristic as show n in Fig. 17-54. The rectifier can be controlled to m aintain l d equal to its com m anded o r reference value Id rtf. The actual current Id is m easured, and the error f). if positive, increases the rectifier delay angle a ; if the e n o r is negative, a is decreased. A high-gain current controller results in a nearly vertical rectifier characteristic in Fig, 17-56 at Idl t f . The intersection o f the two characteristics in Fig. 17-56 establishes the transm ission line voltage Vd and the current Id. T he foregoing discussion show s how the pow er flow P d = Vd!d from term inal A to term inal B can be controlled in Fig. 17-5 by controlling Id, while m aintaining the transm ission line voltage as high as possible to m inim ize pow er loss in the transm ission line. T his type of control also results in a sm all value of a in the rectifier and a sm all -y = 7 mm in the inverter, thus m inim izing the reactive pow er dem and by both the rectifier and the inverter. In practice, the transform ers at both the term inals consist o f tap changers, w hich can control the ac voltage supplied to the converters in a sm all range, thus providing an additional degree o f control. T he control characteristics show n in Fig. 17-56 can be extended for negative values o f Vd so that the pow er flow can be controlled sm oothly in m agnitude as well as in direction. A detailed discussion can be found in reference 2. T his capability to be able to reverse the pow er flow is useful if the two ac system s interconnected by the dc transm is sion line have loads that vary differently with seasons or the tim e o f day. T he sam e may be the case if one o f the ac system s contains hydro generation whose output depends on seasons. A nother application o f this control capability is to m odulate the pow er flow on the dc line to dam p out the ac system oscillations.
1 7 -2 -4
HARM ONIC F IL T E R S A N D POW ER FACTOR CORRECTION CAPACITORS
17-2-4-1
dc-Side H arm onic Filters
T o m inim ize the inductively coupled harm onic interference produced in the telephone system and other types o f control/com m unication channels in parallel w ith the HVDC transm ission lines, it is im portant to m inim ize the m agnitudes o f the current harm onics on the dc transm ission line. The voltage harm onics are o f the order 12k, where k is an integer. T h e m agnitudes o f the harm onic voltages depend on a , Ls, and l d for a given ac system voltage. U nder a balanced 12-pulse operating condition, the 12-pulse converter can be represented by an equivalent circuit as show n in Fig. 17-6a, where the harm onic voltages are connected in series w ith the dc voltage Vd. A large sm oothing inductor L d o f the order o f several hundred m illihenries is used in com bination with a high-pass filter, as show n in Fig. 17-6a, in order to lim it the flow o f harm onic currents on the transm ission line. The im pedance o f the high-pass filter in Fig. 17-6i! is plotted in Fig. 17-66, where the filter is designed specifically to provide a low im pedance at the dom inant tw elfth harm onic frequency.
17-2-4-2
ac-Side H arm onic F ilters and Pow er F actor C orrection C apacitors
In a 12-pulse converter, the ac currents consist o f the characteristic harm onics o f the order 12k I {k - an integer), as given by E q. 17-4. T he harm onic currents can be represented
1 7-2
H IGH-VOLTACF. dc TRANSM ISSION
469
Im pedance
lb> Figure 1 7 -6F ilter for de-side voltage harmonics-, (a)