POWER FREQUENCY CONTROL

Transcription

1 ower requency Control OWE EQUENCY CONOL NOUCON SMALL SNAL ANALYSS O OWE SYSEMS 5 3 SAC EOMANCE O SEE CONOL 6 HE OWE SYSEM MOEL 8 5 HE ESE LOO 6 OOL OEAON 7 SAE-SACE EESENAON O A WO AEA SYSEM 9 EEENCES 3

2 ower requency Control ntroduction he general requirement or the operation o a power network are that the requency and voltage be maintained within deignated limit requency i a ytem-wide parameter in the teady tate a a ytem or a number o interconnected ytem ha the ame requency throughout Voltage varie coniderably within a power network and depend on the loading ypically, the limit or requency variation are ±% ±Hz in a 5Hz ytem or a requency band o 98 5Hz hi i the normal range or the rih ytem he range during tranmiion diturbance i 8Hz to 5Hz and during eceptional tranmiion diturbance i 7Hz to 5Hz he permiible variation in voltage i much greater, typically ± 6% A ha been een rom load low analyi, there i a trong correlation between load or rotor angle and hence requency and active power and between voltage and reactive power V Q Eentially, requency in a power ytem i controlled by enuring that the injected power rom the connected generator matche the ytem load, with all loe taken into account Voltage i controlled by the injection o reactive power to meet the reactive demand, together with other meaure uch a tranormer tap changing and automatic voltage regulator AV action igure how the AV and turbine control loop in a generation tation igure AV and urbine Control Loop rid Code, wwweirgridie

3 ower requency Control hi ection conider the control o requency in a power ytem and the eect o interconnection to other ytem on power low and requency he ytem requency i determined by the peed o rotation o the generator in the ytem, which in turn i determined by the balance between generator and load power; eentially the balance between input and output power igure how a chematic repreentation o a oil uel ired boiler/turbine/generator he voltage and peed control input can be identiied igure oil ired drum boiler/turbine/generator chematic diagram Voltage control i conidered eparately We can ay that there are two control loop in a power ytem: the automatic load requency control loop ALC and the automatic voltage control loop AV here i little interaction rom the ALC loop to the AV loop but the AV loop doe aect the ALC loop to a certain etent he AV loop tend to be much ater than the ALC loop with time contant o much le than one econd 3

4 ower requency Control Automatic eneration Control nterchange ower requency Electrical Sytem a enerator b Network c Load Electrical ower Aigned Unit eneration Speed Angle urbine/enerator ntertia overnor Speed Changer Speed overnor Speed Control Mechanim overnor-controlled Valve or ate urbine Mechanical ower Speed-overning Sytem urbine and Energy Sytem igure 3 Location o peed-governing ytem and turbine relative to complete ytem [5] igure ypical repone time o ome control unction igure 3 how the location o the peed-governing ytem and the turbine relative to the complete ytem A can be een, the angle and peed i determined by the dierence between the electrical and mechanical power, acting on the inertia o the turbine/generator combination he peed and the aigned unit generation determine the mechanical power being produced by the turbine he angle o the generator in combination with the network, generator and load determine the electrical power output he automatic generation control ytem determine the aigned unit generation

5 ower requency Control igure how the typical repone time o ome control unction within the power network he high-peed ecitation and governing control unction can be identiied on the let o the diagram with repone time between and econd he repone time to ytem ault by protection ytem will be ater than thi characteritic time in the range o multiple o power cycle, up to econd Small Signal Analyi o ower Sytem Analyi o power network can be divided into mall-ignal and large-ignal analyi or the time-domain analyi o event, uch a major ault where voltage can change by up to %, large-ignal analyi i required or mall change, where the repone can be conidered linear over the typical range, mall-ignal or linear analyi can be ued Hence the Laplace tranorm can be ued to conider the time domain and requency domain repone o uch linear ytem ower requency control in power ytem i uually invetigated uing linear or mall-ignal method igure 5 ower control mechanim [] igure 5 how a phyical repreentation o an automatic load requency control ytem or a turbine/generator hi analyi i taken rom Elgerd book [] he actual control ytem on a modern generator would be quite dierent to that hown here but the ytem in igure 5 i ueul or the purpoe o illutration he aim i to maintain the deired MW output o the generator and the rated requency by controlling the power to the turbine hi in turn i determined by the poition o the valve team or water he power output i changed by changing the reerence power peed changer which indirectly change the peed he peed and hence requency i meaured by the peed governor he preure on the valve and hence poition o the main piton i proportional to the luid into the hydraulic ampliier he poition o the valve in the Laplace domain i given by: 5

6 ower requency Control e C i in Hz/MW and i reerred to the regulation or droop i the Laplace tranorm o the change in the reerence power etting and i the change in the requency We have a relationhip between the power into or piton poition the turbine and the reerence power and the requency We now require the traner unction or the turbine relating the power in to the mechanical power out ypically, the ollowing traner unction are ued or turbine: Steam turbine, no reheat e α H H re Steam turbine, with reheat 3 W Hydro W hee traner unction alo incorporate the generator repreentation where can alo be conidered to equal the Laplace tranorm o the electrical power output o the generator a well a the mechanical power output o the turbine enerally we take igure 6 Small ignal repreentation o power control mechanim 3 Static erormance o Speed Control he teady tate repone o the peed control ytem can be determined by applying the inal Value theorem to the ytem hown in igure 6 c, which i the cae where a generator i connected to an ininite bu, then c and changing the reerence power i relected a a change in the power being delivered to the ininite bu or an iolated generator without changing reerence, on the other hand, we have: 3 6

7 ower requency Control and an increae in output power i relected a a drop in requency hi drop in requency i determined by the droop characteritic i a meaure o how reponive the peed controller i to change in requency and i meaured in Hz/MW or more uually Hz/pu MW or %Hz/pu MW or eample, % droop mean Hz/pu MW or a 5Hz ytem With change in both reerence power output and requency, we have a amily o curve a hown in igure 7 3 igure 7 Static peed control repone we have two generator rated at 5MW and 5MW repectively connected to a common bu and each are at hal loading, then a change in the load o MW reult in a requency drop to 96Hz he regulation can be calculated a ollow: Hz / MW Hz / MW Small unit Large unit which give the correct ditribution o : between the machine he regulation can be epreed a ollow: Hz / MW 5 pu Hz / pu MW %Hz / pu MW 5 Hz / MW 5 pu Hz / pu MW %Hz / pu MW 5 and or correct ditribution o load, when epreed a %Hz/pu MW 7

8 ower requency Control he ower Sytem Model o cloe the ALC loop, we now require a model or the power ytem n other word, we need a repreentation o the dynamic relationhip between the change in the ytem requency and the change in demand power and the output o the generator hi allow u to invetigate how the change in load will aect the requency nitially, we identiy the ollowing, pre-diturbance operating condition: - initial requency W kin - initial kinetic energy With change in the ytem requency, there are change in the kinetic energy o the rotating machinery: W kin Wkin he change in power which accompanie thi change in energy i given by: change in generator output - change in cutomer demand d dt W kin where i the change in ytem demand due to a change in requency and i aumed poitive he requency can be decribed in term o the initial requency and the change in requency: 3 and thereore: W kin W W W kin kin kin W kin d dt [ ] he kinetic energy can be decribed in term o the inertia contant H where kinetic energy MW H econd rated MW MW 5 8

9 ower requency Control 9 n term o per unit we have: dt d H pu pu 6 we take the Laplace tranorm o thi equation, and dropping the pu notation, we have: H 7 or [ ] 8 H relate the change in power to the change in requency he tatic perormance o the power ytem i given by: [ ] 9 igure 8 Single control area he combined turbine/generator/peed control and power ytem model i hown in igure 8 above he combined traner unction, relating change in requency to change in the reerence power and to change in the power demand in the ytem i given by: C C no change in reerence power and i a tep change occur in the load demand:

10 ower requency Control M then the change in requency i given by: M 5 5 % change in requency, Hz % time,econd igure 9 Step repone o ytem, -5 pu igure 9 how the repone in ytem requency or two dierent value o regulation he tep load change i -5 pu decreae in load in both cae he teady-tate requency change can be determined by applying the inal Value heorem to the above equation: t L p M / M M / β where β / and i called the Area requency epone Characteritic AC Conidering the cae hown in igure 9 above where 5pu and pumw/hz, or %, β 5 5, 98Hz %, β, 5Hz

11 ower requency Control or, β and the change in requency i 5Hz n thi cae, the original change in demand i completely balanced by an equal and oppoite drop in ytem demand becaue o the drop in requency and there i no increae in output power We can identiy three ource o power in the ytem to meet an increae in demand which i accompanied by a requency drop: a he change in kinetic energy o the rotating machinery A the requency drop, energy i releaed by the machine and thi provide a hort-term ource o power b ncreaed generation becaue o the peed control loop c A reduction in load due to a decreae in requency Oten, the time contant and are et to zero to impliy the analyi a thi reduce the ytem to a irt order model he teady-tate value remain unchanged but the dynamic behaviour change greatly 6 change in requency, Hz 8 6 tg t,t time,econd igure Eect o time contant 5 he eet Loop With the peed governor action only, there i a inite error in the requency when the ytem ettle down again to the teady-tate and i given by: M 5 β hereore, integral control action i added which change the reerence power level and return the ytem requency error to zero dt C 5

12 ower requency Control he change in reerence power i proportional to the integral o the requency error there i a negative decreae change in requency, the reerence power increae to retore the requency to it nominal value he reerence power continue to increae until the requency error i zero, ater which it remain contant at C he ytem with reet loop included i hown in igure below igure Single control area with integral control we et and to zero to impliy the analyi, the traner unction o the above ytem become: / / / / 53 he characteritic equation can be re-written a: / / 5 and i / > 55 the ytem will be ocillatory or eample, with ec, pumw/hz, Hz/puMW, the ytem become ocillatory at 35 he repone or two dierent value o integral gain are hown in igure below

13 ower requency Control change in requency, Hz 5 3 i3 i time,econd igure Eect o integral control gain A higher gain in the reet loop will lead to a ater repone but will alo caue ocillation and, i thi gain eceed a critical value, caue intability or clock which are controlled by the ytem requency, every change in the requency even tranient change will caue time error he error introduced over a time can be epreed a: t e dt roblem: By applying the inal Value heorem, calculate the time error due to a change in demand o 5pu in the ytem hown in igure above i the integral control gain i 7 Sugget how thi error might be ubequently et to zero 56 3

14 ower requency Control 6 ool Operation We have conidered the operation o a ingle, iolated power ytem n ituation where a number o ytem are connected by intertie, then there are advantage to be gained or the overall ytem both in term o the normal operation and or emergency condition nterconnected ytem can provide upport or each other in the event o a udden application o a large load or ault condition A combined ytem will lead to more economic operation he rule o pool operation are uually uch that each area carrie it own load ecept under mutually agreed circumtance Becaue a number o ytem connected together repreent a much large ytem, the impact o any load change in term o requency change will be much maller than it would be on ingle ytem igure 3 how the repone o a ingle area and igure how the repone o a two area ytem to the ame load change 6 change in requency, Hz 8 6 change in requency, Hz 8 6 Area Area time,econd igure 3 epone o ingle area time,econd igure epone o two area he power traner over a connection between two area i given by: V V in δ δ 6 X where i the power low rom area to area, V δ and V δ are the voltage at each end o the connecting line and X i the reactance o that line nitially, the operating point i given by: V V in δ δ 6 X and mall deviation rom thi point are given by: V V co δ δ δ δ 63 X where the any change in the voltage magnitude in each ytem are neglected hi equation may be written a: V V X δ δ co δ δ i called the ynchroniing coeicient and i determined by the operating point he change in requency i given by: 6

15 ower requency Control d d δ δ δ π dt 65 π dt t δ π dt 66 and thereore t t π dt dt 67 or taking the Laplace ranorm give: π 68 igure 5 raner unction repreentation o two area 5

16 ower requency Control igure 5 above how the repreentation o a two-area ytem with the interconnection between the area included he requency deviation or area and are given by: / / a 69 π 6 ower Bae Area a 6 ower Bae Area Combining thee three equation allow u to calculate the requency deviation or each area and the power traner between the area Conider a change in load o M in area and a change in load o M in area By the inal Value heorem, we can how that the teady-tate power low between thee area a a reult o thee load change i given by: where: β M β M 6 a β β β β / / and the requency deviation are given by: M a M a M β β M β β 63 Obviouly ince the area are interconnected, they will both ettle down to the ame requency deviation roblem: wo area connected by a tranmiion line and have the ollowing value: Area : %, ec,, -5 Area : 8%, ec, 5, 3 Calculate the eventual teady-tate power low between the area and the requency deviation 6

17 ower requency Control 5 change in requency, Hz 5 5 Area A -5 Area B time,econd igure 6 epone o area without interconnection 5 change in requency, Hz Area A Area B power low, pu time,econd time,econd igure 7 epone o area with interconnection, requency and power igure 6 above how the repone o thee ytem without an interconnection he requency change are dierent a there i no connection he ituation with an interconnection i hown in igure 7 Obviouly, with thi ytem, there i a inite requency error again the ame or both area and an uncheduled power low between the area A beore, we wih to return both the change in requency and the power to zero and thi i accomplihed by integral control action he area control error ACE conit o component o the power error and the requency error and i given by: ACE ACE B B and B i the requency bia parameter he change in reerence power now become: 6 7

18 ower requency Control C C B dt B dt and taking the Laplace ranorm: C C B he tatic repone i given by: ACE ACE B B B B B and thi condition i met or and igure 8 epreentation o two-area ytem with ACE control igure 8 above how the two-are repreentation with both requency and power integral control he relative value o B and are elected to control how quickly the requency and power are driven to zero ater a diturbance or eample, in igure 9 below, the requency and power low between the area i hown where B i zero or both area and 5 or both area A can be een, the power low return to zero but a utained requency error i preent 8

19 ower requency Control On the other hand, i we make B or both area and i i very mall, then a can be een in igure, the power low i very low in returning to zero even though the requency error rapidly die away igure how a reaonable compromie between thee two etreme Area 3 change in requency, Hz 8 6 power low, pu - Area time,econd igure 9 ower integral control only time,econd 5 3 Area 5 change in requency, Hz 5 Area power low, pu time,econd igure requency integral control only time,econd change in requency, Hz 5 Area Area power low, pu time,econd time,econd igure Combined requency and power integral control 7 State-Space epreentation o a wo Area Sytem or analyi o larger linear ytem, the tate-pace repreentation i ued hi allow or a more convenient approach to analyi and controller deign hi ection look at the tatepace repreentation o the two-area ytem i developed 9

20 ower requency Control igure epreentation o two-area ytem igure how the block diagram repreentation o the two-area ytem a dicued earlier he individual tate are identiied a ollow: [ ] [ ] [ ] a C C π

21 ower requency Control and the correponding dierential equation are given by: [ ] a C C π hee equation can we written in conventional tate-pace orm a ollow: p Bu A Γ 7 where: ; C C u u u ; p p p a A π π

22 ower requency Control B ; Γ igure 3 wo-area ytem with ACE ACE control i implemented, a hown in igure 3, then the tate-pace repreentation i augmented to include the reerence power or each area C and C a tate and become: [ ] [ ] 9 8 C C a B B and thee change are made to the dierential equation: a B B and the tate-pace repreentation become:

23 ower requency Control 3 p A Γ 7 where: Γ a B B a A π π eerence O Elgerd, Electric energy ytem theory: An ntroduction, Mcraw Hill, 983 CA ro, ower ytem analyi, Wiley, BM Weedy, Electric power ytem, Wiley, 97 W Stevenon, Element o power ytem analyi, Mcraw Hill, 986, Chap 8 5 ynamic model or team and hydro turbine in power ytem tudie, EEE Committee report, EEE ran, Vol AS-9, No 6, Nov/ec M Athay, eneration cheduling and control, roc EEE, Vol 75, No, AJ Wood and B Wollenburg, ower generation, operation, and control, Wiley, 98 8 O Elgerd and CE oha, Optimum megawatt-requency control o multiarea electric energy ytem, EEE ran, AS-89, No, April 97, p undur, ower Sytem Strability and Control, Mcraw-Hill, 99, Chap Michael Conlon September 3