SENSITIVITY BASED VOLT/VAR CONTROL AND LOSS OPTIMIZATION

Transcription

1 SENSITIVITY BASED VOLT/VAR CONTROL AND LOSS OPTIMIZATION By ANURAG R. KATTI A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2012

2 c 2012 ANURAG R. KATTI 2

3 To my parents 3

4 ACKNOWLEDGMENTS I thank all the people who have supported me over the duraton of ths thess and beyond. In partcular I would lke to thank my parents and my advsor Dr. Pramod Khargonekar at the Dept. of Electrcal and Computer Engneerng. I would also lke to thank Dr. Wonsuk Danel Lee at the Dept. of Agrculture and Bologcal Engneerng, Unversty of Florda for gvng me the opportunty to work on nterestng proects, my frends and colleagues n the Precson Agrculture Laboratory. And last but not the least, I would lke to thank my frends and past roommates Dwakar Raghunathan, Kran Tumkur, Nk Nachappa and Ugandhar Reddy and all my frends over the years. 4

5 TABLE OF CONTENTS page ACKNOWLEDGMENTS LIST OF TABLES LIST OF FIGURES ABSTRACT CHAPTER 1 INTRODUCTION OVERVIEW Motvaton Dstrbuted Generaton Dstrbuton Networks Voltage and Reactve Power Control PROBLEM DESCRIPTION LITERATURE REVIEW VOLTAGE-VAR CONTROL AND LOSS MINIMIZATION Voltage Senstvty Centralzed Voltage Control and Loss Optmzaton Obectve Functon Constrants and Optmzaton Problem Decentralzed Voltage Control and Loss Optmzaton Optmzaton Algorthm Quadratc Programmng Partcle Swarm Optmzaton Results and Observatons GENERATOR SITING AND SIZING Generator Stng Generator Szng Impact of DG Penetraton on Loss CONCLUSION APPENDIX: FEEDER CONFIGURATIONS REFERENCES

6 BIOGRAPHICAL SKETCH

7 Table LIST OF TABLES page 2-1 Comparson of voltage, current and loss wth and wthout DG Comparson of optmzaton performance for case Comparson of optmzaton performance for case Comparson of optmzaton performance for case

8 Fgure LIST OF FIGURES page 2-1 Schematc of a Power grd N+1 load feeder wth a dstrbuted generator connected at the last node Current drawn at dfferent voltages for dfferent load types Senstvty of 34 node feeder for four dfferent DG postons Varaton of senstvty No result condton of the 13 node feeder Senstvty of 34 node feeder for sx dfferent DG postons Senstvty for a decreasng voltage profle Senstvty for an ncreasng voltage profle Senstvty of current to DG locaton Senstvty of power loss to DG locaton Varaton of losses for dfferent penetraton levels and number of DGs A-1 Schematc of IEEE 13 node test feeder A-2 Schematc of IEEE 34 node test feeder

9 Abstract of Thess Presented to the Graduate School of the Unversty of Florda n Partal Fulfllment of the Requrements for the Degree of Master of Scence SENSITIVITY BASED VOLT/VAR CONTROL AND LOSS OPTIMIZATION By ANURAG R. KATTI May 2012 Char: Pramod Khargonekar Maor: Electrcal and Computer Engneerng The obectve of ths study s to control voltage at dfferent ponts n a dstrbuton grd to wthn a specfed range and mnmze power loss. Senstvty coeffcents are used to determne the reactve power dspatch of dstrbuted generators connected n the grd. Power loss s also represented n terms of senstvty coeffcents to smultaneously optmze the voltage profle and power loss. Two varants of the optmzaton algorthm are dscussed - a centralzed control algorthm based on the complete state of the system and a decentralzed algorthm usng only the local nformaton. To study the nfluence of the locaton of generators n the grd, the propertes of senstvty and ts varaton for dfferent generator locatons are studed. Two dfferent senstvty coeffcents - current and power loss senstvty wth respect to locaton of generator are developed from the voltage senstvty values. The use of these senstvty coeffcents n stng and szng of generators are dscussed. And fnally the nfluence of the number of generators and penetraton of dstrbuted generaton on voltage and dstrbuton loss are dscussed through smulatons. 9

10 CHAPTER 1 INTRODUCTION Dstrbuton systems are the last stage n the delvery of power to the customer. Power produced by generators s transported through the transmsson network at hgh voltages to dstrbuton networks and delvered to the customer at the utlty voltage typcally around 120V/240V for resdental customers and possbly for other types of customers wth larger power requrements. The transfer of power from the substaton - the begnnng of the tradtonal dstrbuton system to the customer causes current to flow downstream n the dstrbuton grd. Currents n a crcut cause a voltage drop between nodes and power loss n the conductor onng them. To delver the maxmum power to the end user, the power lost durng the transfer of energy must be mnmzed. Utlty companes must also ensure the qualty of power at the output termnals. One aspect of power qualty deals wth the voltage magntude voltage at the outlets must not vary more than 5% of the nomnal voltage (120V) accordng to ANSI standards [1]. To ensure qualty of power and provde the most effcent transfer of power, the dstrbuton company has to perform voltage control and loss mnmzaton respectvely. In the tradtonal dstrbuton grd, control was acheved by adustng the taps on the on load tap change transformer and voltage regulators or adustng the reactve power compensaton of any capactor banks or other compensaton devces. To ensure the most economcal compensaton, optmzaton was necessary. Because of the use of reactve power (VAR) sources for compensaton, the operaton s called Volt/VAR control. The optmzaton functon could be the cost of compensaton, the number of tap changes snce the lfetme of tap change transformers s lmted, loss, etc. In recent tmes however, there s been a call to upgrade the dstrbuton grd and make t more smarter and allow t to handle power flow n the opposte drectons as well, among a lst of other mprovements.e. allow for generators to be connected at the dstrbuton level (called dstrbuted generators or DGs) and not ust at the hgh 10

11 voltage (HV) level. Ths ntatve has come to be known as smart grd and a few such nstallatons are already n development [2]. Customers who use generators for stand-by power or cheap, alternatve power are embracng the dea of DGs. Ths has encouraged planners to envson a grd that can accommodate generators on the consumer sde from whch the utltes can purchase excess energy durng shortages. Such mprovements would make t unnecessary to buy more power or nvest n expensve generators to satsfy the growng demands. Whle dstrbuted generaton has many advantages to offer, ts effect on the grd s stll beng studed, especally at hgh penetratons. In the current state of low penetraton of DGs n the grd, ther effect s neglgble. However, t s expected that the penetraton of DGs wll ncrease n the future. Ambtous targets of 30% renewable penetraton n the US grd by 2030 have been made. Although not all of t s n the form of DGs, they are expected to form a sgnfcantly large porton of renewable sources. European countres already have a sgnfcant percentage of ther generaton produced by DGs and renewable energy [3] and t s estmated to grow further n the future. Wth the growng presence of DGs, studyng ts effects at hgh penetratons becomes necessary because generators wll affect the drecton of power flow; ther effects need to be consdered more carefully when multple generators are connected at multple locatons. Integraton of new sources leads to problems wth control, protecton, slandng and mantenance, to lst a few. Multple new sources embedded nto the grd would only complcate the matter. Ths study explores one aspect of ntegraton of DGs called Voltage/VAR Control whch ams to control the voltage and power flow n the dstrbuton grd through VAR compensaton usng DGs. Another am of ths study s to mnmze loss durng power flow n the dstrbuton grd - called dstrbuton losses. Loss profle can also beneft from the proper placement of DGs on the grd; for example, a thumb rule s lne currents can be reduced by placng power sources close to load centers. Snce loss s drectly proportonal to the square of magntude of lne 11

12 current, reducng the lne current reduces losses. Smlarly, observatons can be made on szng of DGs n a grd and the effect of hgher penetraton of DGs on the loss profle. Senstvty s a concept assocated wth the power flow Jacoban and s calculated by nvertng the Jacoban matrx. Senstvty of a node denotes the change n voltage at that node for a unt change n power at some node on the grd. If the power change can be affected by a DG, senstvty can ndcate the amount of power output necessary to effect a requred change. Based on the concept of senstvty VVC, loss mnmzaton, stng and szng of DGs and the effect of DG penetraton on losses are studed. The study has been organzed as follows: chapter 2 dscusses the motvaton for the study and gves an overvew of dstrbuton networks, dstrbuted generaton, the Voltage-VAR control problem and dstrbuton losses. Chapter 3 formulates the voltage/var control problem mathematcally. Chapter 4 lsts past studes n Voltage-VAR control, use of dstrbuted generators for voltage control, dstrbuton loss and optmzaton and a compensaton technque based on senstvty. Chapter 5 dscusses a modfed algorthm based on senstvty to ncorporate loss optmzaton n the Volt-VAR control problem. Chapter 6 dscusses stng and szng of DGs and the effect of ncreasng DG penetraton n dstrbuton networks. Chapter 7 concludes the study wth a note on the applcatons of DGs, VVC and loss mnmzaton usng DGs and future work. 12

13 CHAPTER 2 OVERVIEW The power ndustry s expermentng wth changes n the manner of power delvery and new avenues of power generaton and mprovement n delvery are beng sought. The changes brng wth them a new set of challenges and problems. Ths study ams to tackle a small set of those challenges pertanng to the ncluson of dstrbuted generaton and comment on the effect of ncreased penetraton of these generators n the grd and ther effect on the dstrbuton system losses. 2.1 Motvaton Ths study ams to accomplsh a fourfold obectve: 1. Voltage control wth reactve power compensaton usng DGs 2. Dstrbuton loss mnmzaton 3. Stng and szng of DGs 4. Study the effect of ncreasng penetraton of DGs n the dstrbuton grd Voltage control s a necessary operaton requred to be performed by a dstrbuton company to mantan power qualty. Tradtonally DGs haven t been ncluded n the control operatons but wth the ncreasng number of DGs [4], [5], t may soon become feasble to use them for control operatons. DGs, especally the nverter nterfaced DGs have quck response rates and can respond quckly to changng condtons. Losses are a bg concern n electrcty transmsson and dstrbuton. The U.S. s among the bggest consumers of electrc power but t loses over 260 bllon kwh every year - the hghest n the world, despte havng an effcent system that loses only 6% [6], [7]. The lost energy translates to a cost of about $20 bllon [5], [7]. Chna, wth comparable power consumpton to the U.S. loses less power n transmsson and dstrbuton. European countres have a smlarly effcent system. Smaller land area also lmts the losses n these natons. But larger countres lke Inda and Brazl wth much lower consumptons than the U.S. lose nearly a quarter and a sxth of ts energy respectvely n transmsson and dstrbuton. Inda s n fact second only to the U.S. n 13

14 the absolute amount of power lost (nearly 220 bllon kwh). There s thus a need to mprove effcency n both transmsson and dstrbuton for economc reasons. Increasng dstrbuton effcency would also reduce the energy loss n the transmsson system due to the reducton n power transmtted over long lnes. DGs wth ther local stng offer the possblty of reducng energy transmsson over long ranges. Technologcal mprovements n the feld of renewable energy generaton also offers the possblty that further expanson n generaton dstrbuted or otherwse and power consumpton can be from clean energy wth a smaller carbon footprnt. However a framework for ther use and control needs to be developed. Ths study s a step n that drecton wth control and compensaton acheved usng senstvty coeffcents. Chapter develops the mathematcal formulaton of the voltage control problem but a bref overvew of the popular DG technologes, dstrbuton systems and voltage and loss control n sectons Dstrbuted Generaton Dstrbuted generaton s a blanket term used to descrbe small scale power generators that are connected at the dstrbuton level or on the customer sde of power meter [8]. Whle there s no consensus on the power output of DGs, most studes consder outputs rangng from klowatts (KW) to a few megawatts (MW) as dstrbuted generaton. DGs have been classfed n some studes [4] nto mcro: up to 5KW; small: 5KW-5MW; medum: 5MW-50MW; and large: 50MW-300MW. Despte the growng nterest and the reducng costs of renewable electrcty such as wnd and solar, fossl fuel based generators are stll the most economcal and relable forms of generaton and mcro turbnes are among the cleanest of combuston based generators and when used as a cogeneraton unt t can have effcences of 80% and above. Mcro turbnes burn fuel at hgh temperature and pressure and the resultng fumes cause rotaton of turbnes blades at hgh speeds. When coupled wth an alternator, ths produces electrcty. Mcro turbnes can be desgned for a wde varety of 14

15 fuels such as fuel ol, natural gas, etc. Mcro turbnes are small n sze, clean and can operate for long perods of tme wth low mantenance [8]. Fuel cells [8] generate electrcty through electrons generated by an electrochemcal reacton. The electrons travel through the electrcal crcut connected to the cell producng drect current. Fuel cells requre a constant supply of fuel - for example, hydrogen to operate. Fuel cells can have an effcency of over 50% even wthout CHP and over 80% wth cogeneraton. Unlke fuel based generators, renewables harness the natural sources of energy whch also makes them ntermttent sources; for example: solar cells cannot work effcently on a cloudy day, a wnd turbne cannot generate electrcty when there s no wnd and droughts wll halt producton n a hydroelectrc power staton. The most popular forms of renewable energy are solar-thermal power, solar photo-voltac cells but the most popular s probably wnd energy. Wnd energy has been used to do work for a long tme and they re beng used to generate electrcty as well. Wnd turbnes are desgned to ntercept the path of the wnd whch causes rotaton of the turbne blades. They are typcally connected to an nducton generator to produce electrcty but synchronous generators are n use as well [9]. To produce usable electrcty, steady wnds are necessary. Wde open spaces are therefore deal to set up wnd turbnes and wnd farms; for example, Mdwest USA s well suted for large wnd farms. But some of the strongest wnds are observed over the sea and t s estmated that wnd energy s more abundant off-shore than on-shore [10]. Despte havng one of the largest nstalled wnd capactes n the world, USA does not have many off-shore farms. Off-shore farms are abundant n many European countres where wnd power s already a sgnfcant porton of the generated power; example: 20% n Denmark or 10% n Ireland and Span [11]. Solar power s utlzed n two ways - drectly convertng to electrcty wth a photovoltac cell or ndrectly wth a concentrated solar power where the sunlght s 15

16 focused to a small regon usng lenses and mrrors to generate steam to rotate turbnes. Photovoltac cells convert solar energy to electrcty usng the photovoltac effect where a voltage dfference s nduced across P-N uncton by shnng radaton (solar radaton) on one of the surfaces [12]. Photovoltac cells generate DC voltage and addtonal electroncs (called nverters) are needed to convert t to AC for nterconnecton wth the grd. Whle the cost of solar generator modules s reducng, t s stll more expensve to produce a unt of energy usng solar that the more tradtonal generators. Wth the emphass on revampng the grd nto a smart grd whch seeks to support plug and play usage capablty for DGs, t can be assumed that DGs are gong to become an ntegral part of the electrc grd because DGs can be used to expand the power capacty of a dstrbuton system wthout purchasng addtonal power or buld expensve, new generator statons. Another advantage of dstrbuted generaton s that the generators are much smaller than the centralzed generaton resources and therefore cheaper. Therefore new technologcal mprovements can easly be deployed n the form of dstrbuted generators. Dstrbuted generators do not currently have an actve role n provdng ancllary servces to the grd; they are nstead expected to produce power at a constant rate at a constant power factor. Durng low voltage stuatons they are requred to rde through or dsconnect from the grd n severe cases. Two reasons [13], [14] for ther passve connecton are 1> DGs do not have suffcent generaton capablty to have a sgnfcant effect and 2> a control algorthm operatng n parallel wth the utlty control operatons mght aggravate the stuaton. However wth modern, fast actng, electronc control systems and communcaton networks, DGs can be ncluded n a coordnated control plan to provde voltage and power support. Ths study s an attempt to devse such a coordnated control technque. 16

17 2.3 Dstrbuton Networks Due to economes of scale, generaton of power was tradtonally done at remote locatons close to the fuel source and away from the consumers. Dstrbuton networks are delvery systems to brng power from the generators though the transmsson grd to the consumer. The transmsson system whch begns at the generator and ends at the dstrbuton substaton s a meshed network for ncreased relablty and power sharng. But the dstrbuton system (begnnng at the dstrbuton substaton and endng at the customer s premses) s manly radal.e. lnes startng from the substaton rarely form loops. Fgure 2-1. Schematc of a Power grd. Source: US Department of Energy [15] Most nodes of a dstrbuton system are rarely connected to more than two other nodes. The seres of branches formng a chan are known as feeder lnes and the feeder(s) connected to the substaton bus are known as the man feeder. The others are known as laterals or sub-feeders. Nodes are any ponts of nterest n the network, generally ponts wth a connected load, a lateral, a transformer, DG, regulator, etc. Another dfference between dstrbuton and transmsson systems s that seres resstance of dstrbuton lnes as a fracton of the seres reactance (typcally referenced by R/X rato) s much hgher for dstrbuton lnes whereas n transmsson lnes the reactance s domnant. A consequence of ths property s real power can also be dspatched for voltage regulaton whereas n transmsson systems, reactve power produces a bgger voltage change for the same amount of dspatch. Although ths 17

18 study s lmted to the conventonal reactve power (VAR) support, from a voltage regulaton stand-pont, real power dspatch can produce a smlar result assumng the lne reactance and resstance are comparable. A dstrbuton system may also be unbalanced.e. all three phases of the power system may not be equally loaded; one or more phases may not even be used. Ths s one of the reasons that tradtonal power flow algorthms used for transmsson systems cannot be used for dstrbuton systems. Due to the unbalanced nature, the hgh R/X ratos and the radal nature of the grd, Newton-Raphson type methods may fal to converge. Therefore other methods better suted for radal dstrbuton system condtons have been developed. The forward-backward method sweep based on ladder theory [16] s used n ths study for all power flow operatons. The power flow algorthm treats the substaton bus as the slack node and the remanng nodes as PQ nodes. Includng PV nodes n the feeder complcates power flow because keepng a constant voltage at a partcular node requres a VVC operaton. Therefore, for smplcty even DGs are consdered as PQ nodes wth a negatve load value to ndcate that they feed power nto the network nstead of consumng t. As evdenced by the radal topology, the dstrbuton grd was not orgnally desgned for a bdrectonal flow of power. Although the cables can handle the reverse flow of current, protecton devces such as dstance relays assume a undrectonal flow of current. A bdrectonal flow wll cause a reducton n lne currents whch can adversely affect the detecton capactes of the relay. It s also a concern for servce personnel operatng on a faulty lne - n a radal structure t s easy to de-energze a lne by cuttng off the man supply to the lne. But wth DGs connected, the lne may be slanded - whch mples that the lne s carryng current from the DGs but not the man supply. Lne voltage regulators operaton s also affected snce they estmate voltage at a downstream node based on the current through ts lne compensaton crcut and a secondary source located downstream dsrupts ths relaton. Therefore a control 18

19 procedure that does not depend heavly on lne currents to estmate voltage must be made avalable for use wth DGs. 2.4 Voltage and Reactve Power Control The ANSI standard [1] requres the voltages durng steady state operaton to be as follows: on a nomnal voltage of 120V, the servce voltage s allowed a leeway of Voltage-VAR control or VVC refers to regulatng the voltage by feedng or consumng reactve power as necessary. Whle real and reactve powers and node voltage and phase are all ntrcately lnked, there s a stronger relaton between reactve power and voltage magntude; between real power and voltage angle. Ths phenomenon exsts because of the decouplng of real and reactve power that occurs f the lne resstance s much smaller than the reactance and voltage magntude at all nodes s mantaned at around 1pu. Lne mpedance s a fxed parameter and has to be chosen durng system desgn but the second condton s vald when the grd s adequately controlled and mantaned. For the case of transmsson lnes, lne reactve mpedance s ndeed more than resstance, but for dstrbuton lnes t s not necessarly true. Dependng on the rato of reactance and resstance of a lne both actve and reactve power may have equal effect on the voltage of the grd but by conventon, reactve power s chosen for compensaton. In case of reactve power (VAR) compensaton, the rule of thumb s: nectng VAR nto the grd ncreases the voltage whle absorbng t reduces the voltage. Tradtonally voltage control has been done usng swtchng crcuts, transformers, lne drop compensators, step voltage regulators, load sheddng, reactve power compensaton usng capactor banks, etc. Wth the growng popularty of dstrbuted generaton or dsperse generaton other avenues of compensaton have opened up. Ths study s concerned wth VVC but one that s based on senstvty of voltage to reactve power nectons from DGs. The study also explores the possblty of usng voltage senstvty and VVC to reduce dstrbuton power loss. 19

20 Reducng losses nvolves reducng lne currents all along the feeder. Ths can also be restated as reducng the voltage dfference between adacent nodes. It s easy to prove that dstrbutng power sources across the feeder reduces the lne current and thereby losses. For example n Fgure 2-2, a sngle DG s connected at the last node of an N + 1 node feeder. Assumng all the nodes have an equal szed load connected to t and they draw the same amount of current rrespectve of the voltage at the node, the current at the source bus s N I load wthout the DG. If the DG assumes an equal load, the current drawn from each source would be N I load /2. Table 1 compares the lowest voltage, maxmum current and losses for the case wth and wthout DG. Wthout any form of voltage control or compensaton, voltage magntude decreases steadly along the length of the feeder begnnng at the substaton (node 0). Fgure 2-2. N+1 load feeder wth a dstrbuted generator connected at the last node Wth the DG however, the decrease n voltage s lower because the net current from a sngle source s smaller than the current drawn from the substaton wthout any DG. Therefore, the voltage reduces movng from ether end of the feeder towards the center. For smplcty N s taken to be even. Table 2-1. Comparson of voltage, current and loss wth and wthout DG Wthout DG Wth DG Lowest voltage V0 Z lne NI load V0 Z lne NI load /2 Maxmum current NI load 1 2 NI load Total power loss 1 6 N(N + 1)(2N + 1)I 2 load lne 1 12N(N + 1)(N + 2)I 2 load lne 20

21 It can be nferred that ncreasng the number of power sources reduces the maxmum lne current. Snce loss s proportonate to the square of the lne current, reducng the maxmum current magntude has a huge mpact on the total dstrbuton loss n a feeder. In the example, reducton s by almost a factor of 4. In the example of Fgure 2-2 the type of load used s constant current load - where the current drawn s ndependent of the voltage. Power consumed by a load s gven by VI*, therefore f a constant current load s connected at a hgher voltage t consumes more power. The other commonly used types of load are constant power and constant mpedance. Constant power loads draw the same amount of power rrespectve of the voltage but current drawn reduces wth ncreasng voltage. Constant mpedance loads have constant mpedance regardless of the voltage but power ncreases as the square of voltage and current ncreases lnearly wth voltage. Fgure 2-3. Current drawn at dfferent voltages for dfferent load types If all loads on a grd were of the same type, loss mnmzaton would be a smple problem. For a constant power load a hgher voltage load s preferred therefore lettng the node wth the hghest voltage to be at 1.05 pu. (maxmum allowed voltage accordng to ANSI standards) would be suffcent. For constant mpedance lettng the lowest voltage be 0.95 pu. would solve the control problem. For constant current loads as long as the nodal voltages are wthn allowable lmts, no control s necessary. For a 21

22 homogeneous load type control s smple rrespectve of the load szes but actual loads are not homogeneous and optmzaton s requred to determne the best confguraton and dspatch. Chapter 3 lsts some of the technques used n prevous studes. 22

23 CHAPTER 3 PROBLEM DESCRIPTION An electrcal system s governed by power flow equatons whch are a result of Krchhoff s current law and Ohm s law. These equatons defne the relatonshp between the voltage at each node n the grd and the loads or generators connected to them. Knowng the voltage at each node, t s possble to know the current n all the lnes; the exact power consumed or nected at each node and other metrcs such as stablty of the grd etc. The voltages at all nodes (defned by a voltage phasor magntude and angle) are known as the state of the system. The set power flow equatons can be represented as F (x, u) = 0 where x s the state vector and u s the vector of all control varables such as tap poston or voltage regulator, on load tap changng transformer, generator power output, etc. and the loads at dfferent nodes. F s the relaton between x and u defned by Krchhoff s current law and Ohm s law. For ease of calculaton all varables are represented n the per unt system. Voltage control accordng to ANSI standards requres that the utlty voltage not vary more than 5% from the nomnal voltage of 1 pu. If x can be separated as x = V θ where V s the vector of node voltage magntudes and θ s the bus angle, then voltage control mples 0.95 V 1.05 for all nodes = 1, 2,... N f V goes out of bounds, u control can be adusted so that V s wthn lmts agan. In u = u control u load 23

24 u control s a vector of all control varables and u load s the vector of load values. The vector of control sgnals, u control, can be chosen n dfferent ways to acheve the requred result. Hence an obectve functon s necessary to choose best vector based on some crtera. If tap changng transformers are used, the number of tap changes s often a crteron. If compensaton methods are beng used and t costs the utlty dfferent rates for dfferent types of compensaton then the most economcal dspatch s sought. Lne losses are also often consdered for optmzaton snce losses can be controlled by varyng the voltage at the dfferent nodes. The power lost as heat on a sngle lne between nodes,, s gven as P loss = I 2 R = (V V ) 2 /R where V = V e θ and R s the resstance of the lne between nodes and. Power systems however, are not sngle lnes but have three phases, whch n case of a dstrbuton network may be unbalanced. Therefore the total loss s calculated as a product of vectors and matrces as: P loss = Real {VI } = Real { (V V )Z 1 (V V ) } If the system s three phase, V s a 3 1 complex vector of voltages of the three phases of each node and Z s a 3 3 complex matrx. The total system loss s obtaned by addng the loss over all the lnes P loss total =, Real { (V V )Z 1 (V V ) } (3 1) For two nodes, not connected to each other, Z 1 s a zero matrx and doesn t contrbute to the loss. Therefore the general VVC wth loss optmzaton problem can be wrtten as 24

25 Mnmze P loss total =, Real { (V V )Z 1 V V } (3 2) Such that F (x, u) = pu V 1.05pu and u mn u u max = 1, 2,... M where u are the control varables. In ths study the control varables used are the reactve power produced by DGs connected at dfferent nodes n the dstrbuton grd. Adustng the power producton may not always be suffcent control mechansm and voltage regulators may need to be adusted as well. The tap changng operaton s not ncluded n the optmzaton but performed f optmzaton fals to produce a feasble result. The optmzaton and results are dscussed n depth n chapter 5. Chapter 4 dscusses the past studes done n the feld of voltage VAR control, stng and szng of reactve power sources and use of voltage senstvty for control. In addton to VAR optmzaton, placement of DGs on the feeder can also be used to adust losses - some postons are better suted for loss reducton than others. Smlarly the capacty of the DGs can also be optmzed for a better performance. The optmal stng and szng of DGs s dscussed n chapter 6. Also dscussed n the chapter s the effect of ncreasng penetraton of DGs on dstrbuton losses. 25

26 CHAPTER 4 LITERATURE REVIEW Voltage and reactve power control (Volt/VAR control or VVC) s an mportant task that has been studed many tmes for both the transmsson grd and dstrbuton grd. Whle new nnovatve technques are beng sought for voltage control, the most commonly used methods are stll the tme tested ones such as feeder reconfguraton [17], [18] to mnmze lne currents. The radal structure of the dstrbuton system also supports regulaton through step voltage regulator wth lne drop compensator [16]. Inectng reactve power usng compensaton devces such as statc VAR compensators (SVCs), statc synchronous compensators (STATCOMs) and other flexble alternatng current transmsson system (FACTS) devces can be used to boost voltage as well as control the phase angle [19]. The smplest and most commonly used form of compensaton though s capactor banks whch may be located at the substaton or along the feeder lne. Tradtonal control technques have dealt wth optmzng the postons of the taps n the transformers or controllng the output of the compensaton devces [20] or both whle optmzng for economc or other system constrants. Due to the non-lnearty of the control problem, evolutonary algorthms such as partcle swarm optmzaton [21], [22] or genetc algorthm [23], [24] have been extensvely used for optmzaton. Recent technologcal mprovements have made DGs popular as a parallel source of power for mportant or senstve loads. Ther capacty to nect excess power nto the grd has made them a vable opton for compensaton. Although DGs are beng connected to the grd, ther nvolvement n provdng ancllary servces s neglgble. There s stll concern regardng ntegraton and control of new generators n the dstrbuton grd although extensve lterature s avalable on varous aspects of DG ntegraton and utlzaton from the varous technologes t entals [4], [5], [8], [25], ther mpact - both economc [26] and on the voltage profle [27], [28]; and ncentves to promote ther use 26

27 [29]; to the concerns and challenges of usng DGs [25], [30]. A lot of research work has also been done on control nvolvng DGs [13], [27], [31], [32] and more mportantly szng and stng the DGs on the grd [28], [33], [34]. Wth the current focus on upgradng the electrc grd to a smart grd wth support for decentralzed control, dfferent methods of decentralzed control are beng researched. Mult agent systems (MAS) [35], [36] are among the deas beng explored. The algorthm developed by Baran and Markab [37] to determne the optmum reactve power dspatch of DGs usng lnear programmng, s an example. A smlar algorthm that dspatches both real and reactve s dscussed n [38]. Senstvty of dfferent types have also been used to determne the locaton of DGs on the grd [39], [40] as well. But Gozel and Hocaoglu [41] wth an ntenton to avod Jacoban and admttance matrx, developed an analytcal method to locate and sze DGs on a radal system usng a loss senstvty factor based on the current necton matrx. The goal was to determne the amount of necton requred to reduce the losses to a mnmum. But wth a loss functon that can be derved from measured voltage senstvtes, t may be easer to calculate the loss senstvty coeffcents. Voltage and Reactve Power control usng Senstvty. The algorthm developed by Markab and Baran [37] mplemented a smple mult-agent dstrbuted VVC algorthm based on senstvty coeffcents. They used senstvty coeffcents derved from the power flow Jacoban to determne dspatch usng lnear programmng. However, to make the algorthm decentralzed and ndependent of the grd archtecture, senstvty coeffcents of nodes wthout a DG were elmnated through Kron reducton. But the new coeffcents are not measurable quanttes snce they have been adusted by Kron reducton and made system dependent. Nevertheless, the concept of usng senstvty to determne dspatch s a useful result. Dspatch s can stll be calculated usng the measured senstvty values whch are the true nstantaneous senstvty values. 27

28 A sngle feeder lne wth multple DGs connected along the length of t wth the DGs carryng most of the load was consdered n the study. Each DG s assumed to be an agent wth ntellgence. The remanng nodes are passve wth no ntellgence. All the agents can communcate among themselves to share any necessary nformaton. Each agent performs three mportant tasks montorng, moderatng and dspatch. Montorng refers to checkng the node voltage and verfyng that t s always wthn the specfed range (wthn 5% of the nomnal). When the voltage s no longer wthn lmts, the agent correspondng to the (most) affected node acts as the moderator. They note that the voltages of the downstream nodes are usually the most severely affected and t mght be necessary to have a dummy DG wth no output connected at these nodes to montor the voltage at the these ponts. It essentally translates to havng a measurng devce lke a PMU connected at the end node and extendng the communcaton networks tll the end of the feeder. If that may not be possble then some method of estmatng the voltage at the end s necessary for example by assumng a constant voltage dfference between the end of the feeder and ts nearest DG unt. When a nodal voltage volates the operatng lmts, the closest DG senses t and communcates wth the other DGs and requests for reactve support and receves ther bds. The bds are the maxmum support each DG can lend and the senstvty coeffcent for the partcular node. The moderator then decdes the optmal dspatch scheme for DGs. The DGs on recevng the dspatch change the output power to sut requrements. Ths s the dspatch mode. In general, feedng reactve power nto the grd ncreases the voltage whle consumng t reduces the voltage magntude. Ths behavor s captured by the senstvty coeffcents and smple lnear programmng can calculate the dspatch scheme. The problem s formulated as Mnmze Q (4 1) 28

29 Such that V k = V mn V 0 k and Q mn Q 0 + Q Q max where Q s the change n reactve power output of th DG, V 0 k s the current voltage at node k and Q 0 s the current reactve power output of th DG. The DG causng the hghest senstvty to the affected node s chosen and t supports the node to whatever extent t can. If the reactve power support of that DG does not suffce, the DG wth the next hghest senstvty helps and so on untl the voltage excess or defcency has been compensated and all the voltages are wthn the specfed lmts. If there are n nodes n the dstrbuton system and V1, V2... V n are the node voltage magntudes (assumng a balanced feeder, but the theory can easly be expanded to unbalanced systems) and there are m (m n) DGs wth reactve power Q1, Q2... Q m, the voltage senstvty s defned as β = V Q = 1, 2,... n and = 1, 2... m (4 2) The partal dervatves form the Jacoban matrx used n Newton-Raphson power flow and t defnes the relaton between VAR support of the DGs and voltage at the nodes. The effect of the m DGs on ts node voltage can be more accurately expressed by consderng that the net reactve power necton at most nodes s zero. Hence n voltage equatons can be reduced to only m equatons by Kron reducton. The coeffcents of the varables obtaned thus are the requred senstvtes. It s easy to determne the VAR support from equatons (4 3) and (4 4). If H s the Jacoban matrx, P s the vector of real power nectons are each node, Q s the reactve power nected, x s the vector of voltage magntudes and θ s the vector of node voltage angles, then f = P Q and x = θ V 29

30 H = f = H x H P θ H Q θ H P V H Q V (4 3) H Q V s the partal of reactve power wth respect to voltage magntude. Reactve support can be obtaned usng real and reactve power decouplng, whch s based on the fact that the voltage magntude at a node affects the reactve power nected at that node rather than the real power whch s affected by the voltage angle. Hence Q/V = H Q V V (4 4) Q s dvded by the node voltage, V, to lnearze the power flow equatons. Snce Q s zero for the load nodes, the rows and columns of H Q V can be rearranged to where H Q V = B 11 B21 B11 = partal dervatve of reactve power necton at the load nodes wth respect to voltages at the DG nodes B12= partal dervatve of reactve power necton at the load nodes wth respect to voltages at the DG nodes B21= partal dervatve of reactve power necton at the DG nodes wth respect to voltages at the load nodes B22= partal dervatve of reactve power necton at the DG nodes wth respect to B12 B22 voltages at these nodes. 0 Q/V = B 11 B21 B12 B22 V L V D G (4 5) V L s the vector of voltages at the load nodes. 30

31 Therefore, V D G = (B22 B21B1 1 1 B 12) 1 Q D G /V or (4 6) V D G = βq D G (4 7) β s the senstvty matrx. The elements of β determne the reactve support that each DG provdes. Therefore equaton (4 1) changes to Mnmze Such that V k = Q (4 8) m β k Q = V mn V 0 k =1 0 Q 0 + Q Q max Equaton (4 8) ndcates that the best soluton to ths problem s to have maxmum dspatch for the DG wth the hghest senstvty untl generator capacty s reached. If that s not suffcent, DG wth the next largest senstvty adusts ts output and so forth untl the voltage drop has been compensated. A drawback of ths algorthm s that t adusts the voltage to brng t wthn acceptable operatng range but only barely. So f voltage exceeds 1.05pu t s lowered to 1.05pu, f t falls below 0.95pu t s rased to 0.95pu. Ths may not be the best voltage profle for a dstrbuton feeder snce the load s always changng; even small varatons n load or DG output can cause the voltages to go out of range agan. To mantan t at a voltage slghtly hgher than acceptable level mght seem lke a good opton but that only nvtes the queston, how hgh?. The answer les not n rasng or lowerng the voltage to a fxed level, but to optmze the voltage for other parameters. Loss s the obectve chosen n ths study because t not only reduces the wastage of energy lnes but also frees up the lne capacty for more useful power flow. A new set of constrants and optmzaton functon can therefore be devsed to account for these. A few modfcatons to the algorthm are suggested whch employ a quadratc optmzaton functon rather than a lnear one. Ths s dscussed n chapter 31

32 5. Chapter 5 also dscusses voltage senstvty and ts behavor to changes n load and power generaton. 32

33 CHAPTER 5 VOLTAGE-VAR CONTROL AND LOSS MINIMIZATION The obectve of voltage-var control can be expanded from ust mantanng the voltage at the end of each feeder node wthn the specfed voltage range to also protect the voltage aganst varatons n the system condtons such as loadng, faults, loss of power, etc. Wth access to power generaton sources at dfferent locatons n the grd t becomes possble to not only mantan voltages wthn operable regons but manpulate the power flow so that other obectves can be acheved. The most mportant advantage of usng voltage senstvty for ths purpose s t allows for the estmaton of the new state - and subsequently other parameters that are a functon of nodal voltage - wthout performng load flow analyss. A complex set of nonlnear equatons can be approxmated to a lnear combnaton of senstvty coeffcents, savng precous computaton resource and tme. 5.1 Voltage Senstvty Senstvty has been defned n chapter 4 (equaton (4 5)) as the nverse of the power flow Jacoban. Voltage senstvty wth respect to change n reactve power necton at a node (hereby referred to as voltage senstvty or ust senstvty; ths study deals exclusvely wth reactve power and voltage change unless otherwse specfed) s an n n block n the 2n 2n Jacoban matrx. Senstvty s an easy way of estmatng the new state of the grd when the DG outputs are changed snce t s the observed, steady state voltage change for a unt change n power producton. Fgure 5-1 shows the senstvty of phase A for all nodes of a 34 node feeder for 1KVAR change n output power of a DG when connected at four dfferent locatons. The mssng senstvty values are a consequence of an unbalanced feeder - not all nodes utlze all three phases. Usng senstvty, for some change n power producton, the voltage change n the feeder nodes can be estmated by scalng the senstvty at these nodes the approprate amount. The relaton s descrbed by equaton (4 7). However, the expresson for β, 33

34 the senstvty s modfed from equaton (4 6); nstead of usng senstvty of only small subset of nodes from a reduced set of power flow equatons, the senstvty of all nodes represented by the columns of H Q 1 V are used. Equaton (4 6) explots the fact that power necton at non-dg nodes s zero. Hence the senstvty calculated from only DG connected nodes does not represent the the measurable change n voltage at the partcular nodes; t s a calculated quantty, although t may stll be numercally smlar to the measurable senstvty. Snce the magntude of voltage change s qute small (of the order of 10 4p.u./KVAR change n power necton), the msmatch between the calculated and the observed value may go unnotced. Patterns and trends [42] smlar to those of the calculated senstvty of equaton (4 6) are also observable for the actual measured senstvty coeffcents. Fgure 5-1. Senstvty of 34 node feeder for four dfferent DG postons For a perfectly decoupled system, the senstvty parameters are a constant wth H Q V gven by the admttance matrx. But even for a lossless lne t s not possble to have a perfectly decoupled system and the senstvty vares wth voltage. Over large voltage ranges senstvty s non-lnear but over smaller ranges - such as n LV or MV compensaton schemes t can be approxmated to a lnear trend (fgure 5-2). Mathematcally ths observaton can be made by not approxmatng the nodal voltage to 34

35 1pu. Ths s also the expresson used n ths study. But the most accurate value can be obtaned by nvertng the Jacoban H = H P θ H Q θ H P V H Q V wth no assumptons or approxmatons. The columns represent the senstvty coeffcents for all the nodes - except the substaton bus - for all possble DG locatons. The senstvty of the substaton bus s 0 due to the control acton of the substaton control system. In the Jacoban of dmenson 2n 2n (when number of nodes n the feeder s n + 1; senstvty of the substaton bus s zero) and the voltage senstvty to reactve power s a n n block n the bgger matrx. Fgure 5-2 s the plot of senstvty of a partcular node wth DG fxed at a dfferent node and the reactve power output of the DG s vared from from -100 KVAR to +100KVAR n steps of 1 KVAR. Plot A s the result of repeatng the process for dfferent values of real power output. Whle plot A s for all three phases, plot B dsplays the senstvty for a sngle phase (phase A) wth respect to the node voltage nstead of the reactve power output. Fgure 5-2 s typcal of most nodes. It s observed that whle senstvty s not a constant, t can be approxmated as a lnear functon for most cases. The centralzed voltage control optmzaton functon s derved assumng a constant senstvty and the consequences of assumng lnearly varyng senstvty are explaned. 5.2 Centralzed Voltage Control and Loss Optmzaton If the senstvty s farly constant, a sngle coeffcent can be selected for each node and phase for control. But due to the varyng voltage and loadng and necton condtons, senstvty also vares. Hence there are fewer approxmatons. The centralzed control approach uses all the voltage and approxmate senstvty values for voltage and loss estmaton. The decentralzed algorthm whch s gven to a coordnated 35

36 A Varaton wth change n reactve dspatch Fgure 5-2. Varaton of senstvty B Varaton wth node voltage control structure based on local nformaton s dscussed n secton 5.3 but both of them optmze the same quantty - loss. The decentralzed verson s an extenson of the centralzed verson. 36

37 5.2.1 Obectve Functon (3 1) as The expresson for dstrbuton loss on a sngle branch was derved n equaton Mnmze P loss total =, Real { (V V )Z 1 (V V ) } Such that F (x, u) = pu V 1.05pu and u mn u u max = 1, 2,... M where Z s the mpedance between two nodes and. Consderng the total loss and not only the real power loss, loss = (V2 V1)Z 1 12 (V 2 V1) If the voltages after optmzaton are V 1 and V 2 then loss = (V 2 V 1 )Z 1 12 (V 2 V 1 ) but V = V + V and V can be estmated usng voltage senstvty as loss = (V2 + V2 V1 V1)Z 1 12 (V 2 + V2 V1 V1) Smplfyng, loss =(V2 V1)Z 1 12 (V 2 V1) + (V2 V1)Z 1 12 (V 2 V1) + (V2 V1)Z 1 12 (V 2 V1) + (V2 V1)Z 1 12 (V 2 V1) The frst term on the rght of the equaton s loss hence loss loss = (V2 V1)Z 1 12 (V 2 V1) + (V2 V1)Z 1 12 (V 2 V1) + (V2 V1)Z 1 12 (V 2 V1) (5 1) 37

38 Snce loss denotes the ntal (or current) state of loss n the lne, t s a constant wth respect to optmzaton and can be neglected. Ths corresponds to optmzng for change n total loss rather than the total loss tself. Thus the new value of f s f f = +, (V V )Z 1 (V V ) + (V V )Z 1 (V V ) (V V )Z 1 (V V ) (5 2), The change n voltage at k th node V k, can be represented as Or, n vector form: V k = β k Q DG V k = Q T DGβ (5 3) Substtutng n equaton (5 1) and smplfyng, f = + (V V )Z 1 (β Q DG ) + (QDGβ T )Z 1 (V V ),, (QDGβ T )Z 1 (β Q DG ) where β = β β s a 3 m matrx contanng the senstvty coeffcents of each of the three phases of a partcular node wth respect to all the connected DGs. Therefore, f = +,, ((V V )Z 1 β )Q DG + Q DG (β Z 1 (V V ) ) Q DG (β Z 1 β )Q DG Ths can be further smplfed to a quadratc equaton n vector form as f = AQ DG + Q T DG B + Q T DG C Q DG 38

39 Consderng only the real power loss, the fnal obectve functon s f = PQ DG + Q T DG QQ DG (5 4) where P = Real{A + B} and Q = Real{C} A second voltage regulator control level exsts above ths DG dspatch control to utlze the control optons already ncorporated n the feeder. Due to the exstence of DGs, tap postons cannot be accurately selected by the lne compensator crcut and downstream voltage has to be communcated to the regulator controller or the tap can be shfted by one poston at a tme. For each change n tap settngs, the optmzaton algorthm for the DGs s executed. The combnaton of both these operatons determnes the deal settngs. Unlke the compensaton algorthm of Markab and Baran, ths method of loss control s not gven to dspersve control; ths s a centralzed power flow and loss control algorthm because to develop the obectve functon all the node voltages are necessary. An agent based decentralzed varant of ths algorthm can also be devsed; dscussed n secton 5.3. However wth the ncreasng ncorporaton of communcaton channels between the agents of a power grd, t becomes possble to locate the control center at any locaton, ncludng a node on the feeder lne. It s through the communcaton network that a dspersed control of the grd can be acheved. Another mportant note regardng the centralzed algorthm s that V used n the dervaton s a complex quantty whereas voltage senstvty n the Jacoban s the change n voltage magntude wth respect to DG output, whch s a real number. Usng angular senstvty and voltage senstvty to reactve power and the voltage profle, the complex V can be calculated. In the smulatons however, the complex voltage change s measured. By choosng a small enough change n reactve power necton and usng that for senstvty the magntude of the complex value and the actual change n voltage 39