STATCOM:In the electrical distribution industry, engineers are taskedwith manipulating basically two major system constraints;these are providing sufficient current capacity to the entireload while maintaining an acceptable voltage level. Sinceelectrical circuits operate within the laws of physics,typically the system planner will confront both of theseproblems at once, trying to maintain each within acceptablelimits. Feeder conductors within loaddense urban areastypically experience thermal limitations due to heavy feederloading. Corresponding I*X losses result in reduced systemvoltage, but feeders in these areas are limited by ampacitycontstraints. In distinction, feeders in rural areas aresubject to lighter loading but they may span great distances.This increased distance between the source and the load(s)may result in gradual voltage degradation, which causes anincreased current demand to fulfill the power requirements.This exacerbates the problem.Historically, low voltage conditions have been addressedthrough the conventional means of voltage regulators andsystem shunt capacitors. Although these electrical devicescan sometimes be successfully integrated into a distributionsystem to provide a balance between the power components,this is not always the case. Simply stated, when regulatorsthat operate by adjusting their taps to maintainpredetermined setpoint voltage levels are coupled withcapacitors that are switched on and off to regulate voltage,the voltage swings that the a circuit endures (sometimesresulting in "hunting") can cause concerns for customersdue to adverse effects from reduced power quality. Thedevelopment of the electronic Distribution StaticCompensator, or D-STATCOM, provides the distributionplanner with a new tool to alleviate these conditionsthrough dynamic voltage regulation.We propose a solution to the concern of voltageregulation on long, voltage-limited feeders through dynamicvoltage regulation with the D-STATCOM, a fast electricalpower controller under development. The D-STATCOMhas a constant current capability at its reactive output limit,anaiogous to a synchronous generator. Consequently, thereactive power output of a D-STATCOM is proportional tothe system voltage rather than the square of the systemvoltage, as in a capacitor.

In the effort to develop a distribution system which willcontinually provide quality power while maintainingfreedom from the transients, Westinghouse has developedthe D-STATCOM as part of their program for advanceddistribution. The D-STATCOM is a solid-state dc to acswitching power converter that consists of a three-phase,voltage-sourced inverter. In its basic form, the DSTATCOMinjects a voltage in phase with the systemvoltage, thus providing voltage support and regulation ofVAr flow. Because the device generates a synchronouswaveform, it is capable of generating continuously variable

reactive or capacitive shunt compensation at a level up tothe maximum MVA rating of the D-STATCOM inverter.This equipment is forced-air-cooled is available in ratingsfrom 1 to 10 MVA in 1 MVA modular increments.The easiest way to understand the operation of a DSTATCOMis by analogy to a synchronous machine. Thebasis of operation of a synchronous machine is that it can beoperated with either an overexcited field, causing it tosupply reactive power to the system, or an underexcitedfield, causing it to absorb reactive power from the system.Synchronous machines can also adjust their outputcontinuously to compensate for system conditions, and,being inductive in nature, are seldom a source of switchingtransients or other disturbances. Synchronous machines areseldomly applied in distribution systems, however, becausethey have relatively high energy losses, and, being rotatingmachines, have high maintenance requirements and lowavailabilities compared to static passive devices. Also, theycontribute large amounts of short circuit current. In thetypical utility, these machines cannot be applied easily as acorrective measure in an everyday distribution environment.Conceptually, the D-STATCOM performs like a staticsynchronous machine. Over 15 years ago, Gyugyi [l]suggested an analogue to synchronous machine that did nothave any moving parts. The device was described as a“static condenser”, or “STATCON, by a member of a U.S.utility. The name was quickly adopted by the powerindustry in the U.S. The name was changed recently tostatic synchronous compensator, or “STATCOM inrecognition of international practice (i.e. the term“synchronous condenser” is used only in the U.S.). The DSTATCOMuses an electronic inverter connected to the lineby tie reactors to generate reactive power.

DFC

Adynamic flow controller (DFC) is composed of: 1) a mechanically-

switched phase-shifting transformer (PST);2) a multimodule thyristor-switched series capacitor (TSSC);3) a multimodule thyristor-switched series reactor (TSSR); and4) a mechanically-switched shunt capacitor (MSC) unit [1].DFC can provide steady-state and dynamic power flow controlfor power lines and is considered as a FACTS controller. Due tothe discrete switching nature of PST, TSSC, TSSR, and MSCunits, which constitute a DFC: 1) these units are best modeledas finite automata and 2) then a discrete event system (DES)supervisory control can be used to design and implement theoverall control logic.A DES is a dynamic system that evolves in accordance withthe sudden occurrence of physical events at possibly unknownirregular intervals [2]. The supervisory control technique is aneffective analytical tool for automation and control of DES [3].Discrete-event models are generally used to describe systemswhere coordination and control are required to ensure the orderlyflow of events, and/or to prevent the occurrence of undesiredchains of events. DES serves to describe a wide varietyof behaviors in industrial and physical systems. These includeManuscript received February 06, 2007; revised November 21, 2007. Firstpublished April 03, 2008; current version published December 24, 2008. Paperno. TPWRD-00063-2007.A. A. Afzalian is with the Shahid Abbaspour University of Technology,Tehran 171916765, Iran (e-mail: afzalian@ieee.org).S. A. Nabavi Niaki, M. R. Iravani, and W. M.Wonham are with the Universityof Toronto, Toronto, ON M5S 3G4, Canada (e-mail: nabavi.niaki@utoronto.ca;iravani@ecf.utoronto.ca; wonham@control.toronto.edu).Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TPWRD.2008.921114control and scheduling of electrical power systems, manufacturingsystems, queuing systems and communication protocols,and database management systems. Applications of DES theoryto power systems [4]–[7] include: 1) supervisory control, 2)modeling and analysis, and 3) monitoring and diagnosis. Thesynthesis of a DES-based supervisory control for an underloadtap-changing transformer (ULTC) is introduced in [8].In the last two decades, DES have been studied with respectto modeling, analysis, and control. Synthesis methods for DEScontrols have been developed and implemented in a softwareenvironment called TCT [9] to compute controllers that are optimalin the sense that the controlled system not only satisfiesthe specifications but is also as permissive as possible. The developedsoftware [9] is used in this study for synthesizing thesupervisory controllers.DFC components and the control specifications in each modeof operation are modeled as finite automata. Then supervisorycontrol is designed for the DFC in automatic and auto/manualmodes of operation, and in centralized and decentralizedstructures.DFC consists of discrete-event dynamic components that areevent-driven and exhibit discrete-event behavior. Neglectingdiscrete properties of these components in modeling and control

of the system reduces the accuracy of the model and resultsin a suboptimal control strategy [12]. Supervisory controlof discrete-event systems (SCDES) is a systematic approachto synthesize a control system for plants with discrete-eventcomponents. SCDES evaluates controllability of specifications(control logic) with respect to the plant and guarantees thenonblocking and nonconflicting properties for the supervisor(controller) using a systematic formulation on a rigorous mathematicalbasis.Since the DFC components have a discrete-event nature,the conventional controllers (e.g., PI controllers) are not fullyapplicable. The proposed DES controller has the followingadvantages.1) It copes with the discrete-event dynamic nature of the components,rather than their approximate continuous models.2) It constructs the optimal controllable approximation to thecontrol specifications.3) It guarantees required properties for the supervisor, such asthe nonblocking and nonconflicting properties.4) It formulates the control solution in a hierarchical structurefor large plants, such as microgrids.II. PRINCIPLES OF DFC OPERATION

Fig. 1 shows a schematic diagram of a DFC that is connectedbetween buses and within a transmission line and comprises:0885-8977/$25.00 © 2008 IEEE220 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 24, NO. 1, JANUARY 2009Fig. 1. Schematic diagram of a DFC.Fig. 2. One-line diagram of the study system.• a conventional (mechanically switched) phase-shiftingtransformer (PST), which can inject a lead/lag quadraturephasevoltage;• a series-connected multimodule thyristor-switched seriescapacitor (TSSC) system that can insert series capacitivereactance in discrete steps to adjust the line seriesreactance;• a series-connected multimodule thyristor-switched seriesreactor (TSSR) system that can insert series inductive reactancein discrete steps primarily to prevent over flow inthe line;• a shunt-connected mechanically-switched capacitor(MSC) for voltage control or reactive power compensation.DFC belongs to the family of hybrid compensators sinceit provides power flow control through series and/or shuntcompensation, analogous to the unified power flow controller(UPFC) [11]. Although DFC does not offer all versatility andtechnical features of the UPFC, its salient features make it analternative to the UPFC.Furthermore, since TSSC and TSSR modules are not phasecontrolledand only switched in and out by thyristor switches,DFC does not generate harmonics and has no adverse impact onpower quality and does not require filters.Owing to their large inherent time-constants, PST and MSCcan only provide slow steady-state power flow control, whilethe TSSC and TSSR modules can provide both dynamic andsteady-state power flow control. Since the tap control of PSTand the switching actions of TSSC and TSSR are discrete in

nature, a discrete-eve nt control strategy is best suited.

III. SUPERVISORY CONTROLLER DESIGN

A. Supervisory Control TheoryThe supervisory control problem for a discrete-eventsystem is formulated by modeling the plant as well as itscontrol logic (specifications) as some DES. A discrete-eventplant must be controlled based on some specifications(requirement behavior logic). By adjoining controllerstructure to the plant, it is possible to vary the languagegenerated by the closed loop system within certain limits.The desired performance of such a controlled plant will bespecified by stating that its generated language must becontained in some specification language. It is oftenpossible to meet these specifications in a minimal restrictiveway which is addressed by optimal supervisor in DESliterature. To solve the supervisory control problem, it isnecessary to show that a controller which forces thespecification to be met exists and is constructible [10].A DES model is specified by; the set of states (includingan initial state, and marker state which can be desired statesin some applications), the set of events, and the statetransition function of the system. Formally, a DES isrepresented by an automaton G = (Q, Σ, δ, q0, Qm) in which;Q is a finite set of states, with q0 ∈Q as the initial state andQm ⊆Q being the desired (marker) states; Σ is a finite setof events (σ) which is referred to as an alphabet; and finallyδ(q, σ) is a transition mapping δ: Q×Σ →Q which gives thenext state after occurrence of an event (σ). G plays the roleof the plant and together with its states, events and transitionoperator (mapping) model a physical process. G is calledgenerator, as it generates a set of strings (sequence of eventsor concatenated events). In other words it generates alanguage L(G), consisting of strings of events which arephysically possible in the plant.The supervisor controls the behavior of a discrete-eventsystem by enabling and disabling events, therefore affectsthe event sequences and state trajectories of the plant. Thesupervisor can be considered as a functionV : L(G)→.

() 0 means that the event is disabled and () 1indicates that the event left enabled.

B. DES Modeling of DFCAs shown in Figure 4, a DFC (plant) consists of threecomponents: Power-meter, TSC, and PST. Moreover we

need a model for the operator's action to switch the modesand to override in abnormal situations. Each component ismodeled as a DES. DES models of plant components aresynchronized to form the plant model.

POWER-METERThe (measured) real power passing through the line mustbe within a dead-band. The power meter reports thefollowing events associated with the load active power(Figure 5-a):−Power meter Initialized (ev11)−Report decrease in power is demanded, (ev10)−Report normal situation (ev12)Report increase in power is demanded, (ev14)TSCEvents associated with the TSC are (Figure 5-b):−Capacitor decrease command (ev31)−Capacitor decrease successful (ev32)−Capacitor increase command (ev33)−Capacitor increase successful (ev34)−Capacitor decrease/increase failed (ev30)PSTThe phase shifting transformer controls the transformerratio in order to increase or decrease the line power flow.Events associated with the PST are (Figure 5-c):−Tap down command (ev41)

−Tap down successful (ev42)−Tap up command (ev43)−Tap up successful (ev44)−Tap up/down failed (ev40)

OPERATOROperator can switch operation mode of DFC. Events 51and 53 are defined for operator actions (Figure 5-d):Enter “Automatic” Mode (ev51)Enter “Manual” Mode (ev53)The operator can force the system from Automatic toManual mode at any time (ev53). System switches toManual mode from Automatic mode by a “Manual”command from operator (ev53), or an abnormal situationsuch as, failed TSC step up/down or PST tap up/down.C. DES model of the Control SpecificationThe following specifications are considered to designsupervisory control.- TSC has 7 steps. (Figure 6-a)-Tap-changer of the PST has 19 steps. (Figure 6-b)-The DFC works in Auto/Manual operation modeaccording to the following logic (Figure 6-c)a. If “a decrease in power is demanded” (ev10), thenrun the following commands:1) Decrease TSC steps (ev31) until it reaches thenew operating point (ev12).2) Decrease one PST tap (ev41).3) Increase one TSC step (ev33).4) Go to (2) until all the decreased TSC steps arebrought back inb. If “an increase in power is demanded”(ev14), thenrun the following commands:1) Increase TSC steps (ev33) until it gets to thenew operating point (ev12).2) Increase one PST tap (ev43).3) Decrease one TSC step (ev31).4) Go to (2) until all the increased TSC steps areremoved.c. System switches to Manual mode from Automaticmode by a “Manual” command from an operator

(ev53) at any time, or an abnormal situation suchas, failed TSC step up/down (ev30) or PST tapup/down (ev40). In Manual mode the system iswaiting for “tap/step Up”, “tap/step Down”,“Automatic”, or “Stop” commands. On returningto Automatic mode the controller is reinitialized at“state 0” of the specification.As shown in Figure 6, three separated automata areemployed to represent the control logic (a, b, and c).D. Supervisory Control Design for DFCUsing three specifications shown in Figure 6 and thelocal plant models the supervisory control is synthesizedin centralized and decentralized structure using TCTsoftware. TCT is software developed for modeling andsynthesis supervisory control for discrete-event systems indifferent structures.