8/12/2019 00983729

1/10

The Theory of Hybrid Control Systems and ItsApplication Perspective in Electric Power Systems*

Shi-Yin QinBeijing Polytechnic University, 100022, Beijing, P. R. China; qinsvl @bipu.edu.cn)

Yong-Hua Song(Brunel University,U.K.; y.h.sonn@brunel.ac.uk)

Abstract: In this paper, taking the architecture and configuration of hybrid control systems HCS) as a key g i s t some concepts,characteristics and properties of HCS are discussed in depth. Meanwhile the hybrid characteristics and the related issues of electricpower systems are briefly analyzed so that the advantages and originalities of HCS methodology in tackling some difficult problemsof optimizing schedule and stabilized control for large scale electric power systems are manifested. Thus he modeling and theoptimizing control of large scale hybrid electric power systems HEPS) re M e r ddressed and studied. Finally a brief conclusionand some remarks are given to look forward to the application perspective of the theory of HCS n large scale hybrid electric powersystems and other complex systems.Keywords: hybrid control system, electrical power system, hybrid electrical power system, modeling and simulation, optimizing

controls

1. IntroductionThe theory of hybrid control systems (HCS) is a currently new and fascinating discipline bridging control

engineering, system science, applied mathematics and com puter science etc., its applications are of very extensiveFor a large-scale electric power system (EPS) distributed in a very wide region, it is a typical complex

network system and composed of a large number of generators, transmitting networks, transformer and switchsystems. In a regular stable operation status, the actu al load (includes transmitting losses) must be equal to theelectric energy generated by groups of generators in the system at any time. Thus, based on the decentralizedcontrols in variou s local subsystems, it is necessary for the dispatch center of electric power system to b e able toexecute a series of dispatch strategies and schedu les accurately and real timely according to the real op erationstates and the corresponding objectives so as to enable the operation cost of the system to be the most econom icalone under the prerequisite for the guarantee of stability, safety and service quality of EPS. It is obvious that forsuch a comp lex large scale dynamical network system in which various sub systems with different characteristicsare interconnected as a w hole, besides high dimensionality, heavy non -linearity and multi-time-scale properties,the most outstanding characteristics can be concluded as: the dynam ic continuity of electric energy productionprocess; the algebra logic constraints of transmitting and distribution networks and the requirement for themulti-objective optimization of dispatch and schedule processes in which some discrete events are alwaysincluded an do r are often driven by discrete events .All of these characteristics are similar to the o nes of the HCSboth in o rganization structu re and behavior configuration. Therefore it is a very effective approach to working ou ta solution for the optimizing dispatch and schedule and stabilizing controls of large scale EPS to employ thetheory of hybrid control systems. In this p aper, some concepts, characteristics and pro perties of HCS are brieflydiscussed at first, then the hybrid charac teristic s and the related issues of EPS are analyzed in depth so that theadvantages and origin alities of HCS methodology in tackling some difficult problems of optimizing schedu les andstabilizing controls for EPS are manifested. The key points in this paper lie in the mod eling and optimizin g control'Supported by National Key Basic R esearch Special Fundof China (No. G199 80203 10) National Natural Scie nce Foundation of China (No. 60074024).

0-7803-7010-4/01/ 10.0002001 IEEE.85

8/12/2019 00983729

2/10

of hybrid electric power systems HEPS). For a hierarchical organization structure of HEPS, in orde r to tackle thedifliculties of event identification, the discrete event dynamic system PEDS) is rationally transformed into adiscrete state dynamic system, but the event attribute of the discrete state is still reserved. In this way, thePetri nets and/or automata networks are employed to build the mod el of discrete state dynamic system, and thewhole model of the HEPS can be obtained through interface transformation and synthetic integration. Moreoverthe design and implementation of the interface which interconnects the discrete event dynamic system andcontinuous variable controlled system in the HCS are discussed. Afterwards the im plem enting strategy andmethods of optimizing controls for HEPS are studied based on the separation principle and the priority rule.Finally the paper is concluded with some remarks about the future application perspectives of the theory of HCSin the HEPS.2. The ArchitectureandProperties of HybridControl System

A typical function architecture of general hybrid control systems may be showed as a triunity organization,Fig. 1 illustrates its basic organization structure and the corresponding configuration, in which both th e continuousvariable controlled system (CVCS) and the discrete event dynamic system P E D S ) are included, the former isgoverned by the causation law of Newtonian mechanics, and the later obeys the information logic principle ofoptimization decision, moreover these two components are organically restricted to a kind of constraintmechanism of stron g interaction through a key component nterface.

r Discrete decision operationmechanism based on DEDS

= U t

Continuous variable con-trolled process (CVCS)

A__

Y__

Fig.1 The organization structureand configurationof hybrid control system

As is shown in Fig. 1, the open model of a triunity hybrid control system may be repre sented as a nonupleset as follows

SH= XD, 6Zc, V , g; Y, ) 2.1)where the hybrid control system SH is partitioned into 3 parts such as the discrete event dynamical system(DEDS), the continuous variable controlled system (CVCS) and the interface, which can be analysed andexplained in detail below.

86

8/12/2019 00983729

3/10

(1) discrete decision and operation mechanism driven by ev ents (DEDS)It is obvious that this discrete decision and operation system is, in fact, a triple which consists of XD,

Z nd 6, here XD s a finite state set of discrete events, generally speaking, biz'ExD represents some statesubset (or domain) in the continuous state space of controlled system under various implem enting modules an d ordifferent control levels.Z s an event set of hybrid control syste m H , which may be decomposed as:Z=ZuU (2.2)where Zu is a subset of general physical events whose occurrence conditio ns are based on th e evolution results ofcontinuous states thus is uncontrollable, and ZC s a subset of control and decision events, which is controllable.Yet Gis a mapping function of state transition in the part of DED S:For example, driving by any event OEZ a discrete state transition from q1 EX, o q2'EXDay be represented by aGtransition mapping relationship as follows

X D x Z +XD (2.3)

(2) continu ous variable controlled system CVCS)In this part, the configuration and structure of controlled process is similar to that of convenient controlsystems, but its real structure constraint relationships are extended yet. Xc-d is the state space of continuous

variables, X(?) C is the corresponding n-dimension state vector; UGR is a m-dimension co ntrol space; U,, ?)@,and u(t)_cV are the corresponding internal control vector and external control vector respectively. The statemapping functionf( 0 ) is the vector field of state vector x(t), as is shown belowwhich may be generally represented by a differential equation

f: xxu+x (2.5)

However, it may also be expressed as a type of differential inclusion under extended conditions, viz.i t ) = Inczusion f,x ( t ) , d t ) , u ( t ) ) 9 f 2 ( x ( t ) 9 d ( t ) , (2.7)

where Iy.),fi *) andh .)re smooth or segment smooth hn cti on vector, wherefi(+[fii(.> fi2(*) -.fii(*)...fin(*)IT (2.8)fi(.)=[f21 (.) f22(.) .fii(.)..-f2n(.)1~ (2.9)fii(*)< 2X'), (i=1,2, ... n) (2.10)

g: XC X x D X ~ ~ x C (2.11)(2.12)

And g s a condition mapping relationship function for the discontinuous transition of state vector x(0,In general situations, it may be an algebra constraint equation

x(t+o) =gMt--O),a a)3) the interfaceIn hybrid control systems, the interface plays a very important role, by which the dyn amical behavioral

response relationships between the D EDS and CVCS are formed, as a matter of fact, these two different parts aregoverned by totally different mechanism of signal processing in n ature. y is a mapping from the continuous statespaceXC o the discrete event set Zu, iz.

y: XC+ZU (2.13)It is obvious that yplays a role of event generator whose behavior characteristics are in correspondencewith the transitions among different continuous state regions wh ich connect with the physical m odes of differentevolution stages. For C= cq, 02, ... ok), where every event q corresponds with a certain state region in the

87

8/12/2019 00983729

4/10

continuous state space X,.The generator of control law a I'is a mapping from the discrete state setXD o control space U , iz.

a: --?,U (2.14)From a viewpoint of the configuration structure of HCS, it is by the generator of control law, a, ased on thestates of discrete events that the decision result of discrete operation mechanism of HCS can be made use of todominate the dynam ical behaviors of continuous variable controlled process.

In Fig.1, the constraint relationships of external discrete event control input T nd continuous variablecontrol input U . of HCS, and also the coupling relationships of discrete event observation A and continuousvariable observation y ( . are illustrated, all these terminal constraint mechanism and characteristics are close to theentirety structure properties of HCS.

As a summary of above discussion, we can give.a basic statement about the optimal control problem ofHCS as follows:

According to the entirety objectives and constraints of hybrid control system (HCS), the principles ofdecomposition coordination and global optimization are employed to synthesize proper controllers for both theDEDS and the CVCS in the corresponding permissible control domain, meanwhile a reliable interface withfunctions of event identification and instruction transformation is designed and implemented, so that in thedynamical operation process of HCS its CVCS part can always operate in an optimal or satisfactory state locushence to retain an optimal or satisfactory performance index wh ile some optimal strateg ies of dynamical evo lutionare implemented based o n the logic constraints of optimizing decision-making in its DED S part.3. The H ybrid Characteristics of Electric Power Systems and Some Related Issues

As is well-known, a large-sc ale electric power system (EPS) distributed in a very w ide region is, in fact, atypical complex network system and consists o f a large number of generators, transmitting netw orks, transformerand switch systems. It is obvious that for such a large scale dynamical network system in which varioussubsystems with different characteristics are interconnected as a whole, besides high dimensionality, heavynon-linearity and multi-time-scale properties, the most outstanding characteristics can be concluded as: thedynamic continuity of electric energy production process; the algebra logic constraints of transmitting anddistribution networks and the requirement for the m ulti-objective o ptimization of dispatch and schedule processesin which some discrete events are always included andlor are often driven by discrete events.Al1 of thesecharacteristics are provided with remarkable hybridity both in organization structure and behavior c ~n fi gu ra tio n[ ~*I. However, since 1990s it is a distinct trend to com bine the theory of economics and market with the technologyand engineering problems of electric power systems in the global reform of electric power industry. Thus somenew challenges and opportunities are put forward to the optimizing control and schedule of EPS. In this w ay, aseries of problems of multilevel and multi-objective optimizing control and decision in the EPS are becomingmore and more complex and significant. However the hybridity is surely a very outstanding key factor whichresults in such complexity in the EPS, hence we call it as hybrid electric power system (HEPS). In fact, all ofthose characteristics of HEPS are similar to the ones o f the HCS both in organization structure and beh aviorconfiguration. Therefore it is a very effective approach to working ou t some solutions for the optimizing dispatchand/or schedule and stabilizing controls of large scale HEPS to apply the theory and method of hybrid control

Generally speaking, two classes of constraints must be satisfied in the normal operation status of the HEPS,the first is the balance constraints between load and power supply, which may be expressed as equality byequations of power balance in various contacts (or nodes). The second is the constraints o f operation parameters,which may be represented by inequality and requires the parameters of voltages and powers in various contacts

88

8/12/2019 00983729

5/10

(nodes) and components to be in a permissible and feasible range. Based on the above analysis and statementabout the hybrid characteristics of I-EPS, the logic relationships among the o pera tion 'state transitions and the

?REPLACECOMPONENTS

control

QINITIATECORRECTIONS

implementations are illustrated as Fig.2.[61

E: Emergency ; D: Disturbed ; V Vulnerable ; N: Normal ;EMERGENCY DISTUIU3ED VULNE RABLE NORM AL

MINIMUMDURATIONMAXIMUMLOADCOVERAGESECURITY

ECONOMY

SECURITYMONITORING

MINIMIZECOSTS

Fig.2 The logic relationships among operation state transitions and control implementations

As is show n in Fig. 2, for every transition of discrete operation state and its correspo ndin g mplementationof new control strategy, a series of interactions between some discrete event dynamic beh aviors and some certainof continuous variable evolution processes take place. In such heterogeneous complex o rganization structu res andinformation coupling relationships, it is impossible to resolve all of problems in the HEPS with some beautifuland uniform modeling methods and analysis tools. Although it is an effective approach to resolv e some significantproblems in the HEPS with the theory and methodology of the HCS, some theoretical metho ds and mathematicaltools of multidiscipline may also be brought into play. According to the characteristics of HEPS, it is necessary inthe practical applications to adjust measures to concrete conditions so as to achieve some extent of optimal orsatisfactory applicatio n results. However, the key points for the hybrid electrical power system s are still themodeling and the optimization of control law yet, thus we will carry on more in-depth discussion about them inthe following two sections respectively.4. Modeling of Hybrid Electrical Power Systems '

In view of the triunity organization structure of hybrid control systems, not only th e identification of themodel structure and the estimate of the model parameters are dealt with, but also some complicated eventidentification must be confronted with. From the viewpoint of practical application, it is possible to make areasonable transformation from the discrete event dynamic system (DEDS) to a discrete state dynamic system

89

8/12/2019 00983729

6/10

(DSDS) in order to reduce or tackle the difficulties of event identification. But it must be pointed out that thediscrete state in such a transformation still reserves its event attribute in nature, and can absolutely not beconfused it with a geneml discrete variable dynamic system obtained by sampling from a continuous variabledynamic system. As a matter of fact, in this transformation all of events are generalized as p rocess event s whichmay be treated as instantaneous events reflected directly in the discrete observation space when the states andorbehavior configuration of some process variables transit from one specific condition to another one. Generallyspeaking in some certain sense, the transformation from the DEDS to the DSDS is a kind of quantification forevents so that the description languages or modeling languages for the two parts in the HCS with differentattributes in nature can be unified in their formats. Therefore the complexity of modeling for the HCS can begreatly reduced.

After a transformation from DEDS to DSDS, the triunity organization structure of HCS still holds the line,which may be sho wed as Fig.3.

DSDS/X(k)- TFig.3 The reduced structure ofHCS

In the reduced model structure of HCS hen the transformation interface is opened the dynamics of itsX k + U = F o Y UO) 4.1)Y k)=G X k),U k)) k= 1,2,.. 4.2)

discrete state dynamic system (DSDS) is governed by

where

where X i 0 ) E {Oyly...yZx 1) = w i=1,2,..,NUJ.) E {oyly...yzu1} = I i=1,2 ...

In the above equation (4.1) and (4.2), various events are transformed into (or quantified as) variables byencoding form, in fact, every ordinal number variable in the ordinal number set represents a concrete eventand various event set is finite. It is obvious that in this DSDS there are N state (event) variables, R control

90

8/12/2019 00983729

7/10

8/12/2019 00983729

8/10

According to its organization structure , the dynamic behavior of HCS may be governed by thefollowing equations

(4.4)

x ( t ) E R , u ( t ) R ' , y ( t ) E R ,y(t) E R h , a= {a,,a2,..,aH}, t ,T R is a given samplingtT(holding) time period, k = Integer -) the coupling variable of event generation from CSDS to DSDS, U t )

will carry out its sampling with time period T. The holding time of the dominant coupling variable I k),which isgoverned by the internal control law from the DSDS to CSDS, is T also. In this way, the configurationstructure of HCS in reduced modeling sense may be formed as Fig, 6.

92

8/12/2019 00983729

9/10

4.11)4.12)

4.13)4.14)4.15)

kTTk=0,1,2 ...; =0,1,2...; =Integer[-1; i T T then k=l=h.

According to the above discussion it may be realized in depth that the modeling of H CS is more operableafter a transformation from the DEDS to DSDS is completed. The convenient methodology and tools may beemployed in the modeling of CSDS part. However in the modeling of D SDS part a series of useful tools such asautomata networks, Petri nets and lattice theory may play im portant roles and can be turned to good account basedon a sequence of cardinal number variables formed in the partition of state domains in the state space ofcontinuous evolution process. It sho uld be emphasized that there may exist different time scales in the DSD S partand CSDS part respectively, which reflect a class of relationship of attribute characteristics among different datagranularities, thus may be sufficiently considered in the modeling process of HCS. In the interface between theDSDS and the CSDS , there exist two basic h nct ion modules y(t) and a(k), whose structure and synthetic designcan also be reduced with the partition of state space and the completion of transformation from events to somestate domains.5. The Op timizing Control of Hybrid Electric Power Systems

In view of the triunity architecture of HCS and the outstanding characteristics of hybrid electric powersystems, the separation principle should be employed in the design strategy of its optimizing control laws forhybrid electric power sy stems. Thus the whole design task may be decomposed into three parts: 1) the design ofCSDS part; 2) the design of DSDS part; and (3) the design of a proper and reliable transformation interfacewhich couples the DSDS and the CSDS. In order to pursue an optimal performance index for the entire system, auniform m easure with additivity for the performance indices of various different parts should be em ployed. It isundoubted that the integrative information entropy is an optimal selection[]. In addition th e priority principle ofperformance indices should be emphatically considered in the whole design process of control laws andmechanisms for the HEPS, the first key point may be concluded as safety is the first and efic ienc y is followed.As a matter of fact, the safety and the2tability of HEPS are two close correlated key topics which may be studiedin depth in another paper by the authors of this paper.

In the synthesis and optimizing design of control laws and mechanisms for HEPS, the followingpropositions may be dealt with, which can be listed as (1) the synthesis of the most economical structure ofcontrol m echanism; 2) the synthetic integration with multi-objective optimization; (3) the synthetic design ofsymbolic controller in the DSD S (or D EDS) part; (4) the optimizing synthesis and design o f the transformationinterface; ( 5 ) the H m design of control mechanism with gain schedu le; 6) the robust analysis and design ofcontrol m echanism; (7) the synthetic integration based on m ulti-agent system. However all of these propositionsmust be combined with concrete practical engineering background so as to promote som e successful applicationsof the theory of HCS in the HEPS. Therefore it should be given full play to the meta integration method from

93

8/12/2019 00983729

10/10

qualitative analysis to quantitative synthesis[ ].

6. Conclusion and RemarksThe theory of hybrid control systems is a new and fascinating develop ing branch o f learn ing in thecontrol science and control engineering, which is greatly emphasized in both the theoretical research and

engineering applications. Although there still exist many theoretical topics to be studied in depth, its powerfdstrength has been dem onstrated in a lot of industrial application fields such as intelligent transpo rt system s (ITS),air traffic management and sea traffic management, intelligent robot systems, as well as smart manufacturingsystems. A number of typical engineering applications have shown that only by combining its theoretical resultswith some practical engineering applications for the researches on the HC S can it have g reat vitality. In view ofthe outstanding hybridity of large-scale elec&cal p ower sys tems it is sure that the theo ry of hybrid control systemswill play a very important role in the optimizing controls and decision of the HEPS thus have an extensive andbright application perspective. Otherwise it also has pow erful extended strength to large-scale complex industrialprocesses and the implementation of intelligent automation in internet and/or intranet enviro nm ent.References[ l ] Antsak lis, P. J. ,Nerode, A., Hybrid Control Systems: An Introductory Discussion t o the Sp ecial Issue, IEEE[2] Morse, A. S. antelides C. C. ,Sastry S. S. and Schumacher, J. M. , ntroduction to the Special Issue on[3] Qin, S. Y. Song, Y. ., The Analysis of Architecture of Hybrid Control Systems, Automation of Electric[4] Han, Y D., Wang, Z. H., Chen, H. J., Optimal Decentralized Coordination Controls for Electric Power[ 5 ] Ti, Z. X., Chen, C. P., Au tomation of Comp uter Dispatch for Electric Power Syste ms (in Chinese), Shanghai:161 Esselman, W H., Sobajic, D . and Maulbetsch, J., Hybrid Discrete and Conti nuo us Control for Power[7] Dogruel, M. and Ozguner, U. Modeling and Stability Issues in Hybrid Systems, Hybrid Syste ms 11, 148-165,[SI Han, J. H., Qin, S. Y., ong, Y. ., The Frequency Control in Emergency of Hybrid Power System Based on

Learning Automata, Automation of Electric Power S ystems, (in Chinese), 2000,24(18): 8-12[9] Lu, S. Q., Qin, S. Y.,ong, Y. H., Modeling and Sinulation of Emergent Frequency C o ~ t ro lor Hybrid Power

Systems Based on Differential Petri Nets, Automation of Electric Power Systems, (in Chinese), 2001,25(6):4-8

[ lo] Luo, G L., Qin, S. Y., An Introduction to Intelligent Controls, (in Ch inese), Hangzou: Z hejian g Scienc e andTechnology Publishing House, 1997

Trans. on Automatic Control, 1999 ,43 (4): 457-460Hybrid S ystems, Automatica, 1999,35 (3): 347-348Power S ystems, (in Chinese), 20 00, 24 ( 11): 5-9Systems (in Chinese), Beijing: Hsinghua University Press, 1997Shanghai Jiaotong University Press, 1995Systems, Discrete Event Dynamic Systems: Theory and Applications, 1999,9(4 ): 297-3 18

Lecture Notes in Computer Science, 999, Springer-Verlag, 1995

94