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750 (if not its solution) would be simpler to develop and easier for the student to understand than this highly complex, but still approximate, version. The last major sect.ion is entit.led “The General Optimum Operational Problem,” wit.h pena1t.y factors used to place “softf’ constraints on state variables. The theory is applied to a simple problem based onsome original work by the author and his students. Althoughstill concerned with the power system in the steady st.at.e, Chapter 9 deals with control devices and the application of cont.ro1 theory. Block diagrams, schematics, and mathemat,ical models are int.roduced for turbines, governors, and ent,ire power systenls or *‘controlareas.” The main topic of the chapter is “the megawatt frequency control problem” or, as it is usually called, load-frequency control. A good development is given of the “uncontrolled” system behavior, then the improvementsobtained by control of frequency and interchange flow. Bnother major section covers “the megavar voltage control problem.” This is all material close to the author’s research interests and as such shows both his enthusiasm and ingenuity. In the development of “optimum syst.ems control,” the author alludes to his quite controversial proposals for improved loadfrequency control, based on linear-quadratic optimal control theory. In itssimplest. ternls, his studies show that the “bias” setting,which weights frequency errors with respect to tie-flow errors, should be about ‘‘ $6’’ instead of “g,” where p is anatural system characteristic. Use of this setting will show considerable improvement in certain situations, and indeed there is considerable room for improvement in t.he dynamic performance of present-day controls. This approach unfortunately ignores the need to send power to a control area with a generation deficiency that it cannot make up from its own resources. The last three chapters are devoted to “energy system t,ransients.” Chapter 10 (40 pages) begins with a classification of transient.s according t.0 speed. Class A: Ultrafast transients (lightning, switching surges). Class B: Medium-fast transients (faults or short circuits). Class C: Slow transients (electromechanical or transient stability). This is a useful division in that the three typescover reasonably well the important transientphenomena encountered in a power system, and the t,hree are both analyzed and dealt with in actual systems in dstinctly different ways. The “ultrafast” surges are discussed only briefly. Then, more to balance thechapterlengthsthan logically to divide thesubject material, the remainder of the chapter is given over to symmetrical (t.hree-phase) fault analysis. The difficult subject of the behavior of synchronous machines under sudden short circuits is discussed. Finallya systematic procedure is presented for the solution of fault, currents and voltages by one of t.he two widely used methods, the bus impedance matrix method. Chapter 11 (47 pages) is a continuation of fault analysis, extended to unbalanced faults (single line to ground, t.wo lines shorted together, etc.). This is almostalways dealt with by the method of “symmetrical components,” which the author develops in a modern operator notation. R‘hile brief, the development. is adequate for a first course. Incidentally, the first book on this subject., by Wagner and Evans[ 11, was published in 1933 and i s still in print. The author seeking lastingfame would do well to scrutinizet.hatvenerable book-and t.0 choose a subject that does not change too rapidly. The finalchapter (56 pages) deals with the topic from power systems best known to control engineers, t.hat of transient stability. The author, a control man himself, is obviously well equipped to deal wit.h the theory of electromechanical t.ransients (after presenting a somewhat misleading analogy, he does so). The pertinent different.ia1 equations are developed, leading up to the “swing equation.” The “classical” assumpt,ion of “constant voltagebehind transient reactance” (constant. f l u linkages) is made t.o simplify the analysis. Both analog computer and numerical integration methods are used to comput.e “swing curves.” Direct met,hods, such as the equal-area criterion and Lyapunov’s direct method, are mentioned, but. are noted to be of little practical use at t.he present t.ime.
IEEE TRXNS.KX‘IONS ON OCTOBER AIJTOMATfC CONTROL,
About the only modern book that can be considered a competitor is the book by Neuenswander [ 2 ] ,excellent in many ways also, but quit,e different from this one. Prof. Elgerd’s book is much broader and, wit.h nearly 40 percent more pages, given a better overview of t.he entire subject. Mr. Neuenswander, as a practicing power system engineer, makes a sharper present.ation of certain analysis topics. The book is eminently readable and therefore recommendable for self-study. A great variety of problems-nearly all good, some quite difficult-is given at the end of eachchapter. The st.yle is a bit wearing for someone accustomed to more detached scientific writing -there are many italicized, capit,alized, or other-irise emphasized words and phrases-but probably effective for students. It is clearly t.he author’s intention to teach, and the book is a credit to t,hat. motive.
REFERENCES [ l ] C. F. Wagner and R. D. Evans, Symmetrical Camponenis. K e a York: hlcGraa-Hill. 1933.  J . R. Keuenswander, Modern Power Systems. Scranton, Pa.: International Textbook, 1971.
Optimization: Theory and Practice-G. S. G. Beveridge and R. S. Schechter (New York: McGraw-Hill, 1970, 773 pp., $18.60). Reviewed by David H . Finfield.
David H. Winfield received the A B . , A.M., and Ph.D. degrees f r o m HarvardUniversity,Cambridge, Mass., in 1952, 195.4, and1970, respectively. From 195.4 to 1963 he worked et the Air Force Cambridge Research Laboratory, performed two years military s a k e , an.d worked at R C A . I n 1963 he joined the I B X Federal Systems Dieision, where he presentlymanages the Department of Estimationand Catrol in Burlington,Mass.His interests incluak functionminimization, computationalsimplification of the extended Kalman.filter, and ree n t y trajectories of the shuttle orbiter.
This addit.ion to the McGraw-Hill Chemical Engineering Series, written by two professors of chemical engineering, is largely directed to students and practitioners of chemical engineering and to managers of industrial plants. The Epilogue of this book summarizes its content and emphasis: “In this presentation an integrated account of the general organization required before optimization can take place and of the full range of opt.imization methods has been given. While o p timization t.heory is ezsentiaLly complete for well-defined systems with specifiedobjectives and models, there is much room for improvement in the area of model building, objectivespecification, and the handling of uncertainty and compet.ition, the accuracy and reliability of any study being wholly dependent upon their correct formulation. The successful conclusion of any optimization however, always depend uponthe critical familiarity analysis d, of the user.” The book is divided into three parts. Part I (103 pages), titled “The Organization for Optimization,” discusses system models and performance objectives. Included are criteria of plant profit.ability, the construction of system block diagrams, the system response surface, degrees of freedom, t.he form of the objective function and constraints; system models based on knowledge of the physical process versus system models based on Taylor series modeling of outputsas afunction of inputs;and distributed and lumped paramet.er systems. Following t.he sections on problem statement are extremely brief sections (but with adequat,e references)on numerical solut.ionof algebraic equations (secant method,Newton-Raphson), integration of differential equations, and Monte Carlo methods. Part I1 (490 pages), titled “OptimizationTechniques,”surveys analytical and numerical methods for extremizing a function of a single variable, a function of a finit.e number of variabls, and a
funct,ion of a function. This is much the same mat,erial as in Wilde and Beightler [l], and is good preparation for reading current journals. The Appendix summarizes Stocker’s tests [a] of five nonlinearprogramming codes. The reports of numerical tests are much less extensive than t.hose of Kowalik and Osborne . It is unfortunate that, perhaps due to a publicat.ion deadline, Beveridge and Schecht.er did not reference Koaalik and Osborne. Part I1 of the book by Beveridge and Schecht,er exceeds in length theentiretext (469 pages) of the book by Wilde and Beightler [l]. This is partly due to the Beveridge and Schecter practice of elaborating the obvious. For example, we read on p. 103 the following: “A function can be represented in severalwags. In general, the dependent. variable is expressed in terms of the independent variables, y(z) being said to be a function of 5 , deiined in some region, if we have any rule which allows us to determine y for any set of z in the region. Any analysis of the function is then
carried out by examining this expression.” On p. 105, we read the folloxing: “Although higher-dimensional systems cannot be represented geometrically, it is convenient t o discuss and visualize the objective function as a geometric surface-a practice which seems to be deriwd from the work of statisticians. This lends a considerable simplification t o the concepts, even if the mathematical labor in optimizat.ion is not diminished, and allowsone to discuss the scaling of mountains or the descent into valleys,even if these are in an n-dimensional terrain. I n general, within this text., most procedures will be illustrated by a simplifiedgeometric represent.at.ionto indicate the significant features.”
For each new idea, there is excessive preamble and excessive recapitulation. The length of Part I1 is also due t.0 a commendable concern with details when a t last the authors describe mathematical techniques. For example, in Section 3.2.2, which develops t.he necessary conditions for an extremum subject to constraints, the authors do not hesitatetoaidthe reader by writing out each argument. of t,he Jacobian in long equations involving summations of Jacobian determinants. There is even an Appendix on t,he properties of determinants and Cramer’s rule. Part 111 (133 pages), titled “Optimization in Practice,” concmm the difficulty of optimizing systems of high dimension, systems wit.h some states unknown, and systems in which an opponent controls certain variables. Here the authors treatoptimization in thecontext of corporate decision making. For example, a company considers the profitability of producing phenol. Four chemical procesm for producing phenol are considered. For each process the cost and availabilit,y of rawmaterials and t,he market for by-products are assessed. For each process the profit per ton of phenol is computed based on the following assumpt.ions: 1) all by-products are sold; and 2) no by-products are sold. For each process the required of return on investment capital investmentis &mated and the rate is estimated based on hypothesis 1 ) or 2). The aut.how are generous in assisting the reader with numerical examples and problems. There are approximat.ely 547 references, of which many are from journals of chemical engineering, industrial engineering, management science, and operations rsearch. A p proximately 86 percent of these references were published in 1965 or earlier. I recommend the book as an introduct,ory text in opt.imization for college seniors or first yeargraduat.est,udents of chemical engineering. Many chapt.ers would be good supplement.al reading in a course in business administration or industrial engineering.
REFEREKCES 111 D. J. \Wde and C. 8. Reight.ler. Foundations of Optimization. Englewood Cliffs. N.J.: PrentieeHall, 1967. ‘‘A comparative study of nonlinearprogrammingcodes.” Iv1.S. thesis, Univ. Texas, Austin. 1969. 131 J. Kowalikand &I. R. Osborne, Methods for Cnconstrained Optimization Problems. New York: Elsevier. 1968.
(21 D. C. Stocker
Feedback Systems-J. B. Cruz, Ed. (New York: McGraw-Hill, 1972, 324 pp., 516.50). Reuiaoed by Huibert Kzcakeraak.
HuibertKwakenzaak receieed thediploma in engineeringphysics from Delft Gniversity of Technology, Delft, The Xetherlantls, and the Ph.D. degree in ekctricul engineering from the University of California, Berkeley, in 1960 and 1963, respectively. F T O ~1964 to 1970 he was zcriul the Department of EngineeringPhysics,DelftVnivusity of Technology. Currently he i s a P.rofessor in the Departmnt of Applied Mathematics, Twente L7niversity of Technology, Enschede, The Xetherlands. His interests are in the &Ms of linearand stochasiic control theory. He is coauthor of Linear Optimal Control Systems (Wiley, 1972). This book is Volume 14 in t.he McGraw-Hill Inter-University Electronics Series. Consistent with the format of other volumes in this series, the book is built. up from a number of chapters mitten by different authors, each of whom is an acknowledged expert on t.he topic of his chapter. The editor, J. B. Cruz, wrote Chapters 1, 3, and 6. W. R. Perkins is responsible for Chapter 2; P. IT. Kokotovii. authored Chapter 4; E. Kreindler wrote Chapter 5, while Chapters 7 and 8 originate from I. W . Sandberg and P. E. Sarachik, respectively. It is gratifying to note a revival of interest in feedback theory among control theoreticians. Duringthe optimalcontroldecade (1960-1970) the overriding importance of feedback in control was all too often lost from view. It is significant that the last. book on control published in the United States before the present book that cont,ains t.heword “feedback” in its title seems to be Horowitz’s Synthesis of Feedback Systems [l],which appeared in 1963. Of course, interest. in feedback theory never completely died, and the present book describes the developments t,hat.are current,ly taking place. The prerequisites for being able to profit. from t.he book are not explicitly st.ated, but they seem to consist, of an acquaintance with the state-space approach to continuous-time system t,heory and the principalresults of opt.imal controltheory,toget,herwith the appropriatemathenlatical background. The most. important results that areneeded are dequat.elysummarized in all instances. Chapter 1, which i s very brief, sets the st,age. The quest.ion “Why use feedback?”is answered bystatingthatitmay serve: 1) to stabilize an unstable system; 2) to reduce sensitivity t.0 parameter variations and noise, as well as to decrease nonlinear distort.ion; or 3) to maintainoptimalitg. Chapter 2 is devoted to a presentation of sensitivity analysis. The clear distinct.ion that is made between various types of sensitivity analysis is very welcome indeed. First, comparison. sensilicity analysis is introduced (Bode’s familiar approach [Z],such as generalized to the multivariable case and reinterpreted by Cruz and Perkins 131 ). More suited to the time domain approach dominant in the optimal control era is the concept of trajectory sennsitivity, which is next discussed. In this approach the changes in t,he systemtrajectories due to (small) parameter changes are analyzed. The great benefit of the “sensitivity model” is very clearly pointed out. The fact that. performancesensitivity is not mentioned in this chapter, but. is introduced only in Chapter 5, points to an inherent weakness of books such as t.his, caused by thenear impossibility of coordinating the efforts of six different authors. This weakness is even more poignantlybrought out by the fact that Frkchetderivatives are mentioned and used in this chapter 220 pages before t.he definit,ion of such a derivat.ive in Chapter 8. However, the reader is alerted on page 57 to a possible necesity for him to consult, Chapter 8. The subject of Chapter 3 is the effect of feedback on signal distortion in nonlinear systems. Because reduction of signal distortion may be a prime reason for introducing feedback, the inclusion of this chapter is very appropriate. The beneficial effect. of feedback on signal distortion is first extensively demonstratedby means of a nondpamic example. That. for extension of t.he results t,o dynamic feedback systems functional analysis is required does not come as a surprise; once again the fact t.hat, functional analysis is not treated until Chapter 8 strikes the reader as an imperfection. The derived