Editor'sNoteo Below are aseriesofarticles(ppo 752-792, 803-80'/) on questions brought up for discussion at the VIII lntemarional Symposium on Hydraulic Machines, Equipment, and Cavitation. The selection of articles was prepared by M. F. Skhadnev, chairman of the National Committee of the IAHR of the USSR (SNC IAHR) and associate editor of the journal, V. Ya. Karelin, M. F. Krasirnikov, and V. S. Serkov, members of ~he editorial board, and L. A. Zolotov, deputy chairman of the SNC IAHR. A specific characteristic of pumped-storage plants (PSP) is the frequent change in the operating regime accompanied by various uansients occurring both at a constant and variable frequency of revolution of the units. Under these conditions, it is necessary to make a complete analysis of transients with consideration of the characteristics of the penstocks and hydraulic machines when designing PSP in order to assign a rational scheme, composition, and parameters of the structures and to optimize ~e regimes for regulating the units. COMPUTER-AIDEDEven in the case when the law of variation of opening of the guide apparatus is assigned, i.e., when an open control system is being considered, the characteristics of the system of penstocks and the virtual impossibility of representing the total overallcharacteristicsofthe hydraulic machine in an analytic form lead to extremely complex and laborious calculations. At the deparunent of hydropower use of the V. V. Kuibyshev Moscow Institute of Civil Engineering computers are used for investigating transients of PSP along with the development of graphic calcularion methods and use of analog computers, especially in cases where it is necessary to make numerous calcularions or when complex branched penstock systems are being considered and the effect of various factors is being studied. The methods developed permit obtaining more complete data needed for the design of structures and equipment of PSP.Differential equations of individual elements and links of the entire system are the basis for the calculations, The following symbols are used: H, head, m; Q, discharge, m3/sec; M, moment of the runner, ton" m; n, rate of rotation, rpm; D, runner diameter, m; Q~ = Q/DZ4-H'~, reduced discharge; M~ = M/D3H, reduced moment; ni = nD/4"~, reduced rate of rotation; h = H/Hb; q = Q/Qb; m = M/Mb; 8 = rt/n b are the relative values of the head, discharge, moment, and rate of rotation; ql = QI/QIb; mI = MVM~b; /~ = ni/nib are the relative values of the reduced discharge, moment, and rate of rotation; a is the opening of the guide apparatus, mm;is the constant of inertia of the penstocks, see; g, acceleration of gravity, m/secZ; L, length of a section of the penstock, m; F, cross-sectional area of the penstock, mZ; Twu s, Twd s, Tw h, respectively the constants of inertia of the upstream and downstream penstocks and hydraulic machine; T u = (GDZnb/375 Mb), constant of inertia of the unit, see; GD z, moment of inertia, ton* mZ; Ts~ rime of the total linear travel of file guide apparatus, see; Qd, Qst,

At hydroelectric stations with a high-inertia pressure system, one of the means of reducing water hammer is to slow the closing of the gate apparatus. But in this ease, the rotational speed when dropping the load can reach values exceeding the allowable from the viewpoint of the mechanical strength of the generator. Naturally, the thought arises of using braking of the unit, which in principle can be realized by various methods, including connecting the generator through a switch unit to a specially selected electrical load resistance. Such costly measures as using a surge tank, thickening the walls of the conduits, or the use of idle discharges are alternatives to this method.The use of idle discharges can be commensurate in cost to electrical braking, but in the event of failure of idle discharges,the real danger of an impermissible water hammer arises, since the movement of the gate apparatus is designed to be fast. In the event of failure of the electrical breaking system, an increase of the rotational speed above the design necessitates only an unscheduled inspection of the generator.We will examine the method of determining the parameters of an electrical braking system and its effect on fluid mechanical transients after dropping the load for the example of a hydrostation with long intake works and mixed-flow turbines of type RO-230 for which the runaway speed exceeds the rated by almost 2 times, and with slow closing of the gate apparatus providing acceptable values of water hammer, the temporary increase of speed of the unit reaches 90%.Electrical braking is taken into account by adding to the right-hand side of the equation the torque m e acting on the rotor of the unit from the electrical machine Tu(d~/dt) =mt-m e. (1) Here fl = n/nno m and m t = M/M o are the relative speed and moment developed by the turbine referred to the base values; T u is the mechanical constant of inertia of the unit: TuGDZnoZI365No.Equation (1) is solved simultaneously with the "chain" equation of water hammer set up for the section of the conduit adjacent to the hydraulic machine and relating the relative discharges q = Q/Qo and heads h -H/H o for two times separated by interval 0 = eAB/C (where CAB is the length of the section and C is the propagation velocity of the pressure waves along the conduit)(2) Here p = CQdgHbF; F is the cross-sectional area of the conduit; Qb and H b are the discharge and head taken as the base ones, and g is the acceleration of gravity [1]. For simultaneous solution of Eqs. (1) and (2) it is necessary to represent the first in finite differences, having replaced dt by 0. It will take the form Q ~(n+l)~ --~nO = -~u (mr nO --ma n0 + mt (n+l)0 --me (.+1)0)"(3)To close system (2-3), it is necessary to take into account the effect of the head on the relative parameters Q~ H ,q --~ --= ql I/h QIb and MI . m --------ra I h, Mlb H b

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