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By M.E. El-Hawary and G.S. Christensen (Eds.)

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K~)(x~, - xi+1, o) = &), This accounts for the absence of the o terms in Eq. 10). The utilization of this river flow model will be shown in Chapter 6. 5 Appvoxirnarions. 15) with si being the storage volume. In the terminology of Eq. 18) ri(djsi/dt') with ai, q i , and ri being constants. 20) In the hydrologist's standard notation we let ki = (1/ai)'/"' The exponent y i is normally taken to be unity. 21a) This result is commonly known as the Muskingum's storage equation. A special case of the Muskingum's equation results from setting ri = 0.

This model is a consequence of the equations based on the detailed Park's transformation. The basic assumptions involved are those of balanced loading and sinusoidal steady state operation. We can thus avail ourselves of the conveniences offered by phasor diagram techniques. Fig. 9 Equivalent circuit and phasor diagram of a synchronous machine The simplest equivalent circuit and the associated phasor diagram for a synchronous machine are shown in Fig. 9. The armature resistance is neglected in this presentation since our object is to demonstrate the basis for limitations accounted for in our type of study.

The second set is solely determined by the discharge capacity of the power plant as well as its efficiency. The last inequality constraint would be imposed by irrigational, navigational, recreational, and flood prevention considerations. I. A SIMPLEOVERALL MODEL In Chapters 5 and 6 we will find it necessary to adopt a simple overall model for the plant and reservoir dynamics. This is obtained by assuming constant efficiency, no spillage, invariant tailrace elevation, negligible penstock losses, and a vertical-sided reservoir.

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