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Nonlinear predictive control for a NNARX hydro plant model

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Abstract

A neural network (NN)-based nonlinear predictive control (NPC) is described for control of turbine power with variation in gate position. The studied plant includes the tunnel, surge tank and penstock effect dynamics. Multilayer perceptron neural network is chosen to represent a neural network nonlinear autoregressive with exogenous signal model of hydro power plant. With the said NN model configuration, quasi-Newton and Levenberg–Marquardt iterative optimization algorithms are applied in order to determine optimal predictive control parameters. The controlled response is simulated on different amplitude step function and trapezoidal shape reference signal. The study also discusses comparison with an approximate predictive control approach, being linearized around operating points. It is shown that NPC strategy gives impressive results in comparison to the approximated one.

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Abbreviations

\(\overline {H}_{\rm surge}, \overline {H}_{\rm turbine}\) :

head available in riser of surge tank, turbine (p.u.)

\(\overline {H}_{\rm tunnel}, \overline {H}_{\rm penstock}\) :

head loss in tunnel, penstock (p.u.)

\(\overline {U}_{\rm tunnel}, \overline {U}_{\rm turbine}, \overline {U}_{\rm surge}\) :

velocity of water in tunnel, turbine, surge tank (p.u.)

\(\overline {U}_{\rm no load}\) :

velocity of water at no load (p.u.)

\(f_{\rm tunnel}, f_{\rm penstock}, f_0\) :

head loss coefficient in tunnel, penstock, riser (p.u.)

\(C_{\rm surge}\) :

storage constant of surge tank (s)

\(\overline {H}_{\rm devia,tunnel}\) :

head deviation in tunnel (p.u.)

\(\overline {H}_{\rm devia,penstock}\) :

head deviation in penstock (p.u.)

Z p :

hydraulic surge impedance of water in penstock (=T w / T ep )

T w :

water time constant in penstock (s) \(\left( {=\frac{LU_0 }{gH_0}} \right),\) T w varies with load

T ep :

water elastic time in penstock (s)

T wc :

water time constant in tunnel (s)

T a :

mechanical starting time (s)

L :

length of penstock

U 0 :

velocity of water in penstock at rated head (p.u.)

g :

acceleration due to gravity, (m/s 2 )

H 0 :

rated turbine head (p.u.)

\(\Delta \overline {\omega }\) :

deviation of rotor speed (p.u.)

\(\overline {G}_{\rm opening}\) :

gate opening (p.u.)

D turbine :

damping factor or coefficient in p.u. torque/p.u.speed deviation

A gain :

turbine gain

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Authors and Affiliations

  1. Alternate Hydro Energy Centre, Indian Institute of Technology, Roorkee, 247667, India

    Nand Kishor

  2. Department of Electrical Engineering, Indian Institute of Technology, Roorkee, 247667, India

    S. P. Singh

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  1. Nand Kishor
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Correspondence to Nand Kishor.

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Kishor, N., Singh, S.P. Nonlinear predictive control for a NNARX hydro plant model. Neural Comput & Applic 16, 101–108 (2007). https://doi.org/10.1007/s00521-006-0043-0

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