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Development and Simulation of Mathematical Modelling of Hydraulic Turbine

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Power system performance is affected by dynamic
characteristics of hydraulic governor-turbines during and
following any disturbance, such as occurrence of a fault,
loss of a transmission line or a rapid change of load. Accurate
modelling of hydraulic System is essential to characterize
mathematical modeling of hydraulic turbine is presented. The
model is capable to implement the digital systems for
monitoring and control replacing the conventional control
systems for power, frequency and voltage. This paper presents
the possibilities of modeling and simulation of the hydro power
plants and performs an analysis of different control structures
and algorithms.

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Development and Simulation of Mathematical Modelling of Hydraulic Turbine

1. 1. ACEEE Int. J. on Control System and Instrumentation, Vol. 02, No. 02, June 2011 Development and Simulation of Mathematical Modelling of Hydraulic Turbine 1 2 Gagan Singh and D.S. Chauhan 1 Uttarakhand Technical University, Dehradun, (U.K), India. hod_ee@dit.edu.in 2 Uttarakhand Technical University, Dehradun,(U.K),India. pdschauhan@gmail.comAbstract- Power system performance is affected by dynamic low water storage capacity in the reservoir; therefore thecharacteristics of hydraulic governor-turbines during and plant operation requires a permanent balance between thefollowing any disturbance, such as occurrence of a fault, water flow through turbines and the riverloss of a transmission line or a rapid change of load. Accuratemodelling of hydraulic System is essential to characterizeand diagnose the system response. In this article themathematical modeling of hydraulic turbine is presented. Themodel is capable to implement the digital systems formonitoring and control replacing the conventional controlsystems for power, frequency and voltage. This paper presentsthe possibilities of modeling and simulation of the hydro powerplants and performs an analysis of different control structuresand algorithms. Figure 1: Functional block diagram of hydraulic governor-turbineKey words: mathematical modeling, simulation, hydraulic system interconnected with a power system network.turbine. flow in order to maximize the water level in the reservoir for a maximum efficiency of water use. Next, we will determine the I. INTRODUCTION mathematical model for each component of the hydropower system. Usually, a typical hydroelectric power plant consists ofwater tunnel, penstock, surge tank, hydraulic turbine, speed A. Mathematical modeling of Hydraulic turbinegovernor, generator and electric network. Hydrodynamics The representation of the hydraulic turbine and waterand mechanoelectric dynamics are all involved in such a column in stability studies is usually based on the followingnonlinear dynamic system. Generally, a hydroelectric assumptions:-generating unit has many different operating conditions and  The hydraulic resistance is negligible.change in any operating condition results in small or large  The penstock pipe is inelastic and the water ishydraulic transients. There are many instances of damage to incompressible.penstock or hydraulic turbine which are most probably  The velocity of the water varies directly with theoccurring due to large transients. Hydrodynamics is gate opening and with the square root of the netinfluenced by the performance of hydraulic turbine which head.depends on the characteristics of the water column feeding  The turbine output power is proportional to thethe turbine. These characteristics include water inertia, water product of head and volume flow.compressibility and pipe wall elasticity in the penstock. The hydraulic turbine can be considered as an elementDifferent construction of hydropower systems and different without memory since the time constants of the turbine areoperating principles of hydraulic turbines make difficult to less smaller than the time constants of the reservoir, penstock,develop mathematical models for dynamic regime, in order to and surge chamber, if exists, which are series connecteddesign the automatic control systems. Also, there are major elements in the system. As parameters describing the massdifferences in the structure of these models. Moreover, there transfer and energy transfer in the turbine we will considerare major differences due to the storage capacity of the the water flow through the turbine Q and the moment Mreservoir and the water supply system from the reservoir to generated by the turbine and that is transmitted to thethe turbine (with or without surge chamber).The dynamic electrical generator. These variables can be expressed as non-model of the plants with penstock and surge chamber is more linear functions of the turbine rotational speed N, the turbinecomplicated than the run-of-the-river plants, since the water gate position Z, and the net head H of the hydro system.feed system is a distributed parameters system. This paper Q = Q (H, N, Z) (1)will present several possibilities for the modeling of the M = M (H, N, Z) (2)hydraulic systems and the design of the control system. Through linearization of the equations (1) and (2) around II. MODELING OF THE HYDRAULIC SYSTEM the steady state values, we obtain: For run-of-the river types of hydropower plants have a 55© 2011 ACEEEDOI: 01.IJCSI.02.02. 1