Sumulation of behaviour dynamics of turbine drive generating set
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The aim of this paper is to show the efficiency of the application of the System Dynamics Simulation Modelling in investigation of behaviour dynamics, one of the complex marine system and process i.e. “steam – turbine generator”. Steam turbine and synchronous generator without contact shall be presented with mental verbal, structural and mathematical computing modules, and will simulate working process of ship propulsion complex. 1. SYSTEM DYNAMICS SIMULATION MODELS OF THE MARINE STEAM TURBINE 1.1. Mathematical model of the Marine Steam Turbine and UNIREG-PID regulator The steam turbine working process is the conversion of water steam energy to mechanical energy converted to trust on the mechanical units. Therefore, turbine is subjected to various loads transmitted from the units. The steam turbine working system can be derived into two parts: regulating valve and nozzle ring steam space that can accumulate steam energy and rotational part that accumulate kinetic energy. The mathematical model or level equations could be represented as follows: 3 2 2 1 1 1 1 K K K T dt d (1) 4 1 0 0 2 1 1 K K T dt d (2) The first differential equation for the first part is defined according to (Siromjatnikov 1983): 1 T -Time constant of rotating parts; FI -Relative increment of turbine shaft angular velocity; 2 PSI2 Relative pressure increment in main condenser; ALPHA Relative turbine load change; 3 2 1 K , K , K Gain coefficients. The second differential equation is defined: 2 T Time constant of the steam space; 1 PSI1 Relative value of the steam pressure increment in the steam space; 0 PSI0 Relative value of the steam pressure increment before regulating valve; MI Relative value of regulating valve opening change; 4 0 K , K Gain coefficients. The PID regulator incorporates in itself proportional (M1), integral (M2) and derivation (M3) regulators. The input function in the regulator is the discrepancy: Mathematical model of the UNIREG-PID regulator is: UNIREG = PREG + IREG + DREG PREG KPP X * X KPI IREG * dt * dt dX KPD DREG * Where there are: UNIREG = Output of the Universal-PID regulator, PREG = Proportional regulator, IREG = Integral regulator, DREG = Derivative regulator, X = Input Function in the PID regulator, KPP = Amplification Factor of the Proportional regulator, KPI = Amplification Factor of the Integral regulator KPD = Amplification Factor of the Derivative regulator. In this case, X= input function in the first UNIREGPID regulator is DISC1= discrepancy between CFI= nominal relative changing of angular velocity and = FI= relative changing of angular velocity, or exactly: DISC = CFI – FI The UNIREG= output of the first Universal-PID regulator is function =KAPA= KAPA1= relative shift of high pressure fuel pump. = 1 The UNIREG-PID regulator make connection between angular velocity discrepancy DISC and relative shift of high pressure fuel pump variable =KAPA. In the reality, this UNIREG-PID regulator selfregulated variable to be equal the CFI= goal of regulating process of the relative changing of angular velocity = FI. The PID regulator incorporates in itself proportional (M1), integral (M2) and derivation (M3) regulators. The input function in the regulator is the discrepancyDISC. 1.2. Structural and Mental-Verbal Models of the Marine Steam Turbine and UNIREG-PID regulator Fig.1. determinates the Structural Model of Steam Turbine and PID Regulator. It is determined in the accordance with System Dynamics Methodology. Mathematical model could be very suit for determining the mental-verbal qualitative model of the steam turbine and PID regulator. dFI/dt FI +
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