Abstract-In this work, the Mixed-Integer (MIP) formulation for unit commitment problem (UC) for power systems is discussed. A new formulation for the start-up cost is suggested as well. This new formulation of the start-up cost exploits the transformation of the conditional statements into inequalities that comprise linear combination of binary variables. Solutions of the suggested optimization problem were obtained. A comparison between these solutions and those of a strategy common in literature is held to show that the new strategy gives same results with less number of constraints and tighter capture of the startup cost.
In some designs of power systems for marine vessels, large-size or medium-size Diesel engine(s) is(are) used to drive one synchronous machine to generate electricity, and the main propeller, simultaneously, through a gear box. Such systems are subject to disturbances that may affect performance and fuel consumption. The most important disturbances occur due to the propeller torque, and load demand on the electric network. In this work, a simplified state-space model is suggested for such systems based on well known models of each component. The model considers the dynamics of the shaft, Diesel engine, and synchronous machine with the propeller in their simplest models. The output voltage and torque coefficient were modeled as uncertain parameters. Then, exploiting feedback linearization, two controllers were suggested for the proposed model to regulate the rotational speed of the shaft. Firstly, by pole placement. The second is a robust controller by mixed H 2 /H ∞ synthesis. The results of the simulations of the proposed controller are presented and compared.
A generating set (Genset) comprises a prime mover such as a Diesel Engine, and a synchronous generator. The most important controllers of such systems are the speed governor to regulate the engine or shaft speed and the automatic voltage regulator (AVR) to regulate the terminal voltage. The speed governor is a PID controller that uses the difference between the speed and its desired value as a feedback signal to change the fuel mass input by changing the fuel rack position. AVR is also a PID that uses the difference between the terminal voltage of the generator and its desired value, and changes it by manipulating the voltage of the field excitation circuit. Thus, the two controllers act separately. That is to say, if the speed varies from the desired value, the speed governor will react, while the AVR will not react as long as the voltage is stable, and vice versa. In this work, a control-oriented model is suggested for a Genset, and then a controller, that regulates the shaft speed and the terminal voltage, is designed by feedback linearisation. The proposed controller has two inputs: the fuel mass and the field circuit voltage. Simulations show that the proposed controller makes the two inputs act, simultaneously. Thus, any change of the speed e.g., forces the two input controls to react, in contrast to the ordinary PID controllers. Further, we discuss the robustness of the proposed controller to uncertainties and time delay.
Unit Commitment (UC) is a minimization problem that aims to schedule the required generating units in a power system over some time horizon to meet the demand based on minimizing the production cost. In this paper, we present a novel technique to minimize such functions based on Mixed-integer formulation, neglecting the time horizon and most of the constraints. This technique can be considered as a first step in a better and tighter mixed-integer formulation of the unit commitment problem, especially for isolated power systems that contain a small number of generating units. Data from isolated power systems on marine vessels are used to test this technique. The proposed technique requires more constraints and binary variables. However, the numerical results presented in this work, show that the proposed method gives more efficient results for low demand, and close results to those obtained from local minimizers when the demand is high. The computational time of the suggested method does not seem to be explicitly longer than the time taken by the local minimizers, especially for small isolated power systems.
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