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Swing Equation
A power system consists of a number of synchronous machines operating synchronously under all operating conditions. Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The angle between the two is known as the power angle or torque angle. During any disturbance, the rotor decelerates or accelerates with respect to the synchronously rotating air gap magnetomotive force, creating relative motion. The equation describing the relative motion is known as the swing equation, which is a non-linear second order differential equation that describes the swing of the rotor of synchronous machine. The power exchange between the mechanical rotor and the electrical grid due to the rotor swing (acceleration and deceleration) is called Inertial response. Derivation A synchronous generator is driven by a prime mover. The equation governing the rotor motion is given by: :J\frac = T_a = T_\text - T_\text N-m Where: *J is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power System
An electric power system is a network of electrical components deployed to supply, transfer, and use electric power. An example of a power system is the electrical grid that provides power to homes and industries within an extended area. The electrical grid can be broadly divided into the generators that supply the power, the transmission system that carries the power from the generating centers to the load centers, and the distribution system that feeds the power to nearby homes and industries. Smaller power systems are also found in industry, hospitals, commercial buildings, and homes. A single line diagram helps to represent this whole system. The majority of these systems rely upon three-phase AC power—the standard for large-scale power transmission and distribution across the modern world. Specialized power systems that do not always rely upon three-phase AC power are found in aircraft, electric rail systems, ocean liners, submarines, and automobiles. History In 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Synchronous Machine
Synchronization is the coordination of events to operate a system in unison. For example, the conductor of an orchestra keeps the orchestra synchronized or ''in time''. Systems that operate with all parts in synchrony are said to be synchronous or ''in sync''—and those that are not are '' asynchronous''. Today, time synchronization can occur between systems around the world through satellite navigation signals and other time and frequency transfer techniques. Navigation and railways Time-keeping and synchronization of clocks is a critical problem in long-distance ocean navigation. Before radio navigation and satellite-based navigation, navigators required accurate time in conjunction with astronomical observations to determine how far east or west their vessel traveled. The invention of an accurate marine chronometer revolutionized marine navigation. By the end of the 19th century, important ports provided time signals in the form of a signal gun, flag, or dropping time ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a nonuniform magnetic field exerts minuscule forces on "nonmagnetic" materials by three other magnetic effects: paramagnetism, diamagnetism, and antiferromagnetism, although these forces are usually so small they can only be detected by laboratory equipment. Magnetic fields surround magnetized materials, and are created by electric currents such as those used in electromagnets, and by electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, it is described mathematically by a function assigning a vector to each point of space, cal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly. Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inertial Response
Inertial response is a property of large synchronous generators, which contain large synchronous rotating masses, and which acts to overcome any immediate imbalance between power supply and demand for electric power systems, typically the electrical grid. Due to the ever existing power imbalance between mechanical power supply and electric power demand the rotational frequency of the rotating masses in all synchronous generators in the grid either speed up (excess power supply) or slow down (excess power demand). This enables the grid operator to rebalance the system in order to stop the speed change, resulting in a relatively small variation in AC frequency ideally within the allowable frequency range of that system. i.e. A 50 Hz system may allow a ±0.5 Hz deviation in the frequency of the AC voltage The grid frequency is the combined result of the detailed motions of all individual synchronous rotors in the grid, which are modeled by a general equation of motion cal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Synchronous Generator
In an alternating current electric power system, synchronization is the process of matching the frequency of a generator or other source to a running network. An AC generator cannot deliver power to an electrical grid unless it is running at the same frequency as the network. If two unconnected segments of a grid are to be connected to each other, they cannot exchange AC power until they are brought back into exact synchronization. A direct current (DC) generator can be connected to a power network by adjusting its open-circuit terminal voltage to match the network voltage, by either adjusting its speed or its field excitation. The exact engine speed is not critical. However, an AC generator must match both the amplitude and the timing of the network voltage, which requires both speed and excitation to be systematically controlled for synchronization. This extra complexity was one of the arguments against AC operation during the war of currents in the 1880s. In modern grids, synchro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torque
In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of the body. The concept originated with the studies by Archimedes of the usage of levers, which is reflected in his famous quote: "''Give me a lever and a place to stand and I will move the Earth''". Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object around a specific axis. Torque is defined as the product of the magnitude of the perpendicular component of the force and the distance of the line of action of a force from the point around which it is being determined. The law of conservation of energy can also be used to understand torque. The symbol for torque is typically \boldsymbol\tau, the lowercase Greek letter ''tau''. When being referred to as moment of force, it is commonly denoted by . In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Armature (electrical Engineering)
In electrical engineering, the armature is the winding (or set of windings) of an electric machine which carries alternating current. The armature windings conduct AC even on DC machines, due to the commutator action (which periodically reverses current direction) or due to electronic commutation, as in brushless DC motors. The armature can be on either the rotor (rotating part) or the stator (stationary part), depending on the type of electric machine. The armature windings interact with the magnetic field ( magnetic flux) in the air-gap; the magnetic field is generated either by permanent magnets, or electromagnets formed by a conducting coil. The armature must carry current, so it is always a conductor or a conductive coil, oriented normal to both the field and to the direction of motion, torque (rotating machine), or force (linear machine). The armature's role is twofold. The first is to carry current across the field, thus creating shaft torque in a rotating machine or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coefficient
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression (including variables such as , and ). When the coefficients are themselves variables, they may also be called parameters. For example, the polynomial 2x^2-x+3 has coefficients 2, −1, and 3, and the powers of the variable x in the polynomial ax^2+bx+c have coefficient parameters a, b, and c. The constant coefficient is the coefficient not attached to variables in an expression. For example, the constant coefficients of the expressions above are the number 3 and the parameter ''c'', respectively. The coefficient attached to the highest degree of the variable in a polynomial is referred to as the leading coefficient. For example, in the expressions above, the leading coefficients are 2 and ''a'', respectively. Terminology and definition In mathematics, a coefficient is a multiplicative factor in some term of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inertia Constant
Inertial response is a property of large synchronous generators, which contain large synchronous rotating masses, and which acts to overcome any immediate imbalance between power supply and demand for electric power systems, typically the electrical grid. Due to the ever existing power imbalance between mechanical power supply and electric power demand the rotational frequency of the rotating masses in all synchronous generators in the grid either speed up (excess power supply) or slow down (excess power demand). This enables the grid operator to rebalance the system in order to stop the speed change, resulting in a relatively small variation in AC frequency ideally within the allowable frequency range of that system. i.e. A 50 Hz system may allow a ±0.5 Hz deviation in the frequency of the AC voltage The grid frequency is the combined result of the detailed motions of all individual synchronous rotors in the grid, which are modeled by a general equation of motion call ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equations
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in French an ''équation'' is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. ''Solving'' an equation containing variables consists of determining which values of the variables make the equality true. The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true for particular values of the variables. An equation is written as two expressions, connected by an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
