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SIMULATION OF ELEMENTS AND OPERATING MODES OF INDUSTRIAL POWER SUPPLY SYSTEMS Томский политехнический университет According to EIC power supply system a set of electrical installations, designed to provide consumers with electric energy. Transportation of electrical energy from receiving point to consumption point is carried out via power grids. Power grid is a set of electrical installations for transmission and distribution of electrical energy, consisting of substations, switchgear, conductors, overhead and cable lines, working in a particular area. Power supply system shall be designed and operated in such a way that it keeps performing in all possible operating modes: normal, emergency and post-fault. Moreover, the main parameters of power grid such as frequency and voltage deviations from nominal values, value of limit currents, harmonic distortion, etc. must be within the limits regulated by GOST 13109-97, which determines electricity quality. Томский политехнический университет 2 A convenient tool for calculating and analyzing circuit modes is equivalent circuit, constructed on the basis of idealized simple elements: voltage or current sources and resistors, which are like building blocks that make up overall design – complete equivalent circuit of real component (subject) of power grid. In this case, calculations with respect to complex physical processes associated with transmission of electrical energy via power grids, are reduced to consideration of elementary processes of known methods of electrical engineering. In general, mathematical model of real component is a system of mathematical relationships, clearly linking its input and output characteristics by means of a set of internal parameters, presented in the form of equivalent circuit that reproduces behavior in various modes. Томский политехнический университет 3 There is a number of basic models of electrical components based on which can be designed any electrical model of individual component or entire circuit. Electrical circuit is a set of devices and facilities that form the path for electric current, electromagnetic processes which can be described using concepts of electric current, EMF (electromotive force) and electric voltage. Branch of electrical circuit (schemes) – part of circuit with the same current. Branch may consist of one or more series-connected elements. Limits of branch are called nodes. As a result of combining nodes of certain branches electrical circuit is made up. For mathematical description of processes in electrical circuit equations of two types are used – component and topological. Томский политехнический университет 4 Component equations (equation of branches and circuit elements) establish relationship between currents and voltages in each branch and each element of scheme. These equations are made on the basis of Ohm's law and their number equals the number of branches in equivalent circuit. Topological equations are determined by topology (structure) of the scheme and reflect properties of elements included in the circuit structure. Topological equations are equations compiled on the basis of the first and second laws of Kirchhoff. Томский политехнический университет 5 Elements of the circuit are divided into active and passive. Active are elements that contain a source of electrical energy. Parameters of active elements are value of nominal voltage of EMF (or the value of nominal current for current source) and value of internal resistance. Passive elements are referred to those in which energy of electromagnetic field is either dissipated or stored. Their main parameters are resistivity and conductivity. The main characteristics of the elements are volt-ampere, Weber-ampere and coulomb-volt characteristics described by differential and (or) by algebraic equations. Томский политехнический университет 6 Elements of the circuit are divided into linear and nonlinear. If parameters of element do not depend on current flowing through it, it is linear, otherwise it should be attributed to non-linear. Fore mathematical description of linear elements are used ordinary linear differential or algebraic equations, for nonlinear elements is often used algorithmic simulation. Strictly speaking, all real elements are nonlinear. However, possibility of considering them as linear greatly simplifies mathematical description and analysis of processes occurring in them. Томский политехнический университет 7 Mathematical models of active elements Current sources in electrical circuit are devices which create (generate) currents and voltages. Sources can act as primary devices that convert some form of energy into electrical energy: power generators, batteries, solar cells, etc. and devices that convert electrical energy into energy of primary sources into energy of electrical oscillations of required forms: transformers, converters, etc. For mathematical representation it is reasonable to use ideal active elements – EMF sources (voltage) or current. Depending on type of volt-ampere characteristics (VAC) and control of output parameters it is distinguished dependent and independent voltage and current sources. Томский политехнический университет 8 Independent source of electromotive force (voltage) is called double pole element, when voltage across the terminals is independent from current flowing through it. Equivalent circuit of ideal voltage source and volt-ampere characteristics is shown in Figure. i u e(t) u(t) i Independent ideal source of EMF Томский политехнический университет 9 Equivalent circuit of dependent ideal voltage source and volt-ampere characteristics are shown in Figure. i u rвн u(t) e(t) iкз i Dependent ideal voltage source Томский политехнический университет 10 Equivalent circuits of independent and dependent ideal source are shown in Figure. i i(t) J(t) iвн J(t) gвн а) u б) Ideal current source а – independent; b - dependent Томский политехнический университет 11 Mathematical models of passive elements Passive circuit elements are resistive (resistance or conductance), inductive and capacitive elements. Equivalent circuits of passive elements in electrical circuit а – resistance; b – inductance; c – capacity Томский политехнический университет 12 Voltage and current of resistive element are the same in phase. Instantaneous current, voltage and capacity across resistance Томский политехнический университет 13 Time diagrams of electrical parameters across inductance Томский политехнический университет 14 Time diagrams of electrical parameters across capacity Томский политехнический университет 15 To present in computer characteristics and parameters of power supply system elements, mathematical description – mathematical model is required. In general, any power supply system can be divided into three main groups of elements: power sources; elements of power grids; electric loads. To simulate each group of elements, as a rule, the same methods described in details in [7,8] are used. Consider the basic principles of simulation elements of power systems as an example of each group. Томский политехнический университет 16 Depending on the specific conditions as power sources can be used: power grid; own power plants operating in parallel with grid; in some cases, electrochemical, photovoltaic, and other static sources; in terms of reactive power - its own sources of reactive power. The first two sources are the basis of centralized power supply, whose share in electricity production to meet the needs of economy ranges up to 98%. Томский политехнический университет 17 When simulating power supply it should be remembered that its reduction by constant EMF and inductance is valid only for cases where maximum possible current power source is much less than its nominal current. Typically, maximum currents in power supply system correspond to electrical transients associated with short circuits. In line with this there are two main types of fault: remote and nearby. In the case of remote short circuit, fault current is relatively small compared to PS nominal current, feeding circuit faults. In this case, transients in PS are mild and practically do not change the actual value of periodic component of current over time Ip = Ip0 = const (respectively, E and X in equivalent circuit of power supply can also be assumed as constant). This process is typical for shortcircuit occurring far away from EE sources, and usually occurs when short-circuit current comes into power grid of low voltage (LV) from high voltage (HV) grid via step-down transformer. Томский политехнический университет 18 Simulation of power grid elements When transmitting real power from power source (PS) to power loads (PL) there are inevitable losses in power grid elements, which should be accounted to adjust design loads, determine technical and economic parameters and investigate operating modes of IPSS elements. Since most elements of power supply system are symmetrical three-phase loads, then analysis of power losses should be conducted via single-phase equivalent circuits of each element. As an equivalent circuit is commonly used L – section fourpole network. Томский политехнический университет 19 L-section equivalent circuit of power grid element Томский политехнический университет 20 Losses of active and reactive power in power supply system element are equal: Р = 3I22R + U12G = PR + PG ; Q = 3I22X + U12B = QX + QB,, where PR and QX express losses in longitudinal elements of equivalent circuit and are determined by current I2; components PG and QB express losses in transverse elements and are determined by voltage U1. Equivalent circuit parameters of power supply element are determined by nominal data of equipment. Томский политехнический университет 21 Simulation of electrical loads When calculating operating conditions of power supply systems, bases for simulation of electrical loads are its voltage static characteristics. The most adequate way to account load properties in these calculations is using characteristics that consider consumers of each specific load. However, for most design calculations such refined approach is not feasible and is not necessary. It can be justified only in certain operational calculations. Generally, in operating mode calculations of power supply systems can be used generalized static characteristics. Томский политехнический университет 22 When simulating electrical loads, there are two basic methods. In the first method load is constant value of active and reactive power - curve 1. As figure shows, deviation of conditional characteristics from actual characteristics is not too large only in a small range of voltages. In mode calculation, which is characterized by significant changes in voltage, it is convenient to present load as parallel or series connected constant resistance and reactance (second method). Values of these resistors are chosen so that the power they define at normal voltage would be equal to specified power load. Томский политехнический университет 23 When representing load with constant resistance, its power change is directly proportional to square of applied voltage - curve 2. Comparison of different methods of load simulation shows that the second method is more accurate, thus it became the most widespread. P, Q 1 1,0 P 0,9 Q 0,8 2 0,7 0,8 0,9 1,0 U Static load characteristics and its simulation Томский политехнический университет 24