Download equivalent circuit

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