The Calculation of the Optimal Placement of Reactive
Power Sources in Industrial Enterprises with the Use of Genetic Algorithms
By Tursyn S.K, , Kelbass, S.
V.
Abstract. The problems of
reactive power compensation in EPS and PSS. Calculations of power of the RPS
and the optimal location point by means of the use of the methods of genetic
algorithms in optimization of choice of the RPS.
Keywords: Reactive power
compensation, genetic algorithms, optimal selection, industry.
The total power transmitted
from the power generators to the electrical load is transmitted from the active
component and inactive components of the power, which may include reactive
power and distortion power and unbalance. Inactive power components adversely
affect the modes of operation of the electrical network and power quality. In
particular, additional reactive current loads lines and transformers, affects
voltage levels of the consumer, and also increases the losses of active and
reactive power. Useful work is only performed by the active component of the
total power. Reactive power as well as distortion and unbalance power do not
perform useful work, and therefore should be excluded. In order to compensate
the reactive power various types of reactive power sources are used (RPS).
The results listed in [1] show
that the installation of the RPS at around 0,4 kV line current value decreases
and allows to increase the transmission of active power by 21 %, when
setting the RPS at around 10 kV line current value decreases and allows to
increase the transfer of active power by 8 %. Thus, reactive power
compensation is needed at all levels of stress.
The problem of reactive power
compensation in electric power systems (EPS), and in power supply systems (PSS)
is generally multi-dimensional and multi-modal, complex in terms of algorithmic
problem. There is no any universal method that would allow finding
a solution which is sufficiently close to the optimum to solve the problem
in a short period of time. In this regard, it is necessary to find an
approach that would answer in a better degree the requirements for the
solution of such problems and would take into account their discretion. One
solution could be the use of genetic algorithms to determine the optimal
placement points and deciding on the RPS.
The genetic algorithm is
precisely such a fairly universal method for the determination of some
combination of the optimum. The mechanisms of crossover and mutation, on the
one hand, in a sense, reflect the essence of linear search method that can
be used for any problems with the combinatorial nature. On the other hand, the
gradient method replaces the generation of the best alternatives and solutions,
which in aggregate provides a sufficiently high and stable performance of
the algorithm and guaranteed effective genetic search for all types of modern
optimization problems.
Various modifications of
genetic algorithms have found quite a lot of different applications for
the solution of many scientific and engineering problems. The use of modern
intelligent technology enables to realize very powerful, effective and
practicable optimization algorithms, and genetic algorithms can be fully
assigned to them.
An essential feature of this
approach is to use genetic algorithms in combination with classical techniques.
One of the examples is the optimization of electric power systems (EPS) and
power supply systems (PSS). Optimal planning regimes of reactive power is to
determine the location and capacity of compensating devices, their installation
provides a minimal cost, if some regime restrictions will be set for the
operational parameters. The solution of the problem should provide the maximum
economic effect, subject to technical conditions to ensure normal operation of
electrical networks and industrial systems, as well as all electric appliances.
In some cases, it is advisable to consider separately the design statement of
the problem, when we consider the optimal location and capacity of the RPS and
operational — to select the optimal value of the RPS on the condition of
minimizing the total active power losses.
Briefly, nature and mechanism
of operation can be represented in two ways:
1. Calling a function of
genetic algorithms;
2. Using a complex
Genetic Algorithm Tool.
Both methods, including
a standard set of functions and modules are presented in the environment
of Matlab.
The authors have chosen the
software environment among Delphi, since it represents a great opportunity
for the implementation of genetic algorithms, has a simple interface and
provides better visualization.
The calculation algorithm
includes several separate procedures:
— Formation of a network
configuration;
— Randomly generated power
compensating device from 0 to a maximum reactive power unit, which will be
installed at the RPS, as there is no need to put more power than the power
consumption of the node.
Then you have to calculate the
reactive power factor, established by the Power Supply Company, at the
boundary.
If the condition is satisfied,
then the solution found is the best, if not, the solution proceeds to the next
step. At this point, the genetic algorithms operators are applied.
The proposed by the genetic
algorithm optimization of RPS is formed as follows:
1. Formation of the initial
population by randomly generating a range of acceptable values.
A chromosome consists of making real variables of the reactive power of
RPS, and placements.
2. The life cycle of
a population is realized in the form of sets of genetic operators:
— Select the parental couple
of sets of chromosomes by using the “event”;
— Crossing the selected
chromosomes to produce new solutions with a probability of Pcr and
two-point crossover;
— A random mutation of
the gene of each chromosome with a certain probability;
— Calculation of the objective
functions for a new population of chromosomes and chromosome screening
with a minimum value of the objective function.
3. Checking the conditions of
the end of the cycle, as the maximum amount of generations. Under the
condition, namely the reduction in the rate of reactive power to the required
level, the algorithm is complete, otherwise return to step 2.
The block diagram is shown in
Figure 1.
The main feature of the
algorithm is its novelty and the use in each step of a new generation of
mutations calculating steady state and computation on the basis of its
operating parameters and target functions.
Calculations were made for one
of the workshops of “Angarsk Electrolysis Chemical Complex” (AECC). The problem
of reactive power compensation is still relevant at the AECC, since the cost of
electricity is 10 % of production costs.
The calculations made for
industrial enterprises were compared with the calculations using the method of
Lagrange.
The comparative analysis has
shown that to achieve the desired ratio of reactive power by the method of
Lagrange 1594 kVar to be installed in five sites of power supply system, and
with the help of genetic algorithm the same goal is achieved by setting 1330
kVar. The savings makes 264 kVar, i.e. 16 %.
In addition, the comparative
analysis shows that this algorithm ensures minimum reactive power compensation
required for compliance with the Power Grid Company. In this case, due to the
algorithm as much reactive power is compensated as needed to comply with the
contract, and not much more, as in the simplified calculation. Along with this,
an analysis of the performance of algorithms indicates that with the increasing
amounts of resource nodes spending time in the conventional method of nonlinear
programming increases significantly faster than the method using a genetic
algorithm.
In summary, the effectiveness
of applying genetic algorithm in the optimal placement of the RPS in EPS and
PSS are proved by the following provisions:
— Universal approach, which
allows you to determine quickly the exact solution of complex problems with
multi-dimensional and multi-modal nature;
— The lack of requirements for
continuity, differentiability of flow characteristics of power plants;
— Genetic algorithm realizes
quite simple but at the same time very effective scheme of calculations.
References
1. B.Kochkin
Reactive power in electric networks. Technology-driven compensation // Electrical
Engineering News, number 4 (64), 2010.
2. Order of
the Russian Federation Ministry of Industry number 49 dated 22.02.07 “On
calculation on the ratio of values of active and reactive power for the
individual power receivers (groups of power receivers) consumers of electricity
used for determining the obligations of the parties to the agreements on the
provision of services for the transmission of electrical energy (electricity
contracts)”.
3.
V. Z. Manusov and D. A. Pavlyuchenko Application of
hybrid genetic algorithm for the optimal allocation of reactive power // Power:
Proceedings, Novosibirsk, Publishing House of Novosibirsk State Technical
University 2000, pages 23–30.