Enterkonnekte elektrik güç sistemlerinde kapalı çevrim güç akışlarını önlemeye
düzenlemeye yönelik bulanık karar verme temelli bir yöntem / A fuzzy - decision making based method to prevent / regulate loop flows in interconnected electrical power systems
Yazar: GÜLCİHAN ÖZDEMİR DAĞ
Danışman: PROF. DR. MUSTAFA BAĞRIYANIK
İstanbul Teknik Üniversitesi / Bilişim Enstitüsü / Hesaplamalı Bilimler ve Mühendislik Ana Bilim Dalı
Derece: Doktora, 2011
Konu: Elektrik ve Elektronik Mühendisliği = Electrical and Electronics Engineering ; Enerji = Energy

Özet:
Seksenli yıllara kadar tüm dünyada elektrik enerji sistemlerinin tamamı; üretim, iletim
ve da˘gıtım devletlerin kontrolünde idi. Bunun ba¸slıca nedeni çok büyük yatırım ve
i¸sletme maliyetlerinin olması idi. Kalitenin ve maliyetlerin ancak rekabet ortamlarında
olu¸saca˘gına inanılan kapitalist ekonomilerde, özellikle hava yolu i¸sletmecili˘ginde tekel
sisteminin kaldırılıp serbest piyasa ko¸sullarına geçilmesi ile ula¸sım maliyetlerindeki
ciddi dü¸sü¸s ve yaygın ekonomik servislerin gelmesi ile, benzer bir ba¸sarının elektrik
sektöründe de olu¸saca˘gına olan inançla elektrik güç sistemlerinde de özelle¸stirme
furyası ba¸sladı. ˙Ingiltere, ˙Izlanda ve ABD bu i¸sin öncülü˘günü yaparak sistemlerinin
neredeyse tamamını özelle¸stirerek sektörü özel te¸sebüse bıraktı. Daha do˘grusu elektrik
enerjisinin üretimi, iletimi ve da˘gıtımını farklı farklı firmalara satılarak ba¸ska türlü bir
tekelin olu¸sması da engellenmeye çalı¸sıldı. Devlet kendisi, ya da kurdu˘gu düzenleyici
otoriteler aracılı˘gı ile sektörde yanlızca kontrolör olarak görev üstlendi.
Devlet tarafından i¸sletilen sistemlerde güç kayıplarının yüksekli˘gi, verimin dü¸süklü˘gü,
veya enerjinin çok uzun yollardan (iletim hatlarında dola¸sarak) tüketim noktalarına
varması sorununa ciddi bir ¸sekilde yakla¸sılmadı. Maliyetlerin artması do˘grudan
tüketiciye yansıtıldı˘gından, yada maliyetlerin bir kısmının devlet tarafından kar¸sılanması
nedeni ile enterkonnette sistemlerin do˘gasında var olan kapalı çevrimler içinde
dola¸san enerji (yada bu dola¸sım sonucu hatlarda olu¸san ısı kayıpları) pek sorun
olarak görülmedi. Özelle¸stirme sonucunda; hangi miktarlarda enerjinin hangi iletim
hatlarında iletildi˘gi, hangi firmanın hangi iletim hattını ne kadar süre ile ve hangi
saatlerde kullandı˘gı, enerji iletim sisteminin hatlarının dolulu˘gu nedeni ile e˘ger
sistem bir arıza durumuna geçerse bundan kimin sorumlu oldu˘gu konuları çok önem
kazanmaya ba¸sladı. Elektrik enerjisinin izleyece˘gi yol fizik kurallarına göre yani,
Kirchhoff'un akım yasası ve Ohm yasasına göre belirlenir. Enerji akı¸sı kontrat
yapılan güzer˘gah yerine empedansı en dü¸sük olan iletim hatlarını seçer. Bu durum,
enerjiyi satınalan ile satan arasına üçüncü birinin girmesi sonucunu do˘gurur. Enerji
akı¸sının böyle olması sonucu bazı i¸sletim problemlerini ortaya çıkardı. Þöyle
ki, enerji alı¸s-veri¸s planında sınırlamalar, iletim kapasitesinde de˘gi¸simler, hatların
a¸sırı yüklenmesi, güvenlik ve güvenirlilik konuları ve enerjinin serbest piyasada
fiyatlandırılması komplikasyonları, enerjiyi satınalan ile onu satan arasına üçüncü
birinin (sistemi kullanılan taraf) girmesi sonucu, üçüncü birinin sisteminin kullanım
bedelinin kimler tarafından kar¸sılanaca˘gı gibi.
Kapalı çevrim güç akı¸sı, i¸ste bu üçüncü birimin i¸sgal edilen hatlarında olu¸san enerji
kayıplarının nasıl ücretlendirilece˘gi, kime faturalandırılaca˘gı, sistemde hatların dolu
olması durumunda tıkanıklı˘ga sebep olunmasından, sistemin çöküntüye gitmesinden
kimlerin ne derecede sorumlu tutulaca˘gı gibi konuları içerdi˘ginden çok önem
kazanmı¸stır. Halen aktif bir ara¸stırma konusudur.
Bu çalı¸smada amaç; enterkonnekte elektrik güç iletim sistemlerinde kapalı çevrim
güç akı¸slarını önlemeye/düzenlemeye yönelik bir yöntem geli¸stirmektir. Bunu
gerçekle¸stirirken ilave amaçlar da probleme dahil edilmi¸stir. Bunlar; sistem
baralarındaki gerilim profilinin bozulmaması ve düzeltilmesi (gerilim genliklerinin
arzu edilen de˘gerlerde tutulması), iletim hatlarındaki hem aktif hem de reaktif
kayıpların en aza indirilmesi ve temel durum de˘gerlerinden fazla uzakla¸sılmaması,
hatlardaki güç akı¸slarının iletim hatlarının akım ta¸sıma kapasite limitleri dahilinde
tutulmasıdır. Görüldü˘gü gibi problemimiz çok amaçlı ve çok kısıtları olan
bir problemdir. Bu çoklu amaçlı ve kısıtlı problemde bulanık karar vermeden
yararlanılmı¸stır. Bunun sonucunda elde edilen tek amaçlı en iyileme problemine
evrimsel arama tekniklerinden genetik algoritmalar uygulanmı¸stır.
Bu yöntemi düzenlerken i¸sletim ko¸sullarını etkileyen elektrik güç sistemi kontrol
ve durum de˘gi¸skenleri ve bunların üzerlerindeki kısıtlamalar da göz önünde
bulundurularak, bulanık ortamda her birisi için uygun üyelik fonksiyonlarının tespit
edilmeleri ile modellenmi¸slerdir.
Genetik algoritmaların uygulanması sırasında GA operatörlerininde probleme
uyarlanması açısından çe¸sitli benzetimler yapılmı¸s ve litaratürdeki uygulamalar da
incelenerek çalı¸smaya en uygun olanının tespiti yapılmı¸stır.
Problem günlük bir i¸sletme problemi oldu˘gundan gün içerisinde defalarca çözümü
yapılmaktadır. Bundan dolayı çözüm süreside önem te¸skil etmektedir. Çözüm
süresinin azaltılması için hem genetik algoritmalarda paralel algoritmalar seçilmi¸s
hem de kurumdaki yüksek ba¸sarım labratuvarlarından yararlanılarak yüksek ba¸sarımlı
bilgisayarlarda paralel ortam hesaplama tekniklerinden yararlanılmı¸stır.

Abstract:
After the liberalization of the electricity markets, the operation of the power system has
fundamentally changed. How much power flows on which transmission lines, which
company uses the other's transmission lines and/or the amount and duration of the
transmission line usage have all become very important issues.
When the actual power flow exceeds system-operating limit for a transmission path, the
transmission system operators must immediately mitigate the transmission overloads
to reduce the actual power flow across the path. The deviation of actual electric
power flows in transmission circuits from the scheduled (expected) power flows is
called closed loop flows, and/or unscheduled flows, and these flows may cause the
transmission limit violations. The unscheduled flows have been seen as a serious
problem, since these flows may result in blackouts and affect cross border trading
in the electricity markets. Therefore, such flows in an interconnected power system
should be kept under control to improve both the operation conditions and the market
conditions.
In interconnected power systems there are many parallel transmission lines and closed
loops causing electrical energy to follow different routes to reach load centres. Thus,
when for a reason a transmission line becomes out of service, there are alternative
ways of feeding loads at the end of that particular transmission line. Otherwise, loss
of electrical energy may cause interruption of all types of production, transportation,
communication, entertainment, education and the other life related activities to be
affected partially or totally.
Up until eighties all activities of electrical power systems, such as production,
transmission and distribution, were under the control of governments. The reason
for this was that both investment and operation costs were too high. With the
belief that both the quality and reduced cost would be possible in a free market,
especially considering the success of deregulated aviation systems, electrical power
systems were deregulated. England, Iceland and USA were the first to deregulate their
power systems. Production, transmission, and distribution systems were privatized to
different companies. Either government herself or via regulation authorities took the
regulation role.
High power loses, low efficiencies, or the long paths electrical energy travels through
(using transmission systems) in a government controlled system were not taken into
consideration seriously. Since the rising costs are directly adjusted to the customers'
bill, or part of the cost is subsidized by government, the loop flows, which is a natural
result of an interconnected power system, were not considered as a problem. As a
result of deregulation the following questions have become quite important. How much
power flows on which lines? Who is using a certain transmission line and how long the
line is being used? At which hours a transmission line is used? If, due to overloaded
lines a fault occurs who is responsible for this fault? Electrical power does not follow
a prescribed line, it rather follows ohm's law. That is, energy does not follow from
a contracted path, it flows through the lines which has the least resistance. This fact
brings a third party into a picture when there is an energy seller and a buyer. This, is
turn, creates operational problems, such as limitations on power transactions, changes
in transmission line capacity, lines being overloaded, security and reliability problems,
and complications in pricing the electricity in the market (who pays the transmission
line usage, when there is third party between a buyer and seller on a contracted path).
Closed loop flows, tries to answer the question as to who will be responsible for the line
usage in the third party's system, how the pricing shall be done, who is and how much
responsible for the congestion of transmission lines especially on the third party's
system. This field is still a heavily researched area.
The main purpose of this study is to design a method to control power flows in
closed loops of interconnected electrical power systems. This problem has become
significant due to deregulation in power systems. By this method we aim to prevent
and/or regulate unwanted loop flows. There are some additional purposes needed
to be handled besides the main purpose. These additional purposes are the voltage
profiles of each bus of the system should not be destroyed, active and reactive power
looses of transmission lines must be minimized and should not be far away from the
one of basic case solution. The values of the transferred power must be kept under
the current carrying limits of the transmission lines. As seen the problem has multi
objectives and multi constraints that are needed to be handled. The multi objectives
and multi constraints problem is handled by using fuzzy-decision-making techniques.
The finalized single objective problem is optimized by using genetic algorithms which
is one of the evolutionary search algorithms.
The power system control variables, state variables and the constraints that are
effecting the operational conditions of the system are also taking under considerations
while arranging the method. A membership function is determined to each objectives
and constraints in fuzzy environment. The break-points of the fuzzy membership
functions are tested. After a set of simulations the best form of the membership
functions are determined to improve the success rate of the solution of the problem.
In fuzzification step, the objectives and constraints were fuzzified by using designated
membership functions, where these functions should be properly constructed to
guarantee the overall performance and improve the success rate of the solution of the
problem. After a set of simulations the best form of the membership functions are
determined by arranging the break-points of the fuzzy membership functions. The
value or value of a fuzzy membership function defines the degree of membership that
a crisp value has in a fuzzy set. The closer the value of membership is to one, the better
the solution is for that objective or constraint. In fuzzy decision-making, the optimal
solution is defined to be the one with the highest degree of membership, and thus the
optimization problem becomes that of maximizing the satisfaction with the solution;
subject to the crisp and fuzzy constraints. In the proposed approach, the objective
functions were minimization of the line flows of the closed loop on the contracted
paths, and minimization of both total active losses and total reactive losses. The
constraints (voltages remaining within the limits, line flows remaining within the limits
etc..) were also handled in fuzzy environment by using designated fuzzy membership
functions.
Two different shapes of fuzzy membership functions are tested for the main objective
that is the line flows for the closed loops. One of the shapes is trapezoidal function.
The other shape is exponential function. The study showed that more satisfying results
can be obtained by using exponential form of the membership functions. It is described
by four parameters that are the break-points of the function.
The reason handling the objectives and constraints in fuzzy environment is that the
small variations of power systems variables (bus voltages, line currents etc.,) from
their limit values can be tolerated, and this can help to obtain one of the best solutions
to the problem. Furthermore, one may reach to a better objective function by allowing
small violations of limits. To what degree toleration and/or on which variable of
power systems it is allowed depends on systems operating conditions. In practice,
to determine the break-points of each fuzzy membership function, the experience of
system operators are also taking in considerations.
In optimization step, first, the applications of genetic algorithms in literature are
checked. One of the good characteristics of evolutionary search algorithms is that
they could be easily adapted from one problem to another by modifying related
parameters and the way of application techniques of operators. Then some simulations
are performed to determine the best variety of each operator of genetic algorithms that
they fit better to our problem.
The problem is an operational problem in power systems that is required to solve many
times as a daily routine. That is why the time spent for a solution is gained importance.
To reduce the computational time some parallel computing techniques and some types
of parallel genetic algorithms are also searched. The simulations belong to larger
systems among the test systems are used are performed using the utilities provided
by the high performance computing lab in computational science and engineering
department of informatics institute.
The main disadvantage of genetic algorithms is the high CPU time execution. This
can cause heavy computation demands in a large-scale power system case, resulting
in large dimensional matrix operations. One way to overcome these computation
demand is to use parallel algorithms in multi-processor computers or in distributed
environments.
To solve a computational problem, parallel computing simply involves the
simultaneous use of many computing resources. Computing resources come in the
form of either a single computer with multiple processors or multiple computers
(computing nodes) connected by a fast network.
In most cases, there are both paralleling and unparalleled parts in the problem
formulations. The speed up of a program using multiple processors in parallel
computing is limited by the time needed for the serial part of the program. There
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are also several factors that limit the speed up such as communication time for sending
messages.
Genetic algorithms are very powerful search and optimization techniques that can be
applied to problems in many different areas. They can produce an acceptable solution
to a problem in a reasonable time. However when they are applied to very hard and
large problems it takes quit a long time. In that case there might be some effort to
reduce the time into a reasonable range. One way of reducing execution time is to
implement genetic algorithms in parallel environment.
Master-slave parallelism among the types of parallel genetic algorithms was chosen.
The algorithm was implemented in MATLAB environment using toolboxes such as
genetic algorithm toolbox, parallel computing toolbox, distributed computing server,
and MATPOWER which is an open source power flow program was also used.
The large portion of the computation time is spent for the function evaluation in the
problem. This is due to the nature of the problem solved. Master-slave parallel genetic
algorithm is perfectly matched with the needs. It is concluded that by using a larger
system, we would gain more benefit from using a high performance computing facility
that allows parallel implementation of our program to get the system solution faster
than the serial corresponding.
As a result of this work can be concluded as follows. A fuzzy set theory based
genetic algorithm procedure is proposed to control and/or prevent loop flows. The
problem is formulated as a multi-objective problem subject to operational and electrical
constraints and it is handled in fuzzy environment. The proposed method works well
and very satisfactory results for the objectives such as scheduled path flows, active and
reactive power losses are obtained. When the classical methods are used to control
loop flow in a rigid manner a feasible solution may not be found. However, using the
proposed method one can find a feasible solution. This can be better adjusted using
different membership functions, since the shape of the membership function affects
the satisfaction level appreciably.