Optimisation methods applied to compensator placement

Burger, I. (2004-12)

Thesis (MScIng)--University of Stellenbosch, 2004.

Thesis

ENGLISH ABSTRACT: The optimal placement of different types of compensators on electrical networks is a complex task faced by network planners and operations engineers. The successful placement of these devices normally involves a large number of power flow studies and relies heavily on the experience of the engineer. Firstly the operation and application of the different types of compensators must be clearly understood. Secondly the application of combinations of different compensators on a specific network must be investigated. Then the dynamics of the network and interaction between the network and the compensator/s must be studied under a wide variety of network conditions and load levels. This task is further complicated by the non-linear nature of the mathematical equations that govern the power flow and voltage distribution on an electrical network. Yet another complication is the fact that some of the variables that describe an electrical network can be non smooth or discrete. For instance, the discrete value of a tap position of a power transformer can only assume an integer value. To simplify the problem of compensator placement, advanced software tools are available that are capable of solving power flows of networks containing compensators. To a large degree, however, these tools still rely on the user to make intelligent decisions as to the configuration of networks and the placement of compensators. In many cases trial and error is the only way to find a good solution. The purpose of this thesis is to show the different techniques available to implement intelligent algorithms capable of finding optimal solutions specific to the placement of voltage regulators. State of the art algorithms are implemented in Matlab that can place voltage regulators on sub transmission, reticulation and low voltage networks. The sub transmission and reticulation placement algorithm is a combination of an SQP technique and a simple combinatorial algorithm. The low voltage placement program is based on a simple genetic algorithm with a few customized features that has been developed to ensure fast convergence. The programs developed were used to do optimal voltage regulator placement on a number of networks. As far as possible real world networks were used. Where real world networks were not available test networks were used that closely resemble real networks, as they exist on typical networks owned by Eskom Distribution. It was found that SQP is a very efficient algorithm for optimising large non-linear problems such as the placement of a Step Voltage Regulator on a large electrical network. This algorithm however does not handle discrete variables very well and is also limited in handlingany reconfiguration of the network due to the placement of series devices such as voltage regulators. To cater for reconfiguration, it is necessary to combine the SQP algorithm with a combinatorial algorithm. The genetic algorithm used to do optimal placement of multiple Electronic Voltage Regulators on low voltage networks was found to be very efficient and robust. This can be attributed to the simplicity of the algorithm as well as the fact that it does not rely on the availability of derivative and second derivative information to move towards an optimal solution. Instead, it only uses fitness values obtained from function evaluations to optimise the placement problem. Another useful feature of using a genetic algorithm is that the algorithm does not get stuck in sub optimal areas in the solution space. Both the placement programs developed are relatively simple and do not consider all the factors involved in the placement of voltage regulators. However, the addition of any number of factors is however possible with further development of the programs as presented in this thesis.

AFRIKAANSE OPSOMMING: Die optimale plasing van verskillende kompenseerders op elektriese kragstelsels is ´n moeilike probleem vir beplanners en operasionele personeel. Die plasing van kompenseerders gaan gewoonlik gepaard met ´n groot hoeveelheid netwerk studies en die sukses daarvan berus gewoonlik op die ondervinding van die ingenieur. Eerstens moet die werking en toepassing van elke kompenseerder behoorlik verstaan word. Tweedes moet die plasing van ´n enkele asook kombinasies van verskillende kompenseerders ondersoek word. Dan moet die dinamika van die netwerk en interaksie met die kompenseerder/s bestudeer word vir al die moontlike netwerk konfigurasies en belasting vlakke. Die taak word verder bemoeilik deur die nie-liniêre vorm van die wiskundige vergelykings wat die netwerk vrag en spanning verspeiding beskryf. Nog ´n komplikasie is die feit dat van die veranderlikes wat die probleem beskryf, diskreet is. Byvoorbeeld die tap posisie van ´n transformator kan slegs ´n heel getal aanneem. Om die plasing van kompenseerders te vergemaklik is gevorderde sagteware beskikbaar wat simulasies kan doen van netwerke wat kompenseerders bevat. Tot ´n groot mate is die sagteware nog steeds afhanklik van intellegente besluitneming deur die gebruiker. In die algemeen moet ´n groot hoeveelheid studies nog steeds gedoen work om ´n goeie oplossing te vind. Die doel van hierdie tesis is om die verskillende tegnieke te wys wat beskikbaar is om intelligente algoritmes te implementeer wat optimale oplossings kan vind vir spesifiek die plasing van spanning reguleerders. Moderne algoritmes is in Matlab geimplementeer wat spanning reguleerders op sub transmissie, retikulasie en laag spanning netwerke kan plaas. Die sub transmissie en retikulasie plasings algoritme is gebaseer op ´n kombinasie van ´n sekwensieële kwadratiese programmering metode en ´n eenvoudige kombinatoriese metode. Die laag spanning plasings program is gebaseer op ´n eenvoudige genetiese algoritme met ´n paar unieke verstellings om vinnige konvergensie te verseker. Die twee programme wat ontwikkel is word dan gebruik on spanning reguleerders te plaas op ´n paar netwerke. So ver moontlik is bestaande netwerke gebruik. Waar bestaande netwerke nie beskikbaar was nie is toets netwerke saamgestel wat gebaseer is op bestaande Eskom netwerke. Daar is gevind dat sekwensieële kwadratiese programmering ´n effektiewe algoritme is om groot nie liniêre optimerings probleme, soos die plasing van spanning reguleerders, op te los. Hierdie algoritme is egter nie geskik om diskrete veranderlikes te hanteer nie. Dit is verder ook nie geskik om enige netwerk rekonfigurasie te hanteer tydens die plasing van seriesgeskakelde kompenseerders soos spanning reguleerders nie. Om die rekonfigurasie moontlik te maak is dit nodig om die sekwensieële kwadratiese programmering te kombineer met ´n kombinatoriese algoritme. Daar is verder gevind dat die genetiese algoritme wat gebruik is om elektroniese spanning reguleerders te plaas op laag spanning netwerke baie effektief en robuust is. Dit is as gevolg van die eenvoudigheid van die algoritme en die feit dat dit nie afhanklik is van afgeleide en tweede afgeleide informasie om na die optimale oplossing te beweeg nie. Die algoritme gebruik slegs fiksheid waardes bereken van funksie evaluasies om die probleem te optimeer. Nog ´n voordeel van genetiese algoritmes is dat dit nie in sub optimale gebiede van die oplossing ruimte stil staan nie. Beide die programme wat ontwikkel is, is redelik eenvoudig en neem nie al die faktore in ag wat gepaard gaan met die plasing van spanning reguleerders nie. Addisionele faktore kan egter maklik ingesluit word deur verdere ontwikkeling van die bestaande programme.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/16265
This item appears in the following collections: