Enerji sistemlerinde topraklama ağlarının bilgisayar destekli analizi
Computer aided analysis of grounding grid for power systems
Yazar: MEHMET ÇELİKYAY
Danışman: YRD. DOÇ. DR. ÖZCAN KALENDERLİ
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü
Derece: Yüksek Lisans, 1995
Konu: Elektrik ve Elektronik Mühendisliği = Electrical and Electronics Engineering
Dizin: Bilgisayar destekli analiz = Computer aided analysis ; Enerji sistemleri = Energy systems ; Topraklama = Grounding ; Yüksek gerilim hatları = High voltage lines

Özet:
Yüksek gerilim tesisleri ve istasyonların da, yıldıran boşalmaları açma ve kapama olayları gibi durumlar sonucunda meydana gelebilen yüksek gerilim darbeleri çok yüksek potansiyel artışlarına sebep olmakta bu da canlılar ve aygıtlar için tehlikeli durumlar yaratmaktadır. Yüksek gerilim sistemlerinde insanları tehlikeli gerilimlere karşı korumak için topraklama başlıca çare olarak ortaya çıkmaktadır. Topraklamanın yapılmasındaki amaç, istenmeyen nedenlerden dolayı meydana gelebilecek temas ve adım gerilimlerinin izin verilen sınır değerlerden küçük kalmasını sağlamak ve bu gibi tehlikeli gerilimleri ortadan kaldırmaktır. Topraklama amacıyla kullanılan birçok topraklayıcı çeşidi vardır. Bunlar arasında yaygın kullanıma sahip olan topraklama ağlarının, diğer topraklayıcılara göre daha karmaşık bir yapı içermesi, analizlerde birçok analitik ve sayısal yöntemlerin kullanılmasını zorunlu kılmaktadır. Bu çalışmada bu analitik ve sayısal yöntemlerden, bu çalışmada Bölüm 3'te topraklama levhalarının analizinde Moment Yöntemi, Bölüm 4'te topraklama ağlarının indüktanslârının bulunmasında Reaktif kVA yöntemi ve darbe empedansının bulunmasında amprik yöntemler, Bölüm 5'te topraklama ağlarında topraklama direncinin, akım dağılımının bulunmasında ve toprak yüzeyinde meydana gelen potansiyel değerinin hesabında; Eşdeğer Dairesel Levha Yaklaşım Yöntemi, Elektrostatik Potansiyel Yöntemi, Kaçak Akım Yöntemi ve en son olarak Bölüm 6'da Yük Benzetim Yöntemi (YBY) geniş bir şekilde ele alınmış ve YBY'nin kullandığı bilgisayar programlan yardımıyla, yeryüzeyinde meydana gelen potansiyel dağılımlarının üç boyutlu grafikleri elde edilmiştir. Böylece diğer yöntemlere göre, uygulama kolaylığı ve basitliği ile öne çıkan yük benzetim yöntemi ile topraklama ağlarının analizi gösterilmiş ve uygulanmıştır. vii

Abstract:
Power plants and substations are extremely vulnerable to hazards of lightning strikes, of electrical and mechanical equipment malfunctioning and of human errors in which a surge current of the order of kiloampers is impressed on the plant or is generated from within. Although these surge currents seldom last longer than a few milliseconds, they are long enough to cause severe, irreversible damages to equipment and occasionally fatal injuries to human beings. Personnel and equipment inside are usually protected by dispersing the surge current to the earth through an earthing system to prevent charge accumulation, such that secondary faults can be aborted. In practice, electrical appliances are earthed so that the surge current can be diverted to earth. To prevent secondary faults, an earthing system is used where all earth wires are connected to one or several electrodes driven into the earth, through which the surge current is dissipated. To increase the surface are a for current discharges, the earthing electrode is usually connected to a conducting plate or wire grid buried in earth. On the one hand, earthing grids are used extensively in manufacturing plants and power stations. However, studies on earthing plates are seldom found in recent literature. An earthing plate is usually made of steel, aluminum, or other inexpensive conductors. It is buried beneath and parallel to the surface of the earth. Although the shape of an earthing plate could be tailor-made to conform with a given physical environment, circular and rectangular plates are the most prevalent. Fig. 1. A square earthing plate in a homogeneous earthDependent on applications, the area of the plate ranges from a fraction to tens of square meters. During the emergence of a surge current, current injected into an earthing electrode is free to flow into the earthing plate because both are good conductors. Since the conductivity of an earthing plate is much higher than that of surrounding earth, charges are accumulated on the plate. As electric charges are amassing, the potential of electrode is also increasing. Consequently, the current flow is checked. Eventually the current input into its plate is equal to the current dissipated into its surrounding earth. Until all charges have been dispensed, the fault current injected into the electrode is constant. Depending on the design of an earthing plate and the amplitude of a surge current, an equilibrium state is usually obtained in microseconds. The transient effects are as usual ignored because they are negligible compared with those in the quasi-steady state. Electrostatic analysis sufficient for the study of earthing plates. Dependent on the earthing resistance R; of the earthing system, the injection of a current Ij into the earth would inevitably induce an input potential Vi=Ri I; at the point of disturbance. If the earthing system is composed of a simple conducting rod driven into the earth, the potential on the earth surface would be inversely proportional to the distance from the point of current injection. It then follows that the potential difference between the two feet of an operator in the vicinity of the earthing electrode during fault could be so large that an electric current of the order of amperes would be induced to flow through the body, and which might result in irreversible damage and sometimes fatal damage to the person of correct. Furthermore, consider an operator carrying a metallic ladder or other conducting rod walking inside a substation during fault and accidentally one of the ends of the ladder hits a conducting post the potential difference between the end and the foot of the operator could then be much larger than that between the two feet. The design of grounding systems of substations and electrical systems has the primary purpose of ensuring the safety and well being of personal who may became electrically coupled to the grounding mats during unbalanced fault conditions. In general an unbalanced fault will cause a ground potential rise of the system neutral and any conductive medium electrically connected to the neutral. A person touching grounded structures during this condition may experience an electric shock. The possibility of hazard is usually assessed by computing the maximum touch and step voltage or the maximum body current. The analysis of grounding systems for the purpose of computing touch, step, transfer voltages and body currents due to accidental contact is a complex problem, making the simulation of all potentially hazardous situations very difficult. Since the grounding system is part of the electric power system, complete analysis requires inclusion of all power system elements, resulting in computational problems due to the size of the system. The problem is usually decomposed into two manageable subproblems; 1. Computation of the maximum expected ground potential rise of the grounding system, or alternatively, the maximum earth current, IX2. Computation of the touch and step voltages around the grounding system given the earth current, or alternatively, computation of body currents for a person in accidental contact with the ground. Step and touch voltages are defined as potential differences between two points on the earth surface, or between a point on the earth surface and grounding mat conductors, respectively. For these reason, a practical earthing system must be designed so that the touch potential should always be contained below a predetermined value that it would cause no severe damage to human beings. There are many of methods which are concerned with this problem. In this thesis, moments method for grounding plates [2-3], reactive kVA method and experimental methods, to find inductance and impulse impedance for grounding grids [5-7], equivalent circular plates method [4], electrostatic potential method [8,9], leakage current method [ 10 ] and charge simulation method [1 1-12]^ for computing grounding resistance, current distribution and finding the potential distribution at the grounding grids were studied. Charge Simulation Method is the well-known method. This method was initially proposed by H. Steinbigler, which is sometimes called as the average potential method or matrix method in the grounding mesh analysis, would be an effective method. The principal of this method is such that; Consider an isolated conducting cylinder of radius a and of length b in a homogeneous medium. This method assumes finite line simulation currents, Ii, l2,....,In, flowing in certain parts of the conducting wires. Given the potentials Vi= V2= =V" (surge impedance of the wires are neglected. Traveling waves on the wires are considered as adequate fast.) on the surface of each wire, and say 100 % or V(volt), one can construct an equation in the matrix form. m. m =m o) where [R] is a resistance coefficient matrix [R]; nxn, [I]; nxl and [V]; nxl, with n being the number of unknown currents. The element Ry of the matrix [R] means that a unit current, A, flowing in the j-th wire provides the potential Rij, V, at a point on the i-th wire. An unknown current matrix, I, can be obtained by solving the simultaneous equation given by equation (1).In equation (1), the construction of (R) depends on the geometric position between the wires of earthing grid or the finite line currents. For this reason, in solving the equation (1), 1. Coordinates of the finite line currents 2. Potential of grounding grid must be given. If the entire space is filled with a material of conductivity o, finite line current source, I, located between Xı; (xı, yi, zi) and X2; (x2, y2, z2) hz A(x,yA,zA) (\>\ /(** -x3)a4yi -y2)2Az2-^2 a =medium conductivity = 1/p ( ohm.m)'1 p = medium resistance (ohm.m) Note that, in this computation, image currents must be taken into consideration XIOnce a current matrix (I) is obtained, the potential Vp at any point can be computed by VP= (R) (I) (4) The resistance coefficients, (R) = (Rı, R2 Rn); lxn, are newly defined by geometric configuration between the wires and the point where the potential, Vp, is to be calculated. The resistance of a grounding system is computed by; R = Z/, (5) where; V is the voltage of the grounding system Ii; i= 1,2, n, is the current distribution computed from equation (1). Three dimensional potential distributions on the earth surface can be plotted using charge simulation method by the computer program. The following graphic was plotted for the grounding grid with 2x2 mesh by the computer program. Step and Touch potential can easily be obtained by this method. UCUnll.) ffi /v Y(n) XCm) Fig. 3. Potential Profile of 2x2 Mesh In the design of grounding system, an impulse impedance is the most important topic; because the behavior of grounding systems under lightning discharge conditions governs the degree of protection. When an impulse current is fed to a xngrounding system, its impulse impedance is defined as the ratio of the peak value of the voltage developed at the feeding point to the peak value of current. The ratio of impulse impedance to the power frequency grounding resistance is referred to as impulse coefficient. The impulse impedance of grounding grids depends on the size and shape of the grid, the spacing between electrodes, point of injection of the current, magnitude and wave shape of current and characteristic of the soil. The impulse impedance of the grid is governed by the inductance of the grid and can be computed for square or rectangular grids by empirical formulas. The maximum voltage at the lightning arraster in substation depends on the arrested characteristics, lead inductance and station grounding resistance. To ensure proper protection the impulse impedance should be used to determine the arraster voltage. In the grounding grid the power frequency grounding resistance, step voltage and mesh voltage are within the safe limits. However impulse impedance is higher than the power frequency grounding resistance and it may not give satisfactory protection against direct lightning strokes. In case it is found that the system does not give satisfactory lightning protection. It may be necessary to shift the position of the feeding point to as close to the center of the grid as possible. xui