IEEE Design and Optimize Subs Grounding Grid Matlab

DESIGN AND OPTIMIZE SUBSTATION GROUNDING GRID BASED ON IEEE

STD. 80 - 2000 USING GUI AND MATLAB CODES

Dr. ATTIA A. EL-FERGANY, SENIOR MEMBER ((IACSIT), MEMBER (IEEE) Department of Electrical Power and Machines – Faculty of Engineering

Zagazig University – Zagazig (Egypt) P.O. Box. 4459 (Zagazig)

http://www.zu.edu.eg [email protected]

ABSTRACT: Substation grounding grid design requires a simple, but accurate tool to compute the parameters that guarantees safety of personnel during earth faults. In this article, a Graphical User Interface (GUI) with an interactive computer program using MATLAB 7.10 version has been developed. The developed tool allows the computations of the total grid conductor length required for the earth grid to meet the step and touch potential criterion for safety. The interactive method versatility has allowed configuring the grid according to the availability of land space and value of the native soil resistivity. Calculations of minimum cross sectional Area of grounding conductors are presented. Simple Optimization technique using iterative search are applied to optimal design of grounding grid (conductors and rods as well) to satisfy tolerable safe touch and step voltages. Inequality constraints of ground potential rise (GPR), ground resistance (Rg), step voltage (Estep) and touch voltage (Etouch), are based on latest edition of ANSI/IEEE Std. 80-2000. The viability of results of developed tool are compared with world-wide software’s like ETAP and CYMGRD and showed to be reliable, friendly user interface, easy and practical tool for calculations of Ground grid design. All approved shapes (Square, Rectangle, Triangle, L and T shapes) based on IEEE 80 guidelines and procedures are implemented and tested. Executable versions may be obtained after generating C/C++ plus header files code from MATLAB codes to run standalone. Keywords: Grounding Grid, Step and Touch Potentials, IEEE Std. 80.

1. INTRODUCTION

Substation grounding design considerations are important to ensure the safety of personnel and the public, to minimize hazard from transferred potential, to protect equipment insulation, to provide a discharge path for lightning strikes, and to provide a low-resistance path to ground [1]. A good grounding system provides a low resistance to remote earth in order to minimize the ground potential rise (GPR). For most transmission and other large substations, the ground resistance is usually about 1 Ω or less. In smaller distribution substations, the usually acceptable range is from 1 Ω to 5 Ω, depending on the local conditions. Many commercial tools are available in the market to help in design of Grounding grid like ETAP [2] and CYMGND [3].

The help of Genetic Algorithm optimization of the network [4] was studied but the number conductors and earth have already been fixed and the purpose of minimizing voltage contact, but not compared with the values of tolerance. Optimizing the relationship between the earth systems during consecutive meshes is considered and presented in [5]. But the only optimization variable, the total length of network Conductors earth.

ANSI/IEEE Std.80 has been widely revised for more than ten years and is generally followed as a standard for the grounding systems. In this work, a GUI computer program has been developed. The calculations of the step voltage, touch voltage, GPR, and grounding resistance, are based on ANSI/IEEE Std. 80 - 2000. Very simple approach of iterative search to plan the optimal grounding grid, which includes number of unilateral mesh and depth of the grounding grid conductors were studied and investigated. The results of proposed GGD (Grounding Grid Design) tool compared and verified with the results of ETAP and CYMGND as well.

Dr. Attia A. El-Fergany et al. / International Journal of Engineering Science and Technology (IJEST)

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2. DESCRIPTION OF PROPOSED GGD TOOL

It is convenient to have the main core for a big program spitted into sub-modules. These sub-modules are to be activated by selecting the corresponding item from the main menu and returns for another selection(s). The proposed GGD tool consists of the following four basic sub-modules:

• Tolerable Step and Touch Voltages Module. • Sizing and Selection Earth Conductors Module. • Actual GPR, Ground Resistance, maximum Step and Mesh Potentials Calculations Module. • Optimization Module for optimizing lengths of conductors and/or number of rods and depth of burial

conductors as well. Proposed GGD tool was developed using MATLAB 7.10 release 2010a Statements with GUI and running under PC with windows operating system [8].

2.1 Tolerable Step and Touch Voltages

The potentials and potential differences that determine the safe design of the grounding grid as IEEE 80 - 2000 [1] are tolerable step and touch potentials (for people weighing 50 or 70 kg). The step-voltage criterion (refer to Eq. (1), Eq. (2) and Eq. (3)) is defined as follows: = 1000 + 6 × × 0.116 (1)

= 1000 + 6 × × 0.157 (2)

= 1 − 0.09 1 −2ℎ + 0.09 (3)

Where, CS = reduction factor, ρS = resistivity of crushed rock, Ω.m, tS = fault-clearing time, Sec, hS = the thickness of the high resistivity surface layer material, m, and ρ = the resistivity of the earth below the high resistivity surface material, Ω.m.

The actual step voltage (ES) should be less than the maximum allowable step voltage (Estep). The allowable touch voltage for people weighing 50 or 70 kg, respectively, is defined as follows: (refer to Eq. (4) and Eq. (5)) = 1000 + 1.5 × × 0.116 (4)

= 1000 + 1.5 × × 0.157 (5)

The actual touch voltage, mesh voltage, or transferred voltage should be less than the maximum allowable touch voltage, Etouch, to ensure safety. Generally, Touch voltages represent a much more serious hazard than step voltage; these are the usual basis for design. Fig. 1 shows the GUI window for performing the above procedures based on IEEE 80 -2000.

2.2 Sizing and Selection of Conductors - Minimum Size

Each element of the grounding system, including grid conductors, connections, connecting leads, and all primary electrodes, should be designed so that for the expected design life of the installation. According to ANSI/IEEE Std.80 - 2000, the minimum size of the ground conductor is expressed as a formula of the current duration, shown in Eq. (6) to Eq. (8). Then, select an area which is larger than or equal calculated cross-section of ground conductor. Therefore, the minimum diameter of grid conductor is calculated as shown in Eq. (9). A = I . K . t (6) A = A × 10001973.52 (7)


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Fig. 1. sample of interface of module for Calculating Tolerable step and touch voltages.

K = 197.4Tα . ρ . ln K + TK + T

(8)

d mm = 2. AΠ

(9)

Where, IF = maximum rms current in kA (include for future growth), Kc = conductor Material constant, Amm2 =

conductor cross section, mm2, Tm = maximum allowable temperature, °C, Ta = ambient temperature, °C, Tr = reference temperature for material constants, °C, α0 = thermal coefficient of resistivity at 0 °C , 1/°C, α r = thermal coefficient of resistivity at reference temperature Tr, 1/°C, ρr = resistivity of the ground conductor at reference temperature Tr, μΩ-cm, K0 = 1/ α0 or (1/ αr) – Tr , °C, tc = duration of current, Sec. (between 0.25 to 3 seconds), TCAP = thermal capacity per unit volume, J/(cm3·°C), and dc = minimum diameter of grid conductor cross-section (mm).

Fig. 2 is showing sample of user interface developed to calculate the size of earth wires. Several types of conductors are fed as database to this module with relevant KF. Moreover, for non-available materials, user has facility to feed the relevant material constants manually.

2.3 Calculations of Ground Resistance (Rg)

Estimation of the total resistance to remote earth is one of the first steps in determining the size and basic layout of a grounding system. The resistance depends primarily on the area to be occupied by the grounding system, which is usually known in the early design stage. Sverak [6] expanded Equation (refer to Eq. (10)) to take into account the effect of grid depth.

R = ρ1Lt + 1√20A 1 + 11 + h 20A (10)

Where, h = the depth of the grid in m, Lt = LC+LR the total buried length of conductors in m includes all land rods to meter, A = Total area enclosed by grounding grid in m2, and ρ = Soil resistivity in Ω.m.

Schwarz [7] used the following equation Eq. (11) to combine the resistance of the grid, rods, and mutual ground resistance to calculate the total system resistance, Rg. R = RcR − RRc + R − 2R (11)

Where, Rc = ground resistance of grid conductors in Ω, Rr = ground resistance of all ground rods in Ω, and Rm =

mutual ground resistance between the group of grid conductors, Rc, and group of ground rods, Rr in Ω. Formulas to calculate RC, Rr and Rm are shown in Eq. (12), Eq. (13) and Eq. (14) respectively. R = 0.366ρL log Ld + log L4h + 0.34 (12)


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R = 0.366ρL log 3Ld (13) R = 0.73ρL log 2LL (14)

Where, ρ = Soil resistivity in Ω.m, Lc = Length of Conductor in m, Lr = Length of rods in m, Lt = Total length of Ground Rods and conductors in m, dc = Dia. of conductor in m, dr = Diameter of rod in m, and h = Depth of burial of conductor in m.

Fig. 2. sample of interface of module for Calculating Earth wire cross sectional area

Generally, the combined ground resistance of the grid and the rod bed will be lower than the ground resistance of either component alone, but still higher than that of a parallel combination. the equivalent electrical resistance (Rg) of the system must be low enough to assure that fault currents dissipate mainly through the grounding grid into the earth, while maximum potential difference between close points into the earth’s surface must be kept under certain tolerances (step, touch, and mesh voltages).

2.4 Maximum grid current IG

The maximum grounding grid fault current is calculated using Eq. (15) I = S . D . C . I (15) Where, IG = maximum grid current, Sf = fault current division factor, If = rms value of symmetrical ground fault

current, Df = decrement factor for the entire duration of fault tf, and Cp = Corrective projection factor. The decrement factor (Df) is used to determine the effective current during a given time interval after inception of a fault, refer to Eq. (16). D = 1 + TT 1 − e (16)

Where, Ta = Time constant = . and Tf = Fault time (Sec). This formula gives the equivalent rms asymmetrical fault current flowing between the grounding system and surrounding earth, taking into account the DC component of the initial fault current.

2.5 Ground Potential Rise

During typical earth fault conditions, the flow of current via the grid to earth will therefore result in the grid rising in potential relative to remote earth to which other system neutrals are also connected. This is defined as ground potential rise or GPR and calculated using Eq. (17). GPR = I . R (17) The GPR of a substation under earth fault conditions must be limited so that step and touch potential limits are not exceeded, and is controlled by keeping the earthing grid resistance as low as possible.

2.6 Maximum Mesh and Step voltages

The mesh potential is defined as the potential difference between the centre of an earthing grid mesh and a structure earthed to the buried grid conductors. This is effectively a worst-case touch potential. For a grid


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consisting of equal size meshes, it is the meshes at the corner of the grid that will have the highest mesh potential. However, the touch potential is defined as the potential difference between a person’s outstretched hand, touching an earthed structure, and his foot. A person’s maximum reach is normally assumed to be 1 m. As per ANSI/IEEE Std. 80, the formulas of maximum step voltage and maximum mesh/touch voltage are shown as Eq. (18) and Eq. (19) respectively. E = ρ. K . K . IL (18)

E = ρ. K . K . IL (19)

Where, Ki = correction factor for the grid geometry =0.644 + 0.148n , Ks = spacing factor for the step voltage, Km = spacing factor for the mesh voltage, n = geometric factor composed of the grid, Ls = Effective length of Lc + LR for step voltage, m, Lm = Effective length of Lc + LR for mesh voltage, m.

For further formulas for calculating spacing and geometrical factors, you may refer to [1] for further details.

2.7 Optimization of Conductors, rods and depth of burial

The proposed tool determines the minimum number of conductors and/or rods (i.e. minimum lengths) with very simple iterative approach that satisfy the tolerable limits for the Step and Touch potentials as calculated using procedures of IEEE 80 either for body weight 50 kg or 70 kg. The optimization process begins calculations with a grid consisting of only two conductors on each side and/or one rod. Hence, increasing the number of conductors with proportional to the ratio between length and width of the grid and/or number of rods until a solution is reached. If it fails to satisfy, depth of conductor burial will be considered. Moreover, the following constrains are considered during the process of optimization i.e. three variables are supposed during the optimization process are Nx, Ny and h respectively, where Dx/Dy ∈ [2.5, 22.5 m] , and h ∈ [0.25, 2.5 m]. Subject to the following inequality constrains: (Rg ≤ 1 to 5 Ω, Es ≤ Estep70 / Estep50, and Em ≤ Etouch70 / Etouch50). The constraints of ground resistance (Rg), step voltage (Estep70 / Estep50) and touch voltage Etouch70 / Etouch50), based on ANSI/IEEE Std.80 - 2000.

Fig. 3. sample of interface of module for ground grid dimensioning and calculations of Rg, GPR, and calculated maximum step and mesh

voltages

3. SIMULATION RESULTS, VALIDATIONS AND COMPARISONS WITH ETAP AND CYMGRD

Several test cases were verified and tested with actual project data and outcome of numerical results of proposed GGD tool. The substation GGD was carried out according to IEEE 80 2000 and a GUI program written using MATLAB. The test cases include different type of geometrical shapes (Square/Rectangle, Triangle, L and T) and sound results of calculated the grounding grid design parameters. For sake of comparisons, one Example of IEEE 80 – 2000 will be presented here under. (Refer to IEEE 80 – 2000 page 129). Input data:

Body weight = 70 Kg, Crushed rock surface layer resistivity = 2500 Ω-m, Crushed rock surface layer thickness = 0.102 m, Clearing time = 0.50 Sec, Uniform soil resistivity = 400 Ω-m, Max. LG fault


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current is 6.814 kA, X/R (Local) = 16.2, Conductor material Copper hard-drawn and Ambient temperature = 40 Celsius.

Table 1. Results of Tolerable voltage calculations (refer to Fig. 3).

Reference Max. allowable

touch (V) for 70 kg Max. Allowable

Step (V) for 70 kg Reduction factor CS

IEEE – 80 2000 838.20 2,686.00 0.74 CYMGRD 840.55 2,696.10 0.74 ETAP 840.5 2,696.10 0.743 Proposed GGD 840.548 2,696.10 0.7429

Grid Design Aspects: Square grid 70m x 70m, Nx = 11 and Ny = 11, Grid conductor diameter: 0.01 m i.e 95 mm2,

Burial depth h = 0.5 m, Remote contribution of the LG-fault current: 3.180 kA (suppose X/R=0.1), Split factor Sf = 60% and Uniform soil resistivity= 400 Ω-m

Table 2. Results of calculations of GPR, Rg, total conductors length calculated maximum actual step and mesh potentials

Reference Rg GPR (V) Em (Cal.) in V Es (Cal.) in V Total Length of conductors (m)

IEEE – 80 2000 2.780 5,304.00 1002.1 Not Calculated 1540 CYMGRD 2.675 5,106.61 986.02 611.22 1540 ETAP 2.780 5301.1 985.50 610.9 1540 Proposed GGD 2.77569 5297.71 1001.93 609.921 1540

It is obvious from table1 and 2, the proposed GGD tool are soundly calculated the required parameters with good accuracy. With running the optimization module to satisfy the tolerable touch and step voltages (50 kg) for the above case, without adding any grounding rod, hereunder the obtained results and shown in below Fig. 4:

Nx = Ny = 20 (i.e. total length of conductors = 2800 m). Rg = 2.65881 Ω, GPR = 5074.63 V, Em (Cal.) = 610.619 V < Etouch50 (Tolerable) = 621.042 V Safe, Es (Cal.) = 629.927 V < Estep50 (Tolerable) = 1992.020 V Safe.

Fig. 4 Sample of output result of previous case of optimization for 50 kg body

As, you may note with the optimization feature, the user can satisfy the design easily to relax the requirements of tolerable safe limits of step and touch voltages with Dx and Dy equal 3.68 m (square) ∈ [2.5, 22.5 m] as shown in Fig. 4. Moreover, the Example of L-shape, Page 139 (IEEE 80 -2000) was verified and numerical results compared with the outcome of proposed GGD tool and prove sound results.

4. CONCLUSIONS

In this work, an interactive computer program using MATLAB is developed and presented that allows the computations of the total grid conductor length including rods required for the design of substation grounding grid. The interactive method versatility has allowed configuring the grid according to the availability of land


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space with approved standard shapes of IEEE std. 80 - 2000 with the feature of optimization. The outcome of calculations proves the excellent accuracy of proposed GGD tool with comprehensive reporting. The accuracy and reliability of the developed GGD tool was validated using several test systems, and the results obtained were evaluated against the famous ETAP and CYMGD software’s which are impressive and computationally efficient.

REFERENCES

[1] ANSI/IEEE Std. 80 (2000). IEEE Guide for Safety in AC Substation Grounding, IEEE Society, New York. [2] http://www.etap.com. [3] http://www.cyme.com. [4] F. Neri (2004): A New Evolutionary Method for Designing Grounding Grids by Touch Voltage Control, Industrial Electronics. IEEE

International Symposium, Vol. 2, pp. 1501-1505. [5] M.C. Costa, et al (2003): Optimization of Grounding Grids by Response Surfaces and Genetic Algorithms, IEEE Trans. On Magn.,

Vol. 39, No. 3, pp. 1301-1304. [6] Sverak, J. G (1984): Simplified analysis of electrical gradients above a ground grid. Part I—How good is the present IEEE method?,

IEEE Transactions on Power Apparatus and Systems, vol. PAS-103, no. 1, pp. 7–25. [7] Schwarz, S. J (1954): Analytical expression for resistance of grounding systems, AIEE Transactions on Power Apparatus and Systems.

vol. 73, no. 13, part III-B, pp. 1011–1016. [8] http://www.mathworks.com.


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IEEE Design and Optimize Subs Grounding Grid Matlab