Modeling and Evaluation of Geomagnetic Storms in the Electric Power System

Transcription

1 21, rue d Artois, F PARIS C4-306 CIGRE 2014 http : // Modeling and Evaluation of Geomagnetic Storms in the Electric Power System K. PATIL Siemens Power Technologies International, Siemens Industry, Inc. Schenectady, New York, USA SUMMARY A solar magnetic disturbance in the direction of earth can produce severe fluctuations in the earth s magnetic field. Such geomagnetic storms or geomagnetic disturbances (GMD) induce potential gradients on the surface of the earth causing the earth surface potential (ESP) to rise. ESP rise in the range of 1 to 10 V/km can occur during severe geomagnetic disturbances in certain regions where the earth conductivity is low [1]. These induced voltages can cause induced currents (called geomagnetically induced currents or GICs) to flow on the surface of the earth. GICs induced on the earth s surface can flow into the electric power system if there is a closed path for the current to flow between the electric network and the earth. This path is typically provided by grounding connections of substation transformers and shunts. GICs are often described as being quasi-direct current (DC), although the frequency variation of GICs is governed by the time variation of the induced electric field [2]. The GIC is a low frequency current. Any GIC flow through transformers can cause half-cycle saturation. This can result in highly distorted excitation currents rich in harmonics and consequent increases in reactive power consumption [3-6]. The increased reactive power consumption could cause unacceptable system wide voltage depressions leading to possible voltage collapse and/or erroneous operation of protective relays and consequent system stability issues. The GMD events thus have the ability to disrupt normal operation of the power grid and hence there is a need to model and study the effects of GMD and the consequent GIC on the reliability and secure delivery of electric power. This paper describes the modeling methodologies for studying the effects of GIC on the electric power network for various system planning studies such as power flow, contingency, and voltage stability (QV) analysis. KEYWORDS Geomagnetic Disturbance Geomagnetically Induced Currents Transformer Half Cycle Saturation Power System Modeling Power System Analysis krishnat.patil@siemens.com

2 1 POWER SYSTEM MODELING FOR GIC ANALYSIS GICs are low frequency currents that flow into the electric power system if there is a closed path for the current to flow between the electric network and the earth. This path is typically provided by grounding connections of substation transformers and shunts. For the purpose of GIC analysis the ac power system is reduced to a dc resistive network with the following network assumptions [1]: Transmission lines are modeled with their dc resistance in series with induced dc voltage [7]. Transmission line reactors and charging are ignored. Series compensated transmission lines block GIC flow and hence are ignored. The windings of two and three winding transformers that have ground paths are modeled with their dc resistance to ground. The series winding and common winding (if grounded) of auto transformers are modeled. Bus shunts (if grounded) are modeled with their dc resistance to ground. Equivalent station grounding resistance is considered. A dc network representation of a typical ac power system used in GIC calculations is shown in Figure 1. It is assumed that transmission line Rline4 is terminated into substations Sub2 and Sub4 transformers whose winding 2 is grounded. There are grounded bus shunts in substations Sub2, Sub3 and Sub4. Notations: GIC induced voltages on a transmission lines: V1, V2, V3 and V4 Transmission Line dc resistances: Rline1, Rline2, Rline3, Rline4 Transformer Winding dc resistances: Rtrn1-w2, Rtrn2-w2 Shunt dc resistances: Rsh1, Rsh2, Rsh3 Substation ground dc resistances: Rgrd1, Rgrd2, Rgrd3, Rgrd4 Substations: Sub1, Sub2, Sub3, Sub4 Figure 1: DC representation of AC Power System used in GIC Calculations The induced dc voltages (V1, V2, V3 and V4) in transmission lines are calculated [3] as in equation (1). + (1) where E N and L N are the Northward electric field and Northward distance, while, E E and L E are the Eastward electric field and Eastward distance. Typical power flow programs require ac network data. However, for GIC calculations, dc resistance data of transmission lines, transformer windings, bus shunts, and effective substation ground are required. Additionally, the configuration (vector group) of transformer windings and bus shunts is required to determine their ground connection. In order to calculate the induced dc voltage in transmission lines using equation (1), the geographical location (latitude and longitude) of transmission lines is also required. A power system dc network as shown in Figure 1 is converted into its Norton equivalent and solved to determine the GICs flowing in the network. 1

3 1.1 Effective GIC in a Transformer The effective GIC (I eff ) flow in a transformer due to GICs flowing in one or more of its winding is dependent upon transformer type. Figure 2 illustrates the GIC flows in transformer windings for various transformer configurations. Figure 2: Effective GIC Calculation for Various Transformers (a) Two Winding (b) Two Winding Auto (c) Three Winding (d) Three Winding Auto Assuming I eff is represented on the winding 1 side of a transformer, this can be derived for various transformer types as below. + + ( + ) + + (2) ( 1) + (2) (a) Two Winding Transformers (2) (c) Three Winding Transformers (b) Two Winding Auto Transformers + ( + ) + ( 1) (2) (d) Three Winding Auto Transformers In the above, the ampere per phase GIC flow in various windings is identified as: I 1 Winding 1, I 2 Winding 2, I 3 Winding 3, I C Auto Transformer Common Winding, and I S Auto Transformer Series Winding. 2

4 1.2 Transformer Reactive Power Losses due to GIC Flow One of the effects of the GICs flowing in transformer windings is that the transformer is subjected to half-cycle saturation resulting in increased reactive power (Mvar) losses in these equipments [1]. Using the effective GICs flowing in transformers, the reactive power losses are calculated as [6]:!"# (3) where K factor is Mvar/ampere scaling factor. This scaling factor could be a generic value based on the transformer type, or could be a specific value obtained for the specific transformer. The GIC analysis results presented in the next section use a generic K factor provided in [6]. A different approach for calculating transformer reactive power consumption due to GICs flow is described in [8]. 2 POWER SYSTEM GIC ANALYSIS To study the effects of GMD on power system performance and operation, the transformer reactive power losses due to GIC flow are added to the base power system network as constant reactive current loads. A sample network comprising 42 buses, 23 transformers, 56 branches, and 20 substations is considered for the analysis presented here. For this sample network, the power flow analysis, contingency analysis and QV analysis are discussed, accounting for the effects of GMD. For the purpose of this analysis, the dc resistance values are calculated from ac resistance values and the geographical locations of the substations are assumed. 2.1 Power Flow Analysis For the sample system, the power flow is solved without GMD effects. Figure 3 shows power flow solution minimum voltage of buses terminated in that substation for the base case network. The transmission line colors indicate voltage levels. The bus voltage colors indicate bus voltage range; with green indicating 0.95<pu<1.05. Substations are indicated by numbers, and are located on the map by longitude and latitude. The size of the circle at the substation indicates the deviation of bus voltage from 1 pu. As seen in the network map, all bus voltages are within normal operating limits. Figure 3: Network Bus Voltages without GMD 3

5 Considering a GMD of uniform field strength of 1 V/km, transformer reactive power losses are calculated using varying disturbance directions of 0 through 360 degrees. Figure 4 shows those reactive power losses. The disturbance direction of 96 degrees results in the maximum reactive power loss of Mvar. Figure 4: Transformer Reactive Power Losses for GMD of 1 V/km and direction degrees Next, with GMD direction set to 96 degrees, power flows are solved with varying uniform field strength. The goal at this point is to find the maximum possible disturbance strength for which a converged power flow solution can be found. For the sample network, the maximum disturbance strength with a converged power flow solution is 7 V/km. Figure 5 shows the network bus voltages for a GMD of 7 V/km at 96 degrees. As expected, and as can be seen in Figure 5, the bus voltages are much lower as compared to voltages in Figure 3. The size of the circles easily illustrates the locations of the network with significant voltage dip problems. This analysis demonstrates that the network would need additional capacitive reactive power support for normal operation. Figure 5: Network Bus Voltages with GMD of 7 V/km at 96 degrees 4

6 Figure 6 and Figure 7 show GICs flowing in substation ground and transmission lines for a GMD of 7 V/km at 96 degrees. Figure 6 shows substations that have considerable GIC flow and where GIC mitigation measures may be needed. Figure 6: GICs Flowing in Substation Ground with GMD of 7 V/km at 96 degrees Figure 7: GICs Flowing in Transmission Lines with GMD of 7 V/km at 96 degrees 2.2 Contingency Analysis The contingency events comprising single or parallel transmission line outages are simulated. The GIC flows and transformer reactive power are calculated by varying both disturbance direction and disturbance strength for each contingency. As shown in Figure 8, first, disturbance directions are varied to determine the disturbance directions that result in the largest transformer reactive power losses for each contingency. Using those disturbance directions and as shown in Figure 9, the maximum possible disturbance strength for which a converged power flow solution is found for each contingency is determined. As can be seen from Figure 4, Figure 8, and Figure 9, disturbance strength and direction affect the network differently. Figure 8: Contingency Analysis for Varying GMD Directions (Electric Field1 V/km) 5

7 2.3 QV Analysis Figure 9: Contingency Analysis for Varying GMD Electric Fields Figure 10 shows QV analysis at one of the network buses in substation 1 where the voltage dip is largest. As expected the additional reactive power support needed increases as GMD strength increases. Figure 10: QV Analysis 6

8 3 CONCLUSION This paper outlines the power system modeling requirements for evaluating the effects of GIC on electric power systems. The paper illustrates the techniques for conducting power system planning studies such as power flow, contingency, and QV analysis considering various GMD scenarios. By varying the GMD directions that give maximum transformer reactive power losses, and ascertaining the GMD strength tolerated before voltage collapse, the GMD limits for any network can be determined. BIBLIOGRAPHY [1] IEEE Transmission and Distribution Committee Working Group on Geomagnetic Disturbances and Power System Effects Report, Geomagnetic Disturbances Effects on Power Systems, IEEE Transactions on Power Delivery, Vol. 8, No. 3, July 1993, pages [2] R. Pirjola, Properties of matrices included in the calculation of GICs in power systems and introduction of a test model for GIC computation algorithms, Earth, Planets and Space, Vol. 61, 2009, pages [3] R. Horton, D. Boteler, T.J. Overbye, R. Pirjola, and R.C. Dugan, A Test Case for the Calculation of Geomagnetically Induced Currents, IEEE Transactions on Power Delivery, Vol. 27, No. 4, October 2012, pages [4] North American Electric Reliability Corporation (NERC), 2012 Special Reliability Assessment Interim Report, Effects of Geomagnetic Disturbances on the Bulk Power System. [5] V. D. Albertson, J. G. Kappenman, N. Mohan, G. A. Skarbakka, "Load-flow Studies in the Presence of Geomagnetically-induced Currents", IEEE Transactions on Power Apparatus and Systems, Vol. PAS-100, No. 2, February 1981, pages [6] X. Dong, Y. Liu, J. G. Kappenman, Comparative Analysis of Exciting Current Harmonics and Reactive Power Consumption from GIC Saturated Transformers, Proceedings IEEE, 2001, pages [7] D. H. Boteler and R. J. Pirjola, "Modeling Geomagnetically Induced Currents produced by Realistic and Uniform Electric Fields", IEEE Transactions on Power Delivery, Vol. 13, No. 4, October 1998, pages [8] R.A. Walling and A.H. Khan, Characteristics of Transformer Exciting-Current during Geomagnetic Disturbances, IEEE Transactions on Power Delivery, Vol. 6, No. 4, October 1991, pages