TRANSMISSION lines are important components of modern

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1 6 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL 2, NO 4, DECEMBER 216 Dynamic State Estimation Based Protection of Mutually Coupled Transmission Lines Yu Liu, Student Member, IEEE, A P Meliopoulos, Fellow, IEEE, Liangyi Sun, Student Member, IEEE, and Rui Fan, Student Member, IEEE Abstract Mutually coupled lines create challenges for legacy protection schemes In this paper, a dynamic state estimation based protection (EBP) method is proposed to address these challenges The method requires GPS synchronized measurements at both ends of the line and a high fidelity model of the protected line The paper presents the dynamic model of the protected line and its impact on the performance of the protection scheme Numerical simulations prove that the method can correctly identify faults, independent of position and type The work also demonstrates the advantages of the proposed method versus legacy protection functions such as distance protection and line differential These advantages include reliable and faster detection of internal low impedance faults, inter-circuit faults, and high impedance faults, even in cases of 1) partially coupled lines and 2) lack of measurements in adjacent lines Index Terms Estimation based protection (EBP), high impedance faults, inter-circuit faults, mutually coupled lines, partial coupling I INTRODUCTION TRANSMISSION lines are important components of modern power systems With ever larger demand for power transmission, transmission systems are evolving with more complexity Because of limited right of ways, many transmission circuits share the right of way creating mutually coupled lines [1] [3] The coupling can involve multiple circuits with different lengths of coupling for each circuit The protection challenges for these lines are brought by the magnetic mutual coupling which affects voltages and currents as seen at the terminals of the line under protection Fig 1 shows an example mutually coupled transmission line system The line under protection is line 2 (MN) Known limitations in protection of lines, such as the one shown in Fig 1, are as follows 1) Directional overcurrent protection and distance protection at relay I may occasionally fail to detect fault F 1 The measured voltage at relay I will be affected by Manuscript received September 7, 216; accepted September 23, 216 Date of publication December 3, 216; date of current version October 12, 216 This work was supported by the Electric Power Research Institute (EPRI) and the Power Systems Engineering Research Center (PSERC) Y Liu, A P Meliopoulos, and L Y Sun (corresponding author, e- mail: lsun3@gatechedu) are with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 3332 USA R Fan is with Pacific Northwest National Laboratory, Richland, WA USA DOI: /CSEEJPES21643 Fig c 216 CSEE M I III Mutual coupling I,1 I,3 F 2 Mutually coupled transmission lines F 1 II Line 1 N Line 2 (protected line) Line 3 zero sequence current in lines 1 (I,1 ) and 3 (I,3 ) It is possible that the directional element may not detect the fault while the distance function may see the fault beyond its zone setting [4] 2) Distance protection with compensation [5] is a promising method to compensate for the effects of currents in adjacent lines This method considers the zero sequence current of adjacent lines (I,1 and I,3 ) as inputs to calculate apparent impedance The main disadvantages are as follows: a) The protected line may not be mutually coupled for its entire length with the adjacent lines, as illustrated in Fig 1 In this case the relay may be overcompensated b) Sometimes, measurement of the zero sequence current of adjacent line may require telemetering adding to the complexity of the scheme c) Distance protection may not accurately detect intercircuit internal faults [6], especially when the two lines are operating at different rated voltage levels d) The induced voltage in the protected line is not only influenced by zero sequence current of the adjacent line, but also by positive and negative sequence currents as well (5% 7%) [6], [7] Thus, even in perfect conditions, the compensation method is subject to systematic errors, which will further compromise protection effectiveness 3) Directional comparison scheme will confront similar problems as overcurrent directional element The directional calculation results may be affected by the zero sequence current in adjacent lines [8] 4) Line differential protection is one of the most effective protection schemes for mutually coupled lines [9] However, there are limitations: a) The capacitive current may desensitize the relay, especially for long lines

2 LIU et al: DYNAMIC STATE ESTIMATION BASED PROTECTION OF MUTUALLY COUPLED TRANSMISSION LINES 7 b) High impedance faults are difficult to detect In addition, most legacy protection functions are based phasors, which adds a delay in detecting the onset of a fault We present a protection method that is based on sampled values, requires a high fidelity model of the protection zone, requires only a few settings, and most importantly, it does not require coordination with other protection functions Specifically, the method is based on dynamic state estimation to monitor the health of the protection zone and take protection decision based on the status of the protection zone The method is called the dynamic state estimation based protection (EBP) (also known as setting-less protection) [1] [13] The main idea behind the EBP relay is to monitor the consistency between the measurements and the dynamic model of the protection zone Consistency is expressed in terms of probabilistic and quantifiable measures such as confidence level Here the dynamic model consists of the differential and algebraic equations expressing the physical laws that the protected device(s) must obey The quantification of how well the measurements fit the dynamic model of the protection zone is performed using dynamic state estimation It is important to note that the EBP uses instantaneous values as opposed to phasors of legacy protection, and therefore, can detect faults within one of a few samples after fault initiation This makes it a faster detector of faulty conditions The best implementation of the EBP relay is with merging units (MU) technology: sampled values are transmitted to the process bus where the EBP uses the sample values to perform the analytics In this paper, the EBP algorithm is proposed to protect mutually coupled lines Standard application of the EBP [1] [13] requires that measurements are available at all terminals of the line(s) under protection However, for mutually coupled lines, not all the terminal voltages and currents may be available, since some of the mutually coupled circuits may terminate at different substations than the line under protection In this case, additional techniques such as introducing additional states (eg, currents in mutually coupled lines that are not available as measurements) are necessary to ensure performance of the EBP relay This paper first introduces a systematic way to derive the model of protected lines Next, the performance of EBP relay for mutually coupled lines under several scenarios is presented via numerical experiments Finally, detection and correction for hidden failures, which enhances the security and reliability of the EBP relay, is discussed II EBP METHOD The EBP method has been introduced in [1] [13] In this section, we provide a concise description of the EBP method EBP utilizes dynamic state estimation (DSE), which estimates states x(t, t m ) (with length of m x ) from available measurements z(t, t m ) (with length of m z > m x ) and a dynamic mathematical model of measurements expressed in terms of an algebraic companion form This section will be arranged as follows First, the construction of the dynamic mathematical model of measurements in algebraic companion form is introduced; next, the DSE procedure is described to provide the estimated states x(t, t m ); finally, the trip logic of EBP is provided A Dynamic Measurement Model in Algebraic Companion Form The measurement model is constructed in an object-oriented way First, the device quadratized dynamic model (QDM) for any specific component is introduced; second, the device QDM is equivalently transformed into device algebraic quadratic companion form (AQCF); finally, the measurement definitions are considered to obtain the measurement of the AQCF model The device QDM describes all physical laws that the specific component should satisfy via a set of differential and algebraic equations The device QDM is shown in the following format, dx(t) i(t) = Y eqx1 x(t) + D eqxd1 + C eqc1 dt dx(t) = Y eqx2 x(t) + D eqxd2 + C eqc2 (1) dt = Y eqx3 x(t) + x(t) T Feqxx3 i x(t) + C eqc3 where x(t) and i(t) represent the state vector and the terminal current vector of the model, respectively Usually terminal voltages are included in x(t) Sometimes the protection zone consists of several components (protection unit) The overall protection zone device QDM can be derived by combining the device QDM of each individual component This combination is achieved by observing the fact that, for the shared nodes among these components, the voltages are the same and the currents should be summed up to zero Thereafter, the combined model has the same syntax as the device QDM, shown in (1) Specifically, in this paper, the device QDM of a partially mutually coupled line is constructed as follows 1) The line is divided into several segments where each segment represents a mutually coupled line (an example can be found in Section III) 2) For each mutually coupled line segment, a multisection model is utilized, where each section is a short π- equivalent line The reason to use the multi-section model is to ensure accuracy during numerical calculations The number of sections for the multi-section model is chosen such that the traveling length of electromagnetic waves during one sampling interval is comparable to the length of each section Based on this, the overall model can be generated by combining all sections and segments together The device QDM of the π- equivalent mutually coupled line section is given in Appendix A The device algebraic quadratic companion form (AQCF) is obtained by quadratic integration [14] of device QDM This process transforms device models into algebraic companion form equations that fully retain the dynamics of the model The device AQCF has the syntax described below

3 8 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL 2, NO 4, DECEMBER 216 i(t) i(t m ) = Y eqx x(t, t m ) + x(t, t m ) T Feqx i x(t, tm ) + b (t 2 t) (2) b(t 2 t) = N eqx x(t 2 t) + M eq i(t 2 t) + K eq where x(t, t m ) = [x(t) x(t m )] T, t m = t t, t is the sampling interval, and all other matrices can be directly derived from matrices in (1) The measurement AQCF is formed by expressing each measurement as a function of the protection zone state utilizing the protection zone AQCF For example, consider the measurement of a terminal current of phase A of the line at time t The AQCF model of this measurement will be the first equation of (2), which expresses the phase A current at time t as a function of the line states at time t and t m In general, the measurement AQCF has the following syntax: z(t, t m ) = h(x(t, t m )) = Y m,x x(t, t m ) + x(t, t m ) T Fm,x i x(t, tm ) + b z (t 2 t) (3) b z (t 2 t) = N m,x x(t 2 t) + M m i(t 2 t) + K m Here the measurements z(t, t m ) include: 1) actual measurements measured by VTs/CTs, with standard deviations determined by meters; 2) virtual measurements representing physical laws that must be obeyed by the protection zone, eg, KCL, KVL, etc, and a relatively small standard deviation is assigned; and 3) pseudo measurements representing physical quantities, not directly measured, for which a typical value is expected and a relatively large standard deviation is assigned B Dynamic State Estimation (DSE) Procedure The state vector x(t, t m ) in (3) needs to be estimated We have developed three dynamic state estimators Here only one of the solution methods (unconstraint weighted least square) is provided since the results are statistically similar with other methods For each DSE time step, the method first constructs an unconstrained optimization problem, MinJ = (h(x(t, t m )) z(t, t m )) T W (h(x(t, t m )) z(t, t m )) (4) where W = diag { 1/σ 2 1, 1/σ 2 2, }, and σ i is the standard deviation of each measurement Next, the best estimated state vector is provided by the following iterative algorithm until convergence, x(t, t m ) ν+1 = x(t, t m ) ν (H T W H) 1 H T W (h(x(t, t m ) ν ) z(t, t m )) (5) C Trip Logic of EBP After calculating the best estimated state vector ˆx(t, t m ), the health condition of the protection zone, or the confidence level [15] P conf (t) is calculated as, P conf (t) = P ( χ 2 ζ(t) ) = 1 P (ζ(t), m v ) (6) ζ(t) = ŝ(t, t m ) T ŝ(t, t m ) (7) ŝ(t, t m ) = W ˆr(t, t m ) (8) ˆr(t, t m ) = h(ˆx(t, t m )) z(t, t m ) (9) where P (ζ(t), m v ) is the probability of χ 2 distribution given χ 2 ζ(t) with m v = m z m x degree of freedom, ˆr(t, t m ) is the residual vector, and ŝ(t, t m ) is the normalized residual vector The confidence level acts as an indicator of the consistency between the measurements and the model If the confidence level is high (near 1%), the system is healthy If the confidence level is consistently low, there must be some internal fault inside the protection zone To ensure dependability and security of the EBP scheme, two settings (a user defined time delay τ delay and a reset time τ reset ) are introduced to decide the trip signal as below The trip signal is issued only when the confidence level remains consistently low for a user defined time interval The trip logic settings for the EBP relay are τ reset and τ delay t T ripvalue(t) = (1 P conf (t)) dt (1) t τ reset { 1, if T ripvalue(t) τ delay T rip(t) = (11), if T ripvalue(t) < τ delay III SIMULATION EXAMPLE: PARTIALLY MUTUALLY COUPLED TRANSMISSION LINES In this part, we demonstrate the performance of EBP on partially mutually coupled lines An example system is shown in Fig 2 There are 9 voltage and 9 current measurements Notice that the measurements at side M 1 are easy to obtain since line 1 and line 2 share the same substation M Our objective is to protect line 2 (39 miles in total, 12 ka current rating) The relative positions of these mutually coupled lines Side 1 Relay I 3-phase PTs M 1 LEGEND Protected line P 1 3-phase CTs Fiber optic 69 kv Line 1 Breakers Q kv M 2 P 2 Q 2 S 2 T 2 P 3 Q 3 S 3 Line 2 15 miles 1 miles 8 miles 6 miles T M P Q S 23 kv Line 3 Side 2 Relay II where the Jacobian matrix H = h(x)/ x Fig 2 Example test system: partially mutually coupled transmission lines

4 LIU et al: DYNAMIC STATE ESTIMATION BASED PROTECTION OF MUTUALLY COUPLED TRANSMISSION LINES 9 are given in Fig 3 The device model is built by combining the following four segments: MP (mutually coupled lines M 1 - P 1, M 2 -P 2 ), PQ (mutually coupled lines P 1 -Q 1, P 2 -Q 2, P 3 - Q 3 ), QS (mutually coupled lines Q 2 -S 2, Q 3 -S 3 ) and ST (line S 2 -T 2 ) The model is a physically based, three phase, asymmetric, shields/grounds inclusive transmission line model The sampling rate is 48 samples per second, as defined in IEC standards Fig N 1 A 1 B 1 C 1 Line N 2 A 2 B 2 C 2 Line 2 N 3 N 4 A 3 B 3 C 3 Line 3 unit: ft Tower structures of the protected transmission lines, segment PQ A State and Measurement Additions for EBP Relay As shown in Fig 2, there is a total of 6 terminals (M 1, M 2, P 3, Q 1, T 2, S 3 ); however, measurements are available only at 3 line terminals (M 1, M 2 and T 2 ) While measurements at the other terminals can be telemetered, we elect not to relay on these measurements to minimize the complexity of the scheme Instead, we introduce additional states, such as virtual measurements and pseudo measurements to enable operation of the proposed EBP scheme 1) Additional States Currents in mutually coupled lines are introduced as additional states to be estimated by the EBP algorithm In the example of Fig 2, it will be the currents in lines 1 and 3 To ensure observability of the system, additional virtual and pseudo measurements are considered next 2) Additional Virtual Measurements Additional virtual measurements describe the physical laws influenced by the mutual coupling Voltage drops between two terminals of any line due to the currents through the adjacent lines are introduced as virtual measurements 3) Additional Pseudo Measurements Pseudo measurements are introduced to augment the measurement set, provide redundancy, and ensure observability 1) Pseudo measurements at node Q 1 : Current and voltage measurements at side M, together with the model of line 1 are utilized to estimate the approximate voltages at side Q 1 These voltages are introduced as pseudomeasurements 2) Pseudo measurements at node P 3 and S 3 : The best guess of the voltages at these nodes is selected as follows: Initially, the pseudo voltage instantaneous measurements are calculated from phasors, where the rms values of phasors are chosen as the nominal voltage, and the angles of the phasors are chosen as the voltage angles at node M 1 In subsequent iterations, the estimated values are used to select the values of the pseudo measurements B Settings of Relays Line 2 is assumed to be protected with two legacy protection functions: 1) distance protection with compensation method, and 2) line differential protection It is also protected with an EBP relay The settings of these protection functions are as follows 1) Distance Protection Settings The sequence parameters of the transmission line are computed and shown in Table I The selected settings for this relay are shown in Table II, with zone 1, zone 2, and zone 3 chosen as 8%, 125%, and 26% of the positive sequence impedance of line 2 Here, the zero sequence selfcompensation factor of line 2 is k (2) = (Z (2) L Z(2) L1 )/Z(2) L1, the zero sequence mutual-compensation factor between line 2 and line 1 is k (2,1) M = Z (2,1) M /Z(2) L1, and the zero sequence mutual-compensation factor between line 2 and line 3 is k (2,3) M = Z (2,3) M /Z(2) L1 TABLE I SEQUENCE PARAMETERS OF THE PROTECTED LINE Parameter (per mile) Value Positive (negative) sequence impedance of line 2 (Z (2) L1 ) Ω/mile Zero sequence impedance of line 2 (Z (2) L ) Ω/mile Zero sequence mutual impedance between line 2, 1 (Z (2,1) M ) Ω/mile Zero sequence mutual impedance between line 2, 3 (Z (2,3) M ) Ω/mile Function Line and ground distance, zone 1 Line and ground distance, zone 2 Line and ground distance, zone 3 TABLE II DISTANCE RELAY SETTINGS Settings Ω, 2 s delay, compensation factors: k (2) = k (2,1) M = k (2,3) M = Ω, 15 s delay, compensation factors: k (2) = k (2,1) M = k (2,3) M = Ω, 5 s delay, compensation factors: k (2) = k (2,1) M = k (2,3) M = ) Line Differential Protection Settings The line differential relay uses the alpha-plane method [16] The restraint region is between 1/6 to 6, with total angular extent of 195 The relay trip logic is activated when at least one of the following thresholds is exceeded: 1) phase current exceeds 144 ka, 2) zero sequence current exceeds 12 A, and 3) negative sequence current exceeds 12 A The relay will trip when the trip logic is activated and the ratio falls outside the restraint region, with a delay of 2 s 3) EBP Relay Settings For consistency, the intentional delay is also selected as τ delay = 2 s and the reset time is τ reset = 4 s

5 1 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL 2, NO 4, DECEMBER 216 C Event Studies We compare the performance of the legacy protection functions to the EBP relay performance via specific events Event 1: Bolt phase A to ground external fault in line 1, 1 mile from side M 1 A 1-ohm phase A to ground external fault happens inside segment M 1 -P 1 of line 1, at 1 mile from the side M 1 and time 5 s The results of available current and voltage measurements are shown in Fig 4 This is a severe external fault with large fault currents (see currents at side M 1 ) since the fault is near side M 1 7,8713 A 8,3472 A 7938 A 7935 A 8 A 83 A 5665 kv 5695 kv 8926 kv 884 kv 7757 kv 7757 kv Current_sideM 1 _A (A) Current_sideM 1 _B (A) Current_sideM 1 _C (A) Current_sideM 2 _A (A) Current_sideM 2 _B (A) Current_sideM 2 _C (A) Current_sideT 2 _A (A) Current_sideT 2 _B (A) Current_sideT 2 _C (A) Voltage_sideM 1 _A (V) Voltage_sideM 1 _B (V) Voltage_sideM 1 _C (V) Voltage_sideM 2 _A (V) Voltage_sideM 2 _B (V) Voltage_sideM 2 _C (V) Voltage_sideT 2 _A (V) Voltage_sideT 2 _B (V) Voltage_sideT 2 _C (V) 45 s Time 55 s Fig 4 Current and voltage results of a bolt phase A to ground external fault in line 1 For the distance protection relay, the trace of the impedance seen by the relay is shown in Fig 5 We can observe that the impedance falls into zone 1 during the external fault and line 2 is wrongly tripped at 59 s + 2 s = 529 s This mis-operation is because the zero sequence current through the whole length of line 1 is wrongly assumed as the measured current at side M 1 Imaginary Part of the Impedance (ohm) t=51 s t=55 t =55s s t=515 s t=5 s Real Part of the Impedance (ohm) Fig 5 Trace of impedance during a phase A to ground external fault in line 1 For the line differential protection relay, the phasor ratio trace of phase A is shown in Fig 6 The other phases are not shown Along the trace, the character o means the thresholds are not exceeded while the character x means the thresholds are exceeded (The definitions can be applied to all line differential relay figures) The ratio stays near ( 1, ) both prior to the fault and during the fault, with no thresholds exceeded (with the character o ) Thus, line differential protection relay correctly ignores this external fault Imaginary Part of the Phase A Ratio X O Thresholds are exceeded Thresholds are not exceed Real Part of the Phase A Ratio Fig 6 Trace of the ratios during a phase A to ground external fault in line 1 For the EBP relay, the results are depicted in Fig 7 Here in the first two channels we show the residuals and normalized residuals of three-phase currents of side M 1 Also, the confidence level and the trip signal are given in the next two channels The confidence level stays low for a very short period (around 2 ms) due to transients and then keeps a 1% confidence level during this external fault Therefore, the EBP method also correctly ignores this external fault 9639 A 1359 A 2726 pu 3844 pu Residual_Current_sideM 1 _A (A) Residual_Current_sideM 1 _B (A) Residual_Current_sideM 1 _C (A) 1 % Confidence Level (%) % 1 u 1 u Normalized_Current_sideM 1 _A (pu)normresid Normalized_Current_sideM 1 _B (pu)normresid Normalized_Current_sideM 1 _C (pu)normresid Trip 45 s Time 55 s Fig 7 EBP results of a phase A to ground external fault in line 1 In summary, for this external fault, the distance protection relay wrongly trips the line at 529 s; the line differential

6 LIU et al: DYNAMIC STATE ESTIMATION BASED PROTECTION OF MUTUALLY COUPLED TRANSMISSION LINES 11 protection relay correctly ignores this external fault; EBP relay also correctly ignores this external fault Event 2: Bolt line 2 phase A to line 1 phase C internal inter-circuit fault A 1-ohm line 2 phase A to line 1 phase C internal fault happens inside segment P-Q at 5 miles from side P and time 5 s In line 2, the location of the fault (51% of the line) is within the instantaneous trip zone of the relay (8% of the line) The results of available current and voltage measurements are shown in Fig 8 2,6491 A 3,1493 A 2,8285 A 2,384 A 8555 A 856 A 5574 kv 5513 kv 965 kv 999 kv 8425 kv 8517 kv Current_sideM 1 _A (A) Current_sideM 1 _B (A) Current_sideM 1 _C (A) Current_sideM 2 _A (A) Current_sideM 2 _B (A) Current_sideM 2 _C (A) Current_sideT 2 _A (A) Current_sideT 2 _B (A) Current_sideT 2 _C (A) Voltage_sideM 1 _A (V) Voltage_sideM 1 _B (V) Voltage_sideM 1 _C (V) Voltage_sideM 2 _A (V) Voltage_sideM 2 _B (V) Voltage_sideM 2 _C (V) Voltage_sideT 2 _A (V) Voltage_sideT 2 _B (V) Voltage_sideT 2 _C (V) 45 s Time 55 s Fig 8 Current and voltage results of a bolt line 2 phase A to line 1 phase C internal inter-circuit fault For the distance protection relay, the trace of the impedance seen by the relay is shown in Fig 9 In the figure we can observe that the impedance falls inside of zone 2 during the internal fault Therefore, the distance relay trips this fault with some delay at 512 s + 15 s = 662 s This tripping with delay is because for distance relay it is hard to identify inter-circuit faults, especially between lines with different rated voltage levels and none of the thresholds are exceeded (with the character o ) During the fault, the thresholds are gradually exceeded (from the character o to x ) with the ratio entering the tripping zone The differential protection relay correctly trips this fault at 519 s + 2 s = 539 s Imaginary Part of the Phase A Ratio t=51 s t=5 s t=52 s X Thresholds are exceeded O Thresholds are not exceed Real Part of the Phase A Ratio Fig 1 Trace of the ratios during a line 2 phase A to line 1 phase C internal inter-circuit fault For the EBP relay, the results are depicted in Fig 11 The fault is detected by the drop of the confidence level at 52 s and the trip signal is triggered at 522 s In summary, for this internal fault, the distance protection relay trips the line with delay at 662 s; the line differential protection relay correctly trips the line at 539 s; the EBP relay correctly trips the line at 522 s Event 3: High impedance phase A to ground internal fault in line 2 A 2-ohm phase A to ground internal fault happens inside segment P 2 -Q 2 of line 2 at 5 miles from side P 2 and time 5 s The results of available current and voltage measurements are shown in Fig 12 1,9762 A Residual_Current_sideM 2 _A(A) Residual_Current_sideM 2 _B(A) Residual_Current_sideM 2 _C(A) Imaginary Part of the Impedance (ohm) 8 6 t=51 s t=55 s 4 t=515 s t=5 s 2 t=52 s Real Part of the Impedance (ohm) 2,47 A 3524 pu 4281 pu 1% % 1 NormResid_Current_sideM 2 _A(pu) NormResid_Current_sideM 2 _B(pu) NormResid_Current_sideM 2 _C(pu) Confidence Level(%) Trip Fig 9 Trace of impedance during a line 2 phase A to line 1 phase C internal inter-circuit fault For the line differential protection relay, the phasor ratio trace of phase A is shown in Fig 1 The other phases are not shown Prior to the fault, the ratio of phase A is near ( 1, ), 45 s Time 55 s Fig 11 EBP results of a line 2 phase A to line 1 phase C internal inter-circuit fault

7 Imaginary Part of the Phase A Ratio Imaginary Part of the Phase A Ratio 12 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL 2, NO 4, DECEMBER A 5228 A 1,72 A 1,717 A 8134 A 8132 A 621 kv 5481 kv 9316 kv 8948 kv 812 kv 815 kv Current_sideM 1 _A (A) Current_sideM 1 _B (A) Current_sideM 1 _C (A) Current_sideM 2 _A (A) Current_sideM 2 _B (A) Current_sideM 2 _C (A) Current_sideT 2 _A (A) Current_sideT 2 _B (A) Current_sideT 2 _C (A) Voltage_sideM 1 _A (V) Voltage_sideM 1 _B (V) Voltage_sideM 1 _C (V) Voltage_sideM 2 _A (V) Voltage_sideM 2 _B (V) Voltage_sideM 2 _C (V) Voltage_sideT 2 _A (V) Voltage_sideT 2 _B (V) Voltage_sideT 2 _C (V) 45 s Time 55 s Fig 12 Current and voltage results of a high impedance phase A to ground internal fault in line 2 For the distance protection relay, the trace of the impedance seen by the relay is shown in Fig 13 In the figure we can observe that the impedance falls outside of the tripping zone during this internal fault Therefore, the distance relay wrongly ignores this internal fault This refusal of operation is due to the high fault impedance Imaginary Part of the Impedance (ohm) t=51 s t=52 s t=55 s t=515 s t=5 s Real Part of the Impedance (ohm) Fig 13 Trace of impedance during a high impedance phase A to ground internal fault in line 2 For the line differential protection relay, the phasor ratio trace of phase A is shown in Fig 14 The other phases are not shown The ratio of phase A stays inside the restraint region with no thresholds exceeded (with the character o ) Therefore, the line differential relay also wrongly ignores this internal fault due to high fault impedance For the EBP relay, the results are depicted in Fig 15 The fault is detected by the drop of the confidence level at 52 s and the trip signal is triggered at 522 s In summary, for this internal fault, the distance protection relay and line differential protection relay wrongly ignore the fault; the EBP relay correctly trips the line at 522 s t=51 s t=5 s t=52 s Real Part of the Phase A Ratio X Thresholds are exceeded O Thresholds are not exceed Real Part of the Phase A Ratio Fig 14 Trace of the ratios during a high impedance phase A to ground internal fault in line A 2255 A 426 pu 421 pu 1% % 1 Residual_Current_sideM 2 _A(A) Residual_Current_sideM 2 _B(A) Residual_Current_sideM 2 _C(A) NormResid_Current_sideM 2 _A(pu) NormResid_Current_sideM 2 _B(pu) NormResid_Current_sideM 2 _C(pu) Confidence_Level(%) Trip 45 s Time 55 s Fig 15 EBP results of a high impedance phase A to ground internal fault in line 2 IV SUPERVISION OF DATA INTEGRITY AND CORRECTION The effectiveness of the proposed EBP relay is based on the assumption that there are no hidden failures that deteriorate the measurements We can conclude from this method, therefore, that the inconsistency between the measurements and the model is caused by internal faults of the protection zone Thus, the detection of hidden failures and the correction of corresponding measurements are also essential to reliability and security of EBP relay There are mainly two approaches for detecting hidden failures: 1) The first approach is to estimate the fault related parameters (location of the fault, fault admittance, etc) during internal faults This is achieved by altering the dynamic model of the protection zone to include fault related

8 LIU et al: DYNAMIC STATE ESTIMATION BASED PROTECTION OF MUTUALLY COUPLED TRANSMISSION LINES 13 parameters If the measurements fit the faulted protection zone model with a high confidence level, there exist no hidden failures; otherwise, there are hidden failures 2) The second approach is to utilize redundant measurements High measurement redundancy can be achieved by the use of data from the entire substation, also known as the centralized substation protection (CSP) scheme [17] Once the confidence level is low, the hypothesis test is applied to examine whether this is caused by internal faults or hidden failures The hypothesis test eliminates any suspected measurements and performs the EBP procedure again until a high confidence level is obtained (hidden failures are detected), or all measurements are covered (internal faults are detected) After the detection of hidden failures, the proper correction actions may differ according to different root causes If the root cause can be automatically corrected (eg, a wrong CT ratio), the values will be updated in the database If the root cause cannot be automatically corrected (eg, a blown fuse), the bad data will be replaced with the estimated values and an alarm with the root cause will be sent to the control center for future maintenance From the above detection and correction procedure, the EBP relay can operate continuously, reliably and securely even with the presence of hidden failures V CONCLUSION Mutually coupled lines bring not only benefits, but also protection challenges Legacy protection methods exhibit shortcomings for mutually coupled lines The paper proposes a dynamic state estimation based protection (EBP) that promises better protection for mutually coupled lines The method requires the dynamic model of the line under protection and measurements from both ends of the line It uses a dynamic state estimator to determine the goodness of fit between measurements and the line dynamic model Internal faults are detected by deviations between measurements and model Numerical experiments were performed to compare typical legacy protection systems (distance protection with compensation method and line differential protection) to the EBP method Results show the following advantages of the EBP method: 1) It performs well for lines that are partially coupled 2) It can dependably and securely operate even with limited measurements in adjacent lines 3) It detects internal fault faster than legacy schemes 4) It can reliably detect inter-circuit faults 5) It can reliably detect high impedance faults APPENDIX QDM of π-equivalent Mutually Coupled Line Section This appendix describes QDM of π-equivalent mutually coupled transmission line section An example π-equivalent section with 2 lines is provided in Fig A1 Side 1 i 1 (1) (t) v 1 (1) (t) i 1 (2) (t) v 1 (2) (t) C (1) C (2) R (1) L (1) i L (1) (t) Side 2 i (1) 2 (t) v 2 (1) (t) C (1,2) R (1,2) L (1,2) i (2) C (1,2) Line 1 L (t) i (2) 2 (t) R (2) L (2) C (1) C (2) v 2 (2) (t) Line 2 (protected line) Fig A1 π-equivalent mutually coupled line section (mutual inductances and capacitances inside each line are not shown) The standard format of QDM is given in (1) The QDM parameters of the mutually coupled line section are: [ ] T i(t) = i (1) 1 (t) i(1) 2 (t) i(2) 1 (t) i(2) 2 (t) ; [ ] T x(t) = v (1) 1 (t) v(2) 1 (t) v(1) 2 (t) v(2) 2 (t) i(1) L (t) i(2) L (t) ; [ ] [ ] I C Y eqx1 = ; D I eqxd1 = ; C C eqc1 = ; Y eqx2 = [ I I R ] ; D eqxd2 = [ L ] ; C eqc2 = ; [ ] [ ] R (1) R (1,2) C (1) R = ( ) C (1,2) R (1,2) T ; C = ( ) R (2) C (1,2) T ; C (2) [ ] L (1) L (1,2) L = ( ) L (1,2) T ; L (2) all other vectors and matrices are null; I is the identity matrix; R (1), L (1), C (1), R (2), L (2) and C (2) are the resistance, inductance and capacitance matrices of line 1 and line 2; R (1,2), L (1,2) and C (1,2) are the mutual resistance, inductance and capacitance matrices between line 1 and line 2; i (1) 1 (t), (t), i(1) 2 (t) and i(2) 2 (t) are current vectors of line 1 and line 2 at each side; v (1) 1 (t), v(2) 1 (t), v(1) 2 (t) and v(2) 2 (t) are voltage vectors of line 1 and line 2 at each side; i (1) L (t) and i (2) L (t) are the current vector of line 1 and line 2 through the inductances i (2) 1 REFERENCES [1] C S Chen, C W Liu, and J A Jiang, A new adaptive PMU based protection scheme for transposed/untransposed parallel transmission lines, IEEE Transactions on Power Delivery, vol 17, no 2, pp , Apr 22 [2] A H Osman and O P Malik, Protection of parallel transmission lines using wavelet transform, IEEE Transactions on Power Delivery, vol 19, no 1, pp 49 55, Jan 24 [3] B R Bhalja and R P Maheshwari, High-resistance faults on two terminal parallel transmission lines: analysis, simulation studies, and an adaptive distance relaying scheme, IEEE Transactions on Power Delivery, vol 22, no 2, pp , Apr 27 [4] B Bhalja and R P Maheshwari, Percentage differential protection of double-circuit line using wavelet transform, Electric Power Components and Systems, vol 35, no 8, pp , May 27 [5] Y Hu, D Novosel, M M Saha, and V Leitloff, An adaptive scheme for parallel-line distance protection, IEEE Transactions on Power Delivery, vol 17, no 1, pp 15 11, Jan 22

9 14 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL 2, NO 4, DECEMBER 216 [6] V H Makwana and B Bhalja, New adaptive digital distance relaying scheme for double infeed parallel transmission line during inter-circuit faults, IET Generation, Transmission & Distribution, vol 5, no 6, pp , Jun 211 [7] V H Makwana and B Bhalja, A new adaptive distance relaying scheme for mutually coupled series-compensated parallel transmission lines during intercircuit faults, IEEE Transactions on Power Delivery, vol 26, no 4, pp , Oct 211 [8] D A Tziouvaras H J Altuve, and F Calero, Protecting mutually coupled transmission lines: challenges and solutions, in Proceedings of 67th Annual Conference Protective Relay Engineers, College Station, TX, 214, pp 3 49 [9] S V Unde and S S Dambhare, GPS synchronized current differential protection of mutually coupled line, in International Conference on Power and Energy Systems (ICPS), Chennai, India, 211, pp 1 6 [1] A P S Meliopoulos, G J Cokkinides, Z Y Tan, S Choi, Y Lee, and P Myrda, Setting-less protection: feasibility study, in Proceedings of th Hawaii International Conference on Systems Science (HICSS), Maui, HI, 213, pp [11] A P S Meliopoulos, G Cokkinides, Y Liu, R Fan, S Choi, and P Myrda, Protection and control of systems with converter interfaced generation (CIG), in Proceedings of th Hawaii International Conference on Systems Science (HICSS), Koloa, HI, 216, pp [12] Y Liu, A P Meliopoulos, R Fan, and L Y Sun, Dynamic state estimation based protection of microgrid circuits, in Proceedings of IEEE Power and Energy Society (PES) General Meeting, Denver, CO, 215, pp 1 5 [13] R Fan, A P S Meliopoulos, G J Cokkinides, L Y Sun, and Y Liu, Dynamic state estimation-based protection of power transformers, in Proceedings of IEEE Power and Energy Society (PES) General Meeting, Denver, CO, 215, pp 1 5 [14] A P S Meliopoulos, G J Cokkinides, and G K Stefopoulos, Quadratic integration method, in Proceedings of 25 International Power Systems Transients Conference (IPST), Montreal, Canada, 25, pp 1 8 [15] F C Schweppe and R D Masiello, A tracking static state estimator, IEEE Transactions on Power Application and Systems, vol PAS-9, no 3, pp , May 1971 [16] Schweitzer Engineering Laboratories, Inc (216, Jan) SEL-387L relay instruction manual [Online] Available: [17] H Albinali and A P S Meliopoulos, A centralized substation protection scheme that detects hidden failures, in Proceedings of IEEE Power and Energy Society (PES) General Meeting, Boston, MA, 216, pp 1 5 Yu Liu (S 13) received his BS and MS degrees in electric power engineering from Shanghai Jiao Tong University, China, in 211 and 213; MS degree in electrical and computer engineering from Georgia Institute of Technology, US, in 213 He is currently a PhD candidate in the Department of Electrical and Computer Engineering, Georgia Institute of Technology His research interests include power system protection, parameter estimation, and circuit fault locating A P Sakis Meliopoulos (M 76 SM 83 F 93) received the ME and EE diploma from the National Technical University of Athens, Greece, in 1972; the MSEE and PhD degrees from the Georgia Institute of Technology in 1974 and 1976, respectively In 1971, he worked for Western Electric in Atlanta, Georgia In 1976, he joined the faculty of Electrical Engineering, Georgia Institute of Technology, where he is presently a Georgia Power Distinguished Professor He is active in teaching and research in areas of modeling, analysis, and control of power systems He has made significant contributions to power system grounding, harmonics, and reliability assessment of power systems He is the author of the books, Power Systems Grounding and Transients, Marcel Dekker, June 1988, Lightning and Overvoltage Protection, Section 27, Standard Handbook for Electrical Engineers, McGraw Hill, 1993 He holds three patents and he has published over 3 technical papers In 25 he received the IEEE Richard Kaufman Award and in 21 received the George Montefiori Award Dr Meliopoulos is the Chairman of the Georgia Tech Protective Relaying Conference, a Fellow of the IEEE, and a member of Sigma Xi Liangyi Sun (S 12) received his BS degree in electrical power engineering from Shanghai Jiao Tong University, China, in 21 and the MS degree in electrical and computer engineering from Georgia Institute of Technology, US, in 212 He is currently a PhD candidate in Department of Electrical and Computer Engineering, Georgia Institute of Technology His research interests include power system protection, transient stability, and wind power control Rui Fan (S 12) received his BS degree in electrical engineering from Huazhong University of Science and Technology, China in 211, and MS and PhD degrees in ECE from the Georgia Institute of Technology in 212 and 216, respectively He is currently working at the Pacific Northwest National Laboratory, US His research interests include power electronics, power system protection, reliability analysis, and microgrid autonomous operation