Performance Evaluation of Generator- Transformer Unit Overall Differential Protection in Large Power Plant

Transcription

1 Performance Evaluation of Generator- Transformer Unit Overall Differential Protection in Large Power Plant Wael Yousef, IEEE Senior Member Mahmoud A. Elsadd Almoataz Y. Abdelaziz, IEEE Senior Member Mohamed A. Badr, IEEE Senior Member Power Generation Engineering and Services Company, PGESCO Department of the Electrical Engineering, Faculty of Engineering, Menoufia University Electrical Power and Machines Department, Faculty of Engineering, Ain Shams University Abstract-This paper investigates the performance of the Generator-Transformer unit overall differential protection function (Relay 87O). The Relay 87O is often required for large power generation as a backup protection for Generator, Generator Step-Up Transformer (GSUT), and Unit Auxiliary Transformer (UAT) differential protection systems. Three different methodologies of the relay settings covering all possible design concepts are evaluated. Also, the relay setting increasing the power generation stability and reliability of Egyptian grid is recommended. The performance evaluation of the relay has been conducted by using a dynamic model of ATP/EMTP software for a large steam turbine synchronous generator. The parameters of the selected generator are obtained from the real data in Egyptian power generation station. The performance of the relay is tested under major system disturbances and abnormal operating conditions from dependability, security, and reliability point of view. The sample results of the assessment are declared and discussed. Keywords- ATP/EMTP, Differential Protection, Power Transformer, Protective Relay, Synchronous Generator, Thermal Power Plant. I. INTRODUCTION The large thermal power generating units are a crucial source for producing electric power in any power system grid. Therefore, various protective devices protect the thermal power generation plant to minimize the possibility of occurring a damage, minimize the frequency and duration of unwanted outages, and then increase the power system stability [1-2]. However, Different real problems still encounter the protection system of the power plant [3]. During a North American grid blackout in 2003, 13 types of generating units relays were unnecessarily tripped. This maloperation leads to lost 290 units which are around 52.7 GW [4-5]. Also, during a major system disturbance in western American in 1996, 22.9 GW are lost due to tripping different protective devices of the generation units. The cause of the tripping were 22 cases for power plant problems, 6 cases for excitation control/field problems, and around 35 cases of load rejection/power swing [6]. As a result, The IEEE rotating machinery subcommittee and the power system relaying committee recommended that the coordination between the generation unit protections, system protection, excitation control, and generator capability should be enhanced [7-8]. The differential relay is a reliable method for protecting generators, transformers, large motors, buses, cables, and transmission lines against the effects of internal faults. The main benefits of this relay are the reliability and the speed for isolating the faulty region. Large power generation protection scheme needs adding a backup differential protection for Generator, GSUT, and UAT including buses. The Generator- Transformer unit overall differential protection is designed to be a backup protection for generator and transformers. Consequently, it requires being coordinated with a generator, GSUT, and UAT differential relays by a time delay, pickup current, and/or slop of restrained curve. Therefore, the blinding of the relay during internal faults may occur. On the other hand, the relay may unnecessarily trip in the normal operating conditions or external system disturbances such as synchronization, Full Load rejection, external faults, transient system faults, reverse power, and power swing [9-13] Generally, several researchers carried out a performance evaluation for differential protection relay when it separately protects the power transformer, transmission lines, and bus bars [14-20]. In [14] the performance evaluation of busbar s differential protection relay under different fault scenarios was presented via representing the relay with a combination of biased differential protection algorithm with fast Fourier algorithm. An experimental evaluation of power differential relay for transmission line protection was presented in [15]. The evaluation was accomplished at a different power level (changes in active and reactive power). The relay setting values were determined from the line rating and parameters. The performance evaluation and analysis of power transformer differential protection relay were presented in [16-20] using different methodologies under mal-operation cases such as current transformers (CT) saturation, over excitation, magnetizing inrush, and nonlinear load switch. Up to date, the evaluation of the Generator-Transformer unit overall differential protection performance is not covered. Reference Number: JO-P

2 This paper presents the performance analysis of the generator-transformer unit overall differential protection from dependability, security, and reliability point of view using the ATP/EMTP software. The evaluation of the protection relay (87O) functions is accomplished using mass simulations based on real technical parameters for large thermal power generation plant [21]. The results illustrate the behavior of the protection functions against a wide variety of normal operation and short-circuiting situations using the three different relay settings (sensitive, balanced, and secure). The aim of this evaluation is providing the appropriate choice and better understanding of the differential protection settings of generator-transformer unit overall differential protection. II. FUNDAMENTAL OF GENERATOR-TRANSFORMER UNIT OVERALL DIFFERENTIAL PROTECTION The recommended unit overall differential zone covers both the GSUT and the UAT as shown in Figure (1) [9-10]. In some cases, the UAT may be excluded from the overall differential scheme as in the alternate connection [22]. This approach may introduce a blind spot in the protection of the UAT [9-10]. In this evaluation, the UAT consider within the unit overall differential zone. The algorithm and settings of the unit overall differential relay are illustrated in the following subsections. Tests based on synchronized PMU measurements have shown glimpses of electromechanical wave propagation in the USA [3-4]. A. The Algorithm A percentage differential function is applied to the fundamental component of the currents to decide whether an internal fault occurs or not. The difference between the operating and restraining currents is a small value under normal operating conditions and external faults, while it becomes a significant value under internal faults. The relay with harmonic restraint is the most used protective scheme for the generator, transformer, and generator-transformer unit overall protection. The operating current (I d ) of current differential protection can be obtained by: where: N is the number of current transformers The restraining current (I r ) can be obtained by: (1) System Grid (2) UAT HV BREAKER GCB GSUT where: k is a compensation factor, usually taken as 1 or 0.5. The differential relay generates a tripping signal if the operating current (I d ) is greater than a percentage of the restraining current (I r ) as follows: Tripping Area I ins Alternative GENERATOR Tripping Area with restrain 87O Id/Iref Auxiliary Figure (1):Unit Overall Differential Scheme Recently the spreading of disturbances in the power system has been viewed by modeling the system as a continuum. I PU I r /I ref Blocking Area Figure (2): Percentage Differential Curve Reference Number: JO-P

3 where: SLP is the slope of the straight line which is divided into two slopes (SLP = m 1 or m 2 ) and started from the minimum pickup current value (I PU ) as shown in Figure (2). The relay operating region is located above the SLP characteristic of (3), whereas the blocking region is below the SLP characteristic. Digital differential protection relay uses Discrete Fourier Transformation (DFT) filtration to extract the fundamental differential current. The relay also checks the harmonic percentage values in the operating region located between the SLP curve and the current instantaneous line (I ins ). B. The Settings As matter of fact, there is no a specific setting stated in the international standards for generator-transformer unit overall differential protection but usually, a higher setting above the generator and transformer differential protection setting is used. The relay settings which are practically used by the protection engineers and technologists are discussed in this subsection as follows: Pickup Setting (I PU ): The minimum pickup of the relay should be set at a level greater than the measurement error that is likely to occur at low load levels. The recommended range of the pickup current is 15:35% of the full load current if the restraining current range is 0:2 pu of Ir. Further, it shall be greater than the pickup setting of the generator and transformers differential protections. PercentageSlopes (SLP): The relay protection has a possibility of using two slopes (m 1, m 2 ). The first one is used to lower levels of the operating currents and the other is used to higher levels of the operating currents. First slope s setting is set to ensure the sensitivity against the internal faults at normal operating current and should be sufficiently high to treat the CT mismatch, errors due to the accuracy of the CTs, current variation due to tap changer operation, CT saturation in case of external faults, the accuracy error of the relay, generator field current, and the generator/transformer excitation current. Further, it should be greater than the pickup setting of the generator s and transformers differential protection. The recommended setting range is 15:30% of full load current. Second slope s setting is activated in the infinite region beyond the knee point and should be set to ensure the stability under heavy external fault conditions which could lead to high differential currents as a result of CT saturation. The recommended setting range is 50:80% of full load current. When using CT with high saturation point, the same percentage of the slope one can be used. (3) Instantaneous Pickup (I ins ): The differential relay provides the instantaneous protection under high operating current magnitudes associated with internal faults regardless the magnitude of the restraint current or the harmonic component. The pickup threshold setting should be set above the maximum external fault current or the maximum inrush current according to whichever is higher. Also, the setting should be below the current that may result in CT AC saturation. Harmonic Restraint: Harmonic restraint is used to avoid undesired tripping by the differential relay due to the flow of magnetizing inrush currents when a transformer is energized (2 nd Harmonic) or overexcitation for generator/transformers occurs (5 th harmonic). The recommended setting range is 15:35% of the current fundamental component for 2 nd Harmonic and 10:30% of the current fundamental component for 5 th harmonic [23-25]. III. SIMULATED SYSTEM Figure(3) shows the simulated Egyptian power generation station containing a large steam turbine synchronous generator, a GSUT, and a UAT. The rating, line voltage, and the frequency of the large steam turbine synchronous generator, respectively, are 834 MVA, 22 kv, and 50 Hz. The generator is star-earthed through a (22/ 3/0.5 kv, 70 kva) neutral grounding transformer with a 2.56 ohm grounding resistor. The generator excitation system is supplied from the Figure (3):Single Line Diagram of the Studied System Reference Number: JO-P

4 generator terminals by a (22/0.96 kv, 9000 kva) excitation transformer as illustrated in Figure(3). The generator is simulated using a universal synchronous machine with manufacturers data input (UMSYN) subroutine in ATP/EMTP. The generator is connected to the Generator Circuit Breaker (GCB) through isolated phase bus to both (22/500 kv, 861 MVA) Delta/Star-earthed GSUT and (22/6.6/6.6 kv, 42 MVA) delta/star-earthed/star-earthed UAT. System parameters are given in the Appendix and full detailed data are presented in [21]. The Differential protection current relay with harmonic restraint is simulated using (W1RELAY87T) in ATP/EMTP with three different settings. A model before the relay is used to calculate the phasor in real and imaginary parts of a time domain signal by Fourier transform algorithm. Different settings are used to evaluate the performance of the unit overall differential protection of the power generation unit as shown in Figure(4) and Table (1). Based on the level of differential current, three levels of the settings are considered as follows: Balanced Setting (S 2 ): It uses a setting between two above cases for pickup, slope and harmonic to provide a balanced protection system for security and stability as shown in Table (1). High Secure Setting (S 3 ): It uses a maximum recommended setting for pickup and slope with Minimum harmonic restraint to provide a maximum security for the system as shown in Table (1). The performance evaluation of the three different settings is conducted via evaluating the reliability of each one. The reliability can be defined as the ability to not to fail in its function. The % reliability is 100 % if there no an incorrect trip and number of correct trips are equal to a number of the desired trips. Thus, the % reliability of each relay setting can be calculated as; % High (S 1) Balance (S 2) Secure (S 3) Table (1): Relay Setting Delay Pickup SLP-m 1 SLP-m 2 Harmonic 0 Sec 0.1 Sec 0.2 Sec 15% (up to 2 pu) 15% 15% 35% 25% (up to 1 pu) 25% 50% 25% 35% (up to 0 pu) 30% 80% 15% where no.: refers to the number. The % reliability of each relay setting combines both the % dependability and % security. Dependability is the degree of certainty that the relay will correctly operate. The % dependability is 100 % if the relay trips under all desired trips cases regardless the incorrect trip cases. Thus, the % dependability can be obtained as; (4) High Sensitive Setting (S 1 ): It uses the minimum recommended setting for both pickups and slope with maximum harmonic restraint in order to provide a maximum available sensitivity as depicted in Table (1). On the other hand, the security can be defined as the degree (5) Id Figure (4): Relay Setting of certainty that the relay will not operate incorrectly. The % security is 100 % if the relay does not incorrectly trip and Reference Number: JO-P

5 thenumber of the incorrecttrips is equal to zero. Therefore, the % security can be estimated as; (6) Figure(6.a). Figure(6.b) and Figure(6.c) shows that the relay using the balance setting (S 2 ) and secured setting (S 3 ) are does not sense this fault. Consequently, the balance and the secured settings are the best setting for external fault and grid disturbances as the setting values are very high and relay avoiding to operate. IV. EVALUATION RESULTS AND ANALYSIS Different tested cases (150 cases) are selected based on worst scenarios of either normal or faulty conditions. Simulations have been divided into three main categories and eight groups. The first category is the external faults. The second one is the internal faults. The third one is the normal operations such as load rejection and synchronization of generator with the grid. Many of system and generator prefault parameters are also investigated for max/min active power during zero, minimum, and maximum reactive power covering the generator capability curve limitation. The performance of the three sets had been tested under all possible faults types which are single line to ground, double line, double line to ground, and three line faults. Figure (5): Relay Response under an External Fault The response of the three settings under the, first category, 48 heavy external faults where 24 of these cases are downstream the high voltage side of the GSUT transformer and the others are downstream the Medium voltage side of the UAT transformer are as follows. These faults are tested under two different load levels. Both the balanced Setting (S 2 ) and high Secure Setting (S 3 ) have immunity against these external faults. On the other hand, the high sensitive setting (S 1 ) suffered from 12 false tripping cases where 6 cases were downstream the GSUT transformer and the others were downstream the UAT transformer as illustrated in Table (2). G Table (2): Simulation Results of External Fault Cases N Fault Type Pre-fault No. of False Trip Load S 1 S 2 S Fault at GSUT HV side Light Load Fault at GSUT HV side Full Load Fault at UAT LV side Light Load Fault at UAT LV side Full Load Total No. of Mal-operations Accuracy 75% 100% 100% Note: G denotes group number; N denotes the number of cases studied related to same group tests; and No. number. Figure(5) illustrates the performance of the relay using (S 1, S 2, and S 3 ) under three-phase external fault occurred at the medium voltage side of the UAT transformer. Under this condition, a false tripping is recorded as illustrated in Figure (6): Relay Response under an External Fault a) High Sensitive Setting b) Balanced Setting c) High Secure Setting The response of the three settings under the second category, 72 of internal low current fault cases are between the generator and GSUT/UAT transformers low voltage side. These faults are tested under two different load levels. All settings have failed cases to detect these internal faults. 48 of these cases not detected by secure setting (S 3 ) and 11 cases by balanced setting (S 2 ) and 4 cases by high sensitive setting (S 1 ) as shown in Table (3). The majority of mal-operation for low voltage side of UAT as the current at fault it s very small and near to normal load current (when compared to generator capacity). Two mal-operation for (S 3 ) during single-line-toground fault at GSUT Low voltage side (generator terminal) result from transformer delta connection as isolate a zero sequence component from the network side. In addition to the generator grounded through a transformer, only phase-to- Reference Number: JO-P

6 phase, or three-phase faults can be detected by the differential protection [23]. The remaining three mal-operation cases are for three-phase fault and six cases are for phase-to-phase faults at GSUT LVside with (S 3 ) setting and generator full load. On the other hand, only one mal-operation case occurs for phase-to-phase at GSUT LV side with (S 2 ) setting and generator full load. G TABLE (3): Simulation Results of Internal Fault Cases N Fault Type Pre-faults No. of No-Trip Load S 1 S 2 S Fault at GSUT HV side Light Load Fault at GSUT HV side Full Load Fault at GSUT LV side Light Load Fault at GSUT LV side Full Load Fault at UAT LV side Light Load Fault at UAT LV side Full Load Total No. of Mal-operations Accuracy 94.4% 84.7% 33.3% Figure(7)show the performance of the relay using (S 1, S 2, and S 3 ) under three-phase internal fault occurred at high voltage GSUT transformer side. Under this condition, the relay tripped instantaneous without time delay for high sensitive setting (S 1 ). On the other hand, the setting (S 2 ) and value within tripping zone but the relay trips with delay after 0.38 seconds after fault as shown in Figure(8). The relay with secure setting (S 3 ) does not trip during three line internal fault at GSUT high voltage side. The sensitive setting is the best setting for internal faults as the setting values are low high and relay avoiding a block operation. The balance setting can consider a reliable but with time delay Phase A Phase B Phase C S1 S2 S3 Figure (8): Relay Response in Internal Fault a) High Sensitive Setting b) Balanced Setting c) High Secure Setting The response of the three settings under the third category, 30 of normal operation scenario for load rejection and synchronization. The load rejection cases are tested under full load and 60% of full load with the unit run back to house load (group 1) and zero load (group 2). The high sensitive setting (S 1 ) have false tripping cases with all groups of these normal operation scenarios. The setting is failed to prevent false tripping with all load rejection (house load) cases and 4 cases of load rejection (zero load). 18 synchronization cases are tested when closing the GCB at different angles from -10 to +10 degree and voltage tolerances ±5% of rated voltage. 8 of these cases has false tripping with the high sensitive setting (S 1 ) as shown in 0 G Table (4): Normal Operation Cases N Fault Type No. of Mal-Operation S 1 S 2 S Load Rejection to House Load Load Rejection to Zero Load Synchronization Total No. of Mal-operations Accuracy 40% 100% 100% Restraint Current (A) Figure (7): Relay Response in Internal Fault Figure (9): Active and Reactive Power(Load Rejection to House Load) Reference Number: JO-P

7 72 Internal Fault Normal Operation Total No. of Mal-operations Accuracy 77.3% 92.6% 68% Correct Trip Figure (10): Voltage Per-Unit (Load Rejection to House Load) Incorrect Trip Desired Trip Total Trip Dependability (1) 94.44% 84.72% 33.33% Security (2) 69.38% 100% 100% Reliability (3) 66.67% 84.72% 33.33% Figure (11): Relay Response (Load Rejection to House Load) a) High Sensitive Setting b) Balanced Setting c) High Secure Setting Figure(11) illustrates the performance of the relay using (S 1, S 2, and S 3 ) under full load rejection occurred after the unit run back to house load. In this case, the voltage increase up to 140% of rated voltage until generator excitation control system as shown in Figure(10). Under this condition, a false tripping is recorded for high sensitive setting (S 1 ) as illustrated in Figure(11). Consequently, the balanced and secured settings are the best setting for normal operation and system disturbance condition as the setting values are very high and relay avoiding to operate. The dependability, security, and reliability evaluation are performed based on (4), (5), and (6) and recorded in Table (5) under all studied cases. The % dependable of the three settings S 1, S 2, S 3 is 94.44, 84.72, and %, respectively. On the other hand, % security of the three settings S 1, S 2, S 3 is 69.38, 100, and 100 %. Consequently, the % reliability of the three settings S 1, S 2, S 3 is 66.67, 84.72, and %. Finally, the engineering relay setting designer can use accuracy, dependability, security, and reliability percentage in Table (5) as a guideline to understanding the advantage and disadvantage of each setting. N Fault Type Table (5): Summary of Simulation Results No. of Mal-Operation S 1 S 2 S 3 48 External Fault V. CONCLUSION This paper mainly focuses on the performance evaluation of all possible settings of unit overall differential protection. The investigation is accomplished under normal and abnormal operating conditions. The results showed that the sensitive setting suffered from the unnecessary trip under certain normal operations and external faults conditions. On the other hand, the secure and balanced settings suffered from both disability in avoiding faulty blocking and low-speed tripping under certain internal fault conditions. The high sensitive setting provides high sensitivity for the relay with % dependability percentage, whereas it is accurate with 77.3% accuracy and it is reliable with % due to lowing the security percentage. The balanced setting can avoid the mal-operation cases of the high sensitive setting under external or normal operation conditions, whereas it suffered from mal-operation under other internal fault cases with 92.6% accuracy recording % dependability equal to %. The secured setting can also avoid all mal-operation under external or normal operating conditions but with less accuracy (68%) and dependability (33.33 %) percentages under internal fault conditions compared with the balanced setting. Finally, the engineering relay setting designer can use accuracy percentage presented in this paper as a guideline to understanding the advantage and disadvantage of each setting. Coordinating the unit overall differential protection is the main future prospective work. VI. REFERENCES [1] Das, A., Dhar, S., Royburman, S., &Sanyal, A., The Efficacy of Generator Protection under Sudden Loss of Excitation using Offset-type MHO-relay. Journal of the Institution of Engineers (India): Series B, 98(1), , 2017 [2] S. Patel et al., Performance of generator protection during major system disturbances, IEEE Trans. Power Deliv., vol. 19, no. 4, pp , 2004 [3] G. Roger Bérubé, Les M. Hajagos, Coordination of Under Excitation Limiters and Loss of Excitation Reference Number: JO-P

8 Relays with Generator Capability, in Proceedings of the IEEE Power and Energy Society General Meeting, 2009 [4] M. Elsamahy, S. O. Faried, and T. Sidhu, Impact of Midpoint STATCOM on Generator Loss of Excitation Protection, Power Deliv. IEEE Trans., vol. 29, no. 2, pp , 2014 [5] M. Elsamahy, S. O. Faried, T.S. Sidhu, R. Gokaraju, Enhancement of the Coordination between Generator Phase Backup Protection and Generator Capability Curves in the Presence of a Midpoint STATCOM using Support Vector Machines, IEEE Transactions on Power Delivery, Vol. 26, No. 3, pp , July 2011 [6] North American Electric Reliability Council (NERC), Technical Analysis of the August 14, 2003, Blackout: What Happened, Why, and What Did we learn?, July [7] M. Elsamahy, S. O. Faried, and R. Gokaraju, Impact of Midpoint Statcom on The Coordination between Generator Distance Phase Backup Protection and Generator Capability Curves, presented at the IEEE Power Energy Soc. Gen. Meeting, Minneapolis, MN, USA, [8] C. J. Mozina, M. Reichard, and Z. Bukhala, Working Group J-5 of the Rotating Machinery Subcommittee of the Power System Relay Committee, Coordination of generator protection with generator excitation control and generator capability, Proc. IEEE Power Eng. Soc. Gen. Meeting, FL, pp. 1 17, [9] IEEE Guide for AC Generator Protection,IEEEStd C [10] IEEE Guide for Protecting Power Transformers, IEEE Std C [11] Boldea, Ion., The Electric Generators Handbook- Synchronous Generators. CRC Press, 2015 [12] IEEE Guide for Abnormal Frequency Protection for Power Generating Plants, IEEE Std C [13] C. Mozina and J. Gardell, IEEE tutorial on the protection of synchronous generators (second edition, IEEE Power Eng. Soc. Special Publ. IEEE Power Syst. Relay. Committee, [14] Xu, X., H. Li, and H. Wen., Performance evaluation of busbar protection schemes under different fault scenarios, Power Electronics and ECCE Asia (ICPE-ECCE Asia), 9th International Conference on. IEEE, [15] Darwish, H. A., et al., Experimental evaluation of power differential relay for transmission line protection, Power Systems Conference and Exposition, PSCE'09. IEEE/PES. IEEE, [16] Tavares, Karla Antunes, and KleberMelo Silva. "Evaluation of power transformer differential protection using the atp software." IEEE Latin America Transactions,pp , [17] H. Weng and X. Lin, Studies on the unusual [18] X. Lin, H. Weng, P. Liu, B. Wang, and Z. Bo, Analysis of a sort of unusual mal-operation of transformer differential protection due to the removal of external fault, IEEE Trans. Power Deliv., vol. 23, no. 3, pp , [19] Guzman, Armando, et al., A current-based solution for transformer differential protection. I. Problem statement, IEEE Transactions on power delivery,pp , [20] Guzman, Armando, et al. A current-based solution for transformer differential protection. II. Relay description and evaluation, IEEE Transactions on Power Delivery, pp , [21] W. Yousef, M. A. Elsadd, A. Y. Abdelaziz and M. A. Badr, Simulation of large thermal power plant for protection purposes using ATP/EMTP,Nineteenth International Middle East Power Systems Conference (MEPCON), pp , [22] Blackburn, J. Lewis, and Thomas J. Domin, Protective relaying: principles and applications. CRC press, [23] SIEMENS SIPROTEC 7UT6 Differential Protection Relay, User Manual V4.0, [24] General Electric, G60 Instruction Manual for 7.6 Product version G60 Generator Management Relay, V AF2, [25] ABB, Distribution Automation Handbook, Section 8.12; Generator Protection, Network Parameters: Appendix 500 kv±10%, 50 Hz ±2.5%. Generator Parameters Steam Turbine Synchronous Generator with static excitation 834 MVA, 22 ± 5% kv, 50 Hz, 3000 rpm with power factor ranges: 0.85 lagging to 0.9 leading. Grounding transformer (22/ 3)/0.5 kv, 70 kva, kva, 50 Hz with grounding resistor 2.56, A, 500 V Static Excitation system according to IEEE 421 connected to generator main bus 5722 A/561 V at full load Generator Step Up Transformer Parameters: Bank of three single phase transformer connected Y/ 861 MVA, 50 Hz, 500/22 kv, 15% impedance. Reference Number: JO-P

9 Unit Auxiliary Transformer Parameters: Three winding, three-phase transformer /Y/Y, 42/24/24 MVA, 50 Hz, 22/6.6/6.6 kv, 15% impedance, low voltage wining connected to ground through neutral grounding resistance Reference Number: JO-P