This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2017.2759502, IEEE Transactions on Industrial Informatics Improving Synchronous Generator Parameters Estimation Using d-q Axes Tests and Considering Saturation Effect B. Zaker, G. B. Gharehpetian, Senior Member, IEEE, and M. Karrari, Senior Member, IEEE Abstract— Fundamentals of parameter estimation of SG have already been presented in different standards such as IEEE Std. 115. The first proposed methods require short circuit tests and/or some tests for which the synchronous generator should be out of service. In recent reports, however, to avoid the shortcomings of former methods, partial load rejection tests on d-q axes have been recommended to estimate the electrical parameters of SG such as different reactances and time constants. In this paper, it is first shown that the standard well-known methods are valid when there is no saturation effect. Therefore, a new method is proposed to improve SG parameters estimation taking into account the saturation effect. The proposed method uses saturation curve parameters, rotor angle and analytical equations of the SG alongside the load rejection tests results. To show the accuracy and precision of the proposed method, it is applied to experimental data of an 80 MVA gas turbine unit, and the results are discussed. Xf Total reactance of excitation winding. XD, XQ Total reactances of damper windings. Xmd, Xmq Mutual reactances of direct and quadrature axes. rs, rfd Resistance of stator and excitation windings. rD, r Q Resistance of damper windings. T’do Transient open-circuit time constants of direct axis. T”do, T”qoSubtransient open-circuit time constants of direct and quadrature axes. S1.0 Saturation parameter in 1.0 pu stator voltage. S1.2 Saturation parameter in 1.2 pu stator voltage. Ag, Bg Parameters of quadrature approximation of the saturation curve. csat, ksat Parameters of saturation effect. ym, ys Vectors of measured and simulated signal. Average of measured signal. ym Index Terms—Load rejection test, parameter estimation, rotor angle, saturation, synchronous generator. I. INTRODUCTION NOMENCLATURE E ω, ωb, δ Tm,Te, TD H ψd, ψq ψf ψ D, ψ Q ψm, vm ωb Pe, Qe vt, is vd, vq id, iq vfd, ifd iD, iQ Xld, Xlq Xlf XlD, XlQ Xd, Xq X’d X”d, X”q Internal voltage of machine. Rotor speed, base speed and rotor angle. Mechanical, electrical and friction torques. Rotor inertia. Flux linkage of direct and quadrature axis. Flux linkage of excitation winding. Flux linkage of damper windings. Magnetizing flux and induced voltage. Base speed. Active and reactive powers. Terminal voltage and stator current. Voltage of direct and quadrature axes. Current of direct and quadrature axes. Voltage and current of excitation winding. Current of damper windings. Leakage reactances of direct and quadrature axes. Leakage reactance of excitation winding. Leakage reactances of damper windings. Steady state reactances of direct and quadrature axes. Transient reactance of direct axis. Subtransient reactances of direct and quadrature axes. N R Number of samples. ECENT years, due to development and complexity of the power systems, the monitoring and protection schemes have gained greater importance. In this regard, the first step is having an accurate model of the power system which should be valid for different types of dynamic studies. Therefore, modeling and parameter estimation of power system components have been always a challenging issue. Among all the power system components, SG has been an important starting point for modeling and identification. Two categories of offline and online identification methods have been discussed and published in literature. Different standards have been provided for modeling and identification of power plant and SG parameters [1]-[4]. These standards have mostly used offline procedures to identify different SG parameters such as reactances, time constants, moment of inertia and damping factor. Besides the standards, many academic and industrial studies have been conducted on identification of SG parameters. In [5], Running Time-Domain Response (RTDR) tests such as the field short-circuit test, have been used to estimate the SG parameters. Multi-sinusoidal signals have been generated by a voltage source inverter for SG identification in [6]. Also, mixed stochastic-deterministic algorithms have been used for identification purposes in [7]. In [8], authors have B. Zaker, G. B. Gharehpetian, and M. Karrari are with the Electrical Engineering Department of Amirkabir University of Technology, Tehran, Iran (e-mail: zaker.behrooz@aut.ac.ir, grptian@aut.ac.ir, karrari@aut.ac.ir). 1551-3203 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2017.2759502, IEEE Transactions on Industrial Informatics applied step-voltage tests to SG and have estimated the parameters by means of a hybrid genetic algorithm-based method. DC excitation test has been utilized as a standstill method for identification in [9]. In addition to offline methods, many online ones have also been presented by researchers. In online identification methods, usually a small disturbance such as a step change in reference voltage of Automatic Voltage Regulator (AVR) is applied to SG and measured output signals such as terminal voltage and reactive power are used for identification. Indeed, these methods are a kind of modeling procedure with the aim of finding the best set of parameters to fit the output signals of the simulated system to the measured signals of the plant [10]. A third-order SG model has been identified using nonlinear least square method in [11]. Online measurements alongside rotor angle measurement have been utilized to identify the SG parameters in [12]. Authors in [13], have used measured signals of active and reactive power, terminal and field voltage, field current and rotor angle following of a small perturbation of field voltage to identify a third-order model of SG. Phasor Measurement Unit (PMU) data has been processed using an unscented Kalman filter for online parameter estimation of a fourth-order SG in [14]. SG parameters have been identified based on state space model using online measurements in [15] and [16]. In [17], Heffron-Phillips model of a single-machine infinite bus has been identified using small perturbation of the reference voltage. A multistage genetic algorithm-based identification procedure has been proposed in [18] to simultaneously identify the parameters of SG and excitation system without measuring the field voltage signal. This method is useful for brushless exciters where the field voltage is not accessible. In [19], a nonlinear term selection method has been used to determine the parameters which have considerable impacts on the machine response as an improvement in parameter estimation. Among the aforementioned researches, [10], [11], [13] and [15]-[18] have not considered the saturation effect of the synchronous generator in their proposed models and identification procedure. Although the saturated parameters have been estimated in [12], [14] and [19], but the saturation characteristic and unsaturated parameters have not been identified. In [23], only three parameters of synchronous generator, i.e. Xmd, Xmq and rfd, have been estimated. A parameter has been iteratively estimated for different operating points to consider the saturation effect. In this paper, the parameters of the SG is identified using two load rejection tests; one for d-axis parameters and another for q-axis. These tests have already been recommended in [1]. However, it is shown in the next sections that the proposed procedure of [1] is not accurate enough when the saturation effect is taken into account. Therefore, a new method is presented in this paper to overcome this drawback. Firstly, the saturation curve and corresponding parameters are extracted using experimental test results of an 80 MVA, 10.5 kV gas unit. Using these parameters, results of load rejection tests, and model of SG, the d-q parameters are identified. In the proposed method, d-q components of terminal voltage and stator current should be determined. In order to extract the d-q components of these signals, it is vital to measure the rotor angle. So, an accurate rotor angel metering technique has been designed to measure the rotor angle. Besides the load rejection tests, step changes are applied to reference voltage of excitation system and the measured results are compared to the simulated ones for the validation of the estimated parameters. The rest of the paper is organized as follows: model of SG and basics of load rejection tests are explained in Section II. In Section III, problem statement is outlined. The load angle metering technique is presented in Section IV. Experimental results and validation tests are discussed in Section V. Finally, Section VI concludes the paper. II. SG MODEL AND LOAD REJECTION TESTS A. SG Model The fundamentals of the SG model have well been explained in [20] and [21]. Considering the seventh-order nonlinear model of the SG, the mechanical part is represented by two state equations as follows: 1 2 H Tm Te TD (1) b 1 Besides the mechanical part, five state equations represent the electrical part of the SG as follows: d b v d rs i d q q b v q rs i q d (2) fd b v fd rfd i fd D b rD i D Q b rQ i Q where, d fd D X m d X m d i d Xd 1 X Xf X m d i fd md b X m d X m d X D i D X mq i q q 1 Xq X Q b m q X Q i Q X d X ld X m d X d X ld ( X m d || X lf ) X d X ld ( X m d || X lf || X lD ) X q X lq X m q (3) (4) X q X lq ( X m q || X lQ ) According to (2), the steady state values of the voltage, active and reactive powers are as follows: Pe v d i d v q i q Qe v q i d v d i q v q X d i d rs i q X (5) m d i fd v d X q i q rs i d B. Load Rejection Tests As recommended in [1]-[3], the d-axis load rejection test 1551-3203 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2017.2759502, IEEE Transactions on Industrial Informatics should be applied to SG in order to identify the reactances and time constants of the d-axis. Before the breaker tripping, the excitation system should be switched to manual control and the SG operating point should set to 0.0 pu of active power and about 0.1 pu absorption of reactive power. The zero value of the active power leads to the zero value of the rotor angle with vt=vq and vd=0. Also the stator current is aligned with the d-axis on this condition. The negative value of the reactive power causes under excited situation that consequently leads to voltage drop after breaker tripping. Using Fig.1, the steady state, transient and subtransient reactances are calculated as follows [1]-[3]: v 1 X d I (6) v 2 X d I v 3 Xd I According to annex F of [1], Δv2 and Δv3 are determined using the extended transient and subtransient periods of vt. Similar to aforementioned procedure, the q-axis test is recommended to identify the q-axis parameters. It is necessary to measure the rotor angle in order to set the steady state conditions for q-axis test [3]. The stator current is aligned with the q-axis by matching the rotor angle with power factor angle [3]. To meet this condition, about 0.1 pu of active power and reactive power absorption of a few percent of rated power is needed [3]. However, as it will be explained in Section III, these procedures have some shortcomings that makes them not applicable to real and none-ideal conditions. These drawbacks are as follows: The identification procedure of both direct and quadrature parameters using (6) is only valid when the saturation effect does not exist while the saturation exists in a real SG. To meet the steady conditions of the d-axis test, the active power should be set to zero while it is almost impossible in a power plant due to reverse power and low forward protection functions. In the next section, a new method will be proposed to overcome these shortcomings. III. PROBLEM STATEMENT To show the saturation effects on results of the d-q axes tests, a 50 MVA SG connected to infinite bus through a transformer is simulated by DIgSILENT software with known and preset parameters. The steady state conditions are set to 0 MW and -5 MVAr to meet the d-axis situation. The load rejection is simulated two times; once with and without considering saturation. The results are compared in Fig. 2. It can be seen that the steady state values of terminal voltage after breaker tripping have considerable difference. For analytical studies, it is assumed that the terminal voltages before and after breaker tripping are vq1 and vq2, respectively, in d-axis test. The stator current is equal to zero after breaker tripping. So, using (5), we have: v q 1 (X md v q2 X i fd md X l )i d rs i q X md i fd (7) If the saturation does not exist, Xmd remains constant during the test. Therefore, neglecting the stator resistance, the reactance of the d-axis can be calculated, as follows (as recommended in [1]): v v q 2 (8) X d v q1 id I However, since the saturation affects the mutual reactances of SG, above equations are not valid for real saturated conditions. Considering the saturation, the mutual reactances are not the same before and after breaker tripping while the terminal voltage changes from nominal value to a lower value during the load rejection tests. Therefore, (7) could be written as follows: v q 1 (X v q2 X m ds 1 X l )i d rs i q X i m ds 1 fd (9) m ds 2 i fd where, the s subscript indicates the saturated values. Using (9), the following equation can be written. v q 1 v q 2 X mds 1 X mds 2 i fd ( X mds 1 X l )i d rs i q (10) It can be seen that the reactance of the d-axis could not be easily calculated in this case. Indeed, due to saturation effect, the mutual reactance of the d-axis is not identical before and after breaker tripping. The saturation model could be approximated by different representations such as exponential and quadratic based on two parameters S1.0 and S1.2 of Fig.3 [21], [22]. Considering the scaled quadratic approximation [22], we have: Sat x B g x Ag 2 x (11) 1.2 Ag S1.2 S1.0 1.2 1.0 A 2 g 2 1.2 1.2 Ag 1.0 1.2 S1.2 S1.2 S1.0 S1.0 Bg , 1 A S1.0 2 At each operating point, the magnetizing flux is approximately equal to the induced voltage as follows: m v m v d X l i q rs i d v 2 q X l i d rs i q 2 (12) Finally, the saturation parameters are calculated as follows [22]: if v m A g then c sat B g v m A g vm 2 , k sat 1 1 c sat (13) if v m A g then c sat 0 , k sat 1 For each operating point, the saturated values of mutual reactances are calculated using saturation parameters as follows: 1551-3203 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2017.2759502, IEEE Transactions on Industrial Informatics X m ds k sat X mdu X m qs k sat X mqu (14) where, the u subscript indicates the unsaturated values [22]. Fig. 1. Terminal voltage and stator current during d-axis test. The key point of the SG parameter estimation is calculation of steady state reactances of d-q axes. The proposed method is summarized for a real power plant, as follows: Step1: Determination of saturation curve: Turbine and generator are started to reach the nominal speed (3000 rpm), while the excitation system is switched to manual control in order to control the excitation current. The generator breaker is kept open and the unit is on no load condition. The reference of the field current is manually and continuously changed so that the terminal voltage varies from 0.7 pu to 1.2 pu. The terminal voltage, excitation voltage and current are recorded by a high rate data logger during this test. Using these recorded signals, the saturation curve, S1.0, S1.2, Ag and Bg are determined. Step2: Determination of Xdu: After determining the saturation parameters, the next step is calculation of unsaturated value of Xd. At first, the unit is paralleled to the grid and it is tried to set the operating point to the ideal conditions of the d-axis test. However, as mentioned before, it is almost impossible to exactly set the active power to zero in a power plant due to reverse power and low forward protection functions. When the active power is not exactly equal to zero, the terminal voltage is not completely in the direction of the q-axis. Since the quadrature component of the terminal voltage is required to calculate the Xdu, a rotor angle metering device is designed and built, which will briefly be explained in the next section. Using the measured rotor angle, terminal voltage, stator current, active and reactive powers, the d-q components are calculated as follows: tan 1 Q / P (16) v v sin , v v cos d t q t i d i s sin , i q i s cos Fig. 2. Comparison of saturation effect on load rejection test results. Fig. 3. Obtaining the saturation parameters using open-circuit characteristic. Considering the aforementioned relations, (10) can be written as follows: v q 1 v q 2 X mdu k sat 1 k sat 2 i fd (15) ( X mdu k sat 1 X l )i d rs i q Due to under-excited condition of the test, the terminal voltage drops to much lower value than 1.0 pu after the breaker tripping. Hence, the operating point moves to knee point, where the open-circuit curve meets the air gap line. Therefore, it is assumed that the saturation effect after breaker tripping is negligible and ksat2=1: v q 1 v q 2 X mdu k sat 1 1 i fd (17) ( X mdu k sat 1 X l )i d rs i q The above equation includes two unknown variables Xmdu and Xl. Considering (12) and (13) it can be said that ksat1 is a nonlinear function of d-q components of (16) and Xl. The rs could also be neglected or set to a very small typical value. To solve this equation with two variables, it is assumed that Xl is proportional to Xmdu. The standards and references such as [2] and [21] presents typical values of Xdu and Xl. These data can be used for this purposes. Now, (17) is a nonlinear equation with one variable which could be solved by mathematics tools such as MATLAB software and then Xmdu will be determined. Using this value, Xl and Xdu could be calculated. Step 3: Determination of X’du and X”du: It should be noted that as shown in Fig. 1, Δv1 and Δv2 are considerably smaller than 1551-3203 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2017.2759502, IEEE Transactions on Industrial Informatics Δv3, which means the smaller values of X’du and X”du rather than Xdu. Therefore, these reactances are not significantly affected by the saturation effect. Firstly, using the measured signals and (6), the saturated values of X’d and X”d are calculated. Then, Xlf is calculated using the following equation: (18) X ds X l X mds || X lf where, Xmds is the result of the previous step as well as Xmdu. Finally, X’du could be determined as follows: (19) X du X l X mdu || X lf The same procedure is also carried out for X”du. Step 4: Determination of time constants: The time constants are calculated using extended periods of terminal voltage response as shown in Fig. 1. These parameters may need fine tuning during time-domain validation simulations in order to reach the highest accuracy. Step 5: Determination of q-axis parameters: The operating point is set to ideal conditions of q-axis test as mentioned before. The terminal voltage trend is similar to the d-axis test. However, the direct component of the terminal voltage is used in this step. Using (5), the equation which should be solved is as follows: (20) v d 1 0 (X mqu k sat 1 X l )i q rs i d Since the excitation current is not included in vd of (5), the direct component of the terminal voltage drops to zero after breaker tripping. In addition, Xl has already been determined in Step 2. Therefore, ksat1 is simply calculated using (12) and (13). Solving the linear equation of (20) leads to Xmqu and consequently, Xqu. It should be noted that the aforementioned steps can be used for round-rotor SGs. For salient-rotor SGs, Xld and Xlq are not identical. Therefore, the leakage reactances of (17) and (20) are Xld and Xlq respectively. For a salient-rotor SG, the estimation procedure of d-axis parameters is the same as ones described in Step 2-Step 4. The difference between these two cases is in the solving method of (20). Unlike the round-rotor case, in case of salient-rotor SG, Xlq is still unknown in Step 5. Thus, it is assumed that Xlq is proportional to Xmqu to eliminate one variable and solve (20). The standards and references such as [2] and [21] presents typical values of Xqu and Xlq. These data can be used for this purpose. Besides that, for a salient-rotor SG, ksatq is used to consider the saturation effect on q-axis parameters. According to [22], ksatq, as follows, is used instead of (13), while ksatd is calculated the same as before. 1 (21) k satq X m qu 1 c sat X m du It should be noted that Xmdu has been already determined in Step 2. Therefore, considering (21) and (20) and the aforementioned assumption between Xlq and Xmqu, (20) is changed to a nonlinear equation with one variable which could be solved by tools such as MATLAB software and then Xmqu will be determined. Using this value, Xlq and Xqu could be calculated. IV. LOAD ANGLE METER Load angle is defined as the angle difference between internal voltage E and terminal voltage (vt) of SG. Indeed, load angle could be interpreted as the difference of electrical angle between the terminal voltage and the reference axis on the rotor. In no load condition, vectors of E and vt are identical, so the angle difference between them is zero that means the load angle is equal to zero. When the SG is under load, the reference axis on the rotor advances in phase comparing to the zero crossing of vt. Therefore, as shown in Fig. 4, the load angle could be calculated by measuring the phase angle between a fixed point on the shaft and the zero crossing of vt. A real-time DSP-based load angle meter has been designed and built according to this theory. Two signals are used to obtain and calculate the load angle in this device as shown in Fig. 5. An optical encoder determines physical position and period of the rotor as the first input. The second input is SG voltage transformer (VT) output. Input signals are applied to a DSP based processor board. These signals are processed by DSPIC33J256 processor. Finally, the load angle is calculated as follows: (22) UL NL Fig. 4. Basics of load angle measuring. Fig. 5. Load angle meter connections. V. EXPERIMENTAL RESULTS AND VALIDATION The experimental tests have been applied to an 80 MVA Kraftwerk Union gas unit. The SG type is TLRI 93/36, 50 Hz, 1551-3203 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2017.2759502, IEEE Transactions on Industrial Informatics 10.5 kV with nominal power factor of 0.85. The machine rated values are given in Table I which are used in (1) and (3) as the base values. According to [21], base values of field voltage and currents are such chosen that at these vales, the terminal voltage on the air gap line is equal to nominal value of 10.5 kV. The static excitation system makes the measurement of the filed voltage and current possible. All the required signals have synchronously been measured by a 1 kHz data acquisition device. TABLE I BASE VALUES OF SG Variable Sb vb ib ifdb Value 80 MVA 10.5 kV 4.4 kA 194 A Variable ωb zb Tb vfdb Value 314 rad/s 1.3778 Ω 25.48x104 N.m 68 VDC A. Saturation Curve Test The results of the saturation curve test is presented in Fig. 6. As it is shown in this figure, due to overvoltage and isolation concerns, the terminal voltage has been increased to only about 11.5 kV. However, to determine the S1.2, it should be increased to 12.6 kV (1.2 pu). So, the corresponding field current for 12.6 kV is extrapolated by means of curve fitting toolbox of MATLAB using the measured trends of the terminal voltage and field current. The extrapolated point is shown in red in Fig. 6. Therefore, S1.0 and S1.2 are calculated as follows [21]: BC 220.2 194 0.1351 S 1.0 AB 194 (23) EF 352.58 227 0.5532 S 1.2 DE 227 Consequently using (11), we have Ag=0.8356 and Bg=4.9998. Fig. 7. Raw results of d-axis test. Fig. 8. Results of d-axis test in pu. B. d-Axis Test The raw results of the d-axis test is presented in Fig. 7. The terminal voltage is recorded from the VT. Therefore, the output is an AC signal and the RMS value of this signal is used for calculations. The active and reactive powers are measured as DC signals. The filtered and scaled values of these signals are presented in Fig. 8 in per-unit. As it is shown in Fig. 8, the breaker is opened in Pe=2.8 MW (0.035 pu) and Qe=-20 MVAr (-0.25 pu). Fig. 9. d-q components and rotor angle of d-axis test. Fig. 6. Saturation test result. 1551-3203 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2017.2759502, IEEE Transactions on Industrial Informatics Fig. 10. Excitation current of d-axis test. Using the measured rotor angle and (16), the d-q components of the terminal voltage and stator current of the d-axis test are calculated and presented in Fig. 9. It can be seen in this figure that due to small value of active power before load rejection, vd and iq are not exactly zero. The excitation current during this test is also shown in Fig. 10. Due to manual control mode of excitation, the current remains constant before and after tripping. The steady states values of Figs. 9 and 10 are given in Table II. Using these values, Ag, Bg and (12), (17) could be solved. It should be noted that as mentioned in step 2 of Section II, the ratio of Xl to Xmdu is considered as about 0.055 using the typical values to solve (17). The typical value of 0.001 pu is also considered for rs. The results of this solution are Xmdu, Xl, Xdu and ksat1, which are listed in Table III. The obtained values of the Xdu, Xl and the other parameters will be validated using three tests in different operating points in part D of this section. From (18), (19) and Fig. 11, which is the zoomed part of vq of Fig. 9, the transient and subtransient reactances of the d-axis are calculated as follows: X ds X l X mds || X lf v 2 0.9219 0.8094 0.0946 1.6848 || X i d 0.2701 0 X lf lf 0.3976 pu X du X l X mdu || X lf (24) 0.0946 1.6848 || 0.3976 X du 0.4176 pu The same procedure is done for X”du and the result is 0.3067 pu. The T’do and T”do have been calculated as 3.5 s and 0.45 s using extended periods of voltage as shown in Fig. 11. TABLE II STEADY STATE VALUES OF D-AXIS TEST Value before tripping 2.51 deg 0.0405 pu 0.9219 pu -0.2701 pu 0.0498 pu 106.4432 A Signal δ vd vq id iq Ifd Value after tripping 0.00 deg 0.0000 pu 0.4527 pu 0.0000 pu 0.0000 pu 106.4432 A TABLE III SOLUTION RESULTS OF (17) FOR D-AXIS TEST Parameter Xmdu Xl ksat1 Xdu Xmds1 Value 1.7202 pu 0.0946 pu 0.9794 1.8148 pu 1.6848 pu Fig. 11. Zoomed part of vq during d-axis test. C. q-Axis Test The measured rotor angle and d-q components of terminal voltage and stator current of q-axis test are presented in Figs. 12 and 13. The operating point of this test before breaker tripping is Pe=7.5 MW (0.094 pu) and Qe=-1.5 MVAr (-0.019 pu). The steady states values of Fig. 12 are given in Table IV. Using these values, Ag, Bg and (12), (20) is solved and we have: Xmqu=1.4905 pu. Using the predetermined value of Xl in previous step, we have: Xqu=1.5851 pu. Due to small value of voltage drop of d-axis and signal filtering, it is actually not possible to distinguish the portion of X”q in this drop. Therefore, T”qo and X”qu are considered identical to T”do and X”du. The ultimate parameters of the SG are given in Table V. They will be validated by time-domain tests in the next section. D. Validation Tests For validation purposes, a step additive signal is applied to the reference of AVR in different operating points and desired signals are recorded. The validation tests are carried out in different operating points (especially reactive power) to show the accuracy of the estimated saturation parameters as well as reactances. The measured excitation voltage is used as the input for simulations in DIgSILENT software. The outputs of the simulated SG with parameters of Table V are compared to the measured ones. The results are presented in Figs. 14-16. To evaluate the errors between the measured signals and simulated ones, R-squared index is used for both terminal voltage and reactive power as follows: N SS res y m y s 2 i 1 N SS tot y m y m 2 (25) i 1 R2 1 SS res SS tot where, the value of R2 varies from 0 to 1 and 1 indicates the best fitness and accuracy. The R-squared values for all three validation tests are given in Table VI. As it is shown in Figs. 14-16 and according to the R-squared values, the accuracy of 1551-3203 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2017.2759502, IEEE Transactions on Industrial Informatics the parameters of Table V are completely acceptable. To show and verify the sensitivity of simulation results, the simulations are carried out for operating point of Pe=47 MW and Qe=20 MVAr, while in each simulation, a certain parameter of Table V changes. The results for +10% and -10% change in Xd, -10% change in Xq and +20% change in T’do are shown in Figs. 17-20 respectively. As it is shown and expected, Xd has significant effect on the terminal voltage and reactive power, while Xq has the less. Besides that, when T’do changes from the estimated value of Table V, the settling times of terminal voltage and reactive power differ from the measured signals. Fig. 12. d-q components and rotor angle of q-axis test. Fig. 14. Validation test in operating point of Pe=47 MW and Qe=20 MVAr. Fig. 13. Zoomed part of vd during q-axis test. TABLE IV STEADY STATE VALUES OF Q-AXIS TEST Signal name δ vd vq id iq Value before the trip 9.04 deg 0.1537 pu 0.9621 pu -0.0073 pu 0.1024 pu Value after the trip 0.00 deg 0.0000 pu 0.9621 pu 0.0000 pu 0.0000 pu Fig. 15. Validation test in operating point of Pe=39 MW and Qe=2 MVAr. TABLE V FINAL PARAMETERS OF SG Parameter Xdu Xqu X’du X”du X”qu Xl Value 1.8148 pu 1.5851 pu 0.4176 pu 0.3067 pu 0.3067 pu 0.0946 pu Parameter T’do T”do T”qo S1.0 S1.2 - Value 3.50 s 0.45 s 0.45 s 0.1351 0.5532 - TABLE VI R-SQUARED VALUES OF VALIDATION TESTS Operating point Pe=47 MW, Qe=20 MVAr Pe=39 MW, Qe=2.0 MVAr Pe=44 MW, Qe=7.5 MVAr R-squared for vt 0.9861 0.9923 0.9915 R-squared for Qe 0.9926 0.9950 0.9961 1551-3203 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2017.2759502, IEEE Transactions on Industrial Informatics Fig. 20. Simulation sensitivity to +20% change in T’do in operating point of Pe=47 MW and Qe=20 MVAr. VI. CONCLUSION Fig. 16. Validation test in operating point of Pe=44 MW and Qe=7.5 MVAr. Fig. 17. Simulation sensitivity to -10% change in Xd in operating point of Pe=47 MW and Qe=20 MVAr. In this paper, a new method has been proposed to improve estimation of SG parameters using d-q axes tests considering saturation. It has been shown that the conventional method has shortcomings in presence of saturation. A load angle meter has been designed and built to extract the d-q components of the terminal voltage and stator current. The proposed method has been applied to an 80 MVA Kraftwerk Union gas turbine unit. The validation tests have been carried out in different operating point and the results have been compared to simulations of estimated parameters. It has been shown that the proposed method can accurately estimate the SG parameters taking into account the saturation effect. Besides the saturation effect, temperature variations are also impactful on SG parameters. These effects may be considered in the future works. REFERENCES [1] [2] [3] [4] Fig. 18. Simulation sensitivity to +10% change in Xd in operating point of Pe=47 MW and Qe=20 MVAr. [5] [6] [7] [8] Fig. 19. Simulation sensitivity to -10% change in Xq in operating point of Pe=47 MW and Qe=20 MVAr. “IEEE Guide for Test Procedures for Synchronous Machines Part-I Acceptance and Performance Testing Part-II Test Procedures and Parameter Determination for Dynamic Analysis,” IEEE Std. 115-2009 (Revision of IEEE Std. 115-1995) , pp.1-219, May 7 2010. “WECC Test Guidelines for Synchronous Unit Dynamic Testing and Model Validation,” Western System Coordinating Council, pp. 1-126, March 1997. IEEE Task Force on Generator Model Validation Testing of the Power System Stability Subcommittee, “Guidelines for Generator Stability Model Validation Testing,” 2007 IEEE Power Engineering Society General Meeting, Tampa, FL, pp. 1-16, 2007. “Power Plant Modeling and Parameter Derivation for Power System Studies,” Electric Power Research Institute (EPRI), pp. 1-104, Aug. 2007. R. Wamkeue, C. Jolette, A. B. MpandaMabwe, and I. Kamwa, “CrossIdentification of Synchronous Generator Parameters From RTDT Test Time-Domain Analytical Responses,” IEEE Trans. Energy Conversion, Vol. 26, No. 3, pp. 776-786, Sept. 2011. T. L. Vandoorn, F. M. De Belie, T. J. Vyncke, J. A. Melkebeek, and P. Lataire, “Generation of Multisinusoidal Test Signals for the Identification of Synchronous-Machine Parameters by Using a Voltage-Source Inverter,” IEEE Trans. Industrial Electronics, Vol. 57, No.1, pp. 430-439, Jan. 2010. M. A. Arjona, M. Cisneros-Gonzales, and C. Hernandez, “Parameter Estimation of a Synchronous Generator Using a Sine Cardinal Perturbation and Mixed Stochastic-Deterministics Algorithms,” IEEE Trans. Industrial Electronics, Vol. 58, No.2, pp.486-493, Feb. 2011. M. A. Arjona, C. Hernandez, M. Cisneros-Gonzales, R. Escarela-Perez; “Estimation of Synchronous Generator Parameters Using the Standstill Step-Voltage Test and a Hybrid Genetic Algorithm,” International Journal of Electrical Power and Energy Systems, vol. 35, pp. 105-111, 2012. 1551-3203 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2017.2759502, IEEE Transactions on Industrial Informatics [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] M. Hasni, O. Touhami, R. Ibtiouen, M. Fadel, and S. Caux, “Estimation of Synchronous Machine Parameters by Standstill Tests,” Mathematics and Computers in Simulation, No. 81, pp. 277-289, 2010. B. Zaker, G. B. Gharehpetian, M. Mirsalim, and N. Moaddabi, “PMUBased Linear and Nonlinear Black-Box Modeling of Power Systems,” In Proc. ICEE 2013, Mashhad, 2013, pp. 1-6. M. Dehghani, and S. K. Y. Nikravesh; “Nonlinear state space model identification of synchronous generators,” Electric Power System Research, Vol. 78, pp. 926-940, 2008. M. Karrari, and O. P. Malik, “Identification of Physical Parameters of a Synchronous Generator from Online Measurements,” IEEE Trans. Energy Conversion, Vol. 19, No. 2, pp. 407-415, 2004. E. Ghahremani, M. Karrari, and O. P. Malik, “Synchronous Generator Third-Order Model Parameter Estimation Using On-Line Experimental Data,” IET Gener., Transm. and Distrib., Vol. 2, No. 5, pp. 708-719, 2008. E. Ghahremani, I. Kamwa, “Online Estimation of a Synchronous Generator Using Unscented Kalman Filter From Phasor Measurements Units,” IEEE Trans. Energy Conversion, Vol. 26, No. 4, pp. 1099-1108, Dec. 2011. P. Kou, J. Zhou, C. Wang, H. Xiao, H. Zhang, C. Li, “Parameters Identification of Nonlinear State Space Model of Synchronous Generator,” Engineering Applications of Artificial Intelligence, vol. 24, pp. 1227-12-37, 2011. M. Dehghani and S. K. Y. Nikravesh, “State-Space Model Parameter Identification in Large-Scale Power Systems,” IEEE Trans. Power Systems, Vol. 23, No. 3, pp. 1449-1457, Aug. 2008. B. Zaker, G. B. Gharehpetian, and N. Moaddabi, “Parameter Identification of Heffron-Phillips Model Considering AVR Using On-line Measurements Data,” presented at the Int. Conf. on Renewable Energies and Power Quality (ICREPQ’14), Cordoba, Spain, April 8-10, 2014. B. Zaker, G. B. Gharehpetian, M. Karrari and N. Moaddabi, “Simultaneous Parameter Identification of Synchronous Generator and Excitation System Using Online Measurements,” in IEEE Trans. Smart Grid, vol. 7, no. 3, pp. 1230-1238, May 2016. M. Rasouli and C. Lagoa, “A Nonlinear Term Selection Method For Improving Synchronous Machine Parameters Estimation,” Electric Power and Energy Systems, Vol. 85, pp. 77-86, 2017. Y. N. Yu, Electric Power System Dynamic. New York: Academic Press, 1983. P. Kundor, Power System Stability and Control. New York: McGrawHill, 1994. DIgSILENT Power Factory Technical Reference Documentation, Synchronous Machine. E. Kyriakides, G. T. Heydt and V. Vittal, “Online Parameter Estimation of Round Rotor Synchronous Generators Including Magnetic Saturation,” IEEE Trans. Energy Conversion, Vol. 20, No. 3, pp. 529-537, Sept. 2005. Prof. G. B. Gharehpetian received his Ph.D. degree in electrical engineering 1996 from Tehran University, Tehran, Iran, graduating with First Class Honors. As a Ph.D. student, he has received scholarship from German Academic Exchange Service from 1993 to 1996 and he was with High Voltage Institute of RWTH Aachen, Aachen, Germany. He has been holding the Assistant Professor position at AUT from 1997 to 2003, the position of Associate Professor from 2004 to 2007 and has been Professor since 2007. He was selected by the ministry of higher education as the distinguished professor of Iran and by IAEEE as the distinguished researcher of Iran and was awarded the National Prize in 2008 and 2010, respectively. Based on the ISI Web of Science database (2005-2015), he is among world’s top 1% elite scientists according to ESI (Essential Science Indicators) ranking system. He is the author of more than 1000 journal and conference papers. His teaching and research interest include Smart Grid, DGs, Monitoring of Power Transformers, FACTS Devices, HVDC Systems, and Power System Transients. Prof. M. Karrari received the Ph.D. degree in control engineering from Sheffield University, Sheffield, U.K., in 1991. Since 1991, he has been with the Amirkabir University of Technology, Tehran, Iran. He is author or coauthor of more than 150 technical papers and three books. His main research interests are power system modeling, modeling and identification of nonlinear dynamic systems, and large-scale and distributed systems. B. Zaker was born in Shiraz, Iran in 1989. He received the B.S. degree in electrical power engineering from Shiraz University, Shiraz, Iran, in 2011; the M.S. degree in electrical power engineering from Amirkabir University of Technology Tehran, Iran, 2013. He is currently pursuing the Ph.D. degree in electrical power engineering at Amirkabir University of Technology. He has a lot of practical experience in modeling and parameter estimation of power plants in Iran. His research interests include system identification, power system dynamics, distributed generation systems, and microgrids. 1551-3203 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. 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