阅读说明：本技术 发电机的角确定 (Angle determination of a generator ) 是由 J.德姆哈特 S.达斯古普塔 M.克赖斯尔 A.K.古普塔 V.S.K.M.巴利耶帕利 于 2019-05-30 设计创作，主要内容包括：本文中公开了一种确定发电机系统(10)的负载角和/或转子角的方法,其中所述发电机系统(10)包括发电机(11)、变压器(16)和公共耦合点PCC端子(17),所述发电机(11)具有用于输出由所述发电机(11)生成的电力的发电机端子(15),所述方法包括：确定所述发电机(11)的励磁电流；确定来自所述发电机端子(15)的输出电压、来自所述发电机端子(15)的输出电流和来自所述发电机端子(15)的所述输出电压和所述输出电流的功率因数角和/或功率因数,并取决于所确定的励磁电流、来自所述发电机端子(15)的输出电压、来自所述发电机端子(15)的输出电流和所述功率因数角和/或所述功率因数来确定所述发电机系统(10)的所述负载角。(disclosed herein is a method of determining a load angle and/or a rotor angle of a generator system (10), wherein the generator system (10) comprises a generator (11), a transformer (16) and a point of common coupling, PCC, terminal (17), the generator (11) having a generator terminal (15) for outputting electrical power generated by the generator (11), the method comprising: determining an excitation current of the generator (11); determining an output voltage from the generator terminals (15), an output current from the generator terminals (15) and a power factor angle and/or a power factor of the output voltage and the output current from the generator terminals (15) and determining the load angle of the generator system (10) depending on the determined excitation current, the output voltage from the generator terminals (15), the output current from the generator terminals (15) and the power factor angle and/or the power factor.)

1. a method of determining a load angle and/or a rotor angle of a generator system (10), wherein the generator system (10) comprises a generator (11), a transformer (16) and a point of common coupling, PCC, terminal (17), the generator (11) having a generator terminal (15) for outputting electrical power generated by the generator (11), wherein the transformer (16) is arranged between the generator terminal (15) and the PCC terminal (17), the method comprising:

determining an excitation current of the generator (11);

Determining an output voltage from the generator terminals (15), an output current from the generator terminals (15) and a power factor angle and/or a power factor of the output voltage and the output current from the generator terminals (15) and determining the load angle of the generator system (10) depending on the determined excitation current, the output voltage from the generator terminals (15), the output current from the generator terminals (15) and the power factor angle and/or the power factor; and/or

Determining an output voltage from the PCC terminal (17), an output current from the PCC terminal (17) and a power factor angle and/or a power factor of the output voltage and the output current from the PCC terminal (17) and determining the rotor angle of the generator system (10) depending on the determined excitation current, the output voltage from the PCC terminal (17), the output current from the PCC terminal (17) and the power factor angle and/or the power factor.

2. The method of claim 1, wherein the generator system (10) further comprises a mechanical drive system (12), the mechanical drive system (12) being arranged to drive the generator (11) such that the generator (11) generates electrical power.

3. The method of claim 1, wherein determining the output voltage and the output current from the generator terminal (15) and/or the PCC terminal (17) comprises measuring characteristics of the output voltage and the output current.

4. The method of claim 1, wherein determining the field current of the generator (11) comprises measuring the field current of the generator (11).

5. The method of claim 1, further comprising filtering one or more of the determined output voltage, output current, and excitation current to remove noise components.

6. The method of claim 1, wherein determining the load angle and/or the rotor angle of the generator system (10) comprises:

determining an open circuit voltage of the generator (11) in dependence on the excitation current and an open circuit characteristic of the generator (11); and

Determining the load angle and/or the rotor angle of the generator system (10) depending on the determined open circuit voltage of the generator (11).

7. The method of claim 6, wherein the open circuit characteristic of the generator (11) is predetermined data, the predetermined data being one or more of calculated, simulated, estimated and measured.

8. The method of claim 6, wherein the generator (11) is a non-salient pole rotor; and

The load angle is determined as:

Wherein:

δ is the rotor angle;

V_tIs the rms value of the output voltage from the generator terminal (15);

I_tIs the rms value of the output current from the generator terminal (15);

E is the rms value of the determined open circuit voltage;

θ is the power factor angle; and

R is the internal resistance of the generator (11).

9. the method of claim 6, wherein the generator (11) is a non-salient pole rotor; and

The rotor angle is determined as:

Wherein:

δ is the rotor angle;

V_pIs the rms value of the output voltage from the PCC terminal (17);

I_pis the rms value of the output current from the PCC terminal (17);

E is the rms value of the determined open circuit voltage;

θ is the power factor angle; and

r is the internal resistance of the generator (11).

10. the method of claim 6, wherein the generator (11) is a salient pole machine; and

The load angle is determined as:

wherein:

δ is the rotor angle;

V_tis the rms value of the output voltage from the terminal (15);

I_tIs the rms value of the output current from the terminal (15);

E is the rms value of the determined open circuit voltage;

θ is the power factor angle;

R is the internal resistance of the generator (11);

X_dis a nominal direct axis synchronous reactance; and

X_qIs a nominal quadrature-axis synchronous reactance.

11. The method of claim 6, wherein the generator (11) is a salient pole machine; and

the rotor angle is determined as:

Wherein:

δ is the rotor angle;

V_pis the rms value of the output voltage from the PCC terminal (17);

I_pIs the rms value of the output current from the PCC terminal (17);

E is the rms value of the determined open circuit voltage;

θ is the power factor angle;

r is the internal resistance of the generator (11);

X_dIs a nominal direct axis synchronous reactance; and

X_qIs a nominal quadrature-axis synchronous reactance.

12. the method of claim 1, wherein the power output from the generator system (10) is less than 30 MW.

13. a method of determining whether an out-of-sync condition has occurred, the method comprising:

Determining a load angle and/or a rotor angle of the generator system (10) according to the method of claim 1; and

it is determined whether an out-of-step condition has occurred depending on the determined load angle and/or rotor angle.

14. an electrical generator system (10), comprising:

a generator (11), a transformer (16) and a point of common coupling, PCC, terminal (17), the generator (11) having a generator terminal (15) for outputting power generated by the generator (11), wherein the transformer (16) is arranged between the generator terminal (15) and the PCC terminal (17); and

One or more computing devices (20) configured to determine a load angle and/or a rotor angle of the generator system (10) according to the method of claim 1.

15. An electrical generator system (10), comprising:

a generator (11), a transformer (16) and a point of common coupling, PCC, terminal (17), the generator (11) having a generator terminal (15) for outputting power generated by the generator (11), wherein the transformer (16) is arranged between the generator terminal (15) and the PCC terminal (17); and one or more computing devices (20) configured to determine an out-of-sync condition according to the method of claim 13.

16. a computer program which, when executed by a computing device (20), causes the computing device (20) to determine a load angle and/or a rotor angle of a generator system (10) according to the method of any of claims 1 to 12 and/or to determine an out-of-step condition according to the method of claim 13.

17. A computing device (20) configured to determine a rotor angle and/or out-of-step condition of a generator system (10) by executing the computing program of claim 15.

Technical Field

the present disclosure relates to determining a load angle and/or a rotor angle in an electrical power generator driven by a prime mover, such as a reciprocating engine or a gas/steam/wind turbine or an electric motor for power grid applications. The techniques disclosed herein provide for accurate determination of the load angle and/or rotor angle during high load conditions when magnetic saturation of the generator is prominent. The techniques disclosed herein are particularly useful for detecting when an out-of-sync condition has occurred.

Background

There is a general need to improve upon known load angle and/or rotor angle determination techniques.

disclosure of Invention

according to a first aspect, a method of determining a load angle or a rotor angle of a generator system is provided, wherein the generator system comprises a generator, a transformer and a point of common coupling, PCC, terminal, the generator having a generator terminal for outputting electrical power generated by the generator, wherein the transformer is arranged between the generator terminal and the PCC terminal, the method comprising: determining an excitation current of the generator; determining an output voltage from the generator terminals, an output current from the generator terminals and a power factor angle and/or a power factor of the output voltage and the output current from the generator terminals and determining the load angle of the generator system in dependence on the determined excitation current, the output voltage from the generator terminals, the output current from the generator terminals and the power factor angle and/or the power factor; and/or determining an output voltage from the PCC terminal, an output current from the PCC terminal and a power factor angle and/or a power factor of the output voltage and the output current from the PCC terminal, and determining the rotor angle of the generator system in dependence on the determined excitation current, the output voltage from the PCC terminal, the output current from the PCC terminal and the power factor angle and/or the power factor.

the method may comprise a generator system further comprising a mechanical drive system arranged to drive a generator such that the generator generates electrical power.

The method may comprise determining an output voltage and an output current from the generator terminal and/or the PCC terminal, comprising measuring characteristics of the output voltage and the output current.

The method may comprise determining the field current of the generator by measuring the field current of the generator.

the method may further include filtering one or more of the determined output voltage, output current, and excitation current to remove noise components.

the method may comprise determining a load angle and/or a rotor angle of the generator system by: determining an open circuit voltage of the generator in dependence on the field current and the open circuit characteristic of the generator; and determining a load angle and/or a rotor angle of the generator system in dependence of the determined open circuit voltage of the generator.

the method may include the open circuit characteristic of the generator being predetermined data, the predetermined data being one or more of calculated, simulated, estimated and measured.

The method may include the generator being a non-salient rotor; and the load angle is determined as:

wherein:

δ is the rotor angle;

V_tis the rms value of the output voltage from the generator terminals;

I_tis the rms value of the output current from the generator terminals;

e is the rms value of the determined open circuit voltage;

θ is the power factor angle; and

R is the internal resistance of the generator.

The method may include the generator being a non-salient rotor; and

The rotor angle is determined as:

Wherein:

δ is the rotor angle;

V_pis an rms value of the output voltage from the PCC terminal;

I_pIs an rms value of the output current from the PCC terminal;

E is the rms value of the determined open circuit voltage;

θ is the power factor angle; and

r is the internal resistance of the generator.

the method may include the generator being a salient pole machine; and the load angle is determined as:

Wherein:

δ is the rotor angle;

V_tIs the rms value of the output voltage from the terminal;

I_tis the rms value of the output current from the terminal;

e is the rms value of the determined open circuit voltage;

θ is the power factor angle;

r is the internal resistance of the generator;

X_dis a nominal direct axis synchronous reactance; and

X_qis a nominal quadrature-axis synchronous reactance.

the method may include the generator being a salient pole machine; and the rotor angle is determined as:

wherein:

δ is the rotor angle;

V_pIs an rms value of the output voltage from the PCC terminal;

I_pIs an rms value of the output current from the PCC terminal;

E is the rms value of the determined open circuit voltage;

θ is the power factor angle;

R is the internal resistance of the generator (11);

X_dIs a nominal direct axis synchronous reactance; and

X_qIs a nominal quadrature-axis synchronous reactance.

The method may include the power output from the generator system being less than 30 MW.

According to a second aspect, there is provided a method of determining whether an out-of-sync condition has occurred, the method comprising: determining a load angle and/or a rotor angle of the generator system according to the method of the first aspect; and determining whether an out-of-step condition has occurred in dependence on the determined load angle and/or rotor angle.

According to a third aspect, there is provided a generator system comprising: a generator having a generator terminal for outputting power generated by the generator, wherein the transformer is arranged between the generator terminal and the PCC terminal; and one or more computing devices configured to determine a load angle and/or a rotor angle of the generator system according to the method of the first aspect, and/or to determine an out-of-step condition according to the method of the second aspect.

According to a fourth aspect, there is provided a computer program which, when executed by a computing device, causes the computing device to determine a load angle and/or a rotor angle of a generator system according to the method of any of the first aspects, and/or to determine an out-of-step condition according to the method of the second aspect.

according to a fifth aspect, a computing device is provided that is configured to determine a rotor angle and/or out-of-step condition of a generator system by executing the computing program of the fourth aspect.

Those skilled in the art will appreciate that features or parameters described in relation to any one of the above aspects may be applied to any other aspect, unless mutually exclusive. Furthermore, any feature or parameter described herein may be applied to any aspect and/or in combination with any other feature or parameter described herein, unless mutually exclusive.

drawings

Embodiments will now be described, by way of example only, with reference to the accompanying drawings, in which:

FIG. 1 illustrates components of a generator system according to an embodiment;

FIG. 2 illustrates components of a computing device, according to an embodiment;

FIG. 3 illustrates how the open circuit voltage can be determined from the field current according to an embodiment;

FIG. 4 illustrates an advantage of rotor angle determination according to an embodiment; and

fig. 5 is a flow diagram of a process according to an embodiment.

Detailed Description

The present disclosure provides an improved method of determining a load angle and/or a rotor angle in an electrical generator for an electrical power grid.

in order to clearly present the context of the present disclosure, background details are provided below.

power systems are exposed to various abnormal operating conditions such as faults, generator losses, line trips, and other disturbances that may cause power oscillations and consequent system instability. Under these conditions, proper relay settings are necessary to ensure proper protection (i.e., disconnection of the generator out of synchronization and blocking of undesired operation of the distance relays associated with high voltage, HV, lines).

Under normal operating condition conditions, the electrical output from the generator produces an electrical torque that balances the mechanical torque applied to the generator rotor shaft. With electrical and mechanical torque balance, the rotor operates at a constant speed. When a fault occurs and the amount of power transferred is reduced, the electrical torque that counteracts the mechanical torque is reduced. If the mechanical power is not reduced during a fault, the generator rotor will accelerate due to the unbalanced torque condition.

During unstable power conditions, at least two generators providing power to the power grid rotate at different speeds from each other and lose synchronization. This is referred to as an out-of-sync condition (also referred to as an out-of-sync condition or an out-of-sync condition).

the out-of-step condition can cause high currents and mechanical forces in the generator windings and high levels of transient shaft torque. The torque may be large enough to break the shaft of the generator. Pole slip events can also result in abnormally high stator core end iron flux, which can lead to overheating and short circuiting of the stator core ends. The cell transformer will also be subjected to very high transient winding currents, which impose high mechanical stresses on the windings.

thus, in the event of an out-of-sync condition, it is important that the asynchronously operating generators or system areas be quickly isolated from each other using out-of-sync protection techniques.

at least the out-of-sync protection is described in detail in the following: IEEE course on protection of Sync generators (second edition), published on 8/29.2011, see http:// resource, ie-pes, org/pes/product/tutoreials/PESTP 1001 (as referenced 14/3/2018).

for large power generation systems, the standard for out-of-sync detectors, such as impedance relays, is to determine whether the generator is properly synchronized with the power grid. However, a loss of mains detector is not typically provided for small synchronous generators, i.e. generators in which the power output is less than 30 MW.

A particularly suitable application of small synchronous generators is the smart grid. These are power grids with a variable number of power sources and adjustable power output from the power sources. Another particularly suitable application of a small synchronous generator is the microgrid. Therefore, small synchronous generators are desired to provide out-of-step protection at a much lower cost than current out-of-step detection and prevention techniques for large power generation systems.

A method of determining whether the generator is operating correctly, or whether an out-of-step condition has occurred or is imminent, is by determining and monitoring the rotor angle and/or the load angle of the generator. Accordingly, an accurate and low cost technique for determining the rotor angle and/or the load angle of a generator is desired.

a known and low cost technique for estimating generator load angle is disclosed in d.sub "synchronous generator load angle measurement and estimation" AUTOMATIKA45(2004)3-4, 179-186. This technique allows the load angle to be estimated from the measured output voltage and current. However, the estimation of the load angle depends on the reactance in the system. Therefore, this technique is inaccurate during high load conditions when high currents cause magnetic saturation in the generator core. Therefore, this technique is only applicable to load angle estimation when the system is in steady state operation, and cannot be used to estimate the load angle during the transient of asynchronous protection. In addition, the accuracy of this technique is also reduced when the saturation of the ac core changes due to changes in the power required by the load.

another known technique for estimating the load angle of a generator is disclosed in d.sumina "to determine the load angle" measurement phase angle w of a salient pole synchronous machine, volume 10, No.3, 2010. The load angle is measured using an optical encoder and a digital control system.

Disadvantages of this technique include the need for additional components of the optical encoder and sensor. This adds cost and requires modification of the existing generator in order to install additional components. An idle angle calibration is also required after each synchronization.

The present disclosure provides a new method of determining load angle and/or rotor angle in a synchronous power generator for a power grid.

the disclosed technique differs from the known technique in that the open-circuit voltage (also called back-emf or induced emf) of the generator is derived by measuring the excitation current of the generator in addition to measuring the output voltage and output current at the terminals of the generator. The field current is used to determine the open circuit voltage of the generator. The load angle and/or the rotor angle is determined by the open circuit voltage of the generator and the output voltage and output current at the terminals of the generator.

Advantages include accurate determination of load angle and/or rotor angle during steady state operation, during transients in out-of-step protection, and/or under high load conditions. Furthermore, the disclosed techniques may be implemented at low cost because additional components such as optical encoders and sensors are not required.

Fig. 1 shows a generator system 10 according to an embodiment.

The generator system 10 includes an engine/prime mover 12, which may be, for example, a reciprocating engine or a gas/steam/wind turbine or an electric motor, among others. The generator system 10 further comprises a synchronous generator 11 with a terminal 15, a cell transformer 16 and another terminal 17 at a Point of Common Coupling (PCC). A cell transformer 16 is provided between the generator's terminal 15 and a terminal 17 at the PCC. The engine 12 has a shaft arranged to drive the generator 11 such that the generator 11 generates electrical power from the generator terminal 15 through the unit transformer 16, through the terminals 17 and out of the generator system 10. Power may be supplied to transmission line 18, which supplies power to power grid 19. These components of the generator system 10 and the operation of the generator system 10 may be the same as known generator systems.

the load angle (also referred to as power angle, rotor internal angle or inner rotor angle) is defined herein as the angular difference between the open circuit voltage of the generator 11 (also referred to as open armature voltage, no load voltage, electromotive force, back electromotive force, induced electromotive force or internal voltage of the generator 11) and the voltage at the terminals 15 of the generator 11.

the rotor angle is defined herein as the angular difference between the open circuit voltage of the generator 11 (also referred to as the open armature voltage, the no-load voltage, the electromotive force, the back electromotive force, the induced electromotive force, or the internal voltage of the generator 11) and the voltage at terminal 17 at the PCC.

by monitoring only the load angle, only the rotor angle, or both the load angle and the rotor angle, performance of the generator system 10 may be determined and an out-of-step condition detected depending on operating conditions.

The generator system 10 further comprises a voltage sensor 22 for measuring the voltage at the terminals 15 of the generator 11 (i.e. the generator terminal voltage), a current sensor 23 for measuring the current at the terminals 15 of the generator 11 (i.e. the generator terminal current), and a field current sensor in the generator 11 for measuring the field current.

The generator terminal voltage, generator terminal current, and field current measurements may be time-synchronized samples input to the computing device 20, and the computing device 20 may be a digital signal processor. The computing device 20 may use the received generator terminal voltage, generator terminal current, and field current measurements to calculate a load angle of the generator system 10. The computing device may output data to, for example, display 25 and/or communicate data with other computing devices over a network.

Also shown in fig. 1 are a resistor 14 and an inductor 13. These represent the internal resistance and reactance of the generator 11, respectively.

although not shown in fig. 1, generator system 10 (for voltage sensor 22 and current sensor 23) may additionally or alternatively have a voltage sensor for measuring the voltage at terminal 17 at the PCC and a current sensor for measuring the current at terminal 17 at the PCC. Together with the measurement from the field current sensor, the rotor angle of the generator system can be determined.

in the embodiments described below, only the load angle is determined. However, embodiments also include the same techniques used to determine the rotor angle depending on the voltage and current measurements from terminal 17 at the PCC.

the following explains the derivation according to the calculation techniques disclosed herein.

The active power output (i.e. the actual power output) from the generator 11 with a non-salient rotor structure may be defined as:

P＝V_tI_tcos(θ)+RI_t ²equation 1

wherein:

-P is the active power output;

-V_tIs the rms value of the generator terminal voltage;

-I_tis the rms value of the generator terminal current;

- θ is a power factor angle; and

-R is the internal resistance of the generator 11.

the power factor angle θ is the angle between the generator terminal voltage and the generator terminal current. The power factor angle may be determined from measurements of the generator terminal voltage and the generator terminal current. The power factor of the generator system 10 is cos (θ).

the active power output from the generator 11 with the non-salient rotor structure can also be defined as:

Wherein:

-P、I_tθ is as defined in equation 1;

E is the rms value of the open circuit voltage of the generator 11; and

-is the angle of load

By combining equations 1 and 2, the load angle of the generator 11 with a non-salient rotor can be calculated as:

The computing device 20 may be configured to calculate the load angle using equation 3.

advantageously, the determination of the load angle from equation 3 does not include the reactance of the system. Thus, the accuracy of the determination of the rotor is not affected by any changes in the reactance in the generator system 10, and therefore the load angle can be accurately calculated during steady state operation and also during transient periods of non-synchronous protection.

fig. 2 is a block diagram of computing device 20. The computing device 20 includes an open circuit characteristic OCC block 27 and an angle calculation AC block 32. The measured field current is input to the OCC block 27. OCC block 27 may use the field current and the open circuit characteristics of generator 11 to determine the open circuit voltage of generator 11.

Fig. 3 shows how the open circuit voltage of the generator 11 can be determined from the field current.

the open circuit characteristic of the generator 11 defines the relationship between the open circuit voltage and the field current of the generator 11.

The OCC signature may be derived during one or more experiments during Factory Acceptance Testing (FAT) of the generator when the generator is operated at idle and the field current is varied within the controlled environment. The OCC characteristic may be represented as shown in fig. 3. The horizontal axis represents various values of the field current, and the vertical axis represents various values of the open-circuit voltage of the generator stator. This data is provided to OCC block 27, for example, in a look-up table (LUT) or by a best-fit function that relates open circuit voltage to field current. Thus, the open circuit voltage can be determined from the actual excitation current using an interpolation function in the case of LUT data, or by an equality evaluation in the case of a best fit function. Thus, the open circuit characteristic may be predetermined data of the generator 11, which may be stored in the OCC block 27, stored elsewhere in the computing device 20, or stored remotely from the computing device 20 and provided to the computing device 20 when needed. The open circuit characteristic of the generator 11 may be obtained by one or more of actual measurement, simulation, calculation, and estimation. In fig. 3, the rms value of the excitation current is shown using a per-unit pu system. The determined open circuit voltage may be an rms value of the open circuit voltage.

The AC block 32 of the computing device 20 may receive as inputs the open circuit voltage from the OCC block 27, the measured generator terminal voltage, the measured generator terminal current, and (if not already stored in the AC block 32) the internal resistance of the generator 11.

the AC block 32 may calculate rms values of the received generator terminal voltage, generator terminal current and field current measurements. The received generator terminal voltage, generator terminal current, and field current measurements may be filtered to remove any noise.

the internal resistance of the generator 11 may be predetermined data of the generator 11, which may be stored in the AC block 32, in a computing device including the computing device 20, or stored remotely from the computing device 20 and provided to the computing device 20 when needed. The internal resistance of the generator 11 may be obtained by one or more of actual measurement, simulation, calculation, and estimation.

The AC block 32 may determine the power factor angle from the received generator terminal voltage and generator terminal current measurements.

The AC block 32 may process the received data using equation 3 to facilitate determining the load angle. The determined load angle may be output from computing device 20, for example, to a display and/or another computing device for detecting an out-of-sync condition.

when the generator 11 is a salient pole machine, the AC block 32 of the computing device 20 alternatively calculates the load angle as follows:

wherein:

-δ、V_t、I_te, θ and R are as defined in equations 1 and 2;

-X_dis the nominal direct axis synchronous reactance of the generator 11; and

-X_qIs the nominal quadrature-axis synchronous reactance of the generator 11.

R、X_dAnd X_qIs predetermined data of the generator 11, which may be stored in the AC block 32, in a computing device including the computing device 20, or stored remotely from the computing device 20 and provided to the computing device 20 when needed. R, X of generator 11_dand X_qThe value of (A) can be measured by machine Factory Acceptance Test (FAT)One or more of quantities, simulations, calculations, and estimations.

R, X for 2.5MVA, 400V synchronous generator_dand X_qtypical values of (a) are:

R0.000669767 ohm, X_d0.176625 ohms and X_q0.125 ohm ═ 0.125 ohm

Advantageously, only X is used when determining the load angle by equation 4_dAnd X_qAnd the variation of this difference with load is negligible with load changes and does not significantly reduce the accuracy of the determination of the load angle.

Fig. 4 shows a comparison of the determination of the rotor angle as a function of the active power output for a generator 11 with a non-salient rotor.

fig. 4 shows measured values of rotor angle as a function of active power output. Fig. 4 also shows the determined rotor angle as a function of active power output, where the rotor angle is determined by known techniques disclosed in d.sub, "synchronous generator rotor angle measurement and estimation," AUTOMATIKA45(2004)3-4, 179-186. Fig. 4 also shows the determined rotor angle as a function of active power output, where the rotor angle is determined by the disclosure herein (i.e., according to equation 3, where the voltage and current measurements obtained from terminal 17 at the PCC).

Fig. 4 clearly shows that the rotor angle determined according to the disclosure herein remains accurate as the active power output increases to high values. This is a significant improvement over known techniques in which the accuracy of the determined rotor angle is significantly reduced.

The determined load angle and/or rotor angle may be output from the computing device 20 and used to determine whether an out-of-step condition has occurred or is about to occur, in accordance with known techniques.

An example of how the system operates is for the rotor angle of the generator 11 to be determined continuously. If the power output from the system is greater than, for example, 0.5pu and the determined rotor angle is determined to be outside of an acceptable range of values (e.g., three consecutive time steps), a step loss condition may be detected and a protective relay may be triggered. Thus providing substantially real-time protection of the generator 11.

fig. 5 is a flow chart of a process of determining a load angle and/or a rotor angle of a generator system, wherein the generator system includes a generator having generator terminals for outputting power generated by the generator, a transformer, and a point of common coupling PCC terminal, wherein the transformer is disposed between the generator terminals and the PCC terminal, according to the present disclosure.

In step 501, the process begins.

In step 503, the field current of the generator is determined.

in step 505, an output voltage from the generator terminals is determined, an output current from the generator terminals and a power factor angle and/or a power factor of said output voltage and said output current from the generator terminals are determined, and a load angle of the generator system is determined depending on the determined excitation current, the output voltage from the generator terminals, the output current from the generator terminals and the power factor angle and/or the power factor.

In step 507, the output voltage from the PCC terminal is determined, the output current from the PCC terminal and the power factor angle and/or power factor of the output voltage and output current from the PCC terminal are determined, and the rotor angle of the generator system is determined depending on the determined excitation current, the output voltage from the PCC terminal, the output current from the PCC terminal and the power factor angle and/or power factor.

in step 509, the process ends.