System and method for automatically tuning / configuring a power system stabilizer (PSS) in a digital excitation control system

Through automatic tuning systems and methods, PSO technology is used to automatically generate PSS parameters, which solves the complex and time-consuming problem of manual tuning of existing PSS systems, and realizes fast and low-cost generator debugging.

CN115668071BActive Publication Date: 2025-05-13BASLER ELECTRIC CO
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Patent Information

Application Number
CN202180036501.3
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Priority Date
2020-05-28
Filing Date
2021-02-22
Publication Date
2025-05-13
Estimated Expiration
2041-02-22

AI Technical Summary

Technical Problem

Existing accelerated power integration power system stabilizer (PSS) systems require manual tuning, which is complex and time-consuming, resulting in high costs.

Method used

An automatic tuning system and method was developed to automatically generate the PSS's leading lag phase compensation time constant and gain value using particle swarm optimization (PSO) technology, reducing the number of manual trial and error and generator start/stop.

Benefits of technology

It realizes rapid automatic tuning of PSS parameters, significantly reducing debugging time and cost, and improving the debugging efficiency and performance of the generator.

✦ Generated by Eureka AI based on patent content.

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Abstract

A system and method for automatically tuning / configuring a power system stabilizer (PSS) in a digital excitation control system of a power system having an automatic voltage regulator (AVR), comprising providing a control input to the AVR according to the following steps: generating a set of tuned PSS lead-lag phase compensation time constants based on a received generated terminal voltage, generating an uncompensated frequency response based on the received set of generated terminal voltages and using particle swarm optimization (PSO) based on the generated uncompensated frequency response, generating a tuned PSS gain value based on a determined open-loop frequency response of the power system, determining a PSS gain margin, and determining a tuned PSS gain; and transmitting the determined set of tuning phase compensation time constants and the determined tuning PSS gain value to a control interface of the PSS.
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Description

[0001] Related Applications

[0002] This application claims priority to U.S. Provisional Application No. 63 / 031,308, filed on May 28, 2020, which is incorporated herein by reference.

[0003] Statement Regarding Federally Funded Research

[0004] not applicable Technical Field

[0005] The present disclosure relates to AC power generation systems, and more particularly, to systems and methods for commissioning an excitation control system of a generator. Background Art

[0006] The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.

[0007] The power system or generation system is used to supply power to the distributed power generation system, which usually includes the main power, standby generation and network support. The power generation system usually consists of a prime mover, a synchronous machine or generator, a speed controller of the prime mover and an automatic voltage regulator (AVR). The speed controller of the prime mover usually includes a speed governor and a fuel pump. The AVR also includes a power system stabilizer (PSS) as a control input, which can be a stand-alone system or can be implemented as a module or function of the AVR.

[0008] The power generation system usually consists of a prime mover, a synchronous machine and two controllers (speed regulator and automatic voltage regulator). The synchronous machine usually adopts a circular rotor or a salient pole rotor. Figure 1 illustrates the layout of the power generation system of the prior art system 20. The basic components of the system 20 include Figure 2 2, and the like. These components include a generator 28, an exciter 26, an automatic voltage regulator (AVR) 22, a power system stabilizer PSS 23 (although shown separately, it can be implemented as a separate system or can be implemented as a module or function of the AVR), an amplifier 24, a speed governor 30 and its associated fuel pump 32. As is known, the PSS 23 is used when the power generation system 20 is connected to the grid or power system 88 to provide actual electromechanical power P during commissioning. e 'Power Q e The speed governor 30 has been used to maintain a constant generator speed ω52. The speed governor 30 responds to changes in the generator speed ω52 to act as a feedback controller to control the fuel ratio of the fuel pump 32, thereby minimizing deviations caused by sudden changes in the actual power load of the power generation system.

[0009] As shown in Figure 1, V ref 34 is the generator voltage reference, Vt 36 is the generator terminal voltage and E fd 37 is the field voltage of the exciter 26. Further, in the box 1 / 2H 42, 1 / 2H represents the total moment of inertia of the prime mover (not explicitly shown) and the rotating parts of the generator, T m 44 represents the mechanical torque on the rotating parts of the prime mover and generator, T f 46 represents the friction torque of the rotating parts of the prime mover and generator, T max 48 represents the maximum torque about the prime mover and generator, and ω ref 50 is the generator speed reference and ω 52 represents the generator speed. The "s" in the 1 / s box 54 is the Laplace operator (sometimes also shown as "S" throughout the figures).

[0010] When the power generation system 20 is connected to a power system 88 such as a grid, the actual electromechanical power P e 40 is sensed and provided as feedback to the block 60 and the input 25 of the PSS 23. The speed ω of the generator 28 is also fed as an input to the input interface 25 of the PSS 23. The AVR 22 inputted from the PSS 23 to its summing point is connected to the generator terminal voltage V t 36. Generator voltage reference V ref 34 and PSS output voltage V S 37 performs feedback control of summation 56 to control the field current I to the exciter 26 fd , to maintain a constant generator terminal voltage E t . Generator terminal voltage V t 36 is determined by multiplying the generator output voltage Vt 36 by the generator speed ω 52. The actual electromechanical power generated P e 40 is fed to the speed control loop via 1 / ω52 as shown in block 60. The nominal value of the generator speed ω52 is 1.0 per unit. The 1 / ω block 60 illustrates the unit conversion from electrical power to torque for the speed control loop. The speed control loop is fed to the speed control loop via 1 / ω52 from the generator speed reference ω ref The generator speed ω52 is subtracted from 62 from 50 to provide feedback control of the generator speed ω52.

[0011] As an example, but not limited to, the power generation system can change operation from no load to full load or change load capacity in a short period of time. These changes in load can cause changes in the generator speed ω52 or stalling of the prime mover, as well as other adverse effects.

[0012] In some power generation systems, such as in small power systems, a sudden increase in the power load of the generation system causes an increase in the load torque on the prime mover. Since the load torque exceeds the torque of the prime mover and the governor cannot respond instantaneously, the generator speed ω52 decreases. In such smaller power generation systems, after detecting this deceleration, the governor increases the fuel supplied to the prime mover. Since the generated voltage is proportional to the generator speed ω52, the generator output voltage E t The AVR 22 increases the machine's field current I fd Figure 1 shows a simplified power generation system model with cross coupling when a resistive load is applied through the interaction between voltage and speed control.

[0013] Today's power generation systems are equipped with fast-acting AVRs to control the excitation of the generators. The benefits of fast excitation controllers can improve the transient stability of the generators connected to the system. However, the high performance of these AVRs can have a destabilizing effect on the power system. Power oscillations of small amplitude and low frequency often persist for long periods of time. In some cases, this places a limit on the amount of power that can be transferred within the system. Various power system stabilizers have been developed to help suppress these power oscillations by modulating the excitation supplied to the synchronous machines.

[0014] There are many types of PSS systems. The accelerating power integrating PSS is most commonly used with digitally based excitation systems described in IEEE Standard 421.5 as IEEE Type PSS2A. For this type of PSS, some manufacturer data related to PSS parameters (particularly machine reactance and generating system inertia) need to be verified during commissioning. The lead-lag time constants of the phase compensation and the system gains also need to be tuned for efficient PSS operation.

[0015] Currently, accelerating power integrating PSS systems must be tuned manually. Manually tuning a digital voltage regulator requires expertise and years of experience to determine the optimal PSS parameters to be tuned for a particular generator. In addition, this manual tuning process consumes a considerable amount of time. A. Murdoch, S. Venkatraman, RA Lawson, WR Pearson briefly described the process in "Integral of Accelerating Power Type PSS Part 1 - Theory, Design, and Tuning Methodology" in "IEEE Transactions on Energy Conversion", Vol. 14, No. 4, December 1999. The cost of machine downtime due to this manual tuning and the time required are very expensive for the generator system operator. The combined cost of testing and the fuel used during such manual testing results in a very high cost to the generator system operator. Therefore, there is a need for an improved system and method that can tune an accelerating power integrating PSS system in a quick and less costly manner. Summary of the invention

[0016] A system and method for improving the tuning of a power-accelerating PSS system is disclosed. As described herein, the system and method of the present disclosure provides automatic tuning that provides the setting of PSS parameters without requiring a manual process that includes much trial and error and the starting and stopping of the generator, and the fuel and cost associated with such current trial and error processes. The system and method of the present disclosure has been implemented in a digital excitation control system, and the improved performance provided has been verified using hardware-in-the-loop simulations.

[0017] According to one aspect, a system for automatically tuning / configuring a power system stabilizer (PSS) in a digital excitation control system for controlling an electric power system is implemented, the electric power system having a prime mover system providing rotational energy to a generator having an exciter, a plurality of sensors for measuring operating characteristics of the electric power system, an automatic voltage regulator (AVR) having an input summing point and generating control parameters for the exciter and the generator, the PSS having a memory, a processor, computer executable instructions, a communication control interface for receiving PSS parameters, and an output for generating a control output to the AVR input summing point. The system includes a control module having a processor, a memory, stored computer executable instructions, a control input, and a control output. The computer executable instructions include instructions for configuring the control module to perform a process of generating a set of lead-lag phase compensation time constants for tuning the PSS, the generating including receiving a set of generated terminal voltages during operation of the electric power system, generating an uncompensated frequency response of the electric power system based on the received set of generated terminal voltages, and determining a set of tuning phase compensation time constants, the determining including performing a particle swarm optimization (PSO) based on the generated uncompensated frequency response. The system is further configured to generate a tuned PSS gain value, including determining an open-loop frequency response of the power system to determine a PSS gain margin, and determining a tuned PSS gain based on the determined PSS gain margin. The system is further configured to transmit the determined set of tuning phase compensation time constants and the determined tuned PSS gain value from a control output to a communication control interface of the PSS.

[0018] According to another aspect, a method and computer executable instructions for performing the method for automatically tuning / configuring a power system stabilizer (PSS) in a digital excitation control system for controlling a power system having a prime mover system providing rotational energy to a generator having an exciter, a plurality of sensors for measuring operating characteristics of the power system, an automatic voltage regulator (AVR) having an input summing point and generating control parameters for the exciter and the generator, the PSS having a memory, a processor, computer executable instructions, a communication control interface for receiving PSS parameters, and an output for generating a control output to the AVR input summing point. In a control module having a processor, a memory, stored computer executable instructions, a control input, and a control output, the method includes generating a set of tuning PSS lead-lag phase compensation time constants, the generating including receiving a set of generated terminal voltages during operation of the power system, generating an uncompensated frequency response of the power system based on the received set of generated terminal voltages, and determining a set of tuning phase compensation time constants, the determining including performing a particle swarm optimization (PSO) based on the generated uncompensated frequency response. The method also includes generating a tuned PSS gain value, the generating including determining an open loop frequency response of the power system to determine a PSS gain margin and determining a tuned PSS gain based on the determined PSS gain margin. The method also includes transmitting the determined set of tuning phase compensation time constants and the determined tuned PSS gain value from a control output to a communication control interface of the PSS.

[0019] Other aspects of the present disclosure will be apparent in part and pointed out in part below. It should be understood that the various aspects of the present disclosure can be implemented alone or in combination with each other. It should also be understood that the detailed description and the accompanying drawings, although indicating certain exemplary embodiments, are intended only for illustrative purposes and should not be interpreted as limiting the scope of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] FIG. 1 is a block diagram of a simplified power generation system model with cross coupling when the power generation systems are connected to the power system according to the prior art.

[0021] Figure 2 is a block diagram of a system of a PSS input section of an excitation control system utilizing an accelerating power-integrating PSS with an improved auto-tuning PSS parameter input controller according to an exemplary embodiment.

[0022] Figure 3 is a phasor diagram of a generator according to an exemplary embodiment.

[0023] Figure 4, including Figure 4(a) and Figure 4(b), is a functional block diagram in the form of a Laplace operator, illustrating the generation of derived compensation frequency and PSS gain and phase compensation of an automatic tuning PSS parameter input controller used with an accelerated power-integrated PSS according to an exemplary embodiment.

[0024] Figure 5 is a circuit diagram of a real-time digital simulator (RTDS) for testing one exemplary embodiment of the presently disclosed automatic PSS parameter input controller for use with an accelerated power-integrating PSS.

[0025] Figure 6 is a flow chart of a five-step process for automatically tuning a PSS parameter input controller for use with an accelerating power-integrating PSS, according to an exemplary embodiment.

[0026] Figure 7 is a flow chart of a process for steps 1-3 of verifying and validating manufacturer parameter values ​​and automatically generating estimated PSS parameters in an automatic PSS parameter generation control system for use with an accelerating power-integrating PSS, according to an exemplary embodiment.

[0027] Figure 8 According to the use Figure 3 A test of the test system, illustrating a graph comparing the saturation coefficient generated in step 1 during the test and its measured value compared to the manufacturer's saturation value.

[0028] Fig. 9 is a functional block diagram of generating an estimated power generation system inertia H according to step 3 of the method of the present disclosure for an automatic PSS parameter input controller for use with an accelerating power integrating PSS according to an exemplary embodiment.

[0029] Fig.10 is a graph of generating an estimated generated inertia H using a particle swarm optimization (PSO) method for an automatic PSS parameter generation control system for use with an acceleration power integration PSS according to an exemplary embodiment.

[0030] Fig.11 is a diagram of a particle swarm optimization (PSO) process for steps 3 and 4 of automatically generating estimated PSS parameters in an automatic PSS parameter generation control system for use with an accelerated power-integrated PSS according to an exemplary embodiment.

[0031] Figure 12, including Figures 12(a) and 12(b), is a graph generated from a test of estimated power generation system inertia and spectrum from step 3 of a process for an automatic PSS parameter input controller for use with an accelerating power integration PSS according to an exemplary embodiment.

[0032] Fig.13 is a flow chart of a particle swarm optimization (PSO) process for generating an estimated phase compensation time constant in an automatic PSS parameter generation control system for use with an accelerating power-integrating PSS according to an exemplary embodiment.

[0033] Figure 14, including Figures 14(a), 14(b) and 14(c), are graphs generated from testing of an automatic PSS parameter input controller for phase compensation of step 4 for use with an accelerated power integration PSS according to an exemplary embodiment, wherein Figure 14(a) illustrates voltage changes, Figure 14(b) illustrates active power changes, and Figure 14(c) illustrates phase lag and compensation phase.

[0034] Fig.15 is a block diagram of an improved power generation system having an improved commissioning control system when the power generation system uses a speed-up power integration PSS according to an exemplary embodiment.

[0035] Fig.16 is a graph illustrating gain and phase of an open loop frequency response from 0.1 Hz to 10.0 Hz calculated from a test of an automatic PSS parameter input controller used with an accelerated power integrating PSS according to an exemplary embodiment.

[0036] Figure 17, including Figures 17(a) and 17(b), are actual power response graphs comparing the effectiveness of a test of a prior art system in Figure 17(a) and an automatic PSS parameter input controller used with an accelerated power integration PSS in Figure 17(b) according to an exemplary embodiment.

[0037] Fig.18 is a diagram of a system suitable for implementation of the systems and methods of the present disclosure, according to an exemplary embodiment.

[0038] It should be understood that throughout the drawings, corresponding reference numerals indicate like or corresponding parts and features. DETAILED DESCRIPTION

[0039] The following description is merely exemplary in nature and is not intended to limit the present disclosure or the applications or uses of the present disclosure. The present disclosure provides methods and systems that can be considered as "auto-tuning" of an accelerated power integration PSS. Small random changes in the voltage reference step are desirable for minimal disturbance to the power generation system. As will be described, after verifying the manufacturer's data, the system and process for generating initial PSS parameters (including tuning of the phase compensation lead-lag time constants and PSS gain), have been demonstrated to take less than five minutes and generate a gain margin of 10 dB. Using the presently described method and system for generating initial accelerated power integration PSS parameters, commissioning of the generator can be completed very quickly and with excellent performance results.

[0040] 1. Power generation, control system and test system

[0041] 1.1 Power Generation System

[0042] like Figure 2 As shown, an exemplary embodiment of a generator control system and method may be commissioned and operated using an automatic PSS parameter input controller for use with an accelerating power integrating PSS according to one embodiment.

[0043] The present system and method are applicable to an AC power generator connected to an AC grid. A typical model of such an AC power generator and associated power system components is as follows: Figure 2 As shown, the generator 28 receives a rotational force input from a prime mover 82, which may be, for example, steam turbine driven, gas turbine driven, hydraulic driven, or diesel driven. The generator 28 receives a field voltage E from the exciter 26. fd The exciter 26 supplies power to the field coils in the generator 28 at a variable level. The field voltage E supplied to the generator 28 by the exciter 26 is fd The amount of field voltage E is determined by AVR 22. AVR 22 determines the appropriate amount of field voltage E based on the operational requirements of the power system. fd The power system stabilizer PSS 23 communicates with the AVR 22 to stabilize the power generated by the generator 28. The AVR 22 and / or the PSS 23 monitor the grid and the terminal voltage V at the output of the generator 28. t and terminal current I t , to ensure that the generator 28 operates as desired. In addition, the speed ω of the generator 28 is also monitored and provided as an input to the PSS 23. The power grid 84 is modeled by representing the transformer 86, the transmission line 88, and representing the power factor load 90 and the motor load 92.

[0044] At commissioning, the PSS 23 is required to receive a set of initial parameters at its PSS input interface 25. These initial parameters typically include phase compensation and PSS gain for adjusting the two lead and lag time constants to maximize damping, as described by A. Murdoch, S. Venkatraman, RA Lawson, WR Pearson in "Integral of Accelerating Power Type PSS Part 1 - Theory, Design, and Tuning Methodology", IEEE Transactions on Energy Conversion, Vol. 14, No. 4, December 1999.

[0045] As described in the background, these parameters are typically determined by an engineering operator and input into the PSS 23 on a trial and error basis based on the engineering operator's experience. The current process requires starting the prime mover 82 and then connecting and disconnecting the generator from the grid 88 multiple times.

[0046] The system includes a commissioning control system 100 communicatively coupled to the PSS input interface 25, the commissioning control system for providing the PSS 23 with its initial set of PSS parameters based on the presently disclosed tuning process, which may use a predetermined set or combination of manufacturer specifications. This is particularly useful for accelerating power-integrating PSS systems. The commissioning control system 100 may include, for example, Fig.18 The various features and elements described may include Fig.18 A user input interface 1010 is shown.

[0047] 1.2 Accelerating the Power Integrating Power System Stabilizer (PSS) System

[0048] A brief overview of an accelerated power-integrating PSS is first described to provide context for the systems and methods of the present disclosure.

[0049] The Accelerator Power Integration PSS is a dual-input stabilizer that provides supplementary damping for low-frequency, local mode oscillations and power system oscillations. It uses two signals: shaft speed and electrical power. This approach eliminates undesirable components (such as noise, lateral shaft runout, or torsional oscillations) from the speed signal while avoiding the measurement of the mechanical power signal.

[0050] The direct terminal voltage frequency measured from the generator potential transformer has been used as an input signal in many stabilizers, but it cannot be used directly in the accelerating power integrating PSS. Only the rotor frequency measurement can be used, which is directly coupled to the shaft position change. The generator rotor frequency or speed ω is called the compensation frequency ωcomp .

[0051] Generator rotor shaft and generator terminal voltage E t and the internal voltage E proportional to the generator terminal current It i Related, such as Figure 3 The phasor diagram is shown in .

[0052] For steady state, the generator terminal voltage E t It is expressed by equation (1), where X q represents the impedance proportional to the quadrature axis impedance, and j represents the generator terminal voltage E t The phase shift or phase misalignment component, that is, "j" represents the generator terminal voltage E t The imaginary component of Figure 3 As shown in:

[0053]

[0054] When the rotor is in motion, the compensating reactance should represent the orthogonal reactance applied over the frequency range of interest.

[0055] The equation of motion of the rotor as a function of torque is described in equation (2):

[0056]

[0057] in

[0058] ω=rotor speed

[0059] H = power generation system inertia

[0060] T m = Mechanical torque

[0061] T e =Electromechanical torque

[0062] Using the Laplace operator "s", the motion of the rotor can be rewritten as equation (3):

[0063] 2Hsω=T m -T e (3)

[0064] Since the torque is equal in value to the power per unit of rated speed of the system, the mechanical torque T in equation (3) is m and electromechanical torque T e The mechanical power P m and electromechanical power P e Instead of. Mechanical power P m By rearranging equation (3), we obtain equation (4):

[0065] Pm =2Hsω+P e (4)

[0066] As is known in the art, the mechanical power P m Therefore, the mechanical power P m The quantity is synthesized using equation (4), where the shaft speed ω and the electromechanical power P e Use compensation frequency ω comp and electromechanical power P e Instead. In fact, the mechanical power P m Changes faster than the electromechanical power P e Slower, it usually moves with a ramp rather than a step function. The resultant mechanical power P^m or (Note that as used herein, the "^" above or immediately following a parameter is the same and is used to indicate an estimated value of the parameter.) For example, a ramp tracking filter may be used when T8=MT9, where:

[0067] T8 = lead time constant of the ramp tracking filter;

[0068] N = number of ramp tracking filters;

[0069] M = tracking filter parameter; and

[0070] T9 = the hysteresis time constant of the ramp tracking filter, using equation (4B):

[0071]

[0072] Thus, the acceleration power signal (P acc ) becomes the signal of equation (5):

[0073]

[0074] Use as acceleration power signal (P acc ) as a function of the power generation system inertia constant H and the Laplace operator "s" to obtain the derived compensation frequency ω^[or ]. By converting the acceleration power signal (P acc ) is multiplied by the total moment of inertia, which includes the moment of inertia of the prime mover rotating parts, the generator rotor, etc., which is reflected by 1 / 2Hs as provided by equation (6):

[0075]

[0076] Figure 4(a) shows in block diagram form the use of two dropout filters F W1 and FW2 The above calculation in the form of a process flow is used to eliminate low frequency signals. Input electromechanical power P e The second dropout filter F W2 The numerator of is a multiple of twice the inertia H of the power generation system, the Laplace operator "s" or "2Hs" term and the fourth washout time constant T w4 Combined.

[0077] K s2 =T w4 / 2H. (7)

[0078] As shown in Figure 4(a), the two inputs are the compensation frequency ω in normal operation. comp and electromechanical power P e These inputs ω comp and P e Some steady-state values ​​of can change slowly over a long period of time. Wn The dropout filter F Wn Applied to both inputs to remove low frequency signals.

[0079] Generator compensation frequency ω^ derived based on acceleration power integral comp is the input of the second part of the PSS as shown in Figure 4(b), which uses a 3-level lead-lag compensator C A , C B and C C , system gain K s1 and output maximum / minimum limits V emax / V emin Phase Compensation to generate the PSS output signal voltage V s , this output signal voltage is provided as input to the AVR.

[0080] 1.3 Test Environment

[0081] As will be solved using the steps and implementation system of the method of the present disclosure, the system and method of the present disclosure were tested in an implementation with a commercial regulator. An application with a graphical user interface (GUI) was developed for the setting and testing of AVR and PSS parameters. In this test, all computationally intensive calculations (FFT and PSO routines) were implemented in the developed application.

[0082] These tests are based on Figure 5The hardware-in-the-loop system shown is performed. The actual power system is programmed into the real-time digital simulator RTDS, which includes the generator, step-up transformer and system grid. The generator is a round rotor machine rated at 18kV and 210MVA, 0.85pf, 60Hz. The inertia H is 5.9MWs / MVA. The generator electrical data is provided as follows:

[0083] The electrical parameter data of the generator (210MVA, 18.0KV) are shown in Table A:

[0084] <![CDATA[T do ’=9.47,]]> <![CDATA[T do ”=0.06,]]> <![CDATA[T qo '=1.0,]]> <![CDATA[T qo ”=0.05,]]> <![CDATA[X d =1.81,]]> <![CDATA[X q =1.65,]]> <![CDATA[X d ’=0.187]]> <![CDATA[X q ’=0.6,]]> <![CDATA[X d ”=0.166,]]> <![CDATA[X d ”=0.166,]]> <![CDATA[X l =0.15,]]> s(1.0)=0.1976, s(1.2)=0.4589

[0085] Table A: Test manufacturer's generator parameters

[0086] Assume that the excitation system of the machine is a static exciter as described by the IEEE 421.5 ST4C model with the parameters in Table B:

[0087] <![CDATA[K PR =14.92,]]> <![CDATA[K IR =2.98,]]> <![CDATA[V RMAX =1.0,]]> <![CDATA[V RMIN =-0.8,]]> <![CDATA[K PM =1.0,]]> <![CDATA[K IM =0.0,]]> <![CDATA[V Mmax =99,]]> <![CDATA[V lmin =-99,]]> <![CDATA[T A =0.01,]]> <![CDATA[V Amax =99,]]> <![CDATA[V Amin =-99,]]> <![CDATA[K G =0.0, <!-- 7 -->]]> <![CDATA[T G =0.0,]]> <![CDATA[V Gmax =0.0,]]> <![CDATA[K P =10.0,]]> <![CDATA[K I =0.0]]> <![CDATA[K C =0.15,]]> <![CDATA[X L =0.0,]]> <![CDATA[θ P =0.0]]>

[0088] Table B: IEEE 421.5 ST4C excitation system parameters

[0089] 2. PSS parameter tuning method

[0090] As described herein, the present systems and methods provide tuning of an accelerating power integral PSS by providing initial PSS parameters to the PSS that reduce the time required to commission the accelerating power integral PSS in an electric generator control system. The presently described systems and methods involve a process for generating a set of accelerating power integral PSS parameters determined for a generator and generator system to obtain appropriate damping without the need for manual tuning as currently performed.

[0091] The present system and method include a process of generating tuned phase compensation lead-lag time constants and PSS gains as initial accelerated power integration PSS parameters. In addition, the present system and method may also include a process of estimating (if necessary before generating tuned phase compensation lead-lag time constants and PSS gains), and a process of identifying certain manufacturer data of power generation system parameter values, which may not be currently known or may not be accurate for a particular power generation system due to transportation, small changes during installation, modifications during installation, changes in system components (each of which typically occurs before commissioning).

[0092] While the process of verifying and adjusting all manufacturing generator system parameters is not always required in every implementation, the following process including three verification process steps and an initial step provides a complete process flow that can be implemented in some embodiments. Figure 6, it should be understood that one or more of the first three steps are optional and not always necessary, as the first three steps are used to verify the manufacturer's data of the power generation system parameters and adjust them when determined to be necessary. Figure 6 As shown, the manufacturer's power generation system parameters that can be initially verified and adjusted include the generator saturation coefficients s(1.0) and s(1.2), such as the d-axis synchronous steady-state reactance X d Generator data. Ultimately, the power generation system inertia constant H can be verified and adjusted as needed for a particular implementation. Based on these or based on manufacturer provided parameter data values ​​for these, the present system and method provide for generating tuned phase compensation lead-lag time constants and PSS gains which are then input as initial parameters for the accelerating power integrating PSS system.

[0093] As initially outlined at a high level, Figure 7 A flowchart process 200 is provided for use in steps 1, 2, and 3 for verifying and confirming manufacturer values ​​of parameters. As shown, the process begins and in processes 201 and 202 the system and method receives and stores manufacturer data such as described above. For each of steps 1, 2, and 3, process 204 provides an estimate of the manufacturer data, which is also required in the case where manufacturer data is not provided for one or more power system parameters. If an estimate is not made, the process proceeds to process 208, where the process calculates PSS parameters using the stored manufacturer data. If an estimate is made, process 204 enters process 206, where values ​​of manufacturer data are provided for each such parameter according to the process described below. Once estimated and stored in process 206, the process then continues to calculate the PSS parameters in process 208.

[0094] 2.1 Exemplary complete five-step process flow ( Figure 6 )

[0095] As described above, the complete 5-step process flow will be described as steps 1 through 5. Steps 1-3 provide verification of the manufacturer's parameters, or derivation and adjustment of such parameters to provide adjusted parameters for use in generating the phase in steps 4 and 5. Compensated tuned lead-lag time constants T1–T6 and PSS gain K s Each of these 5 steps will refer to Figure 6 The description is given by way of example.

[0096] 2.1.1 Step 1: Generator saturation coefficients s(1.0) and s(1.2)

[0097] The parameters of synchronous machines change under different load conditions due to changes in the machine's internal temperature, magnetic saturation, aging, and coupling between the machine and external systems. Several assumptions are made in transient stability studies to represent saturation, since it is futile to treat the performance of synchronous machines strictly in saturation. The saturation effect is characterized by the saturation function. This change results in a field voltage E fd To handle the saturation effect based on the simplicity of the estimation method, the field voltage E fd It is determined as a function of the saturation coefficients s(1.0) and s(1.2), and the same is true for the generator saturation coefficient.

[0098] Compensation frequency ω comp will need to be determined. As a first step, in order to determine the compensation frequency ω comp For synchronous machines such as generators, the input requirement for most commercial stability programs to characterize generator saturation is in terms of a saturation coefficient parameter "s". There are usually two saturation coefficients used to characterize the generator, a first generator saturation coefficient s(1.0), which is the saturation coefficient when the open circuit voltage is 1.0 pu, and a second saturation coefficient s(1.2) when the open circuit voltage is 1.2 pu. These quantities are derived based on a recursive least squares method from the measured generator voltage E t and field current I from 0.8 to 1.05 per unit fd The saturation coefficient s(1.0) is determined to be equal to parameter C1 and the saturation coefficient s(1.2) is determined to be equal to C1 multiplied by 1.2 raised to the power of parameter C2. In this way, each saturation coefficient can be determined by determining parameters C1 and C2.

[0099] According to formula (8), the field current I fd Related to C1 and C2:

[0100]

[0101] in:

[0102] C1=s(1.0) (9)

[0103]

[0104] Equation (8) can be rearranged into equation (11):

[0105]

[0106] For the kth sample value, it can be expressed as equation (12):

[0107]

[0108] Taking the logarithm of equation (1) yields equation (13):

[0109]

[0110] Therefore, for n sample values, equation (13) provides:

[0111]

[0112] Thus, the estimated values ​​of the parameters C1 and C2 can be determined by least squares estimation, where the unknown parameters C1 and C2 in equation (14) are selected so that the measured or actually observed generator voltage E t With the calculated generator voltage E^ t The sum of squared errors is minimized.

[0113]

[0114] Parameter α T Defined by equation (16), the parameters Defined by equation (17), y k Defined by equation (18), the parameter α can be solved by the closed-form solution in equation (19).

[0115] α T =[log(C1)C2] (16)

[0116]

[0117]

[0118]

[0119] For efficient real-time estimation, equation (18) is manipulated into a recursive form using a forgetting factor λ, as described in "Self-Tuning of the PID Controller for a Digital Excitation Control System" by Kiyong Kim, Pranesh Rao, and Jeffrey A. Burnworth, IEEE Swarm Intelligence Symposium, St. Louis MO USA, September 21-23, 2008. As an exemplary embodiment, the forgetting factor λ may be selected to have a value of 0.9. However, it will be appreciated by one of ordinary skill in the art that the forgetting factor λ may be selected to have other values ​​and should generally be less than 1.0, where a smaller value results in less influence of old sample data on the estimation result. Thus, the recursive form of equation (19) is provided by equations (20), (21), and (22):

[0120] Lk =P k-1 -P k-1 φ k [φ T k P k-1 φ k +λ] -1 (20)

[0121]

[0122]

[0123] As described above, after parameters C1 and C2 are determined, the saturation coefficient s(1.0) is determined to be equal to parameter C1, and the saturation coefficient s(1.2) is determined to be equal to C1 multiplied by 1.2 to the power of parameter C2, as shown in equations (23) and (24), respectively:

[0124] s(1.0)=C1 (23)

[0125]

[0126] As mentioned above, the saturation coefficients s(1.0) and s(1.2) are used to determine the compensation frequency ω comp , or using equations (23) and (24), parameters C1 and C2 can be used directly for this determination, as will be stated in step 2.

[0127] In one embodiment of the above step 1 process, the two saturation coefficient parameters s(1.0) and s(1.2) are measured while the generator is offline (ie, operating but not attached to the grid or load). Figure 8 As shown in the figure, when the generator voltage increases from 0.9 to 1.05 pu in a step of 0.01, the generator voltage E t and field current I fd Sampling is performed and the saturation coefficients s(1.0) and s(1.2) are calculated using the recursive least squares method described above. In an exemplary test, Figure 8 As shown, the estimated value of the saturation coefficient provided by the process of step 1 described herein provides a close match with the characteristics provided by the manufacturer. As is known, the manufacturer data provides two points on the saturation curve, and various nonlinear curve fitting schemes can be used to obtain saturation values ​​at other points. As an example, one result is shown in Figure 8 In. Figure 8 As shown, as an example, based on Figure 8The measured points shown are used to estimate two points s(1.0) and s(1.2) as the measured points. The estimated curve can then be calculated based on the two estimated points s(1.0) and s(1.2) using equations (8), (9) and (10). In this way, using the estimated saturation coefficient parameters s(1.0) and s(1.2), the present system and method can provide an improved and more accurate set of initial tuning parameters for the PSS.

[0128] 2.1.2 Step 2: Verify and adjust the compensation frequency ω comp

[0129] The tuning parameter is the compensated q-axis reactance X qcomp The compensation frequency is the q-axis reactance X qcomp When the d-axis synchronous reactance X d When estimated in equation (24), the compensated q-axis reactance X qcomp Can be set at a lower level, such as the estimated d-axis synchronous reactance X^ d one third of.

[0130] The generator rotor shaft position is determined by the generator terminal voltage V t and current I t And the compensating reactance X^ d Determine. Appropriate compensation reactance X^ d should be derived from the frequency range of interest. In general, local mode oscillations are around 1 Hz. As is known in the art, most power oscillations exist between 0.1 and 3.0 Hz, which includes the range where intertie and interarea modes exist (0.1-0.9 Hz) as well as the range where local mode power swing modes exist (1-2 Hz). Therefore, it is necessary to approximate the transient quadrature reactance (X' q ) impedance value. On a circular rotor machine, the generator synchronous reactance X q Close to d-axis synchronous reactance X d Therefore, this paper uses the d-axis synchronous reactance X d Replace the generator synchronous reactance X q .

[0131] As an example, for salient pole machines, synchronous impedance provides the required compensation. However, the selection of the correct compensation impedance is more complex and simulations and field tests are usually performed to confirm this setting. However, for this method, in the absence of manufacturer data, as an example of the start-up process, the estimated compensation reactance q-axis synchronous reactance X^ qcomp Set to the generator synchronous reactance (X q ) is one third of the total.

[0132] Under steady-state operating conditions, there is no active power output, X d can be easily estimated, where:

[0133] e q =q-axis generator voltage;

[0134] i d =d-axis generator current;

[0135] E fd = generator field current;

[0136] K^ sd = generator saturation factor under steady-state conditions;

[0137] R a = generator stator resistance;

[0138] X l =Generator leakage reactance;

[0139] Then equation (24) provides the compensating reactance X^ d for:

[0140]

[0141] The saturation coefficient is measured using the terminal voltage E t and the measured terminal current I t Calculated using the air gap flux linkage denoted as Ψ in equation (26):

[0142] Ψ t =|E t +(R a +jX l )I t | (26)

[0143] Therefore, the generator saturation coefficient K^ sd is provided in equation (27) using the saturation parameters C1 and C2 determined as in step 1 above, or based on known or measured generator saturation factors s(1.0) and s(1.2) using equations (23) and (24):

[0144]

[0145] Since the generator saturation coefficient K^ is determined in steady state sd , then the compensation reactance X^ d It can be determined using equation (24). t and I t Given the operating conditions, the steady-state K^ is calculated based on equations (25) and (26) sd, and then substitute it into equation (24) to calculate X^ d As will be understood by those skilled in the art, when there is no active (real) power output, then e q =E t And I t =i d .

[0146] In an exemplary embodiment of practicing step 2, after step 1 is completed, the generator is connected to the grid and is thus online. e Several voltage step tests are performed with the output at 100V. In one exemplary embodiment, five (5) voltage steps are used, but other numbers of steps are possible. Generator synchronous reactance X d is based on the generator voltage E measured under steady-state conditions t and reactive power Q estimated. In the absence of manufacturer data, the compensating reactance q-axis synchronous reactance X^ q The synchronous reactance X d In an exemplary embodiment, the compensating reactance q-axis synchronous reactance X^ q can be estimated as the generator synchronous reactance X d one-third of the estimated value.

[0147] 2.1.3 Step 3: Verify and adjust the power generation system inertia H (and the washout time constant T w )

[0148] As an initial sub-step of step 3, a pseudo white noise signal is added to the AVR summing point and measurements are taken to verify the system parameter values. The local mode frequencies and turbine torsional interaction frequencies are also identified. When the pseudo white noise signal is added to the AVR summing point, the actual electromechanical power of the generator P e Increase to about 0.2pu. Record the generated generator frequency ω, three-phase generator terminal voltage V t and current I t , and can determine terminal voltage changes such as ΔV t changes.

[0149] The measured electromechanical power P caused by the pseudo white noise input to the AVR summing point e Change or ΔP e A Fast Fourier Transform (FFT) was performed to identify all power system oscillation frequencies in the range of 0.1 to 100 Hz. The resulting spectrum gave various power oscillation modes, including the turbine generator torsional oscillation frequencies.

[0150] As shown in Figure 12(b) and as described below based on the maximum amplitude, the local mode frequencies and turbine torsional interaction frequencies are identified using FFT. This process provides the washout time constant T w Determination of the washout time constant T w is chosen to be five times the time constant corresponding to the maximum frequency component between about 0.1 and about 3 Hz to be described. Determining an appropriate washout time constant T w to allow frequencies as low as 0.1 Hz without significant attenuation or adding excessive phase lead. It is typically set in the range of 2 to 10, with the value chosen based on the appropriate response of the PSS function to the power system. If it is 10 seconds, the filter corner frequency is 0.016 Hz, which is well below the cross-region mode frequency. For the tuning scheme of the present disclosure, the washout time constant T w is selected to be five times the time constant corresponding to the maximum frequency component between about 0.1 and about 3 Hz, which is the frequency range where most power oscillations exist, i.e., the main power oscillations are identified as the largest frequency spectrum. Thus, to determine the washout time constant, the maximum frequency component in this range is identified. As described herein, the measured change caused by the induced white noise (such as the change / change ΔV in the terminal voltage) is t ) of the maximum frequency component of the resulting spectrum obtained by FFT. As is known in the art, this process provides an estimate of the power oscillation frequency, local or torsional oscillation mode. Once calculated, the time constant of the selected frequency component is determined and then multiplied by five to determine the "appropriate" washout time constant. Typically, the washout time constant should be in the range of about 2 to about 10 seconds.

[0151] The inertia H of the power generation system is estimated using a partial load dump test. The generator frequency, actual power and current of this test are recorded. Particle swarm optimization (PSO) technology is applied to estimate the power generation system inertia H. PSO is a known computational technique and has been applied to determine AVR gains, but has not been used for PSS parameter estimation. The functional block diagram of the PSO process for identifying the parameters of the equivalent rotor speed or frequency ω control system is shown in Fig. 9 The simulation model parameters are the power generation system inertia H, the fuel pump time constant T A , speed regulator proportional gain K P , speed regulator integral gain K I , no-load fuel consumption W nfl and droop.

[0152] The PSO process is shown in Figure 2 for use Fig.10 The flowchart of PSO generation of estimated power system inertia H is provided in . Fig.10The PSO technique shown generates an estimate of the power generation system inertia H. As shown, adjustments are made to provide the electromechanical power P e , resistor R A , terminal current I t , frequency ω and reference frequency ω ref As input to calculate the frequency ω, and compare it with the actual measured frequency ω. These are compared, and then H (generator system inertia), T A (fuel pump time constant), K P (Speed ​​governor proportional gain), K I (governor integral gain), W nfl One or more of (idle fuel consumption) and speed drop (speed drop) are used to generate adjustment rules.

[0153] The simulation results obtained using the PSO process are compared to the manufacturer values. If the results do not match, the generator parameters are adjusted through the PSO technique to provide the best match. The technique is inspired by the social behavior of flocks of birds or schools of fish. In PSO, potential particles (solutions) fly through the problem space by following the current optimal particle. Each particle keeps track of its coordinates in the problem space and transmits the best solution found to other particles. This transmission allows an informed decision to be made in the next attempt to find the best possible solution (set of generator parameters).

[0154] As about Fig.15 As will be stated, the system and method of the present disclosure can be implemented in conjunction with an actual power generation system using an automatic PSS parameter generation system. In one embodiment, the present method of generating estimated PSS parameters can be implemented in a MICROSOFT WINDOWS-based application operating on a computer system capable of operating a WINDOWS environment, the present invention having its own graphical user interface (GUI) and an interface for transmitting the generated parameters to the PSS system.

[0155] As disclosed in step 3, the estimated parameter values ​​derived by PSO are based on manufacturer values ​​and real-time measurement values. The PSO method estimates the parameter values ​​based on the measurement values ​​to determine whether the parameter values ​​defined by the manufacturer are appropriate, and derives new values ​​of these parameters through the PSO estimation process for use in the generation of PSS parameters in steps 4 and 5 to be described below.

[0156] Using the recorded generator frequency ω, actual electromechanical power P e The time domain simulation of the terminal current It calculates the generator frequency change Δω. In addition, as shown, the generator stator resistance R is used in the process aFor the simulation system model, it is assumed that the governor adopts a proportional and integral governor and a first-order fuel pump dynamic equation. The simulation model parameters are H (generator system inertia), T A (fuel pump time constant), K P (Speed ​​governor proportional gain), K I (governor integral gain), W nfl (no-load fuel consumption) and droop (speed drop).

[0157] The simulation results are compared with the recorded data. If the results do not match, the above model parameters are adjusted through PSO technology to provide the best match.

[0158] The PSO routine starts with a set of ten particles (solutions) and then searches for the optimum in the problem space by following the best particle found so far. The current parameters are considered as particles, and for k = 1, ..., N, for each particle (H, T A , K P , K I , W nfl and speed drop) to calculate the step response Δω of the model m (k). The calculated response is compared with the actual system response. When the sampling value of the actual system response at the kth stage is Δω(k), the fitness function for selecting the best particle is Δω(k) and Δω m (k), k = 1, ..., N, the fitness function is as follows:

[0159]

[0160] Initial generator frequency ω, actual electromechanical power P e and the generated current I t is provided as input. The frequency outputs are compared to estimate each parameter. The simulation model parameters are identified as H, T A , K P , K1, W nfl and rappelling.

[0161] Considering the variable v n is the particle velocity, variable x n is the current particle (solution), the variable and variable P global are defined as the optimal value of a particle and the optimal value of all particles, respectively, and the parameter α is the inertia weight, rand1 and rand2 are random numbers between 0 and 1, and β1 and β2 are learning factors. When using PSO for each parameter H, T A , K P , K I , W nflAfter finding these six optimal values, the particle updates its velocity and position using equations (29) and (30):

[0162]

[0163] x n+1 =x n +v an (30)

[0164] In one embodiment, reference Fig.11 , the calculation procedure of PSO technology is summarized as follows:

[0165] Process 701: Initialize iteration index NOI=0, J=0.

[0166] Process 702: Initialize the position of each particle.

[0167] Process 704: Determine an initial value of the optimal value.

[0168] Process 706: Determine the response of the model using the selected particle positions.

[0169] Process 708: Determine the fitness function based on the obtained model response and the recorded response to check the best particle. If the model response is better, update the best particle. In the case where the parameter is inertia H, as stated, the simulation parameters and equations 28 and 29 apply to the process.

[0170] Process 710: Until all particles are counted in step 710, increment particle counter 711 and repeat steps 704, 706 and 708 for each particle.

[0171] Process 712: Update new particle position and velocity.

[0172] Process 714: Determine whether the maximum number of iterations has been reached. If the maximum number of iterations has not been reached, go to process 716. If the maximum number of iterations has been reached, go to process 717.

[0173] Process 716: Increment iteration counters (NOI and I).

[0174] Process 717: If the index J is 50, go to step 702. If not, go to step 704.

[0175] At the end of the iterative process, the global optimum for each of the six parameters contains the closest estimate of the parameter value.

[0176] Process 708: Compare the estimated value to the received and stored manufacturer's value and variance.

[0177] From this process, H, TA , K P , K I , W nfl and the best estimate of the speed drop, and as referenced Figure 7 The described values ​​are respectively compared with the manufacturer's values.

[0178] In an exemplary embodiment, the estimated power generation system inertia constant H in a test is confirmed using a partial load dump test. As shown in Figure 12, this test result reflects the calculated unit power generation system inertia value H of 5.95MW-s / MVA. The value of the power generation system inertia constant H calculated in step 3 matches the data provided by the manufacturer. The power generation system inertia H can be used to scale the active power input to the acceleration power integral PSS. The derived compensation frequency ω^ is mentioned in equation (6) above.

[0179] 2.1.4 Step 4: Determine the lead-lag phase compensation time constant T1-T6

[0180] To determine the lead-lag time constants for phase compensation, three sub-steps are described, which include an initial frequency response test. First, a pseudo-white noise test input is applied to the AVR summing junction for approximately one minute and the test input and generator voltage V are recorded. t . Change / change in terminal voltage ΔV t can therefore be determined. Second, the recorded signal is used to obtain the frequency response of the uncompensated system using a Fast Fourier Transform (FFT). Third, in order to obtain a compensated phase curve that is close to zero (0 to approximately 30 degrees) within the frequency range where most power oscillations exist (i.e., from 0.1 to 3 Hz), the phase compensation time constants T1, T2, ..., T6 are determined. It will be appreciated by those skilled in the art that it is not possible to achieve or approach zero within the frequency range of 0.1 to 3 Hz. For most cases, amounts up to about 30 degrees have been found to be satisfactory for the process, although other values ​​are possible. These phase compensation time constants are used as shown in FIG. Fig.13 The PSO technique and use described above are similar to Fig.11 Furthermore, it will be appreciated by those skilled in the art that the maximum amplitude of the input pseudo white noise is limited to an amount that ensures a linear or otherwise stable AVR response.

[0181] In step 4, the PSO technique as used and described above with respect to step 3 is used, except that the calculation of the phase compensation of the lead-lag filter with T1, T2, ..., T6 is adjusted by the PSO in the following equation of the transfer function G(s) of the lead-lag filter:

[0182]

[0183] When the compensation phase curve becomes close to zero in the power oscillation frequency range from 0.1 to 3 Hz, the estimated time constant is set for the PSS parameter.

[0184] Thus, estimated phase compensation time constants T1, T2, ..., T6 are generated by the present method and system as PSS parameter inputs.

[0185] In an exemplary embodiment, using the process described in step 4, the phase lead-lag parameters T1, T2, ..., T6 are determined based on the PSO using the measured pseudo-white noise input and the generator voltage output (i.e., the change / variation ΔV in the terminal voltage). t ) is automatically calculated. Figures 14(a) and 14(b) illustrate the generator voltage E generated by a test. t and the actual electromechanical power P e The calculated time constants of the lead-lag phase compensation time constants are T1 = 0.1, T2 = 0.02, T3 = 0.2, T4 = 0.005, T5 = 0.2 and T6 = 0.005. Figure 14(c) illustrates the calculated frequency response of the lead-lag block and the required phase compensation.

[0186] 2.1.5 Step 5: Determine the PSS gain K s

[0187] The final step in the method for automatically tuning the PSS parameter input controller for use with the accelerated power integration, step 5, is to determine the PSS gain K s The PSS gain K generated by the process in step 5 is s The value of is set to a value well below the limit at which the exciter mode is unstable. GM may also be a predetermined gain margin determined to be desirable, such as, for example, one third of the limit at which the exciter mode is unstable.

[0188] To generate this initial PSS gain K for commissioning the generator s , based on the open-loop frequency response of white noise from the input to the AVR summing point to the PSS output with a compensated lead-lag filter, the gain margin is estimated using the open-loop frequency response.

[0189] Since the PSS output is positively added to the AVR summing junction, the gain margin is determined at the phase crossover frequency of zero degrees. Therefore, if a 10dB gain margin is required, which is one-third of the instability gain, the PSS gain is calculated as follows:

[0190] K s1 =10 GM-10 (32)

[0191] GM is the use of K s1= 1. Fig.16 As shown, when the phase angle of the positive feedback system is zero degree, the gain margin GM is calculated.

[0192] With the phase compensation generated in step 4, damping increases with increasing stabilizer gain (Ks). If the stabilizer gain is increased to a value where the exciter mode crosses the right half plane of the s-domain, system instability will result. This value is verified during PSS commissioning from the gain margin GM assumed for a linear system. However, as one skilled in the art will appreciate, since power generation systems are not linear, the gain can be reduced to about one-third of the instability gain. The final value gain setting was chosen to be 15, which is three times smaller than the instability gain generally known in the industry.

[0193] Fig.15 A block diagram of the present system is provided in comparison to the prior art system shown in FIG. 1. As shown, the debug control system 100 is communicatively coupled to the PSS 23 via a PSS input interface 25 for providing the PSS 23 with its initial set of PSS parameters. For debug purposes, V S The output of the PSS 23 and the summing point 56 of the AVR 22 are not connected.

[0194] Fig.16 The open loop frequency response from 0.1 Hz to 10.0 Hz is shown. Fig.16 The phase and gain of the open loop frequency response are shown.

[0195] The test results in the graph of FIG17 illustrate the real-time response of the synchronous machine during commissioning and clearly show the immediate effect of the power system stabilizer as disclosed herein. FIG17(a) is a graph recording and illustrating the MW of a machine without the automatic PSS parameter input controller PSS of the present disclosure when a 2% voltage step is applied. In contrast, FIG17(b) is a graph illustrating the test results of the machine MW with the automatic PSS parameter input controller for PSS of the present disclosure when a 2% voltage step is applied. It can be seen that when commissioning a power generation system with an accelerating power integral PSS as an AVR input, the performance of the power generation system is significantly improved when the automatic PSS parameter input controller of the present disclosure is used.

[0196] 4. Computer environment

[0197] refer to Fig.18The operating environment of the illustrated embodiment of the system and / or method for detecting incipient faults in a generator as described herein is a computer system 1000 having a computer 1002 including at least one high-speed central processing unit (CPU) 1004, a memory system 1006 interconnected with at least one bus structure 1008, an input device 1010, and an output device 1012. These elements are interconnected by at least one bus structure 1008. The memory system 1006 includes a non-transitory memory storing computer executable instructions for enabling and instructing the computer 1002 to perform the method as described herein.

[0198] As described above, the input and output devices may include a communication interface including a graphical user interface. Any or all of the computer components of the network interface and communication systems and methods may be any computing device, including but not limited to laptops, PDAs, cellular / mobile phones, and potentially dedicated devices. In one embodiment, the methods and systems of the present disclosure may be software implemented as any "app" thereon and considered within the scope of the present disclosure.

[0199] The illustrated CPU 1004 of the system for detecting incipient faults of a generator is of a familiar design and includes an arithmetic logic unit (ALU) 1014 for performing calculations, a set of registers 1016 for temporarily storing data and instructions, and a control unit 1018 for controlling the operation of the computer system 1000. For the CPU 1004, any of a variety of processors, including at least those from Digital Equipment, Sun, MIPS, Motorola, NEC, Intel, Cyrix, AMD, HP, and Nexgen are also preferred but not limited thereto. The illustrated embodiment operates on an operating system designed to be portable to any of these processing platforms.

[0200] The memory system 1006 typically includes a high-speed main memory 1020 in the form of a medium such as a random access memory (RAM) and a read-only memory (ROM) semiconductor device on a non-transitory computer recordable medium. The present disclosure is not limited thereto, and may also include an auxiliary memory 1022 in the form of a long-term storage medium (such as a floppy disk, hard disk, tape, CD-ROM, flash memory, etc.) and other devices that use electrical, magnetic, optical or other recording media to store data. In some embodiments, the main memory 1020 may also include a video display memory for displaying images through a display device (not shown). Those skilled in the art will appreciate that the memory system 1006 may include various alternative components with various storage capacities.

[0201] Input devices 1010 and output devices 1012 may also be provided in the system or embodiments thereof as described herein, where applicable. Input devices 1010 may include any keyboard, mouse, physical transducer (such as a microphone), and may be interconnected to the computer 1002 via an input interface 1024 (such as a graphical user interface) associated with or separate from the above-mentioned communication interface including an antenna interface for wireless communication. Output devices 1012 may include a display, a printer, a transducer (such as a speaker), etc., and may be interconnected to the computer 1002 via an output interface 1026 that may include the above-mentioned communication interface including an antenna interface. Some devices, such as a network adapter or a modem, may be used as input and / or output devices.

[0202] As is familiar to those skilled in the art, the computer system 1000 also includes an operating system and at least one application. The operating system is a collection of software that controls the operation and resource allocation of the computer system. The application is a collection of software that uses the computer resources provided by the operating system to perform the tasks required by the method of detecting an incipient fault in a generator and / or any of the above-described processes and process steps.

[0203] According to the practice of those skilled in the art of computer programming, the present disclosure is described below with reference to a symbolic representation of operations performed by computer system 1000. Such operations are sometimes referred to as being computer-executed. It should be understood that the symbolic operations include the manipulation of electrical signals representing data bits by CPU 1004 and the retention of data bits at memory locations in memory system 1006, as well as other processing of signals. The memory locations that retain data bits are physical locations with specific electrical, magnetic, or optical properties corresponding to the data bits. One or more embodiments may be implemented in a tangible form in one or more programs defined by computer executable instructions that may be stored on a computer-readable medium. The computer-readable medium may be any device or combination of devices described above in conjunction with memory system 1006.

[0204] As described herein through various embodiments, a system and method for generating initial PSS parameters is provided that provides very fast commissioning of a generator with excellent performance results. As described, after validating the manufacturer data, the PSS parameters can be quickly estimated using the described PSO performance parameter estimation method, which, when input to the PSS, can provide a very short time for commissioning of the generator compared to existing methods and systems.

[0205] When describing elements or features and / or embodiments thereof, the articles “a,” “an,” “the,” and “said” are intended to indicate that there are one or more elements or features. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements or features other than those specifically described.

[0206] Those skilled in the art will appreciate that various changes may be made to the above exemplary embodiments and implementations without departing from the scope of the present disclosure. Therefore, all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not limiting.

[0207] It should also be understood that the processes or steps described herein should not be construed as necessarily requiring that they be performed in the particular order discussed or illustrated. It should also be understood that additional or alternative processes or steps may be employed.

Claims

1. A system for automatically tuning / configuring an accelerating power integrating type power system stabilizer (PSS) in a digital excitation control system for controlling a grid-connected electric generator system, the grid-connected electric generator system having a prime mover system providing rotational energy to a generator having an exciter, a plurality of sensors for measuring operating characteristics of the power system, an automatic voltage regulator (AVR) having an input summing point and generating control parameters for the exciter and the generator, the PSS having a memory, a processor, computer executable instructions, a communication control interface for receiving PSS parameters, and an output for generating a control output to the AVR input summing point, the system comprising: A control module having a processor, a memory, stored computer executable instructions, a control input, and a control output, wherein the computer executable instructions include instructions for configuring the control module to perform the following process: a. Generate a set of tuning PSS lead-lag phase compensation time constants, the generation comprising: receiving a set of terminal voltages generated during operation of the grid-connected electrical power generator system; generating an uncompensated frequency response of the grid-connected electrical generator system based on the received set of generated terminal voltages; and determining a set of tuning phase compensation time constants including performing a particle swarm optimization (PSO) based on the generated uncompensated frequency response; b. Generating a tuned PSS gain value, the generating comprising: determining an open loop frequency response of a grid connected electric generator system to determine a PSS gain margin; and determining a tuned PSS gain based on the determined PSS gain margin; and c. Transmitting the determined set of tuning phase compensation time constants and the determined tuning PSS gain value from the control output to the communication control interface of the PSS.

2. The system of claim 1, wherein generating an uncompensated frequency response of the grid-connected electrical generator system to generate a set of lead-lag phase compensation time constants further comprises: performing a frequency response test on a grid-connected electric generator system, the frequency response test comprising measuring parameters of the generator, applying pseudo white noise to an AVR input summing junction, and measuring the applied pseudo white noise and the generator parameters induced by the applied pseudo white noise; The control module is configured to perform particle swarm optimization (PSO) on measured parameters of the frequency response test.

3. The system of claim 1 , wherein generating a set of lead-lag phase compensation time constants comprises: Operate power systems with generators in online mode; as well as measuring a collection of generated terminal voltages; The control module is configured to generate an uncompensated frequency response using a fast Fourier transform (FFT) according to the generated terminal voltage.

4. The system of claim 3, wherein generating a set of lead-lag phase compensation time constants further comprises: Record the baseline generator voltage V t A collection of; Apply pseudo white noise to the AVR input summing junction; Record the applied pseudo white noise; as well as Record the induced noise voltage ΔV to which pseudo white noise is applied t A collection of; The control module is configured to generate an uncompensated frequency response using FFT based on the set of induced noise voltages and the recorded applied pseudo white noise.

5. The system of claim 1, wherein the set of tuning lead-lag phase compensation time constants is constants T1, T2, T3, T4, T5 and T6.

6. The system of claim 1, wherein the control module is configured to generate a set of tuning lead-lag phase compensation time constants according to a compensation phase curve between zero and 30 degrees in a frequency range from 0.1 Hz to 3.0 Hz. 7 . The system of claim 4 , wherein the control module is configured to determine the set of tuning phase compensation time constants by performing particle swarm optimization (PSO) based on an uncompensated frequency response caused by the applied pseudo white noise.

8. The system of claim 1 , wherein generating a tuned PSS gain value comprises: A frequency response test is performed on a grid connected electric generator system, the frequency response test comprising measuring parameters of the generator, applying pseudo white noise to an AVR input summing junction, and measuring the applied pseudo white noise and the generator parameters induced by the applied pseudo white noise.

9. The system of claim 8, wherein the control module is configured to determine the tuned PSS gain by applying a predetermined gain margin to a measured parameter of the frequency response test to determine a PSS gain margin.

10. The system of claim 1, wherein determining the open loop frequency response comprises: Apply pseudo white noise to the AVR input summing junction; as well as wherein the control module is configured to apply a compensated lead-lag filter; Wherein the PSS gain margin is determined based on the phase crossover frequency of zero degrees.

11. The system of claim 10, wherein determining the open loop frequency response comprises the control module being configured to: Determine the change in reference voltage input to the AVR input summing junction caused by the applied pseudo white noise; determining the change in the PSS output caused by the applied pseudo white noise; as well as determining the change in PSS gain caused by the applied pseudo white noise; The control module is configured to generate an open-loop frequency response using a fast Fourier transform (FFT) based on the PSS output and the recorded applied pseudo white noise.

12. The system of claim 11, wherein the control module is configured to determine a change in PSS gain caused by the applied pseudo white noise based on the determined change in PSS output caused by the applied pseudo white noise by calculating a gain margin from an open loop frequency response using an FFT.

13. The system of claim 12, wherein the PSS gain margin is determined as one third of the determined change in PSS gain caused by the applied pseudo white noise.

14. The system of claim 1, wherein the control module is further configured to: receiving at a control input a set of configuration data associated with a grid-connected electric generator system, the set of configuration data including component data for a prime mover system, a generator, an AVR, and a PSS; receiving at a PSS control input a value for each of a plurality of operating parameters associated with the power system, the plurality of operating parameters selected from the group consisting of: washout time constant, generation system inertia, quadrature-axis reactance / impedance, phase compensation time constant, and PSS gain; and storing a received operating parameter value for each of a plurality of received operating parameters in a memory, At least one of generating a tuning PSS lead-lag phase compensation time constant and generating a tuning PSS gain value is performed based on the received operating parameter value.

15. The system of claim 14, wherein the control module is further configured to: generating an estimate for at least one of the received power system operating parameters; and comparing the estimated value to a received manufacturer's value of at least the operating parameter, Wherein at least one of generating a tuning PSS lead-lag phase compensation time constant and generating a tuning PSS gain value is performed based on a generated estimated value rather than a received manufacturer value.

16. The system of claim 15, wherein the received operating parameter is a saturation coefficient, further comprising: The collection of generator field current and terminal voltage is measured at each generator operating power unit, The control module is configured to generate an estimate of the saturation coefficient by applying a recursive least squares operation to the measured generator terminal voltage and field current.

17. The system of claim 15, wherein the received operating parameter is a generator data parameter, and wherein generating an estimate of the generator data parameter includes a parameter selected from the group consisting of: synchronous reactance, transient reactance, and transient time constant.

18. The system of claim 15, wherein the received operating parameter is the synchronous reactance X d , and where the compensating synchronous reactance X is generated ^ d The estimates include: A generator that is operating online and connected to the grid load, but is not outputting real power; Measuring a large number of generator terminal voltages in a step test; Determine reactive power under steady-state conditions; and The control module is configured as follows: An estimated value of the estimated generator synchronous reactance is generated based on the measured terminal voltage and the determined reactive power.

19. The system of claim 15, wherein the received operating parameter is the synchronous reactance X d , and where the compensating synchronous reactance X is generated ^ d The tuning values ​​include: Five voltage step tests.

20. The system of claim 15, wherein the control module is configured to generate a compensating reactance q-axis synchronous reactance X qcomp , which is the generated generator synchronous reactance X q One third of the tuning value.

21. The system of claim 15, wherein the received operating parameter is power system inertia, and wherein generating the estimated value of power system inertia is based on a fuel pump time constant T A , speed regulator proportional gain K P , speed regulator integral gain K I , no-load fuel consumption W nfl and rappelling.

22. The system of claim 15, further comprising generating an estimate of the compensation frequency, comprising during operation of the generator: Measuring the frequency of the generator; measuring actual power at the generator output; measuring a terminal current at an output of the generator; as well as Receiving generator stator resistance; The control module is configured to generate an estimated compensation frequency based on a measured frequency of the generator, a measured actual power, a measured terminal current and a received stator resistance of the generator.

23. The system of claim 15, wherein the control module is further configured to: According to the inertia H of the power generation system and the time constant T of the fuel pump A , speed regulator proportional gain K P , speed regulator integral gain K I , no-load fuel consumption W nfl and the speed drop to generate an estimate of the compensation frequency.

24. The system of claim 23, further comprising: During generator operation, measure the power generation system inertia H, fuel pump time constant T A , speed regulator proportional gain K P , speed regulator integral gain K I , no-load fuel consumption W nfl and rappelling; as well as comparing the estimated values ​​of each generator parameter to the measured values ​​to determine if they match or do not match; In the event that the estimated value matches the measured value, determining a compensation frequency based on the estimated value; and In the case where the estimated values ​​do not match the measured values, each generator parameter value is adjusted using particle swarm optimization (PSO) to determine an adjusted estimated parameter value for each parameter, and a compensation frequency is determined based on the adjusted estimated parameter value.

25. The system of claim 15, further comprising: Estimated washout time constant T w .

26. The system of claim 25, wherein the estimated washout time constant T w include: Apply a pseudo white noise signal to the AVR input summing junction; Increase the actual power of the generator; During the said increase period to which the pseudo white noise signal is applied, the generator frequency ω, the three-phase generator terminal voltage V t and terminal current I t ; applying a fast Fourier transform (FFT) to the measured actual power changes caused by the applied pseudo white noise; Identify the maximum frequency component; as well as Generate the tuning loss time constant T based on the identified maximum frequency component w .

27. The system of claim 26, wherein the generation of the washout time constant T w The identified maximum frequency component is multiplied by a predetermined multiplier.

28. The system of claim 27, wherein the predetermined multiplier is five.

29. The system of claim 1, further comprising: The estimated power generation system inertia H is generated by performing particle swarm optimization (PSO).

30. The system of claim 29, wherein generating the estimated power generation system inertia comprises: performing a partial load dump test on the generator to produce measured values ​​of each of a plurality of power generation system inertia-related parameters; A particle swarm optimization (PSO) is performed on each of a set of power generation system inertia related parameters to generate an estimated value of the power generation system inertia.

31. The system of claim 29, wherein particle swarm optimization (PSO) is used for one or more power generation system inertia H related parameters, the related parameters being selected from the list consisting of: power generation system inertia H, fuel pump time constant T A , speed regulator proportional gain K P , speed regulator integral gain K I , no-load fuel consumption W nfl and rappelling.

32. A method for automatically tuning / configuring an accelerating power integrating power system stabilizer (PSS) in a digital excitation control system for controlling a grid-connected electric generator system, the grid-connected electric generator system having a prime mover system providing rotational energy to a generator having an exciter, a plurality of sensors for measuring operating characteristics of the power system, an automatic voltage regulator (AVR) having an input summing point and generating control parameters for the exciter and the generator, the PSS having a memory, a processor, computer executable instructions, a communication control interface for receiving PSS parameters, and an output for generating a control output to the AVR input summing point, in a control module having the processor, the memory, the stored computer executable instructions, the control input, and the control output, the method comprising: generating a set of tuned PSS lead-lag phase compensation time constants including receiving a set of generated terminal voltages during operation of the grid-connected electrical generator system, generating an uncompensated frequency response of the grid-connected electrical generator system based on the received set of generated terminal voltages, and determining a set of tuned phase compensation time constants including performing a particle swarm optimization (PSO) based on the generated uncompensated frequency response; Generating a tuned PSS gain value includes determining an open loop frequency response of a grid-connected electric power generator system to determine a PSS gain margin and determining a tuned PSS gain based on the determined PSS gain margin; as well as The determined set of tuning phase compensation time constants and the determined tuning PSS gain value are transmitted from the control output to the communication control interface of the PSS.

33. The method of claim 32, further comprising: performing a frequency response test on a grid-connected electric generator system, the frequency response test comprising measuring parameters of the generator, applying pseudo white noise to an AVR input summing junction, and measuring the applied pseudo white noise and the generator parameters induced by the applied pseudo white noise; Therein, a particle swarm optimization (PSO) is performed on the measured applied pseudo white noise and the generator parameters induced by the applied pseudo white noise.

34. The method of claim 33, wherein generating a set of lead-lag phase compensation time constants comprises: Operate power systems with generators in online mode; measuring a collection of generated terminal voltages; In the control module, a fast Fourier transform (FFT) is used to generate an uncompensated frequency response according to the generated terminal voltage.

35. The method of claim 33, wherein generating a set of lead-lag phase compensation time constants further comprises: Record the baseline generator voltage V t A collection of; Apply pseudo white noise to the AVR input summing junction; Recording the applied pseudo white noise; and Record the induced noise voltage ΔV to which pseudo white noise is applied t A collection of; In the control module, an uncompensated frequency response is generated using a fast Fourier transform (FFT) based on a set of induced noise voltages and a recorded applied pseudo white noise.

36. The method of claim 32, wherein the set of tuning lead-lag phase compensation time constants is generated based on a compensation phase curve that is between zero and 30 degrees over a frequency range from 0.1 Hz to 3.0 Hz.

37. The method of claim 35, wherein the set of tuning phase compensation time constants is determined by performing particle swarm optimization (PSO) based on an uncompensated frequency response caused by the applied pseudo white noise.

38. The method of claim 32, further comprising: performing a frequency response test on a grid-connected electric generator system, the frequency response test comprising measuring parameters of the generator, applying pseudo white noise to an AVR input summing junction, and measuring the applied pseudo white noise and the generator parameters induced by the applied pseudo white noise; The tuned PSS gain is determined by applying a predetermined gain margin to the measured parameters of the frequency response test to determine a PSS gain margin.

39. The method of claim 32, further comprising: The estimated power generation system inertia H is generated by performing particle swarm optimization (PSO).

40. The method of claim 39, wherein generating the estimated power generation system inertia comprises: performing a partial load dump test on the generator to produce measured values ​​of each of a plurality of power generation system inertia-related parameters; A particle swarm optimization (PSO) is performed on each of a set of power generation system inertia related parameters to generate an estimated value of the power generation system inertia.

41. The method of claim 39, wherein performing particle swarm optimization (PSO) comprises performing PSO on one or more power generation system inertia H related parameters, wherein the related parameters are selected from the following list: power generation system inertia H, fuel pump time constant T A , speed regulator proportional gain K P , speed regulator integral gain K I , no-load fuel consumption W nfl and rappelling.

42. The method of claim 32, further comprising: receiving at a control input a set of configuration data associated with a grid-connected electric generator system, the set of configuration data including component data for a prime mover system, a generator, an AVR, and a PSS; receiving at a PSS control input a value for each of a plurality of operating parameters associated with the power system, the plurality of operating parameters selected from the group consisting of: washout time constant, generation system inertia, quadrature-axis reactance / impedance, phase compensation time constant, and PSS gain; and storing a received operating parameter value for each of a plurality of received operating parameters in a memory, wherein at least one of generating a tuning PSS lead-lag phase compensation time constant and generating a tuning PSS gain value is performed based on a received operating parameter value; generating an estimate for at least one of the received power system operating parameters; as well as comparing the estimated value to a received manufacturer's value of at least the operating parameter, Wherein at least one of generating a tuning PSS lead-lag phase compensation time constant and generating a tuning PSS gain value is performed based on a generated estimated value rather than a received manufacturer value.

43. The method of claim 42, further comprising: The collection of generator field current and terminal voltage is measured at each generator operating power unit, wherein the control module is configured to generate an estimate of the saturation coefficient by applying a recursive least squares operation to the measured generator terminal voltage and field current, wherein the received operating parameter is a generator data parameter, and wherein generating an estimate of the generator data parameter comprises a parameter selected from the group consisting of: a synchronous reactance, a transient reactance, and a transient time constant, The received operating parameter is the synchronous reactance X d , and where the compensating synchronous reactance X is generated ^ d The estimates include: A generator that is operating online and connected to the grid load, but is not outputting real power; Measuring a large number of generator terminal voltages in a step test; Determine reactive power under steady-state conditions; and The control module is configured as follows: An estimated value of the estimated generator synchronous reactance is generated based on the measured terminal voltage and the determined reactive power.

44. The method of claim 42, further comprising generating an estimate of the compensation frequency, comprising during operation of the generator: Measuring the frequency of the generator; measuring actual power at the generator output; measuring a terminal current at an output of the generator; as well as Receiving generator stator resistance; wherein the control module is configured to generate an estimated compensation frequency based on the measured frequency of the generator, the measured actual power, the measured terminal current and the received generator stator resistance, and The control module is further configured as follows: According to the inertia H of the power generation system and the time constant T of the fuel pump A , speed regulator proportional gain K P , speed regulator integral gain K I , no-load fuel consumption W nfl and the speed drop to generate an estimate of the compensation frequency.

45. A computer-readable medium having computer-executable instructions configured to cause a computing system to perform a method comprising: generating a set of tuned PSS lead-lag phase compensation time constants including receiving a set of generated terminal voltages during operation of the power system, generating an uncompensated frequency response of the grid-connected power generator system based on the received set of generated terminal voltages, and determining the set of tuned phase compensation time constants including performing a particle swarm optimization (PSO) based on the generated uncompensated frequency response; Generating a tuned PSS gain value includes determining an open loop frequency response of a grid-connected electric power generator system to determine a PSS gain margin and determining a tuned PSS gain based on the determined PSS gain margin; as well as The determined set of tuning phase compensation time constants and the determined tuning PSS gain value are transmitted from a control output to a communication control interface of a power system stabilizer (PSS) in a digital excitation control system that controls a power system by using an automatic voltage regulator (AVR).

46. ​​The computer readable medium of claim 45 having computer executable instructions configured to further cause a computing system to perform the following steps: A particle swarm optimization (PSO) is performed on a set of measured pseudo white noise applied to the AVR measurement summing points and measured generator parameters resulting from the applied pseudo white noise.

47. The computer readable medium of claim 46 having computer executable instructions configured to further cause a computing system to perform the following steps: receiving a set of generated terminal voltages measured when operating the power system with the generator in an online mode; and The uncompensated frequency response is generated using a fast Fourier transform (FFT) based on the generated terminal voltage.

48. The computer readable medium of claim 46 having computer executable instructions configured to further cause a computing system to perform the following steps: Receive the recorded baseline generator voltage V t A collection of; receiving applied pseudo white noise recorded when the pseudo white noise is applied to an AVR input summing junction; Receive the induced noise voltage ΔV recorded when pseudo white noise is applied t A collection of; and An uncompensated frequency response is generated using FFT from the set of induced noise voltages and the recorded applied pseudo white noise.

49. The computer readable medium of claim 46, comprising computer executable instructions for generating a set of tuning lead-lag phase compensation time constants based on a compensation phase curve between zero and 30 degrees over a frequency range from 0.1 Hz to 3.0 Hz.

50. The computer-readable medium of claim 46, comprising computer-executable instructions for determining a set of tuning phase compensation time constants by performing particle swarm optimization (PSO) based on an uncompensated frequency response caused by applied pseudo white noise.

51. The computer readable medium of claim 45 having computer executable instructions configured to further cause a computing system to perform the following steps: receiving a set of measurement results of a frequency response test on a grid-connected electrical generator system, including measured parameters of the generator, and measured applied pseudo-white noise and parameters of the generator induced by the applied pseudo-white noise; and The tuned PSS gain is determined by applying a predetermined gain margin to the measurement parameters of the received frequency test measurement set to determine a PSS gain margin.

52. The computer readable medium of claim 45 having computer executable instructions configured to further cause a computing system to perform the following steps: The estimated power generation system inertia H is generated by performing particle swarm optimization PSO.

53. The computer readable medium of claim 52 having computer executable instructions configured to further cause a computing system to perform the following steps: receiving a generated measured value of each of a plurality of power generation system inertia H related parameters resulting from performing a partial load dump test on the generator, The computer readable medium is configured to perform particle swarm optimization (PSO) on each of a set of power generation system inertia related parameters to generate an estimated value of the power generation system inertia H.

54. The computer readable medium of claim 52 having computer executable instructions configured to further cause a computing system to perform the following steps: The performing of the particle swarm optimization PSO includes performing the PSO on one or more power generation system inertia H related parameters, wherein the related parameters are selected from the following list: power generation system inertia H, fuel pump time constant T A , speed regulator proportional gain K P , speed regulator integral gain K I , no-load fuel consumption W nfl and rappelling.

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