A fast method for out-of-step protection using state plane trajectories analysis

This thesis proposes a novel out-of-step protection technique using the state-plane representation of the generator speed and power angle. The critical clearing angle is computed using the principle that the total energy of the system at the instant the fault is cleared should be equal to the maximum potential energy of the system. The critical clearing time corresponding to this value of critical clearing angle is obtained directly using the time calibration of the relative speed versus power angle solution curve. The simultaneous calculation of the critical clearing angle and the time makes the proposed state plane approach much faster than the two-blinder scheme, Equal Area Criterion (EAC) method, rate of change of impedance method, the Swing Center Voltage (SCV) technique, transient energy calculation method, and the frequency deviation calculation from voltage signal method discussed in the literature. The proposed state plane prediction scheme is used to detect the first swing out-ofstep condition in single machine infinite bus (SMIB) system as well as larger power system configurations (two-area and IEEE 39-bus test systems) using system wide information. A coherency analysis is performed in a multi-machine system to find out the two critical groups of generators. The critical generator groups are then represented with a SMIB equivalent system, and the state plane algorithm is applied to the reduced equivalent. Electromagnetic transient simulations are carried out using PSCAD/EMTDC™ to test the proposed algorithm in the above discussed test systems. The simulation studies show that the proposed method is computationally efficient, and accurate even for the larger power systems. The technique also does not require any offline studies. This thesis also proposes another out-of-step protection technique using generator state deviations to detect multi-swing instability conditions in power system. It uses wide-area measurements of generator electrical power and speed deviations as inputs to the proposed scheme to detect instability. This technique is not as fast as the state plane approach but can predict multi-swing instability conditions in power system. The state plane method and state deviation method are used together to find first swing and multi-swing instability conditions. Two-area power system configuration is used to demonstrate multi-swing instability prediction. Different power swing conditions such as stable, first swing unstable and multi-swing unstable scenarios are created and the proposed techniques are tested to verify their performance. The proposed techniques are also compared with the conventional two blinder technique. A facility for hardware-in-the-loop testing of the relays using a digital simulator is available in the Power System Laboratory at the University of Saskatchewan. An out-of-step relay module is developed in a digital signal processing board (ADSP − BF533™ from Analog Devices Inc.) and a closed loop test is performed using the real time digital simulator (RTDS™). The simulator mimics the power system behaviour in real time, and the analog time signals from simulator can be communicated to the relay module. The relay can also feed back the signals to the simulator which can be used to operate the circuit breaker elements in the power system. The SMIB and two area systems are used to test the relay in real time. The relay prototypes for both of the proposed techniques are developed in this thesis. The hardware-in-the-loop implementation and testing show that the calculation times required for the proposed methods are small, and the state plane method especially can predict instability condition much faster than all other methods in current literature

Power System Stability Analysis Using Wide Area Measurement System

Advances in wide area measurement systems have transformed power system operation from simple visualization, state estimation, and post-mortem analysis tools to real-time protection and control at the systems level. Transient disturbances (such as lightning strikes) exist only for a fraction of a second but create transient stability issues and often trigger cascading type failures. The most common practice to prevent instabilities is with local generator out-of-step protection. Unfortunately, out-of-step protection operation of generators may not be fast enough, and an instability may take down nearby generators and the rest of the system by the time the local generator relay operates. Hence, it is important to assess power system stability over transmission lines as soon as the transient instability is detected instead of relying on purely localized out-of-step protection in generators. This thesis proposes a synchrophasor-based out-of-step prediction methodology at the transmission line level using wide area measurements from optimal phasor measurement unit (PMU) locations in the interconnected system. Voltage and current measurements from wide area measurement systems (WAMS) are utilized to find the swing angles. The proposed scheme was used to predict the first swing out-of-step condition in a Western Systems Coordinating Council (WSCC) 9 bus power system. A coherency analysis was first performed in this multi-machine system to determine the two coherent groups of generators. The coherent generator groups were then represented with a two-machine equivalent system, and the synchrophasor-based out-of-step prediction algorithm then applied to the reduced equivalent system. The coherency among the group of generators was determined within 100 ms for the contingency scenarios tested. The proposed technique is able to predict the instability 141.66 to 408.33 ms before the system actually reaches out-of-step conditions. The power swing trajectory is either a steady-state trajectory, monotonically increasing type (when the system becomes unstable), or oscillatory type (under stable conditions). Un- der large disturbance conditions, the swing could also become non-stationary. The mean and variance of the signal is not constant when it is monotonically increasing or non-stationary. An autoregressive integrated (ARI) approach was developed in this thesis, with differentiation of two successive samples done to make the mean and variance constant and facilitate time series prediction of the swing curve. Electromagnetic transient simulations with a real-time digital simulator (RTDS) were used to test the accuracy of the proposed algorithm with respect to predicting transient in- stability conditions. The studies show that the proposed method is computationally efficient and accurate for larger power systems. The proposed technique was also compared with a conventional two blinder technique and swing center voltage method. The proposed method was also implemented with actual PMU measurements from a relay (General Electric (GE) N60 relay). The testing was carried out with an interface between the N60 relay and the RTDS. The WSCC 9 bus system was modeled in the simulator and the analog time signals from the optimal location in the network communicated to the N60 relay. The synchrophasor data from the PMUs in the N60 were used to back-calculate the rotor angles of the generators in the system. Once the coherency was established, the swing curves for the coherent group of generators were found from time series prediction (ARI model). The test results with the actual PMUs match quite well with the results obtained from virtual PMU-based testing in the RTDS. The calculation times for the time series prediction are also very small. This thesis also discusses a novel out-of-step detection technique that was investigated in the course of this work for an IEEE Power Systems Relaying Committee J-5 Working Group document using real-time measurements of generator accelerating power. Using the derivative or second derivative of a measurement variable significantly amplifies the noise term and has limited the actual application of some methods in the literature, such as local measurements of voltage or voltage deviations at generator terminals. Another problem with the voltage based methods is taking an average over a period; the intermediate values cancel out and, as a result, just the first and last sample values are used to find the speed. This effectively means that the sample values in between are not used. The first solution proposed to overcome this is a polynomial fitting of the points of the calculated derivative points (to calculate speed). The second solution is the integral of the accelerating power method (this eliminates taking a derivative altogether). This technique shows the direct relationship of electrical power deviation to rotor acceleration and the integral of accelerating power to generator speed deviation. The accelerating power changes are straightforward to measure and the values obtained are more stable during transient conditions. A single machine infinite bus (SMIB) system was used for the purpose of verifying the proposed local measurement based method

Small-Signal Modelling and Analysis of Doubly-Fed Induction Generators in Wind Power Applications

The worldwide demand for more diverse and greener energy supply has had a significant impact on the development of wind energy in the last decades. From 2 GW in 1990, the global installed capacity has now reached about 100 GW and is estimated to grow to 1000 GW by 2025. As wind power penetration increases, it is important to investigate its effect on the power system. Among the various technologies available for wind energy conversion, the doubly-fed induction generator (DFIG) is one of the preferred solutions because it offers the advantages of reduced mechanical stress and optimised power capture thanks to variable speed operation. This work presents the small-signal modelling and analysis of the DFIG for power system stability studies. This thesis starts by reviewing the mathematical models of wind turbines with DFIG convenient for power system studies. Different approaches proposed in the literature for the modelling of the turbine, drive-train, generator, rotor converter and external power system are discussed. It is shown that the flexibility of the drive train should be represented by a two-mass model in the presence of a gearbox. In the analysis part, the steady-state behaviour of the DFIG is examined. Comparison is made with the conventional synchronous generators (SG) and squirrel-cage induction generators to highlight the differences between the machines. The initialisation of the DFIG dynamic variables and other operating quantities is then discussed. Various methods are briefly reviewed and a step-by-step procedure is suggested to avoid the iterative computations in initial condition mentioned in the literature. The dynamical behaviour of the DFIG is studied with eigenvalue analysis. Modal analysis is performed for both open-loop and closed-loop situations. The effect of parameters and operating point variations on small signal stability is observed. For the open-loop DFIG, conditions on machine parameters are obtained to ensure stability of the system. For the closed-loop DFIG, it is shown that the generator electrical transients may be neglected once the converter controls are properly tuned. A tuning procedure is proposed and conditions on proportional gains are obtained for stable electrical dynamics. Finally, small-signal analysis of a multi-machine system with both SG and DFIG is performed. It is shown that there is no common mode to the two types of generators. The result confirms that the DFIG does not introduce negative damping to the system, however it is also shown that the overall effect of the DFIG on the power system stability depends on several structural factors and a general statement as to whether it improves or detriorates the oscillatory stability of a system can not be made

Time domain analysis of switching transient fields in high voltage substations

Switching operations of circuit breakers and disconnect switches generate transient currents propagating along the substation busbars. At the moment of switching, the busbars temporarily acts as antennae radiating transient electromagnetic fields within the substations. The radiated fields may interfere and disrupt normal operations of electronic equipment used within the substation for measurement, control and communication purposes. Hence there is the need to fully characterise the substation electromagnetic environment as early as the design stage of substation planning and operation to ensure safe operations of the electronic equipment. This paper deals with the computation of transient electromagnetic fields due to switching within a high voltage air-insulated substation (AIS) using the finite difference time domain (FDTD) metho

NASA advanced aeronautics design solar powered remotely piloted vehicle

Environmental problems such as the depletion of the ozone layer and air pollution demand a change in traditional means of propulsion that is sensitive to the ecology. Solar powered propulsion is a favorable alternative that is both ecologically harmless as well as cost effective. Integration of solar energy into designs ranging from futuristic vehicles to heating is beneficial to society. The design and construction of a Multi-Purpose Remotely Piloted Vehicle (MPRPV) seeks to verify the feasibility of utilizing solar propulsion as a primary fuel source. This task has been a year long effort by a group of ten students, divided into five teams, each dealing with different aspects of the design. The aircraft was designed to take-off, climb to the design altitude, fly in a sustained figure-eight flight path, and cruise for approximately one hour. This mission requires flight at Reynolds numbers between 150,000 and 200,000 and demands special considerations in the aerodynamic design in order to achieve flight in this regime. Optimal performance requires a light weight configuration with both structural integrity and maximum power availability. The structure design and choice of solar cells for the propulsion was governed by the weight, efficiency, and cost considerations. The final design is a MPRPV weighting 35 N which cruises 7 m/s at the design altitude of 50 m. The configuration includes a wing composed of balsa and foam NACA 6409 airfoil sections and carbon fiber spars, a tail of similar construction, and a truss structure fuselage. The propulsion system consists of 98 10 percent efficient solar cells donated by Mobil Solar, a NiCad battery for energy storage, and a folding propeller regulated by a lightweight and efficient control system. The airfoils and propeller chosen for the design were research and tested during the design process

Instrumentation for measuring the dynamic pressure on rotating compressor blades

To establish the capability for measurement of oscillatory pressure on rotating blades, miniature fast response semiconductor strain gage pressure transducers (2mm x 0.33mm) were mounted in several configurations on thin titanium and steel compressor blades and subjected to pressure cycles from 1 to 310 kPa during static tests and spin tests. Static test conditions included 20 C to 150 C, 0 to 3000 tensile microstrain, -1000 to +1000 bending microstrain and + or - 650G vibration. The spin test conditions included 20 C to 82 C at 0 to 90,000G. Durability was excellent. Pressure transducer sensitivity changed by only a few percent over this range of environmental conditions. Noise signal due to oscillatory acceleration normal to the diaphragm was acceptable (0.33Pa/G). Noise signal due to oscillatory strain was acceptable (0.5 Pa/microstrain) when the transducer was mounted on a 0.05mm rubber pad, with a total buildup of 0.38mm on the measure surface. Back mounting or partial recessing to eliminate buildup, increased the strain effect to 1.2 Pa/microstrain. Flush mounting within the blade to eliminate buildup reduced the strain effect, but required development of a special transducer shape. This transducer was not available in time for spin tests. Unpredictable zero drift + or - 14 kPa ruled out the use of these mounting arrangements for accurate steady-state (D.C.) measurements on rotating blades. The two best configurations fully developed and spin tested were then successfully applied in the NAS3-20606 rotating fan flutter program for quantitative measurement of oscillatory pressure amplitudes

Precision Pointing Control System (PPCS) system design and analysis

The precision pointing control system (PPCS) is an integrated system for precision attitude determination and orientation of gimbaled experiment platforms. The PPCS concept configures the system to perform orientation of up to six independent gimbaled experiment platforms to design goal accuracy of 0.001 degrees, and to operate in conjunction with a three-axis stabilized earth-oriented spacecraft in orbits ranging from low altitude (200-2500 n.m., sun synchronous) to 24 hour geosynchronous, with a design goal life of 3 to 5 years. The system comprises two complementary functions: (1) attitude determination where the attitude of a defined set of body-fixed reference axes is determined relative to a known set of reference axes fixed in inertial space; and (2) pointing control where gimbal orientation is controlled, open-loop (without use of payload error/feedback) with respect to a defined set of body-fixed reference axes to produce pointing to a desired target

An example of requirements for Advanced Subsonic Civil Transport (ASCT) flight control system using structured techniques

The requirements are presented for an Advanced Subsonic Civil Transport (ASCT) flight control system generated using structured techniques. The requirements definition starts from initially performing a mission analysis to identify the high level control system requirements and functions necessary to satisfy the mission flight. The result of the study is an example set of control system requirements partially represented using a derivative of Yourdon's structured techniques. Also provided is a research focus for studying structured design methodologies and in particular design-for-validation philosophies