In this paper, we propose a framework for coordinating distributed energy resources (DERs) connec... more In this paper, we propose a framework for coordinating distributed energy resources (DERs) connected to a power distribution system, the model of which is not completely known, so that they collectively provide a specified amount of active power to the bulk power system, while respecting distribution line capacity limits. The proposed framework consists of (i) a linear time-varying input-output (IO) system model that represents the relation between the DER active power injections (inputs), and the total active power exchanged between the distribution and bulk power systems (output); (ii) an estimator that aims to estimate the IO model parameters, and (iii) a controller that determines the optimal DER active power injections so the power exchanged between both systems equals to the specified amount at a minimum generating cost. We formulate the estimation problem as a box-constrained quadratic program and solve it using the projected gradient descent algorithm. To resolve the potential issue of collinearity in the measurements, we introduce random perturbations in the DER active power injections during the estimation process. Using the estimated IO model, the optimal DER coordination problem to be solved by the controller can be formulated as a convex optimization problem, which can be solved easily. The effectiveness of the framework is validated via numerical simulations using the IEEE 123-bus distribution test feeder.
In this paper, we develop a reduced-order model for synchronous generator dynamics via selective ... more In this paper, we develop a reduced-order model for synchronous generator dynamics via selective modal analysis. Then, we use this reduced-order model to formulate a balancing authority (BA) area dynamic model. Next, we use the BA area model to design an adaptive automatic generation control (AGC) scheme, with self-tuning gain, that decreases the amount of regulation needed and potentially reduces the associated costs. In particular, we use the BA area model to derive a relationship between the actual frequency response characteristic (AFRC) of the BA area, the area control error, the system frequency, and the total generation. We make use of this relationship to estimate the AFRC online, and set the frequency bias factor equal to the online estimation. As a result, the AGC system is driven by the exact number of MW needed to restore the system frequency and the real power interchange to the desired values. We demonstrate the proposed ideas with a single machine infinite bus, the 9-bus 3-machine Western Electricity Coordinating Council (WECC), and a 140-bus 48-machine systems.
2013 46th Hawaii International Conference on System Sciences, 2013
ABSTRACT In electric power systems, a key challenge is to quickly and accurately estimate how clo... more ABSTRACT In electric power systems, a key challenge is to quickly and accurately estimate how close the system is to its stability limits. This paper investigates using synchrophasor measurements at two buses connected by a transmission line to calculate parameters for a pair of Thevenin equivalent sources, which when connected by the transmission line model provide an equivalent power system representation. As seen from the transmission line, the angle difference between the two Thevenin equivalent sources is termed the "angle across the system" for that transmission line. In the case of a lossless transmission line with voltage support on both ends, the "angle across the system" (as seen from the line) is the difference between the transmission line bus voltage phase angles, to ensure steady-state stability under these conditions, it is well known that this angle difference must be less than 90 degrees. This paper extends these ideas and proposes the notion of the "angle across the system" described above as a gauge for assessing the system's proximity to its stability limit.
It is often necessary to approximate the probability density function of a random variable from g... more It is often necessary to approximate the probability density function of a random variable from given statistical moments. The Gram-Charlier Type A series is one well known method for such representations. In this note, the Gram-Charlier Type A series is generalized to the multidimensional case.
hroughout the cvolulion of electrical engineering, the spc-T ciiilties lhal attracl sttitleiits h... more hroughout the cvolulion of electrical engineering, the spc-T ciiilties lhal attracl sttitleiits have changed rapidly and of-Len. Sitice the iiitroduclion o r solid-slale clcclronics, engineering education has seen student interest shift further and firther from the electric power area. Huwever, llic need for clectrical engineers with a background in power liiis never driipped hclow Lhc crilical level where all prograins were sliuL down. When otililics experienced slow years, lhc inanufaacluring and
IEEE International Symposium on Circuits and Systems
Modeling issues and results of simulating a disturbance on a realistic system using a supercomput... more Modeling issues and results of simulating a disturbance on a realistic system using a supercomputer as well as parallel processing are discussed. The method is based on algebraizing the DAE equations and solving them using Newton's method. Current work is focused on using the multiple processors in the Clay 2 machine and the time windowing concept. Details like the relay performance and switching operations are included
Traditional load supply and interchange capabilities re¬ present maximums based on steady state g... more Traditional load supply and interchange capabilities re¬ present maximums based on steady state generation, line flow, and voltage constraints. If the system cannot survive a list of transients when operated at these capabilities, the current computational al¬ gorithms do no provide a means for systematically determining alternative secure capabilities. In this paper, the recent results in direct stability methods are applied to give reasonably rapid solu¬ tions to this problem. The concept of a potential energy boundary surface (PEBS) is utilized to obtain transient energy stability margins and their sensitivity to load levels. The energy margins and their sensitivities are used to direct a systematic search for approximate stability limited capabilities.
After nearly four decades of research in power system stability via Lyapunov or energy functions,... more After nearly four decades of research in power system stability via Lyapunov or energy functions, the method is now on the verge of being implemented for assessment of on-line dynamic security. The main bottleneck has been in the proper characterization of the stability boundary and defining the fault-dependent region of attraction locally around the controlling unstable equilibrium points. Now there is a better understanding of this issue and, hence, a number of algorithms have been proposed. Improved generating unit models and transmission network models are now being included in the technique. In this paper, an overview is presented of the theory, practical implementation, and future research issues in this area.
ensure the qualification of environmentally qualified, safety-related equipment is performed Phas... more ensure the qualification of environmentally qualified, safety-related equipment is performed Phase consists of the evaluation of a selected subset of the safety-related equipment For this subset the qualification documen tation was reviewed and the maintenance activities that are required to ensure the qualification of the equipment were determined The actual maintenance being performed at the nuclear power plant on the equipment under consideration was determined Based on this information, recommendations were made for im provements and changes The recommendations included 1) Recommendations for incorporating additional maintenance that should be performed to ensure equipment qualification 2) Recommendations to consider deleting unnecessary or re dundant maintenance, or reducing the frequency of main¬ tenance as a result of qualification data 3) Recommendations to revise the maintenance procedures as a result of qualification considerations 4) Recommendations to revise the maintenance procedure to im¬ prove the overall maintenance activity Examples of each kind of recommendation are included A program to evaluate a subset of the safety-related equipment is an effective way to determine what maintenance, ofthat required for equipment qualification, is in place, and to provide the recommen dations for additional maintenance actions to ensure qualification 83 WM 023-9
for transformers and circuits, respectively, to zero). Although the masking is not completely eli... more for transformers and circuits, respectively, to zero). Although the masking is not completely eliminated, its effects are reduced. In summary, the new ranking algorithms does remarkably well and is superior to the old algorithm. The ranking agrees almost perfectly with the ranking produced by calculating PI from de load flows; the correla¬ tion between overloads and high rank is also quite good, the only difficulty being masking. The effects of masking can be greatly reduced through partitioning followed by multiple rankings.
In this paper, we propose a framework for coordinating distributed energy resources (DERs) connec... more In this paper, we propose a framework for coordinating distributed energy resources (DERs) connected to a power distribution system, the model of which is not completely known, so that they collectively provide a specified amount of active power to the bulk power system, while respecting distribution line capacity limits. The proposed framework consists of (i) a linear time-varying input-output (IO) system model that represents the relation between the DER active power injections (inputs), and the total active power exchanged between the distribution and bulk power systems (output); (ii) an estimator that aims to estimate the IO model parameters, and (iii) a controller that determines the optimal DER active power injections so the power exchanged between both systems equals to the specified amount at a minimum generating cost. We formulate the estimation problem as a box-constrained quadratic program and solve it using the projected gradient descent algorithm. To resolve the potential issue of collinearity in the measurements, we introduce random perturbations in the DER active power injections during the estimation process. Using the estimated IO model, the optimal DER coordination problem to be solved by the controller can be formulated as a convex optimization problem, which can be solved easily. The effectiveness of the framework is validated via numerical simulations using the IEEE 123-bus distribution test feeder.
In this paper, we develop a reduced-order model for synchronous generator dynamics via selective ... more In this paper, we develop a reduced-order model for synchronous generator dynamics via selective modal analysis. Then, we use this reduced-order model to formulate a balancing authority (BA) area dynamic model. Next, we use the BA area model to design an adaptive automatic generation control (AGC) scheme, with self-tuning gain, that decreases the amount of regulation needed and potentially reduces the associated costs. In particular, we use the BA area model to derive a relationship between the actual frequency response characteristic (AFRC) of the BA area, the area control error, the system frequency, and the total generation. We make use of this relationship to estimate the AFRC online, and set the frequency bias factor equal to the online estimation. As a result, the AGC system is driven by the exact number of MW needed to restore the system frequency and the real power interchange to the desired values. We demonstrate the proposed ideas with a single machine infinite bus, the 9-bus 3-machine Western Electricity Coordinating Council (WECC), and a 140-bus 48-machine systems.
2013 46th Hawaii International Conference on System Sciences, 2013
ABSTRACT In electric power systems, a key challenge is to quickly and accurately estimate how clo... more ABSTRACT In electric power systems, a key challenge is to quickly and accurately estimate how close the system is to its stability limits. This paper investigates using synchrophasor measurements at two buses connected by a transmission line to calculate parameters for a pair of Thevenin equivalent sources, which when connected by the transmission line model provide an equivalent power system representation. As seen from the transmission line, the angle difference between the two Thevenin equivalent sources is termed the "angle across the system" for that transmission line. In the case of a lossless transmission line with voltage support on both ends, the "angle across the system" (as seen from the line) is the difference between the transmission line bus voltage phase angles, to ensure steady-state stability under these conditions, it is well known that this angle difference must be less than 90 degrees. This paper extends these ideas and proposes the notion of the "angle across the system" described above as a gauge for assessing the system's proximity to its stability limit.
It is often necessary to approximate the probability density function of a random variable from g... more It is often necessary to approximate the probability density function of a random variable from given statistical moments. The Gram-Charlier Type A series is one well known method for such representations. In this note, the Gram-Charlier Type A series is generalized to the multidimensional case.
hroughout the cvolulion of electrical engineering, the spc-T ciiilties lhal attracl sttitleiits h... more hroughout the cvolulion of electrical engineering, the spc-T ciiilties lhal attracl sttitleiits have changed rapidly and of-Len. Sitice the iiitroduclion o r solid-slale clcclronics, engineering education has seen student interest shift further and firther from the electric power area. Huwever, llic need for clectrical engineers with a background in power liiis never driipped hclow Lhc crilical level where all prograins were sliuL down. When otililics experienced slow years, lhc inanufaacluring and
IEEE International Symposium on Circuits and Systems
Modeling issues and results of simulating a disturbance on a realistic system using a supercomput... more Modeling issues and results of simulating a disturbance on a realistic system using a supercomputer as well as parallel processing are discussed. The method is based on algebraizing the DAE equations and solving them using Newton's method. Current work is focused on using the multiple processors in the Clay 2 machine and the time windowing concept. Details like the relay performance and switching operations are included
Traditional load supply and interchange capabilities re¬ present maximums based on steady state g... more Traditional load supply and interchange capabilities re¬ present maximums based on steady state generation, line flow, and voltage constraints. If the system cannot survive a list of transients when operated at these capabilities, the current computational al¬ gorithms do no provide a means for systematically determining alternative secure capabilities. In this paper, the recent results in direct stability methods are applied to give reasonably rapid solu¬ tions to this problem. The concept of a potential energy boundary surface (PEBS) is utilized to obtain transient energy stability margins and their sensitivity to load levels. The energy margins and their sensitivities are used to direct a systematic search for approximate stability limited capabilities.
After nearly four decades of research in power system stability via Lyapunov or energy functions,... more After nearly four decades of research in power system stability via Lyapunov or energy functions, the method is now on the verge of being implemented for assessment of on-line dynamic security. The main bottleneck has been in the proper characterization of the stability boundary and defining the fault-dependent region of attraction locally around the controlling unstable equilibrium points. Now there is a better understanding of this issue and, hence, a number of algorithms have been proposed. Improved generating unit models and transmission network models are now being included in the technique. In this paper, an overview is presented of the theory, practical implementation, and future research issues in this area.
ensure the qualification of environmentally qualified, safety-related equipment is performed Phas... more ensure the qualification of environmentally qualified, safety-related equipment is performed Phase consists of the evaluation of a selected subset of the safety-related equipment For this subset the qualification documen tation was reviewed and the maintenance activities that are required to ensure the qualification of the equipment were determined The actual maintenance being performed at the nuclear power plant on the equipment under consideration was determined Based on this information, recommendations were made for im provements and changes The recommendations included 1) Recommendations for incorporating additional maintenance that should be performed to ensure equipment qualification 2) Recommendations to consider deleting unnecessary or re dundant maintenance, or reducing the frequency of main¬ tenance as a result of qualification data 3) Recommendations to revise the maintenance procedures as a result of qualification considerations 4) Recommendations to revise the maintenance procedure to im¬ prove the overall maintenance activity Examples of each kind of recommendation are included A program to evaluate a subset of the safety-related equipment is an effective way to determine what maintenance, ofthat required for equipment qualification, is in place, and to provide the recommen dations for additional maintenance actions to ensure qualification 83 WM 023-9
for transformers and circuits, respectively, to zero). Although the masking is not completely eli... more for transformers and circuits, respectively, to zero). Although the masking is not completely eliminated, its effects are reduced. In summary, the new ranking algorithms does remarkably well and is superior to the old algorithm. The ranking agrees almost perfectly with the ranking produced by calculating PI from de load flows; the correla¬ tion between overloads and high rank is also quite good, the only difficulty being masking. The effects of masking can be greatly reduced through partitioning followed by multiple rankings.
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Papers by P. Sauer