Matching Items (5)

Effect of various holomorphic embeddings on convergence rate and condition number as applied to the power flow problem

Description

Power flow calculation plays a significant role in power system studies and operation. To ensure the reliable prediction of system states during planning studies and in the operating environment, a

Power flow calculation plays a significant role in power system studies and operation. To ensure the reliable prediction of system states during planning studies and in the operating environment, a reliable power flow algorithm is desired. However, the traditional power flow methods (such as the Gauss Seidel method and the Newton-Raphson method) are not guaranteed to obtain a converged solution when the system is heavily loaded.

This thesis describes a novel non-iterative holomorphic embedding (HE) method to solve the power flow problem that eliminates the convergence issues and the uncertainty of the existence of the solution. It is guaranteed to find a converged solution if the solution exists, and will signal by an oscillation of the result if there is no solution exists. Furthermore, it does not require a guess of the initial voltage solution.

By embedding the complex-valued parameter α into the voltage function, the power balance equations become holomorphic functions. Then the embedded voltage functions are expanded as a Maclaurin power series, V(α). The diagonal Padé approximant calculated from V(α) gives the maximal analytic continuation of V(α), and produces a reliable solution of voltages. The connection between mathematical theory and its application to power flow calculation is described in detail.

With the existing bus-type-switching routine, the models of phase shifters and three-winding transformers are proposed to enable the HE algorithm to solve practical large-scale systems. Additionally, sparsity techniques are used to store the sparse bus admittance matrix. The modified HE algorithm is programmed in MATLAB. A study parameter β is introduced in the embedding formula βα + (1- β)α^2. By varying the value of β, numerical tests of different embedding formulae are conducted on the three-bus, IEEE 14-bus, 118-bus, 300-bus, and the ERCOT systems, and the numerical performance as a function of β is analyzed to determine the “best” embedding formula. The obtained power-flow solutions are validated using MATPOWER.

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Created

Date Created
  • 2015

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Design of an energy management system using a distribution class locational marginal price as a discrete control signal

Description

The subject of this thesis is distribution level load management using a pricing signal in a Smart Grid infrastructure. The Smart Grid implements advanced meters, sensory devices and near real

The subject of this thesis is distribution level load management using a pricing signal in a Smart Grid infrastructure. The Smart Grid implements advanced meters, sensory devices and near real time communication between the elements of the system, including the distribution operator and the customer. A stated objective of the Smart Grid is to use sensory information to operate the electrical power grid more efficiently and cost effectively. One potential function of the Smart Grid is energy management at the distribution level, namely at the individual customer. The Smart Grid allows control of distribution level devices, including distributed energy storage and distributed generation, in operational real time. One method of load control uses an electric energy price as a control signal. The control is achieved through customer preference as the customer allows loads to respond to a dynamic pricing signal. In this thesis, a pricing signal is used to control loads for energy management at the distribution level. The model for the energy management system is created and analyzed in the z-domain due to the envisioned discrete time implementation. Test cases are used to illustrate stability and performance by analytic calculations using Mathcad and by simulation using Matlab Simulink. The envisioned control strategy is applied to the Future Renewable Electric Energy Distribution Management (FREEDM) system. The FREEDM system implements electronic (semiconductor) controls and therefore makes the proposed energy management feasible. The pricing control strategy is demonstrated to be an effective method of performing energy management in a distribution system. It is also shown that stability and near optimal response can be achieved by controlling the parameters of the system. Addition-ally, the communication bandwidth requirements for a pricing control signal are evaluated.

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Date Created
  • 2013

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Sensitivity-based Pricing and Multiobjective Control for Energy Management in Power Distribution Systems

Description

In the deregulated power system, locational marginal prices are used in transmission engineering predominantly as near real-time pricing signals. This work extends this concept to distribution engineering so that a

In the deregulated power system, locational marginal prices are used in transmission engineering predominantly as near real-time pricing signals. This work extends this concept to distribution engineering so that a distribution class locational marginal price might be used for real-time pricing and control of advanced control systems in distribution circuits. A formulation for the distribution locational marginal price signal is presented that is based on power flow sensitivities in a distribution system. A Jacobian-based sensitivity analysis has been developed for application in the distribution pricing method. Increasing deployment of distributed energy sources is being seen at the distribution level and this trend is expected to continue. To facilitate an optimal use of the distributed infrastructure, the control of the energy demand on a feeder node in the distribution system has been formulated as a multiobjective optimization problem and a solution algorithm has been developed. In multiobjective problems the Pareto optimality criterion is generally applied, and commonly used solution algorithms are decision-based and heuristic. In contrast, a mathematically-robust technique called normal boundary intersection has been modeled for use in this work, and the control variable is solved via separable programming. The Roy Billinton Test System (RBTS) has predominantly been used to demonstrate the application of the formulation in distribution system control. A parallel processing environment has been used to replicate the distributed nature of controls at many points in the distribution system. Interactions between the real-time prices in a distribution feeder and the nodal prices at the aggregated load bus have been investigated. The application of the formulations in an islanded operating condition has also been demonstrated. The DLMP formulation has been validated using the test bed systems and a practical framework for its application in distribution engineering has been presented. The multiobjective optimization yields excellent results and is found to be robust for finer time resolutions. The work shown in this report is applicable to, and has been researched under the aegis of the Future Renewable Electric Energy Delivery and Management (FREEDM) center, which is a generation III National Science Foundation engineering research center headquartered at North Carolina State University.

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Created

Date Created
  • 2012

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A distribution-class locational marginal price (DLMP) index for enhanced distribution systems

Description

The smart grid initiative is the impetus behind changes that are expected to culminate into an enhanced distribution system with the communication and control infrastructure to support advanced distribution system

The smart grid initiative is the impetus behind changes that are expected to culminate into an enhanced distribution system with the communication and control infrastructure to support advanced distribution system applications and resources such as distributed generation, energy storage systems, and price responsive loads. This research proposes a distribution-class analog of the transmission LMP (DLMP) as an enabler of the advanced applications of the enhanced distribution system. The DLMP is envisioned as a control signal that can incentivize distribution system resources to behave optimally in a manner that benefits economic efficiency and system reliability and that can optimally couple the transmission and the distribution systems. The DLMP is calculated from a two-stage optimization problem; a transmission system OPF and a distribution system OPF. An iterative framework that ensures accurate representation of the distribution system's price sensitive resources for the transmission system problem and vice versa is developed and its convergence problem is discussed. As part of the DLMP calculation framework, a DCOPF formulation that endogenously captures the effect of real power losses is discussed. The formulation uses piecewise linear functions to approximate losses. This thesis explores, with theoretical proofs, the breakdown of the loss approximation technique when non-positive DLMPs/LMPs occur and discusses a mixed integer linear programming formulation that corrects the breakdown. The DLMP is numerically illustrated in traditional and enhanced distribution systems and its superiority to contemporary pricing mechanisms is demonstrated using price responsive loads. Results show that the impact of the inaccuracy of contemporary pricing schemes becomes significant as flexible resources increase. At high elasticity, aggregate load consumption deviated from the optimal consumption by up to about 45 percent when using a flat or time-of-use rate. Individual load consumption deviated by up to 25 percent when using a real-time price. The superiority of the DLMP is more pronounced when important distribution network conditions are not reflected by contemporary prices. The individual load consumption incentivized by the real-time price deviated by up to 90 percent from the optimal consumption in a congested distribution network. While the DLMP internalizes congestion management, the consumption incentivized by the real-time price caused overloads.

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Created

Date Created
  • 2013

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Applications and calculation of a distribution class locational marginal price

Description

This thesis presents an overview of the calculation and application of locational marginal prices in electric power systems particularly pertaining to the distribution system. The terminology proposed is a distribution

This thesis presents an overview of the calculation and application of locational marginal prices in electric power systems particularly pertaining to the distribution system. The terminology proposed is a distribution locational marginal price or DLMP. The calculation of locational process in distribution engineering is conjectured and discussed. The use of quadratic programming for this calculation is proposed and illustrated. A small four bus test bed exemplifies the concept and then the concept is expanded to the IEEE 34 bus distribution system. Alternatives for the calculation are presented, and approximations are reviewed. Active power losses in the system are modeled and incorporated by two different methods. These calculation methods are also applied to the 34 bus system. The results from each method are compared to results found using the PowerWorld simulator. The application of energy management using the DLMP to control load is analyzed as well. This analysis entails the use of the DLMP to cause certain controllable loads to decrease when the DLMP is high, and vice-versa. Tests are done to illustrate the impact of energy management using DLMPs for residential, commercial, and industrial controllable loads. Results showing the dynamics of the loads are shown. The use and characteristics of Matlab function FMINCON are presented in an appendix.

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Created

Date Created
  • 2013