BS
B. Sereeter
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Power flow computations are important for operation and planning of the electricity grid, but are computationally expensive because of nonlinearities and the size of the system of equations. Linearized methods reduce computational time but often have the disadvantage that they are not applicable to general grids. In this paper we propose a novel linearized power flow (LPF) technique that is able to handle PQ- and PV-buses, and works on both transmission and distribution networks. This technique is based on previous work on handling PQ-buses by connecting them to artificial-additional ground buses. We extend this idea to PV-buses. Test-cases show that the novel LPF method leads to similar accuracy as nonlinear power flow (NPF) methods while significantly reducing computation time. Therefore, the general LPF methods is a good alternative to NPF methods.
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Power flow computations are important for operation and planning of the electricity grid, but are computationally expensive because of nonlinearities and the size of the system of equations. Linearized methods reduce computational time but often have the disadvantage that they are not applicable to general grids. In this paper we propose a novel linearized power flow (LPF) technique that is able to handle PQ- and PV-buses, and works on both transmission and distribution networks. This technique is based on previous work on handling PQ-buses by connecting them to artificial-additional ground buses. We extend this idea to PV-buses. Test-cases show that the novel LPF method leads to similar accuracy as nonlinear power flow (NPF) methods while significantly reducing computation time. Therefore, the general LPF methods is a good alternative to NPF methods.
Solving the Steady-State Power Flow Problem on Integrated Transmission-Distribution Networks
A Comparison of Numerical Methods
Steady-state power flow models are essential for daily operation of the electricity grid. The changing electrical environment requires a shift from separated power flow models to integrated transmission-distribution power flow models. Integrated models incorporate the coupling of the networks and the interaction that they have on each other, representing the power flow within this changing environment accurately. In this paper we conduct a comparison study on the numerical performance of methods that solve the integrated power flow problem. The methods of study can be divided into unified or splitting methods. In addition, the integrated networks can be modeled as homogeneous or as hybrid networks. Our study shows that the methods have several advantages and disadvantages, but that unified methods in combination with hybrid network models have the best numerical performance. Splitting methods running on hybrid network models have an advantage when full network data sharing between system operators is not allowed.
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Steady-state power flow models are essential for daily operation of the electricity grid. The changing electrical environment requires a shift from separated power flow models to integrated transmission-distribution power flow models. Integrated models incorporate the coupling of the networks and the interaction that they have on each other, representing the power flow within this changing environment accurately. In this paper we conduct a comparison study on the numerical performance of methods that solve the integrated power flow problem. The methods of study can be divided into unified or splitting methods. In addition, the integrated networks can be modeled as homogeneous or as hybrid networks. Our study shows that the methods have several advantages and disadvantages, but that unified methods in combination with hybrid network models have the best numerical performance. Splitting methods running on hybrid network models have an advantage when full network data sharing between system operators is not allowed.
During the normal operation, control and planning of the power system, grid operators employ numerous tools including the Power Flow (PF) and the Optimal Power Flow (OPF) computations to keep the balance in the power system. The solution of the PF computation is used to assess whether the power system can function properly for the given generation and consumption, whereas the OPF problem provides the optimal operational state of the electrical power system, while satisfying system constraints and control limits.
In this thesis, we study advanced models of the power system that transform the physical properties of the network into mathematical equations. Furthermore, we develop new mathematical formulations and algorithms for fast and robust power system simulations, such as PF and OPF computations, that can be applied to any balanced single-phase or unbalanced three-phase network.
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During the normal operation, control and planning of the power system, grid operators employ numerous tools including the Power Flow (PF) and the Optimal Power Flow (OPF) computations to keep the balance in the power system. The solution of the PF computation is used to assess whether the power system can function properly for the given generation and consumption, whereas the OPF problem provides the optimal operational state of the electrical power system, while satisfying system constraints and control limits.
In this thesis, we study advanced models of the power system that transform the physical properties of the network into mathematical equations. Furthermore, we develop new mathematical formulations and algorithms for fast and robust power system simulations, such as PF and OPF computations, that can be applied to any balanced single-phase or unbalanced three-phase network.
A general framework is given for applying the Newton–Raphson method to solve power flow problems, using power and current-mismatch functions in polar, Cartesian coordinates and complex form. These two mismatch functions and three coordinates, result in six possible ways to apply the Newton–Raphson method for the solution of power flow problems. We present a theoretical framework to analyze these variants for load (PQ)buses and generator (PV)buses. Furthermore, we compare newly developed versions in this paper with existing variants of the Newton power flow method. The convergence behavior of all methods is investigated by numerical experiments on transmission and distribution networks. We conclude that variants using the polar current-mismatch and Cartesian current-mismatch functions that are developed in this paper, performed the best result for both distribution and transmission networks.
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A general framework is given for applying the Newton–Raphson method to solve power flow problems, using power and current-mismatch functions in polar, Cartesian coordinates and complex form. These two mismatch functions and three coordinates, result in six possible ways to apply the Newton–Raphson method for the solution of power flow problems. We present a theoretical framework to analyze these variants for load (PQ)buses and generator (PV)buses. Furthermore, we compare newly developed versions in this paper with existing variants of the Newton power flow method. The convergence behavior of all methods is investigated by numerical experiments on transmission and distribution networks. We conclude that variants using the polar current-mismatch and Cartesian current-mismatch functions that are developed in this paper, performed the best result for both distribution and transmission networks.
In this paper, we propose a fast linear power flow method using a constant impedance load model to simulate both the entire Low Voltage (LV) and Medium Voltage (MV) networks in a single simulation. Accuracy and efficiency of this linear approach are validated by comparing it with the Newton power flow algorithm and a commercial network design tool Vision on various distribution networks including real network data. Results show that our method can be as accurate as classical Nonlinear Power Flow (NPF) methods using a constant power load model and additionally, it is much faster than NPF computations. In our research, it is shown that voltage problems can be identified more efficiently when MV and LV are integrally evaluated. Moreover, Numerical Analysis (NA) techniques are applied to the Large Linear Power Flow (LLPF) problem with 27 million nonzeros in order to improve the computation time by studying the properties of the linear system. Finally, the original computation times of LLPF problems with real and complex components are reduced by 2.8 times and 5.7 times, respectively.
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In this paper, we propose a fast linear power flow method using a constant impedance load model to simulate both the entire Low Voltage (LV) and Medium Voltage (MV) networks in a single simulation. Accuracy and efficiency of this linear approach are validated by comparing it with the Newton power flow algorithm and a commercial network design tool Vision on various distribution networks including real network data. Results show that our method can be as accurate as classical Nonlinear Power Flow (NPF) methods using a constant power load model and additionally, it is much faster than NPF computations. In our research, it is shown that voltage problems can be identified more efficiently when MV and LV are integrally evaluated. Moreover, Numerical Analysis (NA) techniques are applied to the Large Linear Power Flow (LLPF) problem with 27 million nonzeros in order to improve the computation time by studying the properties of the linear system. Finally, the original computation times of LLPF problems with real and complex components are reduced by 2.8 times and 5.7 times, respectively.
In this paper, we study four equivalent mathematical formulations of the Optimal Power Flow (OPF) problem and their impacts on the performance of solution methods. We show how four mathematical formulations of the OPF problem can be obtained by rewriting equality constraints given as the power flow problem into four equivalent mathematical equations using power balance or current balance equations in polar or Cartesian coordinates while keeping the same physical formulation. All four mathematical formulations are implemented in Matpower. In order to identify the formulation that results in the best convergence characteristics for the solution method, we apply MIPS, KNITRO, and FMINCON on various test cases using three different initial conditions. We compare all four formulations in terms of impact factors on the solution method such a number of nonzero elements in the Jacobian and Hessian matrices, a number of iterations and computational time on each iteration. The numerical results show that the performance of the OPF solution method is not only dependent upon the choice of the solution method itself, but also upon the exact mathematical formulation used to specify the OPF problem.
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In this paper, we study four equivalent mathematical formulations of the Optimal Power Flow (OPF) problem and their impacts on the performance of solution methods. We show how four mathematical formulations of the OPF problem can be obtained by rewriting equality constraints given as the power flow problem into four equivalent mathematical equations using power balance or current balance equations in polar or Cartesian coordinates while keeping the same physical formulation. All four mathematical formulations are implemented in Matpower. In order to identify the formulation that results in the best convergence characteristics for the solution method, we apply MIPS, KNITRO, and FMINCON on various test cases using three different initial conditions. We compare all four formulations in terms of impact factors on the solution method such a number of nonzero elements in the Jacobian and Hessian matrices, a number of iterations and computational time on each iteration. The numerical results show that the performance of the OPF solution method is not only dependent upon the choice of the solution method itself, but also upon the exact mathematical formulation used to specify the OPF problem.
A general framework is given for applying the Newton-Raphson method to solve power flow problems, using power and current-mismatch functions in polar, Cartesian coordinates and complex form. These two mismatch functions and three coordinates, result in six versions of the Newton-Raphson method for the solution of power flow problems. We present a theoretical framework to compare these variants for PQ-buses and PV-buses. Furthermore, the convergence behavior is investigated by numerical experiments. This enables us to compare new versions with existing versions of the Newton power flow methods. We conclude that the polar current-mismatch and Cartesian current-mismatch versions that are developed in this paper, performed the best result for both distribution and transmission networks.
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A general framework is given for applying the Newton-Raphson method to solve power flow problems, using power and current-mismatch functions in polar, Cartesian coordinates and complex form. These two mismatch functions and three coordinates, result in six versions of the Newton-Raphson method for the solution of power flow problems. We present a theoretical framework to compare these variants for PQ-buses and PV-buses. Furthermore, the convergence behavior is investigated by numerical experiments. This enables us to compare new versions with existing versions of the Newton power flow methods. We conclude that the polar current-mismatch and Cartesian current-mismatch versions that are developed in this paper, performed the best result for both distribution and transmission networks.
Two mismatch functions (power or current) and three coordinates (polar, Cartesian and complex form) result in six versions of the Newton–Raphson method for the solution of power flow problems. In this paper, five new versions of the Newton power flow method developed for single-phase problems in our previous paper are extended to three-phase power flow problems. Mathematical models of the load, load connection, transformer, and dis-
tributed generation (DG) are presented. A three-phase power flow formulation is described for both power and current mismatch functions. Extended versions of the Newton power flow method are compared with the backward-forward sweep-based algorithm. Furthermore, the convergence behavior for different loading conditions, R/X ratios, and load models, is investigated by numerical experiments on balanced and unbalanced distribution networks. On the basis of these experiments, we conclude that two versions using the current mis
match function in polar and Cartesian coordinates perform the best for both balanced and unbalanced distribution networks.
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Two mismatch functions (power or current) and three coordinates (polar, Cartesian and complex form) result in six versions of the Newton–Raphson method for the solution of power flow problems. In this paper, five new versions of the Newton power flow method developed for single-phase problems in our previous paper are extended to three-phase power flow problems. Mathematical models of the load, load connection, transformer, and dis-
tributed generation (DG) are presented. A three-phase power flow formulation is described for both power and current mismatch functions. Extended versions of the Newton power flow method are compared with the backward-forward sweep-based algorithm. Furthermore, the convergence behavior for different loading conditions, R/X ratios, and load models, is investigated by numerical experiments on balanced and unbalanced distribution networks. On the basis of these experiments, we conclude that two versions using the current mis
match function in polar and Cartesian coordinates perform the best for both balanced and unbalanced distribution networks.
Two mismatch functions (power or current) and three coordinates (polar, Cartesian andcomplex form) result in six versions of the Newton–Raphson method for the solution of powerflow problems. In this paper, five new versions of the Newton power flow method developed forsingle-phase problems in our previous paper are extended to three-phase power flow problems.Mathematical models of the load, load connection, transformer, and distributed generation (DG)are presented. A three-phase power flow formulation is described for both power and currentmismatch functions. Extended versions of the Newton power flow method are compared with thebackward-forward sweep-based algorithm. Furthermore, the convergence behavior for differentloading conditions,R/Xratios, and load models, is investigated by numerical experiments onbalanced and unbalanced distribution networks. On the basis of these experiments, we conclude thattwo versions using the current mismatch function in polar and Cartesian coordinates perform thebest for both balanced and unbalanced distribution networks.
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Two mismatch functions (power or current) and three coordinates (polar, Cartesian andcomplex form) result in six versions of the Newton–Raphson method for the solution of powerflow problems. In this paper, five new versions of the Newton power flow method developed forsingle-phase problems in our previous paper are extended to three-phase power flow problems.Mathematical models of the load, load connection, transformer, and distributed generation (DG)are presented. A three-phase power flow formulation is described for both power and currentmismatch functions. Extended versions of the Newton power flow method are compared with thebackward-forward sweep-based algorithm. Furthermore, the convergence behavior for differentloading conditions,R/Xratios, and load models, is investigated by numerical experiments onbalanced and unbalanced distribution networks. On the basis of these experiments, we conclude thattwo versions using the current mismatch function in polar and Cartesian coordinates perform thebest for both balanced and unbalanced distribution networks.