scholarly journals Line-Wise Power Balance Equations and Applications

2021 ◽  
Author(s):  
Amr Adel Fathy Mohamed
Keyword(s):  
Power Flow ◽  
Optimal Power Flow ◽  
Voltage Stability ◽  
Optimization Problems ◽  
Solution Space ◽  
Optimization Techniques ◽  
Power Balance ◽  
Balance Equations ◽  
Stable States ◽  
Optimal Power

Optimal power flow (OPF) refers to optimize power systems considering a chosen objective subject to a set of constraints. Existing OPF formulations used to settle electricity markets include a set of bus-wise power balance equations (PBE) that is comprised exclusively of high order terms which have sinusoidal components. Accordingly, such OPF formulations remain nonlinear and nonconvex optimization problems. Even though commercial OPF solvers are robust and efficient, they still cannot guarantee a global optimum. The US Federal Energy Regulatory Commission estimates that the best commercial OPF solvers are off by 10%, amounting to an annual loss of US $400 billion worldwide. For these motivating reasons, OPF remains a major research focus and forms the topic of this thesis. This thesis aims to: (1) develop new sets of PBE with lower order terms and lesser numbers of sinusoidal terms yielding better solution space, (2) build new OPF formulations using this new set of PBE, and (3) incorporate voltage stability constraints into the developed OPF formulations. The genesis of the new set of PBE stems from: (1) the fact that power of a constant impedance load is proportional to the square of voltage magnitude, and, (2) power flow in branches can be expressed in terms of square of voltage magnitude. Accordingly, a set of line-wise PBE is developed, both in polar and rectangular forms and are solved Newton-Raphson technique. Tests show that the proposed line-wise power flow (LWPF) algorithms are accurate, provide monotonic convergence, and scale well for large systems. The algorithms are faster comparing to classical bus-wise power flow methods. Further, the ability to directly identify the set of critical lines that are the most susceptible to Voltage collapse. A novel line-wise optimal power flow (LWOPF) formulation is developed based on polar LWPF and solved using successive linear programming technique. Tests show that LWOPF consistently yields a better solution than that computed using bus-wise OPF, namely in half the time. LWOPF is extended to include voltage stability constraints and implemented using both linear and nonlinear optimization techniques. It demonstrates improved performance in achieving lower cost optimal solutions with better voltage-stable states.

scholarly journals Line-Wise Power Balance Equations and Applications

2021 ◽  
Author(s):  
Amr Adel Fathy Mohamed
Keyword(s):  
Power Flow ◽  
Optimal Power Flow ◽  
Voltage Stability ◽  
Optimization Problems ◽  
Solution Space ◽  
Optimization Techniques ◽  
Power Balance ◽  
Balance Equations ◽  
Stable States ◽  
Optimal Power

Optimal power flow (OPF) refers to optimize power systems considering a chosen objective subject to a set of constraints. Existing OPF formulations used to settle electricity markets include a set of bus-wise power balance equations (PBE) that is comprised exclusively of high order terms which have sinusoidal components. Accordingly, such OPF formulations remain nonlinear and nonconvex optimization problems. Even though commercial OPF solvers are robust and efficient, they still cannot guarantee a global optimum. The US Federal Energy Regulatory Commission estimates that the best commercial OPF solvers are off by 10%, amounting to an annual loss of US $400 billion worldwide. For these motivating reasons, OPF remains a major research focus and forms the topic of this thesis. This thesis aims to: (1) develop new sets of PBE with lower order terms and lesser numbers of sinusoidal terms yielding better solution space, (2) build new OPF formulations using this new set of PBE, and (3) incorporate voltage stability constraints into the developed OPF formulations. The genesis of the new set of PBE stems from: (1) the fact that power of a constant impedance load is proportional to the square of voltage magnitude, and, (2) power flow in branches can be expressed in terms of square of voltage magnitude. Accordingly, a set of line-wise PBE is developed, both in polar and rectangular forms and are solved Newton-Raphson technique. Tests show that the proposed line-wise power flow (LWPF) algorithms are accurate, provide monotonic convergence, and scale well for large systems. The algorithms are faster comparing to classical bus-wise power flow methods. Further, the ability to directly identify the set of critical lines that are the most susceptible to Voltage collapse. A novel line-wise optimal power flow (LWOPF) formulation is developed based on polar LWPF and solved using successive linear programming technique. Tests show that LWOPF consistently yields a better solution than that computed using bus-wise OPF, namely in half the time. LWOPF is extended to include voltage stability constraints and implemented using both linear and nonlinear optimization techniques. It demonstrates improved performance in achieving lower cost optimal solutions with better voltage-stable states.

Optimal Power Flow Problem Solution Based on Hybrid Firefly Krill Herd Method

2019 ◽  
Vol 44 ◽  
pp. 213-228 ◽  
Author(s):  
Aboubakr Khelifi ◽  
Bachir Bentouati ◽  
Saliha Chettih
Keyword(s):  
Light Intensity ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Optimization Problems ◽  
Test System ◽  
Optimization Techniques ◽  
System Control ◽  
Problem Solution ◽  
Optimal Power ◽  
Krill Herd

Optimal Power Flow (OPF) problem is one of the most important and widely studied nonlinear optimization problems in power system operation. This study presents the implementation of a new technology based on the hybrid Firefly and krill herd method (FKH), which has been provided and used for OPF problems in power systems. In FKH, an improved formulation of the attractiveness and adjustment of light intensity operator initially employed in FA, named attractiveness and light intensity the update operator (ALIU), is inserted into the KH approach as a local search perform. The FKH is prove with the solving of the OPF problem for various types of single-objective and multi-objective functions such as generation cost, reduced emission, active power losses and voltage deviation which are optimized simultaneously on exam system, viz the IEEE-30 Bus test system, which is used to test and confirm the efficiency of the proposed FKH technique. By comparing with several optimization techniques, the results produced by using the recommended FKH technique are provided in detail. The results obtained in this study appear that the FKH technique can be efficiency used to solve the non-linear and non-convex problems and high performance compared with other optimization methods in the literature. This study can achieve a minimum objective by finding the optimum setting for system control variables.

Improved Pseudo-Gradient Search Particle Swarm Optimization for Optimal Power Flow Problem

2016 ◽  
pp. 177-207 ◽  
Author(s):  
Jirawadee Polprasert ◽  
Weerakorn Ongsakul ◽  
Vo Ngoc Dieu
Keyword(s):  
Particle Swarm Optimization ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Voltage Stability ◽  
Stability Index ◽  
Gradient Search ◽  
Fuel Cost ◽  
Swarm Optimization ◽  
Optimal Power ◽  
Voltage Deviation

This paper proposes an improved pseudo-gradient search particle swarm optimization (IPG-PSO) for solving optimal power flow (OPF) with non-convex generator fuel cost functions. The objective of OPF problem is to minimize generator fuel cost considering valve point loading, voltage deviation and voltage stability index subject to power balance constraints and generator operating constraints, transformer tap setting constraints, shunt VAR compensator constraints, load bus voltage and line flow constraints. The proposed IPG-PSO method is an improved PSO by chaotic weight factor and guided by pseudo-gradient search for particle's movement in an appropriate direction. Test results on the IEEE 30-bus and 118-bus systems indicate that IPG-PSO method is superior to other methods in terms of lower generator fuel cost, smaller voltage deviation, and lower voltage stability index.

scholarly journals Computational Impacts of SVCs on Optimal Power Flow using Approximated Active-Set Interior Point Algorithm

2021 ◽  
Author(s):  
Sayed Abdullah Sadat ◽  
Xinyang Rui ◽  
mostafa Sahraei-Ardakani
Keyword(s):  
Interior Point ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Reactive Power ◽  
Optimization Problems ◽  
Interior Point Algorithm ◽  
Active Set ◽  
Computational Performance ◽  
Optimal Power ◽  
Power Dispatch

Interior point methods (IPMs) are popular and powerful methods for solving large-scale nonlinear and nonconvex optimization problems, such as AC optimal power flow (ACOPF). There are various ways to model ACOPF, depending on the objective and the physical components that need to be optimized. This paper models shunt flexible AC transmission systems (FACTS). Shunt FACTS devices such as static VAR compensators (SVCs) are sources for reactive power compensations and addressing voltage stability issues. The co-optimization of SVCs with power dispatch can impact the computational performance of ACOPF. In this paper, we evaluate the performance of different ACOPF formulations with approximated active-set interior point (AASIP) algorithm and co-optimization of SVC set points alongside other decision variables. Our numerical results suggest that both AASIP and SVCs alone improves the computation performance of almost all formulations. The gain in performance, however, depends on the sparsity of the formulation. The most spares formulation, such as branch power flow rectangular voltages (BPFRV), shows the highest gain in performance. In the event of co-optimizing SVCs with power dispatch using AASIP, the performance gain is minimal. Finally, the results are verified using various test cases ranging from 500-bus systems to 9591-bus systems.

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