Approximation Of Power Flow Equations Research Articles

An analysis of zonal electricity pricing from a long-term perspective

In an era of energy transition, it is crucial to ensure that the design of the short-term electricity market provides sufficient cash flows to producers so as to allow the investment of the right technology at the right location. In this paper, we revisit the question of capacity allocation in zonal markets from a long-term perspective. We model the capacity expansion problem in zonal markets in which inter-zonal transmission capacity allocation is organized through flow-based market coupling, which is an approximation of power flow equations in aggregate networks that is employed in European market design. We demonstrate that the classical result of equivalence between centralized and decentralized formulations in transmission-constrained markets ceases to hold in this case. We propose a model of the decentralized capacity expansion problem with flow-based market coupling as a generalized Nash equilibrium that we formulate as a linear complementarity problem. We then perform simulations of the capacity expansion problem with nodal pricing and three variations of zonal pricing on a realistic instance of the Central Western European network and comment on the impacts of flow-based market coupling on investment.

A Robust Decentralized Power Flow Optimization for Dynamic PV System

This paper proposes a robust scheme for optimizing the power flow in a photovoltaic system. The scheme utilizes distributed saddle point dynamics and a decentralized approach to solve the power flow problem. It converts the convex optimization problem of the dynamic system control into the asymptotically stable dynamic systems and employs a linear approximation of power flow equations; specifically, a quadratic programming model is deployed with the aim of minimizing real-power losses to guarantee a globally optimal solution. Then, the photovoltaic inverters and electric networks are analyzed independently in a decentralized manner to exchange injection power among nodes while maintaining their independence to support the plug-and-play feature. A case study and the experimental results show that the proposed scheme achieves higher optimization accuracy and are more economical than the existing state-of-the-art schemes.

Optimal power flow based on successive linear approximation of power flow equations

In this study, the authors introduce a new solution to the alternating current optimal power flow problem based on successive linear approximation of power flow equations. The polar coordination of the power flow equations is used to take advantage of the quasi-linear P– θ relationship. A mathematical transformation for the crossing term of voltage magnitude is used, which guarantees the accuracy of the linear approximation when the quality of initial points regarding voltage magnitude is relatively low in the first few iterations. As a result, the accuracy of the proposed approximation becomes very high in very few iterations. Linearisation method for the quadratic apparent branch flow limits is provided. Methods to recover the AC feasibility from the obtained optimal power flow solution and correct possible constraint violations are introduced. The proposed method is tested in several IEEE and Polish benchmark systems. The difference in objective functions relative to MATPOWER benchmark results is generally <0.1% when the algorithm terminates.

A Modified Newton Method For Optimal Power Flow Using Quadratic Approximated Power Flow

In general, the Han-Powell algorithm is evaluated as the fastest and the most reliable method for small nonlinear programming problems. However, it has one serious disadvantage when applied to a large scale problem such as an optimal power flow. This disadvantage stems from its use of non-sparse approximations to certain Hessian matrices. We propose a modified Newton method to eliminate this disadvantage. Sparsity of the Hessian is maintained by this method, and it can be modified to be a non-negative definite matrix in accordance with simple procedutes. This can be implemented using quadratic approximations of power flow equations. Numerical tests on a real system show the validity of the proposed method.