An Alternating Trust Region Algorithm for Distributed Linearly Constrained Nonlinear Programs, Application to the AC Optimal Power Flow

A novel trust region method for solving linearly constrained nonlinear programs is presented. The proposed technique is amenable to a distributed implementation, as its salient ingredient is an alternating projected gradient sweep in place of the Cauchy point computation. It is proven that the algorithm yields a sequence that globally converges to a critical point. As a result of some changes to the standard trust region method, namely a proximal regularisation of the trust region subproblem, it is shown that the local convergence rate is linear with an arbitrarily small ratio. Thus, convergence is locally almost superlinear, under standard regularity assumptions. The proposed method is successfully applied to compute local solutions to alternating current optimal power flow problems in transmission and distribution networks. Moreover, the new mechanism for computing a Cauchy point compares favourably against the standard projected search as for its activity detection properties

A Coordinate-Descent Algorithm for Tracking Solutions in Time-Varying Optimal Power Flows

Consider a polynomial optimisation problem, whose instances vary continuously over time. We propose to use a coordinate-descent algorithm for solving such time-varying optimisation problems. In particular, we focus on relaxations of transmission-constrained problems in power systems. On the example of the alternating-current optimal power flows (ACOPF), we bound the difference between the current approximate optimal cost generated by our algorithm and the optimal cost for a relaxation using the most recent data from above by a function of the properties of the instance and the rate of change to the instance over time. We also bound the number of floating-point operations that need to be performed between two updates in order to guarantee the error is bounded from above by a given constant

A Review of Recent Advances in Economic Dispatch

A survey is presented of papers and reports that address various aspects of economic dispatch. The time period considered is 1977-88. Four related areas of economic dispatch are identified and papers published in the general areas of economic dispatch are classified into these. These areas are: optimal power flow, economic dispatch in relation to AGC, dynamic dispatch, and economic dispatch with nonconventional generation sources

Linear and Nonlinear Programming Methods for Dispatching Power in an Integrated AC-DC System

As the number of dc systems increases, it is natural to ask what other roles, aside that of bulk power transfer, that these systems could play in the operation of modern power systems. The objective of this research is to develop formulations and methods of solution to coordinate the dispatch of powers in an integrated ac-dc power system for purposes of minimizing transmission losses and production costs. In Section I we present an LP formulation and method of solution to minimize the ac and dc network transmission losses by coordinating the traditional reactive sources with the dispatch of the dc power transfers, taking into consideration the usual constraints on equipment ratings, line flows and bus voltage magnitudes. Results on sample test systems indicate that substantial reduction in network losses can be achieved by a coordinated dispatch involving the dc power transfers. Section II describes the mathematical formulation and method of solution for the optimal power flow problem of an integrated ac-dc power system. The method is capable of handling the network, converter tap, and control constraints of more than one multiterminal dc systems. The method uses a sequence of quadratic programming subproblems to determine the search directions. Also discussed are ways for determining the initial estimates of the Lagrange multiplier. Tests performed on modified IEEE 30 and 118 bus systems gave reasonable solution time and rate of convergence. The results obtained on the sample systems also indicate that there could be further economic advantage when the dispatch of dc powers is coordinated with the conventional controllable sources using the optimal power flow program. Section III reports on the findings from a comparative study of three methods to screen and rank severe contingencies for preventive dispatch

pandapower - an Open Source Python Tool for Convenient Modeling, Analysis and Optimization of Electric Power Systems

pandapower is a Python based, BSD-licensed power system analysis tool aimed at automation of static and quasi-static analysis and optimization of balanced power systems. It provides power flow, optimal power flow, state estimation, topological graph searches and short circuit calculations according to IEC 60909. pandapower includes a Newton-Raphson power flow solver formerly based on PYPOWER, which has been accelerated with just-in-time compilation. Additional enhancements to the solver include the capability to model constant current loads, grids with multiple reference nodes and a connectivity check. The pandapower network model is based on electric elements, such as lines, two and three-winding transformers or ideal switches. All elements can be defined with nameplate parameters and are internally processed with equivalent circuit models, which have been validated against industry standard software tools. The tabular data structure used to define networks is based on the Python library pandas, which allows comfortable handling of input and output parameters. The implementation in Python makes pandapower easy to use and allows comfortable extension with third-party libraries. pandapower has been successfully applied in several grid studies as well as for educational purposes. A comprehensive, publicly available case-study demonstrates a possible application of pandapower in an automated time series calculation

Lattice structures for optimal design and robust implementation of two-channel perfect-reconstruction QMF banks

A lattice structure and an algorithm are presented for the design of two-channel QMF (quadrature mirror filter) banks, satisfying a sufficient condition for perfect reconstruction. The structure inherently has the perfect-reconstruction property, while the algorithm ensures a good stopband attenuation for each of the analysis filters. Implementations of such lattice structures are robust in the sense that the perfect-reconstruction property is preserved in spite of coefficient quantization. The lattice structure has the hierarchical property that a higher order perfect-reconstruction QMF bank can be obtained from a lower order perfect-reconstruction QMF bank, simply by adding more lattice sections. Several numerical examples are provided in the form of design tables