Python for Power Systems Computation Prabakaran. S M.E., Power Systems Engineering, Valliammai Engineering College Chennai, India
[email protected]
Power — Power Abstract
Systems computation which were being computed so far using MATLAB, OCTAVE and other closed software packages could be solved using Python. There are various open source tools available which along with Python could be used to solve complex power system problems. Python with simple and easy to learn syntax along with its power of being a general purpose scripting language enables engineers and researchers to solve complex problems interactively. They could develop their own software package either an open source or even commercial software without any permissions from Python. A test case was conducted using an IEEE 14-bus system in which the small signal stability analysis is performed using Python and it is compared with MATLAB and OCTAVE. Python, tools, power system computations, open — Python, I ndex Terms Terms source, NumPy, SciPy, Matplotlib, CVXOPT.
I. I NTRODUCTION In general, Power System design, analysis and control involve complex mathematical computations exhibiting exhaustive nature. Because of its exhaustive nature it became a hardball for scientists and engineers to solve power system problems, even using computer. This is the reason that most of the power system engineers and researchers use a commercial software package like MATLAB which is a closed software package. However, there are also freely-distributed projects but whose source code is not provided or, if provided, is too complicated to be mastered in a reasonable time. As it can be promptly observed, observed, closed software packages embed and mask the most interesting parts, i.e., the modelling and computer implementation phases. There are at least two important drawbacks in this approach. The first one is that the user has to accept the hypotheses and simplifications used by the authors of the software package. The other one is that the user often ignores the hypotheses and simplifications used by the authors of the software package. A byproduct drawback is also the absent or reduced possibility of modifying the equations and of replacing the algorithms used by the software package. Clearly, the main advantage of using a closed software packages is to save time. For well-assessed and repetitive operations, such as most industry applications, it is also the correct approach. On the other hand, the educational weakness of closed software is evident. The user gives up the possibility of thinking in exchange for setting up input data and adjustments. It has to be noted that setting up a set of
data without having the control or the full knowledge of the model can lead to unpredictable unpredictable results. Python is a safely, dynamically and strongly typed open source language which can be competitive with MATLAB and Octave[14]. Python is inherently object oriented. Almost everything is an object: strings, lists, dictionaries, tuples, functions, classes, and more. The implied usefulness is that these things each have their own members and methods that encapsulate its functionality and information. To get functionalities functionalities of MATLAB and Octave in Python, the NumPy, SciPy and Matplotlib packages should be used. Scipy is a package that has the goal of providing all the other functionality of MATLAB, including those in the MATLAB toolboxes. There are also a handful of IDE's available for Python, most of which are for free. Because Python is open and free, it is very easy for other parties to design packages or other software tools that extend Python. It is possible to create applications using any of the major GUI libraries[1] (TK, WX, GTK, QT ...), use OpenGL, drive your USB port, etc. Another example is Pyrex /Cython to enhance the speed of algorithms by converting Python to C code, and py2exe and the like to create a standalone application from the source. Also the system programming languages are not much faster than efficient scientific scripting languages. However, scripting languages do not perform directly heavy mathematical operations, operations , butcall efficient FORTRAN or C-based libraries. The proposed system for studying a Power System through Python (open software package) is shown in Fig. 1. Thus, the main conclusion is that the interfaces that link scripting languages with external compiled libraries are quite efficient. II. AVAILABLE TOOLS FOR POWER SYSTEM COMPUTATION There are a large number of modules of the libraries available to Python for Power System computations. Also, there is an advanced Python shell, IPython[2], developed specifically for scientific computing. Below are the most potential modules including NumPy[8], SciPy[10], Matpltotlib[11], CVXOPT[12], Pylon, PyPower[13], Minpower[3] that that are standard standard libraries which could be used for Power System computations. A. NumPy A. NumPy The Numeric Python extensions (NumPy) is a set of extensions to the Python programming language which allows
easily describe numerical problems using high-level code, thereby opening the door to scientific code that is both transparent and easy to maintain. B. SciPY
Fig. 1. Approach for studying a system using P ython Python programmers to efficiently manipulate large sets of objects organized in grid-like fashion. These sets of objects are called arrays, and they can have any number of dimensions: one dimensional arrays are similar to standard Python sequences, two-dimensional arrays are similar to matrices from linear algebra. Anything that can be done in NumPy could also be done in standard Python – we just may not be alive to see the program finish. A more subtle reason for these extensions however is that the kinds of operations that programmers typically want to do on arrays, while sometimes very complex, can often be decomposed into a set of fairly standard operations. This decomposition has been developed similarly in many array languages. In some ways, NumPy is simply the application of this experience to the Python language – thus many of the operations described in NumPy work the way they do because experience has shown that way to be a good one, in a variety of contexts. The languages which were used to guide the development of NumPy include the infamous APL family of languages, Basis, MATLAB, FORTRAN, S and S+, and others[4]. This heritage will be obvious to users of NumPy who already have experience with these other languages. When NumPy is skillfully applied, computation time is primarily spent on vectorized array operations instead of in Python for loops (which are often a bottleneck). Further speed improvements are achieved using optimizing compilers, such as Cython, which allow better control over cache effects. In addition to low-level array operations, NumPy provides sub packages for linear algebra, FFTs, random number generation, and polynomial manipulation. Larger scientific packages, such as SciPy, are, in turn, built on this infrastructure. NumPy and similar projects foster an environment in which users can
SciPy is a collection of mathematical algorithms and convenience functions built on the Numpy extension for Python. It adds significant power to the interactive Python session by exposing the user to high-level commands and classes for the manipulation and visualization of data. With SciPy, an interactive Python session becomes a data processing and system-prototyping environment rivaling sytems such as MATLAB, IDL, Octave, R-Lab, and SciLab. The additional power of using SciPy within Python, however, is that a powerful programming language is also available for use in developing sophisticated programs and specialized applications. Scientific applications written in SciPy benefit from the development of additional modules in numerous niche’s of the software landscape by developers across the world. Everything from parallel programming to web and data-base subroutines and classes have been made available to the Python programmer. All of this power is available in addition to the mathematical libraries in SciPy. SciPy makes it easy to integrate C code, which is essential when algorithms operating on large data sets cannot be vectorized. The universality of Python, the language in which SciPy was written, gives the researcher access to a broader set of non-numerical libraries to support GUI development, interface with databases, manipulate graph structures, render 3D graphics, unpack binary files, etc. Python’s extensive support for operator overloading makes SciPy’s syntax as succinct as its competitors, MATLAB, Octave, and R. More profoundly, we found it easy to rework research code written with SciPy into a production application, deployable on numerous platforms. C. CVXOPT CVXOPT is a free software package for convex optimization based on the Python programming language. It can be used with the interactive Python interpreter, on the command line by executing Python scripts, or integrated in other software via Python extension modules. Its main purpose is to make the development of software for convex optimization applications straightforward by building on Python’s extensive standard library and on the strengths of Python as a high-level programming language. CVXOPT extends the built-in Python objects with two matrix objects: a matrix object for dense matrices and a spmatrix object for sparse matrices. Also an API can be used to extend CVXOPT with interfaces to external C routines and libraries. A C program that creates or manipulates the dense or sparse matrix objects defined in CVXOPT must include the cvxopt.h header file in the src directory of the distribution. The best part about CVXOPT is that the matrices from NumPy arrays and CVXOPT are compatible and both these packages could exchange information using the array interface.
For example, in NumPy the matrices could be created from a CVXOPT matrix using the array() method.
DC and AC optimal power flow and
>>> from cvxopt import matrix >>> from numpy import array >>> A = matrix([[1,2,3,4,5],[6,7,8,9,0]]) >>> print(A) [ 1 6] [ 2 7] [ 3 8] [4 9] [5 0] >>> B = array(A) >>> B array([[1, 4], [ 1 6] [ 2 7] [ 3 8] [4 9] [5 0]]) >>> type(B)
Similarly a CVXOPT matrix could be created from a NumPy array using the matrix() method as follows. >>> C = matrix(B) >>> type(C)
D. Matplotlib Matplotlib is a library for making 2D plots of arrays in Python Although it has its origins in emulating the MATLAB graphics commands, it is independent of MATLAB, and can be used in a Pythonic, object oriented way. Although matplotlib is written primarily in pure Python, it makes heavy use of NumPy and other extension code to provide good performance even for large arrays. In matplotlib it is not necessary to instantiate objects, call methods, set properties, and so on to see a histogram of data. It is possible to create simple plots with just a few commands. It is also possible to automatically generate PostScript files to send to a printer or publishers and even to deploy matplotlib on a web application server to generate PNG output for inclusion in dynamically-generated web pages. E. Pylon Pylon is developed by Richard Lincoln, which actually is a port of MATPOWER to the Python programming language. Pylon is funded by the Engineering and Physical Sciences Research Council through Grant GR/T28836/01 to provide a simple yet powerful tool for Power Engineering that is not tied to proprietary software and can be used and extended with ease. Pylon’s features currently include: DC and AC (Newton’s and Fast Decoupled method) power flow,
Fig. 2. TEX Rendering in plots using Matplotlib
PSS/E, MATPOWER and PSAT case and de-serialization.
serialization
F. Minpower Minpower is an open source toolkit for students and researchers in power systems optimization. The toolkit is designed to make working with the classical problems of Economic Dispatch (ED), Optimal Power Flow (OPF), and Unit Commitment (UC) simple and intuitive. Minpower is also built for flexibility and will be a platform for research on smart grids and stochastic resources. Powerful generic optimization solvers (e.g., CPLEX) can be used by Minpower, allowing for reasonable solution times on even large-scale problems. The goal is to create a state-of-the-art open source tool that enables collaboration and accelerates research and learning. The Minpower code is open source and is set up for collaborative authorship and mainte-nance. Minpower is designed to be flexible, extensible, and fast enough for researchers and developers working on the evolution of these problems, while remaining easy to use for students learning the classical formulations. III. CASE STUDY: SMALL SIGNAL STABILITY ANALYSIS . Small signal stability analysis is performed over the IEEE 14-bus system[6] and the eigen values and participation factors are calculated. The below Fig. 1 and Fig. 2 shows the eigen values calculated on both the S-Domain and S-Domain.
A. Eigenvalues of the IEEE 14-Bus System in the S-Domain
C. Computed Participation Factor TABLE I Computed Participation Factors
Fig. 3. Computed Eigen Values in S-domain B. Computed Eigen Values in the Z-domain
IV. CONCLUSION It is seen from the Table. II, that Python solves the Jacobian matrix in 0.0319 seconds, while MATLAB and OCTAVE solves it in 0.0363 and 0.0433 respectively. It is notable that Python requires less time to solve problems even compared to commercial scientific software packages with zero cost spend. Using Python the engineers and scientists could create their own software package to solve their own power system or even to solve any scientific problems tailored to their own need.
Fig. 4.Computed Eigen Values in Z -domain
TABLE II Comparison of runtime to calculate Jacobian matrix
[5] Fernando Perez, Brian E. Granger, John D. Hunter, “Python: An Ecosystem for Scientific Computing” , 2011. [6] Federico Milano, “Power System Modelling and Scripting”, Springer-Verlag London Limited 2010. [7] Stéfan van der Walt, S. Chris Colbert , Gaël Varoquaux, “The NumPy Array: A Structure for Efficient Numerical Computation”, Computing inSCienCe& engineering, 2011. [8] NumPy community, “ NumPy Reference”, March 20, 2009. [9] EuroScipy tutorial team, “Python Scientific lecture notes: Release 2010”, July 09, 2010. [10] SciPy community, “SciPy Reference Guide Release 0.7.dev”, December 07, 2008. [11] John Hunter, Darren Dale, “The Matplotlib User’s Guide”, May 27, 2007.
R EFERENCES [1] Hans Fangohr , “Introduction to Python for Compu tational Science and Engineering”, September 18, 2012. [2] Fernando Perez, Brian E. Granger, “IPython: A System for Interactive Scientific Computing”, May/June 2007. [3] Adam Greenhall, Rich Christie, Jean-Paul Watson, “Minpower: A Power Systems Optimization Toolkit”, [4] Travis E. Oliphant, “Python for Scientific Computing in Science and Engineering, 2007.
Computing”,
[12] Joachim Dahl, Lieven Vandenberghe , “CVXOPT: Convex optimization with Python”, Workshop on Machine Learning Open Source Software NIPS 2006. [13] Richard Lincoln, “PYPOWER Documentation Release 4.0.1”, July 15, 2011. [14] Hans Petter Langtangen, “A Primer on Scientific Programming with Python”, Springer, 2nd Edition, S pringer-Verlag Berlin Heidelberg 2009, 2011.
