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PyPSAL - Python Power System Analysis Library
Preprint · March 2020
DOI: 10.13140/RG.2.2.36254.48969
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PyPSAL - Power System Analysis Library
Olav Bjarte Fosso
Department of Electric power Engineering
Norwegian University of Science and Technology (NTNU)
Norway
Email: olav.fosso@ntnu.no
Abstract—This paper describes a library for power system
analysis. It is based on an object-oriented representation of the
transmission system components and the design of the library
is also object-oriented. The data description is connected to a
CSV-file format where either Microsoft Excel or Open Office
Spreadsheet may be used. Currently the tools available for load
flows are Newton-Rhapson, Decoupled Power Flow, DC Power
Flow, Continuation Power Flow, Contingency Analysis, SecurityConstrained DC Power Flow. The program frame work is written
in Python 3.6 and and it is tested on Windows 10 and Ubuntu
18.04. The main motivation for the work has been to establish
a flexible library with a significant number of functions working
seamlessly on the same data representation to facilitate rapid
development of new methods based on existing functionality.
Keywords—Continuation Power Flow, Contingency Analysis,
Power Flows, Python, Object-oriented programming, Securityconstrained optimization, Bender’s decomposition
I.
I NTRODUCTION
A number of toolboxes are available today for different
kind of power system network analysis where Python, Matlab
and other languages are used. Examples are PSAT and DOME
[1], PyPSA [2], MatPower [3]. PyPSAL (Fig. 1 and Fig 2)
is a library with its origin on a program system developed
by the author in Fortran 77 [4], which was designed to work
on large scale systems. Therefore, state-of-the-art for sparse
matrix representation, efficient numerical solvers and Inverse
Matrix Modification Lemma (IMML) [5] were used for making
the computations faster. This new implementation is using
similar techniques as in [4] but has its advantage in using
the Python programming language with an object-oriented
design. This makes the development to be fast and flexible.
The key is to have an effective object-oriented model and
topology representation to organize the calculations from. It is
here chosen to have the full AC, the decoupled representation
(DEC) and the DC representation as main classes while the
different implementations are organized as sub-classes.
II.
U SER I NTERFACE
The library is currently not provided a graphical interface.
However, the data is connected to a spreadsheet representation
in a CSV-format. The routines for running the main applications are supplied with a number of options for controlling the
cases. Each option is supplied with a default value, which can
be user controlled when defining the total sequence of studies.
Examples of such user controlled options are sparse/non-sparse
solvers and which solver to use, to verify the contingency
cases with full AC load flow, the amount of summary provided
during the simulation/optimization and the way of presenting
data or results (graphical tables or summary to screens).
Fig. 1.
System Objects of PyPSAL
A. External data format
The data representation is closely connected to the IEEEformat, the representation used in Matpower and the PSSE
Rawd. To avoid being too strongly connected with a specific
representation of the data format, a representation where each
case is given by individual sheets within a spreadsheet file as
shown in Fig 3, is chosen. The sheets in Excel are currently:
Parameters, Buses, Loads, Transmission lines, Generators,
Shunts and Transformers.
The data within each sheet follows essentially the format
of IEEE and the representation used in Matpower. When importing such a description into a spreadsheet in a CSV-format,
it is easy to copy the blocks into the right component sheet.
For some data there are routines for automatic conversion of
data.
B. Internal object representation
For each electrical component, the required data is read
from each cell of the relevant sheet using Python library
functions for working on spreadsheets. As mentioned, there
are sheets for the main component classes of a power system.
However, the design of the interface is flexible and new classes
and component attributes can easily be added. Additionally,
there are a number of methods defined under each class
Fig. 2.
Fig. 3.
Classes and subclasses of PyPSAL
Fig. 4.
Bus loads
Fig. 5.
Transmission line flows
Transmission line representation in Excel
A. AC Power Flow
of components transforming the data to a useful internal
representation. The main system objects with some of the
system variables are shown in Fig. 1.
C. Topology representation
When creating the instances of each object class, the
instance is added to a list of same type of objects. On toplevel there are lists such as: GenList, BusList, TransList and
LoadList. These are holding the instances for each class.
Additionally, there are a number of pointers making it fast
to identify associated objects in the topology. Iteration over
any of these lists, will effectively identify the relevant objects
and associated parameters of each task.
III.
M ODULE DESCRIPTIONS
This section describes the individual modules implemented
and the methods which can be used in other computational
schemes. The main classes and sub-classes are shown in Fig.
2.
The AC Power Flow is implemented through the object
ACPowerFlow with a wide range of methods appropriate to
deal with such cases. There are methods for calculating the
classical Jacobian matrix, net power injections, mismatches,
activation and deactivation of reactive limits of generators,
flow calculations, flow violations using different flow criteria
and ratings. The storage scheme when building the system
matrices is based on a list of sub-lists where each sub-list is
the matrix element along with its matrix coordinates. Such
a storage scheme makes it simple to map the sparse matrix
structure into either a full matrix description, the sparse rowwise format(CSR) and the sparse column-wise format(CSC)
[6]. The last two formats are widely used in equation solvers
for sparse systems. Currently, solvers used are from the linalg
and sparse.linalg modules of the Scientific Python (Scipy) but
there are also interfaces to solvers from CVXOPT [7]. The
user can chose which solver to use when calling the individual
modules. The individual methods are supplied with user controlled parameters for choosing solvers, maximum number of
iterations and the amount and style of result presentation. Both
input data and the results can be presented either as standard
output to screen or in a standardised graphical table format.
Examples are given in Fig. 4 and Fig. 5.
One of the methods implemented is the standard NewtonRhapson power flow method. The component models used in
the implementations are similar to those described in [8].
B. Decoupled Power Flow
There are three methods for decoupled power flow implemented, reflecting different assumptions in simplifying the
matrices. The methods included are the XX, BX and XB
where X and B reflects the assumptions made in developing
the matrices of the active power and the reactive power
load flow matrices. This is further discussed in [9] and [10].
The experience shows different behaviour on different system
characteristics as when there are lines with low X/R-ratios
and there are cases where the standard decoupled power flow
fails in convergence while one of the others has excellent
performance. Essentially the same methods are available for
the decoupled power flow but in a decoupled manner.
C. DC Power Flow
The DC Power Flow uses a simple flow representation
where the losses are represented as equivalent loss vectors on
the individual buses [9]. In other words, after the power flow
calculation, the losses of each transmission line are estimated
and 50% allocated to each node [17]. This is a widely used
but very simple representation. The methods relevant for result
and data representation are the same as the ones for the AC
and decoupled methods.
D. Contingency Analysis
The contingency analysis are based on the decoupled power
flow model. The implementation is much in line with what
is presented in [11]. The user can choose the sparse/nonsparse representation, the maximum number of iterations of
each case, reactive limits enforcement of generators as well
as the amount of results presented during the analysis. There
is also an option to check contingency cases with a regular
load flow. This is also user-controlled and is a useful option in
case one of the contingency cases fails to converge, to check
specific solutions or in the case of multiple contingencies. The
standard technique for solving contingencies are based on the
Inverse Matrix Modification Lemma (IMML) as described in
[5] where the pre-compensation technique is used on iterative
cases. This approach also effectively identifies cases causing
separation in the grid. The user can specify which solver to use
(sparse/non-sparse). The fact that the same matrices are used
for all contingencies is utilized by doing the preparatory work
as LU-decomposition before the contingency analysis starts. In
such a case, only a forward and backward substitution is used
in the iterative solution as well as for calculating the required
inverse factors for compensation.
E. Continuation Power Flow
The implementation of the Continuation Power Flow essentially follows the implementations as described in [12] and
[13]. Besides the methods inherited from the ACPowerFlow
class, there are own methods within this class for administration of the continuation parameters, for deciding on the
loading profile, implementing the prediction and the correction
steps as well as a method implementing this into a increased
system loading from a voltage collapse viewpoint. However,
there is also an implementation of the technique as a tool for
performing system simulations according to a time varying
load and generation profile. The advantage of the method is the
ability to, in a quasi-static procedure, follow the tap-changing
of transformers, system overloads and possible discrete actions
as tripping of equipment.
F. Security-constrained Economic Dispatch
The security-constrained economic dispatch is based on a
DC-formulation of the power flow equations [14] and [15].
However, there are options for using the standard DC, the
incremental and the hot-start alternative. The incremental and
the hot-start [17] can be combined with an AC load flow
and will therefore give an improved accuracy as it gives an
accurate loss and initial flows for the transmission lines at the
linearization point. The optimization is based on a compact
formulation where the flow on the individual transmission lines
is expressed as a function of the net-injection on the individual
nodes. This is the well-known distribution factor formulation
[18] and [19] but implemented in a scheme as given in [20].
Only the transmission lines experiencing overload will be
included in the calculations and the distribution factors for
each line is calculated by a forward and backward substitution
when it is needed.
For the contingency cases, it may either be chosen a preventive
strategy or a post-contingency rescheduling approach. In the
case of a preventive approach, the flow after a contingency
is calculated using the IMML, but in this case the postcompensation method is used. For transmission lines experiencing flow violation, a constraint is formulated and corrected
based on the IMML and next added to the main optimization
problem. After all the constraints are added, a new optimization is conducted before the post-contingency flows are
checked in a new contingency analysis. In this process, the
user can choose which rating or which multiplier to used for
the post-contingency flow. The output of such a study is a
base case which keeps the flow after contingencies under a
user-defined level.
The other option is to use the post-contingency rescheduling
based on Bender’s decomposition as described in [20] and [21].
The approach here is to formulate a sub-problem according to
a minimized deviation from the initial generation profile and to
solve this using the permitted free rescheduling options given.
Based on the result of this optimization, a new constraint may
be formulated indicating how the base case problem could be
changed to make the sub-problem feasible. This constraint is
known as Bender’s Cut [20]. Both these approaches for taking
into account the contingencies, have demonstrated excellent
performance. Several optimization packages are available under this scheme and depending on the formulation it may be
convenient to use LP, QP, MILP or Barrier. For large systems,
the computation time may be significant since this will involve
a large number of optimization cases. Solvers available are
LPSOLVE [23], COIN [24] and GLPK [25]. An option is also
to use Interior solvers interface through CVXOPT [7].
IV.
C ONCLUSION
The paper describes an implementation of a set of library
functions for power system analysis. It is implemented in
Python and contains standard modules such as: AC Power
Flow, Decoupled, Decoupled Power Flow, Continuation Power
Flow, Contingency Analysis and Security-constrained Economic Dispatch. The data representation is object-oriented and
this is also true for the design of the modules. The Python
library is interfaced to a spreadsheet in CSV-format. The
modules are tested on the following test systems: IEEE 9-bus,
IEEE 14-bus, IEEE 30-bus and the IEEE 118-bus systems. The
modules implemented are verified to give the same voltage
profiles and power flow results as the ones published in the
literature on these systems. The main features of this library
is its flexibility as it provides a framework for rapid development of new tools, expansion of functionalities of existing
techniques, and for modelling new electrical components to
enhance utilization of the power system. The common data
structure with the object-oriented design is a main contributor
to the flexibility as it makes it possible to work on local copies
and to compare alternatives. The number of specialized solvers
make it possible to choose the right solver for the current case
and by this it may reduce the computation time significantly. In
addition, it increases the portability between different operating
systems and between Python versions as there may be delays
in development on different platforms.
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