The linearisation is restricted to calculating active power flows based on voltage angle differences and branch series reactances. This makes it suitable for short overhead transmission lines close to their natural loading. In this case it can be shown [ 6 ] that the voltage angles are related to the active power injections by a matrix.
Labeau, Pierre-Etienne [WorldCat Identities]
The matrix KBK T is singular with a single zero eigenvalue for a connected network and can be inverted by first deleting the row and column corresponding to the slack bus. PyPSA is a partial equilibrium model that can optimise both short-term operation and long-term investment in the energy system as a linear problem using the linear power flow equations.
PyPSA minimises total system costs, which include the variable and fixed costs of generation, storage and transmission, given technical and physical constraints. The objective function is given by. The optimisation is run over multiple time periods t representing different weather and demand conditions.
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The dispatch can also be limited by ramp rate constraints ru n,r and rd n,r per unit of the generator nominal power:. The dispatch of storage units h n,s,t , whose energy carriers are labelled by s , is constrained by a similar equation to that for generators in equation 6 :. The power capacity H n,s can also be optimised within installable potentials. The energy levels e n,s,t of all storage units have to be consistent between all hours and are limited by the storage energy capacity E n,s.
The initial energy level can be set by the user, or it is assumed to be cyclic, i. The energy capacity E n,s can also be optimised within installable potentials. Global constraints related to primary energy consumption, such as emission limits, can also be implemented. Power flows in networks of passive branches lines and transformers according to the linear power flow equations.
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KVL states that the voltage differences around any closed cycle in the network must sum to zero. In a recent paper it is demonstrated that this formulation of the linear load flow using cycles solves up to 20 times faster than standard formulations using the voltage angles [ 30 ]; voltage angle and PTDF formulations are also implemented in PyPSA and deliver identical results. Another author has implemented an integer transmission expansion in PyPSA [ 34 ] that bypasses the bilinearity with a disjunctive big -M relaxation [ 44 ]; this will be incorporated into the main code base of PyPSA soon.
PyPSA can also optimise operation and investment in other energy sectors, such as natural gas, heating and transport. These sectors can be modelled using a network of links with efficiencies for energy conversion losses; an example from a recent paper [ 29 ] is shown in Figure 2. Depletable resources such as natural gas are modelled with stores. Example of the coupling in PyPSA between electricity at top and other energy sectors: transport, hydrogen, natural gas and heating. There is a bus for each energy carrier, to which different loads, energy sources and converters are attached.
Unit commitment can be turned on for any generator.
The restrictions on generator output now become:. The variable satisfies. The ramp-rate limits in equation 7 can also be suplemented by ramping limits at start-up and shut-down. PyPSA has functionality to examine the steady state of the power system after outages of passive branches, based on an analysis of the linear power flow. PyPSA also implements a variety of network clustering algorithms to reduce the number of buses in a network while preserving important transmission lines. PyPSA is currently in version 0.
PyPSA has been designed to be modular, so that it is possible to develop the code for many other types of calculations. Currently features being considered by the development team include, in rough order of priority:. PyPSA was written in the Python programming language [ 49 ] because it is widely used in the modelling community, it is easy to learn and its implementation is also free. PyPSA has been tested with versions 2.
This enables easy and efficient indexing of the data, while mantaining the fast calculation speeds of the underlying array objects of the Python library NumPy [ 51 ]. For each of the components listed in Table 2 except the overall Network container component there is a DataFrame listing the static attributes such as line impedance or capital cost and a dictionary of DataFrames containing the time-varying attributes such as wind power availability or consumer demand that are in addition indexed by the list of snapshots. The specification of some attributes such as generator maximum output can be either static or time-varying; if the time series is not specified, then the static value is taken.
All matrix calculations and solutions of linear equation systems are carried out either with NumPy [ 51 ] or, in the case of sparse matrices, with SciPy [ 52 ]. These Python libraries interface with lower-level programming language libraries to benefit from the speed of strongly-typed languages. Optimisation problems are formulated using the Python-based optimization modeling language Pyomo [ 53 , 54 ], which is solver agnostic and intuitive to extend. The use of Pyomo also allows inter-operability with other energy system frameworks that use Pyomo, such as calliope [ 11 ], oemof [ 14 ] and urbs [ 20 ].
Set points for loads and generation are stored separately from the power values which are actually dispatched. PyPSA comes with a large test suite that covers all of its major functionality. Tests are implemented using the Python library pytest [ 58 ]. Users can and do report bugs by raising issues in the GitHub repository [ 24 ] or on the forum [ 27 ]. The timings were averaged over 10 attempts for each network.
If the admittance matrix remains the same for several calculations, PyPSA has the option to avoid recalculating it, which can save some of this time; further acceleration is possible by using the just-in-time jit compiler numba [ 61 ], as has been done in the pandapower project [ 9 ] with success for larger networks. For the linear optimal power flow LOPF the computation performance depends strongly on the choice of linear solver.
To give an indication of typical calculation times, if dispatch in the SciGRID model of the German transmission network described in Section 7 buses, generators including curtailable wind and solar at each node, 38 pump storage units, lines, 96 transformers is optimised over 4 snapshots, it takes 5 seconds using the COIN-OR Clp free solver on the computer described above. Extensive timings for different formulations of the LOPF problem can be found in [ 30 ].
Given the proliferation of software tools available for modeling power systems, a guide is provided here that briefly compares PyPSA to other power system tools, with a particular focus on free software in the Python programming language. The advantages of Python are discussed above in Section 3. Selected features for a selection of different software tools are compared in Table 3.
Many power system tools concentrate on steady-state, dynamic i. They neglect the multi-period unit commitment, investment optimisation and energy system coupling which PyPSA offers. It has no functionality to deal with multi-period OPF, which makes it unsuitable for unit commitment, storage optimisation or investment optimisation. PyPSA differs from more general energy system models such as calliope [ 11 ], oemof [ 14 ], OSeMOSYS [ 15 ] and urbs [ 20 ] by offering more detailed modelling of power networks, in particular the physics of power flow according to the impedances in the network.
PyPSA can model a more general energy network using link components see Section 2. These differences with other software tools are the reason that it was decided to develop a new tool rather than to extend an existing one. Existing tools for power flow such as PYPOWER did not have the internal code and data structures for economic optimisation over multiple time periods with many inter-temporal actors, whereas the energy system tools were missing the tight integration with power flow analysis that we believe is necessary for future research.
On the PyPSA website [ 26 ] a large number of examples of code using PyPSA is linked for reference and to help users just starting out with the software. These range from basic small-scale networks demonstrating the features of PyPSA, to a one-node-per-country model of the European power system with high shares of renewables [ 62 ], to full transmission network models available as open data from the SciGRID [ 63 ] and GridKit projects [ 64 ], [ 65 ] which we demonstrate here.
In one code example, data from openly-available sources on power plant locations and capacities, load distribution and time series are added to the SciGRID data so that load flow calculations can be carried out. The results of one such simulation for Germany with nodal pricing is shown in Figure 4.
Transmission bottlenecks in the middle of Germany prevent the transportation of this cheap electricity to the South, where more expensive conventional generators set the price. The linearly-optimised dispatch was then fed into a full non-linear power flow calculation where each bus was set to maintain nominal voltage; the resulting reactive power feed-in is also shown in Figure 4.
e-book Transmission Grid Security: A PSA Approach (Power Systems)
The details of how load, conventional power plants and renewable generation time series and expansion potentials were added to the grid data are provided in a forthcoming paper [ 67 ]. The lack of grid expansion forces some balancing of renewable variability locally with storage. Short-term battery storage grey combines with solar power yellow in Southern Europe, while longer-term hydrogen storage purple pairs with wind power blue in Northern Europe. The grid topology is based on the GridKit network for Europe, clustered from buses to buses. In this paper a new toolbox has been presented for simulating and optimising power systems.
Python for Power System Analysis PyPSA provides components to model variable renewable generation, conventional power plants, storage units, coupling to other energy sectors and multiply-connected AC and DC networks over multiple periods for the optimisation of both operation and investment.
Tools are also provided for steady-state analysis with the full load flow equations. As free software, the code of PyPSA can easily be inspected and extended by users, thereby contributing to further research and also transparency in power system modelling.
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Given that public acceptance of new infrastructure is often low, it is hoped that transparent modelling can contribute to public understanding of the various options we face when designing a sustainable energy system. The exact code contributions of each person to version 0.
Licence: GPLv3 [ 21 ]. Modelling of the electrical power system is becoming increasingly important thanks to the liberalisation of the power system, the rise of variable renewable energy to combat global warming, and the electrification of transport and heating. PyPSA provides a modular, object-oriented framework for simulating power systems that can be used for research and case studies, and also easily extended beyond its existing functionality. To maximise its reuse potential, PyPSA is written as abstractly as possible, making no assumptions about network topology, infrastructure parameters or asset technologies.
Judging by traffic on the forum [ 27 ], the website [ 26 ] and private communications, PyPSA is already being used by more than a dozen research institutes. Support for new users is provided on the PyPSA website [ 26 ] in the form of documentation and extensive usage examples, as well as on the PyPSA forum [ 27 ]. We thank the community of PyPSA users for bug reports, improvement suggestions and their general friendly support and encouragement for the further development of PyPSA.
Power Syst. Aug July New York: McGraw-Hill. June Krekel, H, et al. Brown, T. Journal of Open Research Software , 6 1 , p. Journal of Open Research Software. Journal of Open Research Software , 6 1 , 4. Journal of Open Research Software 6 1 : 4.
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Journal of Open Research Software 6, no. Journal of Open Research Software , vol. Start Submission Become a Reviewer. Abstract Python for Power System Analysis PyPSA is a free software toolbox for simulating and optimising modern electrical power systems over multiple periods. Keywords: Power system simulations, energy system simulations, Load flow calculations, optimal power flow, security-constrained optimal power flow, unit commitment, renewable energy.