Background

Energy-economic background

Feel free to skip this section if you are familiar with power markets design as well as fundamental bottom-up power market modeling.

Wholesale power markets in Europe are organized as a sequential series of markets from futures and forwards markets to short-term markets (spot markets). Since futures and forwards markets mostly serve for hedging price risks of short-term markets, we only focus on the spot markets which determine the actual operation of plants and include a physical delivery of electricity to the system.

There are two kinds of spot markets, the day-ahead market as well as intraday markets (auctions and continuous trading). We in turn focus on the day-ahead market which is the most relevant one.

Our model in a way abstracts from the real market constellations and assumes all plant operators to bid into the day-ahead market. We in turn do not explicitly model power plant operators’ (or other traders’) bidding behaviour, but assume them to offer their capacities at their marginal costs in a perfectly competitive quasi day-ahead market in order to serve an inflexible and exogenously given demand. We also include power storages and demand response. The latter enables parts of the demand to adjust in a flexible manner. Thus, the aggregated power plants’ capacities which are sorted by their marginal costs result in a merit order that is similar to the aggregated supply curves in the real day-ahead auction procedure in competitive power markets.

The perspective of our model is to assume that there is a “social planner” optimizing the power system in terms of minimizing its overall (dispatch) costs under the prevalent constraints, such as demand coverage or power plants capacity limits. We assume this social planner to have perfect foresight over the entire simulation time frame. We offer a Rolling horizon approach to break with this assumption. Our basic approach is quite common for fundamental bottom-up modeling of power systems since using a sound model parameterization, it enables the modeler to produce close to reality dispatch and price results in a highly simplified modeling setting with quite large system boundaries.

What is more, is that power markets in Europe are interconnected and operated within (mostly national) bidding zones. We model the German neighboring countries and their power plants in a rather aggregated manner in order to improve our day-ahead price prognosis and the dispatch result for Germany.

In order to improve our model results, we account for some power system inflexibilities that lead to a deviation from the cost optimum and are expressed by introducing additional constraints (such as minimum load profiles for CHP power plants that are empirically derived to serve heat demands) or adjusting parameter values (such as the overall capacities of coal power plants that has not been fully made use of).

Model granularity

• Technical granularity:

For Germany, every conventional block or power plant is modelled individually, whereas storages are aggregated to one cluster per technology. Renewable energy sources (RES) units are clustered based on their value applied from the market premium model leading to roughly 20 units per technology as a default. For the neigbouring countries which have interconnections with Germany, we consider one cluster per technology.

The following fuels and technologies are considered by default:

Renewable technologies

fuel	technologies
Solar	solar PV plants
Wind onshore	wind onshore plants
Wind offshore	wind offshore plants
Run of River	run of river plants
Biomass	solid biomass ST, biogas GT, biogas ST, biogas M

Conventional / backup technologies

fuel	technologies
Uranium	Nuclear ST
Lignite	Lignite ST
Hard coal	Hard coal ST
Natural gas	Natural gas CC, natural gas GT, natural gas M
Oil	Oil CC, oil GT
waste / mixed / other fossils	other CC, other GT, other M

All conventionals and backup plants as well as biomass plants may optionally be combined heat and power (CHP) or industrial power plant (IPP). This alters their minimum output profile.

Storage technologies

energy source	technologies
electricity	pumped hydro energy storage
electricity	reservoir energy storage

Battery energy storage systems (BESS) are not yet considered since these are mostly used for own consumption or provision of ancillary services and not so much for arbitrage trading (as of now). Since net network extraction as well as net feedin of PV power plants are modelled, the BESS used for own consumption in combination with PV are already taken care of. Since the usage of BESS in the DA market is limited, their price effect is (assumed to be) not very big. What is more, is that remaining system is already parameterized to be quite flexible.

Abbreviations:

• BESS: battery energy storage systems

• CC: combined cycle (gas turbine)

• CHP: combined heat and power

• GT: gas turbine

• IPP: industry power plants

• M: combustion engine (German: “Motor”)

• PV: photovoltaics

• RES: renewable energy sources

• ST: steam turbine

• Temporal granularity:

The default model resolution is hourly due to the resolution of the given time series inputs, either as an integral optimization run for all hours of a year (or another simulation time frame) or using a Rolling horizon approach.

• Spatial granularity:

There is one spatial node per bidding zone for Germany and its 10 electric neighbors, thus representing real market area boundaries and processes without taking network congestions within bidding zones into account.

The following countries and bidding zones are considered by default:

country code	country	bidding zone(s)
AT	Austria	AT
BE	Belgium	BE
CH	Switzerland	CH
CZ	Czech Republic	CZ
DE	Germany	DE-LU
DK	Denmark	DK1, DK2
FR	France	FR
NL	Netherlands	NL
NO	Norway	NO1, NO2, NO3, NO4, NO5
PL	Poland	PL
SE	Sweden	SE1, SE2, SE3, SE4

Mathematical background

Feel free to skip this section if you are familiar with fundamental bottom-up power market modeling using a linear programming approach.

From a mathematical point of view, our model is formulated as a linear program with the following characteristics:

• goal: Minimize total power system costs

• constraints:

  • demand coverage

  • power plants constraints: capacity limits, ramping constraints

  • storage constraints: power limits, energy limits, storage losses, storage transition

  • demand response constraints: power limits, energy limits, time restrictions

  • constraints for interconnection: power limits, transmission losses

  • optional emissions constraint

Fixed time series, such as the demand time series or the fixed renewable infeed, as well as scalar values we read in, are provided as parameters from a mathematical point of view.

Our model has a block-angular structure since the constraint formulations and objective terms are encapsulated in the components definitions of oemof.solph. Thus, in general decomposition techniques could be applied to speed up computation.

The model formulation ends in a sparse matrix. The complexity of the model is determined by the Model granularity which may be altered. The model statistics for the default granularity used are summarized in the table below (48 hours simulation time frame):

element	No.
rows	93821
columns	129653
nonzeros	309613

For the mathematical formulation, please see Mathematical formulation. You may also refer to the oemof.solph API reference for a documentation of the constraints and objective terms introduced with the individual components.

Technical background

pommesdispatch builds on the framework oemof.solph which allows modeling energy systems in a graph-based representation with the underlying mathematical constraints and objective function terms implemented in pyomo. Some of the required oemof.solph features - such as demand response modeling - have been provided by the POMMES main developers which are also active in the oemof community. Users not familiar with oemof.solph may find further information in the oemof.solph documentation.

We use the following components from the oemof.solph framework in order to represent the following units of the power system:

• Transformer: (conventional) power plants, renewable units for Germany in the market premium scheme, interconnectors to other bidding zones

• Source: commodity sources, fixed renewable units infeed

• Sink: national electricity demands

• GenericStorage: electricity storage units (pumped storage and reservoir)

• Buses: Elements to connect all power resp. energy flows

Rolling horizon approach

A rolling horizon approach can be used for multiple use cases, e.g.

• to force a break with the perfect foresight paradigm and to model imperfect foresight

• to reduce model complexity and ensure model solvability.

The idea is to slice your overall optimization time frame into shorter horizons and thus loose the perfect foresight assumption as well as the global optimum over the entire simulation time frame. In order to prevent storage units from being emptied at the end of each time slice, an overlap should be defined. I.e., only parts of the next time slice are used while the overlap is dropped.

The following figure explains the basic idea.

Image based on Büllesbach (2018), p. 62 and Marquant et al. (2015), p. 2141

The model results are then obtained by concatenating the results for the individual time slices. There is a rolling horizon implementation integrated as an alternative to a perfect foresight simulation in pommesdispatch, see Using pommesdispatch.

References

Büllesbach, Fabian (2018): Simulation von Stromspeichertechnologien in regionaler und technischer Differenzierung. Freie wissenschaftliche Arbeit zur Erlangung des Grades eines Master of Science am Fachgebiet Energie- und Ressourcenmanagement der TU Berlin.

Marquant, Julien F. ; Evins, Ralph and Carmeliet, Jan (2015): Reducing Computation Time with a Rolling Horizon Approach Applied to a MILP Formulation of Multiple Urban Energy Hub System. In: Procedia Computer Science 51 (2015), S. 2137–2146. – ISSN 18770509.