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The impact of short-term variability and uncertainty on long-term power planning

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Abstract

Traditionally, long-term investment planning models have been the apparent tool to analyse future developments in the energy sector. With the increasing penetration of renewable energy sources, however, the modelling of short-term operational issues becomes increasingly important in two respects: first, in relation to variability and second, with respect to uncertainty. A model that includes both may easily become intractable, while the negligence of variability and uncertainty may result in sub-optimal and/or unrealistic decision-making. This paper investigates methods for aggregating data and reducing model size to obtain tractable yet close-to-optimal investment planning decisions. The aim is to investigate whether short-term variability or uncertainty is more important and under which circumstances. In particular, we consider a generation expansion problem and compare various representations of short-term variability and uncertainty of demand and renewable supply. The main results are derived from a case study on the Danish power system. Our analysis shows that the inclusion of representative days is crucial for the feasibility and quality of long-term power planning decisions. In fact, we observe that short-term uncertainty can be ignored if a sufficient number of representative days is included.

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Abbreviations

\({\mathcal {G}}\) :

Set of production units

\({\mathcal {G}}^w\) :

Set of wind production units

T :

Set of time periods

\(T_d\) :

Set of time periods, except the last, within an aggregation period (e.g. \(\{1,\ldots ,23\}\) for a day)

S :

Set of scenarios for short-term uncertainty

\(c_{g}^I\) :

Linear investment cost of unit g (€/MW)

\(c_{g}\) :

Linear production cost of unit g (€/MWh)

\(c_{g}^+\) :

Additional cost of upward balancing of unit g (€/MWh)

\(c_{g}^-\) :

Opportunity cost of downward balancing of unit g (€/MWh)

\(r_g^D\) :

Ramp down rate of unit g (p.u.)

\(r_g^U\) :

Ramp up rate of unit g (p.u.)

\(\rho _{gt}\) :

Predicted production factor of unit g at time t (p.u.)

\({\tilde{\rho }}_{gts}\) :

Realised production factor of unit \(g \in {\mathcal {G}}^w\) at time t in scenario s (p.u.)

\(\kappa \) :

Minimum wind penetration (%)

\(v^L\) :

Cost of load shedding (€/MWh)

\(v^S\) :

Cost of wind curtailment (€/MWh)

\(\nu _{t}\) :

Load factor at time t (p.u.)

\({\bar{d}}\) :

Maximum load (MWh)

\(\tau _t\) :

Duration of time period t

\(\pi _{s}\) :

Probability of short-term scenario s

\({\bar{p}}_{g}\) :

Investment capacity of unit g

\(p_{gt}\) :

Scheduled production of unit g at time t

\(k_{t}\) :

Scheduled load shedding at time t

\(l_{t}\) :

Scheduled wind curtailment at time t

\(p_{gts}^+\) :

Real-time upward balancing of unit \(g \in {\mathcal {G}}{\setminus }{\mathcal {G}}^w \) at time t in scenario s

\(p_{gts}^-\) :

Real-time downward balancing of unit \(g \in {\mathcal {G}}{\setminus }{\mathcal {G}}^w \) at time t in scenario s

\({\tilde{p}}_{gts}\) :

Real-time production of unit \(g \in {\mathcal {G}}{\setminus }{\mathcal {G}}^w \) at time t in scenario s

\(\varDelta k_{ts}\) :

Real-time load shedding at time t in scenario s

\(\varDelta l_{ts}\) :

Real-time regulating wind curtailment at time t in scenario s

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Acknowledgements

T. K. Boomsma gratefully acknowledges support from the project Analyses of Hourly Electricity Demand (AHEAD) funded by ForskEl 2017.

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Authors and Affiliations

  1. Department of Mathematics, University of Copenhagen, Copenhagen, Denmark

    Henrik C. Bylling & Trine K. Boomsma

  2. Department of Electrical Engineering, University of Malaga, Málaga, Spain

    Salvador Pineda

Authors
  1. Henrik C. Bylling
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  2. Salvador Pineda
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Correspondence to Henrik C. Bylling.

A: Results tables

A: Results tables

All results listed in two Tables: one for non-zero balancing costs and one for balancing costs equal to zero.

See Tables  7 and 8.

Table 7 Investment decisions and runtimes for the different models in the case of \(c^+_g = 0.05{c_g}/{r_g^u}\) and \(c_g^-=0.05{c_g}/{r_g^d}\)
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Table 8 Investment decisions and runtimes for the different models in the case of zero balancing costs for all units
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Bylling, H.C., Pineda, S. & Boomsma, T.K. The impact of short-term variability and uncertainty on long-term power planning. Ann Oper Res 284, 199–223 (2020). https://doi.org/10.1007/s10479-018-3097-3

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