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Investigating the impact of stochasticity in microgrid energy management

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Abstract

Various stochastic programming methods have been used to account for penetration of uncertain renewable energy generation in microgrids. However, these stochastic methods may be unnecessary. Energy storage combined with rescheduling based on a rolling time horizon gives a microgrid powerful tools to adapt to any unexpected events. Add to that the natural tendency to over-engineer new systems and one begins to wonder how much value can be gained by stochastic optimization over deterministic methods. We investigated this question by looking at an existing residential microgrid in Hoover, AL. We compare various stochastic approaches for scheduling with deterministic approaches and show that there is little value of using stochastic programming. Instead, we find that considering longer time horizons is a better use of computational resources.

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Abbreviations

\(u_{gt}^s\) :

Commitment status for each generator g in time t, for scenario s, \(\in \{0,1\}\)

\(v_{gt}^s\) :

Generator start up indicator for each generator g in time t, scenario s \(\in \{0,1\}\)

\(u_{bt}^{Cs},u_{bt}^{Ds}\) :

Battery charging/discharging status, respectively in time t, scenario s, \(\in \{0,1\}\)

\(P_{gt}^s\) :

Total power (kW) at each generator g in time t, for scenario s, \(\in \mathbb {R}^+\)

\(P_{bt}^{Cs},P_{bt}^{Ds}\) :

Battery charging/discharging power (kW), respectively, \(\in \mathbb {R}^+\)

\(p_{gt}^{ms}\) :

Power at mth generator interval (kW), \(\in \mathbb {R}^+\)

\(P_{vt}^s\) :

PV power which is not curtailed at time t, scenario s (kW), \(\in \mathbb {R}^+\)

\(E_{bt}^s\) :

Energy in battery b at time t for scenario s (kWh), \(\in \mathbb {R}^+\)

\(E_{bt}^{EX,s}\) :

Amount of battery extreme energy in time t, scenario s (kWh), \(\in \mathbb {R}^+\)

\(P^{Vs}_{bt}\) :

Difference in battery power between time t and \(t-1\), scenario s, \(\in \mathbb {R}\)

\(L_t^s\) :

Load shed at time t scenario s, \(\in \mathbb {R}^+\)

\(k_{g}\) :

minimum up cost of generator g

\(C_{gt}^m\) :

Marginal cost for mth generator interval (strictly increasing)

\(C^{v}_{gt}\) :

Start up cost for generator g

\(C_{bt}\) :

Battery operational cost

\(\eta _b^C\) :

Charging efficiency of battery b

\(\eta _b^D\) :

Discharging efficiency of batter b

\(P_g^{min}\) :

Generator min up power

\(P_{b,INIT}\) :

Initial power output of battery b

\(D_{t}\) :

Real demand at time t

\(P_{vt}^{Fs}\) :

Forecasted PV power at time t for scenario s

\(E_b^{min}\) :

Minimum allowable energy for battery b

\(E_b^{max}\) :

Maximum allowable energy for battery b

\(E^{cap}_b\) :

Maximum energy capacity for battery b

\(E_{b,INIT}\) :

Initial state of charge of batter b

\(TU_g\) :

Minimum up-time for generator g

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

Set of generators

\(b \in \mathcal {B}\) :

Set of batteries

\(v \in \mathcal {V}\) :

Set of PV panels

\(m \in \mathcal {I}\) :

Set of piecewise generator power components

\(t \in \mathcal {T}\) :

Set of timeperiods

\(s \in \mathcal {S}\) :

Set of scenarios

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Authors and Affiliations

  1. Industrial and Systems Engineering, University of Tennessee, Knoxville, TN, 37996, USA

    Amelia McIlvenna & James Ostrowski

  2. Oak Ridge National Laboratory, Oak Ridge, TN, 37830, USA

    Ben Ollis

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  1. Amelia McIlvenna
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  2. Ben Ollis
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  3. James Ostrowski
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McIlvenna, A., Ollis, B. & Ostrowski, J. Investigating the impact of stochasticity in microgrid energy management. Energy Syst 13, 493–508 (2022). https://doi.org/10.1007/s12667-021-00437-9

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