An MIP-Based Heuristic Decomposition Approach for Distributed Energy Resource Scheduling

Zusammenfassung

The decentralization of the power infrastructure poses new challenges for power plant operators and aggregators. A large number of power plants must be coordinated to successfully participate in energy markets. This requires to take uncertain exogenous influences, such as weather and market price, into account when determining operational schedules of energy resources and quantity-price tuples for bids to energy and reserve markets. Stochastic programming techniques are commonly applied to these decision problems. But, the resulting models are usually large-scale and hard to solve. We propose a temporal decomposition heuristic to speed-up the solution process of such models. The heuristic is based on mixed-integer programming formulations. Therefore, it is flexible with respect to the kinds of power plants and market environments that can be considered. We validate our findings on a realistic benchmark set of large stochastic programs and confirm its suitability to significantly reduce computational effort while retaining near-optimal solution quality.

Appendix

List of Symbols

CPP:

Conventional Power Plant

MG:

Microgrid

MIP:

Mixed-Integer Programm

RER:

Renewable Energy Resource

SPP:

Storage Power Plant

VPP:

Virtual Power Plant

List of Symbols

Indices

i :

cell

j :

production level

k :

price bid level

s :

scenario

t :

period

Sets

$\mathscr {I}$ :

set of all cells i

$\mathscr {J}_i$ :

set of all production levels j of the conventional power plant in cell i

$\mathscr {S}$ :

set of all scenarios s

$\mathscr {T}$ :

set of all periods t

:

set of first time periods of storage recharge intervals for reserve provision

:

set of interim time periods of storage recharge intervals for reserve provision

Variables of the first stage

:

day-ahead spot market sell bid price indicator in period t at price

:

day-ahead spot market purchase bid price indicator in period t at price

:

negative reserve bid price indicator in period t at price

:

positive reserve bid price indicator in period t at price

:

negative reserve bid quantity in period t at price

:

positive reserve bid quantity in period t at price

:

start-up status of the conventional power plant in cell i in period t

:

commitment status of the conventional power plant in cell i in period t

:

shut-down status of the conventional power plant in cell i in period t

:

day-ahead spot market purchase bid quantity in period t at price

:

day-ahead spot market sell bid quantity in period t at price

Scenario independent parameters

$C_{i}^{\text {u}}$ :

start-up costs of the conventional power plant in cell i

:

marginal costs for one unit of power at production level j in cell i

:

shut-down costs of the conventional power plant in cell i

$\underline{C}_{i}^{\mathrm {v}}$ :

operating costs at the minimum power output level in cell i

$V_{i0}$ :

initial commitment status of the conventional power plant in cell i

:

minimum power output of the conventional power plant in cell i

:

maximum power output of the conventional power plant in cell i

:

maximum power output at production level j in cell i

:

maximum ramp-up rate of the conventional power plant in cell i

:

maximum ramp-down rate of the conventional power plant in cell i

:

start-up rate of the conventional power plant in cell i

:

shut-down rate of the conventional power plant in cell i

:

charge efficiency of the storage power plant in cell i

:

discharge efficiency of the storage power plant in cell i

:

maximum state of charge of the storage plant in cell i

:

minimum state of charge of the storage plant in cell i

:

initial state of charge of the storage plant in cell i

:

charge rate limit of the storage plant in cell i

:

discharge rate limit of the storage plant in cell i

Variables of the second stage

:

negative reserve contribution of the storage plant in cell i in scenario s in period t through discharging to the grid: nominally discharge to the grid; cease discharge on reserve activation

:

negative reserve contribution of the storage plant in cell i in scenario s in period t through charging from grid: nominally idle; charge on reserve activation

:

positive reserve contribution of the storage plant in cell i in scenario s in period t through discharging to the grid: nominally idle; discharge on reserve activation

:

positive reserve contribution of the storage plant in cell i in scenario s in period t through charging from grid: nominally charge from the grid; cease charge on reserve activation

:

negative reserve contribution of the conventional power plant in cell i at production level j in scenario s in period t

:

positive reserve contribution of the conventional power plant in cell i at production level j in scenario s in period t

$s_{it}$ :

state of charge of the storage power plant in cell i in scenario s at the end of period t

$\underline{s}_{it}$ :

virtual state of charge for the low state of charge contingency case of the storage power plant in cell i in scenario s at the end of period t

$\overline{s}_{it}$ :

virtual state of charge for the high state of charge contingency case of the storage power plant in cell i in scenario s at the end of period t

:

charging status of the storage in cell i in scenario s in period t

:

discharging status of the storage in cell i in scenario s in period t

$y_{sijt}^{\text {c}}$ :

power output of the conventional power plant in cell i at production level j in scenario s in period t

$y_{sit}^{\text {s,c}}$ :

power charge to the storage plant in cell i in scenario s in period t

$y_{sit}^{\text {s,d}}$ :

power discharge from the storage plant in cell i in scenario s in period t

$z_{sit}^{-}$ :

power draw of cell i in scenario s in period t

$z_{sit}^{+}$ :

power feed-in of cell i in scenario s in period t

Scenario dependent parameters

$D_{sit}$:

energy demand of the load in cell i in scenario s in time period t

$M_{tk}^{\text {x}^-}$:

upper bound on the day-ahead spot market purchase bid quantity at price in time period t

$M_{tk}^{\text {x}^+}$:

upper bound on the day-ahead spot market sell bid quantity at price in time period t

$M_{tk}^{\text {r}^-}$:

upper bound on the negative reserve bid quantity at price in time period t

$M_{tk}^{\text {r}^+}$:

upper bound on the positive reserve bid quantity at price in time period t

$P_s$:

Probability of scenario s

:

day-ahead spot market purchase price in scenario s in period t

:

day-ahead spot market sell price in scenario s in period t

:

negative reserve market price in scenario s in period t

:

positive reserve market price in scenario s in period t

:

power output of the renewable energy resource in cell i in scenario s in period t