Robust Economic Emission Dispatch of Thermal Units and Compressed Air Energy Storages

Abstract

In recent years, different energy storage technologies are attracting world’s attention due to their capabilities in adding more flexibility on power system operation and planning. Meanwhile, compressed air energy storages are able to participate in bulk energy management with higher power capacity for long discharge time period. In addition, advanced adiabatic compressed air energy storage (AA-CAES) has an overall efficiency up to 70% with near-zero carbon footprints in comparison with conventional types. Hence, this chapter aims to present a day-ahead robust dynamic economic emission dispatch model for wind, thermal, and AA-CAES units taking into account some operational constraints such as power balance criterion, ramp up and down limits, generation capacity, transmission losses, charge and discharge constraints of AA-CAES, etc. A mixed integer nonlinear programming (MINLP) problem is solved using SBB solver under general algebraic modeling system (GAMS) software package to minimize total operating cost and emissions of thermal units considering wind uncertainties and participating AA-CAES over a 24-h time interval.

Nomenclature

α ^inj :

Efficiency of injected power

α ^pump :

Efficiency of produced power

γ _i , η _i , δ _i , ξ _i , φ _i :

Emission characteristics of thermal generation station i

λ _t :

Electricity price at time horizon t [$/MWh]

ω :

Weighting factor ∈[0, 1]

a _i :

No-load cost coefficient of thermal generator i [$]

b _i :

Linear cost coefficient of thermal generator i [$/MWh]

B _ij :

ijth element of loss coefficient square matrix of size N _Gen[1/MW]

c _i :

Quadratic cost coefficient of thermal generator i [$/MW²h]

e _i , f _i :

Cost coefficient of thermal generator i reflecting the valve point effect respectively in [$] and [1/MW]

P _{Comp, t} :

Power consumed by CAES at time t for compressing and injecting air [MWh]

P _{Gen, t} :

Power output of CAES at time horizon t [MWh]

P _{i, t} :

Active power output of thermal generation station i at time t [MW]

${P}_i^{\mathrm{min}},{P}_i^{\mathrm{max}}$ :

Minimum and maximum power generation of ith thermal unit, respectively

${P}_d^t$ :

Electrical demand at time t [MW]

${P}_{\mathrm{Loss}}^t$ :

Active power losses of transmission lines at time t [MW]

SOC _t :

Amount of stored energy at time t [MWh]

SOC_min :

Minimum level of storage [MWh]

SOC_max :

Maximum level of storage [MWh]

${u}_t^{\mathrm{inj}}$ :

Binary variable, which is equal to 1 if air injected by CAES at time t, and 0 otherwise

${u}_t^{\mathrm{pump}}$ :

Binary variable, which is equal to 1 if air pumped by CAES at time t, and 0 otherwise

${V}_t^{\mathrm{inj}}$ :

Energy equivalent of injected air to storage at time t [MW/h]

${V}_{\mathrm{min}}^{\mathrm{inj}}$ :

Minimum level of injected air into storage [MW/h]

${V}_{\mathrm{max}}^{\mathrm{inj}}$ :

Minimum level of injected air into storage [MW/h]

${V}_t^{\mathrm{pump}}$ :

Energy equivalent of pumped air to combustion chamber at time t [MWh]

${V}_{\mathrm{min}}^{\mathrm{pump}}$ :

Minimum level of pumped air from storage to combustion chamber [MW/h]

${V}_{\mathrm{max}}^{\mathrm{pump}}$ :

Maximum level of pumped air from storage to combustion chamber [MW/h]