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Robust Optimal Scheduling with a Grid-Connected Microgrid Installed in a Large-Scale Power Consumer

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Abstract

This paper presents a methodology to determine a robust optimal operational schedule of the grid-connected microgrid installed in a large-scale electricity consumer. We propose a novel two-stage robust optimization (TSRO) model to address the worst case under the uncertainty set of consumer’s load and renewable energy resources. The proposed model is formulated as a mixed integer linear programming considering technical constraints of the energy storage system (ESS) and distributed conventional generator (DG). The objective of the TSRO problem is to minimize the customer’s total cost including the operation cost of DGs, the electric bill with demand and energy charges, and the operation cost of ESS. Benders decomposition and outer approximation algorithms are applied as the solution methodologies of master-problem and sub-problem of TSRO, respectively. The proposed TSRO model is validated in a test system by analyzing the sensitivity to uncertainty budget ratio, the effect of the demand charge consideration, the appropriate historical peak load, and the real-time cost efficiency. The optimization modeling is implemented using Matlab with CPLEX 12.6.

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Abbreviations

\(\varDelta ^{d}\) :

Uncertainty budget limit of the electric load for the decision horizon.

\(\varDelta ^{s}\) :

Uncertainty budget limit of WTs for the decision horizon.

\(\varDelta ^{z}\) :

Uncertainty budget limit of PVs for the decision horizon.

\(\delta _{j}^{\ell }\) :

Incremental cost of block-\(\ell\) of the piecewise linear cost function of the DG-j.

\(\varDelta {L}_{t}\) :

\((L_t^{max} - L_t^{min})/2\).

\(\varDelta {P}_{t}^{PV}\) :

\(( P_t^{PV,max} - P_t^{PV,min})/2\).

\(\varDelta {P}_{t}^{WT}\) :

\(( P_t^{WT,max} -P_t^{WT,min})/2\).

\(\eta _{m}^{c}\) :

Charging efficiency of the ESS-m.

\(\eta _{m}^{d}\) :

Discharging efficiency of the ESS-m.

\(\overline{L_t}\) :

Estimated consumer’s electric load at time-t.

\(\overline{P_t^{PV}}\) :

Forecasted generation of PVs at time-t.

\(\overline{P_t^{WT}}\) :

Forecasted generation of WTs at time-t.

\(a_j, b_j, c_j\) :

Coefficients of the quadratic cost function of DG-j.

\(ACL_{m}\) :

Average cycle-life of the ESS-m.

\(AWC_{m}\) :

Average wear cost of the ESS-m.

\(C_{j}^{min}\) :

Coefficient of the piecewise linear cost function of the DG-j.

\(C_{j}^{SD}\) :

Shut-down cost of the DG-j.

\(C_{j}^{SU}\) :

Start-up cost of the DG-j.

\(D_{j}^{\ell }\) :

Upper bound of block\(-\ell\) of the piecewise linear cost function of DG-j.

\(DoD_{m}\) :

Depth of discharge of the ESS-m.

\(DT_j\) :

MDT of DG-j.

\(E_{m,0}\) :

Initial state of energy stored in the ESS-m.

\(E_{m,T}^{Lower}\) :

Lower bound set value of the state of energy stored in the ESS-m at time-T.

\(E_{m,T}^{Upper}\) :

Upper bound set value of the state of energy stored in the ESS-m at time-T.

\(E_{m}^{max}\) :

Upper bound of the state of energy that can be stored in the ESS-m.

\(E_{m}^{min}\) :

Lower bound of the state of energy that can be stored in the ESS-m.

\(EP_{m}^{max}\) :

Rated charging/discharging power of ESS-m.

\(F_j\) :

Number of periods that DG-j must be initially offline due to its MDT.

\(G_j\) :

Number of periods that DG-j must be initially online due to its MUT.

\(L_t^{max}\) :

Upper bound of the estimated consumer’s electric load at time-t.

\(L_t^{min}\) :

Lower bound of the estimated consumer’s electric load at time-t.

\(L_{max}^0\) :

The historical peak load that determined the previous demand charge of the power consumer.

\(N^E\) :

The number of ESS.

\(N^G\) :

The number of DG.

\(P_j^{max}\) :

Upper generation bound of DG-j.

\(P_j^{min}\) :

Lower generation bound of DG-j.

\(P_t^{PV,max}\) :

Upper bound of the forecasted generation of PVs at time-t.

\(P_t^{PV,min}\) :

Lower bound of the forecasted generation of PVs at time-t.

\(P_t^{WT,max}\) :

Upper bound of the forecasted generation of WTs at time-t.

\(P_t^{WT,min}\) :

Lower bound of the forecasted generation of WTs at time-t.

\(R^{D}\) :

The price imposed on the peak load of electric power consumers.

\(R_t^{E}\) :

Energy price imposed on the load at time-t.

\(RD_j\) :

Ramping down limit of DG-j.

\(RU_j\) :

Ramping up limit of DG-j.

T :

Decision horizon.

\(UT_j\) :

Minimum-up-time of DG-j.

\(\varvec{\lambda }\), \(\varvec{\eta }\), \(\varvec{\mu }\), \(\varvec{\phi }\) :

Vectors of dual decision variables for the constraints in the set \(\mathcal {X} (\mathbf {v,d,s,z})\).

\(C^{D}\) :

Cost of the demand charge.

\(C_{j,t}^{F}\) :

Generating fuel cost of the DG-j at time-t.

\(C_{j,t}^{SD}\) :

Shut-down cost of the DG-j at time-t.

\(C_{j,t}^{SU}\) :

Start-up cost of the DG-j at time-t.

\(C_{m,t}^{ESS}\) :

Operating cost of the ESS-m at time-t.

\(C_{t}^{E}\) :

Cost of the energy charge at time-t.

\(E_{m,t}\) :

State of energy stored in the ESS-t at time-t.

\(EP_{m,t}^{c}\) :

Charging power stored in the battery of ESS-t at time-t.

\(EP_{m,t}^{d}\) :

Discharging power from the battery of ESS-m at time-t.

\(L_{max}\) :

The peak load that determines the demand charge of the power consumer.

\(L_{t}\) :

Consumer’s estimated electric load at time-t.

\(L_{t}'\) :

Consumer’s adjusted electric load at time-t.

\(P_{j,t}^{DG}\) :

Power generation of the DG-j at time-t.

\(P_{t}^{PV}\) :

Power generation of the PVs at time-t.

\(P_{t}^{WT}\) :

Power generation of the WTs at time-t.

\(q_{j,t}^{\ell }\) :

Generation in block-\(\ell\) of the piecewise linear cost function of the DG-j at time-t.

\(u_{j,t}\) :

Binary variable of DG-j at time-t.

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Acknowledgements

This work was supported by Youngsan University Research Fund of 2019.

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Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Konkuk Univerity, Seoul, Korea

    Jong-Bae Park

  2. Department of Electrical and Electronic Engineering, Youngsan Univerity, Yangsan, Korea

    Yong-Gi Park

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Park, YG., Park, JB. Robust Optimal Scheduling with a Grid-Connected Microgrid Installed in a Large-Scale Power Consumer. J. Electr. Eng. Technol. 14, 1881–1892 (2019). https://doi.org/10.1007/s42835-019-00227-5

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