Bi-Level Operation Scheduling of Distribution Systems with Multi-Microgrids Considering Uncertainties
Abstract
:1. Introduction
- Proposing a bi-level operation scheduling framework for decision making of DSO and MMGs in an uncertain environment,
- Proposing a scenario matrix based on the HMM method to achieve the stochastic moments and correlations among the historical scenarios,
- Transforming the non-linear bi-level optimization problem into the single-level MISOCP optimization problem through linearization techniques and KKT optimality conditions.
2. Uncertainties Modelling
Modeling of Scenario Matrix
3. Problem Formulation
3.1. Upper-Level: Distribution System Operator (DSO) Decision Making
Constraints
- Bus voltage limits constraint:
- Line current limits constraint:
- Exchanged power limit with the wholesale electricity market:In order to deal with the limited capacity of sub-transmission transformer, the exchanged power between the wholesale market and DSO should be guaranteed as follows:
- Exchanged power limit between DSO and MGs:Based on the aforementioned limitations in the contract for the exchanged power between DSO and MG operators, constraint (15) should be met.
3.2. Lower-Level: Multi-Microgrids (MMGs) Decision Making
Constraints
- Exchanged power limit between DSO and each MG:
- Exchanged power limit between MGp and MGq:
- Operation limit of MTs:
- Operation limits of ESSs:
- Power balance of pth MG:
3.3. Solution Methodology
4. Numerical Results and Discussion
4.1. Test System
4.2. Simulation Results
4.2.1. Operation Scheduling
4.2.2. Considering Uncertainties
4.2.3. Large-Scale Test Systems
4.2.4. Performance Evaluation of the Proposed Heuristic Moment Matching (HMM) Method
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
t | Index of hours. |
Index of buses. | |
Index of DERs (PVs, MTs, and ESSs). | |
br | Index of branches. |
Index of MGs. | |
Set of scenarios. | |
Wholesale market/retail market price at time t ($/MWh). | |
The amount of exchanged power with wholesale market at time t (MW). | |
The amount of exchanged power between DSO and MGp at time t (MW). | |
The total load demand at time t (MW). | |
The amount of exchanged power between MGp and MGq at time t (MW). | |
Output power of DER at time t (MW). | |
Output power of th PV (MW). | |
Operation & maintenance cost coefficient of DER . | |
Voltage at bus m (p.u.) | |
Line current between bus m and bus n at time t (kA) | |
/ | Charging/discharging power of ESS at time t (MW). |
Charging/discharging efficiency of ESS . | |
Initial amount of stored energy for ESS (MWh). | |
Stored energy for ESS at time t (MWh). | |
Binary variable for the charging/discharging status of ESS at time t. | |
Auxiliary variable used for linearization of the complementary conditions. | |
Maximum allowable exchanged power between DSO and wholesale market (MW). | |
Maximum allowable exchanged power between DSO and each MG (MW). | |
Maximum allowable exchanged power between MGp and MGq (MW). | |
Cost of exchanging power between DSO and MGs ($). | |
Cost of exchanging power between DSO and wholesale market ($). | |
Profit of selling power to loads ($). | |
Profit of exchanging power between DSO and MGp ($). | |
Profit of exchanging power between MGp and MGq ($). | |
Profit related to the generated power of DERs. | |
kth target moment/normalized target moment of i uncertain parameter. | |
Randomly generated matrix | |
L | Lower-triangle matrix of the correlation matrix |
R | Correlation matrix |
Cubic transformation coefficients | |
Non-normal random variable to satisfy the normalized target moments of the historical scenarios | |
Correlation error/the moment errors | |
Scenario matrix | |
Moments of target scenarios | |
Dual variable. | |
Greater than or equal to zero constraints. |
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Parameter | Value | Parameter | Value |
---|---|---|---|
15 | 65 | ||
36 | 13 | ||
20 | 1.3 | ||
0.95, 1.05 | 5 | ||
Ii,j,max(kA) | 1.8 | 2 | |
0.5, 2 | 2.5 | ||
0.92, 0.92 | 1 |
Parameter | Case Study 1 | Case Study 2 | Case Study 3 | |
---|---|---|---|---|
Without Correlation (SC2) | Cost of DSO | 71,418 | 73,926 | 69,104 |
Profit of MG1 | 6314 | 6210 | 6411 | |
Profit of MG2 | 4788 | 4696 | 4859 | |
Profit of MG3 | 4006 | 3931 | 4082 | |
With Correlation (SC2) | Cost of DSO | 71,952 | 74,519 | 69,828 |
Profit of MG1 | 6293 | 6195 | 6396 | |
Profit of MG2 | 4761 | 4676 | 4834 | |
Profit of MG3 | 3978 | 3903 | 4054 | |
Without Correlation (SC3) | Cost of DSO | 71,364 | 73,868 | 69,052 |
Profit of MG1 | 6392 | 6297 | 6499 | |
Profit of MG2 | 4859 | 4753 | 4914 | |
Profit of MG3 | 4097 | 4026 | 4159 | |
With Correlation (SC3) | Cost of DSO | 71,973 | 74,482 | 69,578 |
Profit of MG1 | 6357 | 6249 | 6451 | |
Profit of MG2 | 4812 | 4715 | 4867 | |
Profit of MG3 | 4043 | 3974 | 4102 |
84-Bus TPC | IEEE 119-Bus | IEEE 1300-Bus | |
---|---|---|---|
Calculation time (s) | 21.7 | 26.2 | 89.4 |
Average cost (k$) | 71.42 | 105.29 | 1202.67 |
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Esmaeili, S.; Anvari-Moghaddam, A.; Azimi, E.; Nateghi, A.; P. S. Catalão, J. Bi-Level Operation Scheduling of Distribution Systems with Multi-Microgrids Considering Uncertainties. Electronics 2020, 9, 1441. https://doi.org/10.3390/electronics9091441
Esmaeili S, Anvari-Moghaddam A, Azimi E, Nateghi A, P. S. Catalão J. Bi-Level Operation Scheduling of Distribution Systems with Multi-Microgrids Considering Uncertainties. Electronics. 2020; 9(9):1441. https://doi.org/10.3390/electronics9091441
Chicago/Turabian StyleEsmaeili, Saeid, Amjad Anvari-Moghaddam, Erfan Azimi, Alireza Nateghi, and João P. S. Catalão. 2020. "Bi-Level Operation Scheduling of Distribution Systems with Multi-Microgrids Considering Uncertainties" Electronics 9, no. 9: 1441. https://doi.org/10.3390/electronics9091441