Location and Sizing of Micro-Grids to Improve Continuity of Supply in Radial Distribution Networks
Abstract
:1. Introduction
2. Problem Statement
3. Terminology and Mathematical Formulation
- Smart Switches (ssa): Tele-controlled switching devices able to isolate damaged parts of the network when a failure or contingency takes place. It is assumed that their actuation—status change to open and network reconfiguration—is fast enough to avoid worsening reliability indexes commonly counted for interruption durations longer than 3 min [27]. The set that includes all the smart switches located in the network is defined as SS, while A is the total number of elements—number of smart switches—as shown in Equation (1)
- Zone (zb): Network subset bounded by smart switches. The set that includes all the network zones is defined as Z, and B is the total number of zones. B can be obtained as the number of smart switches A plus one. The proposed notation is shown in Equation (2).
- Group of Zones (gzc): Set of adjacent network zones potentially supplied by the same generation and storage installations under islanded operation. The set that includes all the possible groups of zones is defined as GZ, and the total number is C. This value depends on the network topology and the number/location of smart switches, and it is calculated as the number of different sets of connected zones as Equation (3) shows.
- ○
- “P (input element)” is a function that provides the power-set of an input set, in this case, the Zones set. The power-set, in mathematics, is defined as the set of all the subsets of a set.
- ○
- “Zones (input element)” is a function that provides the set of zones of which the input element is composed.
- Distributed Energy Resources (dersd): Tuple of generation facilities and storage installations as shown in Equation (4). In this paper, different solar PV installations (pvi), diesel units (duj), and batteries (bessk) are considered. The indexes i, j, and k determines which elements of the equipment catalog are selected for each DERs design derd. The PV installations and the diesel units are defined by their rated power (kW). The storage installations are defined by their rate capacity (kWh) and their ratio power/capacity (kW/kWh). In addition, the annualized CAPEX (Capital Expenditure) and OPEX (Operating Expenditures) are considered for all the installations. The set that includes all the possible distributed energy resources combinations, according to the equipment catalog, is defined as DER, and the total number is equal to D.
- Micro-Grid (mgf): Tuple composed by a group of zones gzc, a tuple of optimal DERs der_optce feeding that group of zones, and the zone zb, where the DERs are located as shown in Equation (6).The set that includes all the possible MG designs is defined as MG, and the total number is equal to F.
- Network Solution (nsg): Subset of the micro-grids (MG) set, where all the zones are included but only once, as Equation (7) details. In other words, all the network is included in a network solution like the combination of different MGs. The set that includes all the possible network solutions is defined as NS, and the total number is equal to G.
4. Methodology
4.1. Network Partition
4.2. Micro-Grid Building
4.2.1. DER Sizing
NSE Computing Based on Power-Limitation
NSE Computing Based on Energy-Limitation
Combined Power and Energy-Based NSE Computing
4.2.2. DER Siting
4.3. Network Solution Building
- These Groups of Zones that compose the network combinations are substituted with all the MGs that contain them to create the Network Solutions set, NS. It should be emphasized that more than one MG may contain the same group of zones.
4.4. Reliability Assesment
4.5. Optimal Non-Dominated Network Solutions
5. Case Study
5.1. Description
5.2. Results
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A. DER Investment
Rated Capacity (kW) | Investment Cost (€/kW) |
---|---|
0 | 850 |
100 | O&M (€/kW-year) |
200 | 18.08 |
400 | Useful life (years) |
800 | 23 |
Rated Power (kW) | Power (kW)—Capacity (kWh) Ratio | Investment Cost (€/kW) |
---|---|---|
0 | 3.33 | 314.26 |
100 | 1 | Investment cost (€/kWh) |
200 | 0.4 | 346.21 |
400 | 0.25 | O&M (€/kWh) |
800 | 0.356 | |
Useful life (years) | ||
15 |
Rated Capacity (kW) | Investment Cost (€/kW) | O&M (€/kW-year) |
---|---|---|
0 | 0 | 8 |
100 | 223.34 | O&M (€/kWh) |
200 | 125.76 | 0.3 |
400 | 121.26 | Useful life (years) |
20 |
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Pseudocode |
---|
GZ = ø; c = 0 |
for each “element” in P(Z) |
if the “element” is connected |
Add “element” to GZ |
c += 1 |
Pseudocode |
---|
Combination Number | Network Combination |
---|---|
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 |
Zone | Number of Supply Points | Overhead Length (km) | Underground Length (km) |
---|---|---|---|
z1 | 0 | 10.99 | 0.04 |
z2 | 585 | 9.54 | 0.82 |
z3 | 1386 | 9.94 | 2.07 |
z4 | 771 | 6.04 | 0.15 |
nsg | Annualized Investment (€) | SAIDI Overall Network (h) | SAIDI Reduction (%) | SAIDI Standard Deviation (%) | SAIDIz1 (h) | SAIDIz2 (h) | SAIDIz3 (h) | SAIDIz4 (h) |
---|---|---|---|---|---|---|---|---|
1 | 25,263 | 6.7 | −67% | 14% | 7.8 | 7.1 | 4.4 | 0.0 |
2 | 24,945 | 6.7 | −67% | 14% | 7.8 | 7.1 | 4.4 | 0.0 |
3 | 22,291 | 6.7 | −67% | 14% | 7.8 | 7.1 | 4.4 | 0.0 |
4 | 21,052 | 6.7 | −67% | 14% | 7.8 | 7.1 | 4.4 | 0.0 |
5 | 18,947 | 6.7 | −67% | 14% | 7.8 | 7.1 | 4.4 | 0.0 |
6 | 17,980 | 6.9 | −66% | 16% | 8.1 | 7.2 | 4.4 | 0.0 |
7 | 15,975 | 6.9 | −66% | 13% | 8.0 | 7.3 | 4.8 | 0.0 |
8 | 15,875 | 7 | −65% | 17% | 8.3 | 7.2 | 4.4 | 0.0 |
9 | 14,736 | 7 | −65% | 14% | 8.1 | 7.3 | 4.8 | 0.0 |
10 | 12,632 | 7.1 | −65% | 15% | 8.3 | 7.3 | 4.8 | 0.0 |
11 | 11,664 | 8.8 | −56% | 32% | 8.3 | 15.0 | 5.1 | 0.0 |
12 | 9560 | 9 | −55% | 30% | 8.3 | 15.0 | 5.6 | 0.0 |
13 | 8592 | 12.2 | −40% | 19% | 14.7 | 15.0 | 5.6 | 0.0 |
14 | 6488 | 12.4 | −39% | 19% | 15.1 | 15.0 | 5.6 | 0.0 |
15 | 6316 | 12.8 | −37% | 17% | 8.3 | 15.0 | 19.4 | 0.0 |
16 | 5348 | 16.1 | −20% | 7% | 14.7 | 15.0 | 19.4 | 0.0 |
17 | 3244 | 16.3 | −19% | 7% | 15.1 | 15.0 | 19.4 | 0.0 |
18 | 2105 | 20 | −1% | 11% | 22.4 | 15.0 | 19.4 | 0.0 |
Base Case | 0 | 20.2 | 0% | 11% | 22.8 | 15.0 | 19.4 | 0.0 |
nsg | DERs Zone | z1 | z2 | z3 | z4 | PPV (kW) | PBAT (kW) | EBAT (kWh) | PDIE (kW) |
---|---|---|---|---|---|---|---|---|---|
1 | 2 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 200 |
3 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 400 | |
4 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 200 | |
2 | 3 | 0 | 1 | 1 | 0 | 0 | 100 | 250 | 400 |
4 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 200 | |
3 | 3 | 0 | 1 | 1 | 0 | 0 | 100 | 100 | 400 |
4 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 200 | |
4 | 3 | 0 | 1 | 1 | 0 | 0 | 100 | 30 | 400 |
4 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 200 | |
5 | 3 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 400 |
4 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 200 | |
6 | 2 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 100 |
3 | 0 | 0 | 1 | 0 | 0 | 100 | 30 | 200 | |
4 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 200 | |
7 | 3 | 0 | 0 | 1 | 0 | 0 | 100 | 100 | 200 |
4 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 200 | |
8 | 2 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 100 |
3 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 200 | |
4 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 200 | |
9 | 3 | 0 | 0 | 1 | 0 | 0 | 100 | 30 | 200 |
4 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 200 | |
10 | 3 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 200 |
4 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 200 | |
11 | 3 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 200 |
4 | 0 | 0 | 0 | 1 | 0 | 100 | 30 | 100 | |
12 | 3 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 200 |
4 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 100 | |
13 | 3 | 0 | 0 | 1 | 0 | 0 | 100 | 30 | 100 |
4 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 100 | |
14 | 3 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 100 |
4 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 100 | |
15 | 3 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 200 |
16 | 3 | 0 | 0 | 1 | 0 | 0 | 100 | 30 | 100 |
17 | 3 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 100 |
18 | 3 | 0 | 0 | 1 | 0 | 0 | 100 | 30 | 0 |
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Postigo Marcos, F.; Mateo Domingo, C.; Gómez San Román, T.; Cossent Arín, R. Location and Sizing of Micro-Grids to Improve Continuity of Supply in Radial Distribution Networks. Energies 2020, 13, 3495. https://doi.org/10.3390/en13133495
Postigo Marcos F, Mateo Domingo C, Gómez San Román T, Cossent Arín R. Location and Sizing of Micro-Grids to Improve Continuity of Supply in Radial Distribution Networks. Energies. 2020; 13(13):3495. https://doi.org/10.3390/en13133495
Chicago/Turabian StylePostigo Marcos, Fernando, Carlos Mateo Domingo, Tomás Gómez San Román, and Rafael Cossent Arín. 2020. "Location and Sizing of Micro-Grids to Improve Continuity of Supply in Radial Distribution Networks" Energies 13, no. 13: 3495. https://doi.org/10.3390/en13133495