Stochastic Planning of Distributed PV Generation
Abstract
:1. Introduction
1.1. Motivation and Context
1.2. Literature Review
1.3. Contributions and Paper Organization
- In line with standard practice based on the PVWatts calculator, an analytical model for PV units is presented that rigorously maps solar irradiance to the injected AC power. It is shown that the analytical model is nonconvex. Two engineering designs are then offered to bypass the non-convexity.
- Based on realistic data, several homes are considered per node of the distribution network. Together with linearized network equations that adequately describe the relationships between powers and voltages of the distribution network, the developed framework is intended as a tool for utility-level studies.
- Extensive numerical studies on the IEEE 34-bus distribution feeder are carried out. It is shown that the degree of freedom between DC and AC sizes can be leveraged to lower installation costs through reduction of the panel area, in comparison to a scheme where the DC and AC sizes are restricted to conform to a known DC:AC ratio.
2. Network Model and the Optimization Problem
2.1. PV Module Model
2.2. Inverter Model
2.2.1. Optimal Inverter Sizing
2.2.2. Alternative Inverter Sizing
2.3. Placement and Sizing Constraints
2.4. Real Power and Reactive Power Consumption
2.5. Power Flows
2.6. Objective Function
- PV panel area cost for and . The cost per is represented by .
- Inverter nameplate apparent power capacity cost denoted by for and . The cost per is represented by .
- The term that captures thermal losses [4] multiplied by the price, denoted by , that utility buys from the market.
2.7. Optimization Problem
2.7.1. Placement and Sizing with Optimal Inverter Design
2.7.2. Placement and Sizing with Alternative Inverter Design
3. Numerical Data for Experiments and Design Procedure
3.1. The Test Network
3.2. Load Scenarios and Allocation of Users per Node
3.3. Irradiance Scenarios
3.4. Installation and Electricity Costs
- Electricity Costs: According to the Wholesale Electricity Market Data of 2016 [41], a representative price of electricity at which the utility buys from the market is .
3.5. Design Procedure
4. Results and Discussion
4.1. Results of Placement and Sizing with Optimal Inverter Design
4.2. Comparison between Optimal and Alternative Inverter Design
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Line | Line | Line | ||||||
---|---|---|---|---|---|---|---|---|
() | () | () | () | () | () | |||
1 | 0.0005 | 0.0005 | 12 | 0.0013 | 0.0007 | 23 | 0.0002 | 0.0001 |
2 | 0.0004 | 0.0004 | 13 | 0.0002 | 0.0002 | 24 | 0.0000 | 0.0000 |
3 | 0.0065 | 0.0066 | 14 | 0.0060 | 0.0044 | 25 | 0.0108 | 0.0080 |
4 | 0.0012 | 0.0013 | 15 | 0.0000 | 0.0000 | 26 | 0.0002 | 0.0001 |
5 | 0.0076 | 0.0077 | 16 | 0.0017 | 0.0013 | 27 | 0.0068 | 0.0053 |
6 | 0.0060 | 0.0061 | 17 | 0.0008 | 0.0006 | 28 | 0.0014 | 0.0011 |
7 | 0.0001 | 0.0001 | 18 | 0.0014 | 0.0011 | 29 | 0.0006 | 0.0004 |
8 | 0.0007 | 0.0004 | 19 | 0.0003 | 0.0002 | 30 | 0.0001 | 0.0001 |
9 | 0.0205 | 0.0109 | 20 | 0.0001 | 0.0001 | 31 | 0.0007 | 0.0004 |
10 | 0.0059 | 0.0031 | 21 | 0.0004 | 0.0003 | 32 | 0.0109 | 0.0408 |
11 | 0.0030 | 0.0022 | 22 | 0.0011 | 0.0008 | 33 | 0.0021 | 0.0022 |
Bus | Peak | Peak | Bus | Peak | Peak |
---|---|---|---|---|---|
() | () | () | () | ||
3 | 0.1100 | 0.0580 | 20 | 0.1340 | 0.0820 |
5 | 0.0320 | 0.0160 | 22 | 0.8280 | 0.6400 |
10 | 0.0680 | 0.0340 | 23 | 0.0900 | 0.0460 |
11 | 0.2700 | 0.1400 | 24 | 0.1660 | 0.1180 |
12 | 0.0100 | 0.0040 | 28 | 0.0080 | 0.0040 |
13 | 0.0800 | 0.0400 | 29 | 0.0300 | 0.0140 |
14 | 0.0080 | 0.0040 | 30 | 0.4120 | 0.2420 |
15 | 0.1040 | 0.0460 | 32 | 0.0040 | 0.0020 |
17 | 0.0640 | 0.0340 | Shunt Capacitors () | ||
18 | 0.1640 | 0.0860 | 22 | 0.6 | |
19 | 0.0560 | 0.0280 | 24 | 0.9 |
Parameter | Value | Parameter | Value |
---|---|---|---|
11,540 | |||
C | |||
d | |||
3 | see Section 4 |
Bus | Bus | Bus | Bus | Bus | |||||
---|---|---|---|---|---|---|---|---|---|
3 | 9 | 19 | 5 | 13 | 7 | 28 | 1 | 12 | 1 |
5 | 3 | 20 | 7 | 14 | 1 | 29 | 3 | 24 | 4 |
10 | 5 | 22 | 1 | 15 | 1 | 30 | 24 | 18 | 14 |
11 | 22 | 23 | 8 | 17 | 5 | 32 | 1 |
Month | Average POA | Average no. | Scenario |
---|---|---|---|
Irradiance | of Hours with | ||
Non-Zero Irradiance | |||
January | 3.91 | 11.19 | 0.349 |
February | 4.68 | 12 | 0.39 |
March | 5.32 | 12.77 | 0.41 |
April | 5.55 | 13.2 | 0.420 |
May | 5.87 | 14.838 | 0.395 |
June | 6.29 | 15 | 0.42 |
July | 6.83 | 14.70 | 0.46 |
August | 6.57 | 13.77 | 0.477 |
September | 5.87 | 13 | 0.45 |
October | 5.40 | 12.45 | 0.43 |
November | 4.47 | 11.33 | 0.39 |
December | 3.78 | 11 | 0.34 |
# of Installations | Max. of Average | Max. of Average |
---|---|---|
Allowed per node | Panel Area | Inverter Capacity |
100.00 | 39.65 | |
83.95 | 33.25 | |
69.95 | 27.70 | |
32.32 | 12.80 | |
32.32 | 12.80 |
Optimal | Inverter | DC | Thermal | |
---|---|---|---|---|
Value | Cost | Cost | Loss Cost | |
1,891,670 | 262,230 | 1,629,400 | 57.4959 | |
1,576,210 | 218,530 | 1,357,600 | 60.6561 | |
1,576,140 | 218,510 | 1,357,600 | 60.6873 | |
1,576,090 | 218,520 | 1,357,500 | 60.6467 | |
1,576,090 | 218,520 | 1,357,500 | 60.6478 |
Method | Max. of Average | Max. of Average |
---|---|---|
Panel Area | Inverter Capacity | |
Optimal | 32.32 | 12.8 |
Alternative | 93.6115 | 13.6 |
Method | Optimal | Inverter | DC | Thermal Loss |
---|---|---|---|---|
Value | Cost | Cost | Cost | |
Optimal | 1,576,090 | 219,000 | 136,000 | 60.6702 |
Alternative | 3,361,030 | 187,500 | 3,173,500 | 61.7727 |
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Bazrafshan, M.; Yalamanchili, L.; Gatsis, N.; Gomez, J. Stochastic Planning of Distributed PV Generation. Energies 2019, 12, 459. https://doi.org/10.3390/en12030459
Bazrafshan M, Yalamanchili L, Gatsis N, Gomez J. Stochastic Planning of Distributed PV Generation. Energies. 2019; 12(3):459. https://doi.org/10.3390/en12030459
Chicago/Turabian StyleBazrafshan, Mohammadhafez, Likhitha Yalamanchili, Nikolaos Gatsis, and Juan Gomez. 2019. "Stochastic Planning of Distributed PV Generation" Energies 12, no. 3: 459. https://doi.org/10.3390/en12030459