Transmission Grid Expansion Planning of a High Proportion Renewable Energy Power System Based on Flexibility and Economy
Abstract
:1. Introduction
2. Power Grid Flexibility Index Evaluation
2.1. Analysis of the Main Factors Affecting Power Grid Flexibility
2.2. Power Grid Flexibility Index during the Normal Operation State
2.3. Power Grid Flexibility Index during the N-1 Operation State
2.4. N-1 Operation State Power Flow Calculation
3. Power Grid Planning Model Based on Flexibility and Economy
3.1. Optimize Model Structure
3.2. Upper Layer Planning Model
3.3. Lower Layer Operating Model
4. Multi-Objective Programming Model Solution
4.1. Model Solving Algorithm
4.2. Optimal Solution Calculation
5. Case Study
5.1. Garver-6 System
5.1.1. The Deterministic Economic Planning
5.1.2. The Flexibility Planning
5.2. IEEE RTS-24 System
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
Parameters | |
the maximum transmission capacity of the lth line | |
the average load rate of the ith line in T time period | |
the flexibility weighting coefficient of the lth line | |
the overflow flexibility weighting coefficient | |
the probability of the kth line disconnected in T time period | |
the number of lines in Ω3 | |
the discount rate | |
the service life of the project | |
the fixed annual operating rate of the project | |
the construction cost of a new line between nodes i and j | |
the number of existing lines/new-built lines between nodes i and j | |
the upper/lower limit of the construction line between nodes i, j | |
the occurrence probability of sth scenario | |
the gth generator cost coefficient | |
the ith renewable energy abandoned penalty coefficient | |
the overflow penalty coefficient | |
the ramp rate | |
the scheduling time interval | |
the maximum transmission power of a single line in branch ij | |
the upper/lower output limit of generator g | |
the upper/lower phase angle limit of node i | |
the upper/lower limit of the objective function | |
the weighting coefficient of the nth objective function | |
the number of objective functions | |
the number of Pareto non-inferior solutions | |
Variables | |
the current transmission power of the lth line at time t | |
the load rate of the lth line at time t | |
the ith line calculated load rate when the kth line is disconnected | |
the line flexibility index of the normal operating state at time t | |
the line overflow flexibility index when the kth line is disconnected | |
the power grid average load rate when the kth line is disconnected at time t | |
the N-1 line over-limit flexibility index at time t | |
the N-1 line flexibility index at time t | |
the system normal power grid flexibility index | |
the N-1 gird over-limit flexibility index | |
the N-1 power grid flexibility index | |
the node injection power vector/the node voltage phase angle vector/the DC power flow susceptance matrix under normal operating state | |
the node voltage phase angle vector/the DC power flow susceptance matrix under N-1 operating state | |
the node voltage phase angle vector/the susceptance matrix variation | |
the output vector of generators/renewable energy/load power | |
the total annual planning cost | |
the equivalent annual construction cost | |
the annual operating cost | |
the upper limit of the equivalent annual construction cost | |
the power generation cost in the sth scenario | |
the penalty cost in the sth scenario | |
the output power of the generator g at time t in the sth scenario | |
the maximum/actual generating capacity of the ith renewable energy at time t in the sth scenario | |
the total transmission power of branch ij at time t in the sth scenario | |
the overload power of the grid when the line k is broken at time t | |
the phase angle of node i at time t in the sth scenario | |
the mth solution membership degree of the nth objective function | |
the value of the nth objective function in the mth solution | |
Sets | |
T | the set of flexibility evaluation moments |
the set of flexibility evaluation lines | |
the line set for N-1 verification | |
the set of lines participating in the N-1 line flexibility evaluation | |
the set of system existing nodes and nodes to be expanded | |
the set of lower layer operating scenario | |
the set of generators | |
the set of renewable energy |
Appendix A. The Modified Garver-6 Node System Related Data
Number | Node Number | Reactance/pu | Capacity/MW | Length/km | The Number of Existing Lines | Maximum Number of Construction |
---|---|---|---|---|---|---|
1 | 1–2 | 0.40 | 100 | 40 | 1 | 4 |
2 | 1–3 | 0.38 | 100 | 38 | 0 | 4 |
3 | 1–4 | 0.60 | 80 | 60 | 1 | 4 |
4 | 1–5 | 0.20 | 100 | 20 | 1 | 4 |
5 | 1–6 | 0.68 | 70 | 68 | 0 | 4 |
6 | 2–3 | 0.20 | 100 | 20 | 1 | 4 |
7 | 2–4 | 0.40 | 100 | 40 | 1 | 4 |
8 | 2–5 | 0.31 | 100 | 31 | 0 | 4 |
9 | 2–6 | 0.30 | 100 | 30 | 0 | 4 |
10 | 3–4 | 0.59 | 82 | 59 | 0 | 4 |
11 | 3–5 | 0.20 | 100 | 20 | 1 | 4 |
12 | 3–6 | 0.48 | 100 | 48 | 0 | 4 |
13 | 4–5 | 0.63 | 75 | 63 | 0 | 4 |
14 | 4–6 | 0.30 | 100 | 30 | 0 | 4 |
15 | 5–6 | 0.61 | 78 | 61 | 0 | 4 |
Generator Number | G1 | WT1 | G3 |
---|---|---|---|
Generator access node | 1 | 3 | 6 |
Generator capacity/MW | 150 | 360 | 600 |
Ramp rate/(MW·h−1) | 40 | / | 120 |
a/($·(MW2·h)−1) | 3.597 | / | 0.33 |
b/($·(MW·h)−1) | 0 | / | 0 |
c/($·h−1) | 0 | / | 0 |
Node Number | Maximum Load/MW | Node Number | Maximum Load/MW |
---|---|---|---|
1 | 80 | 4 | 160 |
2 | 240 | 5 | 240 |
3 | 40 | 6 | 0 |
Appendix B. The Modified IEEE RTS-24 Node System Related Data
Number | Name | Generator Type | Generator Access Node | Generator Capacity/MW |
---|---|---|---|---|
1 | PV1 | photovoltaic | 1 | 576 |
2 | WT1 | wind power | 15 | 645 |
3 | WT2 | wind power | 21 | 1200 |
4 | HT1 | hydropower | 22 | 900 |
Node | Maximum Load/MW | Node | Maximum Load/MW | Node | Maximum Load/MW |
---|---|---|---|---|---|
1 | 324 | 9 | 525 | 17 | 0 |
2 | 291 | 10 | 585 | 18 | 999 |
3 | 540 | 11 | 0 | 19 | 543 |
4 | 222 | 12 | 0 | 20 | 384 |
5 | 213 | 13 | 795 | 21 | 0 |
6 | 408 | 14 | 582 | 22 | 0 |
7 | 375 | 15 | 951 | 23 | 0 |
8 | 513 | 16 | 300 | 24 | 0 |
Number | Node Number | Reactance/pu | Capacity/MW | Length/km | The Number of Existing Lines | Maximum Number of Construction |
---|---|---|---|---|---|---|
1 | 1–2 | 0.0139 | 350 | 3 | 1 | 3 |
2 | 1–3 | 0.2112 | 350 | 55 | 1 | 3 |
3 | 1–5 | 0.0845 | 350 | 22 | 1 | 3 |
4 | 2–4 | 0.1267 | 350 | 33 | 1 | 3 |
5 | 2–6 | 0.192 | 350 | 50 | 1 | 3 |
6 | 3–9 | 0.119 | 350 | 31 | 1 | 3 |
7 | 3–24 | 0.0839 | 1200 | 0 | 1 | 0 |
8 | 4–9 | 0.1037 | 350 | 27 | 1 | 2 |
9 | 5–10 | 0.0883 | 350 | 23 | 1 | 2 |
10 | 6–10 | 0.0605 | 350 | 16 | 1 | 2 |
11 | 7–8 | 0.0614 | 350 | 16 | 2 | 2 |
12 | 8–9 | 0.1651 | 350 | 43 | 1 | 2 |
13 | 8–10 | 0.1651 | 350 | 43 | 1 | 2 |
14 | 9–11 | 0.0839 | 1200 | 0 | 1 | 0 |
15 | 9–12 | 0.0839 | 1200 | 0 | 1 | 0 |
16 | 10–11 | 0.0839 | 1200 | 0 | 1 | 0 |
17 | 10–12 | 0.0839 | 1200 | 0 | 1 | 0 |
18 | 11–13 | 0.0476 | 1000 | 33 | 1 | 3 |
19 | 11–14 | 0.0418 | 1000 | 29 | 1 | 3 |
20 | 12–13 | 0.0476 | 1000 | 33 | 1 | 3 |
21 | 12–23 | 0.0966 | 1000 | 67 | 1 | 3 |
22 | 13–23 | 0.0865 | 1000 | 60 | 1 | 3 |
23 | 14–16 | 0.0389 | 1000 | 27 | 1 | 4 |
24 | 15–16 | 0.0173 | 1000 | 12 | 1 | 3 |
25 | 15–21 | 0.049 | 1000 | 34 | 2 | 2 |
26 | 15–24 | 0.0519 | 1000 | 36 | 1 | 2 |
27 | 16–17 | 0.0259 | 1000 | 18 | 1 | 2 |
28 | 16–19 | 0.0231 | 1000 | 16 | 1 | 2 |
29 | 17–18 | 0.0144 | 1000 | 10 | 1 | 2 |
30 | 17–22 | 0.1053 | 1000 | 73 | 1 | 2 |
31 | 18–21 | 0.0259 | 1000 | 18 | 2 | 2 |
32 | 19–20 | 0.0396 | 1000 | 27.5 | 2 | 2 |
33 | 20–23 | 0.0216 | 1000 | 15 | 2 | 2 |
34 | 21–22 | 0.0678 | 1000 | 47 | 1 | 2 |
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Total Cost Ctotal/104 $ | Annual Construction Cost Ccons/104 $ | Annual Operating Cost Coper/104 $ | Flexibility Index | |
---|---|---|---|---|
The economic planning | 32,182.4 | 1009.2 | 31,173.2 | 0.7951 |
The flexibility planning | 30,962.9 | 1342.5 | 29,620.4 | 0.6130 |
Plan | New-Built Line | Ccons/104 $ | Coper/104 $ | Cpenalty/104 $ | Cov/104 $ | ||
---|---|---|---|---|---|---|---|
A | l1–2 = 1, l3–9 = 1, l5–10 = 1, l6–10 = 2, l8–9 = 1, l11–14 = 1, l12–23 = 1, l14–16 = 2, l16–17 = 2, l17–18 = 1, l17–22 = 1, l20–23 = 1 | 1925.8 | 90,680.1 | 0 | 0 | 0.4858 | 0.5327 |
B | l6–10 = 1, l8–10 = 2, l11–14 = 1, l14–16 = 2, l15–21 = 1, l16–17 = 1 | 1097.2 | 90,680.1 | 0 | 1114.8 | 0.5418 | 0.6492 |
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Chen, Z.; Hu, Y.; Tai, N.; Tang, X.; You, G. Transmission Grid Expansion Planning of a High Proportion Renewable Energy Power System Based on Flexibility and Economy. Electronics 2020, 9, 966. https://doi.org/10.3390/electronics9060966
Chen Z, Hu Y, Tai N, Tang X, You G. Transmission Grid Expansion Planning of a High Proportion Renewable Energy Power System Based on Flexibility and Economy. Electronics. 2020; 9(6):966. https://doi.org/10.3390/electronics9060966
Chicago/Turabian StyleChen, Zhanpeng, Yan Hu, Nengling Tai, Xiangying Tang, and Guangzeng You. 2020. "Transmission Grid Expansion Planning of a High Proportion Renewable Energy Power System Based on Flexibility and Economy" Electronics 9, no. 6: 966. https://doi.org/10.3390/electronics9060966