TSODSO Coordination Schemes to Facilitate Distributed Resources Integration
Abstract
:1. Introduction
1.1. Literature Review
1.2. Gap Analysis
1.3. Contributions
2. Optimal Power Flow Formulation
2.1. Transmission Level
2.2. Distribution Level
3. Proposed Coordination Schemes
3.1. Decentralised Scheme
Algorithm 1 Iterative algorithm for solving (26) 

3.2. Centralised Scheme
4. Numerical Results
4.1. System Description
4.2. Decentralised Coordination Scheme
4.3. Centralised Coordination Scheme
5. Conclusions and Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Nomenclature
A  reduced branchtonode incidence matrix 
${B}_{d}$  diagonal branch susceptance matrix 
${B}_{{B}_{i}}$  cost of the battery system at node i 
${B}_{P{V}_{i}}$  cost of PV generation at node i 
${c}_{i}\left(t\right)$  cost of generator i at time t 
${E}_{0,i}$  initial value of the energy stored at battery system at node i 
${E}_{\mathrm{min},i}$  minimum energy that can be stored at battery system at node i 
${E}_{\mathrm{max},i}$  maximum energy that can be stored at battery system at node i 
$f\left(t\right)$  vector of line power flows at time t 
${f}^{M}$  vector of maximum real power flows 
${f}^{m}$  vector of minimum real power flows 
${f}_{1}\left(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\right)$  TSO objective function 
${f}_{2}\left(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\right)$  all DSOs objective functions 
${g}_{1}\left(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\right)$  TSO inequality constraints 
${g}_{2}\left(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\right)$  DSO inequality constraints 
${h}_{1}\left(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\right)$  TSO equality constraints 
${h}_{2}\left(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\right)$  DSO equality constraints 
$\mathcal{I}$  set of I generators 
$\mathcal{J}$  set of J loads 
${\mathcal{J}}_{k}$  set of loads connected to bus k 
$\mathcal{K}$  set of K nodes 
$\mathcal{L}$  set of L lines 
M  graph incidence matrix 
${\mathcal{N}}_{PV}^{d}$  set of PVs connected to distribution system d 
${\mathcal{N}}_{B}^{d}$  set of battery systems connected to distribution system d 
${p}_{i}^{d}\left(t\right)$  net real power at node i at time t in distribution system d 
${P}_{{B}_{i}}^{\mathrm{dis}}\left(t\right)$  discharging power of the battery system at node i at time t 
${P}_{B,i}^{\mathrm{dis},min}$  discharging power of the battery system at node i lower limit 
${P}_{B,i}^{\mathrm{dis},max}$  discharging power of the battery system at node i upper limit 
${P}_{{B}_{i}}^{\mathrm{ch}}\left(t\right)$  charging power of the battery system at node i at time t 
${P}_{B,i}^{\mathrm{ch},min}$  charging power of the battery system at node i lower limit 
${P}_{B,i}^{\mathrm{ch},max}$  charging power of the battery system at node i upper limit 
${P}_{{L}_{j}}\left(t\right)$  load j at time t 
${P}_{{\mathrm{load}}_{i}}\left(t\right)$  real load at node i at time t 
${P}_{\mathrm{grid}}^{d}\left(t\right)$  amount of power purchased from the transmission system at time t for 
distribution system d  
${P}_{\mathrm{grid}}^{d,min}$  minimum amount of amount of power purchased from the transmission 
system for distribution system d  
${P}_{{G}_{i}}\left(t\right)$  the power injection of generator i at time t 
${P}_{G}^{m}$  vector of lower generation limits 
${P}_{G}^{M}$  vector of upper generation limits 
${P}_{P{V}_{i}}\left(t\right)$  power output of PV at node i at time t 
${P}_{PV,i}^{min}$  power output of PV at node i lower limit 
${P}_{PV,i}^{max}$  power output of PV at node i upper limit 
${q}_{i}^{d}\left(t\right)$  net reactive power at node i at time t in distribution system d 
${Q}_{{\mathrm{load}}_{i}}\left(t\right)$  reactive load at node i at time t 
R  positive definite matrix representing the network 
$\mathcal{T}$  time period of interest 
${V}_{i}\left(t\right)$  voltage level at node i at time t 
${V}_{i}^{min}$  voltage level at node i lower limit 
${V}_{i}^{max}$  voltage level at node i upper limit 
${V}_{\mathrm{ref}}$  voltage reference value 
X  positive definite matrix representing the network 
$\alpha $  the voltage regulation cost 
$\Delta t$  simulations time interval 
${\eta}_{\mathrm{ch},i}$  charging efficiency of battery system at node i 
${\eta}_{\mathrm{dis},i}$  discharging efficiency of battery system at node i 
${\theta}_{k}\left(t\right)$  angle at node k at time t 
${\lambda}_{k}\left(t\right)$  locational marginal price at node k at time t 
Appendix B. Decentralised Scheme Detailed Formulation
Appendix C. Centralised Scheme Detailed Formulation
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Feeder  Variable  Value  Unit 

All  ${P}_{PV}^{min}$  0  MW 
All  ${P}_{PV}^{max}$  30  MW 
All  ${B}_{PV}$  2.584  €/MW 
${F}_{1}$, ${F}_{3}$  ${P}_{B}^{\mathrm{dis},min}$  0  MW 
${F}_{1}$, ${F}_{3}$  ${P}_{B}^{\mathrm{dis},max}$  30  MW 
${F}_{1}$, ${F}_{3}$  ${P}_{B}^{\mathrm{ch},min}$  0  MW 
${F}_{1}$, ${F}_{3}$  ${P}_{B}^{\mathrm{ch},max}$  30  MW 
${F}_{1}$, ${F}_{3}$  ${B}_{B}^{\mathrm{dis},min}$  0.380  €/MW 
${F}_{2}$, ${F}_{4}$  ${P}_{B}^{\mathrm{dis},min}$  0  MW 
${F}_{2}$, ${F}_{4}$  ${P}_{B}^{\mathrm{dis},max}$  15  MW 
${F}_{2}$, ${F}_{4}$  ${P}_{B}^{\mathrm{ch},min}$  0  MW 
${F}_{2}$, ${F}_{4}$  ${P}_{B}^{\mathrm{ch},max}$  15  MW 
${F}_{2}$, ${F}_{4}$  ${B}_{B}^{\mathrm{dis},min}$  0.380  €/MW 
${F}_{1}$, ${F}_{3}$  ${P}_{\mathrm{grid}}^{min}$  –110  MW 
${F}_{2}$, ${F}_{4}$  ${P}_{\mathrm{grid}}^{min}$  –60  MW 
Hour  Node 1  Node 2  Node 3  Node 4  Node 5 

1  12.67  28.15  25.22  17.15  13.46 
2  12.62  28.01  25.10  17.08  13.41 
3  12.62  28.01  25.10  17.08  13.41 
4  12.64  28.08  25.16  17.11  13.44 
5  12.76  28.42  25.45  17.30  13.56 
6  12.93  28.89  25.87  17.55  13.74 
7  13.09  29.36  26.28  17.80  13.92 
8  13.21  29.70  26.58  17.99  14.05 
9  13.23  29.77  26.64  18.02  14.08 
10  13.32  30.04  26.88  18.17  14.18 
11  13.51  30.58  27.35  18.46  14.39 
12  13.53  30.65  27.41  18.49  14.41 
13  13.68  31.05  27.76  18.71  14.57 
14  13.44  30.38  27.17  18.35  14.31 
15  13.39  30.24  27.05  18.28  14.26 
16  13.32  30.04  26.88  18.17  14.18 
17  13.44  30.38  27.17  18.35  14.31 
18  13.51  30.58  27.35  18.46  14.39 
19  13.32  30.04  26.88  18.17  14.18 
20  13.21  29.70  26.58  17.99  14.05 
21  13.09  29.36  26.28  17.80  13.92 
22  12.88  28.75  25.75  17.48  13.69 
23  12.81  28.55  25.57  17.37  13.62 
24  12.71  28.28  25.34  17.22  13.51 
Hour  Node 1  Node 2  Node 3  Node 4  Node 5 

1  12.27  12.28  12.28  12.27  12.27 
2  12.13  12.14  12.14  12.14  12.13 
3  12.13  12.14  12.14  12.14  12.13 
4  12.20  12.21  12.21  12.21  12.20 
5  12.54  12.55  12.55  12.54  12.54 
6  13.01  13.02  13.02  13.01  13.01 
7  12.55  28.14  25.19  17.06  13.35 
8  12.88  12.89  12.89  12.88  12.88 
9  12.90  12.91  12.91  12.90  12.90 
10  12.98  12.99  12.99  12.99  12.98 
11  13.15  13.16  13.16  13.15  13.15 
12  13.17  13.18  13.18  13.17  13.17 
13  11.93  11.94  11.94  11.94  11.93 
14  13.08  13.10  13.10  13.09  13.08 
15  13.04  13.06  13.06  13.05  13.04 
16  12.98  12.99  12.99  12.99  12.98 
17  13.08  13.10  13.10  13.09  13.08 
18  13.15  13.16  13.16  13.15  13.15 
19  12.98  12.99  12.99  12.99  12.98 
20  12.88  12.89  12.89  12.88  12.88 
21  12.55  28.14  25.19  17.06  13.35 
22  12.87  12.89  12.89  12.88  12.87 
23  12.67  12.68  12.68  12.68  12.67 
24  12.40  12.41  12.41  12.41  12.40 
Hour  ${\mathit{P}}_{{\mathit{G}}_{1}}$  ${\mathit{P}}_{{\mathit{G}}_{2}}$  ${\mathit{P}}_{{\mathit{G}}_{3}}$  ${\mathit{P}}_{{\mathit{G}}_{4}}$  ${\mathit{P}}_{{\mathit{G}}_{5}}$ 

1  110  18.53  19.52  0  110 
2  110  15.09  13.36  0  110 
3  110  15.09  13.36  0  110 
4  110  16.81  16.44  0  110 
5  110  25.41  31.84  0  110 
6  110  37.45  53.39  0  110 
7  110  49.5  74.95  0  110 
8  110  58.1  90.35  0  88.4 
9  110  59.82  93.43  0  90.88 
10  110  60  110  2.45  100.81 
11  110  43.78  110  57.07  110 
12  94.58  60.36  110.71  60  110 
13  62.8  0.03  116.72  42.99  110 
14  110  55.25  110  31.2  110 
15  110  60  110  16.85  108.26 
16  110  60  110  2.45  100.81 
17  110  55.25  110  31.2  110 
18  110  43.78  110  57.07  110 
19  110  60  110  2.45  100.81 
20  110  58.1  90.35  0  88.4 
21  110  49.5  74.95  0  110 
22  110  34.01  47.23  0  110 
23  110  28.85  38  0  110 
24  110  21.97  25.68  0  110 
Hour  ${\mathit{P}}_{{\mathit{G}}_{1}}$  ${\mathit{P}}_{{\mathit{G}}_{2}}$  ${\mathit{P}}_{{\mathit{G}}_{3}}$  ${\mathit{P}}_{{\mathit{G}}_{4}}$  ${\mathit{P}}_{{\mathit{G}}_{5}}$ 

1  39.14  0  0  0  110 
2  30.02  0  0  0  110 
3  30.02  0  0  0  110 
4  34.58  0  0  0  110 
5  57.38  0  0  0  110 
6  89.3  0  0  0  110 
7  107.99  6.66  6.58  0  110 
8  82.98  0  0  0  88.4 
9  85.82  0  0  0  90.88 
10  91.19  0  0  0  100.81 
11  101.05  0.88  0  0  110 
12  101.78  1.49  0  0  110 
13  9.58  0  0  0  110 
14  97.9  0  0  0  110 
15  95.22  0  0  0  108.26 
16  91.19  0  0  0  100.81 
17  97.9  0  0  0  110 
18  101.05  0.88  0  0  110 
19  91.19  0  0  0  100.81 
20  82.98  0  0  0  88.4 
21  107.99  6.66  6.58  0  110 
22  80.18  0  0  0  110 
23  66.5  0  0  0  110 
24  48.26  0  0  0  110 
Hour  ${\mathit{P}}_{{\mathit{G}}_{1}}$  ${\mathit{P}}_{{\mathit{G}}_{2}}$  ${\mathit{P}}_{{\mathit{G}}_{3}}$  ${\mathit{P}}_{{\mathit{G}}_{4}}$  ${\mathit{P}}_{{\mathit{G}}_{5}}$ 

1  52.05  0  0  0  110 
2  42.45  0  0  0  110 
3  42.45  0  0  0  110 
4  47.25  0  0  0  110 
5  71.25  0  0  0  110 
6  102.64  2.2  0  0  110 
7  110  10.87  17.58  0  110 
8  0  0  0  0  88.4 
9  0  0  0  0  90.88 
10  0  0  0  0  100.81 
11  10.67  0  0  0  110 
12  13.15  0  0  0  110 
13  28.05  0  0  0  110 
14  3.22  0  0  0  110 
15  0  0  0  0  108.26 
16  0  0  0  0  100.81 
17  3.22  0  0  0  110 
18  10.67  0  0  0  110 
19  0  0  0  0  100.81 
20  0  0  0  0  88.4 
21  110  10.87  17.58  0  110 
22  95.25  0  0  0  110 
23  80.85  0  0  0  110 
24  61.65  0  0  0  110 
Hour  Node 1  Node 2  Node 3  Node 4  Node 5 

1  14.52  14.53  14.53  14.53  14.52 
2  14.42  14.43  14.43  14.43  14.42 
3  14.42  14.43  14.43  14.43  14.42 
4  14.47  14.48  14.48  14.48  14.47 
5  14.71  14.72  14.72  14.72  14.71 
6  15.03  15.04  15.04  15.03  15.03 
7  15.13  27.74  25.35  18.78  15.78 
8  11.24  11.24  11.24  11.24  11.24 
9  11.27  11.27  11.27  11.27  11.27 
10  11.41  11.41  11.41  11.41  11.41 
11  14.11  14.11  14.11  14.11  14.11 
12  14.13  14.13  14.14  14.13  14.13 
13  14.28  14.28  14.29  14.28  14.28 
14  14.03  14.03  14.04  14.04  14.03 
15  11.52  11.52  11.52  11.52  11.52 
16  11.41  11.41  11.41  11.41  11.41 
17  14.03  14.03  14.04  14.04  14.03 
18  14.11  14.11  14.11  14.11  14.11 
19  11.41  11.41  11.41  11.41  11.41 
20  11.24  11.24  11.24  11.24  11.24 
21  15.13  27.74  25.35  18.78  15.78 
22  14.95  14.97  14.97  14.96  14.95 
23  14.81  14.82  14.82  14.81  14.81 
24  14.62  14.63  14.63  14.62  14.62 
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Najibi, F.; Apostolopoulou, D.; Alonso, E. TSODSO Coordination Schemes to Facilitate Distributed Resources Integration. Sustainability 2021, 13, 7832. https://doi.org/10.3390/su13147832
Najibi F, Apostolopoulou D, Alonso E. TSODSO Coordination Schemes to Facilitate Distributed Resources Integration. Sustainability. 2021; 13(14):7832. https://doi.org/10.3390/su13147832
Chicago/Turabian StyleNajibi, Fatemeh, Dimitra Apostolopoulou, and Eduardo Alonso. 2021. "TSODSO Coordination Schemes to Facilitate Distributed Resources Integration" Sustainability 13, no. 14: 7832. https://doi.org/10.3390/su13147832