# Long-Term Expansion Planning of the Transmission Network in India under Multi-Dimensional Uncertainty

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions. This sector is being fundamentally transformed with steadily increasing electrical demand across other sectors, including agriculture, transport, industry, commercial and residential. Electricity is becoming more and more accessible to the wider population. For instance, around 700 million people in India gained access to electricity between 2000 and 2018 and the government has recently stated that 100% of its villages have been connected to the electricity grid [4]. In addition, the government has announced investment plans aiming to significantly reduce the frequency of power outages [5]. In this context, it is expected that the country’s continued economic and population growth, as well as its fundamental electrification, will lead to higher levels of electricity demand in the near future [6].

- Quantification of the Option Value of investing in energy storage across India, covering the period 2020–2060.
- Presentation of key investment insights and notable conclusions for India’s electricity system covering the period 2020–2060.
- Application of an advanced decomposition approach to overcome the increased complexity related to the application of stochastic optimization under multi-dimensional uncertainty, to the India context.

## 2. Energy Storage and Option Value in the India Context

## 3. Planning Model Formulation and Solution Procedure

#### 3.1. Advanced Decompostion of the Large-Scale Transmission Planning Problem

#### 3.2. Mathematical Formulation

#### 3.3. Solution Algorithm and Convergence

## 4. Case Study

#### 4.1. Description

#### 4.2. Results

#### 4.3. Discussion

#### 4.3.1. Investment Flexibility

#### 4.3.2. Future Generation Mix

#### 4.3.3. Stochastic versus Deterministic Planning

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Sets and indices | |

${\mathsf{\Omega}}_{B}$ | Set of all demand blocks, indexed b |

${\mathsf{\Omega}}_{G}$ | Set of all generation units, indexed g |

${\mathsf{\Omega}}_{G}^{{H}_{rr}}$ | Set of all hydro run of river generation units |

${\mathsf{\Omega}}_{G}^{{H}_{res}}$ | Set of all hydro reservoir generation units |

${\mathsf{\Omega}}_{H}$ | Set of all storage units, indexed h |

${\mathsf{\Omega}}_{H}^{T}$ | Set of candidate storage technologies, indexed h |

${\mathsf{\Omega}}_{L}$ | Set of all transmission lines, indexed l |

${\mathsf{\Omega}}_{L}^{AC}$ | Set of all AC transmission lines |

${\mathsf{\Omega}}_{M}$ | Set of all scenario-tree nodes, indexed m |

${\mathsf{\Omega}}_{E}$ | Set of all stages, indexed by e |

${\mathsf{\Omega}}_{N}$ | Set of all system buses, indexed n |

${\mathsf{\Omega}}_{T}^{b}$ | Set of all time periods in demand block b, indexed t |

${\mathsf{\Omega}}_{W}$ | Set of all conventional expansion options, indexed ω |

${N}_{E}$ | Number years in the planning horizon |

${\mathcal{N}}^{+}\left(m\right)$ | Set of all children nodes of scenario-tree node m |

$p\left(m\right)$ | Parent node of scenario-tree node m |

$\u03f5\left(m\right)$ | Stage to which scenario-tree node m belongs |

${y}_{e}$ | First year of stage e |

Parameters | |

${D}_{m,t,n}^{b}$ | Demand at bus n for 0 operating point (m,t) in demand block b |

${\underset{\_}{E}}_{t,g}^{{H}_{q}}$ | Minimum energy capacity storage equivalent of hydro generation unit ^{g} at time t, where q ∈ {rr,res} for run of river and reservoir units, respectively |

${\overline{E}}_{t,g}^{{H}_{q}}$ | Maximum energy capacity storage equivalent of hydro generation unit g at time t, where q ∈ {rr,res} for run of river and reservoir units, respectively |

${F}_{l}^{0}$ | Initial transmission capacity of line l |

${\mathcal{F}}_{l,\omega}^{max}$ | Maximum capacity upgrade of option $\omega $ for line $l$ |

${H}_{n,h}$ | Bus-to-storage incidence matrix |

${I}_{n,g}$ | Bus-to-generator incidence matrix |

${J}_{n,l}$ | Bus-to-line incidence matrix |

${\overline{P}}_{m,t,g}$ | Maximum output of generation unit $g$ for operating point (m,t) |

$R{D}_{g}$ | Ramp-down capability (MW/h) for generation technology g |

$R{U}_{g}$ | Ramp-up capability (MW/h) for generation technology g |

${P}_{tg}^{{H}_{d,in}}$ | Hourly water inflow (capacity) for hydro d ∈ {rr,res}, generation unit g at time t |

${\overline{P}}_{h}^{c}$ | Maximum charge rate of storage device h (MW) |

${\overline{P}}_{h}^{d}$ | Maximum discharge rate of storage device h (MW) |

${\widehat{S}}_{h}$ | Maximum storage investment size of technology h in one stage (MW) |

${S}_{h}^{r}$ | Rated discharge duration (energy over power capacity) of a new storage unit (h) |

${W}_{b}$ | Weighting of demand block b |

${X}_{l}$ | Reactance of transmission line l |

${c}_{g}$ | Generation cost of unit g (GBP/MWh) |

${c}_{VoLL}$ | Value of lost load (GBP/MWh) |

${r}_{\u03f5\left(m\right)}^{L}$ | Cumulative discount factor for line investments in epoch ϵ(m) |

${r}_{h,\u03f5\left(m\right)}^{S}$ | Cumulative discount factor for storage investments in technology h in epoch ϵ(m) |

${r}_{\u03f5\left(m\right)}^{O}$ | Cumulative discount factor for system operation in epoch ϵ(m) |

$r$ | Interest rate |

${u}_{l}$ | Start bus of line l |

${v}_{l}$ | End bus of line l |

${\eta}_{h}^{c}$ | Charging efficiency of storage technology h |

${\eta}_{h}^{d}$ | Discharging efficiency of storage technology h |

${\gamma}_{l,\omega}$ | Build time for line l and expansion option ω |

${\gamma}_{h}$ | Build time of candidate storage technology $h\in {\Omega}_{H}^{T}$ |

${\delta}_{h}$ | Lifespan of candidate storage technology h |

${\kappa}_{l,\omega}^{L,f}$ | Annual fixed investment cost of line l and option ω (GBP/yr) |

${\kappa}_{l,\omega}^{L,v}$ | Annual variable investment cost of line l and option ω (GBP/MW yr) |

${\kappa}_{m,h}^{S,v}$ | Annual variable investment cost of storage h in node m (GBP/MW yr) |

${\pi}_{m}$ | State probability of scenario-tree node m |

$\tau $ | Time duration of a demand period t |

Decision variables | |

$\mathbf{x}$ | Note that the vector x represents all decision variables involved in the optimization problem. |

${E}_{m,t,g}^{{H}_{q}}$ | Equivalent amount of stored energy of hydro generation unit $g$ at operating point (m,t), where q ∈ {rr,res} for run of river and reservoir units, respectively |

${F}_{m,l,\omega}^{I}$ | Transmission line capacity upgrade for line l using option ω at node m |

${\tilde{F}}_{m,l}^{I}$ | Aggregate transmission line capacity upgrades of line $l$ at node $m$ |

${P}_{m,t,g}$ | Output of generation unit g at operating point (m,t) |

${P}_{m,t,h}^{c}$ | Charging power of storage device h at operating point (m,t) |

${P}_{m,t,h}^{d}$ | Discharging power of storage device h at operating point (m,t) |

${P}_{m,t,g}^{{H}_{q}}$ | Output of hydro generation unit g at operating point (m,t), where q ∈ {rr,res} for run of river and reservoir units, respectively |

${P}_{m,t,g}^{{H}_{q,shed}}$ | Water shed equivalent of hydro generation unit $g$ for $q\in \left\{rr,res\right\}$ at operating point (m,t) |

${S}_{m,h}^{I}$ | Decision variable modelling investment in storage asset h at node m |

${\tilde{S}}_{m,h}^{I}$ | Aggregate storage capacity investment for asset h at node m |

${d}_{m,t,n}$ | Demand curtailment at bus n and operating point (m,t) |

${f}_{m,t,l}$ | Power flow on line l at operating point (m,t) |

${x}_{m}^{I}$ | Decision vector coupling investments in node $m$ with those in its parent node $p\left(m\right)$, where $I\in \left\{\beta ,c,F,S,{S}^{R}\right\}$ for line investment decisions, transmission capacity investment, aggregate transmission capacity investment, storage investment decisions, and storage decommissioning decisions, respectively |

${y}_{m}$ | Linear combination of ${x}_{m}^{I}$, where $I\in \left\{\beta ,c,F,S,{S}^{R}\right\}$ for line investment decisions, transmission capacity investment, aggregate transmission capacity investment, storage investment decisions, and storage decommissioning decisions, respectively |

${\beta}_{m,l,\omega}^{I}$ | Binary decision variable modelling investment in transmission capacity in line $l$ using option ω at node m |

${\theta}_{m,t,n}$ | Voltage angle at bus n at operating point (m,t) |

${\sigma}_{m,t,h}$ | State of charge of storage device h at operating point (m,t) |

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**Figure 2.**Diagram of the electricity grid of India, which consists of 5 regions and 30 states (shown as blue circles along with their abbreviations).

**Figure 3.**Diagram of the electricity grid of India, with the 62 transmission lines appearing where six of them are HVDC (shown in blue).

**Figure 4.**Scenario tree structure, consisting of 11 scenario-tree nodes, illustrating the uncertainty around three quantities in the following order; namely around battery storage investment cost (in £k/ kW), around the installed generation capacity of solar PV across India (GW) and around the installed generation capacity of wind units across India (GW). Note that epoch1 (1 January 2020–31 December 2029) covers node 1, and epoch2 (1 January 2030–31 December 2039) covers nodes 2–3, while epoch3 (1 January 2040–31 December 2049) covers nodes 4–7 and epoch4 (1 January 2050–31 December 2059) covers nodes 8–11. Very high values for wind and solar were applied to the period 2050–2060 (last epoch) to also account for future increases beyond the problem horizon. The values over the straight lines connecting nodes indicate probabilities of transition (e.g., it is 60% likely to go from node 3 to node 6), while the probability from nodes of the third epoch (nodes 4–7) to those of the last epoch (nodes 8–11) is 100% (i.e., deterministic transition).

**Figure 5.**Peak demand (GW) across India for each of the four epochs (2020–2029, 2030–2039, 2040–2049, 2050–2059).

**Figure 6.**Optimal investment strategy for the case with only conventional investments. The notation (i-j) represents the upgrade of the capacity of the transmission line connected buses (i.e., India states) i and j. Note that the scenario tree depicts investment decisions, i.e., the capacity upgrades will become operational one epoch afterwards (this is why there are no investment decisions taken in the last epoch as there is no epoch5).

**Figure 7.**Optimal investment strategy for the case with conventional and energy storage investments. The notation (z) represents energy storage investment in bus (i.e., India state) z.

**Figure 8.**Aggregate investments in the transmission system of India as of 2050 (scenario-tree node 8) with conventional reinforcements only. Dashed lines represent existing transmission lines and full lines represent transmission lines that are reinforced.

**Figure 9.**Aggregate investments in the transmission system of India as of 2050 (scenario-tree node 8) with the possibility to invest in conventional reinforcements and in energy storage. Dashed lines represent existing transmission lines, full lines represent transmission lines that are reinforced, and squares represent energy storage investment in the corresponding bus.

**Figure 10.**Generation mix in the year 2050 according to scenario 1 (i.e., scenario-tree node 8), with the availability of storage, in four typical days. Figure (

**a**) reports a typical day within the period January–March, (

**b**) a typical day within April–June, (

**c**) a typical day within July–September, and (

**d**) a typical day within October–December.

**Figure 11.**Generation mix in the year 2050 according to scenario 4 (specifically, scenario-tree node 11), with the availability of storage, in four typical days. Figure (

**a**) reports a typical day within the period January–March, (

**b**) a typical day within April–June, (

**c**) a typical day within July–September, and (

**d**) a typical day within October–December.

**Figure 12.**Generation mix in the year 2020 (specifically, scenario-tree node 1), with the availability of storage, in four typical days. Figure (

**a**) reports a typical day within the period January–March, (

**b**) a typical day within April–June, (

**c**) a typical day within July–September, and (

**d**) a typical day within October–December.

**Figure 13.**Generation mix in the year 2050 (specifically, scenario-tree node 8), without the availability of storage, in four typical days. Figure (

**a**) reports a typical day within the period January–March, (

**b**) a typical day within April–June, (

**c**) a typical day within July–September, and (

**d**) a typical day within October–December.

**Figure 14.**Generation mix in the year 2050 (specifically, scenario-tree node 11), without the availability of storage, in four typical days. Figure (

**a**) reports a typical day within the period January–March, (

**b**) a typical day within April–June, (

**c**) a typical day within July–September, and (

**d**) a typical day within October–December.

**Figure 15.**Generation mix in region ER according to scenario node 8, with the availability of storage, in four typical days. Figure (

**a**) reports a typical day within the period January–March, (

**b**) a typical day within April–June, (

**c**) a typical day within July–September, and (

**d**) a typical day within October–December.

**Figure 16.**Generation mix in region NER according to scenario node 8 with the availability of storage, in four typical days. Figure (

**a**) reports a typical day within the period January–March, (

**b**) a typical day within April–June, (

**c**) a typical day within July–September, and (

**d**) a typical day within October–December.

**Figure 17.**Generation mix in region NR according to scenario node 8 with the availability of storage, in four typical days. Figure (

**a**) reports a typical day within the period January–March, (

**b**) a typical day within April–June, (

**c**) a typical day within July–September, and (

**d**) a typical day within October–December.

**Figure 18.**Generation mix in region SR according to scenario node 8 with the availability of storage, in four typical days. Figure (

**a**) reports a typical day within the period January–March, (

**b**) a typical day within April–June, (

**c**) a typical day within July–September, and (

**d**) a typical day within October–December.

**Figure 19.**Generation mix in region WR according to scenario node 8 with the availability of storage, in four typical days. Figure (

**a**) reports a typical day within the period January–March, (

**b**) a typical day within April–June, (

**c**) a typical day within July–September, and (

**d**) a typical day within October–December.

**Figure 20.**Optimal accumulated line investment cost per scenario for the stochastic studies with and without storage.

**Figure 21.**Optimal operation cost in the last epoch per scenario for the stochastic studies with and without storage.

**Figure 22.**Difference between the optimal accumulated line investment costs for the stochastic studies with and without storage, for every scenario-tree node.

**Figure 23.**Difference between the optimal operation costs for the stochastic studies with and without storage, per scenario-tree node.

**Figure 24.**Optimal investment cost in line reinforcement for the deterministic and stochastic formulations for each epoch and scenario.

Conventional Reinforcement Only | Conventional Reinforcement and Storage Investment | |
---|---|---|

Expected investment cost (GBP) | 12,097,947,208 | 26,732,242,295 |

Conventional reinforcement (GBP) | 12,097,947,208 | 10,123,219,872.03 |

Energy storage (GBP) | / | 16,609,022,423 |

Expected system operation cost (GBP) | 507,853,578,872 | 480,318,047,587 |

Expected total system cost (GBP) | 519,951,526,080 | 507,050,289,882 |

Option Value (GBP) | / | 12,901,236,198 |

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## Share and Cite

**MDPI and ACS Style**

Giannelos, S.; Jain, A.; Borozan, S.; Falugi, P.; Moreira, A.; Bhakar, R.; Mathur, J.; Strbac, G.
Long-Term Expansion Planning of the Transmission Network in India under Multi-Dimensional Uncertainty. *Energies* **2021**, *14*, 7813.
https://doi.org/10.3390/en14227813

**AMA Style**

Giannelos S, Jain A, Borozan S, Falugi P, Moreira A, Bhakar R, Mathur J, Strbac G.
Long-Term Expansion Planning of the Transmission Network in India under Multi-Dimensional Uncertainty. *Energies*. 2021; 14(22):7813.
https://doi.org/10.3390/en14227813

**Chicago/Turabian Style**

Giannelos, Spyros, Anjali Jain, Stefan Borozan, Paola Falugi, Alexandre Moreira, Rohit Bhakar, Jyotirmay Mathur, and Goran Strbac.
2021. "Long-Term Expansion Planning of the Transmission Network in India under Multi-Dimensional Uncertainty" *Energies* 14, no. 22: 7813.
https://doi.org/10.3390/en14227813