# The Human Factor in Transmission Network Expansion Planning: The Grid That a Sustainable Energy System Needs

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## Abstract

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## 1. Introduction

**Technical:**What human decisions have been made to simplify the planning problem? In particular, what physical phenomena have been approximated? What decisions have been simplified?**Regulatory:**What current and new regulatory elements to consider in the operation of power systems (new legislation associated with the energy transition) may have a relevant impact on the investment plan?**Behavioural:**To what extent are there behavioural phenomena that can have an impact on operation? In particular, is there a consideration of risk that should be incorporated to the analyses?

## 2. Models and Methods Used for Representing and Solving the TEP Problem: A Simple Formulation

#### 2.1. Models

**Time representation:**- -
- Static: It focuses on one single expansion horizon.
- -
- Dynamic: several time horizons are considered and solved simultaneously, with inter-temporal constraints linking the horizons.
- -
- Sequentially static: several time horizons are considered, but instead of being solved simultaneously, they are solved sequentially.

**Power flow formulation:**Several power flow formulations can be used, with different implications.- -
- Transportation problem: A very crude description of the use of the network, which does not consider the physics of power flows. This is the one that is considered in most existing models [5].
- -
- DC Optimal Power Flow (DC OPF): An approximated linear form of the AC power flow.
- -
- AC Optimal Power Flow (AC OPF): This would be the most accurate description of network physics, but its non-linearity means that it is impractical to include it in optimization models. When it is included indeed, it is usually approximated as Linear Problem (LP) relaxed into Second Order Conic (SOC), QC (Quadratic constraints), and SDP (Stochastic Dynamic Programming) to solve it. Besides, some meta-heuristic methods can be used to solve a non-linear AC OPF formulation. However, they typically do not work well in real-size case studies.

**Decision dimension:**The scope of the decisions taken into account for the problem can cover:- -
- Transmission lines
- -
- Other technologies such as FACTS (Flexible AC Transmission Devices) and Phase-Shifting Transformers.

**Uncertainty dimension:**Several researchers have widely studied this dimension during the last decades because of its impact on the TEP problem. In the beginning, the works focused on deterministic approximations to solve the TEP problem due to the lack of computation resources. This approach has been changing until now, motivated by the increasing renewables shares and their uncertain nature. This uncertainty leads to fluctuating reserve capacities, and varying line power flows across the network; therefore, the TEP problem should include it. Some surveys, like [1,2], make references to this dimension and its importance. Note that the uncertainty approaches are the same as in other power system optimization problems, as presented, for instance, in [6].**Reliability:**Based on different international standards [7,8], a power system must operate in a such way that the outage of a single component does not interrupt supplying demand. Analyzing outage events in TEP models is a common practice called the N-1 criterion. Multiple studies have included this criterion in their mathematical formulations [9,10,11,12]. The application of N-1 analysis results in a list of congestions in the network, requiring a possible additional transmission investment. Modeling the N-1 criterion has an important impact on the size of the problem since restrictions related to the first and second Kirchhoff Law must be formulated for each contingency. This fact highlights the challenge of development methodologies to solve the problem with an acceptable computational burden.

#### 2.1.1. Notation

$\mathcal{B}$ | Set of buses. |

$\mathcal{C}$ | Set of circuits. |

$\mathcal{G}$ | Set of generating units. |

$\mathcal{L}$ | Set of branches, where $\mathcal{L}\subseteq \mathcal{B}\times \mathcal{B}$. |

${\mathcal{L}}^{e},{\mathcal{L}}^{c}$ | Set of existing and candidate lines. |

${\mathcal{L}}^{c1}$ | Set of alternative candidate lines |

$\mathcal{N}$ | Set of load levels. |

$\mathcal{W}$ | Set of weather scenarios. |

$\mathcal{SG}$ | Set of supergrid approach. |

i | Bus. |

$ijc$ | Line. |

c | Circuit. |

g | Generator (thermal, RES, or ESS). |

n | Load level. |

$\nu $ | Time-step. Duration of each load level (e.g., 2 h). |

i/k | Index for discharging/charging sample data. |

t | Index for time step. |

w | Index for weather scenario. |

$sg$ | Index for supergrid approach. |

${C}^{te},{C}^{op}$ | Network investment and operating cost. |

${C}^{ess}$ | Storage investment cost. |

${S}_{B}$ | Base power. $\left[\mathrm{MW}\right]$ |

${D}_{n}$ | Duration of each load level. $\left[\mathrm{h}\right]$ |

${C}^{ens}$ | Energy not served cost. [€/$\mathrm{MWh}]$ |

${P}_{i}^{d}$ | Active power demand. $\left[\mathrm{MW}\right]$ |

${\delta}^{d}$ | Price elasticity of demand, parameter only used in the additional equations. $\left[\mathrm{MW}/\mathrm{EUR}\right]$ |

${\overline{P}}_{g},{\underline{P}}_{g}$ | Maximum and minimum active power generation. $\left[\mathrm{MW}\right]$ |

$C{V}_{g}$ | Variable cost of a generator. Variable cost includes fuel, O&M and emission cost. [€/h, €/MWh] |

${C}_{ijc}^{line},{C}_{ijc}^{f}$ | Annualized fixed cost of a candidate line or FACTS device respectively. [€] |

${X}_{ijc}$ | Reactance. $\left[\mathrm{p}.\mathrm{u}.\right]$ |

${B}_{ijc}$ | Susceptance. (inverse value of the reactance). $\left[\mathrm{p}.\mathrm{u}.\right]$ |

${\overline{S}}_{ijc}$ | Net transfer capacity (total transfer capacity multiplied by a security coefficient) of a line. $\left[\mathrm{MW}\right]$ |

${\overline{S}}_{ijc}^{{}^{\prime}}$ | Maximum flow used in the Kirchhoff’s 2nd law constraint (e.g., disjunctive constraint for the candidate line). $\left[\mathrm{MW}\right]$ |

${l}_{ni}^{shed}$ | Load shedding. $[\%]$ |

${p}_{ng}$ | Active power generation. $\left[\mathrm{MW}\right]$ |

${\theta}_{ni}$ | Voltage angle. $\left[\mathrm{rad}\right]$ |

${f}_{nijc}^{P}$ | Active power flow. $\left[\mathrm{MW}\right]$ |

${\lambda}_{ni}$ | Nodal prices. $\left[\mathrm{EUR}/\mathrm{MWh}\right]$ |

$ic{t}_{ijc}$ | Candidate line installed or not. $\{0,1\}$ |

#### 2.1.2. A Standard Mathematical Formulation of the TEP Problem

**Objective function:**Transmission expansion planning aims to obtain a technically feasible expansion plan at a minimum cost for the end-users (those who ultimately pay for the assets of the energy system and their operation through the electricity bill). In this way, the objective function includes all possible costs in the mathematical model: investment, operating system that comprises the generation, and reliability. The decision-maker should assign the importance of each of these components. Equation (1) represents the minimization of total (investment and operating) cost for the scope of the model.

**Constraints:**

#### 2.2. Solution Methods

## 3. The Human behind the Technical

#### 3.1. New Technologies Considered

#### 3.1.1. Smart Elements

#### 3.1.2. Energy Storage

- Lithium ion reserves, by 2040, could be in a critical state given the number of batteries that are planned to be installed worldwide [46]. Although the trend in ESS costs is downwards, it is possible that in the future, costs will increase given the limited reserves. Thus, the uncertainty about the evolution of ESS costs should be a parameter bear in mind by TEP models and it will be deeply influenced by subjective assumptions. As an example of this growing concern, the US government recently commissioned a study on the risk that the state of material reserves may represent [47].
- Recent studies call for a better assessment of the cost of batteries to consider their long-term degradation [48].
- It is expected to be an important support for the integration of renewables. However, ESS’ ownership and operation may change their utility. To this end, TEP models could be useful to explore this multi-disciplinary issue [49].

**Additional Notation:**

${C}^{ess}$ | Storage investment cost. |

$C{V}_{i}^{ess}$ | Variable cost of a generator. [€/$\mathrm{MWh}]$ |

${E}_{i}^{ess},{P}_{i}^{ess}$ | Maximum energy and maximum power of an energy storage unit. $[\mathrm{MWh},\mathrm{MW}]$ |

${\eta}_{ni}$ | Efficiency of an energy storage unit. $\left[\mathrm{pu}\right]$ |

${p}_{ni}^{d-ess}$ | Discharging power of the storage unit. $\left[\mathrm{MW}\right]$ |

${p}_{ni}^{c-ess}$ | Charging power of the storage unit. $\left[\mathrm{MW}\right]$ |

$v{E}_{ni}^{ess}$ | Stored energy of a unit of energy in a period n. $\left[\mathrm{MWh}\right]$ |

$iess{e}_{i},iess{p}_{i}$ | Candidate storage unit installed or not (energy and power, respectively). $\{0,1\}$ |

**Objective function:**

**Constraints:**

#### 3.1.3. Hydrogen

**Energy storage:**Authors highlight that hydrogen has high energy storage capacity, a long storage period, and flexibility.**Power-to-gas:**Hydrogen can be converted into methane and injected into the natural gas grid or stored, providing a balancing service to the energy market.**Co- and tri-generation:**Fuel cells can be used as prime movers for combined heat and power (CHP) generation or combined cold and power (CCP) generation, known as co-generation, or to be used for combined cold heat and power (CCHP) generation, known as tri-generation.**Transportation:**Authors highlight the expected growth of hydrogen-based transportation (around 36% of global vehicle sales in 2050).

- Subsets:
- Set of generation units based on hydrogen: ${G}^{H}\subseteq \mathcal{G}$
- Set of nodes of the hydrogen network: ${B}^{H}\subseteq \mathcal{B}$
- Set of pipeline of the hydrogen network: ${L}^{H}\subseteq \mathcal{L}$

- Indexes:
- Index of generation units: $gh\in {G}^{H}$
- Index of nodes: $bh\in {B}^{H}$
- Index of pipelines: $ijc\in {L}^{H}$

- Parameter:
- Pipeline capacity: ${F}_{nijc}^{h}$
- Storage Capacity: ${S}_{gh}^{h}$
- Efficiency power-to-hydrogen: ${\eta}_{nbh}^{ph}$
- Efficiency hydrogen-to-power: ${\eta}_{nbh}^{hp}$
- Hydrogen from another sources: ${H}_{nbh}^{s}$
- Hydrogen to another demand: ${H}_{nbh}^{d}$
- Maximum hydrogen charge ${H}_{ngh}^{c}$

- Variables:
- hydrogen shedding ${l}_{nbh}^{h}$
- hydrogen flow ${f}_{nijc}^{h}$
- hydrogen stored ${i}_{ngh}^{h}$
- hydrogen charged ${h}_{ngh}^{c}$
- hydrogen spillage ${h}_{ngh}^{s}$
- Electrolyzer demand: ${d}_{nbh}^{h}$

- Constraints:$$\begin{array}{cccc}& \sum _{g\in {\mathcal{G}}_{i}}\left[{p}_{ng}\right]-{P}_{ni}^{d}-{d}_{nbh|bh=i}^{h}-{l}_{ni}^{shed}-\sum _{ijc\in \mathcal{L}}\left[{f}_{nijc}^{P}\right]+\sum _{jic\in \mathcal{L}}\left[{f}_{njic}^{P}\right]=0\hfill & \hfill \hspace{1em}\hspace{1em}:{\lambda}_{ni};\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\forall ni& \hfill \end{array}$$$$\begin{array}{cc}\hfill {d}_{nbh}^{h}{\eta}_{nbh}^{ph}+{H}_{nbh}^{s}& -\sum _{gh\in {G}_{i|bh=i}^{H}}\left[{p}_{ngh}/{\eta}_{ngh}^{hp}\right]-{H}_{nbh}^{d}-{l}_{nbh}^{h}\hfill \\ & -\sum _{bhjc\in {L}^{H}}\left[{f}_{nbhjc}^{h}\right]+\sum _{jbhc\in {L}^{H}}\left[{f}_{njbhc}^{h}\right]=0,\phantom{\rule{1.em}{0ex}}:{\lambda}_{nbh}^{\prime};\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\forall nbh\hfill \end{array}$$$$\begin{array}{cccc}& {i}_{n-1,gh}^{h}-{p}_{ngh}/{\eta}_{ngh}^{hp}+{h}_{ngh}^{c}={i}_{ngh}^{h}+{h}_{ngh}^{s}\hfill & \hfill \hspace{1em}\hspace{1em}:{\mu}_{nbh}^{1};\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\forall nbh& \hfill \end{array}$$$$\begin{array}{cccc}& -{F}_{nijc}^{h}\le {f}_{nijc}^{h}\le {F}_{nijc}^{h}\hfill & \hfill \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}:{\mu}_{nijc}^{2};\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\forall nijc|ijc\in {L}^{H}& \hfill \end{array}$$$$\begin{array}{cccc}& 0\le {l}_{nbh}^{h}\le \sum _{gh\in {G}_{i|bh=i}^{H}}\left[{p}_{ngh}/{\eta}_{ngh}^{hp}\right]+{H}_{nbh}^{d}\hfill & \hfill \hspace{1em}\hspace{1em}:{\mu}_{nijc}^{3};\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\forall nijc|ijc\in {L}^{H}& \hfill \end{array}$$$$\begin{array}{cccc}& 0\le {i}_{ngh}^{h}\le {S}_{gh}^{h}\hfill & \hfill \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}:{\mu}_{ngh}^{4};\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\forall ngh& \hfill \end{array}$$$$\begin{array}{cccc}& 0\le {h}_{ngh}^{c}\le {H}_{gh}^{c}\hfill & \hfill \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}:{\mu}_{ngh}^{5};\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\forall ngh& \hfill \end{array}$$$$\begin{array}{cccc}& 0\le {h}_{ngh}^{s}\hfill & \hfill \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}:{\mu}_{ngh}^{6};\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\forall ngh& \hfill \end{array}$$

#### 3.2. New Grid Framework: Smart-Grids/Distributed Generation

- Two-stage approach: (a) First stage: solving the TSO-DSO coordination with microgrids, and then (b) Second stage: modifying the profile of the electricity demand to be used as a parameter to solve the TEP problem. This option could be suitable for large-scale problems, but it is probably not to get an optimal solution since it depends of iterations and couldn’t have a finite convergence.
- Considering exchange variables on the power transformers at the border between the transmission and distribution network. It is suitable for medium-scale problems and consider the local flexibility within the TEP [56], but it is complex to apply for solving large-scale problems.
- Considering a tri-level [53], it is a suitable way to consider the TSO-DSO coordination within the TEP problem; however, it is hard to be applied in large-scale problems, even for medium-scale due to the computational burden.

#### 3.3. Critical Events

## 4. The Human Factor at the Institutional Level

#### 4.1. Regulation and Markets

**Generation companies (GENCO):**GENCOs own one or more generating units. GENCOs can bid the generating unit output into the competitive market.**Transmission companies (TRANSCO):**TRANSCOs move power in large quantities from where this is produced to where it is consumed. The TRANSCO owns and maintains the transmission lines under the monopoly in some deregulated industries but does not operate them; in most countries, it is usual that an Independent System Operator (ISO) drives the operation of the electric network. The TRANSCO is paid for the use of its lines. The operation of the transmission system is not a competitive market.**System Operator (SO):**The SO is an entity responsible for ensuring the reliability of the power system. The SO is an independent authority in some countries, and it does not participate in the electricity market trades and does not own electric infrastructure. SO is generally called Independent System Operator (ISO) in this case. In other ones, TRANSCOs are also system operators, and they are usually called Transmission System Operators (TSO). They have a regulatory framework to carry out the operation reliably and economically.

#### 4.2. Environmental Protection at the Institutional Level

## 5. The Human Factor at the Individual Level: Attitudes and Behaviour

**Consumers:**For them, the desired transmission plan is the plan that reduces transmission constraints between demand and generation and provides the cheapest energy price. Network charges are also important for customers, and they prefer low network charges. They are also concerned with the reliability of the network.**Prosumers:**From a prosumer’s viewpoint, the desired transmission plan is the plan that reduces transmission constraints and allows bidirectional power flows to switch between its consumer and generator behaviors. They are also interested in seeking a plan with a minimum network charge.**Generators:**They are interested in removing the transmission constraints for dispatching generators and provides a competitive environment. Reliability is also important for power producers to sell their power without interruptions.**System operator:**It seeks an investment plan that provides the most flexibility in the system operating, increasing network reliability, avoiding congestion, and reducing energy losses on the transmission.**Network owners:**their objective is to maximize their revenue. In most regulatory frameworks, this implies increasing their assets under management as much as possible, hence favouring the most expensive transmission expansion plans.**Regulators:**the desired plan for them is the plan which encourages competition, provides equity for all parties seeking network access, whilst the network reliability is maximized, minimizing operation cost and environmental impact.

#### 5.1. Austerity and Waste Avoidance vs. the Need to Display Social Status By Consumption

#### 5.2. Inter-Generational Dependence

#### 5.3. Confidence Given to Devices of the Market vs. the Need for Regulation and Institutions

#### 5.4. Consideration of the Individual vs. the Community vs. the National or Supranational

- Include social and public acceptance constraints in the selection of candidate infrastructure. The results of this process are one of the inputs of a TEP model; therefore, the set of candidate inversions will change:$$\begin{array}{c}\hfill {\mathcal{L}}^{c}\to {\mathcal{L}}^{c1}\end{array}$$
- Include acceptance criteria for every candidate through an additional charge depending on preliminary social studies. This fact affects the benefits of a project and, therefore, produces different inversion plans; in this case, we can change the network investment function as follows:$$\begin{array}{c}\hfill {C}^{te}=\sum _{ijc\in {\mathcal{L}}^{c}}\left[\left({C}_{ijc}^{line}+{C}_{ijc}^{charge}\right)ic{t}_{ijc}\right]\end{array}$$
- Include acceptance criteria for every candidate through additional constraints. This way implies modeling other systems, for instance, environmental systems; a way to model this kind of constraint is by designing a measure for different geographical paths for every candidate inversion. In this case, we need to model the geographical system, and we must also carry out additional studies to establish referenced values of the measure. A way to model this concept is as follows:$$\mathcal{M}\left(ic{t}_{ijcxy}\right)\le {\mathcal{M}}_{xy}^{ref}$$$$\bigcup _{xy}ic{t}_{ijcxy}=ic{t}_{ijc}$$
- Finally, suboptimal inversion plans can be proposed. The main feature of these alternative plans is to avoid candidates with low social acceptance. It would be desirable that their objective functional value will not be significantly high in comparison with a reference plan (a plan without social acceptance constraints).

#### 5.5. The Importance of Independence/Autonomy Regarding Energy and Other Strategic Resources

#### 5.6. Perceptions of Social Risk and Responsibility

## 6. Conclusions

**The human factor behind the technical**

**The human factor at the institutional level**

**The human factor at the individual level**

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**MDPI and ACS Style**

Lumbreras, S.; Gómez, J.D.; Alvarez, E.F.; Huclin, S.
The Human Factor in Transmission Network Expansion Planning: The Grid That a Sustainable Energy System Needs. *Sustainability* **2022**, *14*, 6746.
https://doi.org/10.3390/su14116746

**AMA Style**

Lumbreras S, Gómez JD, Alvarez EF, Huclin S.
The Human Factor in Transmission Network Expansion Planning: The Grid That a Sustainable Energy System Needs. *Sustainability*. 2022; 14(11):6746.
https://doi.org/10.3390/su14116746

**Chicago/Turabian Style**

Lumbreras, Sara, Jesús David Gómez, Erik Francisco Alvarez, and Sebastien Huclin.
2022. "The Human Factor in Transmission Network Expansion Planning: The Grid That a Sustainable Energy System Needs" *Sustainability* 14, no. 11: 6746.
https://doi.org/10.3390/su14116746