Valuing flexibility in transmission expansion planning from the perspective of a social planner: A methodology and an application to the Chilean power system

Abstract

We study the value of adding flexibility to Transmission Expansion Planning (TEP) projects from the perspective of a social planner using real options. Due to the deregulation of electricity markets, TEP projects currently face multiple uncertainties. These uncertainties often cause traditional project valuation methods to recommend sub-optimal investment decisions. Additionally, to incorporate the effects of uncertainties on the valuation of TEP projects, current literature rely on some critical simplifications that do not fit well with the real operations of a power market. This paper models the power market in a realistic way by combining an equilibrium model, to assess the power market equilibrium that the TEP project will generate, with a valuation model based on real options, to incorporate the value of flexibility. The methodology is applied to determine the value of adding capacity expansion flexibility to a portion of the rigid TEP project that connects the main two interconnected systems in Chile since 2018. Our results show that, in this case, adding flexibility increases the net expected social welfare by $14.03 million. Several sensitivity analyses confirm that this flexibility has more value when uncertainty is higher and/or investment costs are lower.

Acknowledgments

We also acknowledge Laboratorio de Finanzas Itaú of the Pontificia Universidad Católica de Chile for providing access to data.

Notes

1 For the use of real options on the valuation of other types of energy projects, see among others: Africa et al. (2013); Biondi and Moretto (2015); Kucsera and Rammerstorfer (2014); Tandberg et al. (2016); Xian et al. (2015).

2 Binomial trees typically assume a unique initial value for the underlying risky asset and constant volatility over its evolution through time.

3 In this context, power market equilibrium is defined as the optimal operational condition of the power market determined by the economic rules of the power dispatch (Wang et al., 2007).

4 It is worth clarifying that, in this study, each period corresponds to a temporal spot within the valuation horizon while each time block only represents a set of hours in a day in which the power system has similar demand levels.

5 PTDF represent the relative change in power flow experienced by a transmission line due to the power input or output in some specific system nodes. These factors are characterized by the network topology and the impedances of its transmission lines (Barbulescu et al., 2009).

6 The sum of consumers’ surplus, producers’ surplus, and congestion rents is equivalent to subtracting the area under the inverse supply curve from the area under the inverse demand curve.

7 The numerical value of the inverse demand curve is equivalent to the energy price that prevails at node$i$ in the time slot $h$ of period $t.$

8 When the periods are years, “per-period value” means “annualized value.”

9 In particular, in the case study presented in Section 3, we include some variability over time in the parameters that define energy supply and demand.

10 Since we use linear regression to estimate the conditional expectation function, it is straightforward to add additional base functions as explanatory variables in the regression if they are needed. Using more base functions, however, does not change significantly our numerical results; i.e., the base functions in Equation (15) are sufficient to obtain effective convergence of the algorithm in our case.

11 Kirschen and Strbac (2004) argue that the useful life of a transmission line is between 20 and 40 years, which is consistent with information provided by energy transmission companies.

12 The Ministry of Social Development of Chile uses a discount rate of 6% in real terms (Subsecretaría de Evaluación Social, 2016).

13 For nodes with no demand, a zero demand curve is considered ($P_{i,h,2015}\left(d_{i,h,2015}\right)=0$) and the existence of demand parameter takes a value of zero ($e_{i,h,t}^D=0$). Conversely, in cases in which a non-zero demand curve can be estimated, this parameter takes a value of 1 ($e_{i,h,t}^D=1$).

14 For the years 2015-2029, the expected growth in demand (${GF}_{t-1,t}$) is based on the CNE’s estimates (Comision Nacional de Energia, 2016). After 2029, demand growth is estimated using 5-year moving averages of previous values.

15 All generators that, in the real system, are connected to nodes that are not modeled in the stylized representation of the system are connected to the nearest nodes included in the model.

16 To compute the accumulated net energy (${CE}_{j,i,t}^o$), we sum the net energy (${NE}_{j,i,t}^o$) of all generators that are connected to node $i$ and have lower marginal costs than generator $j$ (i.e., ${CE}_{j,i,t}^O=\sum _{\begin{array}{c}j\in J_{i,t}\\ CM{G}_{J_{i,t},i,t}\le CM{G}_{j,i,t}\end{array}}{NE}_{j,i,t}^o$). In turn, net energy for generator $j$ is calculated as the gross generation capacity (${GC}_{j,i,t}$) multiplied by its plant factor ($P{F}_{j,i,t}$) (i.e., ${NE}_{j,i,t}^o=P{F}_{j,i,t}·{IC}_{j,i,t}$).

17 If there are no generators connected to a given node, a zero supply curve is assumed (i.e., $C_{i,h,t}\left(q_{i,h,t}\right)=0$).

18 Although we recognize that transmission expansions occur in lumpy amounts in practice, this assumption is made to avoid a situation in which network congestion becomes so high that the methodology proposed is applied to a rather unlikely extreme case. Estimating the exact transmission projects likely to be installed after 2030 is a complex task and does not alter our conclusions.

19 For lines between nodes Cardones and Kapatur, no data is available on the CNE; their impedances are estimated by weighting the distance-capacity of the relevant line by the average impedance per distance-capacity of the lines between nodes Polpaico and Cardones.

20 Generation capacities are assumed constant across hours. Additionally, if there are no generators connected to a given node, its generation capacity is zero (i.e., $G_{i,t}=0$).

21 To validate the assumption that the optimization model converges to an optimal and unique solution, it was solved using different initial values for its decision variables; the solution remained the same each time.

22 Average Energy Price, Annual Energy Demanded, and Annual Energy Produced are computed from the decision variables $d_{i,h,t}$ and $q_{i,h,t},$ and the demand curves ($p_{i,h,t}\left(·\right)$) of the model. The specific calculations are presented in Appendix A.1.

23 2029 is the last year of the actual planning defined by the CNE.

Additional information

Funding

This work was partially supported by CONICYT, FONDECYT/Regular 1161112, 1171894, and 1190253 grants and by CONICYT, FONDAP 15110019 grant (SERC-CHILE).

Notes on contributors

F. Mariscal

Francisco Mariscal holds a M.S. in Engineering (Jan. 2017) and an Industrial Engineering degree (Dec. 2015) from the School of Engineering at the Pontificia Universidad Católica de Chile. During his professional career, he has worked in Investment Banking, advising multiple power companies in topics related to generation, transmission and distribution, and in business development. His main area of interest include financial and energy markets, project modeling and valuation, and real options.

T. Reyes

Tomas Reyes is an Associate Professor of Finance and the Director of the Finance Lab Itaú at the Pontificia Universidad Católica de Chile. He earned a Ph.D. (Dec. 2012) and an M.S. (Dec. 2010) both in Finance from the Haas School of Business at the University of California, Berkeley. His research lies at the intersection between finance, economics, management and psychology. His work has been funded by the National Science and Technology Foundation (CONICYT), presented at major international conferences and been recognized with best paper awards.

E. Sauma

Enzo Sauma is a Professor of the School of Engineering and the Director of the UC Energy Research Center at the Pontificia Universidad Catolica de Chile. He is both Ph.D. (Dec. 2005) and M.S. (Dec. 2002) in Industrial Engineering and Operations Research at University of California, Berkeley. His interest includes power systems economics, environmental economics, mathematical programing, energy efficiency, renewable energy, and energy policy. He has received several international awards (INFORMS, ICORAID, NEXUS-Fulbright, etc.). He is member of INFORMS, IAEE, and Senior Member of IEEE.