Innovative Applications of O.R.A robust decision-support method based on optimization and simulation for wildfire resilience in highly renewable power systems☆
Introduction
In recent years, natural disasters have significantly increased in frequency, causing important contingencies that affect the normal operation of the electric grid (Dept. de Cambio Climático del Ministerio del Medio Ambiente, 2015). In fact, natural disasters can force the output of various power system components, or even damage them permanently, which significantly impacts the operation of the system and the corresponding power supply security. Further, many disasters lead to cascading effects that can have unexpected consequences (Golari, Fan, & Wang, 2017). Given this, increasing the resilience and develop efficient tools for the power system operator has become a critical task for society as a whole. Resilience is understood as the ability of the system to absorb variable changes and mitigate the danger by anticipation, adaptation, and recovery of the system (Huang, Wang, Chen, Guo, & Zhu, 2017), and as such, it is critical to cope with increasing disasters
In the literature, different ways to quantify and increase the resilience of the power system have been studied, see the references in Kim, Wright, Bienstock, and Harnett (2016); Panteli, Pickering, Wilkinson, Dawson, and Mancarella (2016a); Wang, Chen, Wang, and Baldick (2015). In general, resilience improvement mechanisms are divided into three categories depending on the stage of the disaster. The first category, focused on the pre-disaster stage, considers all methods of improvement in forecasting and preparation of the system through planning and investment decisions. This group includes works related to expansion planning with the use of distributionally robust models (Bagheri, Zhao, Qiu, & Wang, 2018), two-stage robust optimization model (Yuan et al., 2016), adjustable robust reinforcement planning in Postek, Den Hertog, Kind, and Pustjens (2019), and the use of stochastic models in distribution networks (Ma, Chen, & Wang, 2016). The second category considers emergency response actions. Some mechanisms included in this group are dispatch distributed generators and demand response (Ansari & Mohagheghi, 2015), generators dispatch adjustments (Mohagheghi & Rebennack, 2015), and topology changes (Mahdi & Genc, 2015). The third category is focused on post-disaster restoration. In this group we can find models for scheduling the repair of transmission lines, load pickups, and generation assets (Coffrin, Van Hentenryck, 2015, Sedzro, Shi, Lamadrid, Zuluaga, 2019), and also resource allocation problems (Arab, Khodaei, Han, & Khator, 2015).
The treatment of wildfire contingencies in power systems has been studied mainly along two different directions. The first direction focuses on modeling the changes in the characteristics of transmission lines (Choobineh, Ansari, Mohagheghi, 2015, Mohagheghi, Rebennack, 2015). The second direction proposes schemes to define and coordinate the resource allocation for the restoration of possible damages (Bertsimas, Griffith, Gupta, Kochenderfer, Mišić, 2017, Coffrin, Van Hentenryck, 2015).
The massive integration of variable renewable energy sources in modern power systems is also a very relevant factor that has to be taken into account in understanding the resilience of such systems. In this context, many efforts have been undertaken for the efficient operation of power networks given the uncertainty from renewable sources. In particular, the scientific literature presents two main approaches to deal with such uncertainty, namely, stochastic programming and robust optimization. Many stochastic programming models use a finite set of scenarios to represent the probability distribution of uncertain values. The use of this type of representation can be found in expansion planning problems (Ahmed, King, & Parija, 2003), security-constrained unit commitment (Lamadrid et al., 2018), and economic dispatch problems (Li, Lin, Ji, & Wu, 2018). In contrast, robust optimization methods look for preparing the system for any possible realization of uncertainty within given uncertainty sets. In recent years its use has been extended to several problems, such as unit commitment problems (Bertsimas, Litvinov, Sun, Zhao, Zheng, 2012, Lorca, Sun, 2016, Wang, Liu, Wang, Qiu, Wei, Mei, Lei, 2016), real-time power dispatch (Li, Wu, Zhang, Wang, 2015, Lorca, Sun, 2017) and expansion planning (Verastegui, Lorca, Olivares, Negrete-Pincetic, Gazmuri, 2019, Wu, Liu, Gu, Wang, Chen, 2018). Besides stochastic and robust models, there are hybrid approaches, sometimes referred as distributionally or ambiguity robust approaches (Bagheri, Zhao, Qiu, Wang, 2018, Delage, Ye, 2010).
As power systems evolve towards a larger integration of variable renewable energy sources, it becomes even more challenging to increase their resilience to natural disasters, due to the much higher real-time uncertainty that such systems are exposed to. In particular, wildfires are one type of natural hazard that requires an effective response in the operational operation of power networks. If such power networks are also exposed to uncertainty in renewable power sources, then an appropriate real-time response has to be carried out taking into account these two aspects, which is the challenge that drives this paper.
In this context, this paper develops a practical decision-support method based on optimization and simulation for analysis of the operation of highly renewable power systems as they respond to the evolution of wildfire threats. The main features of this research are summarized as follows:
- 1.
The proposed approach employs a stochastic wildfire simulation method to generate wildfire scenarios, which are given as input to an attacker-defender model that identifies worst-case contingencies induced by the wildfire and associated worst-case renewable power profiles, over a given time horizon. Further, this allows the evaluation of various user-defined topology configurations of the power system, namely, based on switching selected transmission lines on or off, in terms of power supply security, to jointly cope with wildfire-induced contingencies and renewable power uncertainty.
- 2.
The attacker-defender model in this paper finds a worst-case realization for (i) transmission line and generator contingencies, out of those that can potentially be affected by a given wildfire scenario, and for (ii) wind and solar power trajectories, based on a max-min structure where the inner min problem represents a best adaptive response on generator dispatch actions. For this, we employ a traditional uncertainty set for renewable power availability, and develop a novel uncertainty set of variable size that depends on the wildfire dynamics. Further, to solve the overall attacker-defender model, duality and binary-expansion techniques are employed to obtain a mixed-integer formulation that can be efficiently solved with off-the-shelf solvers.
- 3.
Extensive computational experiments inspired by recent wildfire events on a real-world test case based on the Chilean power system with up to 278 buses show empirical evidence of the practical applicability and scalability of the wildfire response analysis method developed in this paper. The results obtained provide insight into the relation between wildfire evolution uncertainty and renewable power variability, and the potential topological mitigation actions from the power system operator, showing the practical effectiveness of the proposed approach for enhancing wildfire resilience in highly renewable power systems.
Section snippets
Context on wildfire simulation methods
The evolution of wildfires presents a complex dynamic behavior. In particular, the spread of a given wildfire depends on factors such as the amount of fuel in the area, weather conditions, wind speeds, topography, etc. These characteristics determine the time and area where the zone has a predisposition to burn, and therefore, the moment in which an element of the power system can potentially be affected.
The literature presents two types of models to describe fire dynamics.The first type is
The proposed attacker-defender model
This Section proposes a novel attacker-defender model for wildfire response analysis. The model takes as input a given fire spread scenario (e.g., simulated based on the method in Section 2) and analyzes its impact on the power network operations. See the extended nomenclature in the Appendix.
Solution approach for the proposed attacker-defender model
The max-min structure of the attacker-defender model (3) allows to reformulate such model as a pure maximization problem by taking the dual of the inner min problem (based on strong duality of linear programming), which leads into the following equivalent bilinear optimization problem:
Computational experiments
The computational experiments presented in this section are inspired by recent wildfires that occurred in Chile and affected its power system. We employ two representations of the system, the first one with 65 buses and 82 transmission lines, and the second one with 278 buses and 360 transmission lines. The second one is based on the current representation employed by the Chilean system operator. These systems are shown in Appendix 4. Both test cases consider a total of 80 conventional
Conclusion
This paper develop a practical decision-support method based on optimization and simulation for wildfire response analysis in highly renewable power systems. The proposed approach employs a stochastic wildfire simulation method to generate wildfire scenarios, which are given as input to an attacker-defender model that identifies worst-case contingencies induced by the wildfire and associated worst-case renewable power profiles, over a given time horizon. Moreover, this paper proposed an
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This work was supported by ANID/FONDEF/IT19I0113, SERC-Chile (ANID/FONDAP/15110019), and the Complex Engineering Systems Institute (ANID/FB0816).