(117a) Optimization Model and Algorithm for Capacity Planning and Operation of Reliable and Carbon-Neutral Power Systems with High Penetration of Renewable Generation

Ensuring high reliability in power systems is a critical issue that must be addressed, especially given the increase in renewable generation. Power system reliability can be classified into “design reliability” and “operation reliability” [1]. Operation reliability refers to the ability of power systems to supply uninterrupted electricity to customers (also called power system flexibility in some previous works), while design reliability refers to the ability of power systems to withstand a failure that can cause a power outage [1]. In literature, operation reliability has been actively accounted for by constraining load-shedding, whereas design reliability has been simplified to reduce complexity, such as by using a reserve margin method [2,3]. However, since individual power generators and transmission lines have different failure rates depending on their capacities and lifetimes, more sophisticated methods to predict design reliability are needed. An analytical method estimates design reliability based on the failure rates of generators and/or transmission lines, which is mathematically challenging in that it enumerates all possible capacity failure states and calculates the probability of each state [4]. One unique feature of the analytical method is that it can capture the impact of a network structure on design reliability. It is economically favorable to install a small number of large-sized facilities for economies of scale. However, in this case, the power loss caused by the failure of some generators cannot be effectively solved as there are not enough generators to act as backups for the failed ones. On the other hand, as the number of available generators and lines increases, if some generators/lines fail, others can replace the failed ones (can act as backups), resulting in improved design reliability. The analytical method can effectively consider these properties, which other methods cannot represent.

In this work, we propose a Generalized Disjunctive Programming (GDP) [5] model that optimizes both long-term capacity planning (such as the number and size of dispatchable/renewable generators, batteries, and transmission lines) and hourly operation (such as on/off schedules of dispatchable generators, power output from each generator, and power flow) to maximize power system reliability while minimizing total cost and CO₂ emissions. The design reliability is estimated by considering the probability of failure of generators/lines and possible capacity failures. To avoid a computational challenge that could result from enumerating all possible failure states, this work first selects several critical generators that could have a severe impact on the power system and then considers reliability constraints for those generators only. Loss of load expectation (LOLE) and expected energy not served (EENS) [6] are used as reliability criteria calculated using the probability of failure, capacity factor, and available capacity. Since the proposed model not only considers multi-period planning and hourly operations but also estimates the design reliability, a solution method that can reduce the computational expense must be developed. We propose a bilevel decomposition with tailed cuts to address this computational challenge.

The proposed model and algorithm are applied to the San Diego, California, case study. The case study is a 10-year planning problem with five representative days from each year (four average days and one extreme day). Based on California’s energy policy on carbon-neutral and renewable power systems, a total of three scenarios with two different solutions are generated: Scenario #1 – a) Solution A: Business-as-usual (BAU) scenario (no reliability and environmental constraints), b) Solution B: with only design reliability consideration, Scenario #2 – c) Solution A: with only CO₂ emission constraint, d) Solution B: with both CO₂ emission and design reliability consideration, Scenario #3 – e) Solution A: with CO₂ emission and renewable share constraints, f) Solution B: with CO₂ emission, renewable share, and reliability consideration [7]. As a result, the design reliability of the system could be improved by increasing the number of dispatchable generators. However, due to the higher failure rate of individual dispatchable generators, more capacity needs to be expanded to secure the target reliability level. The model chooses to expand dispatchable power to increase reliability despite renewable generators having a lower failure rate.

Keywords: Reliability, renewable generation, carbon-neutral power systems, expansion planning

Disclaimer This project was funded by the Department of Energy, National Energy Technology Laboratory an agency of the United States Government, through a support contract. Neither the United States Government nor any agency thereof, nor any of their employees, nor the support contractor, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

Acknowledgments This work was conducted as part of the Institute for the Design of Advanced Energy Systems (IDAES) with support from the U.S. Department of Energy’s Office of Fossil Energy and Carbon Management through the Simulation-based Engineering Research Program.

References

[1] Cho, S., Li, C., Grossmann, I.E., “Recent advances and challenges in optimization models for expansion planning of power systems and reliability optimization”, Computers and Chemical Engineering, 165, 107924 (2022).

[2] Lara C.L., Mallapragada D.S., Papageorgiou D.J., Venkatesh A., Grossmann I.E.,

“Deterministic electric power infrastructure planning: Mixed-integer programming model and nested decomposition algorithm”, European Journal of Operation Research, 271 (3), 1037-1054 (2018)

[3] Li C., Conejo A.J., Liu P., Omell B.P., Siirola J.D., Grossmann I.E., “Mixed-integer linear programming models and algorithms for generation and transmission expansion planning of power systems”, European Journal of Operation Research, 297 (3), 1071-1082 (2021)

[4] Cho, S., Tovar-Facio, J., Grossmann, I.E., “Disjunctive optimization model and algorithm for long-term capacity expansion planning of reliable power generation systems”, Computers and Chemical Engineering, 174, 108243 (2023).

[5] Grossmann, I.E., and Trespalacios, F., “Systematic Modeling of Discrete-Continuous Optimization Models through Generalized Disjunctive Programming,” AIChE Journal, 59, 3276-3295 (2013).

[6] Medjoudj, R., Bediaf, H., Aissani, D., “Power System Reliability: Mathematical Models and Applications”, IntechOpen, 279-298 (2017).

[7] PSE Healthy Energy, “California Peaker Power Plants: Energy Storage Replacement Opportunities” (2020)