UC Berkeley

For over 30 years we have been negotiating agreements that try to reduce greenhouse gas emissions. The aim is to stabilize their concentration in the atmosphere at a level that would prevent dangerous anthropogenic interference with the climate system. In 2018, the Intergovernmental Panel on Climate Change stated that the 1.5°C goal could be achieved if the electricity sector would become net zero emissions by 2050. Different countries have been pushing the frontier to reduce their emissions by deploying renewable energy sources (RES). Despite these efforts, we still have a long way to go. Research on how and when to install and how to operate more RES in power systems needs to continue advancing as we aim to reach higher levels of penetration. In addition, academics need to translate and communicate these findings to policy makers.

The contributions of this dissertation in this field have been to:

1. propose a new time-varying representation for power dynamics that reflects the presence of RES,

2. design through machine learning a stable time-invariant frequency controller for the new time-varying power dynamics,

3. explore the trade-off between information availability to the frequency control agents and their performance and stability,

4. show the cost effectiveness of stronger RES targets in the U.S. by 2030 given the carbon reductions goals of 2050, and

5. model climate change uncertainty through a stochastic formulation of the capacity expansion of power systems in the U.S. with high penetration of RES.

As more non-synchronous RES participate in power systems, the system's inertia decreases and becomes time dependent, challenging the ability of existing control schemes to maintain frequency stability. System operators, research laboratories, and academic institutes have expressed the importance to adapt to this new power system paradigm. However, power dynamics have been modeled as time-invariant, by not modeling the variability in the system's inertia. To address this, we propose a new modeling framework for power system dynamics to simulate a time-varying evolution of rotational inertia coefficients in a network. Power dynamics are modeled as a hybrid system with discrete modes representing different rotational inertia regimes of the network.

Using this new hybrid model for power dynamics, we present a framework to design a fixed learned controller based on datasets of optimal time-varying LQR controllers. We test the performance of the controller in a twelve-bus system. By adding virtual inertia we can guarantee stability of high-renewable (low-inertia) modes. The novelty of our work is to propose a design framework for a stable controller with fixed gains for time-varying power dynamics. This is relevant because it would be simpler to implement a proportional controller with fixed gains compared to a time-varying control. To expand this work, we introduce a framework to learn sparse time-invariant frequency controllers in a power system network with a time-varying evolution of rotational inertia. We design a controller that uses as features the system’s states. In other words, we design a control proportional to the angles and frequencies. Virtual inertia is included in the controllers to ensure stability. One of the findings is that it is possible to restrict communication between the nodes by reducing the number of features in the controller (from 22 to 10 in our case study) without disrupting performance and stability. Furthermore, once communication between nodes has reached a threshold, increasing it beyond this threshold does not improve performance or stability. There is a correlation between optimal feature selection in sparse controllers and the topology of the network.

In the second part of this dissertation we study the cost and lock in of carbon intensive technologies due to weak medium-term policies. We use SWITCH WECC-- a power system capacity expansion optimization model with high temporal and geographical resolution. We test three carbon cap scenarios. For each scenario, we optimize the power system for a medium timeframe (2030) and a long timeframe (2050). In the medium timeframe optimizations, by 2030 coal replaces gas power. This occurs because the long optimization foresees the stronger carbon cap in 2050. Therefore, it is optimal to transition towards cleaner technologies as early as 2030. The medium-term optimization has higher costs in 2040 and 2050 compared to the long optimization. Therefore, to minimize total costs to reduce emissions by 80% in 2050, we should optimize until 2050 or have stronger carbon cap policies by 2030 (such as a 26% of emissions reductions from 1990 levels by across the WECC).

Typical electricity-grid capacity expansion models make investment decisions with fixed inputs (e.g., fixed electricity demands and hydro-power availability). The resultant electricity supply system may not be robust to future climate change-driven uncertainties in energy demand and supply. We present the first climate change stochastic long-term (2050) capacity expansion and operation electricity grid model for the Western North America electricity region, with high temporal and spatial resolution. The Stochastic SWITCH WECC model generates a least cost portfolio of power plants that is robust to varying future climate conditions using a multi-stage optimization approach with varying electricity-demand and hydropower-availability inputs under three climate change scenarios. Results show that an optimal robust electricity supply portfolio in the WECC for 2050 has about 4% higher overall installed capacity than the average mix of the three scenarios modeled separately, and about 5.6% higher installed gas capacity, due to the greater need for operational flexibility under the wider range of possible conditions.