Multi-Stage Decision Rules for Power Generation & Storage Investments with Performance Guarantees

We develop multi-stage linear decision rules (LDRs) for dynamic power system generation and energy storage investment planning under uncertainty and propose their chance-constrained optimization with performance guarantees. First, the optimized LDRs guarantee operational and carbon policy feasibility of the resulting dynamic investment plan even when the planning uncertainty distribution is ambiguous. Second, the optimized LDRs internalize the tolerance of the system planner towards the stochasticity (variance) of uncertain investment outcomes. They can eventually produce a quasi-deterministic investment plan, which is insensitive to uncertainty (as in deterministic planning) but robust to its realizations (as in stochastic planning). Last, we certify the performance of the optimized LDRs with the bound on their sub-optimality due to their linear functional form. Using this bound, we guarantee that the preference of LDRs over less restrictive -- yet poorly scalable -- scenario-based optimization does not lead to financial losses exceeding this bound. We use a testbed of the U.S. Southeast power system to reveal the trade-offs between the cost, stochasticity, and feasibility of LDR-based investments. We also conclude that the LDR sub-optimality depends on the amount of uncertainty and the tightness of chance constraints on operational, investment and policy variables

Impact of Demand Response on Thermal Generation Investment with High Wind Penetration

We present a stochastic programming model for investments in thermal generation capacity to study the impact of demand response (DR) at high wind penetration levels. The investment model combines continuous operational constraints and wind scenarios to represent the implications of wind variability and uncertainty at the operational level. DR is represented in terms of linear price-responsive demand functions. A numerical case study based on load and wind profiles of Illinois is constructed with 20 candidate generating units of various types. Numerical results show the impact of DR on both investment and operational decisions. We also propose a model in which DR provides operating reserves and discuss its impact on lowering the total capacity needed in the system. We observe that a relatively small amount of DR capacity is sufficient to enhance the system reliability. When compared to the case with no DR, a modest level of DR results in less wind curtailment and better satisfaction of reserve requirements, as well as improvements in both the social surplus and generator utilization, as measured by capacity factors

Temporal vs. Stochastic Granularity in Thermal Generation Capacity Planning with Wind Power

We propose a stochastic generation expansion model, where we represent the long-term uncertainty in the availability and variability in the weekly wind pattern with multiple scenarios. Scenario reduction is conducted to select a representative set of scenarios for the long-term wind power uncertainty. We assume that the short-term wind forecast error induces an additional amount of operating reserves as a predefined fraction of the wind power forecast level. Unit commitment (UC) decisions and constraints for thermal units are incorporated into the expansion model to better capture the impact of wind variability on the operation of the system. To reduce computational complexity, we also consider a simplified economic dispatch (ED) based model with ramping constraints as an alternative to the UC formulation. We find that the differences in optimal expansion decisions between the UC and ED formulations are relatively small. We also conclude that the reduced set of scenarios can adequately represent the long-term wind power uncertainty in the expansion problem. The case studies are based on load and wind power data from the state of Illinois

Evaluating Stochastic Methods in Power System Operations with Wind Power

Wind power is playing an increasingly important role in electricity markets. However, it's inherent variability and uncertainty cause operational challenges and costs as more operating reserves are needed to maintain system reliability. Several operational strategies have been proposed to address these challenges, including advanced probabilistic wind forecasting techniques, dynamic operating reserves, and various unit commitment (UC) and economic dispatch (ED) strategies under uncertainty. This paper presents a consistent framework to evaluate different operational strategies in power system operations with renewable energy. We use conditional Kernel Density Estimation (KDE) for probabilistic wind power forecasting. Forecast scenarios are generated considering spatio-temporal correlations, and further reduced to lower the computational burden. Scenario-based stochastic programming with different decomposition techniques and interval optimization are tested to examine economic, reliability, and computational performance compared to deterministic UC/ED benchmarks. We present numerical results for a modified IEEE-118 bus system with realistic system load and wind data