Towards a Sustainable Power Grid: Stochastic Hierarchical Planning for High Renewable Integration (2107.14558v1)

Abstract: Driven by ambitious renewable portfolio standards, large-scale inclusion of variable energy resources (such as wind and solar) are expected to introduce unprecedented levels of uncertainty into power system operations. The current practice of operations planning with deterministic optimization models may be ill-suited for a future with abundant uncertainty. To overcome the potential reliability and economic challenges, we present a stochastic hierarchical planning (SHP) framework. This framework captures operations at day-ahead, short-term and hour-ahead timescales, along with the interactions between the stochastic processes and decisions. In contrast to earlier studies where stochastic optimization of individual problems (e.g., unit commitment, economic dispatch) have been studied, this paper studies an integrated framework of \emph{planning under uncertainty}, where stochastic optimization models are stitched together in a hierarchical setting which parallels the deterministic hierarchical planning approach that is widely adopted in the power industry. Our experiments, based on the NREL-118 dataset, reveal that under high renewable penetration, significant operational improvements can be expected by transitioning to the SHP paradigm. In particular, the computational results show that significant improvements can be achieved in several metrics, including system reliability, environmental sustainability, and system economics, solely by making a strategic choice to adopt the new SHP paradigm.

• The paper demonstrates that stochastic hierarchical planning significantly reduces unmet demand and reserve requirements in high renewable grids.
• It leverages two-stage stochastic mixed-integer and linear programs across day-ahead, short-term, and hour-ahead stages to optimize grid operations.
• The study shows cost reductions up to 10.4% and lower GHG emissions, highlighting the environmental and economic benefits of the approach.

This paper investigates the transition from traditional Deterministic Hierarchical Planning (DHP) to a Stochastic Hierarchical Planning (SHP) framework for power system operations, particularly focusing on grids with high penetration of variable renewable energy sources (VERs) like wind and solar (2107.14558). The core argument is that the increased uncertainty from VERs makes traditional DHP, which relies on point forecasts, inadequate, potentially leading to reduced reliability and increased costs. The SHP framework aims to mitigate these issues by explicitly incorporating uncertainty using stochastic optimization models within the established hierarchical planning structure used by system operators (ISOs/TSOs).

Hierarchical Planning Framework

The proposed SHP framework mirrors the typical multi-layer planning process used in practice, adapting it for stochastic optimization:

1. Day-Ahead Unit Commitment (DA-UC):
   • Horizon/Resolution: 24 hours / 60 minutes. Solved once per day.
   • Purpose: Commits slower-ramping generators based on day-ahead forecasts.
   • Model: A two-stage stochastic mixed-integer program (SMIP).
     • First Stage: Generator on/off (commitment) decisions ($x$).
     • Second Stage: Economic dispatch (generation levels, flows, etc.) ($y$) under various renewable/demand scenarios ($\tilde{\xi}^d$), minimizing expected operating costs.
   • Deterministic Equivalent (in DHP): Standard MIP using point forecasts.
2. Short-Term Unit Commitment (ST-UC):
   • Horizon/Resolution: 4 hours / 15 minutes. Solved every 3 hours (rolling horizon).
   • Purpose: Commits faster-ramping generators based on updated, shorter-term forecasts, refining DA plans.
   • Model: A two-stage SMIP.
     • Respects DA commitments for DA-only generators (${\x}_{[j]}^d = {\x}_{[j]}^{\star,d}$).
     • Allows limited deviation ($\epsilon_j$, set to ramping limits) in generation levels for DA-committed units compared to the DA plan ($|{\y}_{[j]}^d - {\y}_{[j]}^{\star,d}| \leq \epsilon_j$) to avoid myopic decisions.
   • Deterministic Equivalent (in DHP): Standard MIP using updated point forecasts. Note: Due to computational challenges with SMIP solvers, the experiments primarily use a deterministic ST-UC model even within the SHP framework.
3. Hour-Ahead Economic Dispatch (HA-ED):
   • Horizon/Resolution: 75 minutes / 15 minutes. Solved every 15 minutes (rolling horizon).
   • Purpose: Finalizes generation dispatch levels for all committed units based on the latest forecasts, closest to real-time.
   • Model: A two-stage stochastic linear program (SLP) since commitment decisions ($x$) are fixed from DA-UC and ST-UC.
     • First Stage: Generation levels ($y$) for the immediate next 15-minute interval (using actual observations for evaluation).
     • Second Stage: Generation levels for the remaining horizon under various scenarios ($\tilde{\xi}^r$).
     • Respects all upstream commitments (${\x}_{[k]}^d = {\x}^{\star,d}_{[k]},~ {\x}_{[k]}^s = {\x}^{\star,s}_{[k]}$).
     • Allows limited deviation ($\epsilon_k$) from ST-UC generation plans ($|{\y}_{[k]} - {\y}_{[k]}^{\star,s}| \leq \epsilon_k$).
   • Implementation: Only the first-stage "here-and-now" dispatch decision is implemented before the model is resolved for the next interval.
   • Deterministic Equivalent (in DHP): Standard LP using latest point forecasts.

The overall framework can be visualized as follows:

graph TD subgraph Day i DA_UC(DA-UC Model) --> ST_UC1(ST-UC 1) DA_UC --> ST_UC2(ST-UC 2) DA_UC --> ST_UC8(ST-UC 8) end subgraph Rolling Horizon ST_UC1 --> HA_ED1(HA-ED 1) ST_UC1 --> HA_ED12(HA-ED 12) HA_ED1 --> HA_ED2(HA-ED 2) HA_ED11 --> HA_ED12 ST_UC2 --> HA_ED13(HA-ED 13) ST_UC2 --> HA_ED24(HA-ED 24) HA_ED12 --> HA_ED13 ST_UC8 --> HA_ED85(HA-ED 85) ST_UC8 --> HA_ED96(HA-ED 96) HA_ED84 --> HA_ED85 end subgraph Evaluation HA_ED1 -- Implemented --> Metrics1(Metrics 1) HA_ED2 -- Implemented --> Metrics2(Metrics 2) HA_ED96 -- Implemented --> Metrics96(Metrics 96) end style DA_UC fill:#f9f,stroke:#333,stroke-width:2px style ST_UC1 fill:#ccf,stroke:#333,stroke-width:2px style ST_UC2 fill:#ccf,stroke:#333,stroke-width:2px style ST_UC8 fill:#ccf,stroke:#333,stroke-width:2px style HA_ED1 fill:#9cf,stroke:#333,stroke-width:2px style HA_ED2 fill:#9cf,stroke:#333,stroke-width:2px style HA_ED12 fill:#9cf,stroke:#333,stroke-width:2px style HA_ED13 fill:#9cf,stroke:#333,stroke-width:2px style HA_ED24 fill:#9cf,stroke:#333,stroke-width:2px style HA_ED85 fill:#9cf,stroke:#333,stroke-width:2px style HA_ED96 fill:#9cf,stroke:#333,stroke-width:2px

Implementation Details

• Mathematical Models: Standard UC and ED formulations are used, including generator limits, ramping, min up/down times, DC power flow approximations for transmission constraints (flow balance, line limits, bus angle limits), and reserve requirements. Detailed formulations are in Appendix A.
• Objective: Minimize total costs (startup, no-load, variable generation) plus penalties for unmet demand, over-generation, and renewable curtailment.
• Uncertainty Modeling: Time series models (Vector Autoregressive - VAR) are trained on historical forecast data to generate scenarios for wind and solar outputs, capturing spatio-temporal correlations. Forecasts and scenario distributions are updated closer to real-time using a simple update rule combining recent observations and original forecasts (Appendix B).
• Solution Algorithms:
  • Deterministic MIP/LP: Solved using commercial solvers (CPLEX).
  • Stochastic UC (SMIP): Solved using the L-shaped method (Benders decomposition). 100 scenarios used.
  • Stochastic ED (SLP): Solved using regularized Stochastic Decomposition (SD), a sequential sampling method suitable for large numbers of scenarios (minimum 256 multivariate time series used).
• Evaluation: The performance of different hierarchical settings (DDD: all deterministic; DDS: deterministic UC, stochastic ED; SDS: stochastic DA-UC, deterministic ST-UC, stochastic ED) is evaluated using a rolling horizon simulation over 7 days on the NREL-118 test system against actual historical renewable/demand data.

Key Findings and Practical Implications

The experiments, conducted on the NREL-118 system (high VER penetration), compared DHP (DDD) with variants of SHP (DDS, SDS) under different VER levels and reserve requirements.

• Reliability: SHP significantly reduces unmet demand compared to DHP, particularly under high VER and low reserve settings. SHP can achieve the same reliability level (e.g., zero unmet demand) with substantially lower mandated reserve requirements. For instance, under high solar/wind integration, DDD required high reserves, DDS required medium reserves, and SDS required low reserves to eliminate unmet demand. This implies stochastic models intrinsically manage uncertainty better, reducing the need for large, fixed reserve buffers. SHP also reduced the reliance on last-minute commitments from ST-UC.
• Economics: By enabling lower reserve requirements to meet reliability targets, SHP leads to lower overall system operating costs. The paper found cost reductions of up to 10.4% when comparing the SHP settings to the DHP setting at the minimum reserve level needed for zero unmet demand.
• Environmental Impact: Higher VER integration generally reduces GHG emissions. While SHP might lead to slightly more renewable curtailment and conventional over-generation (used as a buffer against uncertainty), the ability to operate reliably with lower reserves (meaning fewer fossil fuel plants running unnecessarily) results in lower overall emissions compared to DHP operating at the higher reserve levels needed to achieve comparable reliability.
• Trade-offs: SHP results in more proactive buffering through over-generation and curtailment compared to DHP, which relies more heavily on reactive ST-UC commitments. This suggests SHP dynamically positions the system to handle upcoming variability.

Conclusion

The paper provides strong evidence, based on simulations with the NREL-118 dataset, that adopting an SHP framework offers significant advantages over the traditional DHP approach in power systems with high VER integration. SHP leads to improved reliability, reduced operating costs, and lower environmental impact, primarily by allowing the system to operate reliably with lower reserve margins. The practical implication is that investing in advanced stochastic optimization modeling and solution techniques for operations planning can be a cost-effective strategy to manage the challenges of a renewable-heavy grid. The paper explicitly notes the computational limitations of current SMIP solvers as a barrier to implementing fully stochastic hierarchies (especially ST-UC) and calls for further research in algorithms and short-term probabilistic forecasting. The code and data were made available to enhance reproducibility [github].