Stochastic Optimal Power Flow with Network Reconfiguration: Congestion Management and Facilitating Grid Integration of Renewables (1911.12961v1)

Abstract: There has been a significant growth of variable renewable generation in the power grid today. However, the industry still uses deterministic optimization to model and solve the optimal power flow (OPF) problem for real-time generation dispatch that ignores the uncertainty associated with intermittent renewable power. Thus, it is necessary to study stochastic OPF (SOPF) that can better handle uncertainty since SOPF is able to consider the probabilistic forecasting information of intermittent renewables. Transmission network congestion is one of the main reasons for renewable energy curtailment. Prior efforts in the literature show that utilizing transmission network reconfiguration can relieve congestion and resolve congestion-induced issues. This paper enhances SOPF by incorporating network reconfiguration into the dispatch model. Numerical simulations show that renewable curtailment can be avoided with the proposed network reconfiguration scheme that relieves transmission congestion in post-contingency situations. It is also shown that network reconfiguration can substantially reduce congestion cost, especially the contingency-case congestion cost.

• The paper introduces an enhanced SOPF model with network reconfiguration that reduces congestion cost by 21.9% and eliminates renewable curtailment in contingency scenarios.
• It compares four distinct SOPF formulations, revealing a trade-off between improved grid operation and increased computational complexity (144.9s vs 0.344s).
• The study demonstrates that corrective network reconfiguration lowers average LMPs and overall load payments, thereby promoting economic efficiency and social welfare.

This paper addresses the challenges of integrating high levels of variable renewable energy (VRE) into power grids using traditional deterministic Optimal Power Flow (OPF) methods, which ignore VRE uncertainty and often lead to renewable curtailment due to transmission congestion (Stochastic Optimal Power Flow with Network Reconfiguration: Congestion Management and Facilitating Grid Integration of Renewables, 2019). The authors propose incorporating network reconfiguration (NR) into a Stochastic Optimal Power Flow (SOPF) framework to better manage uncertainty and alleviate congestion, particularly in post-contingency situations.

Four distinct SOPF models are developed and compared:

1. R-SOPF (Relaxed SOPF): Ignores all network constraints, serving as a baseline to measure congestion costs.
2. N-SOPF (Normal SOPF): Includes base-case network constraints (branch thermal limits).
3. E-SOPF (Enhanced SOPF): Enforces both base-case and N-1 contingency-case network constraints (using emergency short-term limits for contingencies).
4. E-SOPFwNR (Enhanced SOPF with Network Reconfiguration): Extends E-SOPF by allowing corrective transmission line switching after a contingency occurs.

The core idea is that SOPF handles the uncertainty from VRE forecasts across multiple scenarios ($s \in S$), while NR provides flexibility to reroute power flow and relieve congestion after a line outage (contingency $c \in C$).

Mathematical Formulation:

The objective is to minimize the total expected generation cost across all scenarios:

min GenCost = Σ_{g∈G} Σ_{s∈S} W_s * f(P_{gs})

where $W_s$ is the probability of scenario $s$, and $f(P_{gs})$ is the (linearized) cost of generator $g$ producing power $P_{gs}$.

Key constraints include:

• Power Balance: Nodal power balance must hold in the base case (for all models) and post-contingency (for E-SOPF and E-SOPFwNR).
  • Base case: Σ{g∈G(n)} P{gs} + Σ{i∈IR(n)} pIR{is} + Σ{k∈K(n+)} P{ks} - Σ{k∈K(n-)} P{ks} = L_n
  • Contingency case: Σ{g∈G(n)} P{gs} + Σ{i∈IR(n)} pIR{is} + Σ{k∈K(n+)} P{ksc} - Σ{k∈K(n-)} P{ksc} = L_n
• Generator Limits: Ramping rates, min/max output power.
• Renewable Generation: $pIR_{is} + cIR_{is} = pIR^{max}_{is}$ (Scheduled + Curtailed = Max Forecasted).
• Base-Case Branch Limits: $-LimitA_k \le P_{ks} \le LimitA_k$
• Spinning Reserve: Based on the "largest generator" rule, ensuring sufficient ramp capability.
• Post-Contingency Branch Limits (E-SOPF): $-LimitC_k \le P_{ksc} \le LimitC_k$
• Post-Contingency Branch Limits with NR (E-SOPFwNR): Uses a binary variable $Z_{sck}$ (1 if line $k$ is in service post-contingency $c$ in scenario $s$, 0 otherwise) and the Big-M method to model switching:
  • $-Z_{sck} LimitC_k \le P_{ksc} \le Z_{sck} LimitC_k$
  • $$P_{ksc} - (\theta_{n(k-)sc} - \theta_{n(k+)sc})/x_k + (1 - Z_{sck}) M \ge 0$$
  • $$P_{ksc} - (\theta_{n(k-)sc} - \theta_{n(k+)sc})/x_k - (1 - Z_{sck}) M \le 0$$
  • $\sum_{k \in \{K-c\}} (1 - Z_{sck}) \le z_{max}$ (Limit number of switched lines)

Implementation and Results:

The models were tested on a modified IEEE 24-bus system with 5 VRE units and 10 forecast scenarios.

• Cost Reduction: E-SOPFwNR significantly reduced the total operating cost compared to E-SOPF. It achieved a 21.9% reduction in total congestion cost and a 34.8% reduction in contingency-case congestion cost compared to E-SOPF.
• Renewable Curtailment: E-SOPF resulted in VRE curtailment (14.2 MW and 3.8 MW) in 2 out of 10 scenarios to maintain N-1 security. E-SOPFwNR avoided all VRE curtailment by using NR to resolve post-contingency congestion.
• Computational Cost: E-SOPFwNR introduces binary variables and Big-M constraints, significantly increasing model complexity and solution time (144.9s vs 0.344s for E-SOPF on the test system). This poses a challenge for real-time application on large systems.
• Market Impact: E-SOPFwNR led to lower average and weighted Locational Marginal Prices (LMPs), reduced overall load payments, and lower generator revenues compared to E-SOPF, suggesting improved economic efficiency and social welfare.

Practical Implications:

• Using SOPF with corrective NR (E-SOPFwNR) can enhance grid reliability (N-1 security) while maximizing the utilization of renewable resources by preventing curtailment caused by post-contingency congestion.
• It offers significant operational cost savings by alleviating expensive congestion, especially under contingency conditions.
• The main barrier to practical implementation is the high computational burden associated with the mixed-integer programming formulation of E-SOPFwNR. Future work focuses on developing efficient decomposition algorithms to make it scalable for real-world power systems.