Distributionally robust multi-stage stochastic programming for mid- and long-term cross-regional power markets

• Proposes a novel distributionally robust multi-stage stochastic programming model for cross-regional power markets. • Designs a distributionally robust stochastic dual dynamic programming algorithm with risk-averse strategies to resolve the premature problem. • Transforms the nested “max–min-max” structure in dual problem derivation by employing a 1-norm ambiguity set. The widespread integration of renewable energy sources (RESs) has presented significant challenges in deregulated power markets. The inherent uncertainty of RES poses challenges for clearing cross-temporal and cross-regional transactions, manifesting as curses of dimensionality and premature convergence in conventional approaches. This paper proposes a distributionally robust multi-stage stochastic programming model for cross-regional power market clearing considering available transfer capacity constraints. The uncertainties from RESs are modeled through distributionally robust formulations circumventing exact probability distributions, while multiple stages are introduced to maintain applicability to mid- and long-term trading. To overcome the premature convergence problem in conventional methods, a distributionally robust stochastic dual dynamic programming algorithm is proposed to give an exact upper bound. To resolve the nested “max–min-max” structure preventing direct dual problem derivation, a 1-norm ambiguity set is employed to reformulate the nested structure into a single “max” structure. Numerical results for a practical power system in Northwestern China demonstrate that the proposed method provides an exact upper bound that avoids premature convergence for better accuracy at the cost of longer computation time.