New bounding and decomposition approaches for MILP investment problems: Multi-area transmission and generation planning under policy constraints

Abstract

We propose a novel two-phase bounding and decomposition approach to compute optimal and near-optimal solutions to large-scale mixed-integer investment planning problems that have to consider a large number of operating subproblems, each of which is a convex optimization. Our motivating application is the planning of power transmission and generation in which policy constraints are designed to incentivize high amounts of intermittent generation in electric power systems. The bounding phase exploits Jensen's inequality to define a lower bound, which we extend to stochastic programs that use expected-value constraints to enforce policy objectives. The decomposition phase, in which the bounds are tightened, improves upon the standard Benders' algorithm by accelerating the convergence of the bounds. The lower bound is tightened by using a Jensen's inequality-based approach to introduce an auxiliary lower bound into the Benders master problem. Upper bounds for both phases are computed using a sub-sampling approach executed on a parallel computer system. Numerical results show that only the bounding phase is necessary if loose optimality gaps are acceptable. However, the decomposition phase is required to attain optimality gaps. Use of both phases performs better, in terms of convergence speed, than attempt

An efficient model and algorithm for the transmission-constrained multi-site combined heat and power system

“…NPS is 7 to 360 (average 30) times faster than the CPLEX code. This will lay foundation for efficiently addressing more advanced CHP systems incorporating different types of storages and unit commitment to achieve high utilization of RES and for addressing investment planning for large CHP systems considering the intermittent RES, similar to large power-only systems [37].…”

Valuation of Flexible Transmission Investment Options Under Uncertainty

“…The application of Benders decomposition [20] in the context of power systems has been carried out successfully in the past [21]. Transmission and generation planning models in particular exhibit problem structures highly exploitable by such decomposition methods [22]. Benders is an iterative method that decomposes the original problem into a master problem (transmission investment) and several sub-problems (power system operation).…”

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Analysis and Optimization of Power Supply Structure Based on Markov Chain and Error Optimization for Renewable Energy from the Perspective of Sustainability

“…The contradiction between economic development and environmental protection have become increasingly prominent. Against the backdrop of exhausted traditional fossil fuels and environmental deterioration, renewable energy has been particularly favored by countries all over the world for its environmental friendliness, low pollution and regenerative ability [1]. Under With the encouragement and support of national policy, renewable energy power generation in China has developed rapidly over the past decade.…”