Lizhi Wang

Cutting plane algorithms for the inverse mixed integer linear programming problem

We present cutting plane algorithms for the inverse mixed integer linear programming problem (InvMILP), which is to minimally perturb the objective function of a mixed integer linear program in order to make a given feasible solution optimal.

National long-term investment planning for energy and transportation systems

The most significant energy consuming infrastructures and the greatest contributors to greenhouse gases in the US today are electric and freight/passenger transportation systems. Technological alternatives for producing, transporting, and converting energy for electric and transportation systems are numerous. Selecting from among them requires long-term assessment since these capital-intensive infrastructures take years to build with lifetimes approaching a century. The advent of electrified transportation creates interdependencies between the two infrastructures that may be both problematic and beneficial. We are developing modeling capability to perform long-term electric/transportation infrastructure design at a national level, accounting for their interdependencies. The approach combines network flow/DC-flow modeling with a multiobjective solution method. We motivate the need for this work by summarizing attributes and issues related to the investment planning problem so as to find minimum-cost, low-emission, resilient infrastructure portfolios for the future. State-of-the-art energy planning models are summarized, and we describe our software design which includes a multiobjective evolutionary algorithm with a network linear programming cost minimization fitness evaluation, together with metrics for evaluating resiliency and sustainability.

National Energy and Transportation Systems: Interdependencies within a Long Term Planning Model

The most significant energy consuming infrastructures and the greatest contributors to greenhouse gases for any nation today are electric and freight/passenger transportation systems. Technological alternatives for producing, transporting, and converting energy for electric and transportation systems are numerous. Addressing costs, sustainability, and resiliency of electric and transportation needs requires long-term assessment since these capital-intensive infrastructures take years to build with lifetimes approaching a century. Yet, the advent of electrically driven transportation, including cars, trucks, and trains, creates potential interdependencies between the two infrastructures that may be both problematic and beneficial. We are developing modeling capability to perform long-term electric and transportation infrastructure design at a national level, accounting for their interdependencies. The approach combines network flow modeling with a multiobjective solution method. We describe and compare it to the state of the art in energy planning models. An example is presented to illustrate important features of this new approach.

Potential Impacts of Plug-in Hybrid Electric Vehicles on Locational Marginal Prices

This paper analyzes the potential impacts of plug-in hybrid electric vehicles (PHEVs) on locational marginal prices (LMPs). PHEVs are the next generation of hybrid electric vehicles with batteries that can be recharged by plugging into a standard electric power outlet. On the one hand, PHEVs produce less emissions, have higher mileage, and reduce dependency on foreign supplies of oil. On the other hand, economic and technical obstacles still exist, and potential impacts on both transportation and electric power systems need to be studied. Simulation results from a PJM five-bus test example show that, if the electricity load increases by 10% due to recharging PHEVs, the load-weighted mean and standard deviation of LMPs would increase by more than 26% and 62%, respectively. The effects of battery stations that provide hot-swap services are also studied. If the load increases by 10%, by taking advantage of the spatial price differences and shipping batteries between different locations, the battery stations could recharge the batteries at 73% of what it would cost for PHEV drivers to recharge in home garages. At the same time, the mean of LMPs would only increase by about 6% and the standard deviation would even decrease.

Interdependencies between Energy and Transportation Systems for National Long Term Planning

The most significant energy consuming infrastructures and the greatest contributors to greenhouse gases for any nation today are electric and freight/passenger transportation systems. Technological alternatives for producing, transporting, and converting energy for electric and transportation systems are numerous. Addressing costs, sustainability, and resiliency of electric and transportation needs requires long-term assessment since these capital-intensive infrastructures take years to build with lifetimes approaching a century. Yet, the advent of electrically driven transportation, including cars, trucks, and trains, creates potential interdependencies between the two infrastructures that may be both problematic and beneficial. We are developing modeling capability to perform long-term electric and transportation infrastructure design at a national level, accounting for their interdependencies. The approach combines network flow modeling with a multiobjective solution method. We describe and compare it to the state-of-the-art in energy planning models. An example is presented to illustrate important features of this new approach.

A Power Market Model with Renewable Portfolio Standards, Green Pricing and GHG Emissions Trading Programs

Models based on complementarity formulation have been a useful tool to simulate the interactions between environmental policies and the power market. This paper presents a power market model that considers renewable portfolio standards (RPS), greenhouse gas (GHG) emissions cap-and-trade and green pricing programs. These are three concurrent policies in the United States that are expected to be implemented to reduce our reliance of electricity on carbon intensity sources. Under these policies, electricity generated from renewable sources would incur little or no GHG costs, and also can be used to meet RPS, or sell into green pricing programs. Therefore, load serving entities (LSEs) would view electricity as differential products and price it differently based on its emission rate. As an illustration, the model is applied to analyze the interactions of three policies using a three-node power system. The result suggests that the green premium and the price of renewable energy credits (RECs) are closely related and the interactions among three policies can effectively increase profits earned by renewables generators. RECs market needs to be carefully designed to prevent double counting.

Security Constrained Economic Dispatch: A Markov Decision Process Approach with Embedded Stochastic Programming

The main objective of electric power dispatch is to provide electricity to the customers at low cost and high reliability. Transmission line failures constitute a great threat to the electric power system security. We use a Markov decision process (MDP) approach to model the sequential dispatch decision making process where demand level and transmission line availability change from hour to hour. The action space is defined by the electricity network constraints. Risk of the power system is the loss of transmission lines, which could cause involuntary load shedding or cascading failures. The objective of the model is to minimize the expected long-term discounted cost (including generation, load shedding, and cascading failure costs). Policy iteration can be used to solve this model. At the policy improvement step, a stochastic mixed integer linear program is solved to obtain the optimal action. We use a PJM network example to demonstrate the effectiveness of our approach.

Effective incentives design for renewable energy generation expansion planning: An inverse optimization approach

We present an incentive policy design model consisting of lower level and upper level optimization to promote renewable energy. The lower level optimization is a generation expansion planning (GEP) problem, in which the planner aims to expand an energy systems generation capacity to serve projected load with minimum cost. In the upper level optimization, to achieve the goal of specific percentage of renewable energy, the policy maker minimizes the total incentive cost and applies incentive policy to influence the decision of lower level generation planner. We introduce an effective cutting plane algorithm to solve our model. The model is implemented for a simple coal and electricity network. Different effects of mandatory policy model and incentive policy design model are analyzed to provide the optimal policy.

A New Hybrid Inexact Logarithmic-Quadratic Proximal Method for Nonlinear Complementarity Problems

In this paper, the authors present and analyze a new hybrid inexact Logarithmic-Quadratic Proximal method for solving nonlinear complementarity problems. Each iteration of the new method consists of a prediction and a correction step. The predictor is produced using an inexact Logarithmic-Quadratic Proximal method, which is then corrected by the Proximal Point Algorithm. The new iterate is obtained by combining predictor and correction point at each iteration. In this paper, the authors prove the convergence of the new method under the mild assumptions that the function involved is continuous and monotone. Comparison to another existing method with numerical experiments on classical NCP instances demonstrates its superiority.