Publications

The anticipated magnitude of needed investments in new transmission infrastructure in the U.S. requires that these be allocated in a way that maximizes the likelihood of achieving society's goals for power system operation. The use of state-of-the-art optimization tools can identify cost-effective investment alternatives, extract more benefits out of transmission expansion portfolios, and account for the huge economic, technology, and policy uncertainties that the power sector faces over the next several decades.

Current commercial software tools for transmission and generation investment planning have limited stochastic modeling capabilities. Because of this limitation, electric power utilities generally rely on scenario planning heuristics to identify potentially robust and cost effective investment plans for a broad range of system, economic, and policy conditions. Several research studies have shown that stochastic models perform significantly better than deterministic or heuristic approaches, in terms of overall costs. However, there is a lack of practical solution techniques to solve such models. In this paper we propose a scalable decomposition algorithm to solve stochastic transmission and generation planning problems, respectively considering discrete and continuous decision variables for transmission and generation investments. Given stochasticity restricted to loads and wind, solar, and hydro power output, we develop a simple scenario reduction framework based on a clustering algorithm, to yield a more tractable model. The resulting stochastic optimization model is decomposed on a scenario basis and solved using a variant of the Progressive Hedging (PH) algorithm. We perform numerical experiments using a 240-bus network representation of the Western Electricity Coordinating Council in the US. Although convergence of PH to an optimal solution is not guaranteed for mixed-integer linear optimization models, we find that it is possible to obtain solutions with acceptable optimality gaps for practical applications. Our numerical simulations are performed both on a commodity workstation and on a high-performance cluster. The results indicate that large-scale problems can be solved to a high degree of accuracy in at most 2 h of wall clock time.

Current commercial software tools for transmission and generation investment planning have limited stochastic modeling capabilities. Because of this limitation, electric power utilities generally rely on scenario planning heuristics to identify potentially robust and cost effective investment plans for a broad range of system, economic, and policy conditions. Several research studies have shown that stochastic models perform significantly better than deterministic or heuristic approaches, in terms of overall costs. However, there is a lack of practical solution approaches to solve such models. In this paper we propose a scalable decomposition algorithm to solve stochastic transmission and generation planning problems, respectively considering discrete and continuous decision variables for transmission and generation investments. Given stochasticity restricted to loads and wind, solar, and hydro power output, we develop a simple scenario reduction framework based on a clustering algorithm, to yield a more tractable model. The resulting stochastic optimization model is decomposed on a scenario basis and solved using a variant of the Progressive Hedging (PH) algorithm. We perform numerical experiments using a 240-bus network representation of the Western Electricity Coordinating Council in the US. Although convergence of PH to an optimal solution is not guaranteed for mixed-integer linear optimization models, we find that it is possible to obtain solutions with acceptable optimality gaps for practical applications. Our numerical simulations are performed both on a commodity workstation and on a high-performance cluster. The results indicate that large-scale problems can be solved to a high degree of accuracy in at most two hours of wall clock time.

In the United States, individual states enact Renewable Portfolio Standards (RPSs) for renewable electricity production with little coordination. Each state imposes restrictions on the amounts and locations of qualifying renewable generation. Using a co-optimization (transmission and generation) planning model, we quantify the economic benefits of allowing flexibility in the trading of Renewable Energy Credits (RECs) among the U.S. states belonging to the Western Electricity Coordinating Council. The flexibility was analyzed in terms of the amount and geographic eligibility of out-of-state RECs that can be used in meeting state RPSs' goals. Although more trade would be expected to have economic benefits, the magnitude of these benefits relative to the cost of additional transmission infrastructure is less certain. It is also unclear the effects of such trading on CO₂ emissions and energy prices. We find that most of the economic benefits are captured with approximately 25% of interstate exchange of RECs. Furthermore, increasing REC trading flexibility does not necessarily result in either higher transmission investment costs or a substantial impact on CO₂ emissions. Finally, increasing REC trading flexibility decreases energy prices in some states and increases them in others, while WECC-wide average energy price slightly decreases.

There exist several different reliability- and approximation-based methods to determine the capacity contribution of solar resources towards resource adequacy. However, most of these approaches require knowing in advance the installed capacities of both conventional and solar generators. This is a complication since generator capacities are actually decision variables in capacity planning studies. In this article we study the effect of time resolution and solar PV penetration using a capacity planning model that accounts for the full distribution of generator outages and solar resource variability. We also describe a modification of a standard deterministic planning model that enforces a resource adequacy target through a reserve margin constraint. Our numerical experiments show that at least 50 days worth of data are necessary to approximate the results of the full-resolution model with a maximum error of 2.5% on costs and capacity. We also show that the amount of displaced capacity of conventional generation decreases rapidly as the penetration of solar PV increases. We find that using an exogenously defined and constant capacity factor based on time-series data can yield relatively accurate results for small penetration levels (less than 5%). For higher penetration levels (up to 20%), the modified deterministic planning model better captures avoided costs and the decreasing value of solar PV. Although our results are not general, they highlight the importance of accounting for the variation in both energy and capacity value of solar resources endogenously in capacity planning models. A11 numerical experiments are performed using the IEEE Reliability Test System and 7 years worth of demand and solar data from a utility in Arizona.