Risk Limiting Dispatch with Ramping Constraints

Reliable operation in power systems is becoming more difficult as the penetration of random renewable resources increases. In particular, operators face the risk of not scheduling enough traditional generators in the times when renewable energies becomes lower than expected. In this paper we study the optimal trade-off between system and risk, and the cost of scheduling reserve generators. We explicitly model the ramping constraints on the generators. We model the problem as a multi-period stochastic control problem, and we show the structure of the optimal dispatch. We then show how to efficiently compute the dispatch using two methods: i) solving a surrogate chance constrained program, ii) a MPC-type look ahead controller. Using real world data, we show the chance constrained dispatch outperforms the MPC controller and is also robust to changes in the probability distribution of the renewables.Comment: Shorter version submitted to smartgrid comm 201

Limits on the Benefits of Energy Storage for Renewable Integration

The high variability of renewable energy resources presents significant challenges to the operation of the electric power grid. Conventional generators can be used to mitigate this variability but are costly to operate and produce carbon emissions. Energy storage provides a more environmentally friendly alternative, but is costly to deploy in large amounts. This paper studies the limits on the benefits of energy storage to renewable energy: How effective is storage at mitigating the adverse effects of renewable energy variability? How much storage is needed? What are the optimal control policies for operating storage? To provide answers to these questions, we first formulate the power flow in a single-bus power system with storage as an infinite horizon stochastic program. We find the optimal policies for arbitrary net renewable generation process when the cost function is the average conventional generation (environmental cost) and when it is the average loss of load probability (reliability cost). We obtain more refined results by considering the multi-timescale operation of the power system. We view the power flow in each timescale as the superposition of a predicted (deterministic) component and an prediction error (residual) component and formulate the residual power flow problem as an infinite horizon dynamic program. Assuming that the net generation prediction error is an IID process, we quantify the asymptotic benefits of storage. With the additional assumption of Laplace distributed prediction error, we obtain closed form expressions for the stationary distribution of storage and conventional generation. Finally, we propose a two-threshold policy that trades off conventional generation saving with loss of load probability. We illustrate our results and corroborate the IID and Laplace assumptions numerically using datasets from CAISO and NREL.Comment: 45 pages, 17 figure

An Assessment of PIER Electric Grid Research 2003-2014 White Paper

This white paper describes the circumstances in California around the turn of the 21st century that led the California Energy Commission (CEC) to direct additional Public Interest Energy Research funds to address critical electric grid issues, especially those arising from integrating high penetrations of variable renewable generation with the electric grid. It contains an assessment of the beneficial science and technology advances of the resultant portfolio of electric grid research projects administered under the direction of the CEC by a competitively selected contractor, the University of California’s California Institute for Energy and the Environment, from 2003-2014

Intelligent Microgrids

Center for Electromechanic

Thermomechanical degradation mechanisms of silicon photovoltaic modules

The durability and lifetime of photovoltaic (PV) modules is one of the chief concerns for an industry which is rapidly approaching maturity. Guaranteeing the economic viability of potential PV installations is paramount to fostering growth of the industry. Whilst certification standards have helped to improve the reliability of modules, with a significant reduction in early failures, long-term performance degradation and overall lifetimes are yet to be addressed in a meaningful way. For this, it is necessary to quantify the effects of use-environment and module design. Long-term degradation of the solder bonds in PV modules causes steady power loss and leads to the generation of more devastating, secondary mechanisms such as hot-spots. Whilst solder bond degradation is well-recognised and even tested for in certification protocols, the potential rate of degradation is not well understood, particularly with respect to different environmental conditions and material selection. The complex nature of a standard silicon PV module construction makes it difficult to observe the stresses experienced by the various components during normal operation. This thesis presents the development of a finite-element model which is used to observe the stresses and strains experienced by module components during normal operating conditions and quantifies the degradation of solder bonds under different environmental conditions. First, module operating temperatures are examined across a range of climates and locations to evaluate the thermal profiles experienced by modules. Using finite-element techniques, the thermomechanical behaviour of modules is then simulated using the same thermal profiles and a quantification of solder bond degradation potential in each location is achieved. It is shown that hot climates are responsible for the highest degradation potential, but further to this, hot environments with many ii clear sky days, allowing for large swings in module temperature, are significantly more damaging. A comparison is drawn between indoor accelerated stress procedures and outdoor exposure, such that an equivalence between test duration and location-dependent outdoor exposure can be determined. It is shown that for the most damaging climate studied, 86 standard thermal cycles is appropriate for one-year of outdoor exposure whereas the least damaging environment would require 11 standard thermal cycles. However, these conclusions may only be applicable to the specific module design which was modelled as the material selection and interaction within a device plays a major role in the thermomechanical behaviour and degradation potential. In addition to a study on the influence of use-environment, a study on the influence of the encapsulating material is conducted with a particular focus on the effects of the viscoelastic properties of the materials. It is shown that the degradation of solder bonds can vary depending on the encapsulating material. Furthermore, the intended use-environment could inform the selection of the encapsulating material. The temperature-dependency of the material properties means that some materials will mitigate thermomechanical degradation mechanisms more than others under certain conditions i.e. hotter or colder climates

On the Economic Value and Price-Responsiveness of Ramp-Constrained Storage

The primary concerns of this paper are twofold: to understand the economic value of storage in the presence of ramp constraints and exogenous electricity prices, and to understand the implications of the associated optimal storage management policy on qualitative and quantitative characteristics of storage response to real-time prices. We present an analytic characterization of the optimal policy, along with the associated finite-horizon time-averaged value of storage. We also derive an analytical upperbound on the infinite-horizon time-averaged value of storage. This bound is valid for any achievable realization of prices when the support of the distribution is fixed, and highlights the dependence of the value of storage on ramp constraints and storage capacity. While the value of storage is a non-decreasing function of price volatility, due to the finite ramp rate, the value of storage saturates quickly as the capacity increases, regardless of volatility. To study the implications of the optimal policy, we first present computational experiments that suggest that optimal utilization of storage can, in expectation, induce a considerable amount of price elasticity near the average price, but little or no elasticity far from it. We then present a computational framework for understanding the behavior of storage as a function of price and the amount of stored energy, and for characterization of the buy/sell phase transition region in the price-state plane. Finally, we study the impact of market-based operation of storage on the required reserves, and show that the reserves may need to be expanded to accommodate market-based storage