With the increasing uncertainty brought by renewable energy sources, it is crucial to price uncertainty and quantify the impact on operation costs. For certain types of uncertainty, such as those following jointly Gaussian distributions, the price of uncertainty has been defined. However, the definition of prices for uncertainties following more general parametric forms of distributions is not clear. To fill the gap, this article proposes a uniform price definition of uncertainties with general parametric distributions and a practical calculation method. First, the price definition for uncertainty is proposed based on the marginal pricing principle, which can be derived from the Lagrangian function of the chance-constrained optimal power flow (CCOPF) problem. Next, the scenario-based method is used to analytically transform CCOPF into a deterministic form. The prices of uncertainties in each scenario can be calculated from the Lagrangian function of the scenario-based model. Then, the relationship between the distribution parameters and the uncertainties in scenarios is revealed. We compute the prices of distribution parameters through the prices of uncertainties in multiple scenarios and their relationship. Finally, this article demonstrates the entire calculation procedure using the correlated non-Gaussian uncertainties as typical examples. The performance of proposed method is verified in the PJM 5-bus, IEEE 30-bus, and 118-bus test systems. It shows that the proposed method can accurately compute the price of uncertainty, ensuring nonnegative market surplus, and keeping the constraint violation probability within the tolerance.

We study the optimal control of multiple-input and multiple-output dynamical systems via the design of neural network-based controllers with stability and output tracking guarantees. While neural network-based nonlinear controllers have shown superior performance in various applications, their lack of provable guarantees has restricted their adoption in high-stake real-world applications. This paper bridges the gap between neural network-based controllers and the need for stabilization guarantees. Using equilibrium-independent passivity, a property present in a wide range of physical systems, we propose neural Proportional-Integral (PI) controllers that have provable guarantees of stability and zero steady-state output tracking error. The key structure is the strict monotonicity on proportional and integral terms, which is parameterized as gradients of strictly convex neural networks (SCNN). We construct SCNN with tunable softplus-$\beta$ activations, which yields universal approximation capability and is also useful in incorporating communication constraints. In addition, the SCNNs serve as Lyapunov functions, giving us end-to-end performance guarantees. Experiments on traffic and power networks demonstrate that the proposed approach improves both transient and steady-state performances, while unstructured neural networks lead to unstable behaviors.

Renewable resources are starting to constitute a growing portion of the total generation mix of the power system. A key difference between renewables and traditional generators is that many renewable resources are managed by individuals, especially in the distribution system. In this paper, we study the capacity investment and pricing problem, where multiple renewable producers compete in a decentralized market. It is known that most deterministic capacity games tend to result in very inefficient equilibria, even when there are a large number of similar players. In contrast, we show that due to the inherent randomness of renewable resources, the equilibria in our capacity game becomes efficient as the number of players grows and coincides with the centralized decision from the social planner's problem. This result provides a new perspective on how to look at the positive influence of randomness in a game framework as well as its contribution to resource planning, scheduling, and bidding. We validate our results by simulation studies using real world data.

Load forecasting is an integral part of power system operations and planning. Due to rising penetrations of rooftop PV, electric vehicles and demand response programs, forecasting the load of individual and a small group of households is becoming increasingly important. Forecasting the load accurately, however, is considerably more difficult when only a few households are included. A way to mitigate this challenge is to provide a set of scenarios instead of one point forecast, so an operator or utility can consider the full range of behaviors. This paper proposes a novel scenario forecasting approach for residential load using flow-based conditional generative models. Compared to existing scenario forecasting methods, our approach can generate scenarios that are not only able to infer possible future realizations of residential load from the observed historical data but also realistic enough to cover a wide range of behaviors. Particularly, the flow-based models utilize a flow of reversible transformations to maximize the value of conditional density function of future load given the past observations. In order to better capture the complex temporal dependency of the forecasted future load, we extend the structure design for the reversible transformations in flow-based conditional generative models by strengthening the coupling between the output and the conditioning input. The simulation results show the flow-based designs outperform existing methods in scenario forecasting for residential load by providing both more accurate and more diverse scenarios.

Paid curbside parking can be advantageously modeled as a network of interdependent queues. To this end, we introduce methods for analyzing a special class of networks of finite capacity queues where drivers arrive from an exogenous source, join the queue if there is an available parking space, or continue to search at an adjacent queue for an available space. Furthermore, we apply this model to estimate the proportion of drivers cruising in the neighborhood of Belltown, Seattle, WA, USA. Using occupancy approximated by parking transaction data, we estimate the percentage of drivers cruising for curbside parking by comparing the rate of drivers unable to find parking to bulk through-traffic measurement data. We find percentages of up to 50% for a Belltown's 1st Ave. depending on the time, day, and direction of travel. We then calculate a per vehicle travel-time cost to social welfare incurred by this proportion: upward of a 10% increase in travel time to all drivers along 1st Ave. Last, we introduce a simulation tool and test assumptions made when estimating interesting performance metrics like the probability of a block-face being full. Our results suggest that while assuming exponential service time distributions is not justified, mean rate solutions under a Markovian relaxation of the problem is comparable to service times representative of parking transaction data in simulation.

We consider the problem of online active learning to collect data for regression modeling. Specifically, we consider a decision maker with a limited experimentation budget who must efficiently learn an underlying linear population model. Our main contribution is a novel threshold-based algorithm for selection of most informative observations; we characterize its performance and fundamental lower bounds. We extend the algorithm and its guarantees to sparse linear regression in high-dimensional settings. Simulations suggest the algorithm is remarkably robust: it provides significant benefits over passive random sampling in real-world datasets that exhibit high nonlinearity and high dimensionality — significantly reducing both the mean and variance of the squared error.

We consider the setting where a collection of time series, modeled as random processes, evolve in a causal manner, and one is interested in learning the graph governing the relationships of these processes. A special case of wide interest and applicability is the setting where the noise is Gaussian and relationships are Markov and linear. We study this setting with two additional features: firstly, each random process has a hidden (latent) state, which we use to model the internal memory possessed by the variables (similar to hidden Markov models). Secondly, each variable can depend on its latent memory state through a random lag (rather than a fixed lag), thus modeling memory recall with differing lags at distinct times. Under this setting, we develop an estimator and prove that under a genericity assumption, the parameters of the model can be learned consistently. We also propose a practical adaption of this estimator, which demonstrates significant performance gains in both synthetic and real-world datasets.

We consider the problem of efficiently determining whether two microphones are listening to the same acoustic signal. This “reference free” acoustic match problem is useful, for example, for allowing networked computers or phones to automatically rendezvous and collaborate whenever they are within earshot. We describe how this problem differs from the well-studied music identification problem. We cast the problem as a hypothesis test, and argue that an effective test statistic may be found using frequency-domain inner products. We validate our approach using a set of 75 speech samples together with inexpensive microphones built in to notebook computers.