inproceedings by Desmond Cai
Economic dispatch and frequency regulation are typically viewed as fundamentally different proble... more Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems, and hence are typically studied separately. In this paper, we frame and study a joint problem that optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We provide sufficient conditions under which the joint problem can be decomposed without loss of optimality into slow and fast timescale problems. These slow and fast timescale problems have appealing interpretations as the economic dispatch and frequency regulation problems respectively. Moreover, the fast timescale problem can be solved using a distributed algorithm that preserves the stability of the network during transients. We also apply this optimal decomposition to propose an efficient market mechanism for economic dispatch that coordinates with frequency regulation.
Papers by Desmond Cai
We study the role of a market maker (or market operator) in a transmission constrained electricit... more We study the role of a market maker (or market operator) in a transmission constrained electricity market. We model the market as a one-shot networked Cournot competition where generators supply quantity bids and load serving entities provide downward sloping inverse demand functions. This mimics the operation of a spot market in a deregulated market structure. In this paper, we focus on possible mechanisms employed by the market maker to balance demand and supply. In particular, we consider three candidate objective functions that the market maker optimizes - social welfare, residual social welfare, and consumer surplus. We characterize the existence of Generalized Nash Equilibrium (GNE) in this setting and demonstrate that market outcomes at equilibrium can be very different under the candidate objective functions.
2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2013
Driven by the national policy to expand renewable generation, as well as the advances in renewabl... more Driven by the national policy to expand renewable generation, as well as the advances in renewable technologies that reduce the cost of small-scale renewable generation units, distributed generation at end users will comprise a significant fraction of electricity generation in the future. We study the problem faced by a social planner who seeks to minimize the long-term discounted costs (associated with both the procurement and the usage of conventional and distributed generation assets), subject to meeting an inelastic demand for electricity. Under mild conditions on the problem parameters, we fully characterize the optimal investment policy for the social planner. We also analyze the impact of problem parameters (e.g., asset lifespans) on the optimal investment policy through numerical examples.
53rd IEEE Conference on Decision and Control, 2014
We study the role of a market maker (or market operator) in a transmission constrained electricit... more We study the role of a market maker (or market operator) in a transmission constrained electricity market. We model the market as a one-shot networked Cournot competition where generators supply quantity bids and load serving entities provide downward sloping inverse demand functions. This mimics the operation of a spot market in a deregulated market structure. In this paper, we focus on possible mechanisms employed by the market maker to balance demand and supply. In particular, we consider three candidate objective functions that the market maker optimizes -social welfare, residual social welfare, and consumer surplus. We characterize the existence of Generalized Nash Equilibrium (GNE) in this setting and demonstrate that market outcomes at equilibrium can be very different under the candidate objective functions.
52nd IEEE Conference on Decision and Control, 2013
IEEE Transactions on Power Systems, 2015
2012 Proceedings IEEE INFOCOM, 2012
Rate adaptation and power control are two key resource allocation mechanisms in multiuser wireles... more Rate adaptation and power control are two key resource allocation mechanisms in multiuser wireless networks. In the presence of interference, how do we jointly optimize end-to-end source rates and link powers to achieve weighted max-min rate fairness for all sources in the network? This optimization problem is hard to solve as physical layer link rate functions are nonlinear, nonconvex, and coupled in the transmit powers. We show that the weighted max-min rate fairness problem can, in fact, be decoupled into separate fairness problems for flow rate and power control. For a large class of physical layer link rate functions, we characterize the optimal solution analytically by a nonlinear Perron-Frobenius theory (through solving a conditional eigenvalue problem) that captures the interaction of multiuser interference. We give an iterative algorithm to compute the optimal flow rate that converges geometrically fast without any parameter configuration. Numerical results show that our iterative algorithm is computationally fast for both the Shannon capacity, CDMA, and piecewise linear link rate functions.
2012 IEEE Third International Conference on Smart Grid Communications (SmartGridComm), 2012
2011 International Symposium of Modeling and Optimization of Mobile, Ad Hoc, and Wireless Networks, 2011
ABSTRACT
2011 IEEE International Conference on Communications (ICC), 2011
Typical formulations of max-min weighted SIR problems involve either a total power constraint or ... more Typical formulations of max-min weighted SIR problems involve either a total power constraint or individual power constraints. These formulations are unable to handle the complexities in multicell networks where each base station can be subject to its own sum power constraint. This paper considers the max-min weighted SIR problem subject to multiple weighted-sum power constraints, where the weights can represent relative power costs of serving different users. First, we derive the uplink-downlink duality principle by applying Lagrange duality to the single-constrained problem. Next, we apply nonlinear Perron-Frobenius theory to derive a closed-form solution for the multiple-constrained problem. Then, by exploiting the structure of the closed-form solution, we relate the multiple-constrained problem with its single-constraint subproblems and establish the dual uplink problem. Finally, we apply nonlinear Perron-Frobenius theory to derive an algorithm which converges geometrically fast to the optimal solution.
2010 IEEE International Symposium on Information Theory, 2010
Designing fast algorithms that adapt the transmit and receive power and beamformers to optimize p... more Designing fast algorithms that adapt the transmit and receive power and beamformers to optimize performance for different users is important in wireless MIMO downlink systems. This paper studies the max-min weighted SIR problem in the downlink, where multiple users are weighted according to priority and are subject to a total power constraint. The difficulty of this nonconvex problem is compounded by the coupling in the transmit and receive beamformers, thereby making it hard to optimize in a distributed fashion. We first show that this problem can be optimally and efficiently computed using a fast algorithm when the channels are rank-one. The optimal transmit and receive power and beamformers are also derived analytically. We then exploit the MIMO uplink-downlink duality to adapt our algorithm to compute a local optimal solution for channels with general rank. 978-1-4244-7892-7/10/$26.00
IEEE Transactions on Signal Processing, 2000
This paper considers the max-min weighted signal-to-interference-plus-noise ratio (SINR) problem ... more This paper considers the max-min weighted signal-to-interference-plus-noise ratio (SINR) problem subject to multiple weighted-sum power constraints, where the weights can represent relative power costs of serving different users. First, we study the power control problem. We apply nonlinear Perron-Frobenius theory to derive closed-form expressions for the optimal value and solution and an iterative algorithm which converges geometrically fast to the optimal solution. Then, we use the structure of the closed-form solution to show that the problem can be decoupled into subproblems each involving only one power constraint. Next, we study the multiple-input-single-output (MISO) transmit beamforming and power control problem. We use uplink-downlink duality to show that this problem can be decoupled into subproblems each involving only one power constraint. We apply this decoupling result to derive an iterative subgradient projection algorithm for the problem.
IEEE Transactions on Signal Processing, 2000
This paper studies the max-min weighted signal-to-interference-plus-noise ratio (SINR) problem in... more This paper studies the max-min weighted signal-to-interference-plus-noise ratio (SINR) problem in the multipleinput-multiple-output (MIMO) downlink, where multiple users are weighted according to priority and are subject to a weighted-sum-power constraint. First, we study the multiple-input-single-output (MISO) and single-input-multipleoutput (SIMO) problems using nonlinear Perron-Frobenius theory. As a by-product, we solve the open problem of convergence for a previously proposed MISO algorithm by Wiesel, Eldar, and Shamai in 2006. Furthermore, we unify our analysis with respect to the previous alternate optimization algorithm proposed by Tan, Chiang, and Srikant in 2009, by showing that our MISO result can, in fact, be derived from their algorithm. Next, we combine our MISO and SIMO results into an algorithm for the MIMO problem. We show that our proposed algorithm is optimal when the channels are rank-one, or when the network is operating in the low signal-to-noise ratio (SNR) region. Finally, we prove the parametric continuity of the MIMO problem in the power constraint, and we use this insight to propose a heuristic initialization strategy for improving the performance of our (generally) suboptimal MIMO algorithm. The proposed initialization strategy exhibits improved performance over random initialization.
2015 IEEE Power & Energy Society General Meeting, 2015
Due to the growth in the number of residential photo voltaic (PV) adoptions in the past five year... more Due to the growth in the number of residential photo voltaic (PV) adoptions in the past five years, there is a need in the electricity industry for a widely-accessible model that predicts the adoption of PV based on different business and policy decisions. We analyze historical adoption patterns and find that monetary savings is the most important factor in the adoption of PV, superseding all socioeconomic factors. On the basis of the findings from our data analysis, we created an application available on Google App Engine (GAE), that allows researchers, policymakers and regulators to study the complex relationship between PV adoption, grid sustainability and utility economics. This application allows users to experiment with a variety of scenarios including different tier structures, subsidies and customer demographics. We showcase the type of analyses that are possible with this application by using it to study the impact of different policies regarding tier structures, fixed charges and PV prices.
IEEE Conference on Decision and Control and European Control Conference, 2011
The growth of wind energy production poses several challenges in its integration in current elect... more The growth of wind energy production poses several challenges in its integration in current electric power systems. In this work, we study how a wind power producer can bid optimally in existing electricity markets. We derive optimal contract size and expected profit for a wind producer under arbitrary penalty function and generation costs. A key feature of our analysis is
Energy Policy, 2013
ABSTRACT The price of electricity supplied from home rooftop photo voltaic (PV) solar cells has f... more ABSTRACT The price of electricity supplied from home rooftop photo voltaic (PV) solar cells has fallen below the retail price of grid electricity in some areas. A number of residential households have an economic incentive to install rooftop PV systems and reduce their purchases of electricity from the grid. A significant portion of the costs incurred by utility companies are fixed costs which must be recovered even as consumption falls. Electricity rates must increase in order for utility companies to recover fixed costs from shrinking sales bases. Increasing rates will, in turn, result in even more economic incentives for customers to adopt rooftop PV. In this paper, we model this feedback between PV adoption and electricity rates and study its impact on future PV penetration and net-metering costs. We find that the most important parameter that determines whether this feedback has an effect is the fraction of customers who adopt PV in any year based solely on the money saved by doing so in that year, independent of the uncertainties of future years. These uncertainties include possible changes in rate structures such as the introduction of connection charges, the possibility of PV prices dropping significantly in the future, possible changes in tax incentives, and confidence in the reliability and maintainability of PV.
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inproceedings by Desmond Cai
Papers by Desmond Cai