https://netfiles.uiuc.edu/meyn/www/spm_files/Market06/Market06.html
Abstract:
This paper examines a dynamic general equilibrium model with supply friction. With or without friction, the competitive equilibrium is efficient. Without friction, the market price is completely determined by the marginal production cost and the consumers gain positive surplus from trading. If friction is present, no matter how small, then the market price fluctuates between zero and the ``choke-up'' price, without any tendency to converge to the marginal production cost, exhibiting considerable volatility. The gains from trading can deviate significantly from the prediction of the static model in the efficient market outcome. Also considered is a monopolistic market model in which a single firm determines market prices as a function of time. The market outcome is identical in the case of a continuum of consumers. In a model with a single consumer the market prices increase, and the supplier extracts the entire gain from trading.
The document outlines different SEO packages - Light, Starter, Professional, and Enterprise - offered by Sonitek International. Each package provides various on-page and off-page SEO services and deliverables such as keyword research, content optimization, link building, and social media marketing. The packages differ in the number of guaranteed and targeted keyword phrases, pages optimized, and links submitted. The Light package offers basic services starting at $1,200 for 6 months while the Enterprise package provides advanced optimization starting at $11,500 for 12 months.
The document contains 11 figures showing maps related to the proposed AWA Goodhue, LLC Wind Project in Goodhue County, Minnesota. Figure 1 shows the preliminary turbine layout and relevant infrastructure. Figure 2 shows signed easements and participation agreements from landowners. Figure 3 shows occupied residences and viable turbine areas with setback requirements. Figures 4-5 show further details on viable turbine areas and requested municipal buffer zones. Figures 6-8 provide photos of views from different locations. Figures 9-11 show predicted noise contours from the project in the context of the landscape and infrastructure.
Genesis Social Welfare Foundation celebrated its 21st anniversary this year. For over two decades, the foundation has worked to improve lives and communities through various social programs. These programs provide aid to the underprivileged, homeless, and those in need.
Getting things right: optimal tax policy with labor market dualityGRAPE
This document summarizes an analysis of optimal tax policy in labor markets with duality. It presents a model with two types of labor contracts (typical and atypical) and two types of labor taxes (unavoidable income tax and avoidable social security contributions). The model is calibrated using data from EU countries to examine how tax revenues respond to different tax rates and compositions. The results show that tax revenues are more responsive to avoidable social security taxes than unavoidable income taxes due to evasion incentives. Although the revenue-maximizing tax rate is flat, the model predictions align reasonably well with real-world data on irregular employment across countries.
Sustainable Urban Water Use - University of North CarolinaDanousis85z
The document discusses a conference on sustainable urban water use and conservation planning. It provides an agenda for the day including presentations on using planning tools to project costs and benefits of conservation, driving efficiency through water pricing, and combining price and non-price programs in a new utility business model. The final session will continue the dialogue on these topics in a group discussion.
Smart Energy Utilities based on Real-Time GIS Web Services and Internet of Th...Reza Nourjou, Ph.D.
The document discusses a system for providing real-time outage and economic loss information to support decision making during power outages. The system connects to sensors to collect outage data, connects to web services to calculate economic losses, and publishes a real-time web map service (WMS) displaying outage status and losses. This allows applications to access and display updated outage and loss maps. The system provides situational awareness during disasters and helps prioritize restoration to minimize economic impacts from power outages.
DG Energy’s strategy for stimulating growth and jobs in the renewable energy ...Dublin Chamber of Commerce
Presentation to Dublin Chamber's Brussels study mission on DG Energy’s strategy for stimulating growth and jobs in the renewable energy sector by Tom Howes, Directorate General for Energy.
The study mission was kindly supported by KBC Bank.
State RPS targets and the CEC role in achieving success [CSTP 2010]Smithers Apex
The document discusses California's Renewables Portfolio Standard (RPS) and the role of the California Energy Commission in helping the state achieve its RPS goals. Key points include:
- The RPS was established in 2002 with a goal of 20% renewable energy by 2010. This was later increased to 33% by 2020 under executive orders.
- The Energy Commission certifies renewable facilities, tracks RPS compliance, and distributes incentive payments. It also conducts research and analysis to support renewable energy development.
- California has made progress towards its RPS targets but faces challenges in integrating high levels of renewables and addressing environmental and financing issues for new projects. The report recommends continued efforts to meet the 33% by 2020
The document outlines different SEO packages - Light, Starter, Professional, and Enterprise - offered by Sonitek International. Each package provides various on-page and off-page SEO services and deliverables such as keyword research, content optimization, link building, and social media marketing. The packages differ in the number of guaranteed and targeted keyword phrases, pages optimized, and links submitted. The Light package offers basic services starting at $1,200 for 6 months while the Enterprise package provides advanced optimization starting at $11,500 for 12 months.
The document contains 11 figures showing maps related to the proposed AWA Goodhue, LLC Wind Project in Goodhue County, Minnesota. Figure 1 shows the preliminary turbine layout and relevant infrastructure. Figure 2 shows signed easements and participation agreements from landowners. Figure 3 shows occupied residences and viable turbine areas with setback requirements. Figures 4-5 show further details on viable turbine areas and requested municipal buffer zones. Figures 6-8 provide photos of views from different locations. Figures 9-11 show predicted noise contours from the project in the context of the landscape and infrastructure.
Genesis Social Welfare Foundation celebrated its 21st anniversary this year. For over two decades, the foundation has worked to improve lives and communities through various social programs. These programs provide aid to the underprivileged, homeless, and those in need.
Getting things right: optimal tax policy with labor market dualityGRAPE
This document summarizes an analysis of optimal tax policy in labor markets with duality. It presents a model with two types of labor contracts (typical and atypical) and two types of labor taxes (unavoidable income tax and avoidable social security contributions). The model is calibrated using data from EU countries to examine how tax revenues respond to different tax rates and compositions. The results show that tax revenues are more responsive to avoidable social security taxes than unavoidable income taxes due to evasion incentives. Although the revenue-maximizing tax rate is flat, the model predictions align reasonably well with real-world data on irregular employment across countries.
Sustainable Urban Water Use - University of North CarolinaDanousis85z
The document discusses a conference on sustainable urban water use and conservation planning. It provides an agenda for the day including presentations on using planning tools to project costs and benefits of conservation, driving efficiency through water pricing, and combining price and non-price programs in a new utility business model. The final session will continue the dialogue on these topics in a group discussion.
Smart Energy Utilities based on Real-Time GIS Web Services and Internet of Th...Reza Nourjou, Ph.D.
The document discusses a system for providing real-time outage and economic loss information to support decision making during power outages. The system connects to sensors to collect outage data, connects to web services to calculate economic losses, and publishes a real-time web map service (WMS) displaying outage status and losses. This allows applications to access and display updated outage and loss maps. The system provides situational awareness during disasters and helps prioritize restoration to minimize economic impacts from power outages.
DG Energy’s strategy for stimulating growth and jobs in the renewable energy ...Dublin Chamber of Commerce
Presentation to Dublin Chamber's Brussels study mission on DG Energy’s strategy for stimulating growth and jobs in the renewable energy sector by Tom Howes, Directorate General for Energy.
The study mission was kindly supported by KBC Bank.
State RPS targets and the CEC role in achieving success [CSTP 2010]Smithers Apex
The document discusses California's Renewables Portfolio Standard (RPS) and the role of the California Energy Commission in helping the state achieve its RPS goals. Key points include:
- The RPS was established in 2002 with a goal of 20% renewable energy by 2010. This was later increased to 33% by 2020 under executive orders.
- The Energy Commission certifies renewable facilities, tracks RPS compliance, and distributes incentive payments. It also conducts research and analysis to support renewable energy development.
- California has made progress towards its RPS targets but faces challenges in integrating high levels of renewables and addressing environmental and financing issues for new projects. The report recommends continued efforts to meet the 33% by 2020
Quasi-Stochastic Approximation: Algorithm Design Principles with Applications...Sean Meyn
Many machine learning and optimization algorithms solve hidden root-finding problems through the magic of stochastic approximation (SA). Unfortunately, these algorithms are slow to converge: the optimal convergence rate for the mean squared error (MSE) is of order O(n⁻¹) at iteration n.
Far faster convergence rates are possible by reconsidering the design of exploration signals used in these algorithms. In this lecture the focus is on quasi-stochastic approximation (QSA), in which a multi-dimensional clock process defines exploration. It is found that algorithms can be designed to achieve a MSE convergence rate approaching O(n⁻⁴).
Although the framework is entirely deterministic, this new theory leans heavily on concepts from the theory of Markov processes. Most critical is Poisson’s equation to transform the QSA equations into a mean flow with additive “noise” with attractive properties. Existence of solutions to Poisson’s equation is based on Baker’s Theorem from number theory---to the best of our knowledge, this is the first time this theorem has been applied to any topic in engineering!
The theory is illustrated with applications to gradient free optimization.
Joint research with Caio Lauand, current graduate student at UF.
References
[1] C. Kalil Lauand and S. Meyn. Approaching quartic convergence rates for quasi-stochastic approximation with application to gradient-free optimization. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Systems, volume 35, pages 15743–15756. Curran Associates, Inc., 2022.
[2] C. K. Lauand and S. Meyn. Quasi-stochastic approximation: Design principles with applications to extremum seeking control. IEEE Control Systems Magazine, 43(5):111–136, Oct 2023.
[3] C. K. Lauand and S. Meyn. The curse of memory in stochastic approximation. In Proc. IEEE Conference on Decision and Control, pages 7803–7809, 2023. Extended version. arXiv 2309.02944, 2023.
Lecture 1 from https://irdta.eu/deeplearn/2022su/
Covers concepts from Part 1 of my new book, https://meyn.ece.ufl.edu/2021/08/01/control-systems-and-reinforcement-learning/
Lecture 2 from https://irdta.eu/deeplearn/2022su/
Covers final chapters of my new book, https://meyn.ece.ufl.edu/2021/08/01/control-systems-and-reinforcement-learning/
All about algorithm design for TD- and Q-learning in a stochastic environment.
Lecture 2 from https://irdta.eu/deeplearn/2022su/
Covers concepts from Part 2 of my new book, https://meyn.ece.ufl.edu/2021/08/01/control-systems-and-reinforcement-learning/
Focus on algorithm design in general
https://www.newton.ac.uk/seminar/20190110160017001
Abstract: For decades power systems academics have proclaimed the need for real time prices to create a more efficient grid. The rationale is economics 101: proper price signals will lead to an efficient outcome. In this talk we will review a bit of economics 101; in particular, the definition of efficiency. We will see that the theory supports the real-time price paradigm, provided we impose a particular model of rationality. It is argued however that this standard model of consumer utility does not match reality: the products of interest to the various "agents" are complex functions of time. The product of interest to a typical consumer is only loosely related to electric power -- the quantity associated with price signals. There is good news: an efficient outcome is easy to describe, and we have the control technology to achieve it. We need supporting market designs that respect dynamics and the impact of fixed costs that are inherent in power systems engineering, recognizing that we need incentives on many time-scales. Most likely the needed economic theory will be based on an emerging theory of efficient and robust contract design.
State Space Collapse in Resource Allocation for Demand Dispatch - May 2019Sean Meyn
https://www.newton.ac.uk/seminar/20190503133014301 Abstract: The term demand dispatch refers to the creation of virtual energy storage from deferrable loads. The key to success is automation: an appropriate distributed control architecture ensures that bounds on quality of service (QoS) are met and simultaneously ensures that the loads provide aggregate grid services comparable to a large battery system. A question addressed in our 2018 CDC paper is how to control a large collection of heterogeneous loads. This is in part a resource allocation problem, since different classes of loads are more valuable for different services. The evolution of QoS for each class of loads is modeled via a state of charge surrogate, which is a part of the leaky battery model for the load classes. The goal of this paper is to unveil the structure of the optimal solution and investigate short term market implications. The following conclusions are obtained:
(i) Optimal power deviation for each of the M 2 load classes evolves in a two-dimensional manifold.
(ii) Marginal cost for each load class evolves in a two-dimensional subspace: spanned by a co-state process and its derivative.
(iii) The preceding conclusions are applied to construct a dynamic competitive equilibrium model, in which the consumer utility is the negative of the cost of deviation from ideal QoS. It is found that a competitive equilibrium exists, and that the resulting price signals are very different than what would be obtained based on the standard assumption that the utility is with respect to power consumption. It is argued that price signals are not useful for control of the grid since they are inherently open loop. However, the analysis may inform the creation of heuristics for payments within the context of contracts for services with consumers.
Based on the Berkeley Simons Institute tutorial -- video available here:
https://simons.berkeley.edu/talks/sean-meyn-3-29-18
and the 2018 lecture at ISMP Bordeaux
And, a six hour short course held in France around the same time:
http://www.thematicsemester.com/?p=184#more-184
The slides can be downloaded from this site: click "outline" under the heading
"Reinventing Control and Economics in the Power Grid"
Reinforcement learning: hidden theory, and new super-fast algorithms
Lecture presented at the Center for Systems and Control (CSC@USC) and Ming Hsieh Institute for Electrical Engineering,
February 21, 2018
Stochastic Approximation algorithms are used to approximate solutions to fixed point equations that involve expectations of functions with respect to possibly unknown distributions. The most famous examples today are TD- and Q-learning algorithms. The first half of this lecture will provide an overview of stochastic approximation, with a focus on optimizing the rate of convergence. A new approach to optimize the rate of convergence leads to the new Zap Q-learning algorithm. Analysis suggests that its transient behavior is a close match to a deterministic Newton-Raphson implementation, and numerical experiments confirm super fast convergence.
Based on
@article{devmey17a,
Title = {Fastest Convergence for {Q-learning}},
Author = {Devraj, Adithya M. and Meyn, Sean P.},
Journal = {NIPS 2017 and ArXiv e-prints},
Year = 2017}
Reinforcement Learning: Hidden Theory and New Super-Fast AlgorithmsSean Meyn
A tutorial, and very new algorithms -- more details on arXiv and at NIPS 2017 https://arxiv.org/abs/1707.03770
Part of the Data Science Summer School at École Polytechnique: http://www.ds3-datascience-polytechnique.fr/program/
---------
2018 Updates:
See Zap slides from ISMP 2018 for new inverse-free optimal algorithms
Simons tutorial, March 2018 [one month before most discoveries announced at ISMP]
Part I (Basics, with focus on variance of algorithms)
https://www.youtube.com/watch?v=dhEF5pfYmvc
Part II (Zap Q-learning)
https://www.youtube.com/watch?v=Y3w8f1xIb6s
Big 2017 survey on variance in SA:
Fastest convergence for Q-learning
https://arxiv.org/abs/1707.03770
You will find the infinite-variance Q result there.
Our NIPS 2017 paper is distilled from this.
State estimation and Mean-Field Control with application to demand dispatchSean Meyn
Y. Chen, A. Busic, and S. Meyn.
In 54th IEEE Conference on Decision and Control, Dec. 2015.
See also journal version of the paper,
http://arxiv.org/abs/1504.00088
Demand-Side Flexibility for Reliable Ancillary ServicesSean Meyn
https://vimeo.com/album/3275353
Lecture presented at ANALYTIC RESEARCH FOUNDATIONS FOR THE NEXT-GENERATION ELECTRIC GRID - A National Research Council Workshop. Irvine, California, Feb. 11--12, 2015.
http://sites.nationalacademies.org/DEPS/BMSA/DEPS_152682
Demand-Side Flexibility for Reliable Ancillary Services in a Smart Grid: Elim...Sean Meyn
A survey of our 2015 HICSS article (reference below), which is largely a survey of demand response technology developed at the University of Florida.
Presented at the Workshop on Electricity Markets and Optimization 27th of November 2014. Aalborg University, Denmark
@inproceedings{barbusmey14,
Address = {Kauai, Hawaii},
Author = {Barooah, Prabir and Bu\v{s}i\'{c}, Ana and Meyn, Sean},
Booktitle = {Proc. {48th Annual Hawaii International Conference on System Sciences (HICSS)}},
Note = {(invited)},
Publisher = {University of Hawaii},
Title = {Spectral Decomposition of Demand-Side Flexibility for Reliable Ancillary Services in a Smart Grid},
Year = {2015}}
Why Do We Ignore Risk in Power Economics?Sean Meyn
My personal view of US energy policy, and how we can better incentivize innovation.
Sustainability Lecture delivered November 25th.
Sustainability Science Centre
The Natural History Museum of Denmark
University of Copenhagen
Universitetsparken 15, Building 3, 3. floor,
DK-2100 Copenhagen, Denmark
Distributed Randomized Control for Ancillary Service to the Power GridSean Meyn
Lecture given at MIT May 6, 2014 (shorter version given at ITA UCSD on Valentines Day 2014).
Based on joint research with Ana Busic, Prabir Barooah, Jordan Erhan, and Yue Chen, contained in three papers at http://www.meyn.ece.ufl.edu/pp
Renewable energy sources such as wind and solar power have a high degree of unpredictability and time-variation, which makes balancing demand and supply challenging. One possible way to address this challenge is to harness the inherent flexibility in demand of many types of loads.
At the grid-level, ancillary services may be seen as actuators in a large disturbance rejection problem. It is argued that a randomized control architecture for an individual load can be designed to meet a number of objectives: The need to protect consumer privacy, the value of simple control of the aggregate at the grid level, and the need to avoid synchronization of loads that can lead to detrimental spikes in demand.
I will describe new design techniques for randomized control that lend themselves to control design and analysis. It is based on the following sequence of steps:
1. A parameterized family of average-reward MDP models is introduced whose solution defines the local randomized policy. The balancing authority broadcasts a common real-time control signal to the loads; at each time, each load changes state based on its own current state and the value of the common control signal.
2. The mean field limit defines an aggregate model for grid-level control. Special structure of the Markov model leads to a simple linear time-invariant (LTI) approximation. The LTI model is passive when the nominal Markov model is reversible.
3. Additional local control is used to put strict bounds on individual quality of service of each load, without impacting the quality of grid-level ancillary service.
Examples of application include chillers, flexible manufacturing, and even residential pool pumps. It is shown through simulation how pool pumps in Florida can supply a substantial amount of the ancillary service needs of the Eastern U.S.
Ancillary service to the grid from deferrable loads: the case for intelligent...Sean Meyn
Invited Lecture on Control Techniques for the Future Power Grid, in Modern Probabilistic Techniques for Design, Stability, Large Deviations, and Performance Analysis of Communication, Social, Energy, and Other Stochastic Systems and Networks 12 – 16 August 2013
2012 Tutorial: Markets for Differentiated Electric Power ProductsSean Meyn
ACC 2012 Tutorial
http://accworkshop12.mit.edu
The talk will review the many services needed in today's grid, and those that will be more important in the future. It will also review recent competitive equilibrium theory for the highly dynamic markets that may emerge in tomorrow's grid. In particular, to combat volatility from increasing penetration of renewable energy resources, there will be greater need for regulation services at various time-scales. There is enormous potential to secure these ancillary services via demand response. However, there is an obsession today with the promotion of real time prices to incentivize demand response. All evidence strongly suggests that this is a bad idea: 1) In 2011, massive price swings in the real-time market generated anger in Texas and New Zealand 2) Our own research shows that this is to be expected: in a completive equilibrium real-time prices will reach the choke up price (which was recently estimated at 1/4 million dollars). With transmission constraints, our research concludes that prices can go much higher. 3) A recent EIA study shows that consumers are scared of smart meters - they do not trust utility companies to experiment with their meters, or their power bills. We must then ask, is there any motivation to focus on markets in a real-time setting? The speaker believes there is none. Explanations will be given, and alternative visions will be proposed.
The systems & control research community has developed a range of tools for understanding and controlling complex systems. Some of these techniques are model-based: Using a simple model we obtain insight regarding the structure of effective policies for control. The talk will survey how this point of view can be applied to approach resource allocation problems, such as those that will arise in the next-generation energy grid. We also show how insight from this kind of analysis can be used to construct architectures for reinforcement learning algorithms used in a broad range of applications.
Much of the talk is a survey from a recent book by the author with a similar title,
Control Techniques for Complex Networks. Cambridge University Press, 2007.
https://netfiles.uiuc.edu/meyn/www/spm_files/CTCN/CTCN.html
Tutorial for Energy Systems Week - Cambridge 2010Sean Meyn
The document discusses several issues related to dynamic power systems including:
1) Political mandates for renewable energy are changing rapidly and coupled generators and consumers can lead to instability.
2) Power systems are complex interconnected networks that require reliable operation while market power poses risks.
3) Balancing supply and demand is challenging with intermittent renewable resources like wind.
4) Power flow is subject to physical constraints that create friction in the system.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
Quasi-Stochastic Approximation: Algorithm Design Principles with Applications...Sean Meyn
Many machine learning and optimization algorithms solve hidden root-finding problems through the magic of stochastic approximation (SA). Unfortunately, these algorithms are slow to converge: the optimal convergence rate for the mean squared error (MSE) is of order O(n⁻¹) at iteration n.
Far faster convergence rates are possible by reconsidering the design of exploration signals used in these algorithms. In this lecture the focus is on quasi-stochastic approximation (QSA), in which a multi-dimensional clock process defines exploration. It is found that algorithms can be designed to achieve a MSE convergence rate approaching O(n⁻⁴).
Although the framework is entirely deterministic, this new theory leans heavily on concepts from the theory of Markov processes. Most critical is Poisson’s equation to transform the QSA equations into a mean flow with additive “noise” with attractive properties. Existence of solutions to Poisson’s equation is based on Baker’s Theorem from number theory---to the best of our knowledge, this is the first time this theorem has been applied to any topic in engineering!
The theory is illustrated with applications to gradient free optimization.
Joint research with Caio Lauand, current graduate student at UF.
References
[1] C. Kalil Lauand and S. Meyn. Approaching quartic convergence rates for quasi-stochastic approximation with application to gradient-free optimization. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Systems, volume 35, pages 15743–15756. Curran Associates, Inc., 2022.
[2] C. K. Lauand and S. Meyn. Quasi-stochastic approximation: Design principles with applications to extremum seeking control. IEEE Control Systems Magazine, 43(5):111–136, Oct 2023.
[3] C. K. Lauand and S. Meyn. The curse of memory in stochastic approximation. In Proc. IEEE Conference on Decision and Control, pages 7803–7809, 2023. Extended version. arXiv 2309.02944, 2023.
Lecture 1 from https://irdta.eu/deeplearn/2022su/
Covers concepts from Part 1 of my new book, https://meyn.ece.ufl.edu/2021/08/01/control-systems-and-reinforcement-learning/
Lecture 2 from https://irdta.eu/deeplearn/2022su/
Covers final chapters of my new book, https://meyn.ece.ufl.edu/2021/08/01/control-systems-and-reinforcement-learning/
All about algorithm design for TD- and Q-learning in a stochastic environment.
Lecture 2 from https://irdta.eu/deeplearn/2022su/
Covers concepts from Part 2 of my new book, https://meyn.ece.ufl.edu/2021/08/01/control-systems-and-reinforcement-learning/
Focus on algorithm design in general
https://www.newton.ac.uk/seminar/20190110160017001
Abstract: For decades power systems academics have proclaimed the need for real time prices to create a more efficient grid. The rationale is economics 101: proper price signals will lead to an efficient outcome. In this talk we will review a bit of economics 101; in particular, the definition of efficiency. We will see that the theory supports the real-time price paradigm, provided we impose a particular model of rationality. It is argued however that this standard model of consumer utility does not match reality: the products of interest to the various "agents" are complex functions of time. The product of interest to a typical consumer is only loosely related to electric power -- the quantity associated with price signals. There is good news: an efficient outcome is easy to describe, and we have the control technology to achieve it. We need supporting market designs that respect dynamics and the impact of fixed costs that are inherent in power systems engineering, recognizing that we need incentives on many time-scales. Most likely the needed economic theory will be based on an emerging theory of efficient and robust contract design.
State Space Collapse in Resource Allocation for Demand Dispatch - May 2019Sean Meyn
https://www.newton.ac.uk/seminar/20190503133014301 Abstract: The term demand dispatch refers to the creation of virtual energy storage from deferrable loads. The key to success is automation: an appropriate distributed control architecture ensures that bounds on quality of service (QoS) are met and simultaneously ensures that the loads provide aggregate grid services comparable to a large battery system. A question addressed in our 2018 CDC paper is how to control a large collection of heterogeneous loads. This is in part a resource allocation problem, since different classes of loads are more valuable for different services. The evolution of QoS for each class of loads is modeled via a state of charge surrogate, which is a part of the leaky battery model for the load classes. The goal of this paper is to unveil the structure of the optimal solution and investigate short term market implications. The following conclusions are obtained:
(i) Optimal power deviation for each of the M 2 load classes evolves in a two-dimensional manifold.
(ii) Marginal cost for each load class evolves in a two-dimensional subspace: spanned by a co-state process and its derivative.
(iii) The preceding conclusions are applied to construct a dynamic competitive equilibrium model, in which the consumer utility is the negative of the cost of deviation from ideal QoS. It is found that a competitive equilibrium exists, and that the resulting price signals are very different than what would be obtained based on the standard assumption that the utility is with respect to power consumption. It is argued that price signals are not useful for control of the grid since they are inherently open loop. However, the analysis may inform the creation of heuristics for payments within the context of contracts for services with consumers.
Based on the Berkeley Simons Institute tutorial -- video available here:
https://simons.berkeley.edu/talks/sean-meyn-3-29-18
and the 2018 lecture at ISMP Bordeaux
And, a six hour short course held in France around the same time:
http://www.thematicsemester.com/?p=184#more-184
The slides can be downloaded from this site: click "outline" under the heading
"Reinventing Control and Economics in the Power Grid"
Reinforcement learning: hidden theory, and new super-fast algorithms
Lecture presented at the Center for Systems and Control (CSC@USC) and Ming Hsieh Institute for Electrical Engineering,
February 21, 2018
Stochastic Approximation algorithms are used to approximate solutions to fixed point equations that involve expectations of functions with respect to possibly unknown distributions. The most famous examples today are TD- and Q-learning algorithms. The first half of this lecture will provide an overview of stochastic approximation, with a focus on optimizing the rate of convergence. A new approach to optimize the rate of convergence leads to the new Zap Q-learning algorithm. Analysis suggests that its transient behavior is a close match to a deterministic Newton-Raphson implementation, and numerical experiments confirm super fast convergence.
Based on
@article{devmey17a,
Title = {Fastest Convergence for {Q-learning}},
Author = {Devraj, Adithya M. and Meyn, Sean P.},
Journal = {NIPS 2017 and ArXiv e-prints},
Year = 2017}
Reinforcement Learning: Hidden Theory and New Super-Fast AlgorithmsSean Meyn
A tutorial, and very new algorithms -- more details on arXiv and at NIPS 2017 https://arxiv.org/abs/1707.03770
Part of the Data Science Summer School at École Polytechnique: http://www.ds3-datascience-polytechnique.fr/program/
---------
2018 Updates:
See Zap slides from ISMP 2018 for new inverse-free optimal algorithms
Simons tutorial, March 2018 [one month before most discoveries announced at ISMP]
Part I (Basics, with focus on variance of algorithms)
https://www.youtube.com/watch?v=dhEF5pfYmvc
Part II (Zap Q-learning)
https://www.youtube.com/watch?v=Y3w8f1xIb6s
Big 2017 survey on variance in SA:
Fastest convergence for Q-learning
https://arxiv.org/abs/1707.03770
You will find the infinite-variance Q result there.
Our NIPS 2017 paper is distilled from this.
State estimation and Mean-Field Control with application to demand dispatchSean Meyn
Y. Chen, A. Busic, and S. Meyn.
In 54th IEEE Conference on Decision and Control, Dec. 2015.
See also journal version of the paper,
http://arxiv.org/abs/1504.00088
Demand-Side Flexibility for Reliable Ancillary ServicesSean Meyn
https://vimeo.com/album/3275353
Lecture presented at ANALYTIC RESEARCH FOUNDATIONS FOR THE NEXT-GENERATION ELECTRIC GRID - A National Research Council Workshop. Irvine, California, Feb. 11--12, 2015.
http://sites.nationalacademies.org/DEPS/BMSA/DEPS_152682
Demand-Side Flexibility for Reliable Ancillary Services in a Smart Grid: Elim...Sean Meyn
A survey of our 2015 HICSS article (reference below), which is largely a survey of demand response technology developed at the University of Florida.
Presented at the Workshop on Electricity Markets and Optimization 27th of November 2014. Aalborg University, Denmark
@inproceedings{barbusmey14,
Address = {Kauai, Hawaii},
Author = {Barooah, Prabir and Bu\v{s}i\'{c}, Ana and Meyn, Sean},
Booktitle = {Proc. {48th Annual Hawaii International Conference on System Sciences (HICSS)}},
Note = {(invited)},
Publisher = {University of Hawaii},
Title = {Spectral Decomposition of Demand-Side Flexibility for Reliable Ancillary Services in a Smart Grid},
Year = {2015}}
Why Do We Ignore Risk in Power Economics?Sean Meyn
My personal view of US energy policy, and how we can better incentivize innovation.
Sustainability Lecture delivered November 25th.
Sustainability Science Centre
The Natural History Museum of Denmark
University of Copenhagen
Universitetsparken 15, Building 3, 3. floor,
DK-2100 Copenhagen, Denmark
Distributed Randomized Control for Ancillary Service to the Power GridSean Meyn
Lecture given at MIT May 6, 2014 (shorter version given at ITA UCSD on Valentines Day 2014).
Based on joint research with Ana Busic, Prabir Barooah, Jordan Erhan, and Yue Chen, contained in three papers at http://www.meyn.ece.ufl.edu/pp
Renewable energy sources such as wind and solar power have a high degree of unpredictability and time-variation, which makes balancing demand and supply challenging. One possible way to address this challenge is to harness the inherent flexibility in demand of many types of loads.
At the grid-level, ancillary services may be seen as actuators in a large disturbance rejection problem. It is argued that a randomized control architecture for an individual load can be designed to meet a number of objectives: The need to protect consumer privacy, the value of simple control of the aggregate at the grid level, and the need to avoid synchronization of loads that can lead to detrimental spikes in demand.
I will describe new design techniques for randomized control that lend themselves to control design and analysis. It is based on the following sequence of steps:
1. A parameterized family of average-reward MDP models is introduced whose solution defines the local randomized policy. The balancing authority broadcasts a common real-time control signal to the loads; at each time, each load changes state based on its own current state and the value of the common control signal.
2. The mean field limit defines an aggregate model for grid-level control. Special structure of the Markov model leads to a simple linear time-invariant (LTI) approximation. The LTI model is passive when the nominal Markov model is reversible.
3. Additional local control is used to put strict bounds on individual quality of service of each load, without impacting the quality of grid-level ancillary service.
Examples of application include chillers, flexible manufacturing, and even residential pool pumps. It is shown through simulation how pool pumps in Florida can supply a substantial amount of the ancillary service needs of the Eastern U.S.
Ancillary service to the grid from deferrable loads: the case for intelligent...Sean Meyn
Invited Lecture on Control Techniques for the Future Power Grid, in Modern Probabilistic Techniques for Design, Stability, Large Deviations, and Performance Analysis of Communication, Social, Energy, and Other Stochastic Systems and Networks 12 – 16 August 2013
2012 Tutorial: Markets for Differentiated Electric Power ProductsSean Meyn
ACC 2012 Tutorial
http://accworkshop12.mit.edu
The talk will review the many services needed in today's grid, and those that will be more important in the future. It will also review recent competitive equilibrium theory for the highly dynamic markets that may emerge in tomorrow's grid. In particular, to combat volatility from increasing penetration of renewable energy resources, there will be greater need for regulation services at various time-scales. There is enormous potential to secure these ancillary services via demand response. However, there is an obsession today with the promotion of real time prices to incentivize demand response. All evidence strongly suggests that this is a bad idea: 1) In 2011, massive price swings in the real-time market generated anger in Texas and New Zealand 2) Our own research shows that this is to be expected: in a completive equilibrium real-time prices will reach the choke up price (which was recently estimated at 1/4 million dollars). With transmission constraints, our research concludes that prices can go much higher. 3) A recent EIA study shows that consumers are scared of smart meters - they do not trust utility companies to experiment with their meters, or their power bills. We must then ask, is there any motivation to focus on markets in a real-time setting? The speaker believes there is none. Explanations will be given, and alternative visions will be proposed.
The systems & control research community has developed a range of tools for understanding and controlling complex systems. Some of these techniques are model-based: Using a simple model we obtain insight regarding the structure of effective policies for control. The talk will survey how this point of view can be applied to approach resource allocation problems, such as those that will arise in the next-generation energy grid. We also show how insight from this kind of analysis can be used to construct architectures for reinforcement learning algorithms used in a broad range of applications.
Much of the talk is a survey from a recent book by the author with a similar title,
Control Techniques for Complex Networks. Cambridge University Press, 2007.
https://netfiles.uiuc.edu/meyn/www/spm_files/CTCN/CTCN.html
Tutorial for Energy Systems Week - Cambridge 2010Sean Meyn
The document discusses several issues related to dynamic power systems including:
1) Political mandates for renewable energy are changing rapidly and coupled generators and consumers can lead to instability.
2) Power systems are complex interconnected networks that require reliable operation while market power poses risks.
3) Balancing supply and demand is challenging with intermittent renewable resources like wind.
4) Power flow is subject to physical constraints that create friction in the system.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
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This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
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Webinars: https://pecb.com/webinars
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Slideshare: http://www.slideshare.net/PECBCERTIFICATION
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...Diana Rendina
Librarians are leading the way in creating future-ready citizens – now we need to update our spaces to match. In this session, attendees will get inspiration for transforming their library spaces. You’ll learn how to survey students and patrons, create a focus group, and use design thinking to brainstorm ideas for your space. We’ll discuss budget friendly ways to change your space as well as how to find funding. No matter where you’re at, you’ll find ideas for reimagining your space in this session.
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
Efficiency and Marginal Cost Pricing in Dynamic Competitive Markets with Friction
1. Dynamics of Prices in Electric Power Networks
Sean Meyn Prices
Normalized demand
Reserve
Department of ECE
and the Coordinated Science Laboratory
University of Illinois
Joint work with M. Chen and I-K. Cho
NSF support: ECS 02-17836 & 05-23620 Control Techniques for Complex Networks
DOE Support: http://www.sc.doe.gov/grants/FAPN08-13.html
Extending the Realm of Optimization for Complex Systems: Uncertainty, Competition and Dynamics
PIs: Uday V. Shanbhag, Tamer Basar, Sean P. Meyn and Prashant G. Mehta
2. OREGON
California’s 25,000
Mile Electron Highway COAL
LEGEND
GEOTHERMAL
HYDROELECTRIC
NUCLEAR
OIL/GAS
BIOMASS
MUNICIPAL SOLID
WASTE (MSW)
SOLAR
WIND AREAS
SAN
FRANCISCO
What is the value
of improved transmission? NEVADA
More responsive ancillary service?
How does a centralized planner
optimize capacity?
MEXICO
Is there an efficient decentralized solution?
3. Meeting Calendar | OASIS | Employment | Site Map | Contact Us
HOME | Search
http://www.caiso.com/outlook/outlook.html
September 28, 2008
40,000 MW
4,000
Megawatts
Available Resources
The current forecast of generating and import
resources available to serve the demand for energy 30,000 MW
within the California ISO service area
Forecast Demand
Forecast of the demand expected today.
The procurement of energy resources for the day
is based on this forecast 20,000 MW Day Ahead Demand Forecast Revised Demand Forecast Actual Demand Hour Beginning
Available Resources Forecast
Actual Demand
Today's actual system demand
Revised Demand Forecast
The current forecast of the system demand expected throughout the remainder of the day.
This forecast is updated hourly.
4. Meeting Calendar | OASIS | Employment | Site Map | Contact Us
HOME | Search http://www.caiso.com
Emergency Notices
Generating
Reserves
7.0% Stage 1
Stage 1 Generating reserves less than requirements
Emergency
Emergency (Continuously recalculated. Between 6.0% & 7.0%)
6.0%
5.0%
Stage 2
Stage 2 Generating reserves less than 5.0%
4.0% Emergency
Emergency
3.0%
Stage 3
Stage 3 Generating reserves less than largest contingency
2.0%
Emergency
Emergency (Continuously recalculated. Between 1.5% & 3.0%)
1.0%
0.0%
7. First Impressions:
July 1998: first signs of "serious market dysfunction" in California
Lessons From the California “Apocalypse:”
Jurisdiction Over Electric Utilities
Nicholas W. Fels and Frank R. Lindh
Energy Law Journal, Vol 22, No. 1, 2001
FERC ....authorized the ISO to "[reject]...bids in excess
of whatever price levels it believes are appropriate
... file additional market-monitoring reports".
8. APX Europe, June 2003
Prices (Eur/MWh) Week 25
400 Week 26
350
300
250
200
150
100
50
0
Mon Tues Weds Thurs Fri Sat Sun
9. APX Europe, October 2005
4000
3000 Previous week
2000 Current week (10/24/05)
1000
Volume (MWh)
0
800
Price (Euro)
600
400
200
0
vr za zo ma di wo do
10. Ontario, November 2005
Ancillary service
contract clause:
Minimum overall
ramp rate of 50 MW/min.
Projected power prices
reached $2000/MWh
11. Ontario, November 2005
Ancillary service
contract clause:
Minimum overall
ramp rate of 50 MW/min.
Projected power prices
reached $2000/MWh
12. Ontario, November 2005
Ancillary service
contract clause:
Minimum overall
ramp rate of 50 MW/min.
Projected power prices
reached $2000/MWh
16. Dynamic model
On-line capacity
Forecast
Reserve options for services Actual demand
based on forecast statistics Revised forecast
Centered demand:
D(t) = demand - forecast
t
17. Dynamic Single-Commodity Model
Stochastic model: G Goods available at time t
D Normalized demand
Excess/shortfall: Q(t) = G(t) − D(t)
Normalized cost as a function of Q:
c−
Excess production
c+
Shortfall
q
Scarf, Arrow, Bellman, ...
18. Dynamic Single-Commodity Model
Stochastic model: G Goods available at time t
D Normalized demand
Excess/shortfall: Q(t) = G(t) − D(t)
Generation is rate-constrained:
-ζ-
q
Q(t)
ζ+
t
High cost
21. Ancillary service
G(t)
a
G (t)
The two goods are substitutable, but
1. primary service is available at a lower price
2. ancillary service can be ramped up more rapidly
22. Ancillary service
G(t)
a
G (t)
The two goods are substitutable, but
1. primary service is available at a lower price
2. ancillary service can be ramped up more rapidly
23. Ancillary service
G(t)
a
G (t)
The two goods are substitutable, but
1. primary service is available at a lower price
2. ancillary service can be ramped up more rapidly
24. Ancillary service
a G(t )
G (t )
K
Excess capacity:
Q(t) = G(t) + G a(t) − D (t), t≥ 0.
Power flow subject to peak and rate constraints:
d a d
−ζ a− ≤ G (t) ≤ ζ a+ −ζ − ≤ G(t) ≤ ζ +
dt dt
25. Ancillary service
a G(t )
G (t )
K
Policy: hedging policy with multiple thresholds
Q(t) = G(t) + G a(t) − D (t) -ζ- Downward trend: Ga(t) = 0
d
G (t) = - ζ -
dt
q
ζ+
q
ζ ++ ζ a+ t
Blackout
26. Q(t)
Diffusion model & control X(t) =
G a(t)
Relaxations: instantaneous ramp-down rates:
d d a
−∞ ≤ G (t) ≤ ζ +, −∞ ≤ G (t) ≤ ζ a+.
dt dt
Cost structure:
c(X(t)) = c1G (t) + c2G a(t) + c3|Q(t)|1{Q(t) < 0}
Control: design hedging points to minimize average-cost,
min Eπ [c(Q(t))] .
27. Diffusion model & control
Markov model: Hedging-point policy:
Q(t)
X(t) =
G a(t)
Ancillary service
is ramped-up when
excess capacity falls
below q2
¯
q2
¯ q1
¯
32. Texas model
D1 E1 Gp
1
Line 1
Ga
2
Line 2 Ga
3
D2 D3
Line 3
E2 E3
Resource pooling from San Antonio to Houston?
33. Aggregate model
Line 1 Line 2
Line 3
QA(t) = extraction - demand = Ei(t) − Di(t)
a a
GA(t) = aggregate ancillary = Gi (t)
Assume Brownian demand, rate constraints as before
Provided there are no transmission constraints,
a
XA = (QA ,GA ) ≡ single producer/consumer model
34. Effective cost ¯(xA, d)
c
Line 1 Line 2
Given demand and aggregate state Line 3
find the cheapest consistent
network configuration subject to transmission constraints
p p −
min (ci gi + cagi + cboqi )
i
a
i
s.t. qA = (ei − di) consistency
a
gA = a
gi
p a
0 = (gi + gi − ei ) extraction = generation
q = e−d vector reserves
f = ∆p power flow equations
f ∈F transmission constraints
35. Effective cost ¯(xA, d)
c
Line 1 Line 2
Line 3
a
gA
50
40 xA
1
What do these
30
xA
2 + aggregate states say
X R about the network?
20
10 xA
3
xA
4
qA
0
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 50
36. Effective cost ¯(xA, d)
c
Line 1 Line 2
Line 3
a
gA
50
City 1 in blackout:
q1 = −46,
46, q2 = 3.0564,
3.0564, q3 = 12.9436
12
40 xA
1
Insufficient primary generation:
a a
g1 = −71, g2 = 33.0564,
33 0564, g3 = 6.9436
6.
30
Transmission constraints binding:
20 f1 = 13,
13, f2 = −5, f 3 = −8
10
qA
0
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 50
40. Supply & Demand
Cost of generation depends on source
Price
Supply Curve
Gas Turbine ($20-$30)
Coal ($10 -$15)
Nuclear ($6)
Quantity
41. Supply & Demand
Demand for power is not flexible
High Priority Customers $5,000/MW?
Price Customers with interruptible services
Demand Curve
Quantity
44. www.apx.nl
Main Page Market Results
Welcome to APX!
APX is the first electronic energy trading Prices (Eur/MWh)
400
platform in continental Europe. The daily spot 350
Week 25
market has been operational since May 1999. 300
Week 26
250
The spot market enables distributors, 200
producers, traders, brokers and industrial 150
end-users to buy and sell electricity on a 100
50
day-ahead basis. 0
Volumes (MWh)
The APX-index will be published daily around 2500 MWh
12h00 (GMT +01:00) to provide transparency 2000 MWh
in the market. Prices can be used as a
1500 MWh
benchmark.
1000 MWh
500 MWh
Mon Tue Wed Thu Fri Sat Sun
45. Second Welfare Theorem
Each player independently optimizes ...
Consumer: value of consumption
5000
minus prices paid
4000
minus disaster
WD (t) := v min D(t),G p (t) + Ga (t) − pp Gp (t) + pa Ga (t) + cbo Q− (t)
3000
2000
Supplier: profits from two sources of generation
1000
WS (t) := pp − cp Gp (t) + pa − ca )Ga (t)
13
17
21
13
17
21
13
17
21
13
17
21
13
17
21
1
5
9
1
5
9
1
5
9
1
5
9
1
5
9
46. Second Welfare Theorem
Is there an equilibrium price functional?
Is the equilibrium efficient??
5000
4000
3000
2000
1000
13
17
21
13
17
21
13
17
21
13
17
21
13
17
21
1
5
9
1
5
9
1
5
9
1
5
9
1
5
9
47. Second Welfare Theorem
Is there an equilibrium price functional?
Is the equilibrium efficient??
5000
4000
Yes to all !
3000
2000 p (r , d) = (v + c )I{r < 0}
e e bo e
1000
13
17
21
13
17
21
13
17
21
13
17
21
13
17
21
1
5
9
1
5
9
1
5
9
1
5
9
1
5
9
cbo cost of insufficient service reserve Q(t) = q
v value of consumption demand D(t) = d
50. Conclusions
Spinning Reserve Prices PX Prices
70
250
60
200
50
150 40
30
100
20
50
10
0
Weds Thurs Fri Sat Sun Mon Tues Weds
The hedging point (affine) policy
is average cost optimal
Amazing solidarity between CRW and CBM models
Deregulation is a disaster!
Future work?
51. Extensions and future work 10000
8000
6000
4000
2000
0
Complex models:
Workload or aggregate relaxations
Price caps: No!
Responsive demand: Yes!
Is ENRON off the hook: ?
52. Extensions and future work 10000
8000
6000
4000
2000
0
Complex models:
Workload or aggregate relaxations
Price caps: No!
Responsive demand: Yes!
Is ENRON off the hook: ? What kind of society isn't structured on greed? The
problem of social organization is how to set up an
arrangement under which greed will do the least
harm; capitalism is that kind of system.
-M. Friedman
53. Epilogue 10000
8000
6000
4000
2000
0
Fundamentally, there are only two ways of coordinating
the economic activities of millions.
One is central direction involving the use of coercion
- the technique of the army
and of the modern totalitarian state.
The other is voluntary cooperation of individuals
- the technique of the marketplace.
-Milton Friedman
54. Epilogue 10000
8000
6000
4000
2000
0
Justification: 1. Economic systems are complex
2. Regulators cannot be trusted
55. Epilogue 10000
8000
6000
4000
2000
0
Justification: 1. Economic systems are complex
2. Regulators cannot be trusted
Airplanes, highway networks, cell phones... all complex
56. Epilogue 10000
8000
6000
4000
2000
0
Justification: 1. Economic systems are complex
2. Regulators cannot be trusted
Airplanes, highway networks, cell phones... all complex
Complexity is only inherent in the uncontrolled
system: In each of these examples, the
behavior of the closed loop system is very simple,
provided appropriate rules of use, and
appropriate feeback mechanisms are adopted.
57. References
q1 − q2
¯ ¯ 16
3 q2
¯
1 c
¯∗ ¯∗
q1 − q2 = log 2
γ1 c1
1 c
¯∗
q2 = log 3
γ0 c2
• M. Chen, I.-K. Cho, and S. Meyn. Reliability by design in a distributed
power transmission network. Automatica 2006 (invited)
• I.-K. Cho and S. P. Meyn. The dynamics of the ancillary service prices
in power networks. 42nd IEEE Conference on Decision and Control. De-
cember 2003
• I.-K. Cho and S. P. Meyn. Efficiency and marginal cost pricing in dy-
namic competitive markets. Under revision for J. Theo. Economics. 46th
IEEE Conference on Decision and Control 2006
• P. Ruiz. Reserve Valuation in Electric Power Systems. PhD disserta-
tion, ECE UIUC 2008
58. Poisson’s Equation
First reflection times,
τp :=inf{t ≥ 0 : Q(t) = q p },
¯ τa :=inf{t ≥ 0 : Q(t) ≥ q a }
¯
τp
h(x) = Ex c(X(s)) − φ ds
0
return
59. Poisson’s Equation
First reflection times,
τp :=inf{t ≥ 0 : Q(t) = q p },
¯ τa :=inf{t ≥ 0 : Q(t) ≥ q a }
¯
τp
h(x) = Ex c(X(s)) − φ ds
0
Solves martingale problem,
t
M (t) = h(X(t)) + c(X(s)) − φ ds
0
63. Derivative Representations
τa
1
∇h(x), 1 = Ex λa (X(t)) dt
0
τa
= ca E[τa ] − cbo Ex I{Q(t) ≤ 0} dt
0
Computable based
on one-dimensional height (ladder) process,
H a (t) = q a − Q(t)
¯
64. Dynamic Programming Equations
If q p = q p∗ and ¯ a = ¯ a∗
¯ ¯ q q
Then h solves the dynamic programming equations,
1. Poisson's equation
1
2. ∇h(x), 1 < 0, x ∈ Ra
¯ a∗
q q p∗
1
3. ∇h(x), 0 < 0, x ∈ Rp return