### Citations

760 |
Dynamic noncooperative game theory
- Basar, Olsder
- 1995
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Citation Context ... i t + ∆q i t, t ∈ T − r i ≤ ∆q i t ≤ r i , t ∈ T − q i ≤ q i t ≤ q i , t ∈ T q i 0 = ¯q i 0. d j t, t ∈ T (4a) (4b) (4c) (4d) (4e) (4f) This representation is typical in the dynamic games literature =-=[8]-=-. The state-space representation enables us to analyze the market as a game-theoretical MPC problem. Here, the production quantities qi t can be interpreted as differential states coupled in time, and... |

226 |
On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming
- Wächter, Biegler
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Citation Context ...the prediction horizon and the number of players. To solve these systems, one can use complementarity solvers such as PATH [12] or general nonlinear optimization solvers such as KNITRO [10] and IPOPT =-=[30]-=-. For the problems considered in this work we have found that a nonlinear optimization approach coupled to a ℓ1 penalty formulation is numerically more robust. In this approach, the objective is to mi... |

212 | The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems
- Dirkse, Ferris
- 1994
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Citation Context ...g complementarity systems can be extremely large, depending on the length of the prediction horizon and the number of players. To solve these systems, one can use complementarity solvers such as PATH =-=[12]-=- or general nonlinear optimization solvers such as KNITRO [10] and IPOPT [30]. For the problems considered in this work we have found that a nonlinear optimization approach coupled to a ℓ1 penalty for... |

92 |
An interior point algorithm for large-scale nonlinear programming
- BYRD, HRIBAR, et al.
- 1999
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Citation Context ... the length of the prediction horizon and the number of players. To solve these systems, one can use complementarity solvers such as PATH [12] or general nonlinear optimization solvers such as KNITRO =-=[10]-=- and IPOPT [30]. For the problems considered in this work we have found that a nonlinear optimization approach coupled to a ℓ1 penalty formulation is numerically more robust. In this approach, the obj... |

85 | Strategic gaming analysis for electric power systems: An MPEC approach,
- Hobbs, Metzler, et al.
- 2000
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Citation Context .... E-mail: {akannan,vzavala}@mcs.anl.gov. models range from data-based time-series models [26], [11] to mechanistic models based on agent-based systems [9], [28] and game-theoretical formulations [7], =-=[17]-=-. Game-theoretical models can be used to establish market properties in a systematic manner and thus provide more comprehensive predictive capabilities. Several models based on a range of market struc... |

74 |
Day-ahead electricity price forecasting using the wavelet transform and ARIMA models.
- Conejo, Plazas, et al.
- 2005
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Citation Context ...e with the Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439, USA. E-mail: {akannan,vzavala}@mcs.anl.gov. models range from data-based time-series models [26], =-=[11]-=- to mechanistic models based on agent-based systems [9], [28] and game-theoretical formulations [7], [17]. Game-theoretical models can be used to establish market properties in a systematic manner and... |

62 | Capacity constrained supply function equilibriummodels for electricity markets: Stability, non-decreasing constraints, and function space iterations,
- Baldick, Hogan
- 2002
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Citation Context ..., USA. E-mail: {akannan,vzavala}@mcs.anl.gov. models range from data-based time-series models [26], [11] to mechanistic models based on agent-based systems [9], [28] and game-theoretical formulations =-=[7]-=-, [17]. Game-theoretical models can be used to establish market properties in a systematic manner and thus provide more comprehensive predictive capabilities. Several models based on a range of market... |

43 |
A model-based comparison of pool and bilateral market mechanisms for electricity trading,
- Bower, Bunn
- 1999
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Citation Context ...gonne National Laboratory, Argonne, IL 60439, USA. E-mail: {akannan,vzavala}@mcs.anl.gov. models range from data-based time-series models [26], [11] to mechanistic models based on agent-based systems =-=[9]-=-, [28] and game-theoretical formulations [7], [17]. Game-theoretical models can be used to establish market properties in a systematic manner and thus provide more comprehensive predictive capabilitie... |

43 |
A and Rivier M. Electricity market modelling trends. Energy Policy. 2005: 33(2005
- Ventosa, Baillo, et al.
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Citation Context ...disturbances (e.g., weather, load, fuel prices, and wind supply), physical constraints (e.g., transmission congestion), and gaming behaviors (e.g., bidding strategies) on market efficiency and prices =-=[29]-=-. These A. Kannan and V.M. Zavala are with the Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439, USA. E-mail: {akannan,vzavala}@mcs.anl.gov. models range from ... |

41 | On solving mathematical programs with complementarity constraints as nonlinear programs
- Anitescu
(Show Context)
Citation Context ...ve found that a nonlinear optimization approach coupled to a ℓ1 penalty formulation is numerically more robust. In this approach, the objective is to minimize the complementarity products [21], [14], =-=[4]-=-. For (8), the problem takes the form: III. CLOSED-LOOP CONSIDERATIONS To analyze real-time market operations, one can solve the dynamic game problem in a receding-horizon manner with a predefined for... |

37 |
Ramp-rate limits in unit commitment and economic dispatch incorporating rotor fatigue effect,
- Wang, Shahidehpour
- 1994
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Citation Context ... manipulation of ramp constraints on market behavior was studied in [23]. Ramp rates represent the maximum change that a generator can achieve in their power output level within a given time interval =-=[31]-=-. They implicitly represent the time that it will take the generator control system to move2 the power output level from the current level to the desired target. These ramp rates depend on multiple p... |

36 |
Nash-Cournot equilibria in power markets on a linearized DC network with arbitrage: Formulations and properties.
- Metzler, Hobbs, et al.
- 2003
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Citation Context ...arising in power markets. In particular, the proposed models can be extended to capture transmission constraints, social welfare and transmission costs in the ISO’s problems, and arbitrager decisions =-=[22]-=-. Note also that the models assume that bidding and market clearing occur simultaneously (singleshot game). A more realistic representation can be considered where the bids and market clearing occur s... |

33 |
The stability of power system markets.
- Alvarado
- 1999
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Citation Context ...havior, which is the most common case in real-time operations. Consequently, their use in market monitoring and price forecasting is limited. A widely used dynamic market model originally proposed in =-=[1]-=-, [2] assumes that the players bid recursively in the direction that minimizes their marginal cost. Every bid can be interpreted as a steepest-descent step that converges to a steadystate equilibrium.... |

30 | Bid-based Stochastic Model for Electricity Prices: The Impact of Fundamental Driverson MarketDynamics,”
- Skrmtze, Gubina, et al.
- 2000
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Citation Context ...ala are with the Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439, USA. E-mail: {akannan,vzavala}@mcs.anl.gov. models range from data-based time-series models =-=[26]-=-, [11] to mechanistic models based on agent-based systems [9], [28] and game-theoretical formulations [7], [17]. Game-theoretical models can be used to establish market properties in a systematic mann... |

29 | Using EPECs to model bilevel games in restructured electricity markets with locational prices,
- Hu, Ralph
- 2007
(Show Context)
Citation Context ...that the models assume that bidding and market clearing occur simultaneously (singleshot game). A more realistic representation can be considered where the bids and market clearing occur sequentially =-=[18]-=-. Our objective in this work is to understand how different dynamic factors affect the performance of the market. Because of this, we do not consider these more sophisticated market formulations. Whil... |

27 |
Transmission congestion management in an electricity market,”
- Fang, David
- 1999
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Citation Context ...al-time markets) and thus affect short-term and long-term (dynamic) market stability and performance. In some sense, ramping constraints affect market performance much as transmission congestion does =-=[13]-=-. The key difference, however, is that the effect of ramping constraints propagates forward in time while the effects of transmission congestion are static (instantaneous). The effects of manipulation... |

23 | Stability analysis of interconnected power systems coupled with market dynamics
- Alvarado, Meng, et al.
- 2001
(Show Context)
Citation Context ...r, which is the most common case in real-time operations. Consequently, their use in market monitoring and price forecasting is limited. A widely used dynamic market model originally proposed in [1], =-=[2]-=- assumes that the players bid recursively in the direction that minimizes their marginal cost. Every bid can be interpreted as a steepest-descent step that converges to a steadystate equilibrium. Whil... |

22 | Linear Supply Function Equilibrium: Generalizations, Applications, and Limitations, UCEI Working Paper PWP-078.
- Baldick, Grant, et al.
- 2000
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Citation Context ...d on the ramp rates of the generators. B. Supply-Function Based Formulation An alternative formulation that represents actual market operations more accurately is based on supply functions [25], [7], =-=[6]-=-. Here, we assume that the supplier decisions are the parameters of the supply function q i t(pt) = b i tpt − a i t. (5)3 If we assume that the bids and the market are cleared simultaneously, we get ... |

22 | Numerical experience with solving MPECs as NLPs
- Fletcher, Leyffer
- 2002
(Show Context)
Citation Context ... we have found that a nonlinear optimization approach coupled to a ℓ1 penalty formulation is numerically more robust. In this approach, the objective is to minimize the complementarity products [21], =-=[14]-=-, [4]. For (8), the problem takes the form: III. CLOSED-LOOP CONSIDERATIONS To analyze real-time market operations, one can solve the dynamic game problem in a receding-horizon manner with a predefine... |

18 | On the supply function equilibrium and its applications in electricity markets
- Rudkevich
- 2005
(Show Context)
Citation Context ...horizon, and on the ramp rates of the generators. B. Supply-Function Based Formulation An alternative formulation that represents actual market operations more accurately is based on supply functions =-=[25]-=-, [7], [6]. Here, we assume that the supplier decisions are the parameters of the supply function q i t(pt) = b i tpt − a i t. (5)3 If we assume that the bids and the market are cleared simultaneousl... |

15 | Two-settlement systems for electricity markets under network uncertainty and market power.
- Kamat, Oren
- 2004
(Show Context)
Citation Context ... in a number of ways to consider more detailed physical effects and market design structures such as transmission constraints and coupled dayahead and real-time markets (two-settlement markets) [32], =-=[19]-=-. In addition, it is possible to incorporate effects of uncertainty and risk aversion [20]. The model can also be constructed with more realistic set-ups where the suppliers bid their operational info... |

15 | Computing cournot equilibria in two settlement electricity markets with transmission constraints
- Yao, Oren, et al.
- 2003
(Show Context)
Citation Context ...tended in a number of ways to consider more detailed physical effects and market design structures such as transmission constraints and coupled dayahead and real-time markets (two-settlement markets) =-=[32]-=-, [19]. In addition, it is possible to incorporate effects of uncertainty and risk aversion [20]. The model can also be constructed with more realistic set-ups where the suppliers bid their operationa... |

12 | Simulating the dynamics in two-settlement electricity markets via an agent-based approach
- Veit, Weidlich, et al.
(Show Context)
Citation Context ... National Laboratory, Argonne, IL 60439, USA. E-mail: {akannan,vzavala}@mcs.anl.gov. models range from data-based time-series models [26], [11] to mechanistic models based on agent-based systems [9], =-=[28]-=- and game-theoretical formulations [7], [17]. Game-theoretical models can be used to establish market properties in a systematic manner and thus provide more comprehensive predictive capabilities. Sev... |

6 |
Competitive Bidding and Stability Analysis in Electricity Markets Using Control Theory
- Giabardo, Zugno
- 2008
(Show Context)
Citation Context ...s based on mathematical rather than mechanistic assumptions and thus has limited applicability. Recently, a dynamic market model based on model predictive control (MPC) concepts was proposed in [16], =-=[15]-=-. Here, supply functions and forecast horizon concepts are incorporated into the model. These concepts provide a more natural representation of actual bidding procedures. This model has been used to a... |

6 |
Feedback, competition and stochasticity in a day ahead electricity market
- Giabardo, Zugno, et al.
(Show Context)
Citation Context ..., it is based on mathematical rather than mechanistic assumptions and thus has limited applicability. Recently, a dynamic market model based on model predictive control (MPC) concepts was proposed in =-=[16]-=-, [15]. Here, supply functions and forecast horizon concepts are incorporated into the model. These concepts provide a more natural representation of actual bidding procedures. This model has been use... |

6 | Solving multi-leader-common-follower games
- Leyffer, Munson
(Show Context)
Citation Context ...s work we have found that a nonlinear optimization approach coupled to a ℓ1 penalty formulation is numerically more robust. In this approach, the objective is to minimize the complementarity products =-=[21]-=-, [14], [4]. For (8), the problem takes the form: III. CLOSED-LOOP CONSIDERATIONS To analyze real-time market operations, one can solve the dynamic game problem in a receding-horizon manner with a pre... |

5 |
Industrial application of a model predictive control solution for power plant startups
- Amato
- 2006
(Show Context)
Citation Context ...ll take the generator control system to move2 the power output level from the current level to the desired target. These ramp rates depend on multiple physical factors such as controller performance =-=[3]-=-, [5], thermal stresses, and wall capacitances [27]. Large generators such as those running on coal and nuclear fuel are operated at base load and are not ramped. Smaller generators and combined-cycle... |

5 |
Predictive control of thermal power plants
- Aurora, Magni, et al.
(Show Context)
Citation Context ...ke the generator control system to move2 the power output level from the current level to the desired target. These ramp rates depend on multiple physical factors such as controller performance [3], =-=[5]-=-, thermal stresses, and wall capacitances [27]. Large generators such as those running on coal and nuclear fuel are operated at base load and are not ramped. Smaller generators and combined-cycle plan... |

5 | J.Wang, “Computational and economic limitations of dispatch operations in the next-generation power grid
- Zavala, Botterud, et al.
- 2010
(Show Context)
Citation Context ... (ramp and production limits, cost curves) [23] and the ISO clears the market by solving a unit commitment problem in the day-ahead market and an economic dispatch model in the real-time market [24], =-=[33]-=-. Other settings include information exchange, cooperation, and use of forecasting capabilities by the suppliers. These models, however, pose significant complexity from a theoretical and numerical po... |

4 |
The operation of large steam turbines to limit cyclic thermal cracking
- Timo, Sarney
(Show Context)
Citation Context ... power output level from the current level to the desired target. These ramp rates depend on multiple physical factors such as controller performance [3], [5], thermal stresses, and wall capacitances =-=[27]-=-. Large generators such as those running on coal and nuclear fuel are operated at base load and are not ramped. Smaller generators and combined-cycle plants running on natural gas provide ramping capa... |

3 |
Can we prevent the gaming of ramp constraints? Decis. Support Syst
- Oren, Ross
- 2005
(Show Context)
Citation Context ...mping constraints propagates forward in time while the effects of transmission congestion are static (instantaneous). The effects of manipulation of ramp constraints on market behavior was studied in =-=[23]-=-. Ramp rates represent the maximum change that a generator can achieve in their power output level within a given time interval [31]. They implicitly represent the time that it will take the generator... |

1 |
Risk-averse bidding with uncertain resources in two-settlement markets
- Kannan, Shanbhag, et al.
- 2008
(Show Context)
Citation Context ...es such as transmission constraints and coupled dayahead and real-time markets (two-settlement markets) [32], [19]. In addition, it is possible to incorporate effects of uncertainty and risk aversion =-=[20]-=-. The model can also be constructed with more realistic set-ups where the suppliers bid their operational information (ramp and production limits, cost curves) [23] and the ISO clears the market by so... |

1 |
Modeling competition in eletric energy markets by equilibrium constraints
- Ramos, Ventosa, et al.
- 1998
(Show Context)
Citation Context ...mation (ramp and production limits, cost curves) [23] and the ISO clears the market by solving a unit commitment problem in the day-ahead market and an economic dispatch model in the real-time market =-=[24]-=-, [33]. Other settings include information exchange, cooperation, and use of forecasting capabilities by the suppliers. These models, however, pose significant complexity from a theoretical and numeri... |