The method described in this paper balances power production and consumption with a large number ... more The method described in this paper balances power production and consumption with a large number of thermal loads. Linear controllers are used for the loads to track a temperature set point, while Model Predictive Control (MPC) and model estimation of the load behavior are used for coordination. The total power consumption of all loads is controlled indirectly through a real-time price. The MPC incorporates forecasts of the power production and disturbances that influence the loads, e.g. time-varying weather forecasts, in order to react ahead of time. A simulation scenario demonstrates that the method allows for the integration of flexible thermal loads in a smart energy system in which consumption follows the changing production.
The Kluźniak & Abramowicz model explains high frequency, double peak, "3:2" QPOs observed in neut... more The Kluźniak & Abramowicz model explains high frequency, double peak, "3:2" QPOs observed in neutron star and black hole sources in terms of a non-linear parametric resonance between radial and vertical epicyclic oscillations of an almost Keplerian accretion disk. The 3 : 2 ratio of epicyclic frequencies occurs only in strong gravity. Rebusco (2004) and Horák (2004) studied the model analytically: they proved that a small forcing may indeed excite the parametric 3:2 resonance, but they have not explained the physical nature of the forcing. Here we integrate their equations numerically, dropping the ad hoc forcing, and adding instead a stochastic term to mimic the action of the very complex processes that occur in disks as, for example, MRI turbulence. We demonstrate that the presence of the stochastic term triggers the resonance in epicyclic oscillations of nearly Keplerian disks, and influences their pattern.
A bstract. A modified version of the linear quadratic Gaussian controller is presented, wh.ich is... more A bstract. A modified version of the linear quadratic Gaussian controller is presented, wh.ich is build upon the prediction form of the model. This implies that the controller is more capable of handling non• stationarities, like time-varying model parameters, than the classical type of linear quadratic Gaussian controller, wh.ich usually is based on the solution of the Diophantine or the Riccati Equation (in the state•space case). The linear quadratic Gaussian controller is used in a simulation study together with a transfer function model, with time• varying parameters, that describes the relations between supply temperature of the water from a district heating plant and the supply temperature at specific locations in the distribution network. The simulation results show that the variance of the differenced control signal can be reduced drastically without affecting the performance of the controller significantly.
In this paper we apply receding horizon constrained optimal control to the computation of insulin... more In this paper we apply receding horizon constrained optimal control to the computation of insulin administration for people with type 1 diabetes. The study is based on the Hovorka model, which describes a virtual subject with type 1 diabetes. First of all, we compute the optimal insulin administration for the linearized system using quadratic programming (QP) for optimization. The optimization problem is a discrete-time problem with soft state constraints and hard input constraints. The computed insulin administration is applied to the nonlinear model, which represents the virtual patient. Then, a nonlinear discrete-time Bolza problem is stated and solved using sequential quadratic programming (SQP) for optimization and an explicit Dormand-Prince Runge-Kutta method (DOPRI54) for numerical integration and sensitivity computation. Finally, the effects of faster acting insulin on the postprandial (i.e., post-meal) blood glucose peak are discussed.
International Journal of Electrical Power & Energy Systems, 2014
The objective of this paper is to analyze the value of energy replacement in the context of deman... more The objective of this paper is to analyze the value of energy replacement in the context of demand response. Energy replacement is defined as the possibility of the consumer to choose the most convenient source for providing space heating to a smart building according to a dynamic electricity price. In the proposed setup, heat is provided by conventional electric radiators and a combined heat and power generation system, composed by a fuel cell and an electrolyzer. The energy replacement strategy is formulated using model predictive control and mathematical models of the components involved. Simulations show that the predictive energy replacement strategy reduces the operating costs of the system and is able to provide a larger amount of regulating power to the grid. In the paper, we also develop a novel dynamic model of a PEM fuel cell suitable for micro-grid applications. The model is realized applying a grey-box methodology to the experimental proton exchange membrane fuel cell of the EPFL-DESL micro-grid.
Parameter estimation in general state space models is not trivial as the likelihood is unknown. W... more Parameter estimation in general state space models is not trivial as the likelihood is unknown. We propose a recursive estimator for general state space models, and show that the estimates converge to the true parameters with probability one. The estimates are also asymptotically Cramer-Rao efficient. The proposed estimator is easy to implement as it only relies on non-linear filtering. This makes the framework flexible as it is easy to tune the implementation to achieve computational efficiency. This is done by using the approximation of the score function derived from the theory on Iterative Filtering as a building block within the recursive maximum likelihood estimator.
2013 4th International Youth Conference on Energy (IYCE), 2013
This paper presents the grey-box modeling of a vapor-compression refrigeration system for residen... more This paper presents the grey-box modeling of a vapor-compression refrigeration system for residential applications based on maximum likelihood estimation of parameters in stochastic differential equations. Models obtained are useful in the view of controlling refrigerators as flexible consumption units, which operation can be shifted within temperature and operational constraints. Even if the refrigerators are not intended to be used as smart loads, validated models are useful in predicting units consumption. This information can increase the optimality of the management of other flexible units, such as heat pumps for space heating, in order to smooth the load factor during peak hours, enhance reliability and efficiency in power networks and reduce operational costs.
Users may download and print one copy of any publication from the public portal for the purpose... more Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.
This paper discusses how the control of the flow and the supply temperature in district heating s... more This paper discusses how the control of the flow and the supply temperature in district heating systems can be optimized, utilizing stochastic modelling, prediction and control methods. The main objective is to reduce heat production costs and heat losses in the transmission and distribution net by minimizing the supply temperature at the district heating plant. This control strategy is reasonable, in particular, if the heat production takes place at a combined heat and power (CHP) plant. The control strategy is subject to some restrictions, e.g. that the total heat requirement for all consumers is supplied at any time, and each individual consumer is guaranteed some minimum supply temperature at any time. Another important restriction is that the variation in time of the supply temperature is kept as small as possible. This concept has been incorporated in the program package, PRESS, developed at the Technical University of Denmark. PRESS has been applied and tested, e.g. at Vestkraft in Esbjerg, Denmark, and significant saving potentials have been documented. PRESS is now distributed by the Danish District Heating Association.
ABSTRACT In view of the increasing penetration of wind power in a number of power systems and mar... more ABSTRACT In view of the increasing penetration of wind power in a number of power systems and markets worldwide, we discuss some of the impacts that wind energy may have on market quantities and cross-border power flows. These impacts are uncovered through statistical analyses of actual market and flow data in Europe. Due to the dimensionality and nonlinearity of these effects, the necessary concepts of dimension reduction using Principal Component Analysis (PCA), as well as nonlinear regression are described. Example application results are given for European cross-border flows, as well as for the impact of load and wind power forecasts on Danish and German electricity markets.
This paper presents grey-box modeling of the heat dynamics of an apartment in a highly insulated ... more This paper presents grey-box modeling of the heat dynamics of an apartment in a highly insulated test building located in the Arctic. Data from a 16-day-long experiment is analyzed and used to fit lumped parameter models formulated as coupled stochastic differential equations. The output of the models is the measured indoor air temperature, and the models are fitted using maximum likelihood techniques with the software CTSM-R. Models are compared using likelihood-ratio tests and validated considering autocorrelation and periodograms of residuals. The fitted models facilitate description of both the fast responses to mechanical ventilation and solar radiation through a large window facade, and the slow responses to floor heating and outdoor temperature. To successfully describe the dynamics of the system, solar radiation is given special attention in modeling of both the physical system and the observational noise. The estimated physical parameters which include UA-value, total heat capacity, and time constants for the apartment are discussed. Simulations are performed to illustrate step and impulse responses of inputs.
ABSTRACT Allocation of electricity reserves is the main tool for transmission system operators to... more ABSTRACT Allocation of electricity reserves is the main tool for transmission system operators to guarantee a reliable and safe real-time operation of the power system. Traditionally, a deterministic criterion is used to establish the level of reserve. Alternative criteria are given in this paper by using a probabilistic framework where the reserve requirements are computed based on scenarios of wind power forecast error, load forecast errors and power plant outages. Our approach is first motivated by the increasing wind power penetration in power systems worldwide as well as the current market design of the DK1 area of Nord Pool, where reserves are scheduled prior to the closure of the day-ahead market. The risk of the solution under the resulting reserve schedule is controlled by two measures: the LOLP (Loss-of-Load Probability) and the CVaR (Conditional Value at Risk). Results show that during the case study period, the LOLP methodology produces more costly and less reliable reserve schedules, whereas the solution from the CVaR-method increases the safety of the overall system while decreasing the associated reserve costs, with respect to the method currently used by the Danish TSO (Transmission System Operator).
International Series in Operations Research & Management Science, 2013
America is too dependent upon foreign energy sources, but it has the capabilities to free itself,... more America is too dependent upon foreign energy sources, but it has the capabilities to free itself, while saving money and preserving the environment. If the U.S. Government increased its R&D (Research & Development) spending on renewable energy via Virtual Power Plants (VPP), America could be energy independent; coverting foreign energy dependency into America's renewable freedom. Sustaining and developing a cleaner, safer, more efficient world by implementing and developing VPP's.
For management and trading purposes, information on short‐term wind generation (from a few hours ... more For management and trading purposes, information on short‐term wind generation (from a few hours to a few days ahead) is crucial at large offshore wind farms, since they concentrate a large capacity at a single location. The most complete information that can be provided today consists of probabilistic forecasts, the resolution of which may be maximized by using meteorological ensemble predictions as input. The paper concentrates on the test case of the Horns Rev wind farm over a period of approximately 1 year, in order to describe, apply and discuss a complete ensemble‐based probabilistic forecasting methodology. In a first stage, ensemble forecasts of meteorological variables are converted to power through a suitable power curve model. This model employs local polynomial regression, and is adaptively estimated with an orthogonal fitting method. The obtained ensemble forecasts of wind power are then converted into predictive distributions with an original adaptive kernel dressing m...
Predictions of wind power production for horizons up to 48–72 h ahead comprise a highly valuable ... more Predictions of wind power production for horizons up to 48–72 h ahead comprise a highly valuable input to the methods for the daily management or trading of wind generation. Today, users of wind power predictions are not only provided with point predictions, which are estimates of the conditional expectation of the wind generation for each look‐ahead time, but also with uncertainty estimates given by probabilistic forecasts. In order to avoid assumptions on the shape of predictive distributions, these probabilistic predictions are produced from non‐parametric methods, and then take the form of a single or a set of quantile forecasts. The required and desirable properties of such probabilistic forecasts are defined and a framework for their evaluation is proposed. This framework is applied for evaluating the quality of two statistical methods producing full predictive distributions from point predictions of wind power. These distributions are defined by a number of quantile forecasts...
The method described in this paper balances power production and consumption with a large number ... more The method described in this paper balances power production and consumption with a large number of thermal loads. Linear controllers are used for the loads to track a temperature set point, while Model Predictive Control (MPC) and model estimation of the load behavior are used for coordination. The total power consumption of all loads is controlled indirectly through a real-time price. The MPC incorporates forecasts of the power production and disturbances that influence the loads, e.g. time-varying weather forecasts, in order to react ahead of time. A simulation scenario demonstrates that the method allows for the integration of flexible thermal loads in a smart energy system in which consumption follows the changing production.
The Kluźniak & Abramowicz model explains high frequency, double peak, "3:2" QPOs observed in neut... more The Kluźniak & Abramowicz model explains high frequency, double peak, "3:2" QPOs observed in neutron star and black hole sources in terms of a non-linear parametric resonance between radial and vertical epicyclic oscillations of an almost Keplerian accretion disk. The 3 : 2 ratio of epicyclic frequencies occurs only in strong gravity. Rebusco (2004) and Horák (2004) studied the model analytically: they proved that a small forcing may indeed excite the parametric 3:2 resonance, but they have not explained the physical nature of the forcing. Here we integrate their equations numerically, dropping the ad hoc forcing, and adding instead a stochastic term to mimic the action of the very complex processes that occur in disks as, for example, MRI turbulence. We demonstrate that the presence of the stochastic term triggers the resonance in epicyclic oscillations of nearly Keplerian disks, and influences their pattern.
A bstract. A modified version of the linear quadratic Gaussian controller is presented, wh.ich is... more A bstract. A modified version of the linear quadratic Gaussian controller is presented, wh.ich is build upon the prediction form of the model. This implies that the controller is more capable of handling non• stationarities, like time-varying model parameters, than the classical type of linear quadratic Gaussian controller, wh.ich usually is based on the solution of the Diophantine or the Riccati Equation (in the state•space case). The linear quadratic Gaussian controller is used in a simulation study together with a transfer function model, with time• varying parameters, that describes the relations between supply temperature of the water from a district heating plant and the supply temperature at specific locations in the distribution network. The simulation results show that the variance of the differenced control signal can be reduced drastically without affecting the performance of the controller significantly.
In this paper we apply receding horizon constrained optimal control to the computation of insulin... more In this paper we apply receding horizon constrained optimal control to the computation of insulin administration for people with type 1 diabetes. The study is based on the Hovorka model, which describes a virtual subject with type 1 diabetes. First of all, we compute the optimal insulin administration for the linearized system using quadratic programming (QP) for optimization. The optimization problem is a discrete-time problem with soft state constraints and hard input constraints. The computed insulin administration is applied to the nonlinear model, which represents the virtual patient. Then, a nonlinear discrete-time Bolza problem is stated and solved using sequential quadratic programming (SQP) for optimization and an explicit Dormand-Prince Runge-Kutta method (DOPRI54) for numerical integration and sensitivity computation. Finally, the effects of faster acting insulin on the postprandial (i.e., post-meal) blood glucose peak are discussed.
International Journal of Electrical Power & Energy Systems, 2014
The objective of this paper is to analyze the value of energy replacement in the context of deman... more The objective of this paper is to analyze the value of energy replacement in the context of demand response. Energy replacement is defined as the possibility of the consumer to choose the most convenient source for providing space heating to a smart building according to a dynamic electricity price. In the proposed setup, heat is provided by conventional electric radiators and a combined heat and power generation system, composed by a fuel cell and an electrolyzer. The energy replacement strategy is formulated using model predictive control and mathematical models of the components involved. Simulations show that the predictive energy replacement strategy reduces the operating costs of the system and is able to provide a larger amount of regulating power to the grid. In the paper, we also develop a novel dynamic model of a PEM fuel cell suitable for micro-grid applications. The model is realized applying a grey-box methodology to the experimental proton exchange membrane fuel cell of the EPFL-DESL micro-grid.
Parameter estimation in general state space models is not trivial as the likelihood is unknown. W... more Parameter estimation in general state space models is not trivial as the likelihood is unknown. We propose a recursive estimator for general state space models, and show that the estimates converge to the true parameters with probability one. The estimates are also asymptotically Cramer-Rao efficient. The proposed estimator is easy to implement as it only relies on non-linear filtering. This makes the framework flexible as it is easy to tune the implementation to achieve computational efficiency. This is done by using the approximation of the score function derived from the theory on Iterative Filtering as a building block within the recursive maximum likelihood estimator.
2013 4th International Youth Conference on Energy (IYCE), 2013
This paper presents the grey-box modeling of a vapor-compression refrigeration system for residen... more This paper presents the grey-box modeling of a vapor-compression refrigeration system for residential applications based on maximum likelihood estimation of parameters in stochastic differential equations. Models obtained are useful in the view of controlling refrigerators as flexible consumption units, which operation can be shifted within temperature and operational constraints. Even if the refrigerators are not intended to be used as smart loads, validated models are useful in predicting units consumption. This information can increase the optimality of the management of other flexible units, such as heat pumps for space heating, in order to smooth the load factor during peak hours, enhance reliability and efficiency in power networks and reduce operational costs.
Users may download and print one copy of any publication from the public portal for the purpose... more Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.
This paper discusses how the control of the flow and the supply temperature in district heating s... more This paper discusses how the control of the flow and the supply temperature in district heating systems can be optimized, utilizing stochastic modelling, prediction and control methods. The main objective is to reduce heat production costs and heat losses in the transmission and distribution net by minimizing the supply temperature at the district heating plant. This control strategy is reasonable, in particular, if the heat production takes place at a combined heat and power (CHP) plant. The control strategy is subject to some restrictions, e.g. that the total heat requirement for all consumers is supplied at any time, and each individual consumer is guaranteed some minimum supply temperature at any time. Another important restriction is that the variation in time of the supply temperature is kept as small as possible. This concept has been incorporated in the program package, PRESS, developed at the Technical University of Denmark. PRESS has been applied and tested, e.g. at Vestkraft in Esbjerg, Denmark, and significant saving potentials have been documented. PRESS is now distributed by the Danish District Heating Association.
ABSTRACT In view of the increasing penetration of wind power in a number of power systems and mar... more ABSTRACT In view of the increasing penetration of wind power in a number of power systems and markets worldwide, we discuss some of the impacts that wind energy may have on market quantities and cross-border power flows. These impacts are uncovered through statistical analyses of actual market and flow data in Europe. Due to the dimensionality and nonlinearity of these effects, the necessary concepts of dimension reduction using Principal Component Analysis (PCA), as well as nonlinear regression are described. Example application results are given for European cross-border flows, as well as for the impact of load and wind power forecasts on Danish and German electricity markets.
This paper presents grey-box modeling of the heat dynamics of an apartment in a highly insulated ... more This paper presents grey-box modeling of the heat dynamics of an apartment in a highly insulated test building located in the Arctic. Data from a 16-day-long experiment is analyzed and used to fit lumped parameter models formulated as coupled stochastic differential equations. The output of the models is the measured indoor air temperature, and the models are fitted using maximum likelihood techniques with the software CTSM-R. Models are compared using likelihood-ratio tests and validated considering autocorrelation and periodograms of residuals. The fitted models facilitate description of both the fast responses to mechanical ventilation and solar radiation through a large window facade, and the slow responses to floor heating and outdoor temperature. To successfully describe the dynamics of the system, solar radiation is given special attention in modeling of both the physical system and the observational noise. The estimated physical parameters which include UA-value, total heat capacity, and time constants for the apartment are discussed. Simulations are performed to illustrate step and impulse responses of inputs.
ABSTRACT Allocation of electricity reserves is the main tool for transmission system operators to... more ABSTRACT Allocation of electricity reserves is the main tool for transmission system operators to guarantee a reliable and safe real-time operation of the power system. Traditionally, a deterministic criterion is used to establish the level of reserve. Alternative criteria are given in this paper by using a probabilistic framework where the reserve requirements are computed based on scenarios of wind power forecast error, load forecast errors and power plant outages. Our approach is first motivated by the increasing wind power penetration in power systems worldwide as well as the current market design of the DK1 area of Nord Pool, where reserves are scheduled prior to the closure of the day-ahead market. The risk of the solution under the resulting reserve schedule is controlled by two measures: the LOLP (Loss-of-Load Probability) and the CVaR (Conditional Value at Risk). Results show that during the case study period, the LOLP methodology produces more costly and less reliable reserve schedules, whereas the solution from the CVaR-method increases the safety of the overall system while decreasing the associated reserve costs, with respect to the method currently used by the Danish TSO (Transmission System Operator).
International Series in Operations Research & Management Science, 2013
America is too dependent upon foreign energy sources, but it has the capabilities to free itself,... more America is too dependent upon foreign energy sources, but it has the capabilities to free itself, while saving money and preserving the environment. If the U.S. Government increased its R&D (Research & Development) spending on renewable energy via Virtual Power Plants (VPP), America could be energy independent; coverting foreign energy dependency into America's renewable freedom. Sustaining and developing a cleaner, safer, more efficient world by implementing and developing VPP's.
For management and trading purposes, information on short‐term wind generation (from a few hours ... more For management and trading purposes, information on short‐term wind generation (from a few hours to a few days ahead) is crucial at large offshore wind farms, since they concentrate a large capacity at a single location. The most complete information that can be provided today consists of probabilistic forecasts, the resolution of which may be maximized by using meteorological ensemble predictions as input. The paper concentrates on the test case of the Horns Rev wind farm over a period of approximately 1 year, in order to describe, apply and discuss a complete ensemble‐based probabilistic forecasting methodology. In a first stage, ensemble forecasts of meteorological variables are converted to power through a suitable power curve model. This model employs local polynomial regression, and is adaptively estimated with an orthogonal fitting method. The obtained ensemble forecasts of wind power are then converted into predictive distributions with an original adaptive kernel dressing m...
Predictions of wind power production for horizons up to 48–72 h ahead comprise a highly valuable ... more Predictions of wind power production for horizons up to 48–72 h ahead comprise a highly valuable input to the methods for the daily management or trading of wind generation. Today, users of wind power predictions are not only provided with point predictions, which are estimates of the conditional expectation of the wind generation for each look‐ahead time, but also with uncertainty estimates given by probabilistic forecasts. In order to avoid assumptions on the shape of predictive distributions, these probabilistic predictions are produced from non‐parametric methods, and then take the form of a single or a set of quantile forecasts. The required and desirable properties of such probabilistic forecasts are defined and a framework for their evaluation is proposed. This framework is applied for evaluating the quality of two statistical methods producing full predictive distributions from point predictions of wind power. These distributions are defined by a number of quantile forecasts...
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