A rapid PDE-based optimization methodology for temperature control and other mixed stochastic and deterministic systems

Howell, Sydney; Johnson, Paul V.; Duck, Peter W.

doi:10.1016/j.enbuild.2011.02.009

Cited by 3 publications

(5 citation statements)

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“…As Howell et al [15] have pointed out, the optimal decision function C * (X, Y, Q, t) has set the values of all feasible changes in C * to maximize V. Here V is the integral (from any point in the state space) of the expected time-discounted future value of I. So far I has been used as an indicator for each state point of the actual rate of income earned/paid over dt when the system is at that state space point.…”

Section: Resultsmentioning

confidence: 98%

Partial differential equation methods for stochastic dynamic optimization: an application to wind power generation with energy storage

Johnson

Howell

Duck

2017

Phil. Trans. R. Soc. A.

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A mixed financial/physical partial differential equation (PDE) can optimize the joint earnings of a single wind power generator (WPG) and a generic energy storage device (ESD). Physically, the PDE includes constraints on the ESD's capacity, efficiency and maximum speeds of charge and discharge. There is a mean-reverting daily stochastic cycle for WPG power output. Physically, energy can only be produced or delivered at finite rates. All suppliers must commit hourly to a finite rate of delivery , which is a continuous control variable that is changed hourly. Financially, we assume heavy 'system balancing' penalties in continuous time, for deviations of output rate from the commitment Also, the electricity spot price follows a mean-reverting stochastic cycle with a strong evening peak, when system balancing penalties also peak. Hence the economic goal of the WPG plus ESD, at each decision point, is to maximize expected net present value (NPV) of all earnings (arbitrage) minus the NPV of all expected system balancing penalties, along all financially/physically feasible future paths through state space. Given the capital costs for the various combinations of the physical parameters, the design and operating rules for a WPG plus ESD in a finite market may be jointly optimizable.This article is part of the themed issue 'Energy management: flexibility, risk and optimization'.

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Section: Resultsmentioning

confidence: 98%

Partial differential equation methods for stochastic dynamic optimization: an application to wind power generation with energy storage

Johnson

Howell

Duck

2017

Phil. Trans. R. Soc. A.

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“…Remark 3.1: A poor knowledge of the coefficients in Equation (8) is unavoidable in practice. Lack of space prevents us of confirming via simulations the robustness of our MFC setting in such a situation.…”

Section: A a Simple Mathematical Modelmentioning

confidence: 99%

“…It is clearly a hard requirement to satisfy if one wants to avoid optimization problem, where it is easier to introduce those constraints. The price to pay for such optimization will result in higher computational power, even if sub-optimality mathematical techniques are introduced (see, e.g., [8], [23], [24], [25] and the references therein). A real-time implementation would thus become problematic.…”

Section: Introductionmentioning

confidence: 99%

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Model-free load control for high penetration of solar photovoltaic generation

Bara

Olama

Djouadi

et al. 2017

2017 North American Power Symposium (NAPS)

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This paper presents a new model-free control (MFC) mechanism that enables the local distribution level circuit consumption of the photovoltaic (PV) generation by local building loads, in particular, distributed heating, ventilation and air conditioning (HVAC) units. The local consumption of PV generation will help minimize the impact of PV generation on the distribution grid, reduce the required battery storage capacity for PV penetration, and increase solar PV generation penetration levels. The proposed MFC approach with its corresponding intelligent controllers does not require any precise model for buildings, where a reliable modeling is a demanding task. Even when assuming the availability of a good model, the various building architectures would compromise the performance objectives of any model-based control strategy. The objective is to consume most of the PV generation locally while maintaining occupants comfort and physical constraints of HVAC units. That is, by enabling proper scheduling of responsive loads temporally and spatially to minimize the difference between demand and PV production, it would be possible to reduce voltage variations and two-way power flow. Computer simulations show promising results where a significant proportion of the PV generation can be consumed by building HVAC units with the help of intelligent control.

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“…. See, e.g., [3], [4], [6], [7], [8], [10], [11], [15], [16], [20], [25], [26], [27], [32], [36], [39], [44], [46], [49], [50], [52], [61], [64], [67], . .…”

Section: Introductionmentioning

confidence: 99%

Energy saving for building heating via a simple and efficient model-free control design: First steps with computer simulations

Abouaïssa

Hasan

Join

et al. 2017

2017 21st International Conference on System Theory, Control and Computing (ICSTCC)

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The model-based control of building heating systems for energy saving encounters severe physical, mathematical and calibration difficulties in the numerous attempts that has been published until now. This topic is addressed here via a new model-free control setting, where the need of any mathematical description disappears. Several convincing computer simulations are presented. Comparisons with classic PI controllers and flatness-based predictive control are provided.

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A rapid PDE-based optimization methodology for temperature control and other mixed stochastic and deterministic systems

Cited by 3 publications

References 50 publications

Partial differential equation methods for stochastic dynamic optimization: an application to wind power generation with energy storage

Partial differential equation methods for stochastic dynamic optimization: an application to wind power generation with energy storage

Model-free load control for high penetration of solar photovoltaic generation

Energy saving for building heating via a simple and efficient model-free control design: First steps with computer simulations

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