• Energy Research
• 2016-2025close
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The widespread use of optimization methods in the design phase of District Heating Networks is currently limited by the availability of scalable optimization approaches that accurately represent the network. In this paper, we compare and benchmark two different approaches to non-linear topology optimization of District Heating Networks in terms of computational cost and optimality gap. The first approach solves a mixed-integer non-linear optimization problem that resolves the binary constraints of pipe routing choices using a combinatorial optimization approach. The second approach solves a relaxed optimization problem using an adjoint optimization approach, and enforces a discrete network topology through penalization. Our benchmark shows that the relaxed penalized problem has a polynomial computational cost scaling, while the combinatorial solution scales exponentially, making it intractable for practical-sized networks. We also evaluate the optimality gap between the two approaches on two different District Heating Network optimization cases. We find that the mixed-integer approach outperforms the adjoint approach on a single-producer case, but the relaxed penalized problem is superior on a multi-producer case. Based on this study, we discuss the importance of initialization strategies for solving the optimal topology and design problem of District Heating Networks as a non-linear optimization problem.

The widespread use of optimization methods in the design phase of District Heating Networks is currently limited by the availability of scalable optimization approaches that accurately represent the network. In this paper, we compare and benchmark two different approaches to non-linear topology optimization of District Heating Networks in terms of computational cost and optimality gap. The first approach solves a mixed-integer non-linear optimization problem that resolves the binary constraints of pipe routing choices using a combinatorial optimization approach. The second approach solves a relaxed optimization problem using an adjoint optimization approach, and enforces a discrete network topology through penalization. Our benchmark shows that the relaxed penalized problem has a polynomial computational cost scaling, while the combinatorial solution scales exponentially, making it intractable for practical-sized networks. We also evaluate the optimality gap between the two approaches on two different District Heating Network optimization cases. We find that the mixed-integer approach outperforms the adjoint approach on a single-producer case, but the relaxed penalized problem is superior on a multi-producer case. Based on this study, we discuss the importance of initialization strategies for solving the optimal topology and design problem of District Heating Networks as a non-linear optimization problem.

Electric water heaters have the ability to store energy in their water buffer without impacting the comfort of the end user. This feature makes them a prime candidate for residential demand response. However, the stochastic and nonlinear dynamics of electric water heaters, makes it challenging to harness their flexibility. Driven by this challenge, this paper formulates the underlying sequential decision-making problem as a Markov decision process and uses techniques from reinforcement learning. Specifically, we apply an auto-encoder network to find a compact feature representation of the sensor measurements, which helps to mitigate the curse of dimensionality. A wellknown batch reinforcement learning technique, fitted Q-iteration, is used to find a control policy, given this feature representation. In a simulation-based experiment using an electric water heater with 50 temperature sensors, the proposed method was able to achieve good policies much faster than when using the full state information. In a lab experiment, we apply fitted Q-iteration to an electric water heater with eight temperature sensors. Further reducing the state vector did not improve the results of fitted Q-iteration. The results of the lab experiment, spanning 40 days, indicate that compared to a thermostat controller, the presented approach was able to reduce the total cost of energy consumption of the electric water heater by 15%. Submitted to IEEE transaction on smart grid

Electric water heaters have the ability to store energy in their water buffer without impacting the comfort of the end user. This feature makes them a prime candidate for residential demand response. However, the stochastic and nonlinear dynamics of electric water heaters, makes it challenging to harness their flexibility. Driven by this challenge, this paper formulates the underlying sequential decision-making problem as a Markov decision process and uses techniques from reinforcement learning. Specifically, we apply an auto-encoder network to find a compact feature representation of the sensor measurements, which helps to mitigate the curse of dimensionality. A wellknown batch reinforcement learning technique, fitted Q-iteration, is used to find a control policy, given this feature representation. In a simulation-based experiment using an electric water heater with 50 temperature sensors, the proposed method was able to achieve good policies much faster than when using the full state information. In a lab experiment, we apply fitted Q-iteration to an electric water heater with eight temperature sensors. Further reducing the state vector did not improve the results of fitted Q-iteration. The results of the lab experiment, spanning 40 days, indicate that compared to a thermostat controller, the presented approach was able to reduce the total cost of energy consumption of the electric water heater by 15%. Submitted to IEEE transaction on smart grid

Pathogens represent a significant threat to human health leading to the emergence of strategies designed to help manage their negative impact. We examined how spiritual beliefs developed to explain and predict the devastating effects of pathogens and spread of infectious disease. Analysis of existing data in studies 1 and 2 suggests that moral vitalism (beliefs about spiritual forces of evil) is higher in geographical regions characterized by historical higher levels of pathogens. Furthermore, drawing on a sample of 3140 participants from 28 countries in study 3, we found that historical higher levels of pathogens were associated with stronger endorsement of moral vitalistic beliefs. Furthermore, endorsement of moral vitalistic beliefs statistically mediated the previously reported relationship between pathogen prevalence and conservative ideologies, suggesting these beliefs reinforce behavioural strategies which function to prevent infection. We conclude that moral vitalism may be adaptive: by emphasizing concerns over contagion, it provided an explanatory model that enabled human groups to reduce rates of contagious disease.