Mixed-integer Linear Programming Optimization Model Research Articles

Optimising the regional mix of intermittent and flexible energy technologies

Renewable energy sources could potentially satisfy a much larger part of the energy demand of human societies. When it comes to wind and solar energy, a key technological difficulty is the intermittent nature of these sources of energy. In order to ensure that energy is available at times when it is needed, these renewable energy technologies need to be backed up by storage systems and other more flexible energy systems such as gas engines. This paper presents a multi-period mixed-integer linear programming optimisation model of an energy system featuring multiple alternatives for satisfying variable demands of electricity and heat. The model is used to investigate how the intermittent renewable energy sources could work together with storage technologies, heat pumps, and flexible gas engines in a resource-efficient manner. Case studies are presented to illustrate how suitable technologies could be selected and operated in a region with high seasonal differences in the demands of heat and electricity. The case study suggests that heat pumps could play an important part in optimising the usage rate of wind power.

A general approach for mixed-integer predictive control of HVAC systems using MILP

Abstract The topic of the paper is optimal control of heating, ventilation, and air conditioning (HVAC) systems. Using mixed-integer linear programming (MILP) the main contribution is a flexible and modular MILP model of HVACs. It is the centerpiece of the proposed hierarchical multi-input multi-output (MIMO) model predictive control (MPC) framework for energy, comfort, and wear optimization. On the upper-level a plant MPC takes care of the slow dynamics of a plant. On the lower-level a MILP-MPC based on a MILP optimization model of an HVAC system optimizes the HVAC operation. The MILP-MPC considers the first few samples of the control trajectory of the plant MPC as its reference trajectory. It minimizes power consumption and switching of the HVAC. Thereby it has to obey constraints, consider component characteristics by nonlinearity approximation, and solve a unit commitment problem. The fact that the plant MPC can be based on an almost arbitrary plant model and the MILP model of the MILP-MPC can represent a variety of different HVAC systems unifies HVAC control. Features and results are presented in case studies: The first case study shows that state of the art HVAC operation is outperformed even if the predictive capability is not used. The second case study demonstrates that temperature, CO2 level, and humidity can be controlled simultaneously in a decoupled fashion. The third case study reveals that if also the lower-level MILP-MPC oversees the latency periods of HVAC components optimal switching is achieved.

Optimal battery storage operation for PV systems with tariff incentives

Many efforts are recently being dedicated to developing models that seek to provide insights into the techno-economic benefits of battery storage coupled to photovoltaic (PV) generation system. However, not all models consider the operation of the PV – battery storage system with a feed-in tariff (FiT) incentive, different electricity rates and battery storage unit cost. An electricity customer whose electricity demand is supplied by a grid connected PV generation system benefiting from a FiT incentive is simulated in this paper. The system is simulated with the PV modelled as an existing system and the PV modelled as a new system. For a better understanding of the existing PV system with battery storage operation, an optimisation problem was formulated which resulted in a mixed integer linear programming (MILP) problem. The optimisation model was developed to solve the MILP problem and to analyse the benefits considering different electricity tariffs and battery storage in maximising FiT revenue streams for the existing PV generating system. Real data from a typical residential solar PV owner is used to study the benefit of the battery storage system using half-hourly dataset for a complete year. A sensitivity analysis of the MILP optimisation model was simulated to evaluate the impact of battery storage capacity (kWh) on the objective function. In the second case study, the electricity demand data, solar irradiance, tariff and battery unit cost were used to analyse the effect of battery storage unit cost on the adoption of electricity storage in maximising FiT revenue. In this case, the PV is simulated as a new system using Distributed Energy Resources Customer Adoption Model (DER-CAM) software tool while modifying the optimisation formulation to include the PV onsite generation and export tariff incentive. The results provide insights on the benefit of battery storage for existing and new PV system benefiting from FiT incentives and under time-varying electricity tariffs.

Techno-economic and environmental modelling and optimization of flexible distributed multi-generation options

It is arguable how much flexibility and efficiency from coupling different energy vectors through available technologies is exploited in current energy systems. In particular, in spite of the growing interest for the multi-energy concept, there are very few models capable of clearly explaining the benefits that can be derived from integration of complementary technologies such as cogeneration, electric heat pumps and thermal storage. In this light, this paper introduces a comprehensive analysis framework and a relevant unified and synthetic Mixed-Integer Linear Programming optimization model suitable for evaluating the techno-economic and environmental characteristics of different Distributed Multi-Generation (DMG) options. Each option's operational performance and flexibility to respond to electricity market signals are analysed in detail and assessed against the needed investment costs in different contexts. Numerical case studies focus on highlighting the flexibility benefits that can be gained in economic terms from multi-energy system integration in district heating (DH) applications. Detailed sensitivity analyses of different DMG configurations also clearly show what economic as well as environmental performance (at both global and local levels) can be expected in current and future scenarios when coupling different energy vectors and complementary technologies in a multi-energy context.

Design for Energy-Efficient IP Over WDM Networks With Joint Lightpath Bypass and Router-Card Sleeping Strategies

To reduce the energy consumption of the Internet, much research effort has been dedicated to the design of energy-minimized IP over WDM networks. In this study, we design energy-minimized IP over WDM networks based on modular router cards and by jointly applying the lightpath bypass and router-card sleeping strategies. As a key advantage, the design does not require rerouting of IP flows or optical channels in either the IPor optical layer. Rather, to save energy, we only need to sleep or wake up the router cards according to user traffic demands when applying the sleeping strategy, which significantly simplifies the network control and management. To minimize the total energy consumption of the IPover WDM network in a time period (e.g., 1 day), we develop a mixed integer linear programming (MILP) optimization model. Moreover, to alleviate the computational complexity of the MILP model, we divide the minimization problem into two subproblems, namely, 1) establishing a virtual topology and 2) allocating router ports on router cards to the optical channels on different virtual links. For each of the subproblems, we develop a separate MILP optimization model. Further, for large-network design, we also propose two efficient heuristics to optimize energy consumption. Simulation studies indicate that the joint MILP model with the lightpath bypass and router-card sleeping strategies can maximally reduce energy consumption, up to 40% compared to the nonsleeping case. In addition, under the router-card sleeping strategy, the approach of allocating the router ports on different router cards to the optical channels plays an important role in the design of an energy-minimized IP over WDM network. A mixed mode that jointly performs interleaving and sequential router-port allocations can achieve the highest energy savings.

Design and optimization of industrial power systems for natural gas processing

This paper presents a novel design methodology for power systems. A superstructure-based modelling technique has been applied to identify the cost-effective match between available power generation equipment and energy consumers. Multi-period design is conducted to ensure accurate equipment performance estimation. The proposed MILP (mixed integer linear programming) optimization model is able to reflect the machinery performance variations affected by the environmental conditions, and to estimate the deteriorated machinery performance due to part-load operation. To maintain the linear nature of the overall mathematical model, machinery performance is linearized with reasonable accuracy. Moreover, the multi-period methodology is able to conduct synthesis of power systems for processes with non-constant energy demands. Case studies are illustrated to demonstrate the importance of considering the effect of ambient conditions and part-load operation on machinery performance. With the ability to satisfy varying energy demands, and more accurate description of the machinery performance, the optimal design yielded from the improved model would exhibit better flexibility and reliability.