Energy Cost Optimization of HVAC Loads Under Time-Varying Electricity Price Signals

2016 ◽  
Author(s):  
Saeid Bashash
Keyword(s):  
Dynamic Programming ◽  
Cost Function ◽  
Energy Cost ◽  
Optimal Operation ◽  
Electricity Price ◽  
Programming Approach ◽  
Time Varying ◽  
Temperature Deviation ◽  
Price Signals ◽  
The Cost

This paper presents a dynamic programming approach to optimize energy cost of multiple interacting household appliances such as air conditioning systems and refrigerators with temperature flexibility, under time varying electricity price signals. We adopt a first order differential equation model with a binary (ON-OFF) switching control function for each load. An energy cost minimization problem is then formulated with a pair of constraints on the temperature lower and upper bounds, as well as an equality condition on the initial and final temperature states. We use dynamic programming to compute cost-optimal control inputs and temperature trajectories for a given electricity price profile and ambient temperature condition. To account for temperature deviation from its desired setpoint, a quadratic temperature deviation penalty is added to the cost function. Moreover, to minimize the control input chattering for equipment protection, the cost function is expanded to also minimize the number of on-off switching events. Results for the different weighting combinations of the optimization objectives provide useful insights on the optimal operation of individual and multiple interacting HVAC loads. In particular, we observe that the loads are desynchronized under the cost-optimal operation, in the presence of local (renewable) power generation. The presented optimization algorithm and observed results can lead to the development of novel model predictive and rule-based feedback control policies for optimal energy management in households.

Operation of a CCHP System Using an Optimal Energy Dispatch Algorithm

2008 ◽  
Author(s):  
Heejin Cho ◽  
Sandra D. Eksioglu ◽  
Rogelio Luck ◽  
Louay M. Chamra
Keyword(s):  
Energy Efficiency ◽  
Energy Cost ◽  
Network Flow ◽  
Flow Model ◽  
Energy Requirement ◽  
Optimal Operation ◽  
Operational Conditions ◽  
Optimal Energy ◽  
Network Flow Model ◽  
The Cost

The Combined Cooling, Heating, and Power (CCHP) systems have been widely recognized as a key alternative for thermal and electric energy generation because of the outstanding energy efficiency, reduced environmental emissions, and relative independence from centralized power grids. Nevertheless, the total energy cost of CCHP systems can be highly dependent on the operation of individual components and load balancing. The latter refers to the process of fulfilling the thermal and electrical demand by partitioning or “balancing” the energy requirement between the available sources of energy supply. The energy cost can be optimized through an energy dispatch algorithm which provides operational/control signals for the optimal operation of the equipment. The algorithm provides optimal solutions on decisions regarding generating power locally or buying power from the grid. This paper presents an initial study on developing an optimal energy dispatch algorithm that minimizes the cost of energy (i.e., cost of electricity from the grid and cost of natural gas into the engine and boiler) based on energy efficiency constrains for each component. A deterministic network flow model of a typical CCHP system is developed as part of the algorithm. The advantage of using a network flow model is that the power flows and efficiency constraints throughout the CCHP components can be readily visualized to facilitate the interpretation of the results. A linear programming formulation of the network flow model is presented. In the algorithm, the inputs include the cost of the electricity and fuel and the constraints include the cooling, heating, and electric load demands and the efficiencies of the CCHP components. This algorithm has been used in simulations of several case studies on the operation of an existing micro-CHP system. Several scenarios with different operational conditions are presented in the paper to demonstrate the economical advantages resulting from optimal operation.

scholarly journals Design of Clean Steel Production with Hydrogen: Impact of Electricity System Composition

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8349
Author(s):  
Alla Toktarova ◽  
Lisa Göransson ◽  
Filip Johnsson
Keyword(s):  
Cost Minimization ◽  
Direct Reduction ◽  
Steel Production ◽  
Optimal Operation ◽  
Electricity Price ◽  
Solar Pv ◽  
Electricity System ◽  
Cost Efficient ◽  
The Cost ◽  
Hot Briquetted Iron

In Europe, electrification is considered a key option to obtain a cleaner production of steel at the same time as the electricity system production portfolio is expected to consist of an increasing share of varying renewable electricity (VRE) generation, mainly in the form of solar PV and wind power. We investigate cost-efficient designs of hydrogen-based steelmaking in electricity systems dominated by VRE. We develop and apply a linear cost-minimization model with an hourly time resolution, which determines cost-optimal operation and sizing of the units in hydrogen-based steelmaking including an electrolyser, direct reduction shaft, electric arc furnace, as well as storage for hydrogen and hot-briquetted iron pellets. We show that the electricity price following steelmaking leads to savings in running costs but to increased capital cost due to investments in the overcapacity of steel production units and storage units for hydrogen and hot-briquetted iron pellets. For two VRE-dominated regions, we show that the electricity price following steel production reduces the total steel production cost by 23% and 17%, respectively, as compared to continuous steel production at a constant level. We also show that the cost-optimal design of the steelmaking process is dependent upon the electricity system mix.

scholarly journals Algorithm for Solving Problem of Designing Regional Logistics Infrastructure

2021 ◽  
Vol 20 (4) ◽  
pp. 352-356
Author(s):  
R. B. Ivut ◽  
P. V. Popov ◽  
P. I. Lapkovskaya ◽  
N. E. Sheveleva
Keyword(s):  
Dynamic Programming ◽  
Cost Function ◽  
Methodological Approach ◽  
Optimal Location ◽  
Transport Infrastructure ◽  
Regional Logistics ◽  
Initial Stage ◽  
Nested Sets ◽  
Three Stages ◽  
The Cost

The paper considers an algorithm for solving the problem of finding the optimal location of key objects of transport and warehouse infrastructures within the framework of a methodological approach to designing logistics infrastructure in the territory of the region of the countries. The methodological approach includes three stages. At the first stage, areas  are determined where it is advisable to locate key objects of the regional logistics infrastructure. Further, using the models developed by the authors, the linking of warehouse infrastructure objects on the ground has been carried out and, taking into account the designed warehouse network, the optimal dislocation of transport infrastructure objects has been determined.  To find the optimal locations for the objects for regional logistics infrastructure facilities, the authors propose an algorithm that is applicable both for building warehouse and transport infrastructures due to the similarity of the models. The algorithm is based on the method of constructing a sequence of plans. At the initial stage, the final expansion is constructed for the set of plans under consideration. For a given set, a minorant has been determined for the cost function associated with the placement and maintenance of infrastructure facilities, the movement of goods, and the haul of an empty vehicle. After that, an iterative algorithm has been formed that determines the sequence of optima of the minorant on a sequence of nested sets. At the first step, an element of the set of plans has been found that minimizes the minorant, at the next step, the found element is excluded from the set under consideration, and a new optimum is sought on the remaining set for which the minorant takes the minimum value. To eliminate multiple plans, it is advisable to use dynamic programming procedures. The limits of applicability  of the method for constructing a sequence of plans are determined by the ability to construct an extension of the set of plans for placing objects, select a minorant on it, and build an algorithm for ordering optima.

On the Assignment of Customers to Parallel Queues

1992 ◽  
Vol 6 (4) ◽  
pp. 495-511 ◽  
Author(s):  
Arie Hordijk ◽  
Ger Koole
Keyword(s):  
Dynamic Programming ◽  
Cost Function ◽  
Optimal Policy ◽  
The State ◽  
Arrival Process ◽  
Single Server ◽  
Finite Buffers ◽  
Parallel Queues ◽  
Routing Policy ◽  
The Cost

This paper considers routing to parallel queues in which each queue has its own single server and service times are exponential with nonidentical parameters. We give conditions on the cost function such that the optimal policy assigns customers to a faster queue when that server has a shorter queue. The queues may have finite buffers, and the arrival process can be controlled and can depend on the state and routing policy. Hence our results on the structure of the optimal policy are also true when the assigning control is in the “last” node of a network of service centers. Using dynamic programming we show that our optimality results are true in distribution.

A Fuzzy-Dynamic-Programming Approach to the Scheduling of Cascaded Hydropower Plants

2013 ◽  
Vol 760-762 ◽  
pp. 2028-2036
Author(s):  
Jin Zou ◽  
Feng Pan
Keyword(s):  
Dynamic Programming ◽  
Numerical Test ◽  
Main Idea ◽  
Optimal Operation ◽  
Programming Approach ◽  
Dynamic Programming Approach ◽  
Hydropower Plants ◽  
Hydraulic Coupling ◽  
Hydropower System

An optimization-based algorithm is presented for the optimal operation of hydropower systems with cascaded hydro-plants. Continuous reservoir dynamics and constraints, discrete operating states, and hydraulic coupling of cascaded hydro-plants are considered in an integrated way. The main idea is to decompose the cascaded hydro-plants into individual plants, and then use Fuzzy Dynamic Programming (FDP), rather traditional Dynamic Programming (DP), to solve the subproblem of each plant while considering the hydraulic coupling of the plants. Numerical test shows that this method converges very fast, and is efficient and effective to deal with hydropower system with cascaded hydro-plants.

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