Optimal Real-Time Pricing Algorithm Based on Utility Maximization for Smart Grid
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Citations
Smart Grid — The New and Improved Power Grid: A Survey
Smart Grid - The New and Improved Power Grid:
A Survey on Demand Response Programs in Smart Grids: Pricing Methods and Optimization Algorithms
Advanced Demand Side Management for the Future Smart Grid Using Mechanism Design
A Survey on Demand Response in Smart Grids: Mathematical Models and Approaches
References
Convex Optimization
Optimization flow control—I: basic algorithm and convergence
Optimal Residential Load Control With Price Prediction in Real-Time Electricity Pricing Environments
The concept of demand-side management for electric utilities
A Direct Load Control Model for Virtual Power Plant Management
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Optimal Residential Load Control With Price Prediction in Real-Time Electricity Pricing Environments
Frequently Asked Questions (15)
Q2. What have the authors stated for future works in "Optimal real-time pricing algorithm based on utility maximization for smart grid" ?
In this paper, the authors proposed an optimal real-time pricing algorithm for DSM in the future smart grid. It can be implemented in a distributed manner to maximize the aggregate utility of all users and minimize the cost imposed to the energy provider while keeping the total power consumption below the generating capacity. The ideas developed in this paper can be extended in several directions. A system with multiple energy providers can be considered.
Q3. What is the advantage of the proposed algorithm?
The high utilization of the available resources while keeping the total power consumption below the desired threshold is one of the advantages of the proposed algorithm.
Q4. What is the intended time cycle for the operation of the users?
The intended time cycle for the operation of the users is divided into K time slots, where K |K|, and K is the set of all time slots.
Q5. What is the way to solve the problem?
The problem formulated in (13) is a concave maximization problem and can be solved using convex programming techniques such as the interior point method (IPM) [20] in a central fashion.
Q6. What is the objective function in 14?
Although the objective function in (14) is further separable in xki and Lk, the variables x k i and Lk are coupled by the imposed constraint that the total consumed power cannot exceed the available capacity in (14).
Q7. What is the objective function of the dual optimization problem?
In fact, if the energy provider would be able to charge the users at a rate P = λk∗, and each individual user tries to maximize its own welfare function, it will be guaranteed by strong duality that the total power consumption will not exceed the provided capacity.
Q8. What is the parameter of user i in time slot k?
∀k ∈ K,(13) where U(xki , ω k i ) is defined in (8), Ck(Lk) is defined in (12), and ωki is the ω parameter of user i in time slot k.
Q9. What is the way to calculate the total power consumption of the users?
In the fixed pricing algorithm, the energy provider announces a price for each time slot k ∈ K at the beginning of the time slot which guarantees for any type of users with different choices of the ω parameter that the total consumption level will not exceed the generating capacity.
Q10. What is the effect of malicious users on the energy provider?
Simulation results confirmed that by using their proposed optimization-based real-time pricing model, not only the energy provider, but also the users will benefit.
Q11. What is the general expectation of utility functions?
The authors assume the general expectation that no power consumption brings no benefit, so the authors haveU(0, ω) = 0, ∀ω > 0. (7) Various choices of utility functions are widely used in the communications and networking literature [19].
Q12. How can the proposed algorithm be implemented?
It can be implemented in a distributed manner to maximize the aggregate utility of all users and minimize the cost imposed to the energy provider while keeping the total power consumption below the generating capacity.
Q13. What is the simplest way to optimize the energy consumption schedule?
Having a centralized control over all subscribers, and also being provided with complete information about thesubscribers’ needs, an efficient energy consumption schedule can be characterized as the solution of the following problem:maximize xki ∈Ik i , Lmin k ≤Lk≤Lmaxk ,i∈N , k∈K∑ k∈K ∑ i∈N U(x k i , ω k i ) − Ck(Lk)subject to ∑i∈N x k i ≤
Q14. What is the utility function for each user?
More formally, for each user, the utility function represents the level of satisfaction obtained by the user as a function of its power consumption.
Q15. What is the case scenario for the proposed algorithm?
in the fixed pricing algorithm, the worst case situation where the ω parameter of all the users assumes the maximum value ωmax = 4 is being considered.