Computational Intelligence-Based Demand Response Management in

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIA.2018.2871390, IEEE Transactions on Industry Applications

Computational Intelligence Based Demand Response Management in a Microgrid Pramod Herath, Student Member, IEEE, Vito Fusco, María Navarro, Student Member, IEEE, Ganesh K. Venayagamoorthy, Senior Member, IEEE, Stefano Squartini, Senior Member, IEEE, Francesco Piazza, Senior Member, IEEE and Juan Manuel Corchado, Senior Member, IEEE

Abstract -- A demand response management (DRM) system is proposed here, in which a service provider determines a mutual optimal solution for the utility and the customers in a microgrid setting. Such a system may find use with a service provider interacting with the respective customers and utilities under the existence of some DRM agreements. The service provider is an entity which acts at different levels of the electrical grid and carry out the optimization. The lowest level controls one ‘neighborhood’ while higher levels of service providers control other lower level service providers. A microgrid consisting of a smart neighborhood of twelve customers was used as experimental case study and an advanced metering infrastructure (AMI) was implemented. Based on the formulation of an optimization problem which exploits priceresponsive demand flexibility and the AMI infrastructure, a win-win-win strategy is presented. The interior point method was used to solve the objective function and the application of particle swarm optimization and artificial immune systems for demand response was explored. Results for a range of typical scenarios were presented to demonstrate the effectiveness of the proposed demand-response management framework. Index Terms--Advanced metering infrastructure (AMI), Artificial Immune System, demand response (DR), dynamic pricing, Multi-Objective Optimization, Particle Swarm Optimization, remote management system, smart grid. P. Herath is with the Department of Electrical and Computer Engineering, Clemson University, Clemson, SC, 29634, USA (e-mail: [email protected]). V. Fusco is with the Department of Electrical and Computer Engineering, Clemson University, Clemson, SC, 29634 USA and Universit`a Politecnica delle Marche, 60121 Ancona, Italy (e-mail: [email protected]). M. Navarro and Juan Manuel Corchado are with the University of Salamanca, c/Espejo, s/n, Salamanca 37007, Spain (e-mail: [email protected]; [email protected]). G. Venayagamoorthy is with the Department of Electrical and Computer Engineering, Clemson University, Clemson, SC, 29634, USA and Eskom Centre of Excellence in HVDC Engineering, University of KwaZulu-Natal, Durban, South Africa (e-mail: [email protected]). S. Squartini and F. Piazza are with Universit`a Politecnica delle Marche, 60121 Ancona, Italy (e-mail: [email protected]; [email protected]). This work is supported by the National Science Foundation (NSF) of the United States, under grant IIP #1312260 and #1408141, the Duke Energy Distinguished Professorship Endowment Fund and H2020 DREAM-GO Project (Marie Sklodowska-Curie grant agreement No 641794). Any opinions, findings and conclusions or recommendations expressed in this material are those of author(s) and do not necessarily reflect the views of the supporters.

I.

INTRODUCTION

One of the most important concepts for a reliable operation of electrical grid is the balancing between supply and demand. The requirement however that power generation must meet the energy demand at any time instant is often complicated from the large penetration of intermittent sources of alternative generation. Such an occurrence can result in a significant price volatility that may change from 10-20 cents/kWh during normal periods to more than few US dollars/kWh at peak hours. Therefore, demand response techniques [1] such as direct load control [2], time-of-use (TOU) pricing and [3] real time pricing are used to meet the energy demand and available power, thus improving grid stability to mitigate the negative effects of high price volatility for both the utility and the consumer . Curtailment is one such direct load control scheme in which the utility, based on a pre-agreement with the customers, can send requests for load reductions at critical times. Other DR approaches are used to shape the energy demand indirectly by changing the price. Different demand response strategies have been studied either for the purposes of load shaping by a utility or aggregator, such that a certain social welfare is optimized [4], or in the context of the design of an appropriate market structure that considers the various mechanisms of demand flexibility [5]. In this paper, the utility is assumed as a price taker with the market price remains unaffected by the demand bids. The elasticity matrix is useful in modeling the effect of the price on the customer's demand flexibility [6]. Here, the demand is treated as an exponentially decreasing function with the increase in the price of the commodity, followed by calculating the relative slope via linearization around a given point. This value, which is defined as the 'elasticity coefficient', also introduces the matrices of self and crosselasticity coefficients to model how the effects of changing the demand of one commodity affects the demand of another. The Price Elasticity matrix (PEM) has been used to improve the bidding mechanism by accounting for various forms of demand flexibility [7]. More detailed models of DR have also been developed in which mixed-integer linear programming was used in the optimal scheduling of home appliances and distributed generation systems [8]. Other energy management strategies entail exploring the advantages of introducing the

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thermal and electric storage in a micro-grid scenario [9]. Detailed price responsive customer scenarios have also been used to optimally balance supply and demand via centralized or distributed optimization models to select the optimal schedule of generation and consumption devices. One such scenario involves dividing the consumers into several classifications and then builds a non-linear problem [10]. It assumes knowledge of very detailed information about the price-responsive customers by the utility. Similarly, a modified LRIC pricing model has been developed but must assume detailed customer knowledge or the electric grid [11]. In this paper, for which the basic work is done in [12], the PEM model to influence the price with changing demand is applied. An optimization problem is formulated to minimize the trade-off between energy procurement costs of the load serving entity and an end-customers utility. Assuming the knowledge of the energy demand by forecasting based on historical data, and the knowledge of the day ahead price at the energy market, an optimal set of prices for the next day can be dispatched to the customers such that the resulting load profile in the next day minimizes the cost of both the energy procurement and the energy cost for the end-users while maintaining the comfort of the customer. Various schemes are available for forecasting [13]. The contributions of the paper are as follows: • A viable model based on price elasticity matrix is proposed for time of use pricing. This introduced pricing model can be used in different environments including hierarchical demand response schemes [20]. The DR model has linear constraints and is convex making it easier to solve. • Application of different optimization methodologies for demand response management is explored. • A ‘service provider’ model is introduced who would drive the demand response scheme and would make sure the various stresses (as studied by many different studies [14] [15]), on the power system by demand response system are managed. Under this concept, a neighborhood under the control of a service provider is small and the impact on the power system is considered to be minimal. Such a service provider service would be viable if the service provider operates more than one neighborhood, which would reduce the committing costs. • An environment consisting of hardware and software solutions for a service provider by whom the pricing scheme would be implemented and the residential neighborhood is introduced on which the pricing mechanism is tested on. The rest of the paper is organized as follows. The modeling and the formulation of the optimization problem is detailed in Section II. Section III describes the solution methods tested. The implemented micro-grid scenario along with the data set is detailed in Section IV. The

experiments carried out and their results with a discussion is presented in Section V. And finally Section VI presents the conclusions. II.

COST MINIMIZATION MODEL

A.

Modeling of Participants in Microgrid Customer: The objective function for the customer is the cost function 𝐽1 . Assume that 𝑍 ∈ ℝ𝑝 and 𝜋𝑐 𝜖ℝ𝑝 are the customer’s energy demand and the price of the energy respectively: 𝑍 = 𝐺 + 𝐴. 𝑥 𝜋𝑐 = 𝑝0 + 𝑥

(1) (2)

where 𝐺, 𝑥, 𝑝0 𝜖 ℝ𝑝×1 and 𝐴 ∈ ℝ𝑝×𝑝 , 𝑝 is the number of the samples per day. The vector 𝐺 contains the day ahead forecasted values of the hourly customer’s energy demand without doing demand response. The vector 𝑥 is the set of the price differences between 𝑝0 and 𝜋𝑐 , the vector of the energy prices for the customers without doing DR, and 𝜋𝑐 , which contains their hourly energy prices doing DR. 𝑍 is the energy demand subjected to the price changes, the linear dependence from 𝑥 is through 𝐴: 𝑎11 0 𝐴 = 𝜅( .. 0

0 𝑎22 .. ..

.. .. .. ..

0 0 .. ) 𝑎𝑝𝑝

(3)

where 0 ≤ 𝑎𝑖,𝑗 ≤ 1, 𝜅 ≥ 1. Here, 𝐴 is the elasticity matrix that defines the flexibility of the customer demand. The diagonal element 𝜅. 𝑎𝑖𝑗 represents the demand change responding to the price change at the same time period. The off-diagonal elements represent the demand change due to the price fluctuations over other time periods. Although various forms of the elasticity matrix are used to analyze the DR method, without affecting the generality of the method, 𝐴 is chosen to as diagonal, making it more intuitively reflective of its definition. The objective function for the customers is a cost function 𝐽1 , which can be defined as: 𝐽1 = 𝑍 𝑇 . 𝜋𝑐 = (𝐺 + 𝐴. 𝑥)𝑇 . (𝑝0 + 𝑥)

(4)

To better express the behavior of the customers in response to the changing of the energy price, 𝐽1 can be extended as: 𝐽1 = (𝐺 + 𝐴. 𝑥)𝑇 . (𝑝0 + 𝑥) + 𝛼𝑥 𝑇 . 𝐴𝑇 . 𝐴. 𝑥

(5)

The last term of the equation is the comfort cost, a customer with a high value of 𝛼 prefers paying more than saving money by changing their energy demand. Utility: The objective function for the utility is the cost function 𝐽2 . Considering 𝑍 as the energy demand of the customers, and 𝜋𝑢 as the set of the energy prices from the energy market, 𝐽2 can be written as:



𝐽2 = 𝛽𝑍 𝑇 . 𝜋𝑢 = 𝛽(𝐺 + 𝐴. 𝑥). 𝜋𝑢𝑇

where 𝛽 in ℝ and 𝜋𝑢 𝜖 ℝ𝑝×1 . The energy demand Z, as discussed above, is a linear function of the price differences, 𝑥. The term 𝜋𝑢 is the hourly day ahead energy price for the utility at the energy market. 𝛽, in above equation, is the weighing factor that ensures the balance between the cost functions of the customer and utility. Constraints: In this optimization problem the constraints depend on the price fluctuations and the value of the energy demand. These constraints fix the feasible region for the solution of the optimization process:𝑥. For the price fluctuations, the constraint is on the values of 𝑥 is: 𝑥1 1 1 𝑥 2 1 1 −𝜆 ( ) ≤ ( . . ) ≤ 𝜆 ( ) .. .. 𝑥𝑝 1 1

(7)

where 𝜆 ∈ ℝ. The 𝜆 coefficient is typically chosen to be a percentage value of the energy price without any DR action. For the energy demand 𝑍 the constraints are: 0 𝐺 + 𝐴. 𝑥 ≥ (. .) 0 1𝑇 . 𝐴. 𝑥 = 0

(8) (9)

Constraint (8) is about the positive value of the energy demand, constraint (9) ensures that the total energy consumption by the consumer remains identical to the forecasted total value without DR, even though the consumption pattern changes. The high volatility of the price means that the utility wishes to adapt the energy demand to the cost of the energy to optimize their cost. However the customers tend to optimize the energy management to minimize the bill, depending upon their respective levels of comfort. In this optimization process, based on a deterministic model, the energy procurement for the utility and the bill of the customers are minimized by minimizing the sum of the respective cost functions 𝐽1 and 𝐽2 . This process tends to enhance the participation in the DR programs, making the utility less subject to the price volatility, thus increasing both utility profits and benefits for the end-users. The optimization problem can be written as: 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒𝑥 𝐽1 (𝑥) + 𝐽2 (𝑥) 𝑠𝑢𝑏𝑗𝑒𝑐𝑡𝑒𝑑 𝑡𝑜 𝑀𝑒𝑞 . 𝑥 = 𝑁𝑒𝑞

𝑇

1 1 = ( ) . 𝐴, 𝑁𝑒𝑞 = 0 .. 1

(11)

𝜆. 1 1 𝑀𝑛𝑒𝑞 = ( −1 ) , 𝑁𝑛𝑒𝑞 = (𝜆. 1) −𝐴 𝐺

(12)

(6)

(10)

𝑀𝑛𝑒𝑞 . 𝑥 ≤ 𝑁𝑛𝑒𝑞 Here 𝑀𝑒𝑞 , 𝑁𝑒𝑞 and 𝑀𝑛𝑒𝑞 , 𝑁𝑛𝑒𝑞 are the matrices for the equality and inequality constraints, respectively:

𝑀𝑒𝑞

𝑀𝑛𝑒𝑞 , 𝑁𝑛𝑒𝑞 are used in (10) to express the inequality constraints (7) and (8). The equality constraints (9) have been defined in (10) through 𝑀𝑛𝑒𝑞 and 𝑁𝑛𝑒𝑞 . This problem in (10) is quadratic with linear constraints and efficient solvers based on interior point methods could be used. The solution is the vector 𝑥 ∈ ℝ𝑝×1 , which is used to compute the prices published by the utility for the individual customers the day ahead, such that the resulting load profile in the next day minimizes the costs of energy procurement as well as the energy bill of the customer with a minimum compromise in comfort. III. SOLUTION METHODS In this section, interior-points method, constrained particle swarm optimization and artificial immune system algorithms are explored as possible algorithms to be applied for complex demand response models. In the following subsections, each of these methods are described. A.

Interior-point Method The interior-point method is a popular method utilized in mathematical optimization. The interior-points method is the best for solving this problem as the objective function is a convex differentiable function with linear constraints. The Matlab optimization toolbox is used for the implementation of the interior-point method. In this study, this implementation was utilized to calculate the solution, the results of which are shown in Figs. 4-8. B.

Constrained Particle Swarm Optimization Method

First proposed by James Kennedy and Russel Eberhart [16], Particle Swarm Optimization (PSO) is a nature-inspired algorithm similar to the genetic algorithm, which although simpler and less computationally intensive than the genetic algorithm is nonetheless effective. PSO involves a ‘swarm of particles’ swimming through the solution space searching for the best solution, the movement of which is determined by a set of equations. Although PSO in its original form can only handle unconstrained problems, several adaptations have been proposed for constrained problems. The authors base their approach upon their established procedure in which three equations governing the movement of the particles [17]. Either of the first two equations govern the ‘velocity’ of each of the particle depending on whether that particle is currently in the feasible region. If the particle



is in the feasible region, the equation for velocity is: 𝑉𝑖𝑑,𝑘+1 = 𝑤𝑉𝑖𝑑,𝑘 + 𝑐1 𝑟𝑎𝑛𝑑1 (𝑋𝑝𝑏𝑒𝑠𝑡𝑖𝑑,𝑘 − 𝑋𝑖𝑑,𝑘 ) + 𝑐2 𝑟𝑎𝑛𝑑2 (𝑋𝑔𝑏𝑒𝑠𝑡𝑑,𝑘 − 𝑋𝑖𝑑,𝑘 )(13) Here 𝑉𝑖𝑑,𝑘+1 is the velocity of the 𝑑 𝑡ℎ dimension of the 𝑖 particle in the next (𝑘 + 1𝑠𝑡 ) iteration, 𝑤 is the inertia of the particle, 𝑉𝑖𝑑,𝑘 is the velocity of the 𝑑 𝑡ℎ dimension of the 𝑖 𝑡ℎ particle in the current (𝑘 𝑡ℎ ) iteration. 𝑐1 is the cognitive acceleration constant, 𝑐2 is the social acceleration constant, 𝑋𝑝𝑏𝑒𝑠𝑡𝑖𝑑,𝑘 is the position of the particle in the 𝑑 𝑡ℎ dimension and 𝑐1 and 𝑐2 are random numbers. In this scenario, the particle makes use of both the best solution found by the whole system and the best solution found by itself thus far to determine the next set of arguments used to check the solution. However, if the particle has yet to determine a feasible solution, any influence of an infeasible solution is of no use. Therefore, the velocity for the next iteration for a particle without any feasible solution is defined as: 𝑡ℎ

𝑉𝑖𝑑,𝑘+1 = 𝑤𝑉𝑖𝑑,𝑘 + (𝑐1 + 𝑐2 ) × 𝑟𝑎𝑛𝑑 × (𝑋𝑔𝑏𝑒𝑠𝑡𝑑,𝑘 − 𝑋𝑖𝑑,𝑘 ) (14) Using the velocity calculated, the next position in the search space means that the particle calculating the objective value is expressed as 𝑋𝑖𝑑,𝑘+1 = 𝑋𝑖𝑑,𝑘 + 𝑉𝑖𝑑,𝑘 (15)

created and introduced to the antigens to measure their affinity between each antigen and antibody. An optimization function is used to calculate this affinity. Those antibodies with high affinity are selected and a number of clones 𝑁𝑐 are generated for purposes of mutating each antibody, a process that is controlled according to the affinity values. Therefore, the high values in the fitness function means a low mutation process and vice versa. Here, 𝛿 is lineally combined to produce a new individual, according to Equation (16) 𝛿=

(16)

where 𝛽 is a constant that is empirically obtained to normalize the effect of the fitness rate 𝑓𝑖 obtained by each cell. Likewise, those antibodies with fitness values below a given threshold 𝑡𝑠 are suppressed from the total population. This process is repeated until the solution is achieved and the population converges in one point. The algorithm (Algorithm 1) is summarized below. Algorithm 1: Artificial Immune System Procedure AIS (problem) Set parameters 𝑁, 𝑁𝑐 , 𝑡𝑠 , 𝛽 Initialize population with random values For each iteration, do: a. Calculate Fitness for each antibody b. Reproduce the antibodies with high affinity values c. Mutate the clones of each antibody according to their affinity values d. Suppress individuals with low affinity values e. Generate random individuals and insert them in the population Repeat until convergence criterion is met

. The results obtained by PSO on the model described in this paper are illustrated in Fig. 9. Artificial Immune System Method Bioinspired algorithms (e.g. artificial neural networks, genetic algorithms and swarm intelligence) are widely used to solve different research problems, following biological principles and behaviors. [18]. Following this natural process, De Castro et al. [19] developed the CLONALG algorithm, a clonal selection procedure for use in pattern recognition. The algorithm suppresses, reproduces and mutates the individuals according to the affinity with an external antigen. The new individuals are immersed in the population for evaluation, reproduction, mutation and suppression according to their affinity. Each operation is conditioned by the prior creation of parameters to influence the final results of the mutation, suppression or reproduction processes, respectively. Specifically, in the opt-aiNet formation, developed to optimize such problems via the principles of the CLONALG, the antigens are configured to represent the information recognized by the antibodies [19]. Specifically, this affinity is formalized with a fitness function to optimize so that the higher values of fitness function correspond to a high affinity between the antibodies and antigens. Initially, a certain number 𝑁 of antibodies are randomly

𝑒 𝑓𝑖 𝛽

C.

The results of the algorithm on the system are shown in Figs. 10-13. D. Discussion of Algorithms While the interior point method is suitable for this convex optimization problem, the particle swarm optimization and artificial immune system methods are better at solving more complex, non-linear and non-convex objective functions which arise in more complex demand response systems. IV.

THE MICRO-GRID ENVIRONMENT

A.

Service Provider In this subsection a ‘Service Provider’ (SP) model is introduced for use in the application of the demand response



scheme. The service provider resides between the customer and utility and provides the demand response service. The action is accomplished via interactions with the customers and the utility via the use of suitable existing pre-agreements between each. Using the customer flexibility and comfort and the interest of utility as the criteria, an optimal set of hourly day-ahead prices 𝜋𝑐 are selected for the customers to minimize the cost of energy procurement. Thus, this scheme serves both the interests of the utility and the customers. The conceptual method adopted is shown in Fig. 2 and the software components used by the service provider are described below. The service provider is a hierarchical entity as shown in Fig. 1b. Different levels of service providers are positioned at various levels of the transmission and distribution lines and would control the service providers below. The super service providers will take care of a part of the grid, making sure the service providers below would not violate any grid constraints while carrying out demand response. At the very lowest level, the local service provider will interact with the customers through AMI, and would make sure the correct pricing is offered for the customer. The intent here is to address the lowest level of service providers. Fig. 2. System diagram.

V.

Fig. 1a. Conceptual diagram for local service provider.

RESULTS AND DISCUSSION

The microgrid scenario described in the previous section is used as the test bed for testing the proposed DR strategy. The authors detail in five case studies the exploitation of pricebased DR mechanisms and the optimization of the energy procurement process for the utility illustrating how this change affects thin both customer comfort and flexibility affects the mutual benefits. The values of the optimization problem parameters used for each case study (see Table I) include both customer flexibility and the comfort level. The day-ahead price of the energy procurement, which is from the ISO New England website, is related to the first week of August 2015 in Vermont. The customers outside the DR strategy are assigned a given fix price while those inside the DR are subjected to the day-ahead price chosen by the provider as determined by the optimization process. The forecasted energy demand of the neighborhood, which exhibits two trends during the midweek and the weekend, is obtained by modeling the energy consumption of each neighborhood customer. For example, the houses with students tend to have higher energy demands during the evening with respect to those who are retirees. To show the benefits of the DR strategy for both the customers and the utility, the following formula is used to compute the percentage cost variation:

Fig. 1b. Hierarchical structure of service providers.


𝐶𝑜𝑠𝑡𝑓 − 𝐶𝑜𝑠𝑡𝑖 . 100 𝐶𝑜𝑠𝑡𝑖

(17)


where 𝐶𝑜𝑠𝑡𝑖 is the cost of the energy procurement for the utility, or the cost of the bill for the customers without DR. 𝐶𝑜𝑠𝑡𝑓 is the same cost, but when they take part in the DR programs. 𝐶𝑜𝑠𝑡𝑖 for the customer represents payment for energy at a reasonably fixed price of 14.12 cents per kWh. For the utility it is the hourly day-ahead prices for the energy demand at that time interval.

Case I 𝑎1,1 , 𝑎2,2 , … , 𝑎24,24 𝜅, 𝛼, 𝜆 Case II 𝑎1,1 , 𝑎2,2 , … , 𝑎24,24 𝜅, 𝛼, 𝜆 Case III 𝑎1,1 , 𝑎2,2 , … , 𝑎24,24 𝜅, 𝛼, 𝜆 Case IV 𝑎1,1 , 𝑎2,2 , … , 𝑎24,24 𝜅, 𝛼, 𝜆 Case V 𝑎1,1 , 𝑎2,2 , … , 𝑎24,24 𝜅, 𝛼, 𝜆

TABLE I CASE STUDIES Values −10−2 [17.5, 17.5, 21, 21, 21, 14, 7, 7, 10.5, 14, 21, 10.5, 10.5,17.5, 24.5,24.5, 17.5, 14, 3.5, 3.5, 12.25, 17.5, 17.5, 17.5] [5, 0.1, 3] Values −10−2 [35, 35, 42, 42, 42, 28, 14, 14, 21, 28, 42, 21, 21, 35, 49, 49, 35, 28, 7, 7, 24.5, 35,35,35] [5, 0.1, 3] Values −10−2 [50, 50, 60, 60, 60, 40, 10, 20, 30, 40,60,30,30,30,50,50,50,40,10,10, 35,50,50,50] [5, 0.1, 3] Values as case II [5, 30, 3] Values as case II [5, 60, 3]

The following subsections discuss the observations of the experiment in detail. A.

Sensitivity to Flexibility As defined in (5) and (6), the cost functions 𝐽1 and 𝐽2 depend on flexibility through the elasticity matrix 𝐴. After assigning an appropriate value of 𝜅, matrix 𝐴 is used to obtain the variation of the customer's hourly flexibility by changing the values of the diagonal coefficients (see Table I). The customer flexibility is increased through Case I to III to optimize the cost of the energy procurement and energy consumption for the customers and utility. (See Figs. 4-6). In Case I, the flexibility of the customers is very limited during the breakfast, lunch and dinner hours with of 0.07, 0.1, 0.03, respectively. The DR is applied more during the afternoon and night, where the values of the flexibility increase to around 0.2. In Cases II and III, the flexibility doubles to a value of approximately 2.8 times with respect to the first case. As expected, the greater the level of customer flexibility is, the greater the benefit of DR to both parties. Indeed in Case III for the customers, the percentage cost variation decreases from a weekly average of approximately 2.3% to -4.2% and then to -5.7%; and for the utility from 2.4$% to -4.5% and then to -6.5%.

of 𝛼 makes it possible to model the customer’s inertia that characterizes a change in the energy demand, which depends upon a change in the energy price. The results of the analysis of the comfort dependence, as described in Cases II, IV and V are shown in Figs. 5, 7 and 8. Indeed, assigning 𝛼 the values of 0.1, 30 and 60 increases the weight of the comfort terms in (5), thus reducing the influence of dynamic pricing upon customer energy demands. The percentage cost variation changes around the average values of -4.2%, -1.7% and -0.8% for the customers, and of 4.5\%, -2.5% and -1.4% for the utility in case studies II, IV and V respectively. In summary, higher comfort levels lead to lesser cost savings for both sides. However, this penalizes the customers more than the utility. C.

Sensitivity to Dynamic Pricing As observed, the customers tend to increase the energy demand when the price is low and reduce it when the price is high as expected. As defined in the constraints of the optimization problem (10), however, the energy demand remains the same. The price of the energy procurement, in the first week of December 2015 in Vermont, oscillates from approximately 1 to 5 cents per kWh. Here, the choice of the day-ahead prices for the customer provides an incentive to purchase the energy when the cost for the utility is less. As shown in Fig. 3, the choice of the day-ahead prices for the customers serve as an incentive to purchase the energy when the utility cost is lower. D.

Stochastic Optimization Algorithms The results generated with the stochastic optimization algorithms (PSO and AIS) are comparable to that generated with the interior-points method. The superiority of these algorithms is evident when they are applied to complex DR scenarios that are characterized by an inherently complex objective function.

Fig. 3. Energy Prices.

B.

Sensitivity to Comfort Preference The parameter 𝛼 expresses a weight to the comfort term of the cost function 𝐽1 as defined in (5). An increase in the value



(a)

(a)

(b)

(b)

Fig. 4. Case I simulation results: (a) Percentage cost variation, (b) Energy demand.

Fig. 6. Case III simulation results: (a) Percentage cost variation, (b) Energy demand.

(a)

(a)

(b)

(b)

Fig. 5. Case II simulation results: (a) Percentage cost variation, (b) Energy demand.

Fig. 7. Case IV Simulation results: (a) Percentage cost variation, (b) Energy demand.



(a) Fig. 10. Case I percentage cost variation using AIS.

(b) Fig. 8. Case V simulation results: (a) Percentage cost variation, (b) Energy demand. Fig. 11. Case II energy demand using AIS.

(a)

(a)

(b) Fig. 9. Case I simulation results using PSO: (a) Percentage cost variation and (b) Energy demand.

(b) Fig. 12. Case III simulation results using AIS: (a) Percentage cost variation, (b) Energy demand.



[6]

[7] [8]

[9]

Fig. 13. Case V percentage cost variation using AIS.

VI.

[10]

CONCLUSION

The application of DR techniques provides a number of potential benefits for balancing the energy problems of the grid. In this paper, a simple, but effective DR method is described. The authors show that the simple exploitation of a management framework for the demand response can reduce the exposure of the utility to the market volatility while improving costs for both the utility and customers, avoiding the need of complex technological solutions. The interiorpoints method was used to solve the optimization problem, followed by an exploration of the possible usage of both particle swarm optimization and artificial immune systems. This proposed management system which is also in compliance to the IP technologies, exploits a modern and widely used practical technology for easy adaptation into the power environment to create real-world applications that avoids the expensive and invasive use of complex technology solutions. Future work will focus on the integration of the renewable sources in the problem formulation and modeling the energy behavior of the customer. REFERENCES [1]

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