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Grid Scheduling Considering Energy Consumption Management and Quality of Service

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Abstract

In this research, the grid scheduling problem has been investigated in order to maximize profit considering the dynamic voltage and frequency scaling technique, customer-centric quality of service and time-dependent energy pricing. Mixed-integer linear programming, constraint programming, a greedy heuristic algorithm along with a hybrid method of genetic algorithm and constraint programming are developed. Some techniques are proposed to improve the efficiency of the presented constraint programming model, and their effectiveness is investigated using a full factorial experiment. Parameters of the proposed hybrid algorithm have been set by Taguchi test. The hybrid meta-heuristic algorithm, with a short execution time, generates solutions of about 18% and 88% better than the best solution of the constraint programming model for large-scale problem instances. The results show that the final profit will be reduced by about 22% if the electricity prices are wrongly considered with a flat rate during the scheduling process.

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All data generated or analysed during this study are included in this published article.

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Authors and Affiliations

  1. Faculty of Engineering, University of Isfahan, Isfahan, 81746-73441, Iran

    Samaneh Esmaili & Kamran Kianfar

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  1. Samaneh Esmaili
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  2. Kamran Kianfar
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Correspondence to Kamran Kianfar.

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Appendix 1: Proof of the Lemma

Appendix 1: Proof of the Lemma

Assume that for the set of accepted tasksIaccepted, the value of the objective function is \({objective}^{I^{accepted}}\). Suppose task i is out of the set of accepted tasks and the other tasks are performed on their former resource, VF level and time. Define the value of the objective function as \({objective}^{I^{accepted\backslash \left\{i\right\}}}\) in this case. Here, the revenue from performing task i, which is equal to \(\min \left\{{B}_i,{B}_i-{U}_i\left({t}_i+{ETT}_{i,{r}_i,{k}_i}-{D}_i\right)\right\}\), is deducted from the objective function, and the revenue from performing other tasks does not change. The power consumption of resource ri in interval \(\left[{t}_i,{t}_i+{ETT}_{i,{r}_i,{k}_i}-1\right]\) source changes from \({P}_{r_i,{k}_i}\) to \({P}_{r_i}^{sleep}\). So, the power consumption cost of this resource is reduced by \(\sum_{s={t}_i}^{t_i+{ETT}_{i,{k}_i}-1}{C}_s\times \left({P}_{r_i,{k}_i}-{P}_{r_i}^{sleep}\right)\). The power consumption of other resources does not change and the related cost does not change as well. According to this, eq. (59) is established between \({objective}^{I^{accepted}}\) and \({objective}^{I^{accepted\backslash \left\{i\right\}}}\).

$${objective}^{I^{accepted}}-{objective}^{I^{accepted\backslash \left\{{i}_1\right\}}}=\min \left\{{B}_{i_1},{B}_{i_1}-{U}_{i_1}\left({t}_{i_1}+{ETT}_{i_1,{r}_{i_1},{k}_{i_1}}-{D}_i\right)\right\}-\sum_{s={t}_{i_1}}^{t_{i_1}+{ETT}_{i_1,{r}_{i_1},{k}_{i_1}}-1}{C}_s\left({P}_{r_{i_1},{k}_{i_1}}-{P}_{r_{i_1}}^{sleep}\right)={Profit}_{i_1,{r}_{i_1},{k}_{i_1},{t}_{i_1}}$$
(59)

According to (59), it can be easily seen that the following equation holds.

$$\left\{\begin{array}{c}{objective}^{I^{accepted}}-{objective}^{I^{accepted\backslash \left\{{i}_1\right\}}}={Profit}_{i_1,{r}_{i_1},{k}_{i_1},{t}_{i_1}}\kern4.75em \\ {}{objective}^{I^{accepted\backslash \left\{{i}_1\right\}}}-{objective}^{I^{accepted\backslash \left\{{i}_1,{i}_2\right\}}}={Profit}_{i_2,{r}_{i_2},{k}_{i_2},{t}_{i_2}}\kern2.5em \\ {}{objective}^{I^{accepted\backslash \left\{{i}_1,{i}_2\right\}}}-{objective}^{I^{accepted\backslash \left\{{i}_1,{i}_2,{i}_3\right\}}}={Profit}_{i_3,{r}_{i_3},{k}_{i_3},{t}_{i_3}}\kern1em \\ {}\vdots \\ {}{objective}^{I^{accepted\backslash \left\{{i}_1,{i}_2,\dots, {i}_{n-1}\right\}}}-{objective}^{I^{accepted\backslash \left\{{i}_1,{i}_2,\dots, {i}_{n-1},{i}_n\right\}}}\kern5.5em \\ {}\kern23.25em ={Profit}_{i_n,{r}_{i_n},{k}_{i_n},{t}_{i_n}}\end{array}\right.$$
(60)

By adding the expressions in (60), the following equation will be obtained.

$${objective}^{I^{accepted}}-{objective}^{I^{accepted\backslash \left\{{i}_1,{i}_2,\dots, {i}_{n-1},{i}_n\right\}}}=\sum_{i\in {I}^{accepted}}{Profit}_{i,{r}_i,{k}_i,{t}_i}$$
(61)

Note that \({objective}^{I^{accepted\backslash \left\{{i}_1,{i}_2,\dots, {i}_{n-1},{i}_n\right\}}}={objective}^{\varnothing }\) where objective∅ is the value of the objective function in the mode of not accepting any tasks. Since no task is accepted in objective∅, all resources will be idle, and the value of objective∅ can be expressed as the following equation.

$${objective}^{\varnothing }=-\sum_{r\in R}{cost}_r^{idle}$$
(62)

By combining (61) and (62), Eq. (52) is proved.

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Esmaili, S., Kianfar, K. Grid Scheduling Considering Energy Consumption Management and Quality of Service. J Grid Computing 20, 30 (2022). https://doi.org/10.1007/s10723-022-09620-3

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