# Object-Oriented Usability Indices for Multi-Objective Demand Side Management Using Teaching-Learning Based Optimization

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation

#### 1.2. Literature Review

#### 1.3. Contribution and Paper Organization

## 2. Microgrid Modeling

## 3. Microgrid DSM Problem Formulation

#### 3.1. Objective1: Minimization of the Fuel Cost Function, G(X)

- $l$: Variable to represent conventional generating units. Its value ranges from $1\le \mathrm{l}\le \mathrm{L}$;
- $t$: Dispatch interval, $1\le t\le T;$ in present work, is expanded over T = 24 time horizon.
- G(X): Operating cost function.
- $Cos{t}_{t}$: Total cost at time t to deliver power;
- ${P}_{l,t}$: Conventional generator, number of units;
- ${C}_{l}\left({P}_{l,t}\right)$: Fuel cost function for conventional generators.
- ${C}_{r}\left(P{r}_{t}\right)$: Transferable power cost;
- ${P}_{rt}$: Transferable power;
- $\gamma $: Location marginal prices [33];
- $L$: Total number of the conventional generating unit.

- i: Customer number;
- n: Total number of customers;
- ${x}_{i,t}$: Curtailed power by customer number i, at tth time interval
- ${W}_{t}$: Forecast maximum wind power obtainable by available solar energy generators;
- ${S}_{t}$: Forecast maximum solar power obtainable by available wind energy generators;
- ${P}_{wt}$: Wind generator power availability (during time t)
- ${P}_{St}$: Solar generator power availability (during time t)
- ${D}_{t}$: Load demand at time t;
- $P{r}_{max}$: Denotes maximum allowable exchange between grid and microgrid.

#### 3.2. Objective2: Maximization of Utility Benefit Function, H(X), Using Demand Response

- ${V}_{1}$: Customer benefit in $\$/\mathrm{kWh}$. It must be ${V}_{1}\ge $ 0 for user participation.
- ${V}_{2}$: Utility benefit in $\$/\mathrm{kWh}$.
- $x$: Curtailed power by customer in kW;
- y: Monetary compensation the customer receives in $/kWh;
- λ: Cost of power.

_{1,i}, K

_{2,i}are coefficients related to the costincurred by customer i.

#### 3.3. Multi-Objective Formulation

## 4. Teaching-Learing-Based Optimization (TLBO) Algorithm

- ${X}_{j,kbest,i}$: Result of the best learner in subject j;
- ${r}_{j,i}$: Random number in the range [0, 1]; and
- ${T}_{f}$: Teaching factor. It decides the value of mean to be changed the value of ${T}_{f}$ is selected in random way with equal probability as:

- ${X}_{j,k,i}$: A value in the solution,
- $X{\prime}_{j,k,i}$: Updated value of ${X}_{j,k,i}$. Accept $X{\prime}_{j,k,i}$ if it gives better value of the function
- $j$: jth design variable. Denotes subject chosen by the learners. $j\text{}=\text{}1,\text{}2,\dots ,m$;
- k: kth member of population. Denotes learner. $k\text{}=\text{}1,\text{}2,\dots ,\text{}n$;
- i: ith iteration, $i\text{}=\text{}1,\text{}2,\dots ,{G}_{\mathrm{max}}$,
- ${G}_{\mathrm{max}}$: Denotes maximum iterations.

#### TLBO Steps Adopted to Optimize Multi-Objective DSM Function F(X)

## 5. Object-Oriented Usability Indices (OOUI)

#### Theoretical Analysis of the Proposed Indices

- t: dispatch interval.
- ${d}_{t}$: load demand to utility when no DSM is applied.
- ${d}_{max}$: maximum load over the time period T when no DSM is applied
- ${d}_{t}^{\prime}$: load demand to utility when DSM is applied.
- ${d}_{max}^{\prime}$: maximum load over the time period T when DSM is applied

- Peak power shaving index greater than one that is ${m}_{pps}>1$.
- Peak power shaving index less than one that is ${m}_{pps}<1$.
- Peak power shaving index equal one that is ${m}_{pps}=1$.
- Comparative result of peak power shaving index obtained for DSM solutions.

## 6. Case Studies, Simulation Results, and Discussion

#### 6.1. Case Studies, Simulation Results

#### 6.2. Calaulation of Proposed Indices

#### 6.3. Discussion of the Results with Comparative Analysis

`(`SCADA)-based connected loads and generation units. The formulation of DSM is not discussed, and the mathematical formulation of indicators is not presented through any simulation results. In another work, a decision support framework is presented for selection of the demand response method [44]. The proposed framework of [44] is based on cost minimization and load scheduling. The work, however, does not consider any role of renewable and focuses only on energy management.

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 15.**Plot of OOUI for DSM in different cases and scenarios as described in Table 4.

Parameter | Abbreviations | $\mathbf{D}\mathbf{G}1$ | $\mathbf{D}\mathbf{G}2$ | $\mathbf{D}\mathbf{G}3$ |
---|---|---|---|---|

First fuel cost coefficient $\left(\$/\mathrm{kW}\right)$ | ${a}_{l}$ | 0.06 | 0.03 | 0.04 |

Second fuel cost coefficient ($/kW) | ${b}_{l}$ | 0.5 | 0.25 | 0.3 |

Minimum output power limit (kW) | ${P}_{l,min}$ | 0 | 0 | 0 |

Maximum output power limit (kW) | ${P}_{l,max}$ | 4 | 6 | 9 |

Ramp up rate(kW/hour) | $D{R}_{l}$ | 3 | 5 | 8 |

Ramp down rate(kW/hour) | $U{R}_{l}$ | 3 | 5 | 8 |

Description | Abbr. | Customer Type1 | Customer Type2 | Customer Type3 |
---|---|---|---|---|

Customer type | $i$ | 1 | 2 | 3 |

1st coefficient related to customer cost function | ${K}_{1,i}$ | 1.079 | 1.378 | 1.847 |

2nd coefficient related to customer cost function | ${K}_{2,i}$ | 1.32 | 1.63 | 1.64 |

User Type | ${\theta}_{i}$ | 0 | 0.45 | 0.9 |

Curtail limit $\left(\mathrm{kW}\right)$ | $C{M}_{i}$ | 80 | 85 | 90 |

Cases | Total Demand (kW) | Avg. Demand (kW) | Peak (kW) | Load Factor | Renewable Energy Availability | |
---|---|---|---|---|---|---|

(kW) | (%) | |||||

case 1 | 780.236 | 32.50983 | 39.25754 | 0.828117 | 346.24 | 34.62 |

case 2 | 793.9236 | 33.08015 | 41.66873 | 0.793884 | 400.45 | 40.04 |

case 3 | 767.8551 | 31.99396 | 39.95539 | 0.800742 | 275.03 | 27.50 |

case 4 | 771.3937 | 32.1414 | 40.25102 | 0.798524 | 362.76 | 36.27 |

case 5 | 775.5615 | 32.31506 | 39.35548 | 0.821107 | 296.01 | 29.60 |

Cases | $\mathbf{W}\left(\mathbf{k}\mathbf{W}\right)$ | $\mathbf{S}\left(\mathbf{k}\mathbf{W}\right)$ | ${\mathit{m}}_{\mathit{p}\mathit{p}\mathit{s}}$ | ${\mathit{m}}_{\mathit{r}\mathit{e}\mathit{i}}$ | ${\mathit{m}}_{\mathit{d}\mathit{s}\mathit{m}\mathit{u}\mathit{f}}^{\mathit{s}1}$ | ${\mathit{m}}_{\mathit{d}\mathit{s}\mathit{m}\mathit{u}\mathit{f}}^{\mathit{s}2}$ | ${\mathit{m}}_{\mathit{d}\mathit{s}\mathit{m}\mathit{u}\mathit{f}}^{\mathit{s}3}$ |
---|---|---|---|---|---|---|---|

$({\mathit{w}}_{\mathit{p}\mathit{p}\mathit{s}}$$=\text{}0.5,\text{}{\mathit{w}}_{\mathit{r}\mathit{e}\mathit{i}}=\text{}0.5)$ | $({\mathit{w}}_{\mathit{p}\mathit{p}\mathit{s}}$$=\text{}0.1,\text{}{\mathit{w}}_{\mathit{r}\mathit{e}\mathit{i}}\text{}=\text{}0.9)$ | $({\mathit{w}}_{\mathit{p}\mathit{p}\mathit{s}}$$=\text{}0.9,\text{}{\mathit{w}}_{\mathit{r}\mathit{e}\mathit{i}}\text{}=\text{}0.1)$ | |||||

Case 1 | Average | Average | 0.986 | 0.444 | 0.715 | 0.498 | 0.932 |

Case 2 | Maximum | Average | 0.945 | 0.504 | 0.725 | 0.548 | 0.901 |

Case 3 | Minimum | Average | 0.953 | 0.358 | 0.655 | 0.418 | 0.894 |

Case 4 | Average | Maximum | 0.951 | 0.470 | 0.711 | 0.518 | 0.903 |

Case 5 | Average | Minimum | 0.978 | 0.382 | 0.680 | 0.441 | 0.918 |

Rank | Criteria for Ranking DSM | ||||
---|---|---|---|---|---|

${\mathit{m}}_{\mathit{p}\mathit{p}\mathit{s}}$ | ${\mathit{m}}_{\mathit{r}\mathit{e}\mathit{i}}$ | ${\mathit{m}}_{\mathit{d}\mathit{s}\mathit{m}\mathit{u}\mathit{f}}^{\mathit{s}1}$ | ${\mathit{m}}_{\mathit{d}\mathit{s}\mathit{m}\mathit{u}\mathit{f}}^{\mathit{s}2}$ | ${\mathit{m}}_{\mathit{d}\mathit{s}\mathit{m}\mathit{u}\mathit{f}}^{\mathit{s}3}$ | |

1 | Case 1 | Case 2 | Case 2 | Case 2 | Case 1 |

2 | Case 5 | Case 4 | Case 1 | Case 4 | Case 5 |

3 | Case 3 | Case 1 | Case 4 | Case 1 | Case 4 |

4 | Case 4 | Case 5 | Case 5 | Case 5 | Case 2 |

5 | Case 2 | Case 3 | Case 3 | Case 3 | Case 3 |

S.N. | Point of Comparison | Proposed | Dharme et al. [30] Year: 2006 | Rahman et al. [41] Year: 1993 | Khanh et al. [42] Year: 2011 | Raihab et al. [43] Year: 2016 | Dennis et al. [44] Year: 2018 |
---|---|---|---|---|---|---|---|

1 | Whether system under study is grid-tied microgrid | Yes | No | No | No | Yes | Yes |

2 | DSM Formulation | Multi-objective | Single objective | Single objective | Single objective | Single objective | Single objective |

3 | Optimization performed | Yes | No | Yes | No | No | Yes |

4 | Optimization method/solution strategies used | TLBO | No | Iterative | No | No | Greedy and multi-agent-system-based |

5 | Attributes for decision | OOUI | Index-based | VPI model-based | VPI model-based | Indicator-based | a decision support framework |

6 | Any proposed Indices | Yes | Yes | No | No | Yes | No |

7 | Any index for peak shaving | Yes | No | No | No | No | No |

8 | Any Index for renewable energy | Yes | No | No | No | No | No |

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## Share and Cite

**MDPI and ACS Style**

Singh, M.; Jha, R.C.
Object-Oriented Usability Indices for Multi-Objective Demand Side Management Using Teaching-Learning Based Optimization. *Energies* **2019**, *12*, 370.
https://doi.org/10.3390/en12030370

**AMA Style**

Singh M, Jha RC.
Object-Oriented Usability Indices for Multi-Objective Demand Side Management Using Teaching-Learning Based Optimization. *Energies*. 2019; 12(3):370.
https://doi.org/10.3390/en12030370

**Chicago/Turabian Style**

Singh, Mayank, and Rakesh Chandra Jha.
2019. "Object-Oriented Usability Indices for Multi-Objective Demand Side Management Using Teaching-Learning Based Optimization" *Energies* 12, no. 3: 370.
https://doi.org/10.3390/en12030370