# Co-Optimization of Energy and Reserve Capacity Considering Renewable Energy Unit with Uncertainty

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation

#### 1.2. Scope

#### 1.3. Load Curve

#### 1.4. Integration of RES

#### 1.5. Contribution

#### 1.5.1. Case 1

#### 1.5.2. Case 2

#### 1.5.3. Case 3

#### 1.5.4. Case 4

#### 1.5.5. Case 5

#### 1.5.6. Case 6

#### 1.6. Objectives

## 2. Related Work

## 3. Problem Formulation

- As the reverse balancing energy obtained from i units is denoted by ${R}_{i}^{U}$. Thus, the total amount of output power of unit i can be increased from ${P}_{i}$ to ${P}_{i}+{r}_{i}^{U}$.
- Alternatively, the power output of the thermal unit i can be decreased from ${P}_{i}$ to ${P}_{i}-{r}_{i}^{D}$, where ${r}_{i}^{D}$ is the balancing energy resulting from the deployment of the downward reserve capacity of unit i, represented by ${R}_{i}^{D}$. This makes the cost decrease.
- In case 5, we incorporate wind energy that is considered cost free. An amount ${W}_{\mathrm{Spill}}$ can be curtailed to reduce overall energy generation cost.
- A part of the load can also be curtailed. This involves the value of lost load, ${\ell}^{s}$, which is taken for our system as 200 $/MWh [7].

#### 3.1. System Model

- The net energy generation must be equal to demand. All the production units must generate energy, equal to the demand of load. Mathematically:$$\sum _{\mathrm{i}=1}^{\mathrm{n}}{P}_{\mathrm{i}}={P}_{\mathrm{d}},\phantom{\rule{3.33333pt}{0ex}}\forall i=1\dots n.$$Equation (9) can be written in the form of mismatch between energy demanded and energy supplied.$$\varphi =0={P}_{\mathrm{d}}-\sum _{\mathrm{i}=1}^{\mathrm{n}}{P}_{\mathrm{i}},\phantom{\rule{3.33333pt}{0ex}}\forall i=1\dots n.$$
- As the equal incremental principle has been used for the selection of power generation facilities. Thus, for smooth economic operation of multiple commodities, the incremental fuel rates of all the generation units must be equal. Another operational constraint, i.e., energy produced by each generation unit must be within its minimum and maximum generation limits which can be written as:$${P}_{{\mathrm{i}}_{\mathrm{min}}}\le {P}_{i}\le {P}_{{\mathrm{i}}_{\mathrm{max}}},\phantom{\rule{3.33333pt}{0ex}}\forall i=1\dots n,$$
- The energy produced at each generation unit must be positive such as:$$\sum _{\mathrm{i}=1}^{\mathrm{n}}{P}_{\mathrm{i}}\ge 0,\phantom{\rule{3.33333pt}{0ex}}\forall i=1\dots n.$$
- In the proposed work, the energy losses are not considered because the ELD problem considering network loses needs accurate mathematical models. However, in order to calculate power losses, we can develop a mathematical expression as a function of power output of each generation unit. This method is known as the B-coefficient method [66], while some other techniques are being used to calculate power losses on the basis of network flow equations. As it is understood that the equal incremental rate principle works well if the cost function is a quadratic or a piecewise linear [67], if the cost function is neither linear nor quadratic, this mechanism may be even more complex. Thus, we need other methods to get the optimum solution [68].

#### 3.2. OF and Operational Constraints

## 4. Simulation Methodology

## 5. Results

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${P}_{\mathrm{i},\mathrm{g}}$ | Electrical power generation from ${i}^{\mathrm{th}}$ unit |

${P}_{\mathrm{d}}$ | Electrical power demand |

${x}^{0}$ | Initial state for gradient search method |

${x}^{1}$ | Next state for gradient search method |

$\u03f5$ | Convergence coefficient |

${F}_{\mathrm{T}}$ | Total cost |

$\lambda $ | Incremental cost rate |

$\mathsf{\Delta}P$ | Change in electrical power |

${P}_{{\mathrm{i}}_{\mathrm{min}}}$ | Minimum limit on ${i}^{\mathrm{th}}$ energy generation unit |

${P}_{{\mathrm{i}}_{\mathrm{max}}}$ | Maximum limit on ${i}^{\mathrm{th}}$ energy generation unit |

${S}_{{\mathrm{i}}_{\mathrm{min}}}$ | Minimum level of ${i}^{\mathrm{th}}$ storage unit |

${S}_{{\mathrm{i}}_{\mathrm{max}}}$ | Maximum level of ${i}^{\mathrm{th}}$ storage unit |

${r}_{\mathrm{in}}$ | Increase in energy for ${i}^{\mathrm{th}}$ unit i = 1, 2, 3 … |

${R}_{\mathrm{i}}$ | Reserve capacity for ${i}^{\mathrm{th}}$ unit allocated |

${r}_{\mathrm{i}}$ | Reserve capacity for ${i}^{\mathrm{th}}$ unit utilized |

${e}^{\mathrm{r}}$ | Total reserve capacity |

${F}_{{\mathrm{r}}_{\mathrm{i}}}$ | Cost of reserve capacity for ${i}^{\mathrm{th}}$ unit |

${F}_{\mathrm{i}}$ | Cost of running ${i}^{\mathrm{th}}$ unit |

${\ell}^{\mathrm{s}}$ | Amount of demand not served |

${\tau}^{\mathrm{H}}$ | Probability factor for scenario High |

${\tau}^{\mathrm{L}}$ | Probability factor for scenario Low |

$\tau $ | Probability factor |

$\phi $ | Power loss factor for economic load not served (${\ell}^{s}$ = 0.05) |

$\alpha $ | Quadratic production cost function coefficient of ${i}^{\mathrm{th}}$ power plant |

$\beta $ | Linear production cost function coefficient of ${i}^{\mathrm{th}}$ power plant |

$\gamma $ | Constant production cost function coefficient of ${i}^{\mathrm{th}}$ power plant |

${P}_{\mathrm{w}}$ | Electrical power generated from wind turbine |

${P}_{\mathrm{R}}$ | Rated electrical power of wind turbine |

v | Wind speed |

${v}_{\mathrm{c}}$ | Cut-in wind speed |

${v}_{\mathrm{R}}$ | Rated wind speed |

t | Time horizon |

N | Set of energy generation units |

$\mathcal{L}$ | Lagrangian function |

## References

- Allan, R.N.; Billinton, R. Reliability Evaluation of Power Systems; Springer: New York, NY, USA, 2013. [Google Scholar]
- Wan, C.; Xu, Z.; Pinson, P. Direct Interval Forecasting of Wind Power. IEEE Trans. Power Syst.
**2013**, 28, 4877–4878. [Google Scholar] [CrossRef] - Wan, C.; Xu, Z.; Pinson, P.; Dong, Z.Y.; Wong, K.P. Optimal Prediction Intervals of Wind Power Generation. IEEE Trans. Power Syst.
**2014**, 29, 1166–1174. [Google Scholar] [CrossRef] [Green Version] - Salimi-Beni, A.; Fotuhi-Firuzabad, M.; Gharagozloo, H.; Farrokhzad, D. Impacts of load pattern variation in iran power system on generation system planning. In Proceedings of the Canadian Conference on Electrical and Computer Engineering, Saskatoon, SK, Canada, 1–4 May 2005; pp. 2216–2219. [Google Scholar] [CrossRef]
- Li, B.; Maroukis, S.D.; Lin, Y.; Mathieu, J.L. Impact of uncertainty from load-based reserves and renewables on dispatch costs and emissions. In Proceedings of the 2016 North American Power Symposium (NAPS), Denver, CO, USA, 18–20 September 2016; pp. 1–6. [Google Scholar]
- Stephenson, P.; Paun, M. Electricity market trading. Power Eng. J.
**2001**, 15, 277–288. [Google Scholar] [CrossRef] - Morales, J.M.; Conejo, A.J.; Madsen, H.; Pinson, P.; Zugno, M. Integrating Renewables in Electricity Markets; Springer: Boston, MA, USA, 2014; pp. 57–100. [Google Scholar]
- Vîlceanu, R.C.; Chiosa, N.; Şurianu, F.D. Study of the load variation for an electrical consumer. In IOP Conference Series: Materials Science and Engineering; IOP Publishing: Bristol, UK, 2016; Volume 106, p. 012027. [Google Scholar]
- Barbulescu, C.; Kilyeni, S.; Deacu, A.; Turi, G.M.; Moga, M. Artificial neural network based monthly load curves forecasting. In Proceedings of the 2016 IEEE 11th International Symposium on Applied Computational Intelligence and Informatics (SACI), Timisoara, Romania, 12–14 May 2016; pp. 237–242. [Google Scholar]
- Kateeb, I.A.; Bikdash, M.; Chopade, P. Back to the future Renewable Energy Sources and green Smart Grid. In Proceedings of the 2011 Proceedings of IEEE Southeastcon, Nashville, TN, USA, 17–20 March 2011; pp. 147–152. [Google Scholar] [CrossRef]
- Ribeiro, H.; Unesco. Fossil fuel energy impacts on health. In Encyclopedia of Life Support Systems; Eolss Publishers Co.: Oxford, UK, 2001. [Google Scholar]
- Chen, C.; Wiser, R.; Mills, A.; Bolinger, M. Weighing the costs and benefits of state renewables portfolio standards in the United States: A comparative analysis of state-level policy impact projections. Renew. Sustain. Energy Rev.
**2009**, 13, 552–566. [Google Scholar] [CrossRef] [Green Version] - Noskova, E.V.; Obyazov, V.A. Variations in wind parameters in the Zabaikal’skii krai. Russ. Meteorol. Hydrol.
**2016**, 41, 466–471. [Google Scholar] [CrossRef] - Yan, Q.; Zhu, M.; Lin, W. Regional Variations of Wind Power and the Causes. Int. J. Simul. Syst. Sci. Technol.
**2015**, 16, 1–7. [Google Scholar] - Jun, L. Study on the statistical characteristics of solar power. In IOP Conference Series: Earth and Environmental Science; IOP Publishing: Bristol, UK, 2017; Volume 52. [Google Scholar]
- Afolabi, L.O.; Adewunmi, O.T.; Seluwa, E.O.; Soliu-Salau, G.A.; Odeniyi, O.M. Prediction of solar radiation patterns for sustainable implementation of solar power generation. Ann. Fac. Eng. Hunedoara
**2017**, 15, 153–160. [Google Scholar] - Solar Energy. Available online: https://en.wikipedia.org/wiki/Solarenergy (accessed on 9 March 2018).
- Wind Power Market to Reach 60 GW in 2018, Asia Keeps Lead. Available online: https://renewablesnow.com/news/wind-power-market-to-reach-60-gw-in-2018-asia-keeps-lead-471144 (accessed on 9 March 2018).
- Mishra, S.; Leinakse, M.; Palu, I. Wind power variation identification using ramping behavior analysis. Energy Procedia
**2017**, 141, 565–571. [Google Scholar] [CrossRef] - Bajaj, S.; Sandhu, K.S. Wind turbine economics: A study. In Proceedings of the 2014 IEEE 6th India International Conference on Power Electronics (IICPE), Kurukshetra, India, 8–10 December 2014; pp. 1–5. [Google Scholar] [CrossRef]
- Premalatha, M.; Abbasi, T.; Abbasi, S.A. Wind energy: Increasing deployment, rising environmental concerns. Renew. Sustain. Energy Rev.
**2014**, 31, 270–288. [Google Scholar] [CrossRef] - Walker, R.P.; Swift, A. Wind Energy Essentials: Societal, Economic, and Environmental Impacts; John Wiley & Sons: Hoboken, NJ, USA, 2015. [Google Scholar]
- Breton, S.P.; Moe, G. Status, plans and technologies for offshore wind turbines in Europe and North America. Renew. Energy
**2009**, 34, 646–654. [Google Scholar] [CrossRef] - Parikh, M.M.; Bhattacharya, A.K. Wind data analysis for studying the feasibility of using windmills for irrigation. Energy Agric.
**1984**, 3, 129–136. [Google Scholar] [CrossRef] - Han, X.S.; Gooi, H.B.; Kirschen, D.S. Dynamic economic dispatch: feasible and optimal solutions. IEEE Trans. Power Syst.
**2001**, 16, 22–28. [Google Scholar] [CrossRef] - Castro, J.F.C.; da Silva, A.M.L.; Guaranys, B. Operating reserve requirements and equipment ranking in systems with renewable sources. In Proceedings of the 2018 Simposio Brasileiro de Sistemas Eletricos (SBSE), Niteroi, Brazil, 12–16 May 2018; pp. 1–6. [Google Scholar] [CrossRef]
- Contreras, J.; Asensio, M.; de Quevedo, P.M.; Muñoz-Delgado, G.; Montoya-Bueno, S. Joint RES and Distribution Network Expansion Planning under a Demand Response Framework; Elsevier Science: Amsterdam, The Netherlands, 2016; pp. 14–19. [Google Scholar]
- Song, Y.H. Operation of Market-Oriented Power Systems; Springer Science & Business Media: Berlin, Germany, 2003. [Google Scholar]
- Zhu, J. Optimization of Power System Operation; John Wiley & Sons: Hoboken, NJ, USA, 2015; Volume 47. [Google Scholar]
- Bayasgalan, Z.; Bayasgalan, T.; Muzi, F. Improvement of the dispatching preplanning process in day-ahead electricity market using a sequential method. In Proceedings of the 2017 18th International Conference on Computational Problems of Electrical Engineering (CPEE), Kutna Hora, Czech Republic, 11–13 September 2017; pp. 1–5. [Google Scholar] [CrossRef]
- Faqiry, M.N.; Zarabie, A.K.; Nassery, F.; Wu, H.; Das, S. A day-ahead market energy auction for distribution system operation. In Proceedings of the 2017 IEEE International Conference on Electro Information Technology (EIT), Lincoln, NE, USA, 14–17 May 2017; pp. 182–187. [Google Scholar] [CrossRef]
- Vasilj, J.; Jakus, D.; Sarajcev, P. Energy and reserve co-optimization in power system with wind and PV power. In Proceedings of the 2015 12th International Conference on the European Energy Market (EEM), Lisbon, Portugal, 19–22 May 2015; pp. 1–5. [Google Scholar] [CrossRef]
- Gan, D.; Litvinov, E. Energy and reserve market designs with explicit consideration to lost opportunity costs. IEEE Trans. Power Syst.
**2003**, 18, 53–59. [Google Scholar] [CrossRef] - Santhosh, A.; Farid, A.M.; Youcef-Toumi, K. Real-time economic dispatch for the supply side of the energy-water nexus. Appl. Energy
**2014**, 122, 42–52. [Google Scholar] [CrossRef] - Santra, D.; Mondal, A.; Mukherjee, A. Study of economic load dispatch by various hybrid optimization techniques. In Hybrid Soft Computing Approaches; Springer: New Delhi, India, 2016; pp. 37–74. [Google Scholar]
- Thenmalar, K.; Allirani, A. Optimization Techniques for the Economic Dispatch Problem in Various Generation Plant. Adv. Mater. Res.
**2013**, 768, 323–328. [Google Scholar] [CrossRef] - Sivanagaraju, S. Power System Operation and Control; Pearson Education India: New Delhi, India, 2009. [Google Scholar]
- Sönmez, Y. Estimation of fuel cost curve parameters for thermal power plants using the ABC algorithm. Turk. J. Electr. Eng. Comput. Sci.
**2013**, 21, 1827–1841. [Google Scholar] [CrossRef] - Helseth, A.; Fodstad, M.; Mo, B. Optimal Medium-Term Hydropower Scheduling Considering Energy and Reserve Capacity Markets. IEEE Trans. Sustain. Energy
**2016**, 7, 934–942. [Google Scholar] [CrossRef] - Wang, Z.; Negash, A.; Kirschen, D.S. Optimal scheduling of energy storage under forecast uncertainties. IET Gener. Transm. Distrib.
**2017**, 11, 4220–4226. [Google Scholar] [CrossRef] - Li, Y.Z.; Zhao, T.; Wang, P.; Gooi, H.B.; Wu, L.; Liu, Y.; Ye, J. Optimal Operation of Multi-Microgrids via Cooperative Energy and Reserve Scheduling. IEEE Trans. Ind. Inform.
**2018**, 14, 3459–3468. [Google Scholar] [CrossRef] - Cobos, N.G.; Arroyo, J.M.; Alguacil-Conde, N.; Wang, J. Robust Energy and Reserve Scheduling Considering Bulk Energy Storage Units and Wind Uncertainty. IEEE Trans. Power Syst.
**2018**, 33, 5206–5216. [Google Scholar] [CrossRef] - Tan, Y.T.; Kirschen, D.S. Co-optimization of Energy and Reserve in Electricity Markets with Demand-side Participation in Reserve Services. In Proceedings of the 2006 IEEE PES Power Systems Conference and Exposition, Atlanta, GA, USA, 29 October–1 November 2006; pp. 1182–1189. [Google Scholar] [CrossRef]
- Karangelos, E.; Bouffard, F. Towards Full Integration of Demand-Side Resources in Joint Forward Energy/Reserve Electricity Markets. IEEE Trans. Power Syst.
**2012**, 27, 280–289. [Google Scholar] [CrossRef] - Ehsani, A.; Ranjbar, A.M.; Fotuhi-Firuzabad, M. A proposed model for co-optimization of energy and reserve in competitive electricity markets. Appl. Math. Model.
**2009**, 33, 92–109. [Google Scholar] [CrossRef] - Al-Roomi, A.R.; El-Hawary, M.E. A novel multiple fuels’ cost function for realistic economic load dispatch needs. In Proceedings of the 2017 IEEE Electrical Power and Energy Conference (EPEC), Saskatoon, SK, Canada, 22–25 October 2017; pp. 1–6. [Google Scholar]
- Abido, M.A. Environmental/economic power dispatch using multiobjective evolutionary algorithms. IEEE Trans. Power Syst.
**2003**, 18, 1529–1537. [Google Scholar] [CrossRef] - Shalini, S.P.; Lakshmi, K. Solving Environmental Economic Dispatch Problem with Lagrangian Relaxation Method. Int. J. Electron. Electr. Eng.
**2014**, 7, 9–20. [Google Scholar] - Mohatram, M. Hybridization of artificial neural network and lagrange multiplier method to solve economic load dispatch problem. In Proceedings of the 2017 International Conference on Infocom Technologies and Unmanned Systems (Trends and Future Directions) (ICTUS), Dubai, UAE, 18–20 December 2017; pp. 514–520. [Google Scholar]
- Joya, G.; Atencia, M.A.; Sandoval, F. Hopfield neural networks for optimization: study of the different dynamics. Neurocomputing
**2002**, 43, 219–237. [Google Scholar] [CrossRef] - Santra, D.; Mukherjee, A.; Sarker, K.; Mondal, S. Medium scale multi-constraint economic load dispatch using hybrid metaheuristics. In Proceedings of the 2017 Third International Conference on Research in Computational Intelligence and Communication Networks (ICRCICN), Kolkata, India, 3–5 November 2017; pp. 169–173. [Google Scholar]
- Gautham, S.; Rajamohan, J. Economic load dispatch using novel bat algorithm. In Proceedings of the 2016 IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES), Delhi, India, 4–6 July 2016; pp. 1–4. [Google Scholar]
- Babu, B. Self Adaptive Firefly Algorithm for Economic Load Dispatch. Int. J. Eng. Trends Technol.
**2017**, 48, 110–115. [Google Scholar] [CrossRef] - Alsumait, J.S.; Sykulski, J.K.; Al-Othman, A.K. A hybrid GA–PS–SQP method to solve power system valve-point economic dispatch problems. Appl. Energy
**2010**, 87, 1773–1781. [Google Scholar] [CrossRef] [Green Version] - dos Santos Coelho, L.; Mariani, V.C. An improved harmony search algorithm for power economic load dispatch. Energy Convers. Manag.
**2009**, 50, 2522–2526. [Google Scholar] [CrossRef] - Lingala, R.; Bethina, A.; Rao, P.R.; Sumanth, K. Economic load dispatch using heuristic algorithms. In Proceedings of the 2015 IEEE International WIE Conference on Electrical and Computer Engineering (WIECON-ECE), Dhaka, Bangladesh, 19–20 December 2015; pp. 519–522. [Google Scholar] [CrossRef]
- Chiang, C.L. Genetic algorithm for power load dispatch. In Proceedings of the 2008 IEEE Conference on Cybernetics and Intelligent Systems, Chengdu, China, 21–24 September 2008; pp. 347–352. [Google Scholar] [CrossRef]
- Chellappan, R.; Kavitha, D. Economic and emission load dispatch using Cuckoo search algorithm. In Proceedings of the 2017 Innovations in Power and Advanced Computing Technologies (i-PACT), Vellore, India, 21–22 April 2017; pp. 1–7. [Google Scholar] [CrossRef]
- Gaing, Z.L. Particle swarm optimization to solving the economic dispatch considering the generator constraints. IEEE Trans. Power Syst.
**2003**, 18, 1187–1195. [Google Scholar] [CrossRef] [Green Version] - Dzobo, O.; Shehata, A.M.; Azimoh, C.L. Optimal economic load dispatch in smart grids considering uncertainty. In Proceedings of the 2017 IEEE AFRICON, Cape Town, South Africa, 18–20 September 2017; pp. 1277–1282. [Google Scholar] [CrossRef]
- Shahinzadeh, H.; Fathi, S.H.; Moazzami, M.; Hosseinian, S.H. Hybrid Big Bang-Big Crunch Algorithm for solving non-convex Economic Load Dispatch problems. In Proceedings of the 2017 2nd Conference on Swarm Intelligence and Evolutionary Computation (CSIEC), Kerman, Iran, 7–9 March 2017; pp. 48–53. [Google Scholar]
- Coelho, L.S.; Mariani, V.C. Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect. IEEE Trans. Power Syst.
**2006**, 21, 989–996. [Google Scholar] [CrossRef] - Wood, A.J.; Wollenberg, B.F. Power Generation, Operation, and Control; John Wiley & Sons: Hoboken, NJ, USA, 2012. [Google Scholar]
- Park, J.H.; Kim, Y.S.; Eom, I.K.; Lee, K.Y. Economic load dispatch for piecewise quadratic cost function using hopfield neural network. IEEE Trans. Power Syst.
**1993**, 8, 1030–1038. [Google Scholar] [CrossRef] - Kies, A.; Schyska, B.U.; von Bremen, L. Curtailment in a Highly Renewable Power System and Its Effect on Capacity Factors. Energies
**2016**, 9, 510. [Google Scholar] [CrossRef] - Chang, Y.C.; Yang, W.T.; Liu, C.C. A new method for calculating loss coefficients of power systems. IEEE Trans. Power Syst.
**1994**, 9, 1665–1671. [Google Scholar] [CrossRef] - Zhang, X.; Zhang, B. Equal incremental rate economic dispatching and optimal power flow for the union system of microgrid and external grid. In Proceedings of the 2014 IEEE PES General Meeting Conference & Exposition, National Harbor, MD, USA, 27–31 July 2014. [Google Scholar]
- Elanchezhian, E.B.; Subramanian, S.; Ganesan, S. Economic power dispatch with cubic cost models using teaching learning algorithm. IET Gener. Transm. Distrib.
**2014**, 8, 1187–1202. [Google Scholar] [CrossRef] - Appendix A: DATA SHEETS FOR IEEE 14 BUS SYSTEM. Available online: https://www.researchgate.net/profile/Mohamed_Mourad_Lafifi/post/-\Datasheet_for_5_machine_14_bus_ieee_system2/attachment/59d637fe\79197b8077995409/AS%3A395594356019200%401471328452063/\download/DATA+SHEETS+FOR+IEEE+14+BUS+SYSTEM+19_\appendix.pdf (accessed on 9 March 2018).

**Figure 3.**Power generation and demand profile of different generation unit over the time of 24 h (case 1).

**Figure 6.**Power generation and demand profile of different generation units over the time of 24 h (case 2).

**Figure 8.**Power generation and demand profile of different generation units over the time of 24 h (case 3).

**Figure 10.**Power generation and demand profile of different generation units over the time of 24 h (case 4).

**Figure 12.**Power generation and demand profile of different units along with renewable energy unit to fulfill demand over the time of 24 h (case 5).

**Figure 15.**Power generation and demand profile of different units along with renewable energy unit to fulfill demand over the time of 24 h (case 6).

Ref. | Techniques Used | Objectives | Limitations | RES | Reserve |
---|---|---|---|---|---|

C. Barbulescu et al. [9] | Artificial Neural Network (ANN) | To estimate the monthly load curves | Previous data required on a large scale | ✓ | X |

S. Mishra et al. [19] | Ramping behavior analysis | To study wind power variations | Only significant variations are involved | ✓ | X |

A. Helseth et al. [39] | Stochastic dynamic programming | To optimally schedule the hydro-power generation units | Linearisation of expressions may lead to inaccurate commitment scheduling | X | ✓ |

Z. Wang et al. [40] | Two stage optimization model | To dispatch electrical power optimally involving PV forecasting | Operational cost of storage units are not considered | ✓ | X |

Y. Z. Li et al. [41] | Cooperative model of energy and reserve capacity | To design a model for multi-micro grids involving energy and reserve capacity | Robust optimization is a conservative method | ✓ | ✓ |

G. Noemi et al. [42] | Novel two-stage robust optimization | Co-optimized electricity market of energy and reserve capacity involving wind uncertainty | Lack of non-spinning reserve | ✓ | ✓ |

Y. T. Tan et al. [43] | Mixed integer programming | Co-optimized electricity market of energy and reserve capacity considering demand side | Lack of quadratic nature of cost curves | ✓ | ✓ |

M. A. Abido et al. [47] | Strength pareto evolution algorithm | To solve Economic Load Dispatch (ELD) involving environmental constraints | Security and stability parameters are not involved | X | X |

M. Mohatram et al. [49] | Hybrid ANN & Lagrange Multiplier Method (LMM) | To improve the results of ELD by using non traditional method | In case of more generation units, system complexity may increase | X | X |

S. Gautham et al. [52] | Novel Bat Algorithm (NBA) | To improve the results of ELD by using non traditional method | Convergence time is more due to large number of variable involved | X | X |

Babu et al. [53] | Self Adaptive Firefly Algorithm (SA-FA) | To improve the results of ELD involving valve point effect by using non traditional method | System complexity increases wiht the increase in system variables | X | X |

D. Santra et al. [51] | Hybrid Particle Swarm Optimization (PSO) & Ant Colony Optimization (ACO) algorithm | To solve ELD problem involving transmission losses, ramp rate function and valve point effect | Less optimal results have been produced due to traditional techniques | X | X |

Alsumait et al. [54] | Hybrid Genetic Algorithm (GA) & PSO & Sequential Quadratic Programming (SQP) | To solve ELD problem involving valve point effect | This algorithm is not suitable for small networks as compared with other methods and also reserve capacity is not retained | X | X |

L. dos Santos et al. [51] | Improved harmony search algorithm | To solve ELD involving valve point effect | generation units has not applied with non operating zones and also reserve capacity is not retained | X | X |

O. Dzobo et al. [60] | Quadratic programming | To solve ELD considering uncertainty at the generation end | Very limited number of constraints applied | ✓ | X |

Zwe-Lee Gaing et al. [59] | PSO | To improve the results of ELD by using non traditional method | Less optimal results are found as compared to non-conventional techniques | X | X |

H. Shahinzadeh et al. [61] | Hybrid Big Bang–Big Crunch(BB–BC) algorithm | To solve Non Convex ELD problem | Algorithm requires large number iterations to find optimal solution | X | X |

L. S. Coelho et al. [62] | Hybrid (Chaotic differential algorithm & Quadratic programming) | To solve Non convex ELD problem | More decision and system variable may increase system complexity | X | X |

J. H. Park et al. [64] | Hopfield Neural Network (HNN) | ELD for piecewise quadratic cost curves | Algorithm works only for piecewise cost functions also reserve capacity is not retained | X | X |

**Table 2.**Operating limits of generation units [68].

Generation Unit | Index | Minimum Production (MW) | Maximum Production (MW) | Reserve Energy Cost ($) | Power Plant Cost Coefficients | ||
---|---|---|---|---|---|---|---|

$\mathit{\alpha}$ | $\mathit{\beta}$ | $\mathit{\gamma}$ | |||||

${P}_{{\mathrm{G}}_{1}}$ | ${i}_{1}$ | 50 | 200 | 20 | 1.070 × 10${}^{-2}$ | 1.1699 × 10${}^{+1}$ | 213 |

${P}_{{\mathrm{G}}_{2}}$ | ${i}_{2}$ | 37.5 | 150 | 15 | 1.780 × 10${}^{-2}$ | 1.0113 × 10${}^{+1}$ | 200 |

${P}_{{\mathrm{G}}_{3}}$ | ${i}_{3}$ | 45 | 180 | 22 | 1.480 × 10${}^{-2}$ | 1.0883 × 10${}^{+1}$ | 240 |

Time (HRS) | 12 a.m. | 1 a.m. | 2 a.m. | 3 a.m. | 4 a.m. | 5 a.m. |

Load (MW) | 382 | 409 | 490 | 374 | 510 | 480 |

Time (HRS) | 6 a.m. | 7 a.m. | 8 a.m. | 9 a.m. | 10 a.m. | 11 a.m. |

Load (MW) | 443 | 457 | 405 | 439 | 515 | 452 |

Time (HRS) | 12 p.m. | 1 p.m. | 2 p.m. | 3 p.m. | 4 p.m. | 5 p.m. |

Load (MW) | 448 | 404 | 443 | 464 | 472 | 429 |

Time (HRS) | 6 p.m. | 7 p.m. | 8 p.m. | 9 p.m. | 10 p.m. | 11 p.m. |

Load (MW) | 425 | 519 | 375 | 503 | 507 | 490 |

Case | Load (MW) | Reserve Capacity (MW) | Renewable Generation (MW) | Total Cost ($/MW) |
---|---|---|---|---|

1 | 382 | 50 | X | 6308 |

2 | 382 | 50 | X | 6293 |

3 | 382 | 50 | X | 6319 |

4 | 382 | 50 | X | 6334.2 |

5 | 382 | 50 | ✓ | 6138.0 |

6 | 382 | 50 | X | 1786.2 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hassan, M.W.; Rasheed, M.B.; Javaid, N.; Nazar, W.; Akmal, M.
Co-Optimization of Energy and Reserve Capacity Considering Renewable Energy Unit with Uncertainty. *Energies* **2018**, *11*, 2833.
https://doi.org/10.3390/en11102833

**AMA Style**

Hassan MW, Rasheed MB, Javaid N, Nazar W, Akmal M.
Co-Optimization of Energy and Reserve Capacity Considering Renewable Energy Unit with Uncertainty. *Energies*. 2018; 11(10):2833.
https://doi.org/10.3390/en11102833

**Chicago/Turabian Style**

Hassan, Muhammad Wajahat, Muhammad Babar Rasheed, Nadeem Javaid, Waseem Nazar, and Muhammad Akmal.
2018. "Co-Optimization of Energy and Reserve Capacity Considering Renewable Energy Unit with Uncertainty" *Energies* 11, no. 10: 2833.
https://doi.org/10.3390/en11102833