# A Review of the Optimization and Control Techniques in the Presence of Uncertainties for the Energy Management of Microgrids

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Systematic Literature Review

- S1: microgrid + review + EMS + uncertainties;
- S2: review + modeling + optimization + uncertainties + energy;
- S3: microgrid + EMS + uncertainties + optimization;
- S4: microgrid + EMS + uncertainties + optimization + real-time.

## 3. Uncertainties in Microgrids

#### 3.1. Residential and Commercial–Industrial Applications

#### 3.2. Virtual Power Plants

#### 3.3. Electric Mobility

#### 3.4. Multi-Carrier Microgrids

## 4. Modeling Techniques for Uncertainties in Microgrid Optimization

#### 4.1. Probability Distribution Modeling

#### 4.2. Possibility Theory

#### 4.3. Information Gap Theory

#### 4.4. Deterministic Theory

## 5. Optimization Techniques with Uncertainties

#### 5.1. Stochastic Programming

#### 5.2. Robust Optimization

#### 5.3. Information Gap Decision Theory

#### 5.4. Model Predictive Control

#### 5.5. Multiparametric Programming

#### 5.6. Fuzzy Optimization

#### 5.7. Machine Learning

#### 5.8. Comparison

## 6. Optimization Algorithms

## 7. Software

^{®}CPLEX

^{®}, Gurobi, and others depending on the problem that can be linear, nonlinear, convex, or non-convex. In [175], an energy management system developed in LABVIEW is used to control a microgrid. In this case, the formulation of the problem is written in GAMS, while the optimization problem is solved by IBM ILOG

^{®}CPLEX

^{®}.

## 8. Challenges and Future Trends

## 9. Conclusions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 9.**Information gap decision theory flow chart [91].

**Figure 10.**Block diagram of the model’s predictive control [148].

**Figure 11.**Block diagram of multiparametric programming [2].

**Table 1.**An overview of the review papers on EMS for microgrids. The papers are organized by year of publication and whether they cover optimization and modeling when uncertainties are considered.

Reference | Model Uncertainties | Optimization Techniques with Uncertainties | Survey | Year | Focus |
---|---|---|---|---|---|

[1] | x | - | 2007–2016 | 2016 | Renewable energy availability, heat demand, and load demand |

[4] | - | - | 2005–2014 | 2016 | Architecture, control, common optimization algorithms: heuristic and mathematical methods |

[38] | - | x | 2001–2015 | 2016 | Optimization objectives, heuristic methods, stochastic programming, model predictive control and neural network. |

[35] | x | x | 2002–2016 | 2017 | Energy scheduling for reliability, uncertainty, demand response, emissions, and multi-objective. The uncertainty discussions are covered in a small section where only probabilistic modeling is discussed. |

[18] | x | - | 2000–2017 | 2018 | Robust, and stochastic approach for uncertainty modeling in energy systems |

[3] | x | x | 2002–2017 | 2018 | Robust, stochastic programming and model predictive control. It reviews the architecture, control, and communication. The uncertainties models are not well described |

[16] | - | - | 2001–2020 | 2020 | Architecture, technologies, and market analysis. |

[39] | x | x | 1989–2019 | 2020 | Artificial intelligence and machine learning for energy demand. |

[10] | x | - | 2000–2020 | 2021 | Traditional optimization techniques, the architecture, control, of microgrids. Only a small section is dedicated to uncertainties. |

[11] | - | - | 2005–2020 | 2021 | dc microgrid architecture, control, optimization algorithms, and software. |

[17] | - | - | 2002–2020 | 2021 | Architecture and control |

[37] | - | x | 2002–2021 | 2022 | Control methods: game theory, multi-agent and artificial intelligence, stochastic and robust optimization |

Uncertainty | Residential and Commercial | Virtual Power Plants | Electric Mobility | Multi-Carrier Microgrids |
---|---|---|---|---|

Renewable energy power production | x | x | x | x |

Ambient conditions: solar irradiance, humidity, precipitation, wind speed, temperature | x | x | x | x |

Electricity price | x | x | x | x |

Electricity consumption | x | x | x | x |

Power reserve | - | - | - | x |

Voltage and frequency variations | - | - | - | x |

Electrical failures | x | - | - | - |

Use of appliances | x | - | - | - |

Connection/disconnection EV | x | x | x | x |

Parking availability | - | - | x | - |

Parking queues | - | - | x | - |

User’s comfort | x | - | x | - |

State of charge of battery | x | x | x | x |

Driving pattern | - | - | x | - |

State of health: battery, electrical system, PV modules, generators | x | x | x | - |

Remaining use of life | x | x | x | - |

CO${}_{2}$ emissions | x | - | - | - |

Future installed capacity | - | - | - | x |

Future load demand | - | - | - | x |

House and building occupancy | x | - | - | - |

Maintenance | - | - | - | x |

Power reserves | - | - | - | - |

Type | Multi-Carrier Microgrid | Renewable Energy | Load | Electricity Price | EV | Energy Storage |
---|---|---|---|---|---|---|

Poisson | forecast error | connection/disconnection | spikes | arrival/departure | state of charge | |

random occupancy | connection/disconnection | |||||

number of EVs | ||||||

Binomial | generator outages | connection/disconnection | ||||

transformers failures | ||||||

Uniform | generator outages | load consumption | state of charge | state of charge | ||

number of Evs | ||||||

Gaussian | forecast error | heating loads | price variation | charging time | state of health | |

solar irradiance | cooling loads | arrival/departure | state of charge | |||

sky index | ||||||

PV power | load profile | |||||

temperature | ||||||

Beta | solar irradiance | |||||

Weibull | PV power | degradation | ||||

wind power | ||||||

degradation | ||||||

Gamma | travel time | |||||

travel distance |

Type | Multi-Carrier Microgrid | Renewable Energy | Load | Electricity Price | EV | Energy Storage |
---|---|---|---|---|---|---|

Fuzzy sets | Non applied | forecast error | forecast error | forecast error | total charging amount | maximum charging rate |

spikes of solar irradiance | sudden variations | spikes | connection/disconnection | initial state of charge | ||

PV power | home internal heat | parking availability | final state of charge | |||

Wind power | load power | maximum profit | maximum charging rate | |||

connection/disconnection | operation cost | initial state of charge | ||||

final state of charge | ||||||

battery level anxiety | ||||||

driving pattern | ||||||

Bayesian | failure | forecast error | variations | peak price | connection/disconnection | |

outages | PV power | use factor of appliances | driving pattern | |||

reliability | Wind power | load variation | ||||

Minimum power | connection/disconnection | |||||

Maximum power | heating system | |||||

cooling system | ||||||

peak load |

Multi-Carrier Microgrid | Renewable Energy | Load | Electricity Price | EV | Energy Storage |
---|---|---|---|---|---|

not applied | forecast error | forecast error | forecast error | Not applied | |

thermal power | load power | intervals of bidding prices | |||

PV power | maximum price | ||||

wind power | minimum price |

Type | Multi-Carrier Microgrids | Renewable Energy | Load | Electricity Price | EV | Energy Storage |
---|---|---|---|---|---|---|

Intervals | max/min number of generators | forecast error | max/min consumption | forecast error | max/min number of cars | max/min state of charge |

max/min voltage | max/min production | max/min number of appliances | max/min price | max/min charging points | ||

max/min frequency | ||||||

Robust sets | Installed capacity | forecast error | discomfort level | market price | not applied | |

wind power | variation of temperature | |||||

solar power | expected demand | |||||

consumption |

Probability Theory | Possibility Theory | Information Gap Theory | Deterministic | |
---|---|---|---|---|

Type of uncertainty | Randomness | ambiguity | unmeasured uncertainty | measured uncertainty |

Output of the model | Probability density function/ cumulative density function | Membership function | Uncertain uncertainty set | exact interval |

General mathematical form | e.g., Normal PDF | e.g., envelope | e.g., min/max | |

$N(u,{\sigma}^{2})$ | ${U}_{A}\left(x\right)$ | $U(\alpha ,\tilde{u})$ | $x\subset [min\left(\tilde{u}\right),max\left(\tilde{u}\right)]$ | |

$|u\left(t\right)-\tilde{u\left(t\right)}|\le \alpha |\tilde{u\left(t\right)}|$ |

Phenomena | Monte Carlo | Latin Hypercube | Markov Chain |
---|---|---|---|

Renewable energy power production | x | x | |

Driver pattern | x | x | x |

State of charge of battery | x | ||

Electricity price | x | x | x |

Degradation battery price | |||

Electricity consumption/load profile | x | x | |

Connection/disconnection EV | x | x | |

Electrical failures | x | ||

Ambient conditions: solar irradiance, humidity, precipitation, wind speed | x | ||

Generators failures/reliability | x | x | |

Through life cost | |||

Risk planning | x | x | |

Microgrid operation | x | ||

Power flow direction | x | ||

Range anxiety/ battery level anxiety | x |

Optimization Technique | Uncertainty Model | Input Data | Stages | Computation Time | |
---|---|---|---|---|---|

Day Ahead | Real Time | ||||

Stochastic Optimization | Probabilistic function | Forecast | Yes | Yes | High |

Fuzzy sets | Estimated | ||||

Intervals | Deterministic | ||||

Robust sets | |||||

Robust optimization | Robust sets Intervals | Forecast | Yes | Yes | Medium |

Intervals | Estimated | ||||

Fuzzy sets | Deterministic | ||||

Information gap decision theory | Forecast | Yes | Yes | Medium | |

Variable interval | Estimated | ||||

Deterministic | |||||

Multiparametric | Robust sets | Forecast | No | Yes | Low |

Intervals | Estimated | ||||

Deterministic | |||||

MPC | Probabilistic function | Forecast | No | Yes | High |

Intervals | Estimated | ||||

Deterministic | |||||

Fuzzy optimization | Fuzzy sets | Forecast | Yes | No | Medium |

Estimated | |||||

Deterministic | |||||

Machine learning | Does not require | Forecast | No | Yes | Low |

Estimated | |||||

Deterministic |

Optimization Technique | Main Characteristics | Pros | Cons | Preferred Applications |
---|---|---|---|---|

Stochastic programming | Scenarios based | easy to implement | High computational time | day-ahead optimization |

intractable | electrical distribution | |||

reduce operational cost | short-term uncertainty | |||

large VPPs | ||||

Robust optimization | worst-case scenario | reduce risky operation | Increment cost | Long-term decisions |

Robust | electrical distribution | |||

tractable | day-ahead optimization | |||

IGDT | worst and base case scenario | non-data set | inflexible | long-term uncertainties |

known outcome | tractable | complex | ||

Multiparametric programming | creates critical regions | reduce online computation | intractable | real time systems |

offline calculation | low use of memory | solution grows exponentially | residential and commercial microgrids | |

small applications | ||||

MPC | Model the system | online optimization | needs the model of the system | small time frames decisions |

Predicts the next step | no previous data set | high computation time | react to uncertainties | |

tractable | parking lots | |||

enhanced transient response | electric mobility | |||

receives real time feedback | residential and commercial microgrids | |||

real-time operation | ||||

Fuzzy optimization | membership function satisfaction | tractable | increase exponentially | day-ahead scheduling |

flexible | reduced accuracy | parking lots | ||

rapid operation | VPPs | |||

precision | day-ahead scheduling | |||

V2G | ||||

Machine learning | adaptable | requires historic data set | real time operation | |

flexible | problems with unexpected changes in short-term | VPPs | ||

small online computation time | offline time | digital twins | ||

residential and commercial microgrids | ||||

electric mobility |

Components | Methodology | Uncertainties | Time Horizon | Resolution | Execution Time | Software | Ref. |
---|---|---|---|---|---|---|---|

Diesel generator | IGDT | PV power | 24 h | 1 h | 546.9 s | GAMS | [145] |

PV system | load power | ||||||

ESS | |||||||

load | |||||||

Diesel generator | Probabilistic | PV power | 24 h | 1 h | 131,494.4 s | GAMS | [145] |

PV system | load power | ||||||

ESS | |||||||

load | |||||||

ESS | IGDT | market price | 24 h | 30 min | 360 s | GAMS | [181] |

load | |||||||

smart appliances | |||||||

thermal storage system | |||||||

ESS | Robust optimization | market price | 24 h | 1 h | 0.59 s | MATLAB/CPLEX | [174] |

PV system | PV generation | ||||||

flexible load | |||||||

Wind turbine | Stochastic Adaptive Robust Optimization | wind power | 24 h | 1 h | 2100 s | CPLEX/GAMS | [144] |

ESS | market price | ||||||

flexible load | |||||||

Thermal generators | Fuzzy optimization | wind power | 24 h | 1 h | 9 s | MATLAB/CVX | [158] |

PV systems | PV power | ||||||

Wind turbines | |||||||

industrial load | |||||||

commercial load | |||||||

households | |||||||

Thermal generators | Probabilistic/Monte Carlo | wind power | 24 h | 1 h | 2609.4 s | MATLAB/CVX | [158] |

PV systems | PV power | ||||||

Wind turbines | |||||||

industrial load | |||||||

commercial load | |||||||

households | |||||||

heating system | Multiparametric programming | initial state heat storage | 3 h | 1 h | 32,660 s | MATLAB/CPLEX | [156] |

loads | initial electricity production | ||||||

combined heat and power units | demand for heat | ||||||

electricity consumption | |||||||

CIGRE model | Deep reinforcement learning | PV power | 24 h | 1 h | 0.5 ms | Python | [167] |

load | |||||||

CIGRE model | MPC | PV power | 24 h | 1 h | 228 ms | Python | [167] |

load |

**Table 12.**Summary of the articles reviewed depending on the optimization technique used. (RO: Robust optimization, SO: stochastic optimization, FO: fuzzy optimization, IGDT: information-gap decision theory, MPC: model predictive control, MP: multiparametric programming, ML: machine learning, MS: multiple stages, RT: real time).

Reference | SO | RO | FO | IGDT | MPC | MP | ML | MS | RT | Year |
---|---|---|---|---|---|---|---|---|---|---|

[2] | x | x | x | 2022 | ||||||

[5] | 2022 | |||||||||

[13] | x | 2022 | ||||||||

[88] | x | x | 2022 | |||||||

[89] | x | 2022 | ||||||||

[171] | x | 2022 | ||||||||

[44] | x | x | 2019 | |||||||

[12] | x | x | 2020 | |||||||

[15] | x | 2020 | ||||||||

[25] | x | 2020 | ||||||||

[30] | x | 2020 | ||||||||

[50] | x | 2020 | ||||||||

[64] | x | 2020 | ||||||||

[92] | x | 2020 | ||||||||

[94] | x | 2020 | ||||||||

[97] | x | x | 2020 | |||||||

[147] | x | x | x | 2020 | ||||||

[155] | x | x | 2020 | |||||||

[164] | x | 2020 | ||||||||

[165] | x | 2020 | ||||||||

[14] | x | x | x | 2019 | ||||||

[31] | x | 2019 | ||||||||

[45] | x | 2019 | ||||||||

[93] | x | x | 2019 | |||||||

[122] | x | x | 2019 | |||||||

[140] | x | 2019 | ||||||||

[145] | x | 2019 | ||||||||

[162] | x | 2019 | ||||||||

[170] | x | 2019 | ||||||||

[180] | x | 2019 | ||||||||

[53] | x | 2018 | ||||||||

[58] | x | 2018 | ||||||||

[81] | x | x | 2018 | |||||||

[82] | x | x | 2018 | |||||||

[121] | x | 2018 | ||||||||

[123] | x | 2018 | ||||||||

[131] | x | 2018 | ||||||||

[141] | x | x | 2018 | |||||||

[146] | x | 2018 | ||||||||

[184] | x | 2018 | ||||||||

[166] | x | 2018 | ||||||||

[181] | x | 2018 | ||||||||

[43] | x | x | 2017 | |||||||

[47] | x | 2017 | ||||||||

[84] | x | 2017 | ||||||||

[95] | x | 2017 | ||||||||

[96] | x | 2017 | ||||||||

[142] | x | x | 2017 | |||||||

[144] | x | x | x | 2017 | ||||||

[158] | x | 2017 | ||||||||

[52] | x | 2016 | ||||||||

[149] | x | x | x | 2016 | ||||||

[150] | x | x | x | 2016 | ||||||

[176] | x | 2016 | ||||||||

[177] | x | 2016 |

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**MDPI and ACS Style**

Cabrera-Tobar, A.; Massi Pavan, A.; Petrone, G.; Spagnuolo, G.
A Review of the Optimization and Control Techniques in the Presence of Uncertainties for the Energy Management of Microgrids. *Energies* **2022**, *15*, 9114.
https://doi.org/10.3390/en15239114

**AMA Style**

Cabrera-Tobar A, Massi Pavan A, Petrone G, Spagnuolo G.
A Review of the Optimization and Control Techniques in the Presence of Uncertainties for the Energy Management of Microgrids. *Energies*. 2022; 15(23):9114.
https://doi.org/10.3390/en15239114

**Chicago/Turabian Style**

Cabrera-Tobar, Ana, Alessandro Massi Pavan, Giovanni Petrone, and Giovanni Spagnuolo.
2022. "A Review of the Optimization and Control Techniques in the Presence of Uncertainties for the Energy Management of Microgrids" *Energies* 15, no. 23: 9114.
https://doi.org/10.3390/en15239114