# Application Strategies of Model Predictive Control for the Design and Operations of Renewable Energy-Based Microgrid: A Survey

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## Abstract

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## 1. Introduction

#### Motivation of the Study and Research Gap

## 2. Microgrid Architecture

## 3. MPC Operating Concept and Control Strategy

- ${K}_{i}^{*}$ = reference trajectory;
- ${K}_{i}^{p}$ = predicted value for variable;
- ${X}_{i}$ = variable;
- ${\lambda}_{i}$ = weighting factor;
- i = number of variables.

## 4. MPC-MG Operations

#### 4.1. MPC for Grid-Connected MG Applications

- ${S}_{i},{s}_{i}$ = disturbances vectors;
- $w(k+j)$ = assumed to be known over prediction horizon for $j=0\cdots T-1$;
- $O{M}^{b}{f}^{{}^{\prime}}(k+j)$ = independent of objective function;
- ${C}_{z},{C}_{u}$ = column vectors;
- $(k+j)$ = time step.

- J = Economic criterion;
- u = Linear function;
- ${U}_{*}$ = Optimization control sequence;
- $(u,{x}_{o},c,v)$ = Initial storage state;
- ${P}_{min}^{G},{P}_{k}^{G},{P}_{max}^{G}$ = Minimum grid availability, grid availability at time instant k, and maximum grid availability.

#### 4.2. MPC for Isolated MG Applications

- ${P}_{ij},{Z}_{i}$ = auxiliary variables.

## 5. Superiority of MPC in Microgrid Designs and Operational Management

- In grid-connected microgrids, the prediction of energy market situations is achieved more accurately in terms of the load demand and generation dynamics, especially in the face of the uncertainties introduced by RERs. In isolated microgrids, operating in favorable conditions or deterministic conditions, where demand is known with certainty, is not possible because of the unpredictable nature of RERs. The effectiveness of MPC in tracking the disturbances and uncertainties has led to an increase in the desired operational benefits under these two conditions.
- In hybrid systems with thermal generators, a conventional unit commitment operation cannot accurately predict the output of RERs, which increases the effective operational cost. MPC introduction has, however, helped to achieve better control of prediction errors by the effects of its superior feedback mechanisms. In standalone systems and hybrid systems, MPC encourages multiple residential microgrids to interact effectively. It enhances efficient Peer-to-Peer (p2p) energy trading by cognizant of the differences in the energy needs and energy produced by connected parties known as the ‘Prosumers’ [114].
- Stochastic approaches do not give reliable performances when it comes to forecasting and forecast errors; combining MPC with this operation condition yields improved results in the desired outputs. The MPC exhibits superior performances compared to other options by considering both external and internal factors while solving uncertainty issues.

- One of the biggest challenges of MPC applications is that, it relies on historical information to predict the future. For newly-established energy systems (grid-connected or islanded), the application of MPC looks extremely difficult or impossible.
- MPC applications require high modeling expertise which comes with a high cost.
- The quality and accuracy of the predictive model plays a significant role in the control process. Having a balanced trade-off between the model accuracy and calculation complexity is a serious challenge.
- Another key issue in MPC is the design of the sampling interval. This interval determines the performance of the model. A better performance can be achieved considering small sampling time intervals. This will however reduce computational burden and economy of scale.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Global renewable energy transition [4].

**Figure 2.**Renewable Energy Resources (RERs) growth capacity in gigawatt (GW) by continent [4].

**Figure 3.**A typical MG architecture [2].

**Figure 4.**Hybrid MG architecture [3].

**Figure 5.**MPC control strategy [37].

Uncertainty Optimization Technique | Advantages | Disadvantages |
---|---|---|

Stochastic | 1. Can provide the expected value of perfect information and the cost of the stochastic solution 2. Minimise expected cost than minimizing worst-case cost | 1. Computationally demanding for large scenarios 2. Need to assign probabilities for scenario generation 3. Static assumption of uncertainty |

Robust | 1. No probability distribution 2. Not computationally demanding | 1. Need to use a different algorithm for different uncertainty sets 2. Overconservative solutions |

MPC | 1. Does not require external applications 2. The model dynamics uses the present information to predict future output | 1. Requires high expertise 2. Relies on historical data or information |

Ref. | Proposed Approach | Main Focus | Gap | Parameters to Be Optimized | Uncertainty Handling |
---|---|---|---|---|---|

[77] | Mixed Integer Programming (MILP), MPC | Power dispatching, reducing computational burden introduced by non-linear MILP and disturbances | Power, current | Influence of disturbances on RES is mitigated by receding horizon strategy | |

[78] | MPC, Gaussian process forecasting | Optimal operation planning for EMS to minimize cost of energy from grid | Results did not consider environmental and electricity tariff | Energy cost | At each sampling time predictions are calculated for an MPC execution based on predictions |

[49] | Hierarchical and Distributed MPC (HDMPC) | Main objective is to provide an economic management to maximize benefits | Automatic construction of day-ahead user profile, iterative negotiations between layers and integration of low level controls | Profit | A negotiation phase between the hierarchical and distributed MPC is enhanced to compensate for forecast errors in the system |

[79] | Distributed MPC (DMPC) Cooperative MPC (CMPC) | Maximizing RERs utilization and reducing cost and computational time | Power, cost | Each controller has a private predicting model that can solve global cost function | |

[46] | Stochastic MPC (SMPC), DMPC | A hierarchical predictive control approach to coordinate wind generation and PEV charging | Power balance | Power preferences are computed by uncertainties in both supply and demand | |

[80] | MPC | Integrated method is proposed connecting people’s behavior, appliances, grid behavior, price | Should include price based control devices | Voltage, peak load | MPC close the control loop from power generating to people behavior leading to reduce generation and distribution method |

[81] | MPC | Control the interlinking converter to enhance stable voltage supply, flexible power regulation, and grid support. | Voltage, power | Flexible reactive power is injected onto the main grid for grid support | |

[82] | SMPC, DMPC | MPC is applied with the aim of saving fossil energy and evaluate the potential for component downsizing leading to cost minimization | Power balance | Introducing an affine feedback correction due to uncertain weather fore -cast | |

[83] | Distributed Economic MPC (DEMPC) | A distributed control theory is developed to coordinate individual subsystems leading to suboptimal performance in the MG | State of charge, power balance, price | Each controller can optimize its operation for state of charge, predicted load and electricity price | |

[84] | MPC | The proposed model helps the network MGs to coordinate with each other. This minimizes the power produced by the micro gas turbine | Distributed control scheme will be considered in future analysis | Power balance | Uncertainty is avoided when one MG sells power to another where generation is greater than demand (G > D) |

[50] | MPC | An optimal dispatch problem of controllable loads and generators of an integrated MG is proposed to minimize cost | Accuracy of the proposed model will be correlated in further studies | A feedback mechanism compensates for uncertainties associated with time varying loads, energy prices and RERs power outputs | |

[85] | MPC, MILP | Operation cost is minimized by optimally scheduling generating units while satisfying complex constraints | Will include DMPC and SMPC in further work | Electricity price | A MILP is optimized at each time step based on short term forecast and incorporated into MPC to reduce forecast errors |

[86] | MPC | To generate suitable decisions for all the source and electrical storage components to fulfill load demands | Interconnected MG and combination between multi-agent approaches will be applied in further studies | Power consumption, generation profile, cost | Fault tolerant strategies are inserted to ensureproper amount of energy in storage devices for customers’ demand |

[87] | MPC | Combined economic and environmental energy management to minimize daily generation cost and emission | Dynamic model including electrical components will be included in future work | Cost, emission | Prediction curves, energy generation, load demand are gotten from historical recording data with stochastic uncertainty processing |

[9] | MPC | A hierarchical control scheme is proposed to compute control action needed by a subsystem or neighboring subsystem | Stochastic scenario, direct negotiations should be included in further studies | Voltage, frequency | The supervisory level checks for shortages or excesses of control and also compensate for errors to satisfy the required demand |

[88] | Dual Decomposition DMPC | Focuses on solving economic dispatch at runtime while reducing potential deviations schedules | Stochastic techniques to tackle challenges will be included in further studies | Power balance | Formulation is solved by every power plant to enhance granularity of agent |

[45] | Rolling Horizon (RH) MPC | Energy management system(EMS) is developed to minimize daily operation cost and enhance local self consumption of RERs | Real time pricing scheme will be considered in further work. | RERs | Design and implementation of controller to control accuracy of battery energy storage |

[89] | EMPC | Including an economic cost index and explicit constraint to optimally dispatch power to minimize cost | State of charge of battery | Design of a central control capable to handle multivariable constraints and predictions | |

[90] | SMPC | A two layer algorithm is developed for optimal EMS of the MG | Thermal energy needs of the MG will be considered in further studies | RERs | SMPC regulator at lower layer runs at higher frequency to compensate for uncertainties |

[91] | DMPC | A distributed MPC algorithm is proposed to schedule MG internal devices and optimal power trading | Power balance | Reactive power balance is established |

Ref. | Proposed Approach | Main Focus | Gap | Parameters to Be Optimised | Uncertainty Handling |
---|---|---|---|---|---|

[98] | Mixed integer non linear programming (MINLP) | Developing an advanced model optimization approach using MPC framework to reduce cost and improve robustness of control towards prediction errors and uncertainties | State of charge, power balance | Inclusion of detailed component model limits uncertainties and adaptive forecast algorithm reduces errors | |

[99] | MPC, sliding mode control | To stabilize MG system and maintain output voltage in a layer that can enhance current sharing | Voltage, current | Voltage references are tracked by the sliding mode control | |

[100] | DMPC | Optimization problem is solved by incorporating economic dispatch in secondary layer | Economic efficiency and frequency control performance will be considered in further work | Frequency | Uncertainty effects of RERs is solved by applying MPC online with rolling optimization |

[101] | MPC | Limiting converter current under overloading conditions | Voltage and current | Decoupling of control channels for each DG | |

[102] | MPC | To maintain network variables, provide flexibility and coordination and account for energy storage reserves. | Voltage, frequency | The primary layer modulates DG units in order to limit voltage and frequency from nominal values | |

[103] | MPC | Control voltage and frequency at the generating unit and supply energy for balance load | Voltage, frequency | Addition of fault detection and diagnosis module to MPC structure | |

[104] | SMPC | To provide a solution that can reduce conservativeness by taking into account stochasticity of loads and RERs. | Stochastic and worst case approaches will be consider in further studies | RERs | Models for time series forecast are employed |

[72] | SMPC | Development of advanced control to improve robustness towards prediction errors and uncertainties | Power | Probability constraints are assumed on the battery state of charge | |

[105] | MILP-MPC | An optimization strategy is proposed to attain an optimal generator start up sequence | Transient processes will be treated in further work | Power | Uncertainties are modeled by discretizing the said probability distribution of forecast errors |

[106] | MPC | Minimize voltage unbalance, improve current limiting, and prevent active power overload. | Distributed control scheme will be employed in further work | Power quality | Controls the negative sequence impedance to reduce voltage unbalance and current sharing error |

[107] | MPC | Presents a dynamic reactive power control method to control reactive power | Future analyses will consider large MGs | Power, voltage | Time variant reactive capabilities of distributed generators are used to compensate for reactive power |

[108] | MPC, demand side management (DSM) | Minimize operation cost and maintain power balance considering uncertainties imposed | Practical implementation of MG will be included in further work | Power balance | Faster time scale online power allocation is done to compensate for uncertainties in real time |

[68] | Minimax MPC | A closed-loop minimax MPC is employed to yield a better prediction accuracy and lower cost compared to open loop | Optimal control of MG in a probabilistic manner will be considered in further work | RERs | By paramterization |

[109] | MPC | An interactive energy management is proposed to enhance power balances and uncertainties handling in multi-MGs | Impact assessment of cyber risk and large distribution systems | Power balance | Lower layer runs on high frequency to adjust difference between planned and real time strategies |

[110] | HDMPC | A hierarchical distributed MPC is proposed to coordinate power, flexibility, dispatch, and minimize cost | Robust optimization will be considered in future work | Power balance | Back calculation from lower to upper layer is introduced. |

[69] | MPC | An online optimization approach of a combined cooling, heating and power MG is proposed to reduce running cost and handle uncertainties | Stochastic technique to tackle challenges will be included in further work | RERs | Online optimal approach using MPC to compensate for prediction error |

[73] | MPC | The proposed algorithm reduces operational cost while maintaining power balance | More suitable method will be consider in further work to compensate for forecast errors | Power balance | Scenarios are run in parallel on a semi-physical platform |

[111] | MPC | MPC control strategy is proposed to solve an optimal power flow problem in a MG where assumptions are avoided | Power flow | Nonlinear variations in charge and discharge efficiencies of the battery are analyzed | |

[112] | Robust MPC | Main contribution is a review of the three proposed robust MPC techniques to select best approach | RERs | A single control system is calculated using multi- scenario MPC | |

[113] | MPC | EMS is proposed to minimize daily operating cost where MPC is used to minimize uncertainties | RERs | MPC strategy is implemented |

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**MDPI and ACS Style**

Konneh, K.V.; Adewuyi, O.B.; Lotfy, M.E.; Sun, Y.; Senjyu, T.
Application Strategies of Model Predictive Control for the Design and Operations of Renewable Energy-Based Microgrid: A Survey. *Electronics* **2022**, *11*, 554.
https://doi.org/10.3390/electronics11040554

**AMA Style**

Konneh KV, Adewuyi OB, Lotfy ME, Sun Y, Senjyu T.
Application Strategies of Model Predictive Control for the Design and Operations of Renewable Energy-Based Microgrid: A Survey. *Electronics*. 2022; 11(4):554.
https://doi.org/10.3390/electronics11040554

**Chicago/Turabian Style**

Konneh, Keifa Vamba, Oludamilare Bode Adewuyi, Mohammed Elsayed Lotfy, Yanxia Sun, and Tomonobu Senjyu.
2022. "Application Strategies of Model Predictive Control for the Design and Operations of Renewable Energy-Based Microgrid: A Survey" *Electronics* 11, no. 4: 554.
https://doi.org/10.3390/electronics11040554