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The future smart grid is expected to be an interconnected network of small-scale and self-contained microgrids, in addition to a large-scale electric power backbone. By utilizing microsources, such as renewable energy sources and combined heat and power plants, microgrids can supply electrical and heat loads in local areas in an economic and environment friendly way. To better adopt the intermittent and weather-dependent renewable power generation, energy storage devices, such as batteries, heat buffers and plug-in electric vehicles (PEVs) with vehicle-to-grid systems can be integrated in microgrids. However, significant technical challenges arise in the planning, operation and control of microgrids, due to the randomness in renewable power generation, the buffering effect of energy storage devices and the high mobility of PEVs. The two-way communication functionalities of the future smart grid provide an opportunity to address these challenges, by offering the communication links for microgrid status information collection. However, how to utilize stochastic modeling and optimization tools for efficient, reliable and economic planning, operation and control of microgrids remains an open issue. In this paper, we investigate the key features of microgrids and provide a comprehensive literature survey on the stochastic modeling and optimization tools for a microgrid. Future research directions are also identified.

Energy is and will continue to be the backbone of the global economy in the foreseeable future. However, due to fast rising energy prices, climate change and technology advances, reshaping the energy industry has become an international priority. A critical step is to utilize renewable energy sources for economic and environmentally friendly energy production. According to the International Energy Agency forecast, electric power generation from renewable energy sources will nearly triple from 2010 to 2035, reaching 31% of the world's total power generation, with hydro, wind and solar renewable power providing 50%, 25% and 7.5%, respectively, of the total renewable power generation by 2035 [

Some of the microsources (in terms of small-scale renewable energy sources and CHP plants), energy storage devices and V2G systems can be efficiently integrated in local areas, such as a small community, a university or school, and a commercial area, which leads to the formation of local, small-scale and self-contained grids, typically referred to as microgrids. A microgrid can operate in either a grid-connected mode to enable energy transactions with the main electrical grid or an islanded (or standalone) mode given there is a fault in the main grid. In addition to the economic and environmental benefits of utilizing renewable energy sources and CHP plants, other advantages of microgrids include:

Energy loss reduction: Taking advantage of the proximity between microsources and loads, microgrids can significantly reduce the energy losses in electricity and heat transmission/distribution and improve the utilization of renewable energy;

Reliability improvement: Since a microgrid can operate in an islanded mode if there is a fault in the main grid, the negative impact of the outages in transmission and distribution systems can be reduced, and thus, system reliability can be improved;

Enhancement of energy management: With the microsources and loads in a microgrid being managed in a coordinated way, the electric and/or heat power can be better shared among the local customers;

Benefits to the main grid: Via efficient energy management of microgrids, the energy import from the main grid can be reduced, which relieves power transmission/distribution line congestions. Moreover, microgrids can be used to provide ancillary services (such as frequency regulation) to the main grid, which potentially improves the reliability of the main grid.

In order to realize all the potential benefits of microgrids, effective and efficient management of the microgrids should be in place. Recent advances in information and communication technologies (ICT) have provided opportunities to enable advanced microgrid operation and control, under the umbrella of the smart grid. According to the IEEE 2030 standard [

An electric power system based on the traditional view of the electrical grid, which consists of four main domains for electric power generation, transmission, distribution and consumption;

A communication system, which establishes the connectivity among different systems and devices for information exchange; and

An information system, which stores and processes data information for decision-making on electric power system operation and control.

The same architecture is applicable to microgrids, which are small-scale and self-contained grids in nature. Based on the two-way communications throughout a microgrid, the information system can collect microgrid status information, process the information and make decisions on microgrid operation and control.

The IEEE 2030 standard defines the interoperability of ICT with the electric power system, end-user applications and loads. However, how to acquire the necessary information and act on the acquired information for optimal microgrid operation and control are application-specific and need extensive research. The issue is even more complicated for microgrid planning, as it requires investigations of not only the operation and control functions of microgrids, but also all potential options and/or combinations of microsources and energy storage devices, such that the overall microgrid planning cost throughout the planning horizon is minimized. In order to address various research challenges, stochastic modeling and optimization tools can be used to facilitate microgrid planning, operation and control. Specifically, stochastic models can be established to characterize the randomness in renewable power generation, the buffering effect of energy storage devices and PEV mobility. Then, stochastic optimization tools can be used for the planning, operation and control of microgrids. In the literature, there are a few surveys and tutorials on smart grid architecture [

In this paper, we investigate the architecture of microgrids and identify unique features and challenges in microgrid planning, operation and control, in comparison with traditional power transmission and/or distribution systems. The existing stochastic modeling and optimization tools are presented, and their applications in microgrids are identified. The related literature is surveyed according to different time frames of microgrid planning, operation and control and for microgrids with various types of microsources. Open research issues are also discussed.

The remainder of this paper is organized as follows. Section 2 presents the fundamentals of microgrids and related research challenges. The modeling and analysis tools of microgrids are discussed in Section 3. The state-of-the-art of microgrid planning, operation and control is presented in Sections 4–6, respectively. Section 7 summarizes this study and identifies future research directions.

In this section, we introduce the architecture of a microgrid and the planning, operation and control functions in a microgrid. The related research challenges are discussed.

The typical configuration of a microgrid is shown in

The operation and control of microsources can be established in either a centralized manner or a decentralized manner. Centralized operation and control rely on a central controller (CC) and several microsource controllers (MCs) in the microgrid. Each MC is in charge of the management and protection of individual microsources. The MCs are coordinated by the CC, which provides the overall management of the microgrid in terms of generation scheduling and protection coordination. The information exchanges between the CC and MCs are established via a communication network, typical referred to as the field area network (FAN) or neighborhood area network (NAN) in the future smart grid [

The centralized operation and control have the advantage of high efficiency in terms of global optimality. However, the heavy dependence on the CC may result in the problem of a single point of failure. Moreover, the communication network for information exchanges between the CC and MCs may not exist, especially in remote areas. Therefore, there is a trend in the research community to decentralize the operation and control of microgrids [

Since microgrids are designed to supply electrical and heat loads in a local area, the maximum capacity of each microgrid is limited (e.g., 10 MVA as per IEEE recommendations [

In comparison with the traditional and well-established electrical grid, the concept of a microgrid is new and just beginning to move into the mainstream. Therefore, microgrid planning will be a critical issue in the next few decades. Microgrid planning is typically performed years ahead to find the optimal combination, design and sizing of microsources to meet the future electrical and heat demand at a minimum lifecycle cost, while satisfying the reliability requirements of the system [

Microgrid operation mainly involves unit commitment and economic dispatch. Both functions have their counterparts in the traditional electrical grid [

Unit commitment, typically performed from one day to one week ahead of time, determines which microsource should be on-line at what time, such that the microgrid operation cost can be minimized [

Economic dispatch, typically performed from a few minutes to one hour ahead of time, makes short-term decisions on the output of on-line microsources to minimize the cost of energy production, while meeting the load demand and microgrid operation constraints in terms of system loading, line flow and voltage constraints [

Microgrid control is performed in a relatively small time scale (in terms of minutes/seconds or even shorter) to achieve short-term balance between power generation and demand [

Due to the integration of renewable energy sources and energy storage devices (including V2G systems), new technical challenges arise in microgrid planning, operation and control. The randomness in renewable power generation should be taken into account in addition to the randomness in load demands. As the renewable power generation may deviate from forecasted values, predefined microgrid operation schedules may be violated. Moreover, the seasonal and yearly variation of weather conditions may affect the operation cost of a microgrid in the long run, which should be investigated during microgrid planning. The buffering effect of energy storage devices requires the modeling of inter-period buffer state transitions over the entire time frame of microgrid planning, operation and control, which results in high computational complexity. In addition, the highly dynamic PEV mobility leads to randomness in the number of PEVs at a specific location and, thus, the randomness in the capacity of the V2G system. In order to address these challenges, stochastic modeling and optimization tools can be used for microgrid planning, operation and control. Yet, the unique issues (or features) of microgrids need to be investigated, as follows:

The two operation modes (

A microgrid is designed to supply the electrical and heat loads in a small geographical area, within which the weather conditions, such as wind speeds and solar radiation, are likely to be similar. As a result, the renewable power generation and/or electrical and heat loads may exhibit substantial spatial correlations. The spatial correlation should be investigated to improve the accuracy of microgrid modeling. Exploiting the spatial correlation may facilitate microgrid operation and control in terms of computational complexity reduction, as less variables are needed for microgrid representation and decision-making;

Different from traditional electric power systems, which only supply electrical loads, both electrical and heat loads may exist in a microgrid due to the implementation of CHP plants. A two-dimensional model of electricity and heat flows should be developed for microgrids with CHP plants. Moreover, the differences in the storage and charging/discharging characteristics of electricity and heat buffers should be investigated in microgrid modeling and optimization.

There is a large body of research on stochastic information management in the smart grid [

In the literature, there exist some research works on stochastic modeling of microgrids. These models are developed for microgrid performance evaluation and have the potential to be applied in specific planning, operation or control functions. A summary of the stochastic models is shown in

The framework of a stochastic hybrid system (SHS) can be used to establish a stochastic model for a microgrid [

State estimation is a technique used to estimate power system states (such as bus voltage magnitudes and phase angles of the entire system) based on available measurements [

Analog measurements, which include bus voltage magnitudes, active/reactive power injections and active/reactive power flows;

Logic measurements, which include the status of switches and circuit breakers; and

Pseudo measurements, which include forecasted power generation and loads.

The observability of an electric power system depends on the number of measurements and their geographical distribution. Given a sufficient number of measurements with good geographical distribution, the state estimator can provide estimates of system states. If all states can be determined, the system is observable, and

However, the real-time measurements in a microgrid may be insufficient for system observability, in comparison with that in a traditional electrical grid. The main reason is that each microgrid is a small-scale grid used to supply local loads, so that it is relatively cost-sensitive and not suitable for the extensive deployment of measurement units. In order to address this issue, the theory of the network observability test can be applied [

Microgrid reliability is usually measured through various reliability indices, such as the system average interruption frequency index (SAIFI), the system average interruption duration index (SAIDI), the customer average interruption frequency index (CAIFI), the expected energy not supplied (EENS) and the loss of load expectation (LOLE). Stochastic models are widely used to analyze microgrid reliability, since the outages in a microgrid (possibly due to device failure and/or insufficient output from a renewable energy sources) occur in a probabilistic manner. The stochastic models presented in this subsection can be potentially used to assist microgrid planning, since one of the major requirements of microgrid planning is to ensure system reliability.

Monte Carlo simulation (MCS) can be used to evaluate the reliability of a microgrid [

Load priority is considered in [

Fault: A section may fail, and the microgrid needs to be reconfigured by disconnecting some of the sections;

Insufficient generation: The power generated by renewable energy sources is random, which may not be sufficient to supply all loads.

In either case, the available power in a microgrid is allocated to the sections according to their priorities, such that more frequent or more sustained outages are expected for sections with lower priorities. MCS is used to generate scenarios for component failure and repair processes [

The impact of renewable energy sources on microgrid planning is two-fold. On the one hand, the lifecycle power generation cost in a microgrid can be reduced by utilizing renewable energy sources. On the other hand, the intermittent nature of renewable power generation can lead to insufficient generation and, hence, reliability issues, especially during the islanded operation. If necessary, energy storage devices and traditional dispatchable microsources, such as diesel generators, should be integrated in a microgrid to improve system reliability. Furthermore, microgrid planning is subject to other external uncertainties, such as long-term fluctuations in electricity, fuel and the construction/installation cost of microsources and energy storage devices. Therefore, stochastic optimization tools should be used to take into account the statistics of the uncertainties and make optimal decisions on microgrid planning. A summary of the stochastic optimization tools for microgrid planning is given in

In order to select cost-minimum generation components, the fluctuating electricity price should be investigated [

The problem of optimal sizing of a renewable energy and microturbine combined heat and power (micro-CHP) hybrid energy microgrid is studied in [

The integration of renewable energy sources, energy storage devices and a V2G system in microgrids governs microgrid operation. Its impact (and the corresponding solution) varies with the specific operation functions, which are performed at certain time scales. The stochastic optimization tools for microgrid operation are summarized in

In a microgrid with renewable energy sources, unit commitment is a challenging issue. Due to the uncertainties in forecasting, the realization of renewable power generation may significantly deviate from the forecasted value. Therefore, a significant number of traditional dispatchable (e.g., fossil-fueled) power generators should stay on-line. However, more on-line generators lead to higher microgrid operation cost, due to the non-negligible standby cost of the generators. A solution is to integrate energy storage devices in a microgrid. A long-term unit commitment problem can be formulated to minimize the operation cost of an islanded microgrid and the cost of unreliability [

Economic dispatch in a microgrid is more complicated in comparison with that in the traditional electrical grid. With a relatively small power capacity, the relative load variability in a microgrid is higher than that of the total load in the main grid [

Subject to electricity market fluctuations, a stochastic optimization method can be used for the optimal scheduling of microsources and the energy exchange between the main grid and microgrid [

Market-related inputs, such as electricity prices;

Power-related inputs, such as load forecasting and renewable power generation forecasting.

Stochastic dynamic programming can be used to solve complex stochastic optimization problems by breaking the original problems down into simpler subproblems and solving each subproblem only once. For the daily microgrid operation problem [

To better manage the energy storage devices in a microgrid, the concept of quality-of-service in electricity (QoSE) is introduced in [

The batteries of PEVs in a V2G system can be considered as energy storage devices in microgrids. Different from traditional stationary energy storage devices, PEVs are mobile in nature, which poses new technical challenges on dispatch optimization. In the context of V2G, the coordinated wind-PEV dispatch problem is studied in [

The energy management problem in a microgrid can be investigated from a power market perspective [_{∞} performance index can be used to set the parameters in a pricing control scheme, so that the robustness of market dynamics can be ensured, given the randomness in power generation. Through the participation of a microgrid in a pool-type market, the microgrid is able to purchase energy from the main grid [

In a distribution system, network reconfiguration can be performed to reduce energy losses, maintain power balance and isolate faults, by changing the states of sectionalizing circuit breakers. On the other hand, to better utilize renewable energy, microsources can be grouped in microgrids, which are further connected to a distribution system. Most existing research works investigate economic dispatch in microgrid without taking into account network reconfiguration. However, it is shown in [

Most of the existing research addresses microgrid operation problems in a centralized manner. In order to reduce communication overhead and improve robustness to a single point of failure, there is another stream of research that addresses the economic dispatch problem from a distributed control perspective [

The objective of microgrid control is to achieve a balance between power generation and demand in real time. With the integration of renewable energy sources in a microgrid, a large increment or decrement in renewable power generation may occur due to changes in local weather conditions. The randomness in renewable power generation can jeopardize microgrid stability. One solution is to incorporate stochastic modeling and optimization tools in microgrid control to improve system stability. A summary of the stochastic modeling and optimization tools for microgrid control is given in

Small signal stability analysis can be used to evaluate microgrid stability subject to small disturbances [

Microgrid stability can be improved by utilizing stochastic control to address the uncertainties in renewable power generation. Stochastic model predictive control can be used to improve the utilization of renewable energy sources, while keeping a storage device (

The future smart grid is expected to be an interconnected network of microgrids. Each microgrid plays an important role in facilitating the control of the main grid. Regulation services can be provided by microgrids to balance power generation and demand in the main grid in a small time scale (in a few minutes or an even shorter period). In the conventional electrical grid, the regulation services are mainly provided by centralized generators. To reduce cost and greenhouse gas emissions, enabling microgrids to offer regulation service is promising. Currently, the participation of loads in regulation service reserves has been allowed by PJM, which is a regional transmission organization and independent system operator (ISO) serving all or parts of Delaware, Illinois, Indiana, Kentucky, Maryland, Michigan, New Jersey, North Carolina, Ohio, Pennsylvania, Tennessee, Virginia, West Virginia and the District of Columbia. The other ISOs are contemplating similar regulation service reserves [

In this paper, we have presented the state-of-the-art on stochastic modeling and optimization tools for microgrid planning, operation, and control. The tools can be used to address the randomness in renewable power generation, the buffering effect of energy storage devices and the mobility of PEVs in V2G systems. Furthermore, the unique features of microgrids, such as the dual (islanded and grid-connected) operation modes, the spatial correlation of renewable power generation and the integration of CHP plants with both electricity and heat outputs, are taken into account. Despite there existing stochastic modeling and optimization tools for microgrid planning, operation and control in the literature, many microgrid research issues remain open. As we can observe from this literature survey, a majority of the existing works is based on MCS. Despite the simplicity in microgrid modeling via MCS, its high computational load requires highly efficient computational devices, such as powerful servers and workstations, with a non-negligible cost. Therefore, theoretical models still need to be developed for microgrid planning, operation and control. A few potential stochastic modeling and optimization tools are given below:

Stochastic game: The stochastic game represents a class of dynamic games with one or more players via probabilistic state transitions [

Stochastic inventory theory: The theory concerns the optimal design of an inventory (or storage) system to minimize its operation cost [

Partially observable Markov decision process (POMDP): Low-cost wireless (such as ZigBee and WiFi) networks can be used to facilitate decentralized microgrid control, but with a non-negligible communication delay [

In the practical applications of stochastic modeling and optimization tools, there are two major research challenges:

Computational complexity: In comparison with deterministic modeling and optimization, the computational complexity of the stochastic counterparts is significantly higher. Reducing the computational complexity is a critical step to bridge the gap between research and implementation;

Availability of statistics: The statistics of power generation from renewable energy sources and PEV mobility are needed for stochastic modeling and optimization. However, such information may not be available in microgrid operation. For instance, vehicle traffic monitoring systems, such as piezoelectric sensors and magnetic loops [

Despite all the technical challenges, stochastic information management is a major avenue for microgrid operation in order to harness renewable energy sources and energy storage devices, such that the economical and environmental benefits of microgrids can be fully realized. The related research is interdisciplinary in nature and calls for a close collaboration between the researchers in the power/energy system discipline and in the information/communication system discipline.

The authors declare no conflict of interest.

A typical microgrid configuration [

An islanded microgrid one-distributed generation (DG) microsource [

Local and neighbor areas in a distribution network [

Stochastic models of a microgrid. MCS, Monte Carlo simulation.

State evolution model | Stochastic hybrid system [ |
Trajectory of state evolution |

State estimation | Triangular factorization [ |
Utilization of pseudo measurements |

Belief propagation [ |
Spatial-temporal model for renewable power generation | |

Reliability analysis | MCS with sequential sampling [ |
System operation cycles with temporal correlation |

Markov chain analysis [ |
Spatial-temporal model for renewable power generation | |

MCS with simple random sampling [ |
Load priority |

Stochastic optimization tools for microgrid planning. CHP, combined heat and power.

MCS with genetic algorithm [ |
Fluctuating electricity price |

Stochastic differential equation [ |
Uncertainty in natural gas price |

MCS with particle swarm optimization [ |
Yearly variation of construction and installation cost of microsources and the fluctuation of international price of crude oil |

MCS with simulated annealing algorithm [ |
Model of the micro-CHP plant |

Operation data of a C60 micro-CHP plant from Capstone [

^{3}/h) | ||
---|---|---|

100% | 1.99 | 22.2 |

75% | 2.33 | 17.4 |

50% | 2.84 | 13.2 |

25% | 4.44 | 7.8 |

Stochastic optimization tools for microgrid operation. V2G, vehicle-to-grid.

Unit commitment | MCS with scenario reduction [ |
For islanded microgrid with energy storage devices |

MCS with Latin Hypercube Sampling and scenario reduction [ |
For grid-connected microgrid with energy storage devices | |

Economic dispatch | Stochastic dynamic programming [ |
Uncertainties in electricity price fluctuation |

Chance constrained programming [ |
Model of CHP plants | |

Lyapunov optimization [ |
For microgrids with stationary energy storage devices | |

MCS with Latin Hypercube Sampling |
For microgrids with V2G systems | |

H_{∞} control [ |
Power market perspective | |

Bio-inspired optimization [ |
Joint design of microgrid operation and network reconfiguration | |

Robust optimization [ |
Distributed economic dispatch |

Stochastic modeling and optimization tools for microgrid control.

Two-point estimate method [ |
Small signal stability analysis |

MCS with Latin Hypercube Sampling supplemented with a restricted pairing technique [ |
Capacity factor analysis with spatial correlation of wind speeds |

Stochastic dynamic programming [ |
For a microgrid with a stationary storage device |

Stochastic control [ |
For a microgrid with V2G systems |

Stochastic dynamic programming [ |
Regulation service reserves by microgrids |