Optimization Problems in Microgrids

Optimization Problems in Microgrids

Jae-Won Lee, Michael Pfister

Seoul National University

Power System Optimization Course, 2016.

I. Introduction

Due to increasing environmental awareness, economic incentives and technology progress there has been an active integration of distributed energy resources (DERs) including photovoltaics (PVs), wind turbines (WTs), fuel cells (FCs), etc. which has the advantages of low investment cost compared to traditional generators, system loss reduction and lower emissions in the power system sector. In order to accommodate these resources reliably and securely in the distribution network, the concept of microgrids (MGs) has been actively researched throughout the past few years. The MG is defined as an aggregation of DERs, electrical loads, storages, and generations interconnected among themselves and with distribution network as well [2]. It is a small scale power system with the ability of self-supply and islanding, which provides a distributed local intelligence for the power system to supply loads in a reliable and economic manner [1]. An energy management system (EMS) controls the operation of the MG by coordinating all its distributed generators, distributed energy storages and controllable loads. Control has to comply with different requirements as reliability, sustainability, cost-effectiveness and environmental friendliness. A MG control system aims at meeting its utility demands and if not islanded operated also to participate in the market. The highest priority of the control is to maintain system stability and reacts to disturbances. Secondly it optimizes the power allocation according to an objective function while complying with constraints [20]. A typical EMS looks like the figure shown below. ''Figure 1. Smart energy management system (SEMS) [8]''

Most of the MG operating cost optimization problems have an objective function that is similar to the form shown below. ''Figure 2. Operating cost function of a typical MG [8]''

T_c represents the total operating cost, T is the total number of hours considered, L is the total number of generators and DERs within the MG, u(t) is on/off state of the i th generator, P_G is the active power output of the generator i at time t. B_G is the bidding price of the i th generator at time t, and S_G represents the startup and shutdown cost of a generator. M is the total number of storages within the system, and P_s and B_s are the active power output of the j th storage and the bidding price of jth storage. Most of the EMS systems have very similar objective function. For the constraints, there are power balance, active power output constraints of the generators and storages, and charge and discharge rate of ESSs. Although the considered constraints vary from literature to literature, these are the most commonly considered constraints.

MGs provide a high flexibility since new energy generators or storages can easily be added. Consumers can become independent of big electricity suppliers since MGs are often owned locally by its direct consumers. Overall MGs with sophisticated energy management systems will be likely to play an important role in the future in increasing reliability, cost effectiveness and sustainability of energy supply to end consumers [20].

To analyze the research flow in the subject of MGs, this paper aims to provide an overview of the MG optimization problems. The topics covered in this paper are operation and emission cost minimization, optimal scheduling of MGs, and the effect of integrating numerous MGs on the distribution network.

The paper is organized as follows: in section two, papers dealing with the operation cost minimization of a MG are discussed. In section three, papers solving the optimization problem taking into account both operation cost and emission cost are reviewed. In section four, papers dealing with scheduling of MGs considering its islanding probability are examined. Following in section five, operation cost minimization of islanded MGs are discussed. In section six, papers that analyze the effect of multi-MG in distribution network are discussed, ending with a conclusion in section seven.

'''II. Operation cost minimization of a grid-connected Microgrid'''

One of the first topics researched in the field of MG was its operation cost optimization when it is connected to the main grid or the utility. Although the objective functions and constraints of each paper differ slightly, they are very similar. The objective function of papers is the operation cost minimization of the MG, which includes fuel cost of generators and energy storage systems (ESSs) within the MG and the power exchange cost from the main grid. Some papers also include the operation and maintenance costs of the units within their system. Also, constraints of the optimization problem include power balance, minimum and maximum outputs of the DERs and ESSs, minimum and maximum flow between the MG and the main grid, minimum up and down time of generators, and the charge and discharge rate of ESSs. There are some papers that consider the heat balance constraint; however, it is not a major concern in solving this problem.

In [8], the operation of a MG is optimized using a smart EMS. The EMS used in this paper is a composition of a PV weather-based forecasting module, an ESS operating module, and a MG operation optimization module. The EMS manages the optimal charging state of ESS, economic load dispatch, and the dispatch of DERs. In order to solve this optimization problem, a matrix real-coded genetic algorithm (MRC-GA) is used to realize an economically optimal load dispatch schedule for three different operation modes. The first mode is the islanded operation of the MG where the electrical load and supply is balanced locally, where the overproduction of non-dispatchable resources are stored in the ESS. In the second mode, the EMS operates does not export any power to the main grid, while minimizing the power purchase from the main grid to meet the local demand. This strategy is used to prevent congestions in the main grid during peak demand hours since the MG almost fully able to supply all of its demand by itself. The third case describes a full participation of the MG in the market. The EMS maximizes the profit of the MG. In order to realize the described scenarios, the power balance constraint is modified accordingly to include or exclude the main grid power exchange variable.

In [9], the advantage of integrating a communication link in unit commitment stage is analyzed. In order to explore these benefits, power sharing schemes for different power sources within a MG is considered. There are four power sharing schemes described in this paper, which are linear, nonlinear, dynamic, and optimized. The linear power sharing scheme operates the units within a system so that the sources provide an equal amount of normalized power output when there is a frequency deviation. The second scheme, nonlinear power sharing, the frequency droop curves of the power sources are not linear, allowing the operator to design the droop curve for the generators according to its most efficient point of operation. In dynamic power sharing scheme, the y-intercept (frequency) of each generator droop curves are moved to modify the amount of power each source contributes to the overall change in demand. Lastly, in optimized power sharing scheme, it is a high nonlinear power sharing scheme where the power outputs of each generator are normalized to a unit power setting, and the outputs of generators are considered simultaneously in order to determine the optimal operation of the resources for the entire range of power demand. The input of the optimization problem is the normalized power setting of each unit within the MG, and it outputs total delivered power and the total running cost of the system. Then, the optimal power setting is found, so that the cost is minimal. The constraints include power balance, reserve, and heat. A penalty function is added to the cost function in the case where more heat is delivered than the required amount.

In [4], an efficient online optimal MG operation strategy is implemented, which respects time-varying request and complex constraints. The goal is to minimize operational costs while providing energy for the forecasted amount of load. The problem is formulated using mixed-integer linear programming coupled with a feedback mechanism tackling forecast errors and disturbances in the MG operation, which can be the production fluctuation of non-dispatchable resources or load or energy price volatility. The loads are divided into two categories, controllable and critical, to integrate demand response to the operation system. Furthermore, for every sampling interval (15 minutes), the controller makes decisions whether to start or stop the generators, the output level of each unit, whether the ESS should be charged or discharged, if the power should be bought or sold to the main grid, and if the load curtailment is necessary. The optimization function minimizes the cost from energy production, startup and shutdown cost of generators, and penalty cost from load curtailment. The constraints include minimum and maximum output of DERs and ESSs, ramp up and down rate limits of the units within the system, and the bounds on controllable load curtailments. Experimental results show that the implemented mixed integer programming with feedback control algorithm saves money compared to general practice.

In [13], MG with PV, ESS, FC, and controllable load is modeled. The storage is composed of a battery bank and a hydrogen energy storage system. FC and hydrogen are very promising technologies which will likely gain more importance. An optimal control is sought by optimizing the operation cost of a grid-connected MG, taking into account the value of generated energy, cost of energy storage, and the depreciation cost of the components. The constraints considered are operational constraints of the units within the system and power balance. Then, the optimization problem is formulated using mixed-integer predictive control problem, which is simplified into nonlinear optimization problem with a sampling time. The optimization problem maximizes the profit of MG by maximizing sales and minimizing the purchase from the main grid, while minimizing the depreciation cost of its components from excessive overuse. The operational constraints include a limitation of the hydrogen storage for safe electrolysis operation of the fuel cells. For ESS, the state of charge is set by a minimum and maximum and the applied or drained current is limited. In addition, the proposed controller accurately regulates short-time variations in PV production by exchanging energy not only with its storages but also with the grid. Long-term deviations are handled by using the hydrogen energy storage.

In [17], MG operation is optimized using a robust optimization approach taking into account the wind turbine output uncertainty. The study is simulated in a grid-connected and islanded operation mode. The wind power uncertainty is modeled using ARIMA model. In the grid-connected mode, the MG is able to earn revenue by selling its reserve capacity and excess power to the spot market. Also, MG operator purchases power from the main grid if the spot market prices are lower than the MG’s generation cost. The overall goal of this paper is to minimize the operation cost of the MG. The constraints considered include power balance, transmission capacity, and minimum and maximum power outputs of the units within the system. The deviation between the forecasted and real-time load is compensated by reserve capacity, which can be the dispatchable power units within the MG or the power from the main grid. For the islanded operation of the MG, power exchange cost variable is deleted from the objective function, and load curtailment cost is added. In this mode, real time power balance constraints are met by the reserve capacity. Also, a demand shedding constraint is added, which show that the load curtailment will be less than or equal to the day-ahead forecasted load. The power balance and imbalance constraints are same as the grid-connected mode. Then, a comparison between deterministic, stochastic, and the proposed robust optimization is performed. In both grid-connected and islanded mode, the robust optimization approach provides better results. An interesting point is that the best result for the robust optimization is obtained when the wind parameter is set as uncertain for a whole day.

'''III. Emission and operation cost minimization of a grid-connected Microgrid'''

Following the operation cost optimization section, in this section, the papers that optimize both operation and emission cost of a MG is discussed. The articles in this section solve a multi-objective optimization problem.

''Figure 3. Objective function considering both operation and emission costs [11]'' C_g represents the operating cost of generator i producing power P_i, and C_e represents the emission cost of generator i producing power P_i. Emission cost is modeled with a fixed coefficient, as shown in the equation below.

''Figure 4. Emission cost function [11]'' K_e is the emissions coefficient for i th unit, in (kg/kWh), and M_e is the greenhouse gas emission cost ($/kg).

Most of the papers in this section consider the emission costs from the generator, storage, and the main grid, with the similar constraints from the previous section.

In [7], operation and emission cost of a renewable-based MG were optimized while satisfying power balance and minimum and maximum power generation constraints of the units within the MG. The unit commitment problem of the MG is formulated and solved using a mixed-integer programming using a convex optimization perspective. Emphasis is put on the intermittency behavior of RES and the decision if the MG can operate autonomously or needs a grid connection. The problem statement if the MG is self-sufficient  in supplying local demand is approached probability-based.

Considered constraints comprise minimum and maximum output power of DG, minimum on-time after being switched on and minimum down-time after being switched off, ramp rates, emission limits, operating reserves and a probability of self-sufficiency which shows the probability that the MG can successfully operate in islanded mode by being completely independent from the grid.

Results show no loss of optimality compared to existing algorithms and confirm the essential contribution of ESS in building an independent MG. Also measures for the optimal ESS size of a MG are provided. The problem formulation bases unit commitment successfully on probability of intermittency of FRES, emission limits on and forecast errors in RES production.

In [3], operation of a MG with renewable energy sources and back-up power sources, such as micro-turbine, FC, and ESS is optimized using adaptive modified particle swarm optimization algorithm. The difference of this approach compared to the traditional particle swarm optimization is that the conventional particle swarm optimization depends heavily on its parameter and it can easily settle in local optima. In order to address this problem, a pareto front of optimal solutions are obtained, and fuzzy self-adaptive mechanism and chaotic local search method is used. This approach provides non-dominated pareto-optimal solutions with fast convergence and low computational time. The operational costs considered in this paper are the fuel costs of DERs, startup and shutdown costs of the units, and the power exchange cost between the MG and the main grid. In the emission cost function, carbon, sulfur, and nitro oxide costs from the generators, ESSs, and main grid are considered. The constraints of the optimization problem include power balance, minimum and maximum generation of the generator, storage, and the main grid. Furthermore, charge and discharge rate constraint of ESS is also considered. The results verify that the proposed method is superior to the traditional particle swarm optimization, with dynamic stability and excellent convergence of the swarms. Moreover, the pareto optimal front solutions provide various operation options for the system operator to choose.

In [12], the operation and emission cost are minimized considering separately grid-connected and islanded mode of the MG. The problem is set up to minimize the fuel, depreciation, and emission cost, while satisfying the load balance and system security constraint. Considered MG model includes WTs, micro-turbines, PVs, and FCs. In this paper, in order to analyze the tradeoff between operation cost and emission cost, a weighting factor is applied to the emission cost for the operator to determine the importance of environmental constraint. The constraints of the problem include power balance, minimum and maximum unit output, and line flow. The results show that operation in grid connection is beneficial for the total cost. The total costs of the islanded mode operation simulation are three times higher than in grid-connected operation mode. Also with diminishing the weighting of the environmental factor in the optimization function the total costs decrease.

In [5], scheduling of different power sources, PV, FC, ESS, WT, and micro-turbine, within a MG is solved. Two objective functions are solved, where one minimizes the total operation cost and the other minimizes the total emission caused by the generation units. For the solving method, a lexicographic optimization (optimizing the range of the objective function) and hybrid augmented-weighted epsilon-constraint method (solves the problem of generating dominated or inefficient solutions) have been used to solve the multi-objective optimization, which outputs pareto optimal solutions. Then, the fuzzy satisfying method is used to find the best solution. In previous literatures, the weighted sum method is often used to convert multi-objective problems into single objective problem, which only produced efficient extreme solutions. Also the objective function must be scaled properly in the weighted sum method. These two problems are over come in the epsilon-constraint technique by producing non-extreme efficient solutions and not requiring scaling of the objective functions. The simulation results verified that the proposed method requires less computation time while producing better solutions compared to other methods.

In [11], a chaotic quantum genetic algorithm is used to solve the environmental economic dispatch of a smart MG. The objective function minimizes the fuel cost and emission cost. For the fuel cost, each participating generator’s fuel and operation and maintenance costs are considered, while a linear emission cost is considered in the emission cost function. For the constraints, power balance and minimum and maximum output of DERs are considered. Previously, when a genetic algorithm method is used to solve the operation optimization problem, it takes a long time to solve the problem, and the global solution was not guaranteed. However, in the proposed method, quantum bits were used to encode the chromosomes. This algorithm uses the quantum probability vector encoding mechanism and adopts the genetic algorithm crossover update strategy to effectively improve the global search ability and escape the local optimal solution trap by using chaotic algorithms, so that it can achieve the real objective of the global optimal solutions (chaotic system possesses inherent diversity, which allows the solution to not fall into the local optima during the optimization process). The author compares different solving methods (DP, GA, EP, QGA) with the proposed solving algorithm, where the proposed method achieved the minimum operation cost.

In [10], the operation of a MG consisting of WT, diesel generator, micro-turbine, PV, FC, and ESS is optimized. The costs considered in this paper are fuel, startup and shutdown cost of generators, operation and maintenance cost of the units, and the emission cost of each generator. This problem is modeled and solved using modified game theory to solve the nonlinear constrained multi-objective optimization problem. Player one tries to minimize emission while player two's goal is to minimize the operating cost while the load is met and constraints are complied with. The optimization is performed for three scenarios with increasing complexity. The first scenario describes an islanded operation. In the cost function the fuel consumption rate of different generators, fuel costs and operation-maintenance costs are considered. The constraints are keeping power balance and being inside generation capacity constraints. In the second scenario there is a battery storage added which alters the power balance constraint. In addition to the initial cost function now start-up costs are also considered. In the third scenario the MG is grid-connected. The cost function contains now an adding term representing from the grid bought energy in the case when the load demand can not be covered by the MG's self-production. On the other side there is now also potential for profit when market prices are higher than production costs. Results show that in comparison with other optimization techniques the used multi-objective game theory approach delivers the best results.

In [21], an EMS for the MG operator to determine optimal operating strategy has been designed. The considered MG system includes PV, ESS, WT, and FC. Then, a sensitivity analysis of the investment on ESS capacity and demand has been conducted to determine the optimal investment in generators and ESSs. The optimization problem has been solved using the General Algebraic Modeling System (GAMS) program, specifically the CPLEX solver. The decision variables in the optimization problem include the output levels of PV, WT, biomass, gas turbine, and FC. Then, the maximum profit is calculated using the simple equation where the cost of each generating units are subtracted from the revenues produced by each units. For the constraints, unit capacity, transmission capacity, power balance, and heat balance have been considered. Furthermore, the emission rates of each unit within the MG are also considered to account for the environmental effect. The results show that a greater battery storage capacity requires greater investment, and so installation of additional storage devices might not be profitable when a high fixed cost is considered.

In [19], an optimal EMS is designed, which optimizes the operation and emission cost of a MG. The author claims that the uncertainties of resources within a MG have not been considered in previous literatures, hence, to account for the unpredictability and uncertainty of WT and PV outputs and load demand, a scenario based stochastic programming has been used. The generated scenarios are reduced using a backward method, and the uncertainties have been modeled using a Lattice Monte Carlo simulation method. The operation cost function includes the bidding of each resource and the startup and shutdown costs of the units. For the mission cost function, carbon, sulfur, and nitro oxide emission costs of the DER, ESS, and the main grid have been considered. The constraints include power balance, active power limits of units, spinning reserve requirements, and charge and discharge rate limit related to the storage device. The optimization problem is solved using improved teaching-learning-based optimization, which utilizes self-adaptive probabilistic modification strategy to avoid trapping in local optima. The best advantage of the proposed algorithm is quick transfer of the information between agents which gives more ability to the proposed algorithm in finding the global optima irrespective of the complexity of the problem.

'''IV. Optimal scheduling of a Microgrid considering islanded operation'''

In this section, the optimal scheduling of the islanded MGs and operation of MGs considering islanding are reviewed. Although some papers in previous section have considered the islanded operation, the articles in this section specifically determine the optimal operating parameters of MG or dispatch of generators so that it is able to operate safely even when it is islanded. The main change in the optimization problem is that the after islanding, the objective function changes from operating cost minimization to power balance mismatch minimization. In order to operate the system reliably and securely, demand response function of the loads is more actively considered.

In [18], a dispatch problem for the DERs within a MG has been solved. The fuel cost has been minimized during the grid-connected operation while ensuring stable operation after islanding in case of faults in the main grid. The author utilizes adjustable droop control of the participating generators as a constraint in the optimization problem to ensure a stable islanded operation. The objective function is to minimize the total generation cost, and the constraints include power balance, spinning reserve requirement, and inter-area flow limit. The constraints are formulated using both fixed and adjustable droop, where it was tested on a system with 15 DERs, and it showed that the MG could be operated economically and safely during both grid-connected mode and islanded mode when the droop constraints were considered.

In [1], a centralized MG optimal scheduling was solved considering multi-period islanding constraints. The optimization problem was divided into a master problem and a sub problem. The master problem aimed to minimize day ahead grid-connected operation cost, considering generation cost and power exchange cost, where the sub problem solved the optimal islanded operation of the MG. In order to ensure a safe operation after islanding cuts were made, where the unit commitment and ESS schedule was revised until enough capacity was procured to be islanded. However, in the case where there were not enough dispatchable units within the system, demand response was utilized to account for insufficient generation, and an inconvenience factor (form of penalty function) was added to the objective function. The primary application of ESS in this paper is to coordinate with generators to guarantee the generation adequacy of MG. Furthermore, to operate safely after islanding, T-tau islanding criterion was used where tau is the number of consecutive hours that MG can operate in islanded mode. The problem was formulated using mixed integer programming, and the simulation results verified that although there was a slight increase in the operation cost, the MG was able to be operated more reliably.

V. Operation cost minimization of an islanded Microgrid

In previous section, the optimal scheduling of generators within a MG, considering its islanding probability was considered. In this section, papers discussing the economic operation of islanded or standalone MGs are reviewed.

In [6], operation of a standalone MG considering the lifetime characteristics of ESS is optimized. The operation of WT, PV, diesel generator, and ESS are considered. The multi-objective optimization problem aims to minimize power generation cost and increase the battery lifetime. To find these optimal operation parameters, several costs are taken into account: battery life loss cost, operation and maintenance cost, fuel cost, and environmental cost. Optimization is realized by use of non-dominated sorting genetic algorithm. The different generation sources are modeled taking into account specific behavior of WT, PV, ESS, and diesel power generation. The optimal goal of the multi-objective function is to find a pareto optimal front. One objective is to minimize power generation cost, which is realized by higher utilization or renewables and using less power from the diesel generator. Minimizing the life loss of the battery is the second objective, which can be achieved by maintaining a high level of state of charge. The constraints considered are power balance and minimum and maximum output levels of the units. Accordingly, the results show that in the case of excessive renewable energy output, the battery should be operated at a state of charge stop state of 0.61. In the case of shortage of renewable energy production, battery management relies much more on the usage of diesel generators and therefore a high state of charge stop of 0.9 is needed. This real time operation makes sure that the renewable are fully utilized while the batteries are effectively managed, thus increasing battery life and reducing generation cost.

In [15], the operation cost of an islanded MG consisting of a diesel generator, micro-turbine, WT, PV, ESS, and an inverter/rectifier is optimized. The operation cost function considers the fuel costs and operation and maintenance costs of the units. The main contribution of this paper is the modeling of WT, PV, and its controller, AC/DC converter and the central converter. The optimization problem is formulated using multi-cross learning based chaotic differential evolution algorithm which comes with several advantages including learning capability, high exploitation, and enhanced convergence behavior. In the objective function, fuel, startup and shutdown, operation and maintenance, and gas emission costs are considered. For the constraints, ESS properties, ramp up and down rate limits of diesel generator and micro-turbine, and power balance are considered. The simulation has been conducted in islanded mode, and the results have been compared with 21 other optimization methods. The proposed method shows superiority compared to other methods in terms of effectiveness and robustness.

'''VI. Microgrids on distribution network'''

In this section, the papers dealing with the effect of having a numerous MGs in the distribution network are discussed.

In [2], a fuzzy self-adaptive particle swarm optimization algorithm is proposed and implemented to dispatch the generations in a typical MG considering its operation cost and emission cost. The cost function of the optimization problem considers the fuel cost and startup and shutdown cost of the generators and ESSs, and also considering the power exchange cost between the main grid. Also, the emission cost function includes carbon, sulfur, and nitro oxide emissions from DERs, storages, and the main grid. For the constraints, power balance, active power constraints of the units, and charge and discharge rate limits of storage devices are considered. Previously, conventional particle swarm optimization was used very often to solve the optimization problems in MGs. However, it had the disadvantages of depending heavily upon its learning and weighting factors, and having the possibility of being trapped in local optima. Hence, in this paper, a fuzzy self-adaptive approach is adopted to mitigate this problem. The superior performance of the proposed algorithm is shown in comparison with those of other evolutionary optimization methods, such as conventional particle swarm optimization and genetic algorithm, and the results show that although the suggested algorithm increases the operation cost slightly, it is able to manage the emission to a certain level.

In [16], the effect of integrating multiple MGs in the distribution network is analyzed, especially in the aspect of loss and emission reduction. In order to analyze this effect, a typical low voltage network with DERs operating coordinated as a MG and a typical mid-voltage network comprising of many low voltage networks are used. As generating units are located closer to the load side, the network losses will be reduced. To analyze this effect, power flow analysis has been used to calculate the system loss. Furthermore, since the penetration of MGs is not very high, it is assumed that the unit commitment of the main grid will not change, however, due to the generation capability of the MGs, its economic dispatch results may change, changing the emission output of the generators. The estimation of the avoided emissions due to MGs operation is calculated based on the marginal emissions curve of the upstream network.

'''VII. Conclusion'''

In this paper, previous and current literatures dealing with optimization problems in MGs have been reviewed. Some of the topics discussed were MG operation cost minimization, MG operation and emission cost minimization, MG scheduling considering islanding probability, etc.

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