- Email: [email protected]
Multi-dispatch for Grid-connected Microgrid with Robust Optimization Algorithm
10th IFAC Symposium on Control of Power and Energy Systems 10th IFAC Symposium on Control and Energy Systems Tokyo, Japan, September 4-6, 2018of 10th IFAC Symposium on Control of Power Power and Energy Available online atSystems www.sciencedirect.com 10th IFAC Symposium on Control Power and Energy Systems Tokyo, Japan, September 4-6, 2018of 10th IFAC Symposium on Control of Power and Energy Tokyo, Japan, September 4-6, 2018 10th IFAC Symposium on 4-6, Control of Power and Energy Systems Systems Tokyo, Japan, September 2018 Tokyo, Japan, September 4-6, 2018 Tokyo, Japan, September 4-6, 2018
ScienceDirect
IFAC PapersOnLine 51-28 (2018) 474–479
Multi-dispatch for Grid-connected Microgrid with Robust Optimization Multi-dispatch for Grid-connected Microgrid with Robust Optimization Multi-dispatch Microgrid Algorithm Multi-dispatch for for Grid-connected Grid-connected Microgrid with with Robust Robust Optimization Optimization Multi-dispatch Microgrid with Robust Optimization Multi-dispatch for for Grid-connected Grid-connected Microgrid with Robust Optimization Algorithm Algorithm Algorithm Algorithm Ruifeng Shi*, ShaopengAlgorithm Li*, Changhao Sun**, Kwang Y. Lee***
Ruifeng Shi*, Shaopeng Li*, Changhao Sun**, Kwang Y. Lee*** Ruifeng Ruifeng Shi*, Shi*, Shaopeng Shaopeng Li*, Li*, Changhao Changhao Sun**, Sun**, Kwang Kwang Y. Y. Lee*** Lee*** Ruifeng Shi*, Shaopeng Li*, Changhao Sun**, Kwang Y. Lee*** Ruifeng Shi*, Shaopeng Li*, Changhao Sun**, Kwang Lee*** *School of Control and Computer Engineering, North China ElectricY.Power University, *SchoolBeijing, of Control Control and(e-mail: Computer Engineering, North North China China Electric Power Power University, University, China, [email protected]; [email protected]) *School of and Computer Engineering, Electric *School of Control and Computer Engineering, North China Electric Power University, *School of Control and Computer Engineering, North China Electric Power University, Beijing, China, (e-mail: [email protected]; [email protected]) *School** ofSmart Control and(e-mail: Computer Engineering, North China Electric Power Beijing, China, [email protected]; Energy Institute, Nanjing SAC Power [email protected]) Automation Co., University, Ltd, Beijing, China, (e-mail: [email protected]; [email protected]) Beijing, (e-mail: [email protected]; ** SmartChina, Energy Institute, Nanjing SAC Power Power [email protected]) Automation Co., Co., Ltd, Ltd, Beijing, China, (e-mail: [email protected]; [email protected]) ** Smart Energy Institute, Nanjing SAC Grid Automation Nanjing, 211100, China (e-mail: [email protected]) ** Smart Energy Institute, Nanjing SAC Power Grid Automation Co., Ltd, ** Smart Energy Institute, Nanjing SAC Power Grid Automation Co., Ltd, Nanjing, 211100,Nanjing China (e-mail: [email protected]) ** Smart Energy SAC Power Grid Automation Co., Ltd, Nanjing, 211100, China (e-mail: [email protected]) ***Department of Institute, Electrical and Computer Engineering, Baylor University, Nanjing, 211100, China (e-mail: [email protected]) Nanjing, 211100, China (e-mail: [email protected]) ***Department of Electrical and Computer Engineering, Baylor University, Nanjing, 211100, China (e-mail: [email protected]) ***Department of Electrical and Computer Engineering, Baylor TX 76798 USA (e-mail: [email protected]) ***Department of Electrical and Computer Engineering, Baylor University, University, ***Department of and Engineering, TX 76798 76798 USA (e-mail: (e-mail: [email protected]) ***Department of Electrical Electrical and Computer Computer Engineering, Baylor Baylor University, University, TX USA [email protected]) TX 76798 USA (e-mail: [email protected]) TX TX 76798 76798 USA USA (e-mail: (e-mail: [email protected]) [email protected]) Abstract: Increasing penetration of uncoordinated electric vehicles (EVs) and intermittent renewable Abstract: Increasing penetrationsystems of uncoordinated uncoordinated electric vehicles (EVs) and and intermittent renewable energy generation in microgrid motivates us to explore an effective strategy for therenewable safe and Abstract: Increasing penetration of electric vehicles (EVs) intermittent renewable Abstract: Increasing penetration of uncoordinated electric vehicles (EVs) and intermittent Abstract: Increasing penetration of uncoordinated electric vehicles (EVs) and intermittent energy generation inofmicrogrid microgrid systems motivates(DG) us tosystems. explore an effective effective strategy for the therenewable safe and and economic operation such distributed generation This paper presents a robust economic Abstract: Increasing penetration of uncoordinated electric vehicles (EVs) and intermittent renewable energy generation in systems motivates us to explore an strategy for safe energy generation in microgrid systems motivates us to explore an effective strategy for the safe and energy generation in microgrid systems motivates us to explore an effective strategy for the safe and economic operation of such distributed distributed generation (DG) systems. This paper presents a charging robust economic dispatch strategy for grid-connected microgrids. Uncertainty from wind power and EV loads is energy generation in microgrid systems motivates us to explore an effective strategy for the safe and economic operation of such generation (DG) systems. This paper presents a robust economic economic operation of such distributed generation (DG) systems. paper presents robust economic economic operation of such distributed generation (DG) systems. This paper presents robust economic dispatch strategy strategy for grid-connected microgrids. Uncertainty from This wind power and EVaaa charging charging loadsthe is considered as an uncertain set of interval predictions. Considering the worst application scenario, economic operation of such distributed generation (DG) systems. This paper presents robust economic dispatch for grid-connected microgrids. Uncertainty from wind power and EV loads is dispatch strategy grid-connected microgrids. Uncertainty from wind and EV charging loadsthe is dispatch for microgrids. from power and EV is considered as an an for uncertain set of interval interval predictions. Considering thepower worst application scenario, proposedstrategy strategy cangrid-connected help set to schedule thepredictions. EV Uncertainty charging behaviors and DG outputs order toloads reduce dispatch strategy for grid-connected microgrids. Uncertainty from wind wind power and EVincharging charging loads is considered as uncertain of Considering the worst application scenario, the considered as an uncertain set of interval predictions. Considering the worst application scenario, the considered as an uncertain set of interval predictions. Considering the worst application scenario, the proposed strategy can help to schedule the EV charging behaviors and DG outputs in order to reduce operation cost under practical constraints. In addition, in order to facilitate the decision makers to make considered as an uncertain set of interval predictions. Considering the worst application scenario, the proposed strategy can help to schedule the EV charging behaviors and DG outputs in order to reduce proposed strategy can help to constraints. schedule theInEV charging behaviors and DG in order to proposed strategy can help schedule EV charging behaviors and outputs in order to reduce operation cost under under practical addition, in order to explores facilitate theoutputs decision makers toreduce make decision strategies from theto ofIn economy, thisorder paper relationship between the proposed strategy can help toperspective schedule the the EV charging behaviors and DG DG outputs in makers order toto reduce operation cost practical constraints. addition, in to facilitate the decision make operation cost under practical constraints. In addition, in order to facilitate the decision makers to make operation cost under practical constraints. In addition, in order to facilitate the decision makers to make decision strategies from the perspective of economy, this paper explores relationship between the volatility of uncertain parameters and economy based on the theory of interval forecast. Numerical case operation cost under practical constraints. In addition, in order to facilitate the decision makers to make decision strategies from the perspective of economy, this paper explores relationship between the decision strategies from the perspective perspective of economy, economy, thisthepaper paper explores the relationship relationship betweencase the decision strategies from the of this explores the between the volatility of uncertain uncertain parameters and economy economy based on theory of interval interval forecast. Numerical Numerical study shows the feasibility of perspective the proposed strategy. decision strategies from the ofdispatch economy, thisthe explores the relationship betweencase the volatility of parameters and based on thepaper theory of forecast. case volatility of uncertain parameters and economy based on theory of interval forecast. Numerical volatility of uncertain parameters and economy based on the theory of interval forecast. Numerical case study shows the feasibility of the proposed dispatch strategy. volatility of uncertain parameters and economy based on the theory of interval forecast. Numerical case study showsMicrogrids, the feasibility feasibility of the theOptimization, proposed dispatch dispatch strategy. Electric Vehicles, Wind Power, Economic Keywords: Robust Multi-Dispatch, study shows of proposed strategy. © 2018, IFACthe (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. study shows the of proposed strategy. study showsMicrogrids, the feasibility feasibility of the theOptimization, proposed dispatch dispatch strategy. Electric Robust Multi-Dispatch, Vehicles, Wind Power, Economic Keywords: Analysis Microgrids, Robust Optimization, Multi-Dispatch, Electric Vehicles, Wind Power, Economic Keywords: Microgrids, Robust Optimization, Multi-Dispatch, Electric Vehicles, Wind Power, Economic Keywords: Keywords: Microgrids, Robust Optimization, Multi-Dispatch, Electric Vehicles, Wind Power, Economic Analysis Microgrids, Robust Optimization, Multi-Dispatch, Electric Vehicles, Wind Power, Economic Keywords: Analysis Analysis Analysis Analysis The research on grid-connected microgrid has become one of The research on grid-connected microgrid become one of 1. INTRODUCTION the important research topics in the field of has energy dispatching The research grid-connected microgrid has become one The research on on grid-connected microgrid has become one of of 1. INTRODUCTION The research on grid-connected microgrid has become one of the important research topics in the field of energy dispatching 1. INTRODUCTION nowadays, where grid-connected microgrid is a cluster The research on grid-connected microgrid has become one of the important important research research topics topics in in the the field field of of energy energy dispatching dispatching 1. INTRODUCTION the 1. INTRODUCTION the important research topics in the field of energy dispatching In the power consumption side, electric vehicles (EVs) have nowadays, where grid-connected microgrid isofaadispatching cluster of of 1. INTRODUCTION distributed generations (DGs), resources renewable the important research topics in the field of energy nowadays, where grid-connected microgrid is cluster nowadays, where grid-connected microgrid is aa renewable cluster of In the power consumption electric vehicles (EVs) nowadays, where grid-connected microgrid is cluster of drawn great duringside, the past decades because theyhave are distributed generations (DGs), resources of In the powerattention consumption side, electric vehicles (EVs) have generations (RGs) and conventional generations (CGs), and nowadays, where grid-connected microgrid is a cluster of distributed generations (DGs), resources of renewable In the power consumption side, electric vehicles (EVs) have distributed generations (DGs), resources of renewable In the power consumption side, electric vehicles (EVs) have drawn great attention duringside, the past past decades because they are distributed generations (DGs), resources of renewable seemingly environmentally friendly to the consumers (Lin & In the power consumption electric vehicles (EVs) have generations (RGs) and conventional generations (CGs), and drawn great attention during the decades because they are flexible load (such as EVs) and local loads, are usually distributed generations (DGs), resources of renewable generations (RGs) and conventional generations (CGs), and drawn great attention during the past decades because they are generations (RGs) and conventional generations (CGs), and drawn great attention during the decades because are seemingly the consumers (Lin & generations and conventional generations (CGs), and Tan, 2017). However, duefriendly to past the to dynamic nature they of EV drawn greatenvironmentally attention during the past decades because they are flexible load as EVs) and local loads, are usually seemingly environmentally friendly to the consumers (Lin & managed by (RGs) an(such energy management system (EMS), which is generations (RGs) and conventional generations (CGs), and flexible load (such as EVs) and local loads, are usually seemingly environmentally friendly to the consumers (Lin & flexible load (such as EVs) and local loads, are usually seemingly environmentally friendly to the consumers (Lin & Tan, 2017). However, due to the dynamic nature of EV flexible load (such as EVs) and local loads, are usually charging time, locations, user behaviors, and load profiles, the seemingly environmentally friendly to the consumers (Lin & managed by an energy management system (EMS), which is Tan, 2017). However, due to the dynamic nature of EV becoming one of the fundamental control methods to balance flexible load (such as EVs) and local loads, are usually managed by an energy management system (EMS), which is Tan, 2017). However, due to the dynamic nature of EV managed by an energy management system (EMS), which is Tan, 2017). However, due to the dynamic nature of EV charging time, locations, user behaviors, and load profiles, the managed by an energy management system (EMS), which is large-scale penetration of uncontrolled and uncoordinated EVs Tan, 2017). However, due to the dynamic nature of EV becoming one of the fundamental control methods to balance charging time, locations, user behaviors, and load profiles, the the connection of EVs and renewable energy (Mwasilu et al., managed by an energy management system (EMS), which is becoming one of the fundamental control methods to balance charging time, locations, user behaviors, and load profiles, the becoming one of the fundamental control methods to balance charging time, locations, user behaviors, and load profiles, the large-scale penetration of uncontrolled and uncoordinated EVs becoming one of the fundamental control methods to balance into power systems, especially in distribution networks, may charging time, locations, user behaviors, and load profiles, the the connection of EVs and renewable energy (Mwasilu et al., large-scale penetration of uncontrolled and uncoordinated EVs 2014). Adhikari (2011) has built up multi-objective models of becoming one of the fundamental control methods to balance the connection of EVs and renewable energy (Mwasilu et al., large-scale penetration of uncontrolled and uncoordinated EVs the connection connection of(2011) EVs and and renewable energy (Mwasilu (Mwasilu et al., al., large-scale penetration of and EVs into power systems, in distribution networks, may the EVs renewable energy et cause a high level ofespecially volatility and increase potential sources large-scale penetration of uncontrolled uncontrolled and uncoordinated uncoordinated EVs 2014). Adhikari has built multi-objective of into power systems, especially in distribution networks, may microgrid withof which provide anmodels efficient the connection ofDGs EVsand and renewable energy (Mwasilu et al., 2014). Adhikari (2011) hasloads, built up up multi-objective models of into power systems, especially in distribution networks, may 2014). Adhikari (2011) has built up multi-objective models of into power systems, especially in distribution networks, may cause a high level of volatility and increase potential sources 2014). Adhikari (2011) has built up multi-objective models of for system disturbances (Rahman et al., 2016). into power systems, especially in distribution networks, may microgrid with DGs and loads, which provide an efficient cause a high level of volatility and increase potential sources integrated method of renewable energy, and EVs, but the 2014). Adhikari (2011) has built up multi-objective models of microgrid with DGs and loads, which provide an efficient cause a high level of volatility and increase potential sources microgrid with DGs and loads, which provide an efficient cause a high level of volatility and increase potential sources for system disturbances (Rahman et al., 2016). microgrid with DGs and loads, which provide an efficient cause a high level of volatility and increase potential sources integrated method of renewable energy, and EVs, but the for system disturbances (Rahman et al., 2016). proposed models are lacking practical uncertainty microgrid with DGs and loads, which provide an efficient integrated method of renewable energy, and EVs, but the for system disturbances (Rahman et al., 2016). In addition, clean and effective renewable energy has been integrated method of renewable energy, and EVs, but the for system (Rahman et integrated method of renewable energy, and but for addition, system disturbances disturbances (Rahman renewable et al., al., 2016). 2016). proposed models lacking practical uncertainty considerations. Stochastic optimization (SO) provides an integrated method of are renewable energy, and EVs, EVs, but the the In clean and effective energy has been models are lacking practical uncertainty widely exploited in response to the energy self-sufficiency and proposed In addition, clean and effective renewable energy has been proposed models are lacking practical uncertainty In addition, clean and effective renewable energy has been proposed models are lacking practical uncertainty considerations. Stochastic optimization (SO) provides an In addition, clean and effective renewable energy has been effective way for solving optimization problems, in which proposed models are lacking practical uncertainty widely exploited in response to the energy self-sufficiency and considerations. Stochastic optimization (SO) provides an air addition, pollution emitted by effective conventional fossil-fuel power In clean and renewable energy hasplants been widely exploited in response to the energy self-sufficiency and considerations. Stochastic optimization (SO) provides an widely exploited in response to the energy self-sufficiency and considerations. Stochastic optimization (SO) provides an effective way for solving optimization problems, in which widely exploited in response to the energy self-sufficiency and uncertain numerical data can be assumed to follow a wellconsiderations. Stochastic optimization (SO) provides an air pollution emitted by conventional fossil-fuel power plants effective way for solving optimization problems, in which (Zhang et al., 2017). Researches on absorbing renewable widely exploited in response to the energy self-sufficiency and air pollution emitted by conventional fossil-fuel power plants effective way for solving optimization problems, in which air pollution emitted by conventional fossil-fuel power plants effective way for solving optimization problems, in which uncertain numerical data can be assumed to follow a wellair pollution emitted by conventional fossil-fuel power plants known probability distribution. effective way for solving optimization problems, in which (Zhang et al., 2017). Researches on absorbing renewable uncertain numerical data can be assumed to follow a wellenergy have gradually become the research hotspot (Liu et al., air pollution emitted by conventional fossil-fuel power plants (Zhang et al., 2017). Researches on absorbing renewable uncertain numerical data can be assumed to follow aa well(Zhang et al., 2017). Researches on absorbing renewable numerical data known probability distribution. (Zhang et 2017). Researches on renewable uncertain numerical data can can be be assumed assumed to to follow follow a wellwellenergy have gradually become the research hotspot (Liu etnew al., uncertain known distribution. (Zhang have et al., al., 2017). Researches on absorbing absorbing renewable 2016). The rapid development ofresearch smart grid provides aet energy gradually become the hotspot (Liu al., known probability distribution. Robust probability optimization (RO) has advantages in tolerating energy have gradually become the research hotspot (Liu et al., known probability distribution. energy have gradually become the research hotspot (Liu et al., known probability distribution. 2016). The rapid development of smart grid provides aaetnew energy have gradually become the hotspot al., Robust optimization (RO) has advantages tolerating choice for efficient integration of EVs and (Liu renewable 2016). Thethe rapid development ofresearch smart grid provides new uncertainties in dispatch problems (Bertsimas &in Sim, 2004) Robust optimization (RO) has advantages in tolerating 2016). The rapid development of smart grid provides aa new Robust optimization (RO) has advantages in tolerating 2016). The rapid development of smart grid provides new choice for the efficient integration of EVs and renewable Robust optimization (RO) has advantages in tolerating uncertainties in dispatch problems (Bertsimas & Sim, 2004) 2016). The rapid development of smart grid provides a new energy. choice for for the the efficient efficient integration integration of of EVs EVs and and renewable renewable with reduced complexity of previous robust models. Recently, Robust optimization (RO) has advantages in tolerating uncertainties in dispatch problems (Bertsimas & Sim, 2004) choice uncertainties in dispatch problems (Bertsimas & Sim, 2004) choice for the efficient integration of EVs and renewable energy. uncertainties in dispatch problems (Bertsimas & Sim, 2004) with reduced complexity of previous robust models. Recently, choice for the efficient integration of EVs and renewable energy. many researchers applied RO to decision-making problems in uncertainties in dispatch problems (Bertsimas & Sim, 2004) with reduced complexity of previous robust models. Recently, energy. In the micro-grid environment, the interactive technology with reduced complexity of previous robust models. Recently, energy. with reduced complexity of previous robust models. Recently, many researchers applied RO to decision-making problems in energy. power systems, including EV charging scheduling (Pirouzi et with reduced complexity of previous robust models. Recently, many researchers applied RO to decision-making problems in In the micro-grid environment, the interactive technology between EVs can provide support for on-site consumption and many researchers researchers applied RO RO to decision-making problems in In the micro-grid environment, the interactive technology many applied to decision-making problems in In the micro-grid environment, the interactive technology power systems, including EV charging scheduling (Pirouzi al., 2018) and incorporating PV power to the power grid many researchers applied RO to decision-making problems in In the micro-grid environment, the interactive technology between EVs can provide provide support for on-site consumption and power systems, systems, including including EV EV charging charging scheduling scheduling (Pirouzi (Pirouzi et et while technology renewable stable interconnection of renewable energy, In thegrid micro-grid environment, the on-site interactive between EVs can support for consumption and power et between EVs can provide support for on-site consumption and power systems, including EV charging scheduling (Pirouzi et al., 2018) and incorporating PV power to the power grid (Soares et al., 2017). between EVs can provide support for on-site consumption and power systems, including EV charging scheduling (Pirouzi et while renewable stable grid interconnection of renewable energy, al., 2018) and incorporating PV power to the power grid energy can be absorbed or incorporated into large grids in the between EVs can provide support for on-site consumption and while renewable stable grid interconnection of renewable energy, al., 2018) and incorporating PV power to the power grid while renewable stable grid interconnection of renewable energy, al., 2018) and incorporating (Soares et al., while renewable stable grid interconnection of renewable energy, al., 2018) and2017). incorporating PV PV power power to to the the power power grid grid energy can be absorbed or into large in the (Soares etcharging al., 2017). . EVs cangrids be used as form micro-grids (Cardoso et al., 2014) while renewable stableof grid interconnection ofincorporated renewable energy, energy can be absorbed or incorporated into large grids in the (Soares al., 2017). The EVet loads are influenced by their users’ travel energy can be absorbed or incorporated into large grids in the (Soares et al., 2017). energy can be absorbed or incorporated into large grids in the (Soares et al., 2017). . EVs can be used as form of micro-grids (Cardoso et al., 2014) energy storage for efficient connection renewable energy energy can be units absorbed or incorporated into large grids in the The charging loads are their users’ travel ..ofEVs can be used as form of micro-grids (Cardoso et al., 2014) habits, different EVs and by other related The EV EVcapacities charging of loads are influenced influenced by their users’factors, travel EVs can be used as form of micro-grids (Cardoso et al., 2014) The EV charging loads are influenced by their users’ travel ..of EVs can be used as form of micro-grids (Cardoso et al., 2014) energy storage units for efficient connection renewable energy sources, distributed energy sources and power systems (Aghaei The EV charging loads are influenced by their users’ travel EVs can be used as form of micro-grids (Cardoso et al., 2014) habits, capacities of different EVs and other related factors, energy storage units for efficient connection of renewable energy and these characteristics make it difficult to predict accurate The EV charging loads are influenced by their users’ travel habits, capacities of different EVs and other related factors, energy storage units for efficient connection of renewable energy habits, capacities of different EVs and other related factors, energy storage units energy for efficient efficient connection of renewable renewable energy sources, distributed sources and power systems (Aghaei . units et al., 2016) habits, capacities of EVs and related factors, energy storage for connection of energy and characteristics make it to predict accurate sources, distributed energy sources and systems probability distributions of EV charging Therefore, habits, capacities of different different EVs and other other related factors, and these these characteristics make it difficult difficult toloads. predict accurate sources, distributed energy sources and power power systems (((Aghaei Aghaei and these characteristics make it difficult to predict accurate sources, distributed energy sources and power systems Aghaei . et al., 2016) 2016) and these characteristics make it difficult to predict accurate sources, distributed energy sources and power systems ( Aghaei probability distributions of EV charging loads. Therefore, . et al., and these characteristics make it difficult to predict accurate probability distributions of EV charging loads. Therefore, . et al., 2016) probability distributions of EV charging loads. Therefore, et probability et al., al., 2016) 2016).. probability distributions distributions of of EV EV charging charging loads. loads. Therefore, Therefore,
2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2018, 2018 IFAC 474Hosting by Elsevier Ltd. All rights reserved. Peer review©under of International Federation of Automatic Copyright 2018 responsibility IFAC 474Control. Copyright © 2018 IFAC 474 10.1016/j.ifacol.2018.11.748 Copyright © 2018 IFAC 474 Copyright © 2018 IFAC 474 Copyright © 2018 IFAC 474
IFAC CPES 2018 Tokyo, Japan, September 4-6, 2018
Ruifeng Shi et al. / IFAC PapersOnLine 51-28 (2018) 474–479
uncertainty of EV charging loads should be taken into consideration with the RO.
475
Wind speed is modeled as a random variable with probability density function defined by
This paper proposes an RO model to solve the multi-dispatch problem, which is integrated with diesel engine (DE), wind turbine (WT), micro turbine (MT), and a large number of EVs, and systematically expounds the application of RO in energy economy. The following summarizes its contributions:
f wind V
V2 exp 2 3 2 V
(1)
which is known to be the Rayleigh distribution with V and η as the wind speed and distribution parameter, respectively (Wei et al., 2014). We consider the wind speed prediction as the mean value of Rayleigh distribution, so the Rayleigh parameter is known as
1) The proposed RO model handles the uncertain sets of both EV charging loads and available wind power by taking the worst scenario of uncertain variables into account. The RO dispatch strategy has better performance in tolerating uncertainty, and its robustness is stronger than conventional stochastic dispatch strategies.
(V )
2) The proposed RO model in the paper is a semi-infinite programming model, which has difficulty in obtaining its analytical solution directly. The duality principle is explored to convert the original RO model to a robust counterpart with linear constraint, which can be easily solved with Lagrange relaxation algorithm.
2
(2)
where (V ) is the mean wind speed. The wind speed has
confidence interval P 1 , where α is the confidence level. The confidence interval represents the range of uncertain data with a certain credibility. By giving the wind speed, the output wind generator power is represented by
The paper is organized as following: The uncertainty sets for predicting wind power and EVs are proposed in Section II. Section III expands the robust optimization problem including wind power and EV charging. Case study is presented in Section V, and conclusions are drawn in Section VI. Fig. 1 shows the system structure diagram of this paper.
(3) where Vin ,Vr ,Vout are respectively, cut-in, rated and cut-out
Dispatch Model of Residental in Microgrid Objective function Constraints Minimizing operating cost System operation limits, EV and environment protective characteristics, Power cost balance, Spinning reserve
wind speeds, Wr is rated wind power, and a and b are the wind turbine parameters. According to the prediction interval theory, the uncertain set of wind generation can be estimated with ___ PWT PWTl G,t PWTl G,t PWTl G,t :PWTl G,t PWTl G,t PWTl G,t (4)
Robust dispatch model under the uncertain sets semi-infinitely problem
where variables with G in the superscripts are defined as predicted variables, PWTl G,t is the predicted wind power of the
Converting to the deterministic LP Bertsimas method
l-th wind turbine, PWTl G,t and PWTl G,t are upper and lower limitation of wind turbine uncertain set. Since the prediction
Solving dual problem by
G G interval is symmetric, we have PWTl ,t PWTl ,t .
Lagrange relaxation algorithm
2.2 Uncertain Sets of Electric Vehicles Result analysis
The probability of individual EV travelling a distance d can be represented by a logarithmic normal distribution function
fill the overnight valley in electricity demand and reduce the total cost
h d ; ,
Fig. 1. System structure diagram. 2. RESIDENTIAL MICROGRID WITH WIND POWER AND ELECTRIC VEHICLES
1 d 2
2
e
ln d 2 2 2
(5)
where μ and σ are its mean and standard deviation (Shi et al., 2016). According to parameter d, we can define the initial State of Charge (SOC) of individual EV by
2.1 Uncertain Sets of Wind Generations
475
IFAC CPES 2018 476 Tokyo, Japan, September 4-6, 2018
Ruifeng Shi et al. / IFAC PapersOnLine 51-28 (2018) 474–479
d SOC 1 100% dr
· COM denotes the operation and maintenance (OM) cost
(6)
of all DGs, · Cbat denotes the battery degradation cost of the i-th EV,
where dr is the maximum travel distance of the EV.
· Cgrid ,t denotes the transmission cost between microgrid
According to (Tian, Shi & Zia, 2010), the daily travel (start n charging time) Tstart is formulated as a random variable with normal distribution, the confidence interval of EV’s start charging time can be denoted by the upper and lower bounds as:
and the main power grid. b) Objective 2: Pollutants Emission Minimization The generation cost of the microgrid can be estimated with the following parts: one part is the generation cost of the thermal power units (considering the threshold effect and the blowdown effect); the other part is the daily generation cost of wind power units, which can be formulated as
n n n Tstart Tstart , Tstart (7) The initial SOC of the n-th EV, can be denoted by its upper and lower bounds.
SOC n SOC n , SOC n (8) In order to determine the charging time period for all EVs, which is restricted by the random SOC, we assume that all EVs have the same capacity and the EV charging pile furnish the constant charging power. In summary, the end-time of the i-th n can be calculated as EV’s charging Tend n n Tend Tstart
1 SOC E
i 1
h
h
Ctotal min C1 , C2
(12)
(13)
Where Ctotal is the total cost of microgrid, which takes into account the operation cost and environmental protective cost of the microgrid. 2) Constraints
___ PEVt G PEVt G PEVt G : PEVt G PEVt G PEVt G (10)
a) Conventional Economic Dispatch Constraints Conventional constraints include power balance constraints, operating reserve constraints, output constraints of generators and ramping constraints. The power balance constraints can be defined as,
where PEVt G is the charging power of all EVs at time period t, which also can be defined as the sum of the mean and the variance, with the respective lower and upper limits.
PDE
2.3 Problem Formulation
g ,t
g
PMT j ,t PWTl ,t Pgrid ,t PEVn,t Pload ,t j
l
n
(14) where PDE, PMT, PWT, and PEV are respectively the output of diesel engine, micro turbine, wind turbine, and electric vehicle.
1) Objective Function a) Objective 1: Operating Cost Minimization The total operating cost of the microgrid includes the fuel costs of DGs, operation and maintenance cost, transmission cost between the microgrid and the main power grid (Lu, Zhou & Yang, 2017), and the battery degradation cost (Ma et al., 2017). Such objective function can be formulated as below,
Pi ,min Pi ,t Pi ,max t t
(15)
Pi , down Pi ,t Pi ,t 1 Pi ,up
(16)
where (15) and (16) represent DE and MT limits on power output and the regulation speed, respectively. The operating reserve constraints can be defined as,
C f Pi ,t COM Pi ,t T Cgrid ,t (11) Min f1 x C1 t 1 ig , j ,l , n Cbat PEVi , t · C f () denotes the fuel cost of all conventional generation
H
c) Total Cost Function of Dispatch Problem in Microgrid
The predicted EV charging load is the summed charging power of all EVs. The random behavior characteristics of EV charging can be described as the uncertainty set
where, i represents the type of distributed power, and
H
where h represents the pollutant emission, H represents the total number of the pollutant emissions and ui,t and ugrid,t are the pollutant discharge coefficients of i-th DG and main power. + Pollutant emissions include CO2, SO2 and NOx. And 𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 denotes the output power of the main power grid.
(9) P where E is the battery capacity of an EV and P denotes the charging power of the n-th EV which can be considered as a constant.
U EV
N
min f 2 x =C2 Ch ui , h Pi Ch ugrid ,t Pgrid
PDE g
g ,t
PWTl G,t PMT j ,t Pgrid ,t l
j
1+Lt PEVnG,t Pload ,t n
with respect to Pi ,t , 476
(17)
IFAC CPES 2018 Tokyo, Japan, September 4-6, 2018
Ruifeng Shi et al. / IFAC PapersOnLine 51-28 (2018) 474–479
where, P ,Pgrid ,t 0 Pgrid ,t grid Pgrid ,Pgrid ,t 0
477
L K K L min PWTl G,t t PWTl G,t t PEVkG,t t PEVkG,t t l 1 k 1 k 1 l 1 t t 1 s.t. 1 L (24)
(18)
t
grid
P
represents the microgrid purchasing electricity from the
represents the microgrid selling main power grid, Pgrid
In order to solve the above multi-objective optimization problems, this paper uses a weighted summation method to convert objective function to a single-objective function, and the robust economic dispatch problem is reformulated as,
represent the predictive value of j-th wind turbine and n-th is the operating reserve at period electric vehicle at time t, t.
min sup w1C1 w2 C2 Pi ,t , PEVk ,t G G PWT ,l ,t , PEVk ,t
b) Wind Power Constraints
0 PWTt PWTt
(19)
s.t.
c) EV Charging Constraints
The charge constraint for each EV is defined as
Ek ,t Ek ,t 1 PEV k ,t t
(25)
(14)-(16),(19)-(21),(24)
3.3 Robust Counterpart
Too-high power of charging will damage the battery. In order to prolong the service life of the battery, the EV charging power needs to be constrained by its maximum for each EV as, 0 PEVn,t PEVnmax ,t
t
3.2 Robust Energy Management Model
electricity to the main power grid, and PWT jG,t and PEVnG,t
G
t
t , t , t , t 0
The robust solution is feasible with high probability. The function (26) represents the probability of violation (POV),
_____ PWTl G,t PWTl G,t PMT j ,t Pgrid ,t g l j ___ G 1+Lt PEVn,t PEVnG,t Pload ,t Pr m ,t m ,t t (21) n m V
(20)
PDE
g ,t
Ek ,t and Ek ,t 1 represent the current and the last status of the
(26)
k-th EV, is the charging efficiency which is usually assumed to be a constant value.
Where the parameter t represents the number of uncertainties at time t, and Pr {a b} denotes the probability of violation, and the function (27) provides a bound that is independent of the solution, which can measure the robustness of system, which explained specifically in (Bertsimas & Sim, 2004)
3. ROBUST OPTIMIZATION ALGORITHM 3.1 Robust Equal Conversion Based on the sets of uncertainties shown in Sections 2.1, the inequality constraints (17) can be transformed to, _____ G G PDE PWT PWT g l l ,t g ,t l , t PMT j , t Pgrid , t j ___ 1+Lt PEVnG,t PEVnG,t Pload ,t n
2 Pr m,t m,t t exp t mV 2 J t
4.1 Simulation Scene A period from 4:00 pm to 4:00 am is divided into 24 thirtyminute intervals. A duality theory is employed to transfer the model to a linear robust optimization model in Section 3.2. Lagrange relaxation algorithm, which is effective and easy to implement, is selected to solve the transformed dual problem.
N L F max PWTl G,t 1 Lt PEVnG,t n 1 l 1
s.t.
(27)
4. CASE STUDY
(22)
Let F represents the uncertain part,
PWTl G,t PWTl G,t PWTl G,t
4.2 Problem Description (23)
The microgrid system includes WT, DE, MT and EVs. The system is running in the grid-connected mode. Figure 2 is the initial status of MG, where the EVs are assumed to be charged in the periods of 18:30-21:30, when there is the highest residential load of the day (Xiang et al., 2014). In this case, the high load and low wind power lead to the increase of diesel generator’s output, which means increased operating cost. On
PEVt G PEVt G PEVt G The dispatch objective function is monotonically increasing, strictly convex and differentiable. According to the strong duality its dual problem is also feasible and bounded, and the objective values coincide. Therefore, the dual problem becomes: 477
IFAC CPES 2018 478 Tokyo, Japan, September 4-6, 2018
Ruifeng Shi et al. / IFAC PapersOnLine 51-28 (2018) 474–479
the other hand, during 23:00-2:00, when there is a lower basic load demand but with a high wind power and thus energy is wasted. Therefore, it is crucial to optimize the energy in the microgrid for uncertain turbine output and electric vehicle load.
in robust optimization result. Figure 4(a) shows the RO under the worst scenario (ROW), from which we can see the WT is full in use, the output of DE and MT are increased to meet the remaining load requirements, but there is no excess power providing to the main grid. On the contrary, Fig. 4(b) shows the RO under the best scenario (ROB), from which we can see DE, MT and EV almost stay at the low cost status, and the proportion of wind power is higher than in Fig. 4(a), even if the phenomenon of selling electricity from MG to the main grid has happened.
Fig. 2. Initial status of the MG. 4.3 Stochastic Optimization The stochastic optimization dispatch strategy is used and shows good performance in reducing peak load and fuel cost under a stable operation situation. As shown in Fig 3, EVs are charged in the off-peak hours with high wind power outputs, and diesel generator and transmission power are required to satisfy the power demand. But the uncertainty of predicted variables is not taken into consideration, and the dynamics and robust performance of the system is not optimal.
Fig. 4(a). ROW result.
Fig. 4(b). ROB result. As shown in Table 1, comparing ROW with SO, in order to meet the power balance, system need to increase the output of DE and MT, which led to more economic costs. C1 increases 48.0%, C2 increases 19.2%, and Ctotal increases 42%, and calculation by formula (26), RO has good performance in robustness and make the probability that the constraint is destroyed to be 0, which has a big gap between RO and SO in robustness. Simultaneously, it is not difficult to find that the results have a greater impact on both sides of the robust optimization interval. The disparity is caused by random factors of WTs and EVs, which directly affect the cost of DGs.
Fig. 3. Stochastic optimization result. 4.4 Robust Optimization For RO, the worst scenario means the less available wind generator outputs and more EV charging loads. Therefore, the diesel generator increases its output so as to meet the load demands. Figures 4(a) and 4(b) show the extreme phenomenon
478
IFAC CPES 2018 Tokyo, Japan, September 4-6, 2018
Ruifeng Shi et al. / IFAC PapersOnLine 51-28 (2018) 474–479
479
Table 1. Optimization results under the worst scenario, best scenario and non-robust scenario Type Unit ROB SO ROW
DE
MT
4274.5 5721.7 7812.9
3890.8 4656.8 5562.0
+ 𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 (kW) 18473.9 4292.7 15205.4 6191.8 12234.8 7141.8
WT
− 𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔
EV
C1
-116.5 -2.8 0
2564.4 3522.0 4500.4
4077.1 6272.6 9322.2
5. CONCLUSIONS Optimal load dispatch of microgrid is of great significance to reduce energy consumption, environmental pollution and user's electricity costs. In this paper, a multi-objective optimal dispatch model for microgrid is proposed. The proposed method takes the uncertainties included in the wind turbines and EVs into consideration simultaneously, and robust optimal model is designed to solve the problem under the worst scenario. Through duality theory, the hard-to-solve semiinfinite optimization problem is transformed into a linear programming problem that is easy to solve. And the RO has good performance in robustness, but it will improve system economics. According to different scenarios, this paper combines energy management and economic analysis to illustrate the application of robust optimization in energy management systems. Case study shows that the proposed method can help the decision maker to find the quantified economic operation scheme for the microgrid system. 6. ACKNOWLEDGEMENTS The authors would like to thank the National Natural Science Foundation of China (Grant Number 61203100) and the Fundamental Research Funds for the Central Universities (Grant Number 16MS42) for their financial supports with this research. REFERENCES Adhikari, A. (2011). Multi-objective operation management of a renewable MG (micro-grid) with back-up microturbine/fuel cell/battery hybrid power source. Energy, 36(11): 6490-6507. Aghaei, J., Nezhad, A.E., Rabiee, A., and Rahimi, E. (2016). Contribution of plug-in hybrid electric vehicles in power system uncertainty management. Renewable & Sustainable Energy Reviews, 59: 450-458. Bertsimas, D., and Sim, M. (2004). The price of robustness. Operations Research, 52(1): 35-53. Cardoso, G., Stadler, M., Bozchalui, M.C., Sharma, R., Marnay, C., Barbosa-Povoa, A., and Ferrao, P. (2014). Optimal investment and scheduling of distributed energy resources with uncertainty in electric vehicle driving schedules. Energy, 64(1): 17-30. Lin, B., and Tan, R. (2017). Estimation of the environmental values of electric vehicles in Chinese cities. Energy Policy, 104:221-229. Liu, D., Zhang, G., Huang, B., and Liu, W. (2016). Optimum electric boiler capacity configuration in a regional power 479
C2 (RMB) 125.4 156.5 186.6
Ctotal
POV
4202.5 6695.1 9508.8
一 100% 0%
grid for a wind power accommodation scenario. Energies, 9(3): 144. Lu, X., Zhou, K., and Yang, S. (2017). Multi-objective optimal dispatch of microgrid containing electric vehicles. Journal of Cleaner Production, 165: 1572-1581. Ma, Z., Zou, S., Ran, L., Shi, X., and Hiskens, I.A. (2016). Efficient decentralized coordination of large-scale plug-in electric vehicle charging. Automatica, 69(C):35-47. Mwasilu, F., Justo, J.J., Kim, E.K., Do, T.D., and Jung, J.W. (2014). Electric vehicles and smart grid interaction: A review on vehicle to grid and renewable energy sources integration. Renewable & Sustainable Energy Reviews, 34: 501-516. Pirouzi, S., Aghaei, J., Vahidinasab, V., Niknam, T., and Khodaei, A. (2018). Robust linear architecture for active/reactive power scheduling of EV integrated smart distribution networks. Electric Power Systems Research, 155: 8-20. Rahman, I., Vasant, P.M., Singh, S.M., Abdullah-Al-Wadud, M., and Adnan, N. (2016). Review of recent trends in optimization techniques for plug-in hybrid, and electric vehicle charging infrastructures. Renewable & Sustainable Energy Reviews, 58:1039-1047. Shi, R., Sun, C., Zhou, Z., Zhang, L., and Liang, Z. (2016). A robust economic dispatch of residential microgrid with wind power and electric vehicle integration. Control and Decision Conference. May.28-30, Yinchuan, China. (pp.3672-3676). IEEE. Soares, J., Vale, Z., Borges, N., Lezama, F., and Kagan, N. (2017). Multi-objective robust optimization to solve energy scheduling in buildings under uncertainty. International Conference on Intelligent System Application to Power Systems. Sep.17–21, San Antonio, TX. Tian, L., Shi, S., and Jia, Z. (2010). A statistical model for charging demand of electric vehicles, Power System Technology, 34(11): 127-130. Wei, W., Liu, F., Mei, S., and Hou, Y. (2014). Robust energy and reserve dispatch under variable renewable generation. IEEE Transactions on Smart Grid, 6(1): 369-380. Yue, X., Liu, J., Wei, Z., Cao, Y. and Ai, F. (2014). Robust model of microgrid energy optimization with uncertain renewable energy sources, Proceedings of Chinese Society for Electrical Engineering (Proceedings of CSEE), 34(19): 3063-3072. Zhang, D., Wang, J., Lin, Y., Si, Y., Huang, C., and Yang, J. (2017). Present situation and future prospect of renewable energy in China. Renewable & Sustainable Energy Reviews, 76:865-871.
ScienceDirect
IFAC PapersOnLine 51-28 (2018) 474–479
Multi-dispatch for Grid-connected Microgrid with Robust Optimization Multi-dispatch for Grid-connected Microgrid with Robust Optimization Multi-dispatch Microgrid Algorithm Multi-dispatch for for Grid-connected Grid-connected Microgrid with with Robust Robust Optimization Optimization Multi-dispatch Microgrid with Robust Optimization Multi-dispatch for for Grid-connected Grid-connected Microgrid with Robust Optimization Algorithm Algorithm Algorithm Algorithm Ruifeng Shi*, ShaopengAlgorithm Li*, Changhao Sun**, Kwang Y. Lee***
Ruifeng Shi*, Shaopeng Li*, Changhao Sun**, Kwang Y. Lee*** Ruifeng Ruifeng Shi*, Shi*, Shaopeng Shaopeng Li*, Li*, Changhao Changhao Sun**, Sun**, Kwang Kwang Y. Y. Lee*** Lee*** Ruifeng Shi*, Shaopeng Li*, Changhao Sun**, Kwang Y. Lee*** Ruifeng Shi*, Shaopeng Li*, Changhao Sun**, Kwang Lee*** *School of Control and Computer Engineering, North China ElectricY.Power University, *SchoolBeijing, of Control Control and(e-mail: Computer Engineering, North North China China Electric Power Power University, University, China, [email protected]; [email protected]) *School of and Computer Engineering, Electric *School of Control and Computer Engineering, North China Electric Power University, *School of Control and Computer Engineering, North China Electric Power University, Beijing, China, (e-mail: [email protected]; [email protected]) *School** ofSmart Control and(e-mail: Computer Engineering, North China Electric Power Beijing, China, [email protected]; Energy Institute, Nanjing SAC Power [email protected]) Automation Co., University, Ltd, Beijing, China, (e-mail: [email protected]; [email protected]) Beijing, (e-mail: [email protected]; ** SmartChina, Energy Institute, Nanjing SAC Power Power [email protected]) Automation Co., Co., Ltd, Ltd, Beijing, China, (e-mail: [email protected]; [email protected]) ** Smart Energy Institute, Nanjing SAC Grid Automation Nanjing, 211100, China (e-mail: [email protected]) ** Smart Energy Institute, Nanjing SAC Power Grid Automation Co., Ltd, ** Smart Energy Institute, Nanjing SAC Power Grid Automation Co., Ltd, Nanjing, 211100,Nanjing China (e-mail: [email protected]) ** Smart Energy SAC Power Grid Automation Co., Ltd, Nanjing, 211100, China (e-mail: [email protected]) ***Department of Institute, Electrical and Computer Engineering, Baylor University, Nanjing, 211100, China (e-mail: [email protected]) Nanjing, 211100, China (e-mail: [email protected]) ***Department of Electrical and Computer Engineering, Baylor University, Nanjing, 211100, China (e-mail: [email protected]) ***Department of Electrical and Computer Engineering, Baylor TX 76798 USA (e-mail: [email protected]) ***Department of Electrical and Computer Engineering, Baylor University, University, ***Department of and Engineering, TX 76798 76798 USA (e-mail: (e-mail: [email protected]) ***Department of Electrical Electrical and Computer Computer Engineering, Baylor Baylor University, University, TX USA [email protected]) TX 76798 USA (e-mail: [email protected]) TX TX 76798 76798 USA USA (e-mail: (e-mail: [email protected]) [email protected]) Abstract: Increasing penetration of uncoordinated electric vehicles (EVs) and intermittent renewable Abstract: Increasing penetrationsystems of uncoordinated uncoordinated electric vehicles (EVs) and and intermittent renewable energy generation in microgrid motivates us to explore an effective strategy for therenewable safe and Abstract: Increasing penetration of electric vehicles (EVs) intermittent renewable Abstract: Increasing penetration of uncoordinated electric vehicles (EVs) and intermittent Abstract: Increasing penetration of uncoordinated electric vehicles (EVs) and intermittent energy generation inofmicrogrid microgrid systems motivates(DG) us tosystems. explore an effective effective strategy for the therenewable safe and and economic operation such distributed generation This paper presents a robust economic Abstract: Increasing penetration of uncoordinated electric vehicles (EVs) and intermittent renewable energy generation in systems motivates us to explore an strategy for safe energy generation in microgrid systems motivates us to explore an effective strategy for the safe and energy generation in microgrid systems motivates us to explore an effective strategy for the safe and economic operation of such distributed distributed generation (DG) systems. This paper presents a charging robust economic dispatch strategy for grid-connected microgrids. Uncertainty from wind power and EV loads is energy generation in microgrid systems motivates us to explore an effective strategy for the safe and economic operation of such generation (DG) systems. This paper presents a robust economic economic operation of such distributed generation (DG) systems. paper presents robust economic economic operation of such distributed generation (DG) systems. This paper presents robust economic dispatch strategy strategy for grid-connected microgrids. Uncertainty from This wind power and EVaaa charging charging loadsthe is considered as an uncertain set of interval predictions. Considering the worst application scenario, economic operation of such distributed generation (DG) systems. This paper presents robust economic dispatch for grid-connected microgrids. Uncertainty from wind power and EV loads is dispatch strategy grid-connected microgrids. Uncertainty from wind and EV charging loadsthe is dispatch for microgrids. from power and EV is considered as an an for uncertain set of interval interval predictions. Considering thepower worst application scenario, proposedstrategy strategy cangrid-connected help set to schedule thepredictions. EV Uncertainty charging behaviors and DG outputs order toloads reduce dispatch strategy for grid-connected microgrids. Uncertainty from wind wind power and EVincharging charging loads is considered as uncertain of Considering the worst application scenario, the considered as an uncertain set of interval predictions. Considering the worst application scenario, the considered as an uncertain set of interval predictions. Considering the worst application scenario, the proposed strategy can help to schedule the EV charging behaviors and DG outputs in order to reduce operation cost under practical constraints. In addition, in order to facilitate the decision makers to make considered as an uncertain set of interval predictions. Considering the worst application scenario, the proposed strategy can help to schedule the EV charging behaviors and DG outputs in order to reduce proposed strategy can help to constraints. schedule theInEV charging behaviors and DG in order to proposed strategy can help schedule EV charging behaviors and outputs in order to reduce operation cost under under practical addition, in order to explores facilitate theoutputs decision makers toreduce make decision strategies from theto ofIn economy, thisorder paper relationship between the proposed strategy can help toperspective schedule the the EV charging behaviors and DG DG outputs in makers order toto reduce operation cost practical constraints. addition, in to facilitate the decision make operation cost under practical constraints. In addition, in order to facilitate the decision makers to make operation cost under practical constraints. In addition, in order to facilitate the decision makers to make decision strategies from the perspective of economy, this paper explores relationship between the volatility of uncertain parameters and economy based on the theory of interval forecast. Numerical case operation cost under practical constraints. In addition, in order to facilitate the decision makers to make decision strategies from the perspective of economy, this paper explores relationship between the decision strategies from the perspective perspective of economy, economy, thisthepaper paper explores the relationship relationship betweencase the decision strategies from the of this explores the between the volatility of uncertain uncertain parameters and economy economy based on theory of interval interval forecast. Numerical Numerical study shows the feasibility of perspective the proposed strategy. decision strategies from the ofdispatch economy, thisthe explores the relationship betweencase the volatility of parameters and based on thepaper theory of forecast. case volatility of uncertain parameters and economy based on theory of interval forecast. Numerical volatility of uncertain parameters and economy based on the theory of interval forecast. Numerical case study shows the feasibility of the proposed dispatch strategy. volatility of uncertain parameters and economy based on the theory of interval forecast. Numerical case study showsMicrogrids, the feasibility feasibility of the theOptimization, proposed dispatch dispatch strategy. Electric Vehicles, Wind Power, Economic Keywords: Robust Multi-Dispatch, study shows of proposed strategy. © 2018, IFACthe (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. study shows the of proposed strategy. study showsMicrogrids, the feasibility feasibility of the theOptimization, proposed dispatch dispatch strategy. Electric Robust Multi-Dispatch, Vehicles, Wind Power, Economic Keywords: Analysis Microgrids, Robust Optimization, Multi-Dispatch, Electric Vehicles, Wind Power, Economic Keywords: Microgrids, Robust Optimization, Multi-Dispatch, Electric Vehicles, Wind Power, Economic Keywords: Keywords: Microgrids, Robust Optimization, Multi-Dispatch, Electric Vehicles, Wind Power, Economic Analysis Microgrids, Robust Optimization, Multi-Dispatch, Electric Vehicles, Wind Power, Economic Keywords: Analysis Analysis Analysis Analysis The research on grid-connected microgrid has become one of The research on grid-connected microgrid become one of 1. INTRODUCTION the important research topics in the field of has energy dispatching The research grid-connected microgrid has become one The research on on grid-connected microgrid has become one of of 1. INTRODUCTION The research on grid-connected microgrid has become one of the important research topics in the field of energy dispatching 1. INTRODUCTION nowadays, where grid-connected microgrid is a cluster The research on grid-connected microgrid has become one of the important important research research topics topics in in the the field field of of energy energy dispatching dispatching 1. INTRODUCTION the 1. INTRODUCTION the important research topics in the field of energy dispatching In the power consumption side, electric vehicles (EVs) have nowadays, where grid-connected microgrid isofaadispatching cluster of of 1. INTRODUCTION distributed generations (DGs), resources renewable the important research topics in the field of energy nowadays, where grid-connected microgrid is cluster nowadays, where grid-connected microgrid is aa renewable cluster of In the power consumption electric vehicles (EVs) nowadays, where grid-connected microgrid is cluster of drawn great duringside, the past decades because theyhave are distributed generations (DGs), resources of In the powerattention consumption side, electric vehicles (EVs) have generations (RGs) and conventional generations (CGs), and nowadays, where grid-connected microgrid is a cluster of distributed generations (DGs), resources of renewable In the power consumption side, electric vehicles (EVs) have distributed generations (DGs), resources of renewable In the power consumption side, electric vehicles (EVs) have drawn great attention duringside, the past past decades because they are distributed generations (DGs), resources of renewable seemingly environmentally friendly to the consumers (Lin & In the power consumption electric vehicles (EVs) have generations (RGs) and conventional generations (CGs), and drawn great attention during the decades because they are flexible load (such as EVs) and local loads, are usually distributed generations (DGs), resources of renewable generations (RGs) and conventional generations (CGs), and drawn great attention during the past decades because they are generations (RGs) and conventional generations (CGs), and drawn great attention during the decades because are seemingly the consumers (Lin & generations and conventional generations (CGs), and Tan, 2017). However, duefriendly to past the to dynamic nature they of EV drawn greatenvironmentally attention during the past decades because they are flexible load as EVs) and local loads, are usually seemingly environmentally friendly to the consumers (Lin & managed by (RGs) an(such energy management system (EMS), which is generations (RGs) and conventional generations (CGs), and flexible load (such as EVs) and local loads, are usually seemingly environmentally friendly to the consumers (Lin & flexible load (such as EVs) and local loads, are usually seemingly environmentally friendly to the consumers (Lin & Tan, 2017). However, due to the dynamic nature of EV flexible load (such as EVs) and local loads, are usually charging time, locations, user behaviors, and load profiles, the seemingly environmentally friendly to the consumers (Lin & managed by an energy management system (EMS), which is Tan, 2017). However, due to the dynamic nature of EV becoming one of the fundamental control methods to balance flexible load (such as EVs) and local loads, are usually managed by an energy management system (EMS), which is Tan, 2017). However, due to the dynamic nature of EV managed by an energy management system (EMS), which is Tan, 2017). However, due to the dynamic nature of EV charging time, locations, user behaviors, and load profiles, the managed by an energy management system (EMS), which is large-scale penetration of uncontrolled and uncoordinated EVs Tan, 2017). However, due to the dynamic nature of EV becoming one of the fundamental control methods to balance charging time, locations, user behaviors, and load profiles, the the connection of EVs and renewable energy (Mwasilu et al., managed by an energy management system (EMS), which is becoming one of the fundamental control methods to balance charging time, locations, user behaviors, and load profiles, the becoming one of the fundamental control methods to balance charging time, locations, user behaviors, and load profiles, the large-scale penetration of uncontrolled and uncoordinated EVs becoming one of the fundamental control methods to balance into power systems, especially in distribution networks, may charging time, locations, user behaviors, and load profiles, the the connection of EVs and renewable energy (Mwasilu et al., large-scale penetration of uncontrolled and uncoordinated EVs 2014). Adhikari (2011) has built up multi-objective models of becoming one of the fundamental control methods to balance the connection of EVs and renewable energy (Mwasilu et al., large-scale penetration of uncontrolled and uncoordinated EVs the connection connection of(2011) EVs and and renewable energy (Mwasilu (Mwasilu et al., al., large-scale penetration of and EVs into power systems, in distribution networks, may the EVs renewable energy et cause a high level ofespecially volatility and increase potential sources large-scale penetration of uncontrolled uncontrolled and uncoordinated uncoordinated EVs 2014). Adhikari has built multi-objective of into power systems, especially in distribution networks, may microgrid withof which provide anmodels efficient the connection ofDGs EVsand and renewable energy (Mwasilu et al., 2014). Adhikari (2011) hasloads, built up up multi-objective models of into power systems, especially in distribution networks, may 2014). Adhikari (2011) has built up multi-objective models of into power systems, especially in distribution networks, may cause a high level of volatility and increase potential sources 2014). Adhikari (2011) has built up multi-objective models of for system disturbances (Rahman et al., 2016). into power systems, especially in distribution networks, may microgrid with DGs and loads, which provide an efficient cause a high level of volatility and increase potential sources integrated method of renewable energy, and EVs, but the 2014). Adhikari (2011) has built up multi-objective models of microgrid with DGs and loads, which provide an efficient cause a high level of volatility and increase potential sources microgrid with DGs and loads, which provide an efficient cause a high level of volatility and increase potential sources for system disturbances (Rahman et al., 2016). microgrid with DGs and loads, which provide an efficient cause a high level of volatility and increase potential sources integrated method of renewable energy, and EVs, but the for system disturbances (Rahman et al., 2016). proposed models are lacking practical uncertainty microgrid with DGs and loads, which provide an efficient integrated method of renewable energy, and EVs, but the for system disturbances (Rahman et al., 2016). In addition, clean and effective renewable energy has been integrated method of renewable energy, and EVs, but the for system (Rahman et integrated method of renewable energy, and but for addition, system disturbances disturbances (Rahman renewable et al., al., 2016). 2016). proposed models lacking practical uncertainty considerations. Stochastic optimization (SO) provides an integrated method of are renewable energy, and EVs, EVs, but the the In clean and effective energy has been models are lacking practical uncertainty widely exploited in response to the energy self-sufficiency and proposed In addition, clean and effective renewable energy has been proposed models are lacking practical uncertainty In addition, clean and effective renewable energy has been proposed models are lacking practical uncertainty considerations. Stochastic optimization (SO) provides an In addition, clean and effective renewable energy has been effective way for solving optimization problems, in which proposed models are lacking practical uncertainty widely exploited in response to the energy self-sufficiency and considerations. Stochastic optimization (SO) provides an air addition, pollution emitted by effective conventional fossil-fuel power In clean and renewable energy hasplants been widely exploited in response to the energy self-sufficiency and considerations. Stochastic optimization (SO) provides an widely exploited in response to the energy self-sufficiency and considerations. Stochastic optimization (SO) provides an effective way for solving optimization problems, in which widely exploited in response to the energy self-sufficiency and uncertain numerical data can be assumed to follow a wellconsiderations. Stochastic optimization (SO) provides an air pollution emitted by conventional fossil-fuel power plants effective way for solving optimization problems, in which (Zhang et al., 2017). Researches on absorbing renewable widely exploited in response to the energy self-sufficiency and air pollution emitted by conventional fossil-fuel power plants effective way for solving optimization problems, in which air pollution emitted by conventional fossil-fuel power plants effective way for solving optimization problems, in which uncertain numerical data can be assumed to follow a wellair pollution emitted by conventional fossil-fuel power plants known probability distribution. effective way for solving optimization problems, in which (Zhang et al., 2017). Researches on absorbing renewable uncertain numerical data can be assumed to follow a wellenergy have gradually become the research hotspot (Liu et al., air pollution emitted by conventional fossil-fuel power plants (Zhang et al., 2017). Researches on absorbing renewable uncertain numerical data can be assumed to follow aa well(Zhang et al., 2017). Researches on absorbing renewable numerical data known probability distribution. (Zhang et 2017). Researches on renewable uncertain numerical data can can be be assumed assumed to to follow follow a wellwellenergy have gradually become the research hotspot (Liu etnew al., uncertain known distribution. (Zhang have et al., al., 2017). Researches on absorbing absorbing renewable 2016). The rapid development ofresearch smart grid provides aet energy gradually become the hotspot (Liu al., known probability distribution. Robust probability optimization (RO) has advantages in tolerating energy have gradually become the research hotspot (Liu et al., known probability distribution. energy have gradually become the research hotspot (Liu et al., known probability distribution. 2016). The rapid development of smart grid provides aaetnew energy have gradually become the hotspot al., Robust optimization (RO) has advantages tolerating choice for efficient integration of EVs and (Liu renewable 2016). Thethe rapid development ofresearch smart grid provides new uncertainties in dispatch problems (Bertsimas &in Sim, 2004) Robust optimization (RO) has advantages in tolerating 2016). The rapid development of smart grid provides aa new Robust optimization (RO) has advantages in tolerating 2016). The rapid development of smart grid provides new choice for the efficient integration of EVs and renewable Robust optimization (RO) has advantages in tolerating uncertainties in dispatch problems (Bertsimas & Sim, 2004) 2016). The rapid development of smart grid provides a new energy. choice for for the the efficient efficient integration integration of of EVs EVs and and renewable renewable with reduced complexity of previous robust models. Recently, Robust optimization (RO) has advantages in tolerating uncertainties in dispatch problems (Bertsimas & Sim, 2004) choice uncertainties in dispatch problems (Bertsimas & Sim, 2004) choice for the efficient integration of EVs and renewable energy. uncertainties in dispatch problems (Bertsimas & Sim, 2004) with reduced complexity of previous robust models. Recently, choice for the efficient integration of EVs and renewable energy. many researchers applied RO to decision-making problems in uncertainties in dispatch problems (Bertsimas & Sim, 2004) with reduced complexity of previous robust models. Recently, energy. In the micro-grid environment, the interactive technology with reduced complexity of previous robust models. Recently, energy. with reduced complexity of previous robust models. Recently, many researchers applied RO to decision-making problems in energy. power systems, including EV charging scheduling (Pirouzi et with reduced complexity of previous robust models. Recently, many researchers applied RO to decision-making problems in In the micro-grid environment, the interactive technology between EVs can provide support for on-site consumption and many researchers researchers applied RO RO to decision-making problems in In the micro-grid environment, the interactive technology many applied to decision-making problems in In the micro-grid environment, the interactive technology power systems, including EV charging scheduling (Pirouzi al., 2018) and incorporating PV power to the power grid many researchers applied RO to decision-making problems in In the micro-grid environment, the interactive technology between EVs can provide provide support for on-site consumption and power systems, systems, including including EV EV charging charging scheduling scheduling (Pirouzi (Pirouzi et et while technology renewable stable interconnection of renewable energy, In thegrid micro-grid environment, the on-site interactive between EVs can support for consumption and power et between EVs can provide support for on-site consumption and power systems, including EV charging scheduling (Pirouzi et al., 2018) and incorporating PV power to the power grid (Soares et al., 2017). between EVs can provide support for on-site consumption and power systems, including EV charging scheduling (Pirouzi et while renewable stable grid interconnection of renewable energy, al., 2018) and incorporating PV power to the power grid energy can be absorbed or incorporated into large grids in the between EVs can provide support for on-site consumption and while renewable stable grid interconnection of renewable energy, al., 2018) and incorporating PV power to the power grid while renewable stable grid interconnection of renewable energy, al., 2018) and incorporating (Soares et al., while renewable stable grid interconnection of renewable energy, al., 2018) and2017). incorporating PV PV power power to to the the power power grid grid energy can be absorbed or into large in the (Soares etcharging al., 2017). . EVs cangrids be used as form micro-grids (Cardoso et al., 2014) while renewable stableof grid interconnection ofincorporated renewable energy, energy can be absorbed or incorporated into large grids in the (Soares al., 2017). The EVet loads are influenced by their users’ travel energy can be absorbed or incorporated into large grids in the (Soares et al., 2017). energy can be absorbed or incorporated into large grids in the (Soares et al., 2017). . EVs can be used as form of micro-grids (Cardoso et al., 2014) energy storage for efficient connection renewable energy energy can be units absorbed or incorporated into large grids in the The charging loads are their users’ travel ..ofEVs can be used as form of micro-grids (Cardoso et al., 2014) habits, different EVs and by other related The EV EVcapacities charging of loads are influenced influenced by their users’factors, travel EVs can be used as form of micro-grids (Cardoso et al., 2014) The EV charging loads are influenced by their users’ travel ..of EVs can be used as form of micro-grids (Cardoso et al., 2014) energy storage units for efficient connection renewable energy sources, distributed energy sources and power systems (Aghaei The EV charging loads are influenced by their users’ travel EVs can be used as form of micro-grids (Cardoso et al., 2014) habits, capacities of different EVs and other related factors, energy storage units for efficient connection of renewable energy and these characteristics make it difficult to predict accurate The EV charging loads are influenced by their users’ travel habits, capacities of different EVs and other related factors, energy storage units for efficient connection of renewable energy habits, capacities of different EVs and other related factors, energy storage units energy for efficient efficient connection of renewable renewable energy sources, distributed sources and power systems (Aghaei . units et al., 2016) habits, capacities of EVs and related factors, energy storage for connection of energy and characteristics make it to predict accurate sources, distributed energy sources and systems probability distributions of EV charging Therefore, habits, capacities of different different EVs and other other related factors, and these these characteristics make it difficult difficult toloads. predict accurate sources, distributed energy sources and power power systems (((Aghaei Aghaei and these characteristics make it difficult to predict accurate sources, distributed energy sources and power systems Aghaei . et al., 2016) 2016) and these characteristics make it difficult to predict accurate sources, distributed energy sources and power systems ( Aghaei probability distributions of EV charging loads. Therefore, . et al., and these characteristics make it difficult to predict accurate probability distributions of EV charging loads. Therefore, . et al., 2016) probability distributions of EV charging loads. Therefore, et probability et al., al., 2016) 2016).. probability distributions distributions of of EV EV charging charging loads. loads. Therefore, Therefore,
2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2018, 2018 IFAC 474Hosting by Elsevier Ltd. All rights reserved. Peer review©under of International Federation of Automatic Copyright 2018 responsibility IFAC 474Control. Copyright © 2018 IFAC 474 10.1016/j.ifacol.2018.11.748 Copyright © 2018 IFAC 474 Copyright © 2018 IFAC 474 Copyright © 2018 IFAC 474
IFAC CPES 2018 Tokyo, Japan, September 4-6, 2018
Ruifeng Shi et al. / IFAC PapersOnLine 51-28 (2018) 474–479
uncertainty of EV charging loads should be taken into consideration with the RO.
475
Wind speed is modeled as a random variable with probability density function defined by
This paper proposes an RO model to solve the multi-dispatch problem, which is integrated with diesel engine (DE), wind turbine (WT), micro turbine (MT), and a large number of EVs, and systematically expounds the application of RO in energy economy. The following summarizes its contributions:
f wind V
V2 exp 2 3 2 V
(1)
which is known to be the Rayleigh distribution with V and η as the wind speed and distribution parameter, respectively (Wei et al., 2014). We consider the wind speed prediction as the mean value of Rayleigh distribution, so the Rayleigh parameter is known as
1) The proposed RO model handles the uncertain sets of both EV charging loads and available wind power by taking the worst scenario of uncertain variables into account. The RO dispatch strategy has better performance in tolerating uncertainty, and its robustness is stronger than conventional stochastic dispatch strategies.
(V )
2) The proposed RO model in the paper is a semi-infinite programming model, which has difficulty in obtaining its analytical solution directly. The duality principle is explored to convert the original RO model to a robust counterpart with linear constraint, which can be easily solved with Lagrange relaxation algorithm.
2
(2)
where (V ) is the mean wind speed. The wind speed has
confidence interval P 1 , where α is the confidence level. The confidence interval represents the range of uncertain data with a certain credibility. By giving the wind speed, the output wind generator power is represented by
The paper is organized as following: The uncertainty sets for predicting wind power and EVs are proposed in Section II. Section III expands the robust optimization problem including wind power and EV charging. Case study is presented in Section V, and conclusions are drawn in Section VI. Fig. 1 shows the system structure diagram of this paper.
(3) where Vin ,Vr ,Vout are respectively, cut-in, rated and cut-out
Dispatch Model of Residental in Microgrid Objective function Constraints Minimizing operating cost System operation limits, EV and environment protective characteristics, Power cost balance, Spinning reserve
wind speeds, Wr is rated wind power, and a and b are the wind turbine parameters. According to the prediction interval theory, the uncertain set of wind generation can be estimated with ___ PWT PWTl G,t PWTl G,t PWTl G,t :PWTl G,t PWTl G,t PWTl G,t (4)
Robust dispatch model under the uncertain sets semi-infinitely problem
where variables with G in the superscripts are defined as predicted variables, PWTl G,t is the predicted wind power of the
Converting to the deterministic LP Bertsimas method
l-th wind turbine, PWTl G,t and PWTl G,t are upper and lower limitation of wind turbine uncertain set. Since the prediction
Solving dual problem by
G G interval is symmetric, we have PWTl ,t PWTl ,t .
Lagrange relaxation algorithm
2.2 Uncertain Sets of Electric Vehicles Result analysis
The probability of individual EV travelling a distance d can be represented by a logarithmic normal distribution function
fill the overnight valley in electricity demand and reduce the total cost
h d ; ,
Fig. 1. System structure diagram. 2. RESIDENTIAL MICROGRID WITH WIND POWER AND ELECTRIC VEHICLES
1 d 2
2
e
ln d 2 2 2
(5)
where μ and σ are its mean and standard deviation (Shi et al., 2016). According to parameter d, we can define the initial State of Charge (SOC) of individual EV by
2.1 Uncertain Sets of Wind Generations
475
IFAC CPES 2018 476 Tokyo, Japan, September 4-6, 2018
Ruifeng Shi et al. / IFAC PapersOnLine 51-28 (2018) 474–479
d SOC 1 100% dr
· COM denotes the operation and maintenance (OM) cost
(6)
of all DGs, · Cbat denotes the battery degradation cost of the i-th EV,
where dr is the maximum travel distance of the EV.
· Cgrid ,t denotes the transmission cost between microgrid
According to (Tian, Shi & Zia, 2010), the daily travel (start n charging time) Tstart is formulated as a random variable with normal distribution, the confidence interval of EV’s start charging time can be denoted by the upper and lower bounds as:
and the main power grid. b) Objective 2: Pollutants Emission Minimization The generation cost of the microgrid can be estimated with the following parts: one part is the generation cost of the thermal power units (considering the threshold effect and the blowdown effect); the other part is the daily generation cost of wind power units, which can be formulated as
n n n Tstart Tstart , Tstart (7) The initial SOC of the n-th EV, can be denoted by its upper and lower bounds.
SOC n SOC n , SOC n (8) In order to determine the charging time period for all EVs, which is restricted by the random SOC, we assume that all EVs have the same capacity and the EV charging pile furnish the constant charging power. In summary, the end-time of the i-th n can be calculated as EV’s charging Tend n n Tend Tstart
1 SOC E
i 1
h
h
Ctotal min C1 , C2
(12)
(13)
Where Ctotal is the total cost of microgrid, which takes into account the operation cost and environmental protective cost of the microgrid. 2) Constraints
___ PEVt G PEVt G PEVt G : PEVt G PEVt G PEVt G (10)
a) Conventional Economic Dispatch Constraints Conventional constraints include power balance constraints, operating reserve constraints, output constraints of generators and ramping constraints. The power balance constraints can be defined as,
where PEVt G is the charging power of all EVs at time period t, which also can be defined as the sum of the mean and the variance, with the respective lower and upper limits.
PDE
2.3 Problem Formulation
g ,t
g
PMT j ,t PWTl ,t Pgrid ,t PEVn,t Pload ,t j
l
n
(14) where PDE, PMT, PWT, and PEV are respectively the output of diesel engine, micro turbine, wind turbine, and electric vehicle.
1) Objective Function a) Objective 1: Operating Cost Minimization The total operating cost of the microgrid includes the fuel costs of DGs, operation and maintenance cost, transmission cost between the microgrid and the main power grid (Lu, Zhou & Yang, 2017), and the battery degradation cost (Ma et al., 2017). Such objective function can be formulated as below,
Pi ,min Pi ,t Pi ,max t t
(15)
Pi , down Pi ,t Pi ,t 1 Pi ,up
(16)
where (15) and (16) represent DE and MT limits on power output and the regulation speed, respectively. The operating reserve constraints can be defined as,
C f Pi ,t COM Pi ,t T Cgrid ,t (11) Min f1 x C1 t 1 ig , j ,l , n Cbat PEVi , t · C f () denotes the fuel cost of all conventional generation
H
c) Total Cost Function of Dispatch Problem in Microgrid
The predicted EV charging load is the summed charging power of all EVs. The random behavior characteristics of EV charging can be described as the uncertainty set
where, i represents the type of distributed power, and
H
where h represents the pollutant emission, H represents the total number of the pollutant emissions and ui,t and ugrid,t are the pollutant discharge coefficients of i-th DG and main power. + Pollutant emissions include CO2, SO2 and NOx. And 𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 denotes the output power of the main power grid.
(9) P where E is the battery capacity of an EV and P denotes the charging power of the n-th EV which can be considered as a constant.
U EV
N
min f 2 x =C2 Ch ui , h Pi Ch ugrid ,t Pgrid
PDE g
g ,t
PWTl G,t PMT j ,t Pgrid ,t l
j
1+Lt PEVnG,t Pload ,t n
with respect to Pi ,t , 476
(17)
IFAC CPES 2018 Tokyo, Japan, September 4-6, 2018
Ruifeng Shi et al. / IFAC PapersOnLine 51-28 (2018) 474–479
where, P ,Pgrid ,t 0 Pgrid ,t grid Pgrid ,Pgrid ,t 0
477
L K K L min PWTl G,t t PWTl G,t t PEVkG,t t PEVkG,t t l 1 k 1 k 1 l 1 t t 1 s.t. 1 L (24)
(18)
t
grid
P
represents the microgrid purchasing electricity from the
represents the microgrid selling main power grid, Pgrid
In order to solve the above multi-objective optimization problems, this paper uses a weighted summation method to convert objective function to a single-objective function, and the robust economic dispatch problem is reformulated as,
represent the predictive value of j-th wind turbine and n-th is the operating reserve at period electric vehicle at time t, t.
min sup w1C1 w2 C2 Pi ,t , PEVk ,t G G PWT ,l ,t , PEVk ,t
b) Wind Power Constraints
0 PWTt PWTt
(19)
s.t.
c) EV Charging Constraints
The charge constraint for each EV is defined as
Ek ,t Ek ,t 1 PEV k ,t t
(25)
(14)-(16),(19)-(21),(24)
3.3 Robust Counterpart
Too-high power of charging will damage the battery. In order to prolong the service life of the battery, the EV charging power needs to be constrained by its maximum for each EV as, 0 PEVn,t PEVnmax ,t
t
3.2 Robust Energy Management Model
electricity to the main power grid, and PWT jG,t and PEVnG,t
G
t
t , t , t , t 0
The robust solution is feasible with high probability. The function (26) represents the probability of violation (POV),
_____ PWTl G,t PWTl G,t PMT j ,t Pgrid ,t g l j ___ G 1+Lt PEVn,t PEVnG,t Pload ,t Pr m ,t m ,t t (21) n m V
(20)
PDE
g ,t
Ek ,t and Ek ,t 1 represent the current and the last status of the
(26)
k-th EV, is the charging efficiency which is usually assumed to be a constant value.
Where the parameter t represents the number of uncertainties at time t, and Pr {a b} denotes the probability of violation, and the function (27) provides a bound that is independent of the solution, which can measure the robustness of system, which explained specifically in (Bertsimas & Sim, 2004)
3. ROBUST OPTIMIZATION ALGORITHM 3.1 Robust Equal Conversion Based on the sets of uncertainties shown in Sections 2.1, the inequality constraints (17) can be transformed to, _____ G G PDE PWT PWT g l l ,t g ,t l , t PMT j , t Pgrid , t j ___ 1+Lt PEVnG,t PEVnG,t Pload ,t n
2 Pr m,t m,t t exp t mV 2 J t
4.1 Simulation Scene A period from 4:00 pm to 4:00 am is divided into 24 thirtyminute intervals. A duality theory is employed to transfer the model to a linear robust optimization model in Section 3.2. Lagrange relaxation algorithm, which is effective and easy to implement, is selected to solve the transformed dual problem.
N L F max PWTl G,t 1 Lt PEVnG,t n 1 l 1
s.t.
(27)
4. CASE STUDY
(22)
Let F represents the uncertain part,
PWTl G,t PWTl G,t PWTl G,t
4.2 Problem Description (23)
The microgrid system includes WT, DE, MT and EVs. The system is running in the grid-connected mode. Figure 2 is the initial status of MG, where the EVs are assumed to be charged in the periods of 18:30-21:30, when there is the highest residential load of the day (Xiang et al., 2014). In this case, the high load and low wind power lead to the increase of diesel generator’s output, which means increased operating cost. On
PEVt G PEVt G PEVt G The dispatch objective function is monotonically increasing, strictly convex and differentiable. According to the strong duality its dual problem is also feasible and bounded, and the objective values coincide. Therefore, the dual problem becomes: 477
IFAC CPES 2018 478 Tokyo, Japan, September 4-6, 2018
Ruifeng Shi et al. / IFAC PapersOnLine 51-28 (2018) 474–479
the other hand, during 23:00-2:00, when there is a lower basic load demand but with a high wind power and thus energy is wasted. Therefore, it is crucial to optimize the energy in the microgrid for uncertain turbine output and electric vehicle load.
in robust optimization result. Figure 4(a) shows the RO under the worst scenario (ROW), from which we can see the WT is full in use, the output of DE and MT are increased to meet the remaining load requirements, but there is no excess power providing to the main grid. On the contrary, Fig. 4(b) shows the RO under the best scenario (ROB), from which we can see DE, MT and EV almost stay at the low cost status, and the proportion of wind power is higher than in Fig. 4(a), even if the phenomenon of selling electricity from MG to the main grid has happened.
Fig. 2. Initial status of the MG. 4.3 Stochastic Optimization The stochastic optimization dispatch strategy is used and shows good performance in reducing peak load and fuel cost under a stable operation situation. As shown in Fig 3, EVs are charged in the off-peak hours with high wind power outputs, and diesel generator and transmission power are required to satisfy the power demand. But the uncertainty of predicted variables is not taken into consideration, and the dynamics and robust performance of the system is not optimal.
Fig. 4(a). ROW result.
Fig. 4(b). ROB result. As shown in Table 1, comparing ROW with SO, in order to meet the power balance, system need to increase the output of DE and MT, which led to more economic costs. C1 increases 48.0%, C2 increases 19.2%, and Ctotal increases 42%, and calculation by formula (26), RO has good performance in robustness and make the probability that the constraint is destroyed to be 0, which has a big gap between RO and SO in robustness. Simultaneously, it is not difficult to find that the results have a greater impact on both sides of the robust optimization interval. The disparity is caused by random factors of WTs and EVs, which directly affect the cost of DGs.
Fig. 3. Stochastic optimization result. 4.4 Robust Optimization For RO, the worst scenario means the less available wind generator outputs and more EV charging loads. Therefore, the diesel generator increases its output so as to meet the load demands. Figures 4(a) and 4(b) show the extreme phenomenon
478
IFAC CPES 2018 Tokyo, Japan, September 4-6, 2018
Ruifeng Shi et al. / IFAC PapersOnLine 51-28 (2018) 474–479
479
Table 1. Optimization results under the worst scenario, best scenario and non-robust scenario Type Unit ROB SO ROW
DE
MT
4274.5 5721.7 7812.9
3890.8 4656.8 5562.0
+ 𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 (kW) 18473.9 4292.7 15205.4 6191.8 12234.8 7141.8
WT
− 𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔
EV
C1
-116.5 -2.8 0
2564.4 3522.0 4500.4
4077.1 6272.6 9322.2
5. CONCLUSIONS Optimal load dispatch of microgrid is of great significance to reduce energy consumption, environmental pollution and user's electricity costs. In this paper, a multi-objective optimal dispatch model for microgrid is proposed. The proposed method takes the uncertainties included in the wind turbines and EVs into consideration simultaneously, and robust optimal model is designed to solve the problem under the worst scenario. Through duality theory, the hard-to-solve semiinfinite optimization problem is transformed into a linear programming problem that is easy to solve. And the RO has good performance in robustness, but it will improve system economics. According to different scenarios, this paper combines energy management and economic analysis to illustrate the application of robust optimization in energy management systems. Case study shows that the proposed method can help the decision maker to find the quantified economic operation scheme for the microgrid system. 6. ACKNOWLEDGEMENTS The authors would like to thank the National Natural Science Foundation of China (Grant Number 61203100) and the Fundamental Research Funds for the Central Universities (Grant Number 16MS42) for their financial supports with this research. REFERENCES Adhikari, A. (2011). Multi-objective operation management of a renewable MG (micro-grid) with back-up microturbine/fuel cell/battery hybrid power source. Energy, 36(11): 6490-6507. Aghaei, J., Nezhad, A.E., Rabiee, A., and Rahimi, E. (2016). Contribution of plug-in hybrid electric vehicles in power system uncertainty management. Renewable & Sustainable Energy Reviews, 59: 450-458. Bertsimas, D., and Sim, M. (2004). The price of robustness. Operations Research, 52(1): 35-53. Cardoso, G., Stadler, M., Bozchalui, M.C., Sharma, R., Marnay, C., Barbosa-Povoa, A., and Ferrao, P. (2014). Optimal investment and scheduling of distributed energy resources with uncertainty in electric vehicle driving schedules. Energy, 64(1): 17-30. Lin, B., and Tan, R. (2017). Estimation of the environmental values of electric vehicles in Chinese cities. Energy Policy, 104:221-229. Liu, D., Zhang, G., Huang, B., and Liu, W. (2016). Optimum electric boiler capacity configuration in a regional power 479
C2 (RMB) 125.4 156.5 186.6
Ctotal
POV
4202.5 6695.1 9508.8
一 100% 0%
grid for a wind power accommodation scenario. Energies, 9(3): 144. Lu, X., Zhou, K., and Yang, S. (2017). Multi-objective optimal dispatch of microgrid containing electric vehicles. Journal of Cleaner Production, 165: 1572-1581. Ma, Z., Zou, S., Ran, L., Shi, X., and Hiskens, I.A. (2016). Efficient decentralized coordination of large-scale plug-in electric vehicle charging. Automatica, 69(C):35-47. Mwasilu, F., Justo, J.J., Kim, E.K., Do, T.D., and Jung, J.W. (2014). Electric vehicles and smart grid interaction: A review on vehicle to grid and renewable energy sources integration. Renewable & Sustainable Energy Reviews, 34: 501-516. Pirouzi, S., Aghaei, J., Vahidinasab, V., Niknam, T., and Khodaei, A. (2018). Robust linear architecture for active/reactive power scheduling of EV integrated smart distribution networks. Electric Power Systems Research, 155: 8-20. Rahman, I., Vasant, P.M., Singh, S.M., Abdullah-Al-Wadud, M., and Adnan, N. (2016). Review of recent trends in optimization techniques for plug-in hybrid, and electric vehicle charging infrastructures. Renewable & Sustainable Energy Reviews, 58:1039-1047. Shi, R., Sun, C., Zhou, Z., Zhang, L., and Liang, Z. (2016). A robust economic dispatch of residential microgrid with wind power and electric vehicle integration. Control and Decision Conference. May.28-30, Yinchuan, China. (pp.3672-3676). IEEE. Soares, J., Vale, Z., Borges, N., Lezama, F., and Kagan, N. (2017). Multi-objective robust optimization to solve energy scheduling in buildings under uncertainty. International Conference on Intelligent System Application to Power Systems. Sep.17–21, San Antonio, TX. Tian, L., Shi, S., and Jia, Z. (2010). A statistical model for charging demand of electric vehicles, Power System Technology, 34(11): 127-130. Wei, W., Liu, F., Mei, S., and Hou, Y. (2014). Robust energy and reserve dispatch under variable renewable generation. IEEE Transactions on Smart Grid, 6(1): 369-380. Yue, X., Liu, J., Wei, Z., Cao, Y. and Ai, F. (2014). Robust model of microgrid energy optimization with uncertain renewable energy sources, Proceedings of Chinese Society for Electrical Engineering (Proceedings of CSEE), 34(19): 3063-3072. Zhang, D., Wang, J., Lin, Y., Si, Y., Huang, C., and Yang, J. (2017). Present situation and future prospect of renewable energy in China. Renewable & Sustainable Energy Reviews, 76:865-871.