Probabilistic Optimal Power Dispatch in MultiMicroGrids Using Heuristic Algorithms Nima Nikmehr
Sajad Najafi-Ravadanegh
Smart Distribution Grid Research Lab, Azarbaijan Shahid Madani University Department of Electrical Engineering Tabriz, Iran
[email protected]
Smart Distribution Grid Research Lab, Azarbaijan Shahid Madani University Department of Electrical Engineering Tabriz, Iran
[email protected] grid with a combination of multiply SSERs (including renewable energy sources like solar PV, wind turbine), energy storages, and loads. The Microgrid is operated in two gridconnected and isolated types [2]. From the microgrid energy management point of view, the economic scheduling of generation units, storage systems and loads is a crucial task where the optimization algorithms can be the most important issue that can be regarded as a major component of Distribution Management System (DMS), This management is carried out using the Microgrid Central Controller (MCC) by receiving/sending signals to local controllers. The application of multi-agent system on micro grids operation has been addressed in numerous works that makes the most benefits of system operations [3]. The economic dispatch optimization problem has been solved with different methods in literature. [4] uses PSO algorithm in grid-connected mode of microgrid and multi-objective optimization problem without considering sold and purchase power is regarded in in economic dispatch problem [5]. A stochastic energy schedule model for a MG with intermittent renewable energy sources and plug-in electric vehicles (PEVs) is proposed in [6] and the operation cost and power losses are minimized. Authors in [7] proposes a new control strategy for coordinated operation of networked microgrids in a distribution system. In order to enhance power quality and improve controllability of power flow, [8] presents an energy manager for energy storage system (ESS) in microgrids and by improving the energy efficiency and extending the life expectancy of ESS, satisfies the objective of energy manager work. The economic evaluation of a typical MG participating in a power market under hybrid electricity market policy has been analyzed in [9] and GA-based optimization method is applied to obtain optimum power and price of the MG. In [10] the system uncertainties are modeled with 2 point estimate method (2PEM). The optimization of operation costs and emission has been considered as multiobjective function in [11].
Abstract— Future distribution networks consist of some Micro grids (MGs) or Small Scale Energy Zones (SSEZs). In this paper the economic operation of SSEZs is formulated and solved as an optimization problem. A probabilistic model for Small Scale Energy Resources (SSERs) and load demand is used at each SSEZs to determine the optimal scheduling of microgrids with minimum operating cost. The power transaction between MGs and between MGs and the main is regulated based on the total operating cost and regarding the sold or purchase power either by microgrids or by main grid. The stochastically analysis of generated power with SSERs and their corresponding costs is determined considering optimization constraints and explained as PDF and CDF. The Imperialist Competitive Algorithm (ICA) and Particle Swarm Optimization (PSO) algorithm are applied to comparative study of the results as optimization algorithms. Based on the results, it is possible to determine the power demand and transaction between each SSEZs and the main grid. Besides, the results confirm that the power sharing between microgrids and main grid can decrease the operating cost of the smart distribution grids. Keywords: Microgrid, Power Dispatch, probablity, ICA, PSO
I.
INTRODUCTION
With rapid escalation in fossil fuel price as well as sharp increase in the capital cost of new central generating plant, there is a focused attention on alternate generating system with higher efficiency of energy use. Today, micro-grid, due to its major technological and regulatory innovation of its smallscale has less environmental impact, easy siting, high efficiency, enhanced system reliability and security, improved power quality, lower operating costs due to peak shaving, and relieved transmission and distribution congestion. Optimal operation and planning of future smart distribution grids is a challenging problem with many uncertainties. Based on market operation of MMGs the optimal scheduling of MMGs is an important topic that regulates the transaction the power between each MGs and main grid. Modern infrastructure of power systems, namely, smart grids is described in [1] . A microgrid is a section of the
In this paper with considering probabilistic environment, the optimal power dispatch problem is solved. The uncertainties are entered in load and generated powers by
978-1-4799-8315-5/14/$31.00© 2014 IEEE ١
[W/m2]. Rc is A certain radiation point, usually set to 150W/m2 . RSTD is Solar radiation in the standard conditions usually set to 1000 W/m2 . In this paper, the rated power of PVs has been considered 150kW.
renewable SSERs at presence emission cost function. The problem has been solved with imperialist competitive algorithm (ICA) and particle swarm optimization (PSO) algorithm. So, obtained results from optimal dispatch solution are shown in PDF or CDF forms. The power generation at each MG and main grid, the purchased and sold power by each MG and the power transaction between each MG and main grid are analyzed based on operation and maintenance cost. II.
III.
A. Modelling of Generated Power's Cost by Units The cost of primary energy often determines the cost of generated power by units. These technologies require only wind and sunlight and no other energy fuel. The cost of consumption of these energies is zero. So, their fuel cost are zero.
MODELING OF UNCERTAINTIES
The load power (Pl) absorbed at any load bus is uncertain and assumed to follow a normal distribution within each given interval. The probability density function of (Pl) based on mean ( P Pl ) and standard deviation ( V Pl ) values is given by [12]:
f ( Pl )
1 2S u VPl
exp(
( Pl PPl ) 2 ) 2 u V2Pl
MODELING OF COSTS
Fuel cells show great promise to be an important DG source of the future due to their many advantages, such as high efficiency. The efficiency of FC ( KFC,s ) in sample s depends on output power in same sample. With increasing the output power, the efficiency of FC will be lower. Fuel-power curve of FC is based on [15]. The cost of generated power by FC achieve from follow relation:
(1)
Where Pl is load consumption power.
PG ,W T ( v )
0 ° v v ci ° ®PWT ,r v r v ci ° °P ¯ WT ,r
Micro turbines (MTs) are small high-speed gas turbines. Unlike FC, the efficiency of MT increases with increase of supplies power. The cost function of generated power of MT has been calculated by (5):
(2)
v r d v d v co
CostCHP ,s BCHP ,s
Cost MT ,s BCHP ,s
Cost MT ,s u
(6)
Hrec ( KT ,CHP ,s Ke ,CHP ,s )
(7)
Kb
Where BCHP,s is Cost reduction of generated power by MT in sample s, because of using exhaust gas heat. H rec is heat recovery factor. KT ,CHP , Ke ,CHP and Kb are Total efficiency of CHP, electrical efficiency of MT and efficiency of boiler, respectively. In other hand, composition of (6) and (7) concluded (8):
0 d R d Rc R c d R d R STD
(5)
CHP plants will likely be at the heart of microgrid economics. A CHP system can potentially reaches an efficiency of up to 80 percent to 85 percent. The fuel cost of MT with CHP performance is as follows:
The power generated by a PV power system varies according to the solar radiation on the earth’s surface, which mainly depends on the installation site and the weather conditions. In this paper [14] irradiance is modeled by beta distribution function. The PV modules are tested at standard test condition (STC). The output power of the module can be calculated as follow:
PPV ( R )
C nl Punit ,s u L KMT ,s
Cost MT ,s
Where PG,WT(v) and PWT,r are generated power of wind turbine at speed v. Also vci, vco and vr are wind turbine parameters. Theses parameters are low cut, high cut and rated speed of wind turbine. Maximum value of generated power by WTs has been considered 250kW.
§ R2 · °PPV,r ¨ ¸ © R STD R c ¹ ° ° § R · ° ®PPV,r ¨ ¸ © R STD ¹ ° °P ° PV ,r °¯
(4)
In this paper, Cnl has been considered 0.76$/m3 and L value is 9.7kWh/m3 that these parameters describe Natural gas price value ($/m3) and low-hot value (kWh/m3), respectively. Punit,s is generated power of each unit in sample s.
0 d v d v ci or v co d v v ci d v d v r
C nl Punit ,s u L KFC ,s
Cost FC ,s
Wind speed differs in a wide range in a given geographic site. Power generated by WTs depends on the wind speed. The weibull distribution is used to represent the distribution for the wind speed for long-term planning purposes [13]. But the wind speed is prime energy source and must be converted into power based-on follow equation:
(3)
R STD d R
Cost CHP ,s
Cost MT ,s u ( 1
In this paper percent.
Where, PPV(R) is generated power by PV module. P PV,r describes rated power of PV module. R is Solar radiation
٢
Hrec ( KT ,CHP ,s Ke ,CHP ,s ) Kb
)
(8)
εrec is assumed 0.95. ηb is assumed 80
Fs,Pow = ¦Cost gen ,si Cost O & M ,s Cost ins
B. Operation and Maintenance (O&M) and Installation Costs of Units For the cost function of WT and PV units, only operation and maintenance (O&M) and installation cost have been considered. The cost of O&M (CO&M) for units is as follows:
K O & M u Punit ,s
CO & M ,unit ,s
i
( ¦Cost pur ,sm ¦Cost sell ,sm ) m
Cost gen ,si
K ins u Punit ,r
C O & M ,MT ,s C O & M ,FC ,s C O & M ,CHP ,s C ins ,MT C ins ,FC C ins ,CHP
(10)
m2
u Pbuy ,s ,m m 2
m2 z m
¦d
m
u Psell ,s ,m m 2
m2 z m
m
IV.
V.
(11) (12)
x x x x
(13)
(19)
¦P
gen ,si
i
¦ Pbuy ,sm
(20)
m
REVIEW OF PSO ALGORITHM
Initialization: The velocity and position vectors are initialized randomly. Update velocity: The velocity vector of the all particles is updated by using equation Position update: The position vector of the all particles is updated by using equation Memory update: Pbesti and gbest are updated.
B. ICA Algorithm Imperialist competitive algorithm is a new evolutionary optimization method that is inspired by imperialist competition [20]. Like other evolutionary algorithms, ICA starts with an initial population, which is called country and is divided into two types, colonies and imperialists, which together form empires. That is similar to chromosome in genetic algorithm and particle in particle swarm optimization algorithm. Every country could be defined as a vector with socio-political characteristics such as culture, language, and religion. Stages of our proposed algorithm are explained as
PROBLEM FORMULATION
OF=¦[Fs , Pow Fs , Em ]
(18)
A. PSO Algorithm The main idea of the PSO algorithm is inspired first by Kennedy and Eberhart [19] in 1995. The idea is suggested from offensive particles movement. PSO algorithm can be described as follows steps:
Proposed problem is a non-linear problem. Objective function includes generated power, purchased and sold power, O&M and installation cost. In this problem, the cost of power generation must be minimized. The objective function is as follows: Min :
i 1
(17)
At last, the optimization problem is minimized by PSO and ICA algorithms.
In above equations, Costpur,sm and Costsell,sm are purchased and sold powers cost of MG m in sample s respectively. Pbuy,s,m-m2 is purchased power that MG-m purchases power from MG-m2 and Psell,s,m-m2 is sold power by MG-m to MGm2 in sample s, respectively and m2 can be other MGs or external grid. parameters c and d related to purchased and sold powers prices and each MG has c and d coefficients related itself. The cost of transaction of powers between MGs and external grid has been described as follow: Cost pur ,ms Cost sell ,ms
j 1
Pl ,s ¦ Psell ,sm
m
Cost trans ,ms
9
(16)
OF is objective function which is summation of functions of FPow and FEm. FPow is related to cost of generated and transaction powers and cost of install and O&M costs, too. FEm is cost function of pollutants emission. Pgen,si is generated power by unit i in sample s. Function OF is optimized for each sample by ICA algorithm. Indeed FPow and FEm are a [1u s] function or matrix. The emission coefficients are explained in [18]. The total real power generation plus purchased power from MGs and external grid must balance the predicted power demand plus the sold power to MGs and main grid at any sample of PDF:
m
Cost sell ,sm
3
Fs,Em =¦ J j u (¦ Uij u Pgen ,si )
C. Modeling of Purchased and Sold Powers Costs In proposed method, all MGs are connected together and into main grid. So, each of them are able to inject power into other MGs and external grid. Because of this injection of power, MGs take money from other MGs and network. By selling power to MGs or main grid, the costs of MGs are reduced and this condition is economical for them but it be mentioned that their generated power is reduced. Also, if one of the MGs not be able to supplies own load demand, the MG can purchase electrical power first from other MGs and if other MGs not able to provide its load power, the MG can be supplies the lack of generated power from main grid. With this work, the costs of MG increase. The purchased and sold cost of MGs are described as follow:
¦c
C ins ,W T C ins ,PV
Cost ins
Where, Punit,r is rated power of each unit. Based-on (10) for each unit this cost is calculated based its installation cost coefficient (Kins). In [17] installation cost coefficients (Kins) of all units has been given.
Cost pur ,sm
C O & M ,W T ,s C O & M ,PV ,s
CostO & M ,s
In this paper based-on [16], the O&M cost coefficients (KO&M) of all units has been given. Also, Installation cost of units are calculated as follow:
C ins ,unit
m
Cost gen ,MT ,si Cost gen ,FC ,si Cost gen ,CHP ,si
(9)
(15)
(14)
s
٣
MG1
60
PSO data Normal pdf ICA data Normal pdf
Density
40 30
Density
50
follow: generating initial empires, assimilation, revolution, exchange between the best colony and imperialist, Imperialistic competition, elimination of powerless empire.
20
VI.
RESULTS
MG2
ICA data Normal pdf PSO data Normal pdf
40
20
10
In this section of paper, dispatch of power problem among loads of MGs considering pollutant effects has been tested on supposed network. Fig. 1 shows the structure of sampled network with 3 MGs. Each MG consists 3 micro sources in order to generate power. In this paper, has been used 500 samples for every generated powers by WT and PV units and load demand of each MG in given interval. Load demand of all MGs has been shown in Fig. 2.
0
0
200
50
400
600
800
Generated power (kw)
MG3
200
1000
400
600
Generated power (kw)
800
1000
PSO data Normal pdf ICA data Normal pdf
40
Density
30 20 10 0
200
400
600
Generated power (kw)
800
1000
Fig.3. Generated power's PDF by ICA and PSO in three MGs EXTERNAL NETWORK
G
In order to show purchased powers by MG1 from MG2, MG3 and main grid, Fig. 4 is used.
FC PCC
Micro Grid Control Center (MGCC)
PV CHP
400
(a)
100
100
LC
LC
0 -200
FC
WT
0
200
400
600
800
0 -200
1000
500
PV
MT
Density
WT MG1
(c)
MG2
300
ICA data Normal pdf
400
0
200
400
600
800
1000
Purchased power from MG3 by MG1 (kw)
Purchased power from MG2 by MG1 (kw)
(d)
ICA data Normal pdf
200
300
Density
CHP
ICA data Normal pdf
200
200
LC
(b)
300
Density
LV Substation
400
ICA data Normal pdf
300
Density
MG3
200
100
100
Fig. 1. Structure of network with 3 MGs
0
MG1 MG2 MG3
1200
200
400
600
1000
0 -200
0
200
400
600
800
100
Total purchased power by MG1 (kw)
Differential value of purchased and sold powers describes transaction power between MG and other grids. So, Fig.9 shows PDF of purchased, sold and transaction powers of MG3.
800
200
600
250
(a)
PSO data Normal pdf ICA data Normal pdf
150
400
100
200
100 50
0
100
150
200
250
300
350
400
450
0
500
Sample
Net transaction power (kw)
1000
Fig.2. Consumption power of MGs
PDF of generated power of MGs have been shown in Fig. 3. In this figure, PDF of generated power which has obtained by ICA algorithm has been compared with obtained results of PSO. Since all MGs connected together and main grid, each MG can buy electrical power from external grid when the MG unable to provide the own load demand from its generated power and transaction power between other MGs. Also, MG with surplus power, can sell this surplus electrical power to other MGs and if they cannot be able to purchase power, the MG sell its surplus power to external grid. In other word, priority in purchase or sell power with MGs and then with main or external grid.
200
400
600
800
Purchased power by MG3 (kw)
(c)
0
1000
60
ICA data
50 500
Density
50
0 -500
-1000
PSO data Normal pdf ICA data Normal pdf
150
50
0
(b)
200
Density
1000
0
800
Fig.4. PDF of purchased powers by MG1 obtained by ICA
Density
Consumption power (kw)
0 -200
Purchased power from external grid by MG1 (kw)
1400
40
0
(d)
200 400 600 800 Sold power by MG3 (kw)
1000
PSO data Normal pdf ICA data Normal pdf
30 20 10
0
100
200
300
400
Net transaction power Sample
500
0
-500 0 500 1000 Net transaction power of MG3 (kw)
Fig.5. PDF of purchased, sold and transaction powers by MG3
Each MG emits some pollutant into air. This pollution is achieved from generated powers by every units of MGs that consists NOx, SO2 and CO2. In Fig. 6 the mass of pollutant in each MGs has been shown. Sum of the three pollutants which was mentioned above, form the pollutant emission of MGs.
۴
MG1
50
ICA data Normal pdf PSO data Normal pdf
Density
30
MG2
30
20
powers. The probabilistic analysis about this problem has a good prospect in planning studies, unit commitment problem and etc.
PSO data Normal pdf ICA data Normal pdf
40
Density
40
20
10
10
0
0 0
0.2
0.4
0.6
0.8
1
1.2
0
0.2
MG3
0.6
0.8
1
1.2
1.4
Mass of pollution (Kg/h)
Mass of pollution (Kg/h) 40
0.4
TABLE II. Statistical analysis of emission mass and related cost of MGs Number of Description Mean value Mean value MG ( P ) of cost ( P ) of power
ICA data Normal pdf PSO data Normal pdf
Density
30 20
MG1
10 0
0
0.2
0.4
0.6
Mass of pollution (Kg/h)
0.8
MG2
Fig. 6. PDF of emission mass of MGs
In order to more explanation about power costs of MGs and O&M costs of units, Table I is used. In this table the mean value of generated, purchased and sold powers and O&M costs are described.
MG3
TABLE I. Statistical analysis of power costs Type of cost
Cost of Generated Power Cost of Purchased Power Cost of Sold Power
Cost of O&M
Description
MG1 MG2 MG3 Network MG1 MG2 MG3 MG1 MG2 MG3 Unit1 Unit2 Unit3 MG1 Unit4 Unit5 Unit6 MG2 Unit7 Unit8 Unit9 MG3
Mean value ( P ) of cost
Mean value ( P ) of
(USD/h) ICA
power (USD/h) PSO 27.61 95.45 50.66 13.72 23.82 8.96 28.71 11.81 10.45 18.44 7.98 24.37 9.46 41.80 9.11 24.68 2.25 36.03 8.12 23.27 2.16 33.56
26.28 92.45 49.50 168.23 22.62 10.67 27.29 11.63 10.31 19.89 7.98 24.84 9.46 42.28 9.11 23.42 2.26 34.79 8.12 25.19 2.15 35.47
Emission of all pollutant (kg/h) Emission cost of all pollutant (USD/h) Emission of all pollutant (kg/h) Emission cost of all pollutant (USD/h) Emission of all pollutant (kg/h) Emission cost of all pollutant (USD/h)
(USD/h) ICA
(USD/h) PSO
0.417
0.409
0.302
0.297
0.585
0.600
0.731
0.732
0.304
0.301
0.900
0.880
VII. CONCLUSION In this paper the optimal power dispatch of MGs for an hour period is proposed and discussed at future distribution grids. It is shown that MG can be defined as SSEZ at market operation of the smart grid. The optimal power dispatch problem is solved and compared using by PSO and ICA considering power and load uncertainties.Based on the mean value, PDF and CDF of each random variable, the results is analyzed and illustrated tabular and graphically. Regarding the results the optimal power sharing between MGs and the main grid can lead to lower operation cost at future smart distribution grids with interconnected cooperation of MGs. Based on the results it is possible to regulate the time-varying demand and power transaction between each MG and the main grid under technical, economical and environmental constraints. REFERENCES [1]
[2]
[3]
In Table II the mean value and standard deviation of emission of each pollutant substances and related costs for each MG is described.
[4]
In this paper, distribution of power has been solved with considering pollutants emission in form of Probability Distribution Function for some parameters of power generation and load consumption. Then, based on generated and distributed power between MGs and main or external grid, the cost function of each MGs achieved. Proposed example solved generated and distributed power problem at presence load demand uncertainties and probabilities of generation parameters. The output result expresses of each state of total cost, any states of generated and interaction
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