Optimal operation of distributed generations in micro ... - IEEE Xplore

IET Renewable Power Generation Research Article

Optimal operation of distributed generations in micro-grids under uncertainties in load and renewable power generation using heuristic algorithm

ISSN 1752-1416 Received on 24th October 2014 Revised on 31st May 2015 Accepted on 8th June 2015 doi: 10.1049/iet-rpg.2014.0357 www.ietdl.org

Nima Nikmehr 1, Sajad Najafi-Ravadanegh 2 ✉ 1

Smart Distribution Grid Research Lab, Azarbaijan Shahid Madani University, Tabriz, Iran Smart Distribution Grid Research Lab, Department of Electrical Engineering, Azarbaijan Shahid Madani University, Tabriz, Iran ✉ E-mail: [email protected]

2

Abstract: Microgrid (MG) could allow renewable and clean resources to penetrate into a controllable utility and achieve maximum utilisation of existing energy and demand-side management. This study proposes a new paradigm for distribution system operation considering MG conception. This study is focused on probabilistic analysis of optimal power dispatch considering economic aspects in MGs environment with technical constraints. In this study the economic operation of small scale energy zones is formulated and solved as an optimisation problem. A typical MG consists wind turbine (WT), photo voltaic (PV), micro turbine, fuel cell, combined heat and power and electric loads. Fluctuation behaviour of loads and generated power by WTs and PVs are caused complexity in proposed problem. Cost function includes generated powers by units, power transaction between MGs and main grid, operation and maintenance cost of resources and cost of pollutants emission. Considering MG concept in smart grids, the balance between supply-demand is secured through power exchanging between MGs and main grid, so that the value of objective function be minimised. The imperialist competitive algorithm is applied to solve proposed problem and obtained results are compared with Monte Carlo simulation method.

Nomenclature Y X α, β v PG,WT Pr,WT Vci Vco vr Ppv R Rc RSTD Pr,PV Pl μPl σPl CostMT,s CostFC,s CostCHP,s Fs,Pow Fs,Em Ploss,s L Punit,s ηe,MT,s ηb Cnl BCHP,s εrec

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Vector of uncertain output variables. Vector of uncertain input variables. Shape and scale parameters of weibull distribution function. Wind speed [m/s]. Generated power by wind turbine [kW]. Rated power of wind turbine [kW]. Wind turbine cut-in speed [m/s]. Wind turbine cut-out speed [m/s]. Wind turbine rated speed [m/s]. Generated power by PV [kW]. Solar irradiance [W/m2]. A certain radiation point, usually set to 150 W/m2. Solar radiation in the standard conditions usually set to 1000 W/m2. Rated power of PV [kW]. Consumption power [kW]. Mean value of consumption power. Standard variation of load power. Cost of generated power by MT in sample s [USD/h]. Cost of generated power by FC in sample s [USD/h]. Cost of generated power by CHP in sample s [USD/h]. Related cost to power in sample s [kW]. Related cost to emission in sample s [kW]. Network losses at sample s [kW]. Natural gas low-hot value [kWh/m3] and is 9.7. Generated power in sample s by each unit [kW]. Electrical efficiency of MT. Boiler efficiency and is 0.8. Natural gas price [USD/m3] and is 0.76. Cost reduction of MT at sample s. Heat recovery factor and is 0.95.

CO&M,unit,s Operation and maintenance cost of each unit at sample s [USD/h]. KO&M,unit Operation and maintenance cost coefficient of each unit. Installation cost of each unit [USD/h]. Cins,unit Installation cost coefficient of each unit. Kins,unit Rated power of each unit [kW]. Pr,unit Costbuy,sm Cost of purchased power by MG m in sample s [USD/h]. Costsell,sm Cost of sold power by MG m in sample s [USD/h]. Costtrabs,sm Cost of transaction power by MG m in sample s [USD/h]. Costgen,si Generation Cost of unit i in sample s [USD/h]. c, d Cost of purchased and sold power coefficients [USD/ kWh]. Generated power of unit i at sample s [kW]. Pgen,si Purchased power by MG m from MG m2 in sample s Pbuy,s, [kW]. m-m2 Psell,s,m-m2 Sold power by MG m to MG m2 in sample s [kW]. Bij, Bi0, B00 Loss coefficients. Emission factor of pollutant j by unit i. ρij Price coefficient of pollutant j. γj

1

Introduction

Modern infrastructure of power systems, namely, smart grids is described in [1, 2]. The upgrading of power system towards a smart grid is being developed to improve reliability, facilitate the integration of different types of renewable energies, and improve load management. In these grids, in presence of renewable energy sources, there is bi-directional flow of power in distribution level. Beside, because of new advances in information technology and entrance of these technology in power systems, flow of information and data is bi-directional [3]. One of the important concept in smart grids is microgrids (MGs). With considering this concept, the control and energy management of future networks will be comfortable and easy [4]. The micro-grid control centre

IET Renew. Power Gener., 2015, Vol. 9, Iss. 8, pp. 982–990 & The Institution of Engineering and Technology 2015

(MGCC) [5] plays an important role for optimal power generation dispatch and unit commitment and by arranging the active and reactive power set points for the following day minimises various technical, environmental, and economical objectives. Most works about MG operation problems based on deterministic analysis [6, 7]. In some papers, MG operation and planning problems are analysed under intermittent behaviours of renewable energy resources and the problem is solved using stochastic methods [8, 9]. A stochastic energy schedule model for a MG with intermittent renewable energy sources and plug-in electric vehicles is proposed in [8] and the operation cost and power losses are minimised. Wang et al. [10] propose a new control strategy for coordinated operation of MGs in a distribution system. To enhance the power quality and improve controllability of power flow, Tran and Khambadkone [11] present an energy manager for energy storage system (ESS) in MG and by improving the energy efficiency and extending the life expectancy of ESS, satisfies the objective of energy manager work. In [12] with considering uncertainties for DG units output and load consumption, a stochastic bidding strategy of MG in a joint day-ahead market of energy and spinning reserve service is discussed. The economic evaluation of a typical MG participating in a power market under hybrid electricity market policy is analysed in [13] and GA-based optimisation method is applied to obtain optimum power and price of the MG. In [14] optimal size of battery energy storage based-on operation management is determined using improved bat algorithm which is used to perform least cost dispatches. A linear programming model is presented in [15] to choose the optimal system capacities and operation schedule for a MG. Authors in [16] using particle swarm optimisation (PSO) algorithm, reduce the costs of MGs with controllable loads and battery storage by selling stored energy at high prices and shave peak loads of the larger system. The great penetration of wind energy and photo voltaic (PV) module in power networks has increased the uncertainty of power system operation and management. This uncertainty affects both the long and medium term system planning, and the day-ahead operation. This is why the importance of probabilistic tools for power system analysis is increasingly growing. For the daily operation, an adequate assessment of the system variables may lead to a better management of congestions and other important advantages. All MGs are in interconnected mode and MGs are linked to main grid. It should be mentioned that, in this paper, the duty of each MG is create balance between supply and demand. Considering MG concept in smart grids, the balance between generation and consumption is secured through power exchanging between MGs as well as main grid so that the total cost of power generation in each MG as well as the total cost of power exchanging between MGs and main grid be optimised. In [17] the necessity of extension of large scale power distribution system to a number of MGs to facilitate powerful control and operation infrastructure in future distribution systems has been discussed based on the IEEE Std 1547.4. Moreover, in [18] the advantages of multi-MGs from the economic operation point of view for future smart distribution systems are analysed, extensively. In [19] to improve the system operation performance and controllability a multiobjective optimal power flow algorithm is applied in MMGs based on interline power flow controller. In [20, 21] a distributed power management scheme is used in interlinking independent MGs at different voltages and frequencies. The conventional droop method is applied to avoid fast communication links and control of the sources of each MG. The multi-level clustering power systems concept is used in [22] to enables DERs to actively participate in grid control. Using multi-level control strategy the power dispatch, exchanged power and frequency control can be automatically managed. Optimisation model of economic operation is based on the price difference of different uses and time sequential weight, to get the non-cooperative optimal operation mode of each MG under participation of energy storage [23]. Management of the MG and the central production unit by one entity is studied in [24]. By using two models the interaction of energy services provider, the entity managing a number of MGs and the electricity market are analysed.

Hence, the proposed problem in the paper is an optimisation problem and the defined objective function is minimised by imperialist competitive algorithm (ICA). To assurance of accuracy of obtained results by ICA, the same problem is solved by Monte Carlo simulation (MCS), again. Hence, the contribution of the paper can be represented as below, briefly (i) In this paper considering uncertainties in load and generated powers by SSERs, the optimal power dispatch problem is solved. Hence, to model uncertainties, input data such as load of each MG and generated power by DG units are described in form of PDF. (ii) A framework for interconnected multi-MGs power dispatch at smart distribution grids is proposed. (iii) A heuristic algorithm is applied as optimisation algorithm to solve the problem and MCS is used to compare the results.

2

Proposed MG structure

The microgird normally manage energy and control the power and voltage itself, and may be isolated from the power system or interconnected to the power system at one point. In this paper the configuration of MG is considered as Fig. 1. There is a single point of connection to main grid called point of common coupling. LC is the local controller associated with units/load. Each LC receives its set points from MG central controller. The MGCC has a number of crucial functions and can be seen as the interface between the MG and the main distribution network. MGCC optimises the MG operation based on distributed generator sources, forecasted wind speed, forecasted solar irradiation, forecasted loads and operation policies and sends dispatch signals to the LCs.

3 Probabilistic modelling of power resources and load in MGs 3.1 Modelling of uncertainties in renewable power generation units The power outputs of renewable energy resources (RERs) depend on the availability of the primary resources such as wind speed, solar irradiation etc. The generated power by the wind turbine (WT) depends on the wind speed. Wind speed varies every minute,

Fig. 1 Network structure with three MGs

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hour, day and season of the year, which highlights the importance of a probability model. The weibull distribution is used to represent the distribution for the wind speed for long term planning purposes [25]. Weibull probability distribution function (PDF) is as follow: ⎧ 
 
v b−1 v b ⎨b v≥0 × × exp − fv (v) = a a a ⎩ 0 otherwise

r,WT

CostMT,s =

(1)

Since the simulated wind speed was generated using (1), the real power generation by WT can be obtained based on (2). The real power is as follow: ⎧ 0 ⎪ ⎪ ⎪ ⎨ v2 − v2ci PG,WT (v) = Pr,WT 2 ⎪ vr − v2ci ⎪ ⎪ ⎩P

Micro turbines (MTs) are small high-speed gas turbines. Unlike FC, with increasing the power generation in MT, the efficiency of MT increases. The cost function of generated power of MT is calculated by (6):

CostCHP,s = CostMT,s − BCHP,s (2) BCHP,s = CostMT,s ×

vr ≤ v , vco

Maximum value of generated power by each WT is considered 250 kW. The generated power by a PV module 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 irradiance is modelled by beta distribution function [26]. The PV modules are tested at standard test condition. The output power of the module can be calculated as follow: ⎧   R2 ⎪ ⎪ ⎪ P 0 ≤ R ≤ Rc ⎪ r,PV R R ⎪ ⎨  STD c PPV (R) = R ⎪ Rc ≤ R ≤ RSTD Pr,PV ⎪ ⎪ R ⎪ STD ⎪ ⎩ Pr,PV RSTD ≤ R

  1 (h − he,CHP,s ) CostCHP,s = CostMT,s × 1 − rec T ,CHP,s hb

4.2

Operation and maintenance (O&M)

Another cost of units which is related to their generated power is O&M cost. This cost with a coefficient (KO&M) for each unit can be described as CO&M,unit,s = KO&M,unit × Punit,s

(4)

Cost modelling of MG components Modelling of generated power cost of units

The cost of primary energy often determines the cost of generated power by units. The WTs and PV technologies require only wind and sunlight and no other energy fuel. The cost of consumption of these energies is zero. Hence, their fuel cost are zero. Fuel cells (FCs) 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 (ηFC,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 [13]. The cost of generated power by FC obtains from following relation: CostFC,s =

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(9)

(10)

Modelling of uncertainty in consumption load

  1 (P − mPl )2 exp − l f (Pl ) = √



2 × s2Pl 2p × sPl

4.1

(8)

(3)

The behavioural patterns of different energy consumers caused variations in load demand in each MG. These variations can be obtained by statistical analysis. Consequently, demand load varies continually with a high degree of uncertainty. In this paper load demand is considered as a normal distribution with mean value μ and standard deviation σ. The normal distribution is defined as follow [27]:

4

1rec (hT,CHP,s − he,MT,s ) hb

(7)

where BCHP,s is cost reduction of generated power by MT in sample s, because of using exhaust gas heat. On other hand, composition of (7) and (8) conclude (9):

In this paper, the rated power of each PV is considered 150 kW. 3.2

(6)

A combined heat and power (CHP) system can potentially reaches efficiency up to 80 to 85%. The fuel cost of MT with CHP performance is as follows:

0 ≤ v ≤ vci or v ≥ vco vci , v , vr

Cnl Punit,s × L hMT,s

Cnl Punit,s × L hFC,s

In (10), KO&M for each component of MGs is described in Table 1. The installation cost is constant cost in any of time and is calculated by rated power of each unit. The installation cost is as follow: Cins,unit = Kins,unit × Pr,unit

4.3

Modelling of purchased and sold powers cost

In proposed method, all MGs are connected together and into main grid. Hence MGs 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 reduce and this condition is economical for them but it should be mentioned that their existing power is decreased. Moreover, if one of the MGs not be able to supply 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 provide the lack of generated power from main grid. With this work, the cost of MGs is increased. The MGCC may purchase additional energy from the main grid and other MGs or sell excess energy back to the network and other MGs. Since it is not reasonable for a MG to purchase and sell energy on the market at the same time or sample, we have the following constraints to purchased and sold powers: 

(5)

(11)

sm sm sm − Plsm . 0 ⇒ Pbuy . 0, Psell =0 if Pgen sm sm sm sm if Pgen − Pl , 0 ⇒ Pbuy = 0, Psell . 0

(12)

IET Renew. Power Gener., 2015, Vol. 9, Iss. 8, pp. 982–990 & The Institution of Engineering and Technology 2015

Table 1 Characteristics of generation units MG number

1

Unit type minimum value of generated power, kW maximum value of generated power, kW O&M cost, $/kWh installation cost, $/kW

2

PV

CHP

WT

WT

MT

FC

PV

CHP

FC

0 150 0.1095 3176.9

50 450 0.00587 1772.3

0 250 0.1095 1906.2

0 250 0.1095 1906.2

50 450 0.00587 1588.5

30 200 0.00419 4447.7

0 150 0.1095 3176.9

50 450 0.00587 1772.3

30 200 0.00419 4447.7

and (21):

The purchased and sold costs of MGs are described as follow: NW

Costbuy,sm =

cm−m2 × Pbuy,s,m−m2

MG1 MG2 ⎡ MG1 0.00 0.16 MG2 ⎢ ⎢ 0.16 0.00 c= ⎢ MG3 ⎣ 0.18 0.17 NW 0.20 0.20

(13)

m2=1,2,...;m2=m

NW

Costsell,sm =

3

dm−m2 × Psell,s,m−m2

(14)

m2=1,2,...;m2=m

NW ⎤ 0.20 0.20 ⎥ ⎥ ⎥ 0.20 ⎦

0.18 0.17 0.00 0.20

(20)

0.20

MG1 MG2 MG3 ⎡ MG1 0.00 0.16 0.18 MG2 ⎢ ⎢ 0.16 0.00 0.17 d= ⎢ MG3 ⎣ 0.18 0.17 0.00 NW 0.20 0.20 0.20

Based on Fig. 1 each MG consist three units. Hence, (13) and (14) have three sentences separately for each MG. For example (13) and (14) in MG1 are as follow: Costbuy,s1 = cMG1−MG2 × Pbuy,s,MG1−MG2

MG3

NW ⎤ 0.20 0.20 ⎥ ⎥ ⎥ 0.20 ⎦

(21)

0.20

Table 1 shows some mentioned characteristics of MGs [28, 29].

+ cMG1−MG3 × Pbuy,s,MG1−MG3

(15)

+ cMG1−NW × Pbuy,s,MG1−NW

5

Costsell,s1 = dMG1−MG2 × Psell,s,MG1−MG2 + dMG1−MG3 × Psell,s,MG1−MG3 + dMG1−NW × Psell,s,MG1−NW 

Problem description

Proposed problem is a non-linear problem. Objective function includes generated power, purchased and sold power, O&M cost and cost of pollutants emission. The objective function is as follow:

(16)

Objective function:OF =



[Fs,Pow + Fs,Em ]

(22)

s

The cost of transaction of powers between MGs and external grid is described as follow: Costtrans,sm = Costbuy,sm − Costsell,sm

Fs,Pow =

i

+(

(17)

⎡

0.00 MG1 MG2 ⎢ ⎢ cMG2−MG1 c= . ⎢ .. .. ⎢ ⎣ . NW cNW−MG1

MG2 cMG1−MG2 0.00 .. . cNW−MG2

Costgen,si + CostO&M,s



Costbuy,sm −



m

(23) Costsell,sm )

m

Costgen,si = Costgen,MT,si

Transaction cost coefficient between MGs and MGs-network can be described as follow: MG1



(24)

+ Costgen,FC,si + Costgen,CHP,si CostO&M,s = CO&M,WT,s + CO&M,PV,s

...

NW

... ... .. . ...

cMG1−NW cMG2−NW ⎥ ⎥ ⎥ .. ⎥ ⎦ . 0.00

⎤

d = [c]T

(18)

j=1

(19)

In this paper, the value of c and d for each MG are considered as (20)

(25)

+ CO&M,MT,s + CO&M,FC,s + CO&M,CHP,s   3 9 gj × rij × Pgen,si Fs,Em =

(26)

i=1

Objective function is sum of the functions of generation cost, transaction powers, O&M cost and cost function of pollutants emission. In presented objective function, the installation cost is not considered, because in operation problems mentioned cost is less applied and considered in planning problems. The emission coefficients are explained in Table 2 [29].

Table 2 Emission factors of pollution emissions Pollutant substance NOx SO2 CO2

γ, USD/kg

ρCHP, kg/kWh

ρMT, kg/kWh

ρFC, kg/kWh

ρPV, kg/kWh

ρWT, kg/kWh

10.0714 2.3747 0.0336

0.00010 0.000007 0.001370

0.00003 0.000006 0.001078

0.00044 0.000008 0.001596

0 0 0

0 0 0

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The proposed problem is subjected to the following equality and inequality constraints: The generated power by each generator must be within its lower and upper operating limits. It may mathematically formulated by si si si , Pgen , PMax,gen PMin,gen

(27)

Moreover, the inequality constraints for purchased and sold powers are as follow:

concept to create balance between supply and demand Pl,s + Ploss,s =

i

(28)

sm sm sm , Psell , PMax,sell PMin,sell

(29)

As it was mentioned before, in this paper the authors have used MG



Pbuy,sm −

m



Psell,sm

(30)

m

Ploss,s is the transmission loss of the system in sample s and it is calculated using power flows coefficients by the following formula: Ploss,s =

i=1 j=1

sm sm sm PMin,buy , Pbuy , PMax,buy

Pgen,si +

Pgen,si Bij Pgen,sj +



B0i Pgen,si + B00

(31)

i=1

The economic operation of multi-MGs is formulated as an optimisation problem. A probabilistic modelling of both SSERs and load demand at each MG is done to determine the optimal economic operation of each MG with minimum cost of cost function based on the power transaction between the MGs and main grids.

Fig. 2 Flowchart of implementation of ICA on probabilistic optimal power dispatch problem

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The proposed problem is formulated as follow: Y = f (X )

(32)

The input data (X) and output data (Y) are describe by PDF in probabilistic analysis. Input vector (X) includes load demand and generated power by renewable power generation units. Output variables includes generated powers by MT, CHP and FC units, purchased and sold powers, cost of power generation in each MG, cost of purchased and sold powers, mass of emission in MGs and their related emission cost as well as power losses in network X = [Pl , PG,WT , PPV ] Y = [Pgen,MT , Pgen,CHP , Pgen,FC , Costgen , Costbuy , Costsell , CostO&M , Ploss , . . . ]

(33) (34)

Fig. 3 Load demand in MGs based on normal PDF a Related to MG1 b Related to MG2 c Related to MG3

6

Brief review of ICA

ICA is an evolutionary optimisation method that is inspired by imperialist competition [30]. 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 PSO 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 follow: generating initial empires, assimilation, revolution, exchange between the best colony and imperialist, Imperialistic competition, elimination of powerless empire. Implementation steps of solving probabilistic optimal dispatch problem with ICA, graphically is shown as flowchart in Fig. 2.

7

Fig. 4 PDF of generated power in three MGs a Related to MG1 b Related to MG2 c Related to MG3

Discussion and results

In this section of paper, dispatch of power problem among loads of MGs considering pollutant effects is tested on supposed network. Each MG consists 3 μ sources to generate power. In this paper, 500 samples is used for every input data (X) in given interval. Load demand of all MGs is shown in Fig. 3 based on normal PDF. One of the important output of vector Y in (34) is generated power in each MG. In a MG sum of the generated powers by micro sources

Fig. 5 PDF of purchased powers by MGs

Fig. 6 PDF of sold powers by MGs

a Related to MG1 b Related to MG2 c Related to MG3

a Related to MG1 b Related to MG2 c Related to MG3

IET Renew. Power Gener., 2015, Vol. 9, Iss. 8, pp. 982–990 & The Institution of Engineering and Technology 2015

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Fig. 7 Purchased/sold powers by MG1 from/to other MGs and main grid Fig. 9 PDF of operation cost of MGs a Related to MG1 b Related to MG2 c Related to MG3

Fig. 8 PDF of generation cost in MGs a Related to MG1 b Related to MG2 c Related to MG3

within the same MG determine the total power generation of the MG. Power generation in MGs are shown in PDF form in Fig. 4. In this figure, PDF of generated power which has obtained by ICA algorithm is compared with MCS. 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 traded power with other MGs. Moreover, MG with surplus power can

sell the surplus electrical power to other MGs and if same MGs not be able to purchase power, the MG sells its surplus power to external grid. In other word, priority in purchasing or selling power with MGs and then with main grid. In Figs. 5 and 6 the PDF of total purchased and sold powers are shown and obtained results by two methods are compared together. Total purchased power by MG1 which has been shown in PDF form in Fig. 5 is sum of the purchased powers from MG2, MG3 and main grid. Similarly, this fact is there for sold power. The purchased/sold powers by MG1 from/to other MGs and main grid is shown in Fig. 7 for each sample. After obtaining generated power in MGs, the cost of power generation in MGs can be shown in PDF form. The generation cost of MGs are plotted in Fig. 8. Overall, the operation cost of MGs that equals with power generation cost plus purchased power cost minus cost of sold power, are displayed in Fig. 9. It should be mentioned that all above results have been obtained without considering network losses. To see the loss effects on proposed problem, obtained results in first scenario (without network losses) is compared with results in second scenario (with losses) in Table 3. In Table 3, only the mean value of vector Y is used to show results. The detailed results of problem implementation with ICA and MCS methods are described in Table 3. The PDF of network losses is displayed in Fig. 10. Table 4 shows the comparison and advantages of ICA algorithm in compared of MCS method.

Table 3 Statistical analysis of powers and their related cost Type of analysis

MG

Type

μ of power/cost by ICA without losses

μ of power/cost by MCS without losses

μ of power/cost by ICA considering losses

μ of power/cost by MCS considering losses

power generation/ cost of generation

MG1

power generation, kW cost of generation, USD/h power generation, kW cost of generation, USD/h power generation, kW cost of generation, USD/h purchased power, kW purchased power cost, USD/h purchased power, kW purchased power cost, USD/h purchased power, kW purchased power cost, USD/h sold power, kW sold power cost, USD/h sold power, kW sold power cost, USD/h sold power, kW sold power cost, USD/h

414.57 25.08 438.79 82.21 450.75 45.22 144.01 28.08 225.45 43.02 197.16 38.39 55.14 9.80 47.93 8.39 53.31 9.65

425.41 25.90 445.88 83.80 442.02 44.34 137.95 26.89 221.60 42.86 201.87 39.28 59.93 10.69 50.68 9.03 49.29 9.01

511.14 34.23 588.85 116.42 575.39 63.05 102.31 19.71 161.24 30.69 149.39 28.83 70.01 12.81 68.28 12.53 65.18 12.00

505.98 34.23 590.63 116.80 580.89 63.96 108.91 20.98 159.01 30.22 144.81 27.92 71.45 12.99 67.83 12.46 66.11 12.20

MG2 MG3 purchased power/ cost of purchase

MG1 MG2 MG3

sold power/cost of sell

MG1 MG2 MG3

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Fig. 10 PDF of network losses Fig. 12 PDF and CDF of total emission mass and cost for MG3 Table 4 Comparison of ICA and MCS methods for operation cost, objective function and computation time Method

ICA MCS

Operation cost, USD/h

Objective function

With losses

Without losses

With losses

Without losses

255.59 256.46

233.66 234.37

299.38 300.25

277.07 277.25

a PDF of total mass of pollutions related to MG3 b PDF of total emission cost related to MG3 c CDF of total mass of pollutions related to MG3 d CDF of total emission cost related to MG3

Computation time, s

306 5421

In addition to ICA and MCS methods, another evolution algorithm, namely, particle PSO is used to show the accuracy of obtained results. After executing problem by PSO, the value of objective function was equal to 299.99 considering network losses. The time running of problem by PSO is 293 s. Each MG emits some pollutant into air. This pollution is achieved from generated powers of MGs that consists NOx, SO2 and CO2. In Fig. 11, the mass of pollutant in MGs 1 and 2 is shown in form of PDF and for MG3 the PDF and cumulative distribution function of emission is displayed in Fig. 12. Besides in Figs. 11 and 12 the emission costs are shown. In Table 5 the mean value of emission based on pollutant substances and related costs for each MG are described. In Fig. 13, obtained PDF for objective function, which is optimised by ICA, without considering losses is shown.

In above figure, the objective function is sum of the functions of generation cost, transaction cost, O&M cost and cost function of pollutants emission. To achieve accurate results, the probabilistic framework is applied on proposed problem. As it has been mentioned, for each uncertain variables, 500 samples has been applied for determined interval. The probabilistic analysis will increase the complexity of the optimisation process severely, but the cost function values

Table 5 Statistical analysis of pollutant emission and emission costs MG

Type of pollutant

Type

μ of mass/cost by ICA without losses

μ of mass/cost by MCS without losses

μ of mass/ cost by ICA with losses

μ of mass/ cost by MCS with losses

MG1

NOx

mass, kg cost, USD/h mass, kg cost, USD/h mass, kg cost, USD/h mass, kg cost, USD/h mass, kg cost, USD/h mass, kg cost, USD/h mass, kg cost, USD/h mass, kg cost, USD/h mass, kg cost, USD/h

0.0383

0.0400

0.0528

0.520

0.355

0.368

0.489

0.482

0.0005

0.0005

0.0007

0.0007

0.0011

0.0012

0.0015

0.0015

0.128

0.133

0.176

0.173

0.0040

0.0041

0.0055

0.0054

0.0501

0.0517

0.0712

0.0713

0.464

0.478

0.659

0.660

0.0013

0.0013

0.0019

0.0019

0.0029

0.0029

0.0041

0.0041

0.231

0.236

0.329

0.330

0.0072

0.0073

0.0102

0.0102

0.041

0.0399

0.0533

0.0539

0.380

0.370

0.493

0.499

0.0009

0.0008

0.0012

0.0012

0.0019

0.0018

0.0025

0.0026

0.187

0.183

0.249

0.252

0.0058

0.0057

0.0077

0.0078

SO2

CO2

MG2

NOx

SO2

CO2

MG3

NOx

SO2

Fig. 11 PDFs of total emission mass and cost for MG1 and MG2 a Total mass of pollutions related to MG1 b Total emission cost related to MG1 c Total mass of pollutions related to MG2 d Total emission cost related to MG2

IET Renew. Power Gener., 2015, Vol. 9, Iss. 8, pp. 982–990 & The Institution of Engineering and Technology 2015

CO2

989

Fig. 13 Optimum value of objective function in PDF form a Related to MG1 b Related to MG2 c Related to MG3

obtained by the proposed probabilistic method are more trustworthy from the energy operation management point of view.

8

Conclusion

In this paper the optimal power dispatch of MGs for an hour period is solved and discussed in MG environment. It is shown that MG can be defined as small scale energy zones at market operation of the smart grid. The optimal power dispatch problem is solved by ICA algorithm and obtained results by proposed algorithm has been compared with MCS under uncertainties of load and renewable power generation. Because of probabilistic behaviour of input vector, the extracted results are defined in PDF and CDF forms. Based on the mean value, PDF and CDF of each random variable, the results are analysed 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 decrease the run time of proposed problem by ICA algorithm related to MCS method and this is one of the advantages of proposed algorithm based on heuristic algorithms. Another advantage is in operation cost which decreases the operation cost when compared with MCS method.

9

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