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A new flexible model for generation scheduling in a smart grid
Journal Pre-proof A new flexible model for generation scheduling in a smart grid Atefeh Alirezazadeh, Masoud Rashidinejad, Amir Abdollahi, Peyman Afzali, Alireza Bakhshai PII:
S0360-5442(19)32133-4
DOI:
https://doi.org/10.1016/j.energy.2019.116438
Reference:
EGY 116438
To appear in:
Energy
Received Date: 31 July 2019 Revised Date:
21 October 2019
Accepted Date: 25 October 2019
Please cite this article as: Alirezazadeh A, Rashidinejad M, Abdollahi A, Afzali P, Bakhshai A, A new flexible model for generation scheduling in a smart grid, Energy (2019), doi: https://doi.org/10.1016/ j.energy.2019.116438. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
A New Flexible Model for Generation Scheduling in a Smart Grid Atefeh Alirezazadeha, Masoud Rashidinejada,b,*, Amir Abdollahia, Peyman Afzalia, Alireza Bakhshaib a
Department of Electrical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran
b
Department of Electrical and Computer Engineering, Queen's University, Kingston, Canada *Corresponding Author: [email protected]
Abstract: One of the main challenges and essentials of the power system is the flexibility of generation scheduling. The flexibility of a system can be enhanced by using a smart grid comprising demand response, hybrid/diesel generation units and energy storage system. In this paper, an improved flexibility index is defined with the concept of fast reserve supply. The uncertainties of wind/solar power plants and required reserve of thermal units are considered using Latin Hypercube Sampling (LHS). The smart grid supplies a part of load profile of commercial consumers and a part of charge profile of plug-in hybrid electric vehicles (PHEVs) through wind and solar virtual power plants (VPPs), responsive loads, distributed generators (DGs) and the energy storage system. Moreover, the PHEVs considered in this paper provide a system with more flexibility. This paper has solved the unit commitment problem in a single-node system that has no transmission constraints. The mixed integer linear programming (MILP) and the mixed integer non-linear programming (MINLP) methods have been used in order to solve the unit commitment problem and the smart grid scheduling, respectively. The results show that the presented model can optimize the costs of the system and causes the system to become more flexible. Keywords: Flexibility; unit commitment; demand response; virtual power plant (VPP); plugin hybrid electric vehicles.
1
Index sets and variables G∈λ
Generating thermal units, running from 1 to G. Start-up segments at thermal units, running
ENSt
Energy not served in hour t (MWh).
pG,t
Power output in hour t of unit G, generation above the minimum output P g (MW).
Non-renewable distributed generation units, running from 1 to J. The number of commercial consumers collections, running from 1 to D.
rG,t
t ∈T
Hourly periods, running from 1 to T hours.
z G,t
CGLV
Linear variable cost of unit G ($/MWh).
k G,t
CGNL
No-load cost of unit G ($/hour).
ψ G,sc,t
C ENS
Energy not served cost ($/Mwh).
PtL
CSU G,sc
Coefficients of the start-up cost function of unit G ($). Coefficients of the shutdown cost function of unit G ($). Coefficients of the reserve cost function of unit G ($). Load demand in hour t (MW).
Ps,tL
PG
Maximum power output of unit G (MW).
R Total t
PG
Minimum power output of unit G (MW).
Total R s,t
Rt
Spinning reserve requirement in hour t (MW). Ramp-down rate of unit G (MW/hour).
EC
Spinning reserve provided by unit G in hour t (MW). Commitment status of the unit G for hour t, which is equal to 1 if the unit is online and 0 otherwise. Start-up status of unit G, which takes the value of 1 if the unit starts up in hour t and 0 otherwise. Shutdown status of unit G, which takes the value of 1 if the unit shuts down in hour t and 0 otherwise. Start-up-type of unit G, that takes the value of 1 in hour t where the unit starts up. The hourly demand of smart grid (MW). The uncertainty of smart grid hourly demand at scenario s (MW). Hourly load profile of commercial collection (MW). A part of charge of the available PHEVs in hour t (MW). The percentage of available PHEVs power in the whole PHEVs parking lot in hour t (MW). The average of required reserve of power grid in hour t (MW). The uncertainty of thermal unit's reservation at scenario s in hour t (MW). Energy cost of smart grid ($)
RUR G
Ramp-up rate of unit G (MW/hour).
Pj,tDG
SDCG
Shutdown capability of unit G (MW).
DG Pj,t,s
SUCG
Start-up capability of unit G (MW).
R DG j,t
MDTG
Minimum downtime of unit G (hour).
PjDG.max
MUTG
Minimum uptime of unit G (hour).
PjDG.min
SU TG,sc
Times defining the segment sc limits,
q Rj
sc ∈ SCG
from 1 to SCG .
j∈ J d∈D
CSD G C RG
Lt
RDR G
SU j,t SUC j
SU G,sc
[T
SU G,sc +1
,T
u G,t
PtCC
PtEV PtR-EV
C DG j,t
Hourly fuel cost of DG unit j ($/MWh). Power output of DG unit j in hour t (MW). The uncertainty of DG unit j power output in hour t and scenario s (MW). Reserve commitment of DG unit j in hour t (MW). Maximum power output of DG unit j (MW). Minimum power output of DG unit j (MW). Reserve cost of DG unit j ($/MWh).
), of the start-up cost function
of unit G (hour). Start-up cost of DG unit j in hour t ($). Start-up cost of DG unit j ($).
SOC Max b
Maximum capacities collection b (MW).
of
storage
Pb_Max
The maximum charge of storage collection b (MW).
2
Commitment status of the DG unit j in hour t, which is equal to 1 if the unit is online and 0 otherwise. The cost of commercial consumers due to the load reduction in hour t ($).
+ Pb_Max
The maximum discharge of storage collection b (MW).
Xt
CPd,tR
The reserve commitment cost induced by commercial consumers in hour t ($).
Yt
CC Ed,t
The reduced deterministic load value of commercial consumer d in hour t (MW).
Ptw
The binary variables of the charge status of the storage collection in hour t The binary variables of the discharge status of the storage collection in hour t The averages of wind power in hour t (MW).
CC Rd,t
The residual reserve of the maximum reduction load capability of commercial consumer d in hour t (MW).
Pw (v)
The output power of wind turbine for v speed (MW).
E CCd,t,s
The reduction load of each scenario with the commercial consumer d in hour t and scenario s (MW). The maximum load reduction capability of commercial consumer d in hour t (MW). The cost of reduced deterministic load by commercial consumers in hour t ($/MWh). The cost of residual reserve by commercial consumers in hour t ($/MWh). The hourly cost of the non-renewable DG in hour t and scenario s ($).
Ps,tw
The wind power in hour t and scenario s (MW).
Pwrated
Nominal output power of wind turbine (MW). Speed of wind turbine (m/s).
v j,t CPd,tE
max CC d,t E q d,t R q d,t
C DG j,t,s E CPd,t,s
µs s ∈S w∈W pv ∈ PV
η +b
vw vin
Cut-in speed of wind turbine (m/s).
vr
Nominal speed of wind turbine (m/s).
The load reduction cost induced by commercial consumers in hour t and scenario s ($). The probability of the scenario s.
vout
Cut-out speed of wind turbine (m/s).
Ptpv
The number of scenarios, running from 1 to S. The number of wind turbines, running from 1 to W. The number of solar station, running from 1 to PV. The effective coefficient discharge of storage collection b.
Ppv (sr)
The averages of solar power in hour t (MW). The output power of PV for (sr) radiation (Watt). The solar power in hour t and scenario s (MW). The effective coefficient of PV panel.
Ps,tpv
η pv S pv
Total area of PV (m2).
sr
Solar radiation (Watt/m2).
ENSs,t
The energy not served in smart grid in hour t and scenario s (MW). The cluster quality index.
The effective coefficient charge of storage collection b. The scheduled discharge power of storage collection b in hour t (MW). The scheduled charge power of storage collection b in hour t (MW). The number of storage collection, running from 1 to B. The stored energy in storage collection b in hour t (MW).
SI n
SOC Min b
Minimum capacities of storage collection b (MW).
βn
π n,y
The y attributes value of the n-th observation. The y attribute value from the center of the cluster m.
GD n,m
The Euclidean distance.
R Q.R.G t
supplied reserve by fast ramp units
η -b + Pb,t
− Pb,t
b∈B SOC b,t
τ m,y
y∈Y
αn
The total number of features per observation. The mean incompatibility (unlike) of observing n with all other observations in the same cluster. The least incompatibility n observes with all observations in other clusters.
3
1- Introduction With regard to the variability of network load profile, scheduling is required to provide continuity, sustainability, and speed in reserve supply in a power grid. Nowadays, the use of renewable resources is increasing rapidly due to the high generation speed and the cheapness of these resources, but the generation of these resources is variable. The magnitude of the variations in power generation depends on environmental factors such as existing uncertainties and specific geographical conditions. Therefore, two issues arise as follows. The first relies on the speed rate of reserve supply and the second on the uncertainty of the fast resources generation to the reserve supply. Therefore, in recent years, various concepts have been introduced to express the power grid flexibility. In [1], electric vehicles are called as a power grid flexibility tool and in [2], demand side management has been used to increase flexibility, but in both of them, all resources that are able to increase network flexibility are not used. In [3], the concept of flexibility is generalized to the power system ability in order to adjust variability and uncertainty using available resources during a defined time period by an economic way. In this reference, only the renewable energy constraint is considered and the responsible load, PHEVs and energy storage that can increase network flexibility are not used. In [4], a method for assessing the level of flexibility of a power system is provided by considering units with fast ramps, demand response and energy storage, but in this reference, the uncertainty of the network reservation is ignored and the PHEVs, one of the tools for increasing network flexibility, are not used. Effective resources scheduling is essential for the power generation and operation of the reliable, economic and flexible system. This is achieved by solving the unit commitment problem which the main goal is to minimize the operational cost of the system at a defined time [5], [6]. Conventional generation scheduling needs resources that generate the reserve 4
with a higher speed rate, so that the grid becomes flexible [7], [8]. One of the most important parts of the fast reserve supply is the demand response. Demand response programs, in addition to participating in energy scheduling, are used to provide additional services such as spinning reserve and system security improvements
[9], [10].
In [11], an energy
management system is proposed to encourage residential customers to participate in demand side management programs (DSM) and reduce peak load. Other components of the fast generation of smart grid to provide a part of the reserve are storage resources, renewable resources and plug-in hybrid electric vehicles. The energy stored in the storage resources can be supplied by renewable energy resources or other generation units in off-peak load period and can be discharged at peak times instead of using more expensive and polluting generation units [12], [13]. With regard to the increased greenhouse gas emissions exhausted from thermal power plants and the gradual destruction of fossil resources, the global trend has been towards the use of electric vehicles and renewable resources. PHEVs play an important role in the fast supply of energy and reserve and are able to increase network flexibility. Renewable resources are increasingly effective in reducing costs. The financial benefits of renewable resources as direct economic resources are in reducing operational costs [14], [15]. Variable generation of renewable resources make system operators to consider the uncertainty of these resources. The presence of EVs and renewable resources in the power system can stress the system operation due to their uncertainty. Accordingly, a new method to optimize the location and size of renewable resources and EV charging stations is presented in [16]. In [17], the uncertainty of solar and wind generation has been calculated using the LHS method, but in this reference, the reservation uncertainty has not been considered. The main objective of the present research study is to provide a flexible power grid with an optimized reserve supply using smart grid technology. In this paper, flexibility has been expressed as an index of acceleration in reserve supply. The smart grid containing fast-power 5
generation resources are designed to provide a part of the required reserve for thermal units. The uncertainty of variable generation has also been compensated in the smart grid by responsive loads and DGs. Herein, demand response and DGs generation are not only used to provide a reservation but also used to balance the generation and consumption power of various scenarios induced by uncertainty. The use of smart grid generation and PHEVs charging to provide the reserve has led to a flexible power grid. In the present work, the LHS method is used to make the uncertainties of required reserve in thermal units and also wind and solar power generation. Therefore, the novelties of this paper are as follows: 1)Providing a flexible power system by optimized reserve supply using smart grid. 2)Definition of the index and the concept of flexibility 3)Simultaneous considering the uncertainty of the required reservation for thermal units and the uncertainties of the generation of wind and solar power plants using the LHS method Generation scheduling is optimized using GAMS software. MATLAB programming and LHS method are used to combine and develop the reserve scenarios of thermal units and generation of wind and solar power plants. These scenarios have been reduced by the KMeans algorithm in order to model the uncertainty and reduce the computation time. The organization of the paper is as follows. Section 2 is about the formulation of the problem consists of the objective function and constraints. The numerical studies and the parameters of the problem are presented in section 3. The simulation results and the conclusions are mentioned in section 4 and 5, respectively.
2- Mathematical model The proposed flexible model of the problem including the resources scheduling is presented in Fig. 1. 6
Flexible Model of Smart Grid
Exchange of Information Supply
Thermal Units System
Power of Thermal Unit
Wind Power
Daily Load Profile
DG
PV
Storage
Cut off Load Signal
Required Reserve
Energy Management Centre of Smart Grid
Daily Uncertain Reserve
Daily Requirement Reserve
Demand Response
Required Daily load profile
Supply Reserve
Supply Power
Day Ahead Scheduling System
Certain Load of Plug-In Electrical Vehicle Parking
Smart Grid System
Fig. 1. The proposed model for a flexible smart distribution grid
With regard to the flexibility model presented in Fig. 1 at the first step, a constant load profile and a variable reserve profile are used in thermal units scheduling. A part of the reserve profile that is supplied by thermal units is constant and other parts that are variable are supplied by the smart grid. In fact, the required reserve uncertainty is provided by smart grid. The smart grid consists of renewable resources, small scale DGs, collection of energy storage and curtailment loads. This grid is capable to perform self-scheduling and management by these components which provides a part of load profile of the commercial consumers and a part of PHEVs charge profile. When the thermal units need to use the reservation, the smart grid is responsible to breakdown the charge transfer to the PHEVs and commercial loads and transfer the power generation to the thermal units. Furthermore, the PHEVs parking operator discharges a part of the available stored charge in parked vehicles to supply the thermal units required reserve. Comparing to the thermal units, smart grid components such as wind and solar power plants, curtailment loads, energy storage collection
7
and PHEVs are faster than thermal units in power generation. Therefore, the smart grid makes more flexibility and cost reduction in the power system. The 8-unit thermal system without the presence of smart grid resources has a level of flexibility in operation due to having the units 1, 2, and 8, which have fast ramps, and has been provided a part of the system's reservation by these units. The addition of the smart grid to the system as a part of the required reservation supply has increased the flexibility of operating the 8-unit thermal system as this paper defines the flexibility, increased backup capacity, and accelerated reserve supply. The reserve response flexibility index (RRFI) can be expressed by Eq. (1) that shows the amount of using the power of smart grid resources to supply reserve of the 8-units thermal system.
∑ ∆R RRFI t =
G,t
G
R Total t
=
PtL +PtR-EV R Total t
(1)
Where; PtL is the smart grid power generation per hour which provides a part of PHEVs charge profile and a part of commercial loads; PtR-EV is the percentage of available vehicles power in the whole PHEVs parking which contractually is responsible to provide reserve of thermal units in exchange for free supply of a part of plug-in hybrid electric vehicles charge in the parking lot; R Total is the average of required reserve of power grid per hour. t The improved flexibility index (IFI) can be calculated by Eq. 2, which shows the amount of using the power of smart grid resources and fast ramp units to supply the reserve of 8-units thermal system.
IFI t =
PtL +PtR-EV + R Q.R.G t R Total t
R Q.R.G =rG,t t
∀G ∈ {1,2,8} as Quick Ramp Generator
(2) (3)
8
In Eq. 3, R Q.R.G is a supplied reserve per hour through fast ramp units with a ramp rate of t more than 2 MW per minute. In the 8-unit system studied, units 1, 2, and 8 have fast ramp rates. In order to determine the effects of uncertainty on the parameters of the system, an appropriate method of scenario generation based on average value of wind speed, solar radiation, and reserve system (a linear function of system load) is required. Therefore, the LHS sampling method [18] is used to generate and synthesize the scenarios of wind power, solar radiation and required reserve. In this method, two separated steps are considered for sampling and combining. At the sampling stage, 3000 samples are provided to represent the random nature of wind speed, solar radiation, and reserve. For this purpose, the cumulative distribution function with three variables is divided into 3000 portions having equal probability (1/3000). The gathered scenarios are based on 3000 mixed data with 3 variables at every hour which multiplies the calculation time. The K-Means clustering algorithm is used to overcome this challenge. The foundation of this algorithm is based on the hierarchal clustering of 3 variable scenarios within the initial clusters and depends on the probability, distance and repeating the procedure. The center point of each cluster is indicative of the cluster features including the wind speed, solar radiation, and reserve. Fig. 2 represents a clustering sample with center point and speed of the wind, solar radiation, and reserve. The probability of each scenario is calculated by dividing a number of scenarios at each cluster by the total number of scenarios.
9
Fig. 2. A sample of scenario clustering provided by K-Means algorithm
As stated, the K-Means clustering algorithm has been used to reduce scenarios. This algorithm begins by determining the number of clusters and the position of the center of each cluster, and each observation (result) to the nearest center is allocated using the Euclidean distance ( GD n,m ) as Eq. (4).
G D n,m =
Y
∑ (π
n,y
-τ m,y ) 2
(4)
y=1
In which, π n,y is the y attribute value of the n-th observation, τ m,y is the y attribute value from the center of the cluster m and Y is the total number of features per observation. Then the centers are updated and these steps are repeated until the movement of all centers to be stopped. The K-Means clustering algorithm is the selection of the optimal cluster number (k). The cluster quality is calculated in order to determine the optimal number of clusters by Eq. (5). SI n =
βn − αn max(α n , β n )
(5)
10
In which, αn is the mean incompatibility (unlike) of observation n with all other observations in the same cluster and βn is the least incompatibility observation n with all other observations in other clusters. The higher the SI n value, the more the match between n and its cluster will be greater; therefore, each dataset has an average and the optimal number k is the highest mean SI n for the whole dataset [19]. Laterally, herein, 5 reduced scenarios are chosen among 3000 scenarios by means of the K-Means algorithm. In this paper, the probability distribution functions of Weibull, Beta and Normal are used to model the probabilistic function of variables of the wind speed, solar radiation, and required reserve within 24 hours, respectively [17], [20].
2-1- Modeling of thermal unit commitment With the aim of minimizing the operation costs of thermal units, an objective function is defined as follow: NL NL SU SD R ENS min ∑∑ CG u G,t + CG (P G u G,t + pG,t ) + ∑ CG,sc ψ G,sc,t + CG k G,t + CG rG,t + C ens t 424 3 14444 4244444 3 sc∈SCG 123 { 1 G∈λ t∈Τ iv v iii i 1442443 ii
(6 )
Where; the i-th term denotes the generation cost, ii-th term is related to the start-up cost, iii-th term is the shut-down cost; iv-th term is the supplied reserve cost, and the v-th term denotes the non-supplied power. The generation cost is defined as piecewise-linear approximation having a slope of C LV and a width of origin C NL . The start-up cost which poses an increasing trend is dependent upon the shut-down duration of each unit before starting up. The start-up cost is determined by the following equations:
ψG,sc,t ≤
SU TG,sc+1 -1
∑
SU i=TG,sc
∑
sc∈SCG
SU k G,t-i ∀G,t ∈ TG,sc+1 ,T ,sc ∈ [1,SCG )
ψG,sc,t = z G,t ∀G,t
(7 )
(8 )
11
The total activation time of a segment in Eq. (7) is smaller than/ equal to 1; in Eq. (8), it is equal 1 for the times that are exactly related to the start-up of unit and is equal zero for the other times so that the start-up point of each segment can be determined.
2-2- Thermal unit commitment constraints 2-2-1- Balancing power and reserve constraints In Eq. (9), the balance of generated power with consumed load is equaled and in In Eq. (10), the desired spinning reserve is provided.
∑ P u + p ∑r +P +P G
G∈λ
G∈λ
G,t
G,t
L t
G,t
= L t -ENSt ∀t
(9 )
≥ R Total ∀t t
(10)
R-EV t
The average required reserve is R Total , a part of which is supplied by thermal units and the t other part of which is supplied by the smart grid and PHEVs.
∑r
G∈λ
G,t
denotes the spinning
reserve provided by thermal units. PtR-EV is capacity that injects to the power grid from PHEVs.
2-2-2- The constraints of minimum duration of start-up/ shut-down To solve the mentioned problem, logical conditions should be exactly determined. t
∑
z G,t ≤ u G,t ∀G, t ∈ [MUTG ,T]
(11)
k G,sc,t ≤ 1-u G,t ∀G,t ∈ [ MDTG ,T ]
(12)
i=t-MUTG +1
t
∑ i=t-MDTG +1
At the condition of z=1, all of the u-terms are equal to 1. Eq. (12) is the same as Eq. (11) but differs at the condition of k=1, where all u-terms are equal to zero. Following Eq. is valid for start-up/shut-down procedures:
u G,t -u G,t-1 = z G,t -k G,t ∀G,t
(13)
12
According to Eq. (13), at the start-up cycle of the unit, z =1 and at the shut-down cycle, k =1. Otherwise, when no conditional change occurs in the unit, since k G,t + u G,t ≤ 1, therefore, both parameters are zero.
2-2-3- Generation constraints Equations (14) and (15) are related to the units with MTU = 1. Eq. (16) is related to the units with MTU ≥ 2. p G,t +rG,t ≤ (PG -P G )u G,t − (PG -SUC G )z G,t ∀G ∈ λ1 ,t
(14)
p G,t +rG,t ≤ (PG -P G )u G,t − (PG -SDC G )k G,t+1 ∀G ∈ λ1 ,t
(1 5 )
p G,t +rG,t ≤ (PG -P G )u G,t − (PG -SUC G )z G,t -(PG -SDC G )k G,t+1 ∀G ∉ λ1 ,t
(16)
These equations determine the power constraints at the start-up and shut-down conditions based on upper and lower limits.
2-2-4- Ramping constraints Eqs. (15) and (16) express the constraints of ramp-up and ramp-down unit, respectively.
(pG,t +rG,t ) − pG,t-1 ≤ RUR G (-pG,t +pG,t-1 ) ≤ RDR G
∀G,t
∀G,t
(17) (18)
2-3- Modeling of the smart grid In order to develop a model based on the uncertainty of generation of wind and solar and the reserve scheduling in the smart grid, a two-step stochastic scheduling is performed. The responsive loads and DGs as backup capacities have compensated the uncertainty of the generation of wind and solar and the reserve scheduling. The objective function of this scheduling problem that is modeled as Eq. (19) consists of the expected operation cost of smart grid resources, which should be minimized.
13
T J D DG R E R min EC = ∑ ∑ {CDG +R × q +SU + j,t j,t j j,t } ∑ CPd,t +CPd,t t=1 j=1 d S D T J E +∑ µ s ∑∑ CDG + CPd,t,s ∑ j,t,s s =1 d=1 t =1 j=1
(19)
R DG In Eq. (19); j=1, 2, ..., J is the number of nonrenewable DG units; CDG j,t , R j,t , q j and
SU j,t are the hourly cost of fuel, reserve commitment, reserve cost and start-up cost of nonrenewable DG at a defined time of t, respectively; CPd,tE is the cost of commercial consumers due to the load reduction at the time t; CPd,tR is the reserve commitment cost induced by commercial consumers at the time t. At the second part of the target function, µs is the probability of the wind, solar and thermal system reserve scenarios; C DG j,t,s is the hourly cost of E the non-renewable DG at the time t and scenario s; CPd,t,s is the load reduction cost induced by
commercial consumers at the time t and scenario s. The coefficients of the operational cost function of non-renewable DG units are mentioned in [22]. The constraints of the nonrenewable DG units are given by the following equations: DG.max Pj,tDG +R DG .v j,t j,t ≤ Pj
Pj,tDG ≥ PjDG.min .v j,t
∀j,t
(20)
∀j,t
(21)
SU j,t ≥ SUC j×(v j,t -v j,t-1 )
(22)
SU j,t ≥ 0
(23)
PjDG.min and PjDG.max are the minimum and maximum constraint of the output power of DG
units, respectively. SU j,t and SUC j are the start-up cost of unit j at time t and the start-up cost of unit j, respectively. On the other hand, Eq. (24) expresses that the constraint of DG units should be considered in each scenario:
14
DG DG R DG j,t ≥ Pj,t,s -Pj,t
∀j,t,s
(24)
According to Eq. (24), the output power difference between the DG units in each scenario DG ( Pj,t,s ) and scheduled power ( Pj,tDG ) should not exceed the spinning reserve in DG units.
In the demand response modelling, commercial consumer collection is used that beside the PHEVs is being fed by the smart grid. The collection is used to preserve or reduce the load considering the cost defined for each hour. E R max CCd,t +CCd,t ≤ CCd,t
(25)
E E CPd,tE = CC d,t ×q d,t
(26)
R R CPd,tR =CC d,t ×q d,t
(27)
R E E CCd,t ≥ CCd,t,s -CCd,t
(28)
In Eqs. (25)-(28); d=1, 2, …, D is the number of commercial consumers collections; max CCd,t is the maximum load reduction; CC Ed,t is the reduced deterministic load value; CC Rd,t
is the residual reserve of the maximum reduction load; CC E d,s,t is the reduction load of each scenario with the commercial consumer d at the time t. The constraints of the stochastic scheduling method are as follows: J
W
PV
j=1
W=1
pv=1
∑ Pj,tDG + ∑ Ptw + ∑ Ptpv + η+b × Pb,t+ -η-b × Pb,t− = PtL -∑ CCd,tE
∀t
(29)
d
The constraint of power balance in the smart grid can be obtained by Eq. (29). Where;
Ptw and Ptpv are averages of wind and solar power at time t, respectively. Pb,t+ and Pb,t− are indicators of scheduled battery discharge and charge, respectively. η+b and η-b are the effective coefficients of battery discharge and charge. PtL is the hourly demand for a part of profile load of commercial customers and a part of the available PHEVs charge in parking.
15
The power balance of each system scenario should be preserved in both equations of (29) and (30). J
∑P
DG j,t,s
j=1
W
PV
W=1
pv=1
E + ∑ Ps,tw + ∑ Ps,tpv + η b+ × Pb,t+ -η-b × Pb,t− = Ps,tL -∑ CC d,t,s -ENSs,t
∀t,s
(30)
d
Ps,tL can be obtained from Eq. (31).
∑r
G∈λ
G,t
Total +Ps,tL + PtR-EV ≥ R s,t
(31)
According to the defined provision between the smart grid and thermal reservation Total system, R s,t is the uncertainty of thermal unit reservation. The smart grid should be capable
Total and certain thermal unit reservation by Ps,tL . to provide the difference between R s,t
PtL =PtCC +PtEV
(32)
In Eq. (32), PtCC is a part of load profile of commercial customers and PtEV is a part of the charge of available PHEVs in parking lot that smart grid should supply them. The charging and discharging procedure in the energy storage collection are not optional and hence following constraints should be considered: SOC b,t = SOC b,t-1 +η -b × Pb,t− -η +b × Pb,t+
(33)
SOC Min ≤ SOC b,t ≤ SOC bMax b
(34)
In Eq. (33); SOC b,t is the stored energy in the storage collections. η+b and η-b are the discharge and charge efficiencies of the energy storage collection. In Eq. (34); SOC Min and b are minimum and maximum capacities of energy storage collection, respectively. In SOC Max b the case of charge and discharge constraints, the following equations should be considered: Pb,t− ≤ Pb_Max
(35)
+ Pb,t+ ≤ Pb_Max
(36)
X t +Yt ≤ 1; X,Y ∈ {0,1}
(37)
16
+ In Eqs. (35) and (34) Pb_Max and Pb_Max are maximum discharge and charge of energy
storage collection, respectively. In Eq. (37) X t and Yt as the binary variables denote the energy storage collection charge and discharge status by which the concurrency of charging and discharging at the same hour is prevented. The power supply distribution of the solar station can be obtained by Eq. (38): Ppv (sr)=ηpv ×Spv ×sr
(38)
pv Where; Ppv (sr) is the output power of PV for (sr) radiation; η and Spv are the
efficiency and total area of PV, respectively. The proposed model of wind turbine output regarding the wind speed variation curve is calculated by Eq. (39) [17]. 0 rated ( v w -vin ) Pw × Pw (v) = ( v r -vin ) rated Pw 0
0 ≤ v w ≤ vin vin ≤ v w ≤ v r
(39)
v r ≤ v w ≤ v out v out ≤ v w
Where; Vin, Vr, and Vout are the cut-in speed, nominal speed and cut-out speed of wind turbine, respectively. Fig. 3 shows the flowchart of the flexible system studied and the relationship between the components of the smart grid and the thermal units.
17
start Wind Distribution Function Data
Solar Distribution Function Data
Required Reserve Distribution Function Data
LHS Sampling Method
Optimization Cost Function of Unit Commitment
Decrease Number of Scenarios with K-Means Algorithm
DG Data
Number of Available PHEVs and Load Profile
Smart Grid Uncertainty Model Management
Commercial Load Profile
Storage Collection Data
Evaluate Objective Function Provided Reserve for Thermal units system
Termination Criteria Satisfied?
Yes
Optimized Operation Planning
No End Change the Variables
Fig. 3. Flowchart of the flexible system studied
3- Numerical study A standard system comprising 8 units is used as the simulated thermal unit of the proposed smart grid model [22]. The unit commitment optimization method based on MILP (Mixed Integer Linear Programming) algorithm is used to solve the problem. Table (1) represents the detailed information of 8 units. About 5% of the daily load is considered as the average essential thermal reserve, while in a unit commitment, each thermal unit supplies a part of the reserve with 20% of CLV costs.
18
In order to obtain the uncertainties of the reserve, the average data is gathered from the daily load curve of an 8-unit system. The standard deviation data is assumed to be 4% of daily load curve of an 8- unit system. The total load is 1552 MW. Table 2 represents the load percentage of 8- unit system in 24 hours. Table 1: The information of 8 studied units Gen 1 2 3 4 5 6 7 8
P
P
[MW]
[MW]
455 455 130 130 162 80 85 55
150 150 20 20 25 20 25 10
[h] MUT MDT
[ MW h ] RUR RDR
8 8 5 5 6 3 3 1
225 225 50 50 60 60 60 135
Ste0
TcSU
[h]
[h]
[$ h ]
8 8 -5 -5 -6 -3 -3 -1
14 14 10 10 11 8 6 2
1000 970 700 680 450 370 480 660
CNL
CLV
[$
MWh ]
16.19 17.26 16.60 16.50 19.70 22.26 27.74 25.92
CSU h
CSU c
[$ ]
[$ ]
4500 5000 550 560 900 170 260 30
9000 10000 1100 1120 1800 340 520 60
Table 2: The information of 24-hour load Time[h]
1
2
3
4
5
6
7
8
9
10
11
12
Demand
71%
65%
62%
60%
58%
58%
60%
64%
73%
80%
82%
83%
Time[h]
13
14
15
16
17
18
19
20
21
22
23
24
Demand
82%
80%
79%
79%
83%
91%
90%
88%
85%
84%
79%
74%
In the smart grid related to thermal units, the daily load profile is a part of PHEVs charge and a part of load profile of commercial consumers. Fig. 4 shows the number of available parked PHEVs at each hour of the day [23]. The total PHEVs are equal to 5000, according to the Markov model used for the uncertainty of the presence of plug-in electric vehicles in [23] 50% of the vehicles are in the parking lot, certainly, so 30% of which and 50% of their capacity are programmed to be charged by the smart grid. It is consumed that PHEVs are similar to each other having a battery capacity of 25 KW and charge/discharge coefficient equal to 0.9.
19
Fig. 4. The number of plug-in hybrid electric vehicles available in parking at each hour
On the other hand, according to the assumption, each plug-in hybrid electric vehicle at the time of its call by the electric vehicles operator can supply 10% of its capacity inject to the power grid in an interval of one hour as thermal units reserve for their free power supply through the smart grid. Fig. 5 shows a part of charge of available parked PHEVs and a part of load profile commercial consumers that should be certainly supplied by the smart grid.
Fig. 5. Daily load curve of the smart grid
The summation of reduced loads and their reserve should not exceed the maximum load reduction. The maximum load reduction in the case of the commercial consumer is suggested
20
to be 25% of the demand curve at each hour. The load reduction and reserve costs for commercial consumer collection are presented in Table 3. Table 3: The cost of reduction load and reserve for Commercial customers Commercial Customer Time [hour] 1 2 3 4 5 6 7 8 9 10 6 6 6 6 6 6 6 7 4 Cost of reduction load [$] 6 3 3 3 3 3 3 3 3 3.5 2 Cost of reserve [$] Time [hour] 13 14 15 16 17 18 19 20 21 22 10 50 60 8.5 6 10 20 30 30 30 Cost of reduction load [$] 5 25 30 4.25 3 5 10 15 15 15 Cost of reserve [$]
11
12
10 5
10 5
23
24
30 15
30 15
In the present work, 80 wind turbines with similar features (each of them has a capacity of 0.5 MW) are installed in a wind farm. The specifications of turbines are listed in table 4. Table 4: The specifications of the turbine Parameter Rated power[kW] Cut-in speed [m/s] Nominal speed [m/s] Cut-out speed [m/s]
Value 500 3 13 25
The solar power plants consist of 5 photovoltaic systems, each of them consists of 50 thousand solar panels. The specifications of each photovoltaic panel are listed in Table 5. Table 5: The specifications of the photovoltaic panel Parameter Value [%] η 18.6 SPV [m2] 1 Pmax [W] 250
In addition to the renewable generation, two fast fossil units with small capacity are used in the smart grid. The specifications of the DG units in the smart grid are presented in Table 6 [21]. Table 6: The specifications of the distributed generation
DG
DG1 DG2
Pmin
Pmax
[MW]
[MW]
0.5 1
6 10
a
b
c
Ramp up [MW/h]
2 2
13.3 13.3
50 50
2.5 2
Ramp down [MW/h]
Start up cost [$/MW]
Shut down cost [$/MW]
Minimum Up-time [h]
Minimum Downtime [h]
2.5 2
10 9
15 13
1 2
1 2
The specification of the energy storage collection is assumed in Table 7 [21]. 21
Cap[MW]
Max-dis [MW.h]
10
8
Table 7: The specifications of energy storage collection Max-ch Max-cap Min-cap Deep of [MW.h] [MW] [MW] discharge 5
10
1
0.7
Eta 0.85
4- Numerical results The average generation of wind and solar power plants are shown in Fig. 6 and Fig.7, respectively. The average and standard deviation values of solar radiation and wind speed distribution functions are mentioned in [17].
Fig. 6. The average generation curve for wind power plant
Fig. 7. The average generation curve for the solar power plant
According to the LHS method and the K-means clustering algorithm described in the previous sections, the scenarios of the solar radiation, wind speed, and the amount of reserve required for thermal units are shown in Figs.8-10, respectively. The green, magenta and cyan color in Figs. 8-10 indicate the 3000 distributed scenarios for solar radiation, wind speed, and required reserve for thermal units, respectively. 22
C1 C2 C3 C4 C5
1.6 Radiation(KW/m2)
1.4 1.2 1 0.8 0.6 0.4 0.2 0
2
4
6
8
10
12 14 Time(Hour)
16
18
20
22
24
Fig. 8. The state model scenarios of solar radiation with uncertainty
40 C1 C2 C3 C4 C5
35 Wind Speed(m/s)
30 25 20 15 10 5 0
2
4
6
8
10
12 14 Time(Hour)
16
18
20
22
24
Fig. 9. The state model scenarios of wind speed with uncertainty
23
80
Required Reserve(MW)
75 70 65 60 55 C1 C2 C3 C4 C5
50 45 40 35
2
4
6
8
10
12 14 Time(Hour)
16
18
20
22
24
Fig. 10. The state model scenarios of required reserve for thermal units with uncertainty
As shown in Fig. 11, at the first hours (1 AM–8 AM), all available curtailment load capacities are cut. This result is despite the start-up status of DG1 unit which is due to the lack of the supplied power from solar power plants in the first hours. With increasing the power of solar units at the midday hours (9a.m-4p.m), the reduced load values decrease significantly while in contrast increases the reserve of curtailment load. At the last hours of the day, the reduced load increases again with decreasing solar power.
F ig. 11. The reduced and reserve curtailment load value
24
As shown in Fig. 12, the energy storage collection is discharged when the power consumption is higher than the system power generation.
Fig. 12. The status of battery discharge/charge
According to Fig. 13, the DG units have been activated at separated times based on their capacities. Therefore, the DG1 unit provides power at hours between 1 AM–8 AM and DG2 unit provides power at hours between 9 AM–12 PM. The activation state of DG2 instead of DG1 is due to higher installation capacity for reserve supply system at uncertainty condition to balance the power of different system scenarios.
25
Fig. 13. Reserve and generation of DG units
As previously mentioned in Eq. (8), the smart grid with optimized scheduling delivers the power generation as an offer of reserve supply to system planner according to contract with thermal units at each hour. To provide a part of certain thermal system reserve, the available vehicles in smart grid parking offer a percentage of their power capacity to thermal units each hour. Therefore, thermal collections can schedule their system more flexible and reduce system costs by providing a part of their required reserve by means of the smart grid.
26
Fig. 14. The commitment of thermal units in the absence of smart grid as the reserve system
Fig. 15. The commitment of thermal units in the presence of smart grid as the reserve system
Comparing Figs. 14 and 15 reveals that in the presence of smart grid as the reserve system, 8th thermal unit remains deactivated until the end of the schedule. The power generation of this unit is transferred to the other units and power scheduling changes at 27
different hours. The results obtained for generation scheduling of thermal units per hour without the presence of smart grid generation are in accordance with the results obtained in reference [22].
F ig. 16. The reservation of thermal units in the absence of smart grid as the reserve system
Fig. 17. The reservation of thermal units in the presence of smart grid as the reserve system
Figs. 16 and 17 show the reserve supply profile in the absence and presence of smart grid. Moreover, the reduction in the reserve supply and change in thermal system reserve scheduling can also be observed.
28
Fig. 18. The cost of reservation of thermal units in the absence of smart grid as the reserve system
Fig. 19. The cost of reservation of thermal units in the presence of smart grid as the reserve system
Fig. 18, Fig. 19 and Table 8 presents the operation costs of an 8-unit system. The costs of power generation, system of reserve supply and start-up of thermal units in the presence of smart grid are less than the costs in the absence of smart grid. Table 8: Operation cost of the thermal units system Cost of Thermal Units
Power Cost [$]
Reserve Cost [$]
Start-Up Cost [$]
Total Operational Cost [$]
Without Smart Grid as Reserve Supplier
571490.7
5691.4
3420
580602.1
With Smart Grid as Reserve Supplier
566906.9
1606.8
3080
571593.7
Table 9 is related to the costs of smart grid operation. The results of simulation show that when the uncertainty condition of wind, solar and required reserve is considered, the total costs in flexible smart grid system are reduced. Although the costs of operating the smart grid 29
are imposed on the whole system, reducing the cost of operation and reserve supply in the 8unit system justify generally the suitability of this proposed model. Table 9: Operation cost of smart grid DG Operational Cost [$]
Cut-off Power Cost [$]
Cut-off Reserve Cost [$]
DG Scenarios Operational Cost with uncertainty Coefficient [$]
Cut-off Scenarios Power Cost with uncertainty Coefficient [$]
Total System Cost [$]
4619.3
546.25
564.25
1910.8
251.6
7892.2
Fig. 20 shows how many percent of the required reservation of the 8-unit thermal system is provided by the smart grid. The closer the index to 100, then the smart grid has been able to replace a larger percentage of the system reserve with a quick type of reserve and reflect more flexibility in operating condition and faster responsiveness to changes. As shown in Fig. 20, at the peak hours of the network load (hours 11-15), the reserve response flexibility index (RRFI) has the highest value.
Fig. 20. The variations of flexibility index of reserve response for an 8-unit system
Fig. 21 shows the improved flexibility index of the system with and without the smart grid.
30
Fig. 21. The variations of improved flexibility index for an 8-unit system
As shown in Fig. 21, the flexibility index is improved, especially during peak load times. Therefore, in addition to increasing the backup capacity, the reserve supply speed is also increased every hour.
5- Conclusions The main objective of the present research study is to propose a more flexible model based on fast reserve supply. In this paper, the mixed integer linear programming (MILP) method and the mixed integer non-linear programming (MINLP) has been used in order to solve the unit commitment problem considering operation constraints and smart grid, respectively. Flexibility is defined as an index of the concept of fast reserve supply. The smart grid system possesses resources of the renewable, nonrenewable power plant, PHEVs and demand response as virtual power plant. Demand response and DGs generation are not only used to provide a reservation but also used to balance the generation and consumption power of various scenarios induced by uncertainty. Latin Hypercube Sampling as a stochastic method is used to generate and synthesize wind and solar power generation and required reserve scenarios. In order to investigate the effects of uncertainty phenomena on unit commitment, K-Means algorithm is used to reduce scenarios and complexity of the problem.
31
The results of the proposed model are revealed that despite available costs in the smart grid, it is possible to reduce costs of the power supply and thermal unit reservation. Therefore, the generation of smart grid and PHEVs reduces the total costs of the system.
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33
Highlights:
A flexibility index is defined with the concept of fast reserve supply.
A smart grid containing fast-power generation resources are designed.
The plug-in hybrid electric vehicles provide a system with improved flexibility.
The LHS method is used to make the uncertainties of required reserve.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S0360-5442(19)32133-4
DOI:
https://doi.org/10.1016/j.energy.2019.116438
Reference:
EGY 116438
To appear in:
Energy
Received Date: 31 July 2019 Revised Date:
21 October 2019
Accepted Date: 25 October 2019
Please cite this article as: Alirezazadeh A, Rashidinejad M, Abdollahi A, Afzali P, Bakhshai A, A new flexible model for generation scheduling in a smart grid, Energy (2019), doi: https://doi.org/10.1016/ j.energy.2019.116438. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
A New Flexible Model for Generation Scheduling in a Smart Grid Atefeh Alirezazadeha, Masoud Rashidinejada,b,*, Amir Abdollahia, Peyman Afzalia, Alireza Bakhshaib a
Department of Electrical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran
b
Department of Electrical and Computer Engineering, Queen's University, Kingston, Canada *Corresponding Author: [email protected]
Abstract: One of the main challenges and essentials of the power system is the flexibility of generation scheduling. The flexibility of a system can be enhanced by using a smart grid comprising demand response, hybrid/diesel generation units and energy storage system. In this paper, an improved flexibility index is defined with the concept of fast reserve supply. The uncertainties of wind/solar power plants and required reserve of thermal units are considered using Latin Hypercube Sampling (LHS). The smart grid supplies a part of load profile of commercial consumers and a part of charge profile of plug-in hybrid electric vehicles (PHEVs) through wind and solar virtual power plants (VPPs), responsive loads, distributed generators (DGs) and the energy storage system. Moreover, the PHEVs considered in this paper provide a system with more flexibility. This paper has solved the unit commitment problem in a single-node system that has no transmission constraints. The mixed integer linear programming (MILP) and the mixed integer non-linear programming (MINLP) methods have been used in order to solve the unit commitment problem and the smart grid scheduling, respectively. The results show that the presented model can optimize the costs of the system and causes the system to become more flexible. Keywords: Flexibility; unit commitment; demand response; virtual power plant (VPP); plugin hybrid electric vehicles.
1
Index sets and variables G∈λ
Generating thermal units, running from 1 to G. Start-up segments at thermal units, running
ENSt
Energy not served in hour t (MWh).
pG,t
Power output in hour t of unit G, generation above the minimum output P g (MW).
Non-renewable distributed generation units, running from 1 to J. The number of commercial consumers collections, running from 1 to D.
rG,t
t ∈T
Hourly periods, running from 1 to T hours.
z G,t
CGLV
Linear variable cost of unit G ($/MWh).
k G,t
CGNL
No-load cost of unit G ($/hour).
ψ G,sc,t
C ENS
Energy not served cost ($/Mwh).
PtL
CSU G,sc
Coefficients of the start-up cost function of unit G ($). Coefficients of the shutdown cost function of unit G ($). Coefficients of the reserve cost function of unit G ($). Load demand in hour t (MW).
Ps,tL
PG
Maximum power output of unit G (MW).
R Total t
PG
Minimum power output of unit G (MW).
Total R s,t
Rt
Spinning reserve requirement in hour t (MW). Ramp-down rate of unit G (MW/hour).
EC
Spinning reserve provided by unit G in hour t (MW). Commitment status of the unit G for hour t, which is equal to 1 if the unit is online and 0 otherwise. Start-up status of unit G, which takes the value of 1 if the unit starts up in hour t and 0 otherwise. Shutdown status of unit G, which takes the value of 1 if the unit shuts down in hour t and 0 otherwise. Start-up-type of unit G, that takes the value of 1 in hour t where the unit starts up. The hourly demand of smart grid (MW). The uncertainty of smart grid hourly demand at scenario s (MW). Hourly load profile of commercial collection (MW). A part of charge of the available PHEVs in hour t (MW). The percentage of available PHEVs power in the whole PHEVs parking lot in hour t (MW). The average of required reserve of power grid in hour t (MW). The uncertainty of thermal unit's reservation at scenario s in hour t (MW). Energy cost of smart grid ($)
RUR G
Ramp-up rate of unit G (MW/hour).
Pj,tDG
SDCG
Shutdown capability of unit G (MW).
DG Pj,t,s
SUCG
Start-up capability of unit G (MW).
R DG j,t
MDTG
Minimum downtime of unit G (hour).
PjDG.max
MUTG
Minimum uptime of unit G (hour).
PjDG.min
SU TG,sc
Times defining the segment sc limits,
q Rj
sc ∈ SCG
from 1 to SCG .
j∈ J d∈D
CSD G C RG
Lt
RDR G
SU j,t SUC j
SU G,sc
[T
SU G,sc +1
,T
u G,t
PtCC
PtEV PtR-EV
C DG j,t
Hourly fuel cost of DG unit j ($/MWh). Power output of DG unit j in hour t (MW). The uncertainty of DG unit j power output in hour t and scenario s (MW). Reserve commitment of DG unit j in hour t (MW). Maximum power output of DG unit j (MW). Minimum power output of DG unit j (MW). Reserve cost of DG unit j ($/MWh).
), of the start-up cost function
of unit G (hour). Start-up cost of DG unit j in hour t ($). Start-up cost of DG unit j ($).
SOC Max b
Maximum capacities collection b (MW).
of
storage
Pb_Max
The maximum charge of storage collection b (MW).
2
Commitment status of the DG unit j in hour t, which is equal to 1 if the unit is online and 0 otherwise. The cost of commercial consumers due to the load reduction in hour t ($).
+ Pb_Max
The maximum discharge of storage collection b (MW).
Xt
CPd,tR
The reserve commitment cost induced by commercial consumers in hour t ($).
Yt
CC Ed,t
The reduced deterministic load value of commercial consumer d in hour t (MW).
Ptw
The binary variables of the charge status of the storage collection in hour t The binary variables of the discharge status of the storage collection in hour t The averages of wind power in hour t (MW).
CC Rd,t
The residual reserve of the maximum reduction load capability of commercial consumer d in hour t (MW).
Pw (v)
The output power of wind turbine for v speed (MW).
E CCd,t,s
The reduction load of each scenario with the commercial consumer d in hour t and scenario s (MW). The maximum load reduction capability of commercial consumer d in hour t (MW). The cost of reduced deterministic load by commercial consumers in hour t ($/MWh). The cost of residual reserve by commercial consumers in hour t ($/MWh). The hourly cost of the non-renewable DG in hour t and scenario s ($).
Ps,tw
The wind power in hour t and scenario s (MW).
Pwrated
Nominal output power of wind turbine (MW). Speed of wind turbine (m/s).
v j,t CPd,tE
max CC d,t E q d,t R q d,t
C DG j,t,s E CPd,t,s
µs s ∈S w∈W pv ∈ PV
η +b
vw vin
Cut-in speed of wind turbine (m/s).
vr
Nominal speed of wind turbine (m/s).
The load reduction cost induced by commercial consumers in hour t and scenario s ($). The probability of the scenario s.
vout
Cut-out speed of wind turbine (m/s).
Ptpv
The number of scenarios, running from 1 to S. The number of wind turbines, running from 1 to W. The number of solar station, running from 1 to PV. The effective coefficient discharge of storage collection b.
Ppv (sr)
The averages of solar power in hour t (MW). The output power of PV for (sr) radiation (Watt). The solar power in hour t and scenario s (MW). The effective coefficient of PV panel.
Ps,tpv
η pv S pv
Total area of PV (m2).
sr
Solar radiation (Watt/m2).
ENSs,t
The energy not served in smart grid in hour t and scenario s (MW). The cluster quality index.
The effective coefficient charge of storage collection b. The scheduled discharge power of storage collection b in hour t (MW). The scheduled charge power of storage collection b in hour t (MW). The number of storage collection, running from 1 to B. The stored energy in storage collection b in hour t (MW).
SI n
SOC Min b
Minimum capacities of storage collection b (MW).
βn
π n,y
The y attributes value of the n-th observation. The y attribute value from the center of the cluster m.
GD n,m
The Euclidean distance.
R Q.R.G t
supplied reserve by fast ramp units
η -b + Pb,t
− Pb,t
b∈B SOC b,t
τ m,y
y∈Y
αn
The total number of features per observation. The mean incompatibility (unlike) of observing n with all other observations in the same cluster. The least incompatibility n observes with all observations in other clusters.
3
1- Introduction With regard to the variability of network load profile, scheduling is required to provide continuity, sustainability, and speed in reserve supply in a power grid. Nowadays, the use of renewable resources is increasing rapidly due to the high generation speed and the cheapness of these resources, but the generation of these resources is variable. The magnitude of the variations in power generation depends on environmental factors such as existing uncertainties and specific geographical conditions. Therefore, two issues arise as follows. The first relies on the speed rate of reserve supply and the second on the uncertainty of the fast resources generation to the reserve supply. Therefore, in recent years, various concepts have been introduced to express the power grid flexibility. In [1], electric vehicles are called as a power grid flexibility tool and in [2], demand side management has been used to increase flexibility, but in both of them, all resources that are able to increase network flexibility are not used. In [3], the concept of flexibility is generalized to the power system ability in order to adjust variability and uncertainty using available resources during a defined time period by an economic way. In this reference, only the renewable energy constraint is considered and the responsible load, PHEVs and energy storage that can increase network flexibility are not used. In [4], a method for assessing the level of flexibility of a power system is provided by considering units with fast ramps, demand response and energy storage, but in this reference, the uncertainty of the network reservation is ignored and the PHEVs, one of the tools for increasing network flexibility, are not used. Effective resources scheduling is essential for the power generation and operation of the reliable, economic and flexible system. This is achieved by solving the unit commitment problem which the main goal is to minimize the operational cost of the system at a defined time [5], [6]. Conventional generation scheduling needs resources that generate the reserve 4
with a higher speed rate, so that the grid becomes flexible [7], [8]. One of the most important parts of the fast reserve supply is the demand response. Demand response programs, in addition to participating in energy scheduling, are used to provide additional services such as spinning reserve and system security improvements
[9], [10].
In [11], an energy
management system is proposed to encourage residential customers to participate in demand side management programs (DSM) and reduce peak load. Other components of the fast generation of smart grid to provide a part of the reserve are storage resources, renewable resources and plug-in hybrid electric vehicles. The energy stored in the storage resources can be supplied by renewable energy resources or other generation units in off-peak load period and can be discharged at peak times instead of using more expensive and polluting generation units [12], [13]. With regard to the increased greenhouse gas emissions exhausted from thermal power plants and the gradual destruction of fossil resources, the global trend has been towards the use of electric vehicles and renewable resources. PHEVs play an important role in the fast supply of energy and reserve and are able to increase network flexibility. Renewable resources are increasingly effective in reducing costs. The financial benefits of renewable resources as direct economic resources are in reducing operational costs [14], [15]. Variable generation of renewable resources make system operators to consider the uncertainty of these resources. The presence of EVs and renewable resources in the power system can stress the system operation due to their uncertainty. Accordingly, a new method to optimize the location and size of renewable resources and EV charging stations is presented in [16]. In [17], the uncertainty of solar and wind generation has been calculated using the LHS method, but in this reference, the reservation uncertainty has not been considered. The main objective of the present research study is to provide a flexible power grid with an optimized reserve supply using smart grid technology. In this paper, flexibility has been expressed as an index of acceleration in reserve supply. The smart grid containing fast-power 5
generation resources are designed to provide a part of the required reserve for thermal units. The uncertainty of variable generation has also been compensated in the smart grid by responsive loads and DGs. Herein, demand response and DGs generation are not only used to provide a reservation but also used to balance the generation and consumption power of various scenarios induced by uncertainty. The use of smart grid generation and PHEVs charging to provide the reserve has led to a flexible power grid. In the present work, the LHS method is used to make the uncertainties of required reserve in thermal units and also wind and solar power generation. Therefore, the novelties of this paper are as follows: 1)Providing a flexible power system by optimized reserve supply using smart grid. 2)Definition of the index and the concept of flexibility 3)Simultaneous considering the uncertainty of the required reservation for thermal units and the uncertainties of the generation of wind and solar power plants using the LHS method Generation scheduling is optimized using GAMS software. MATLAB programming and LHS method are used to combine and develop the reserve scenarios of thermal units and generation of wind and solar power plants. These scenarios have been reduced by the KMeans algorithm in order to model the uncertainty and reduce the computation time. The organization of the paper is as follows. Section 2 is about the formulation of the problem consists of the objective function and constraints. The numerical studies and the parameters of the problem are presented in section 3. The simulation results and the conclusions are mentioned in section 4 and 5, respectively.
2- Mathematical model The proposed flexible model of the problem including the resources scheduling is presented in Fig. 1. 6
Flexible Model of Smart Grid
Exchange of Information Supply
Thermal Units System
Power of Thermal Unit
Wind Power
Daily Load Profile
DG
PV
Storage
Cut off Load Signal
Required Reserve
Energy Management Centre of Smart Grid
Daily Uncertain Reserve
Daily Requirement Reserve
Demand Response
Required Daily load profile
Supply Reserve
Supply Power
Day Ahead Scheduling System
Certain Load of Plug-In Electrical Vehicle Parking
Smart Grid System
Fig. 1. The proposed model for a flexible smart distribution grid
With regard to the flexibility model presented in Fig. 1 at the first step, a constant load profile and a variable reserve profile are used in thermal units scheduling. A part of the reserve profile that is supplied by thermal units is constant and other parts that are variable are supplied by the smart grid. In fact, the required reserve uncertainty is provided by smart grid. The smart grid consists of renewable resources, small scale DGs, collection of energy storage and curtailment loads. This grid is capable to perform self-scheduling and management by these components which provides a part of load profile of the commercial consumers and a part of PHEVs charge profile. When the thermal units need to use the reservation, the smart grid is responsible to breakdown the charge transfer to the PHEVs and commercial loads and transfer the power generation to the thermal units. Furthermore, the PHEVs parking operator discharges a part of the available stored charge in parked vehicles to supply the thermal units required reserve. Comparing to the thermal units, smart grid components such as wind and solar power plants, curtailment loads, energy storage collection
7
and PHEVs are faster than thermal units in power generation. Therefore, the smart grid makes more flexibility and cost reduction in the power system. The 8-unit thermal system without the presence of smart grid resources has a level of flexibility in operation due to having the units 1, 2, and 8, which have fast ramps, and has been provided a part of the system's reservation by these units. The addition of the smart grid to the system as a part of the required reservation supply has increased the flexibility of operating the 8-unit thermal system as this paper defines the flexibility, increased backup capacity, and accelerated reserve supply. The reserve response flexibility index (RRFI) can be expressed by Eq. (1) that shows the amount of using the power of smart grid resources to supply reserve of the 8-units thermal system.
∑ ∆R RRFI t =
G,t
G
R Total t
=
PtL +PtR-EV R Total t
(1)
Where; PtL is the smart grid power generation per hour which provides a part of PHEVs charge profile and a part of commercial loads; PtR-EV is the percentage of available vehicles power in the whole PHEVs parking which contractually is responsible to provide reserve of thermal units in exchange for free supply of a part of plug-in hybrid electric vehicles charge in the parking lot; R Total is the average of required reserve of power grid per hour. t The improved flexibility index (IFI) can be calculated by Eq. 2, which shows the amount of using the power of smart grid resources and fast ramp units to supply the reserve of 8-units thermal system.
IFI t =
PtL +PtR-EV + R Q.R.G t R Total t
R Q.R.G =rG,t t
∀G ∈ {1,2,8} as Quick Ramp Generator
(2) (3)
8
In Eq. 3, R Q.R.G is a supplied reserve per hour through fast ramp units with a ramp rate of t more than 2 MW per minute. In the 8-unit system studied, units 1, 2, and 8 have fast ramp rates. In order to determine the effects of uncertainty on the parameters of the system, an appropriate method of scenario generation based on average value of wind speed, solar radiation, and reserve system (a linear function of system load) is required. Therefore, the LHS sampling method [18] is used to generate and synthesize the scenarios of wind power, solar radiation and required reserve. In this method, two separated steps are considered for sampling and combining. At the sampling stage, 3000 samples are provided to represent the random nature of wind speed, solar radiation, and reserve. For this purpose, the cumulative distribution function with three variables is divided into 3000 portions having equal probability (1/3000). The gathered scenarios are based on 3000 mixed data with 3 variables at every hour which multiplies the calculation time. The K-Means clustering algorithm is used to overcome this challenge. The foundation of this algorithm is based on the hierarchal clustering of 3 variable scenarios within the initial clusters and depends on the probability, distance and repeating the procedure. The center point of each cluster is indicative of the cluster features including the wind speed, solar radiation, and reserve. Fig. 2 represents a clustering sample with center point and speed of the wind, solar radiation, and reserve. The probability of each scenario is calculated by dividing a number of scenarios at each cluster by the total number of scenarios.
9
Fig. 2. A sample of scenario clustering provided by K-Means algorithm
As stated, the K-Means clustering algorithm has been used to reduce scenarios. This algorithm begins by determining the number of clusters and the position of the center of each cluster, and each observation (result) to the nearest center is allocated using the Euclidean distance ( GD n,m ) as Eq. (4).
G D n,m =
Y
∑ (π
n,y
-τ m,y ) 2
(4)
y=1
In which, π n,y is the y attribute value of the n-th observation, τ m,y is the y attribute value from the center of the cluster m and Y is the total number of features per observation. Then the centers are updated and these steps are repeated until the movement of all centers to be stopped. The K-Means clustering algorithm is the selection of the optimal cluster number (k). The cluster quality is calculated in order to determine the optimal number of clusters by Eq. (5). SI n =
βn − αn max(α n , β n )
(5)
10
In which, αn is the mean incompatibility (unlike) of observation n with all other observations in the same cluster and βn is the least incompatibility observation n with all other observations in other clusters. The higher the SI n value, the more the match between n and its cluster will be greater; therefore, each dataset has an average and the optimal number k is the highest mean SI n for the whole dataset [19]. Laterally, herein, 5 reduced scenarios are chosen among 3000 scenarios by means of the K-Means algorithm. In this paper, the probability distribution functions of Weibull, Beta and Normal are used to model the probabilistic function of variables of the wind speed, solar radiation, and required reserve within 24 hours, respectively [17], [20].
2-1- Modeling of thermal unit commitment With the aim of minimizing the operation costs of thermal units, an objective function is defined as follow: NL NL SU SD R ENS min ∑∑ CG u G,t + CG (P G u G,t + pG,t ) + ∑ CG,sc ψ G,sc,t + CG k G,t + CG rG,t + C ens t 424 3 14444 4244444 3 sc∈SCG 123 { 1 G∈λ t∈Τ iv v iii i 1442443 ii
(6 )
Where; the i-th term denotes the generation cost, ii-th term is related to the start-up cost, iii-th term is the shut-down cost; iv-th term is the supplied reserve cost, and the v-th term denotes the non-supplied power. The generation cost is defined as piecewise-linear approximation having a slope of C LV and a width of origin C NL . The start-up cost which poses an increasing trend is dependent upon the shut-down duration of each unit before starting up. The start-up cost is determined by the following equations:
ψG,sc,t ≤
SU TG,sc+1 -1
∑
SU i=TG,sc
∑
sc∈SCG
SU k G,t-i ∀G,t ∈ TG,sc+1 ,T ,sc ∈ [1,SCG )
ψG,sc,t = z G,t ∀G,t
(7 )
(8 )
11
The total activation time of a segment in Eq. (7) is smaller than/ equal to 1; in Eq. (8), it is equal 1 for the times that are exactly related to the start-up of unit and is equal zero for the other times so that the start-up point of each segment can be determined.
2-2- Thermal unit commitment constraints 2-2-1- Balancing power and reserve constraints In Eq. (9), the balance of generated power with consumed load is equaled and in In Eq. (10), the desired spinning reserve is provided.
∑ P u + p ∑r +P +P G
G∈λ
G∈λ
G,t
G,t
L t
G,t
= L t -ENSt ∀t
(9 )
≥ R Total ∀t t
(10)
R-EV t
The average required reserve is R Total , a part of which is supplied by thermal units and the t other part of which is supplied by the smart grid and PHEVs.
∑r
G∈λ
G,t
denotes the spinning
reserve provided by thermal units. PtR-EV is capacity that injects to the power grid from PHEVs.
2-2-2- The constraints of minimum duration of start-up/ shut-down To solve the mentioned problem, logical conditions should be exactly determined. t
∑
z G,t ≤ u G,t ∀G, t ∈ [MUTG ,T]
(11)
k G,sc,t ≤ 1-u G,t ∀G,t ∈ [ MDTG ,T ]
(12)
i=t-MUTG +1
t
∑ i=t-MDTG +1
At the condition of z=1, all of the u-terms are equal to 1. Eq. (12) is the same as Eq. (11) but differs at the condition of k=1, where all u-terms are equal to zero. Following Eq. is valid for start-up/shut-down procedures:
u G,t -u G,t-1 = z G,t -k G,t ∀G,t
(13)
12
According to Eq. (13), at the start-up cycle of the unit, z =1 and at the shut-down cycle, k =1. Otherwise, when no conditional change occurs in the unit, since k G,t + u G,t ≤ 1, therefore, both parameters are zero.
2-2-3- Generation constraints Equations (14) and (15) are related to the units with MTU = 1. Eq. (16) is related to the units with MTU ≥ 2. p G,t +rG,t ≤ (PG -P G )u G,t − (PG -SUC G )z G,t ∀G ∈ λ1 ,t
(14)
p G,t +rG,t ≤ (PG -P G )u G,t − (PG -SDC G )k G,t+1 ∀G ∈ λ1 ,t
(1 5 )
p G,t +rG,t ≤ (PG -P G )u G,t − (PG -SUC G )z G,t -(PG -SDC G )k G,t+1 ∀G ∉ λ1 ,t
(16)
These equations determine the power constraints at the start-up and shut-down conditions based on upper and lower limits.
2-2-4- Ramping constraints Eqs. (15) and (16) express the constraints of ramp-up and ramp-down unit, respectively.
(pG,t +rG,t ) − pG,t-1 ≤ RUR G (-pG,t +pG,t-1 ) ≤ RDR G
∀G,t
∀G,t
(17) (18)
2-3- Modeling of the smart grid In order to develop a model based on the uncertainty of generation of wind and solar and the reserve scheduling in the smart grid, a two-step stochastic scheduling is performed. The responsive loads and DGs as backup capacities have compensated the uncertainty of the generation of wind and solar and the reserve scheduling. The objective function of this scheduling problem that is modeled as Eq. (19) consists of the expected operation cost of smart grid resources, which should be minimized.
13
T J D DG R E R min EC = ∑ ∑ {CDG +R × q +SU + j,t j,t j j,t } ∑ CPd,t +CPd,t t=1 j=1 d S D T J E +∑ µ s ∑∑ CDG + CPd,t,s ∑ j,t,s s =1 d=1 t =1 j=1
(19)
R DG In Eq. (19); j=1, 2, ..., J is the number of nonrenewable DG units; CDG j,t , R j,t , q j and
SU j,t are the hourly cost of fuel, reserve commitment, reserve cost and start-up cost of nonrenewable DG at a defined time of t, respectively; CPd,tE is the cost of commercial consumers due to the load reduction at the time t; CPd,tR is the reserve commitment cost induced by commercial consumers at the time t. At the second part of the target function, µs is the probability of the wind, solar and thermal system reserve scenarios; C DG j,t,s is the hourly cost of E the non-renewable DG at the time t and scenario s; CPd,t,s is the load reduction cost induced by
commercial consumers at the time t and scenario s. The coefficients of the operational cost function of non-renewable DG units are mentioned in [22]. The constraints of the nonrenewable DG units are given by the following equations: DG.max Pj,tDG +R DG .v j,t j,t ≤ Pj
Pj,tDG ≥ PjDG.min .v j,t
∀j,t
(20)
∀j,t
(21)
SU j,t ≥ SUC j×(v j,t -v j,t-1 )
(22)
SU j,t ≥ 0
(23)
PjDG.min and PjDG.max are the minimum and maximum constraint of the output power of DG
units, respectively. SU j,t and SUC j are the start-up cost of unit j at time t and the start-up cost of unit j, respectively. On the other hand, Eq. (24) expresses that the constraint of DG units should be considered in each scenario:
14
DG DG R DG j,t ≥ Pj,t,s -Pj,t
∀j,t,s
(24)
According to Eq. (24), the output power difference between the DG units in each scenario DG ( Pj,t,s ) and scheduled power ( Pj,tDG ) should not exceed the spinning reserve in DG units.
In the demand response modelling, commercial consumer collection is used that beside the PHEVs is being fed by the smart grid. The collection is used to preserve or reduce the load considering the cost defined for each hour. E R max CCd,t +CCd,t ≤ CCd,t
(25)
E E CPd,tE = CC d,t ×q d,t
(26)
R R CPd,tR =CC d,t ×q d,t
(27)
R E E CCd,t ≥ CCd,t,s -CCd,t
(28)
In Eqs. (25)-(28); d=1, 2, …, D is the number of commercial consumers collections; max CCd,t is the maximum load reduction; CC Ed,t is the reduced deterministic load value; CC Rd,t
is the residual reserve of the maximum reduction load; CC E d,s,t is the reduction load of each scenario with the commercial consumer d at the time t. The constraints of the stochastic scheduling method are as follows: J
W
PV
j=1
W=1
pv=1
∑ Pj,tDG + ∑ Ptw + ∑ Ptpv + η+b × Pb,t+ -η-b × Pb,t− = PtL -∑ CCd,tE
∀t
(29)
d
The constraint of power balance in the smart grid can be obtained by Eq. (29). Where;
Ptw and Ptpv are averages of wind and solar power at time t, respectively. Pb,t+ and Pb,t− are indicators of scheduled battery discharge and charge, respectively. η+b and η-b are the effective coefficients of battery discharge and charge. PtL is the hourly demand for a part of profile load of commercial customers and a part of the available PHEVs charge in parking.
15
The power balance of each system scenario should be preserved in both equations of (29) and (30). J
∑P
DG j,t,s
j=1
W
PV
W=1
pv=1
E + ∑ Ps,tw + ∑ Ps,tpv + η b+ × Pb,t+ -η-b × Pb,t− = Ps,tL -∑ CC d,t,s -ENSs,t
∀t,s
(30)
d
Ps,tL can be obtained from Eq. (31).
∑r
G∈λ
G,t
Total +Ps,tL + PtR-EV ≥ R s,t
(31)
According to the defined provision between the smart grid and thermal reservation Total system, R s,t is the uncertainty of thermal unit reservation. The smart grid should be capable
Total and certain thermal unit reservation by Ps,tL . to provide the difference between R s,t
PtL =PtCC +PtEV
(32)
In Eq. (32), PtCC is a part of load profile of commercial customers and PtEV is a part of the charge of available PHEVs in parking lot that smart grid should supply them. The charging and discharging procedure in the energy storage collection are not optional and hence following constraints should be considered: SOC b,t = SOC b,t-1 +η -b × Pb,t− -η +b × Pb,t+
(33)
SOC Min ≤ SOC b,t ≤ SOC bMax b
(34)
In Eq. (33); SOC b,t is the stored energy in the storage collections. η+b and η-b are the discharge and charge efficiencies of the energy storage collection. In Eq. (34); SOC Min and b are minimum and maximum capacities of energy storage collection, respectively. In SOC Max b the case of charge and discharge constraints, the following equations should be considered: Pb,t− ≤ Pb_Max
(35)
+ Pb,t+ ≤ Pb_Max
(36)
X t +Yt ≤ 1; X,Y ∈ {0,1}
(37)
16
+ In Eqs. (35) and (34) Pb_Max and Pb_Max are maximum discharge and charge of energy
storage collection, respectively. In Eq. (37) X t and Yt as the binary variables denote the energy storage collection charge and discharge status by which the concurrency of charging and discharging at the same hour is prevented. The power supply distribution of the solar station can be obtained by Eq. (38): Ppv (sr)=ηpv ×Spv ×sr
(38)
pv Where; Ppv (sr) is the output power of PV for (sr) radiation; η and Spv are the
efficiency and total area of PV, respectively. The proposed model of wind turbine output regarding the wind speed variation curve is calculated by Eq. (39) [17]. 0 rated ( v w -vin ) Pw × Pw (v) = ( v r -vin ) rated Pw 0
0 ≤ v w ≤ vin vin ≤ v w ≤ v r
(39)
v r ≤ v w ≤ v out v out ≤ v w
Where; Vin, Vr, and Vout are the cut-in speed, nominal speed and cut-out speed of wind turbine, respectively. Fig. 3 shows the flowchart of the flexible system studied and the relationship between the components of the smart grid and the thermal units.
17
start Wind Distribution Function Data
Solar Distribution Function Data
Required Reserve Distribution Function Data
LHS Sampling Method
Optimization Cost Function of Unit Commitment
Decrease Number of Scenarios with K-Means Algorithm
DG Data
Number of Available PHEVs and Load Profile
Smart Grid Uncertainty Model Management
Commercial Load Profile
Storage Collection Data
Evaluate Objective Function Provided Reserve for Thermal units system
Termination Criteria Satisfied?
Yes
Optimized Operation Planning
No End Change the Variables
Fig. 3. Flowchart of the flexible system studied
3- Numerical study A standard system comprising 8 units is used as the simulated thermal unit of the proposed smart grid model [22]. The unit commitment optimization method based on MILP (Mixed Integer Linear Programming) algorithm is used to solve the problem. Table (1) represents the detailed information of 8 units. About 5% of the daily load is considered as the average essential thermal reserve, while in a unit commitment, each thermal unit supplies a part of the reserve with 20% of CLV costs.
18
In order to obtain the uncertainties of the reserve, the average data is gathered from the daily load curve of an 8-unit system. The standard deviation data is assumed to be 4% of daily load curve of an 8- unit system. The total load is 1552 MW. Table 2 represents the load percentage of 8- unit system in 24 hours. Table 1: The information of 8 studied units Gen 1 2 3 4 5 6 7 8
P
P
[MW]
[MW]
455 455 130 130 162 80 85 55
150 150 20 20 25 20 25 10
[h] MUT MDT
[ MW h ] RUR RDR
8 8 5 5 6 3 3 1
225 225 50 50 60 60 60 135
Ste0
TcSU
[h]
[h]
[$ h ]
8 8 -5 -5 -6 -3 -3 -1
14 14 10 10 11 8 6 2
1000 970 700 680 450 370 480 660
CNL
CLV
[$
MWh ]
16.19 17.26 16.60 16.50 19.70 22.26 27.74 25.92
CSU h
CSU c
[$ ]
[$ ]
4500 5000 550 560 900 170 260 30
9000 10000 1100 1120 1800 340 520 60
Table 2: The information of 24-hour load Time[h]
1
2
3
4
5
6
7
8
9
10
11
12
Demand
71%
65%
62%
60%
58%
58%
60%
64%
73%
80%
82%
83%
Time[h]
13
14
15
16
17
18
19
20
21
22
23
24
Demand
82%
80%
79%
79%
83%
91%
90%
88%
85%
84%
79%
74%
In the smart grid related to thermal units, the daily load profile is a part of PHEVs charge and a part of load profile of commercial consumers. Fig. 4 shows the number of available parked PHEVs at each hour of the day [23]. The total PHEVs are equal to 5000, according to the Markov model used for the uncertainty of the presence of plug-in electric vehicles in [23] 50% of the vehicles are in the parking lot, certainly, so 30% of which and 50% of their capacity are programmed to be charged by the smart grid. It is consumed that PHEVs are similar to each other having a battery capacity of 25 KW and charge/discharge coefficient equal to 0.9.
19
Fig. 4. The number of plug-in hybrid electric vehicles available in parking at each hour
On the other hand, according to the assumption, each plug-in hybrid electric vehicle at the time of its call by the electric vehicles operator can supply 10% of its capacity inject to the power grid in an interval of one hour as thermal units reserve for their free power supply through the smart grid. Fig. 5 shows a part of charge of available parked PHEVs and a part of load profile commercial consumers that should be certainly supplied by the smart grid.
Fig. 5. Daily load curve of the smart grid
The summation of reduced loads and their reserve should not exceed the maximum load reduction. The maximum load reduction in the case of the commercial consumer is suggested
20
to be 25% of the demand curve at each hour. The load reduction and reserve costs for commercial consumer collection are presented in Table 3. Table 3: The cost of reduction load and reserve for Commercial customers Commercial Customer Time [hour] 1 2 3 4 5 6 7 8 9 10 6 6 6 6 6 6 6 7 4 Cost of reduction load [$] 6 3 3 3 3 3 3 3 3 3.5 2 Cost of reserve [$] Time [hour] 13 14 15 16 17 18 19 20 21 22 10 50 60 8.5 6 10 20 30 30 30 Cost of reduction load [$] 5 25 30 4.25 3 5 10 15 15 15 Cost of reserve [$]
11
12
10 5
10 5
23
24
30 15
30 15
In the present work, 80 wind turbines with similar features (each of them has a capacity of 0.5 MW) are installed in a wind farm. The specifications of turbines are listed in table 4. Table 4: The specifications of the turbine Parameter Rated power[kW] Cut-in speed [m/s] Nominal speed [m/s] Cut-out speed [m/s]
Value 500 3 13 25
The solar power plants consist of 5 photovoltaic systems, each of them consists of 50 thousand solar panels. The specifications of each photovoltaic panel are listed in Table 5. Table 5: The specifications of the photovoltaic panel Parameter Value [%] η 18.6 SPV [m2] 1 Pmax [W] 250
In addition to the renewable generation, two fast fossil units with small capacity are used in the smart grid. The specifications of the DG units in the smart grid are presented in Table 6 [21]. Table 6: The specifications of the distributed generation
DG
DG1 DG2
Pmin
Pmax
[MW]
[MW]
0.5 1
6 10
a
b
c
Ramp up [MW/h]
2 2
13.3 13.3
50 50
2.5 2
Ramp down [MW/h]
Start up cost [$/MW]
Shut down cost [$/MW]
Minimum Up-time [h]
Minimum Downtime [h]
2.5 2
10 9
15 13
1 2
1 2
The specification of the energy storage collection is assumed in Table 7 [21]. 21
Cap[MW]
Max-dis [MW.h]
10
8
Table 7: The specifications of energy storage collection Max-ch Max-cap Min-cap Deep of [MW.h] [MW] [MW] discharge 5
10
1
0.7
Eta 0.85
4- Numerical results The average generation of wind and solar power plants are shown in Fig. 6 and Fig.7, respectively. The average and standard deviation values of solar radiation and wind speed distribution functions are mentioned in [17].
Fig. 6. The average generation curve for wind power plant
Fig. 7. The average generation curve for the solar power plant
According to the LHS method and the K-means clustering algorithm described in the previous sections, the scenarios of the solar radiation, wind speed, and the amount of reserve required for thermal units are shown in Figs.8-10, respectively. The green, magenta and cyan color in Figs. 8-10 indicate the 3000 distributed scenarios for solar radiation, wind speed, and required reserve for thermal units, respectively. 22
C1 C2 C3 C4 C5
1.6 Radiation(KW/m2)
1.4 1.2 1 0.8 0.6 0.4 0.2 0
2
4
6
8
10
12 14 Time(Hour)
16
18
20
22
24
Fig. 8. The state model scenarios of solar radiation with uncertainty
40 C1 C2 C3 C4 C5
35 Wind Speed(m/s)
30 25 20 15 10 5 0
2
4
6
8
10
12 14 Time(Hour)
16
18
20
22
24
Fig. 9. The state model scenarios of wind speed with uncertainty
23
80
Required Reserve(MW)
75 70 65 60 55 C1 C2 C3 C4 C5
50 45 40 35
2
4
6
8
10
12 14 Time(Hour)
16
18
20
22
24
Fig. 10. The state model scenarios of required reserve for thermal units with uncertainty
As shown in Fig. 11, at the first hours (1 AM–8 AM), all available curtailment load capacities are cut. This result is despite the start-up status of DG1 unit which is due to the lack of the supplied power from solar power plants in the first hours. With increasing the power of solar units at the midday hours (9a.m-4p.m), the reduced load values decrease significantly while in contrast increases the reserve of curtailment load. At the last hours of the day, the reduced load increases again with decreasing solar power.
F ig. 11. The reduced and reserve curtailment load value
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As shown in Fig. 12, the energy storage collection is discharged when the power consumption is higher than the system power generation.
Fig. 12. The status of battery discharge/charge
According to Fig. 13, the DG units have been activated at separated times based on their capacities. Therefore, the DG1 unit provides power at hours between 1 AM–8 AM and DG2 unit provides power at hours between 9 AM–12 PM. The activation state of DG2 instead of DG1 is due to higher installation capacity for reserve supply system at uncertainty condition to balance the power of different system scenarios.
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Fig. 13. Reserve and generation of DG units
As previously mentioned in Eq. (8), the smart grid with optimized scheduling delivers the power generation as an offer of reserve supply to system planner according to contract with thermal units at each hour. To provide a part of certain thermal system reserve, the available vehicles in smart grid parking offer a percentage of their power capacity to thermal units each hour. Therefore, thermal collections can schedule their system more flexible and reduce system costs by providing a part of their required reserve by means of the smart grid.
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Fig. 14. The commitment of thermal units in the absence of smart grid as the reserve system
Fig. 15. The commitment of thermal units in the presence of smart grid as the reserve system
Comparing Figs. 14 and 15 reveals that in the presence of smart grid as the reserve system, 8th thermal unit remains deactivated until the end of the schedule. The power generation of this unit is transferred to the other units and power scheduling changes at 27
different hours. The results obtained for generation scheduling of thermal units per hour without the presence of smart grid generation are in accordance with the results obtained in reference [22].
F ig. 16. The reservation of thermal units in the absence of smart grid as the reserve system
Fig. 17. The reservation of thermal units in the presence of smart grid as the reserve system
Figs. 16 and 17 show the reserve supply profile in the absence and presence of smart grid. Moreover, the reduction in the reserve supply and change in thermal system reserve scheduling can also be observed.
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Fig. 18. The cost of reservation of thermal units in the absence of smart grid as the reserve system
Fig. 19. The cost of reservation of thermal units in the presence of smart grid as the reserve system
Fig. 18, Fig. 19 and Table 8 presents the operation costs of an 8-unit system. The costs of power generation, system of reserve supply and start-up of thermal units in the presence of smart grid are less than the costs in the absence of smart grid. Table 8: Operation cost of the thermal units system Cost of Thermal Units
Power Cost [$]
Reserve Cost [$]
Start-Up Cost [$]
Total Operational Cost [$]
Without Smart Grid as Reserve Supplier
571490.7
5691.4
3420
580602.1
With Smart Grid as Reserve Supplier
566906.9
1606.8
3080
571593.7
Table 9 is related to the costs of smart grid operation. The results of simulation show that when the uncertainty condition of wind, solar and required reserve is considered, the total costs in flexible smart grid system are reduced. Although the costs of operating the smart grid 29
are imposed on the whole system, reducing the cost of operation and reserve supply in the 8unit system justify generally the suitability of this proposed model. Table 9: Operation cost of smart grid DG Operational Cost [$]
Cut-off Power Cost [$]
Cut-off Reserve Cost [$]
DG Scenarios Operational Cost with uncertainty Coefficient [$]
Cut-off Scenarios Power Cost with uncertainty Coefficient [$]
Total System Cost [$]
4619.3
546.25
564.25
1910.8
251.6
7892.2
Fig. 20 shows how many percent of the required reservation of the 8-unit thermal system is provided by the smart grid. The closer the index to 100, then the smart grid has been able to replace a larger percentage of the system reserve with a quick type of reserve and reflect more flexibility in operating condition and faster responsiveness to changes. As shown in Fig. 20, at the peak hours of the network load (hours 11-15), the reserve response flexibility index (RRFI) has the highest value.
Fig. 20. The variations of flexibility index of reserve response for an 8-unit system
Fig. 21 shows the improved flexibility index of the system with and without the smart grid.
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Fig. 21. The variations of improved flexibility index for an 8-unit system
As shown in Fig. 21, the flexibility index is improved, especially during peak load times. Therefore, in addition to increasing the backup capacity, the reserve supply speed is also increased every hour.
5- Conclusions The main objective of the present research study is to propose a more flexible model based on fast reserve supply. In this paper, the mixed integer linear programming (MILP) method and the mixed integer non-linear programming (MINLP) has been used in order to solve the unit commitment problem considering operation constraints and smart grid, respectively. Flexibility is defined as an index of the concept of fast reserve supply. The smart grid system possesses resources of the renewable, nonrenewable power plant, PHEVs and demand response as virtual power plant. Demand response and DGs generation are not only used to provide a reservation but also used to balance the generation and consumption power of various scenarios induced by uncertainty. Latin Hypercube Sampling as a stochastic method is used to generate and synthesize wind and solar power generation and required reserve scenarios. In order to investigate the effects of uncertainty phenomena on unit commitment, K-Means algorithm is used to reduce scenarios and complexity of the problem.
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The results of the proposed model are revealed that despite available costs in the smart grid, it is possible to reduce costs of the power supply and thermal unit reservation. Therefore, the generation of smart grid and PHEVs reduces the total costs of the system.
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Highlights:
A flexibility index is defined with the concept of fast reserve supply.
A smart grid containing fast-power generation resources are designed.
The plug-in hybrid electric vehicles provide a system with improved flexibility.
The LHS method is used to make the uncertainties of required reserve.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: