Reliability based optimal allocation of distributed generations in transmission systems under demand response program

Electric Power Systems Research 176 (2019) 105952

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Reliability based optimal allocation of distributed generations in transmission systems under demand response program

T

⁎

Hadi Chahkandi Nejada, Saeed Tavakolib, Noradin Ghadimic, , Saman Korjanid, ⁎ Sayyad Nojavane, , Hamed Pashaei-Didanif a

Department of Electrical Engineering, Birjand Branch, Islamic Azad University, Birjand, Iran Faculty of Electrical and Computer Engineering, University of Sistan and Baluchestan, Zahedan, Iran c Young Researchers and Elite Club, Ardabil Branch, Islamic Azad University, Ardabil, Iran d University of Cagliari, Department of Electrical Engineering, Cagliari, Italy e Department of Electrical Engineering, University of Bonab, Bonab, Iran f Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran b

A R T I C LE I N FO

A B S T R A C T

Keywords: Distributed energy resources Demand response Reliability Particle swarm optimization Unit commitment

Rising dependency on reliable electric power has resulted in emerging technologies in power system such as Distributed Generation (DG). Recent developments in Information and Communication Technologies (ICTs), Advanced Metering Infrastructures (AMIs) and Wide Area Measurement Systems (WAMS) will guarantee high penetration of DR programs in near future. In this paper, optimal allocation of DG units in the transmission systems with the aim of improving reliability of power system is carried out through introducing a placement index. The placement index takes both reliability and economic issues into the account. The impacts of DR programs on optimal allocation of DG units are also considered. Power system operation in the presence of DR programs and DG units are implemented through a unit commitment problem and several operational parameters are scrutinized so as to underline the efficiency of the proposed method, considering the complexity of the problem in this paper, population based intelligent search methods have been utilized extensively. The effectiveness of proposed allocation method is illustrated on IEEE RTS-79.

1. Introduction

1.1. Literature review on DG allocation

Restructuring of power system, growth of digital grade loads, increasing importance of reliability issues and minimizing environmental impacts of conventional centralized electric power generation have been leading to integration of dispersed small power generation units [1]. Usually the aforementioned units are connected close to the load points whilst are intended to serve the load in less expensive manner [2,3]. On the other hand, smart grid paradigm with enabling bidirectional communication technologies between demand side and supply side, would result in adjustable load based on Demand Response (DR) programs. In this case, power system operation would be influenced due to integration of Distributed Generation (DG) units [4] and DR programs and it should be investigated specifically.

Fast developing technologies contributed with DG have resulted in several researches through the multiple effects and characteristics of DG units in power system. Optimal allocation of DG units is of the most research interest recently which can be classified into two main categories, DG allocation in radial networks and meshed networks. Radial networks are considered for distribution networks while meshed ones are used for transmission and sub-transmission networks. Characteristics of these two types of topologies have resulted in many optimal allocation methods, which differ in formulations, evaluations and analysis aspects. A brief bibliographical survey about optimal allocation of DG is presented as follows. In a radial distribution network, by using the loss sensitivity index to determine the candidate buses for DGs, optimal sizing and allocation of renewable energy based DGs are investigated proposing the ant lion optimization (ALO) method in Ref. [5].

⁎

Corresponding authors. E-mail addresses: [email protected] (H. Chahkandi Nejad), [email protected] (N. Ghadimi), [email protected] (S. Korjani), [email protected] (S. Nojavan), [email protected] (H. Pashaei-Didani). https://doi.org/10.1016/j.epsr.2019.105952 Received 19 March 2019; Received in revised form 15 July 2019; Accepted 17 July 2019 Available online 02 August 2019 0378-7796/ © 2019 Elsevier B.V. All rights reserved.

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Nomenclature

The weighting coefficients Wi Xnb, k, t Demand reduction at each hour and load point Active power loss of the system LOSSj, t Cn (PGn, t ) Cost function of generation unit n CostEUE (EUEt ) Cost function of expected unserved energy VOLLnb, t Hourly VOLL at each load point QDG, n Output reactive power of DG unit n at hour t Injected reactive power at bus i QGn Voltage magnitude at bus i Vi

Constants Hourly maximum accessible demand reduction through DR programs by each class of consumers Dt Load demand at time t Dpeak Peak load demand of consumers μi Repair rate Failure rate λi Xnb, K , t Hourly percentage of load reduction by kth class of consumers at bus nb through DR programs Dnb, K , t Hourly load demand of kth class of consumers located at bus nb fv Fixed or variable functional value Number of classes of consumers Nk Nb Number of buses Ng Number of generators Number of DG units NDG PGnmax ,PGnmin Maximum output active power of generator n at hour t min max QDG , n , QDG, n Minimum and maximum reactive power generation DG limit of unit n Start up cost of unit i at hour t SCn, t Tnoff, t Duration of continuously off state of unit n at hour t Tnon, t Duration of continuously on state of unit n at hour t Vimin/ Vimax Minimum/maximum limits for voltage magnitude at bus i

ξk, max

Indices k T Acronyms DER EUE FOR GSF LOLP LT MLC NDLM ORR PI RES UC VOLL

Variables

ξk, t CRj, t PRj, t

The specific class of consumers: large consumers, medium consumers, small consumers and residential consumers. Scheduling period

The load ratio which is tended to be curtailed at each hour Total capacity remaining in service of state j Probability service of state j

Distributed energy resource The expected unserved energy Forced outage rate Generation sensitivity factors Loss of Load Probability Lead-time Marginal loss coefficients Network driven load management Outage replacement rate Placement Index Renewable energy source Unit commitment Value of lost load

possible operating conditions of the DGs is proposed in Ref. [13]. In this model, minimization of the annual energy loss is carried out by optimal allocation of various types of the renewable energy based DGs in a distribution system. A new method based on a multi-objective genetic algorithm and a max–min approach is utilized for optimal placement of DG units in Ref. [14]. Due to electricity market price uncertainty the minimization of monetary cost, technical and economic risks are the investigated in the latter reference. A multi-objective formulation including genetic algorithm and ε -constrained methods is presented to get the placement and sizing of DGs into existing distribution networks in Ref. [15]. An improved dynamic programming for optimal allocation of DGs in a distribution network for power loss minimization of the system and enhancing both reliability and voltage profile improvement is addressed in Ref. [16]. A genetic algorithm-based approach for optimal re-closer positioning is addressed in Ref. [17] by deploying distributed generators in a securely optimal manner. For radial distribution networks, an ant-colony algorithm is proposed in Ref. [18] to obtain the optimal placement scheme of the re-closer and DG considering a composite reliability index as the objective function. In Ref. [19], optimal placement and number of DGs are determined using a MINLP approach in hybrid electricity market. The non-linear optimization approach is designated to minimize total fuel cost of both conventional and distributed generation sources as well as minimization of transmission network loss. In Ref. [20], a GA-Fuzzy model is utilized to derive the optimal location and sizing of DGs to maximize the system loading margin and profit of the distribution generation companies over the planning period. Optimal location and size of DG units are determined based on nodal prices for both profit maximization and social welfare in Ref. [21].

In order to cope with the volatile power output of renewable energy sources, a new formulation to obtain the optimal sizing and sitting of renewable energy based DGs including wind, fuel cell, and a solar unit is proposed in Ref. [6]. The problem is solved utilizing Particle Swarm Optimization (PSO) algorithm, which is one the best known optimization techniques with the aim of minimizing total harmonic distortion, the total cost of DG unit, greenhouse gas emissions, and total power losses. The total power loss in distribution systems is minimized using efficient analytical (EA) method by optimal sitting of multiple DG units in Ref. [7]. The proposed method is integrated with the optimal power flow (OPF) algorithm and a new EA-OPF method is developed to model the constraints of the system. The optimal sizing and sitting problem of DG units is solved in Ref. [8] utilizing a comprehensive teaching learning-based optimization (CTLBO) technique. Obtained results in this paper state that the proposed method resulted in significant improvement of distribution systems performance. In Ref. [9], the War optimization method, which is a new swarm method type meta-heuristic approach, is proposed to find optimal sizing of DGs with the aim of power loss minimization. After determining optimal locations, the optimal sizing of the DGs is determined using the OPF. Optimal allocation of wind turbine as a DG is carried out in Ref. [10] to minimize the active power loss in a distributed network. To do so, a new methodology is developed in which the uncertainty of wind speed is taken into account. The optimum location of DG units taking the time-varying loads into the account, with the aim of maximizing reliability improvement and minimizing power loss in distribution network is investigated in Ref. [11]. Considering uncertain and time-varying loads in distribution systems, a probabilistic method is proposed in Ref. [12] to get optimal sizing and sitting of renewable energy based DG. A probabilistic generation-load model to solve the problem combining all 2

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operational parameters is investigated throughout the operation problem. The objective function of the problem is formulated as a mixedinteger non-linear and non-convex programming problem. The developed optimization problem is solved utilizing the binary PSO (BPSO), and then the reliability evaluation is carried out. In order to illustrate the effectiveness of the proposed allocation and operation approach, the methods are applied to IEEE Reliability Test System (IEEE-RTS79). Finally, it should be noted that operation and utilization of renewable energy resources (RESs) such as wind turbine, photovoltaic power plant, etc. is dependent weather condition in the area. Therefore, feasibility studies should be carried out to make sure that using RESs is profitable in the considered region. As RESs is not interest of this paper, only common type distributed generation units are considered.

1.2. Literature review on demand response programs Optimal implementation of DR programs can lead to a more reliable power system, lower operational cost, promoting market efficiency and smoothing the integration of emerging electric power generation technologies such as DG and energy storage units [22]. The impacts of DR programs on several parameters of power system as well as modeling the DR implementation are discussed in several papers. The impact of time-o-use rate of demand response program on determining the selling price of electricity retailer in smart grid in investigated in Ref. [23]. The optimal performance of a grid-connected renewable energy based hybrid system has been evaluated under demand response program in Ref. [24]. In response to hourly electricity prices, a simple optimization model has been also used to allow the consumer to adjust its load model in Ref. [25]. Besides concentrating on the existing DR programs and evolving new schemes at various regional transmission organizations (RTOs) and independent system operators (ISO), the product markets which they can participate under the paradigm of smart grid are also investigated in Ref. [26] addressing the challenges of implementing DR programs in smart grid and market paradigms. A reserve model based on its associated cost function and DR providers are developed in Ref. [27]. In this Ref., the reserve capacity is scheduled using a stochastic model considering the DR resources in the market. The importance of the allocation of network driven load management (NDLM) programs with the aim of composite system reliability and total grid losses improvements have been illustrated in Ref. [28]. Network driven load management programs are a sort of strategic load reduction measures which are executed to maintain the short-term reliability in an acceptable level and they can also postpone the required technical augmentation in power system considering demand growth rate. Network driven load management programs encompass many terms as demand side management, direct load control and DR programs. Based on the flexible price elasticity concept of demand and customer benefit function an economic based model is derived for responsive loads in Ref. [29]. In response to different DR programs, the behavior of consumers is modeled developing an innovative approach through a comprehensive DR model in Ref. [30]. The model is developed with the aim of presenting customer response to incentive-based and time-based DR programs. The effectiveness of DR programs depends on a wide range of considerations like enabling technologies, advanced information and telecommunication systems, advanced metering infrastructure (AMI), availability of dynamic pricing and different states of responses of participants in DR programs. The common output of DR programs which has been mostly discussed in several previous works is the accessible load and energy reduction through DR program.

1.4. Paper organization The remainder of this paper is structured as follows. In Section 2 the concept of implementation of DR programs is delineated as well as the impact of load reduction through DR programs are discussed. Reliability considerations are presented in Section 3. Section 4 discusses a brief description of the proposed heuristic optimization algorithms while Section 5 is assigned to the proposed method for optimal allocation of DG units. The objective function formulation for the best possible operation of power system in the presence of DR programs and optimal allocated DG units is presented in Section 6. Section 7 concludes the paper.

2. Demand response program model The importance and applications of the demand response programs have been discussed in the previous section. In this paper, a linear DR model is proposed to simulate implementation of DR programs in power system. The proposed concept is based on the investigations which are probed in Ref. [31] and also a simple sensible assumption as follows. As load reduction potential at peak hours, corresponding with each class of consumers under full participation scenario is presented in Ref. [31], it makes sense to assign hourly load reduction which can be resulted by each class of consumers with respect to their hourly demand. It should be noticed that in this paper, the effect of load reduction of conducting DR programs is of the concern. In this case, maximum hourly load reduction potential is expressed as follows:

ξk, t = ξk, max × (

Dt ) Dpeak

(1)

Consumers are classified into four categories, large consumers, medium consumers, small consumers and residential consumers. Load reductions through DR programs are triggered in order to prevent violations from desired reliability level. Actually, in this paper, load congestion, voltage violations and short term composite reliability indices are considered to be enhanced due to participation of consumers in DR programs. Cost of DR programs is taken into evaluations based on nodal prices, as incentives which are paid to different classes of consumers to reduce their demand. The values for ξk, peak are presented in Table 1.

1.3. Novelty and contribution This paper proposes a new method for optimal allocation of DG units in the transmission systems based on operational indices for improving the reliability. The proposed procedure takes the effects of DR programs into the account and both DG units and DR programs would be considered in a short-term power system operation study. Demand response programs are modeled as NDLM programs, which are triggered to keep the reliability of the system in an acceptable range. Reliability is a comprehensive term, which consists of adequacy and security. Adequacy refers to adequate amount of available generation sources to meet the demand and security refers to the ability of the system to tolerate probable sudden changes and contingencies. In this paper, the impacts of DR programs are considered on the basis of maximum capability of hourly load reduction. The reductions would be triggered to improve the reliability as well as reducing both apparent power flow of transmission lines and operational costs. The operation of power system in the presence of DR and DG is formulated in a UC problem framework and some reliability index besides prominent

Table 1 Maximum peak reduction potential [32].

3

Consumer type

Peak reduction (%)

Residential Large consumers (greater than 5 MW) Medium consumers (between 1 MW and 5 MW) Small consumers (less than 1 MW) Total

10 7 2 1 20

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3. Reliability evaluation

repaired or replaced [37].

Providing customers with a choice of suppliers based on reliability and price requirements should be available in a restructured power system. It is therefore essential to develop techniques which could be used optimally for planning, operation and nodal reliability evaluation of restructured power systems. Determining probabilistic measure of the undesired events is the main goal of reliability analysis of the power system. Utilized techniques for the reliability analysis of the power system can be categorized as simulation methods, analytical methods, and the most recently intelligent search methods. In addition, state selection, state evaluation, and index calculation are considered as the three basic stages in any reliability technique. Huge amount of mathematical formulations and numerical computations is the inherent part of any analytical method. On the other hand, the deviation of estimations seems to be inevitable in some large problems through simulation methods as Monte Carlo simulation. In this paper, an improved BPSO is used to search the whole state space and sample those which have the greatest effect on composite power system reliability evaluation. Here, BPSO is used as a scan tool to sample dominant failure states and prevent excessive numerical computations based on Ref. [33]. This method can lead to a more optimal computation procedure from both speed and accuracy points of view. As the probabilities of states which cause power system to fail providing operational constraints are of very small values in operational reliability evaluation, the aforementioned technique can prevent excessive computations and misevaluation. After a predefined number of states are sampled or any other stopping criterion is met, composite power system reliability indices for each load bus and for the system can be calculated. For a selected state, if it is recognized as a failure one, loads would be shed through an optimal power flow problem in order to satisfy both adequacy and security constraints [34]. In this paper, the expected unserved energy (EUE) is taken into consideration. Note that the expected energy which will not be served is expressed by the EUE as follows:

Ui (LT ) =

∑ PRj,t × LOSSj,t

Ui (LT = 1) = λi = ORR

1 , if CRj, t < Dt LOSSj, t = ⎧ t ∈ ⎡1, ⎢ ⎨ ⎣ ⎩ 0 , otherwise

4. Modeling of case study Generally, in the UC problem, the scheduling of units and the economic dispatch decision are two basic points, which should be considered in solving the problem. Note that only an exact solution to UC problem can be obtained by using analytical method. On the other hand, considering the DG units and DR programs will impose complication on the UC problem, which means that implementing a flexible computational tool is inevitable. More complications will be imposed to the UC problem by taking the configuration of the network into account thus instead of economic dispatch the optimal power flow should be carried out at each hour. In this paper, RTS-79 is considered as case study and UC is formulated whilst DGs and DR programs are implemented into the transmission network. Reliability consideration has been taken into UC problem in many papers, reliability constrained unit commitment through heuristic and stochastic methods is investigated in Refs. [35,38], healthy operation of power system with a new model for system operating models is introduced and analyzed in Refs. [40,41], and reliable operation assessment with probabilistic spinning reserve in the presence of interruptible loads is probed in Ref. [37]. In this paper, UC problem is formulated so as DR programs can undertake a certain amount of hourly demand and optimally placed gas turbine with rapid start units which are assumed to be available within 10 min are supplying load points besides conventional generation units if needed. EUE is monitored during the scheduling time period to illustrate the impact of DG and DR. As responsive loads would curtail their demand through incentives and it is somehow voluntary, it is expected that the reliability be improved with the propose arrangement of Distributed Energy Resources (DERs, both DG & DR). The cost of total EUE would be taken into account to underline reliability at HLII (Hierarchical Level II) besides considering transmission network security and power flow constraints. In this paper, the objective function of UC problem in the presence of DG units and DR programs with the aim of improving reliability is formulated as follows:

(2)

T⎤ ⎥ ⎦

(3)

n

EUEt =

∑ PRj,t × LOSSj,t × (Dt − CRj,t ) t ∈ [1, T ] j=1

(4)

T

EUETot =

∑ EUEt t ∈ [1, T ] t=1

(7)

The unavailability of ith generating unit which is given by (7) is called the outage replacement rate (ORR). The ORR is similar to the forced outage rate (FOR). The difference between the two indices comes from the fact that the ORR is a time-dependent quantity affected by the value of considered lead-time rather than being simply a fixed characteristic of a unit [36]. Reliability evaluation through EUE and LOLP based on the concept of ORR is well discussed in [35,37–39].

t ∈ [1, T ]

j=1

(6)

In this paper, the lead-time (LT) is assumed 1 h, which is small when compared to repair and sound operating time of the generating units, which means that the repair time can be ignored. On the other hand, by considering LT equal to 1 and approximating the exponential function with first two terms of Maclaurin's polynomial in powers of t, Eq. (7) will be get which simplifies the unavailability of the generating units.

n

LOLPt =

λi (1 − e−(λi + μi) × LT ) λ i + μi

(5)

In Eqs. (2)–(5), CRj, t and PRj, t are total capacity remaining in service of state j and the corresponding probability, respectively. It should be noticed that the aforementioned indices are designated for system reliability indices evaluation. In this paper, the reliability is considered through a short term scheduling of generating units to meet the whole constraints of power system, and the objective function is formulated as a unit commitment problem. This means that only the committed generating units are considered in reliability assessment. An uncertainty, which in this paper is focused on, is random outages of generating units in each hour of the scheduling period and transmission network is assumed to be reliable. Nodal reliability indices are evaluated based on states, which are sampled through intelligent state sampling algorithm as it is discussed in. For the purpose of reliability analysis, the two-state model as shown in Fig. 1 is used to present each generating unit, according to which, a unit is either available or unavailable [35]. Eq. (6) depicts the unavailability of a repairable system at the precise moment t [36]. Note that the lead time is a relatively short period that a failed unit cannot be

Fig. 1. Two state model of generating units. 4

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H. Chahkandi Nejad, et al. Ng + NDG

24

min∑ (

∑

t=1 Nb

+

[Cn (PGn, t ) In, t + SCn, t (In, t − In, t − 1)] + CostEUE (EUEt )

n=1 Nk

∑ ∑

( Xnb, K , t × Dnb, K , t × incentivenb, K , t ) + CostDR)

nb = 1 K = 1

(8)

In (8), the first term models the startup and fuel costs of the conventional and DG units. The second term refers to the hourly cost of expected unserved energy (EUEt ). The paid incentives to consumers are calculated in the third term in which consumers would be paid based on hourly nodal prices to reduce their demands. The fourth term provides to the DR cost if considered. Note that in load points, the impacts of DR programs on demand reduction are considered. The cost of EUE is evaluated by multiplying EUE with a load shedding price for compensating consumers. The load shedding price is also referred as the value of lost load (VOLL) and is expressed in $/kWh. It can be said that VOLL is utilized for the assessment of both generation units and transmission lines outages. The cost of EUE is given by:

VOLLnb, t × EUEnb, t

where fv is a fixed or variable functional value which can be determined through the importance of loads based on socioeconomic concepts. In this manner, the risk of unsupplied energy is taken into objective function monetarily. The objective function which is derived in (8) is subjected to following constraints:

Ng + NDG

∑n=1

(11)

PGn, t = Dt −

N

N

∑nbb=1 ∑k =k 1 LCPnb,k,t + Losst

(12)

Where LCPnb, k, t = Xnb, k, t × Dnb, k, t Ng + NDG

∑n=1

PGnmax × In, t ≥ RL (t ) + Dt −

Nb

N

N

∑k =k 1 LCPnb,k,t = Vi × ∑ j=1 Vj × |Yij | × cos(θi − θj − N

∑k =k 1 LCQnb,k,t = Vi

×

N

∑ j=1 Vj × |Yij| × sin(θi − θj −

≤ PGn ≤

PGnmax

φij )

(16)

min max PDG , n ≤ PDG, n ≤ PDG, n

(17)

min max QDG , n ≤ QDG, n ≤ QDG, n

(18)

QGnmin ≤ QGn ≤ QGnmax

(19)

SCn, t =

off off ⎧ h − costn : MDn ≤ Tn, t ≤ Hn ⎨ c − costn : Tnoff, t > Hnoff ⎩

(20)

(26)

dPloss dPi

(27)

Nodal price = generation marginal cost + congestion cost + cost of marginal loss (28)

where Hnoff = MDn + c − s − houri

(Tnoff, t − 1 − MDTn )(In, t − 1 − In, t ) ≥ 0

(25)

Simax ,j

Small and negative values of MLCs indicate the potential of less increase and decrease, respectively, in loss of transmission network due to increase in power generation at corresponding bus. Nodal prices are the Lagrangian multipliers associated with the active power flow equations for each bus in transmission network. Nodal price at any load point in the system is the dual variable for the equality constraint at that node. Nodal price actually reflects the economically efficient value of electricity at that load point and higher nodal price implies higher the generation pressed by demand at that node [42]. Consequently, buses with higher nodal prices are suitable candidate for the placement of DG units with the aim of minimizing payment of consumers. Although no market vision is considered in this paper, it is important to minimize nodal prices because of the incentives which should be paid to the consumers so as to motivate them to participate in DR programs when needed. As it is probed in Ref. [43], the nodal price is composed of three components as follows as it is well explained in Refs. [19,21,43].

φij )

(15)

PGnmin

Vimin ≤ Vi ≤ Vimax

MLCi =

(14)

QGi − QLi +

(24)

N

∑nb=1 ∑k =k 1 Xnb,k,t × Dnb,k,t (13)

PGi − PLi +

PGn, t − 1 − PGn, t ≤ DRn

The integration of dispersed generation sources into power system can effect on both operation and dynamics of the transmission and distribution networks. Considering the fact that optimal placement of DG units can provide numerous advantages with power system, identification of most suitable area for DG penetration is very imperative in a wide area power system network, such as transmission network. In this paper, operational aspects are taken into account and DG units are planned to be placed on a specified sites. The candidate sites which are load buses in transmission network with no installed generation units would be ranked based on an operational criterion developed for optimal placement of DG units. Several parameters can be utilized to prioritize load buses for implementation of a predefined number to DG units. A Placement Index (PI) which is composed of four operational indices is introduced in this paper. These parameters are marginal loss coefficients (MLC), nodal prices, generation sensitivity factors (GSF) and nodal EUEs. MLC which is also called incremental loss provides information about pattern of losses in the transmission network with the unit power injection at each node. It is derived as follows:

(10)

0 ≤ Xnb, k, t ≤ ξk, t

(23)

5. Optimal allocation of DG units

In (9), VOLLnb, t is the hourly VOLL at each load point and is assigned a value dependent to nodal prices at corresponding hour. Since classified consumers can participate in DR programs and the considered payments are nodal prices as incentives to motivate them for participation in DR, VOLLnb, t is assumed to be a higher value than nodal price. Accordingly, VOLLnb, t is given as follows:

VOLLnb, t = NCnb, t × fv fv > 1

PGn, t − PGn, t − 1 ≤ URn

Demand reduction at each hour and load point is limited by (11) considering the maximum load reduction of consumers’ class. The constraints of reserve and power balance are presented by (12) and (13), respectively. The appropriate operation of generation units under the power flow constraints are ensured by (14)–(19). Startup cost can be evaluated based on (20) as well as it can be considered as a constant value for each generation unit. The constraints of minimum up and down time and ramping up and down rates are provided by (21)–(24), respectively. Finally, constraints (25) and (26) model the network security requirements.

(9)

nb = 1

(22)

|Sij, t | ≤

Nb

∑

CostEUE (EUEt ) =

(Tnon, t − 1 − MUTn )(In, t − 1 − In, t ) ≥ 0

Both nodal prices and MLCs would be calculated at peak hour with all stand-by units which are scheduled to meet the demand and the

(21) 5

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constraint correlated with generation units and transmission network in UC problem. The ratio of the change in unit line power flow due to the change in injected unit power of the designated bus is called GSF. Based on the definition of GSF, buses with higher negative values of GSF is more appropriate for active power injection. In this case, the active power flow of the lines with negative GSFs which correspond to the considered bus would be decreased by an increase in power injection at that bus. It means that a DG unit at buses with more negative values of GSFs is more efficient and could result in low congestion in transmission lines. GSFs depend on configuration and topology of transmission network and both arrangement of generation units and load pattern do not affect them. GSFs are fully probed in Ref. [44]. As the reliability assessment at HLII is about the ability of transmission system to deliver generated energy to the major load points [40], and based on the definition of EUE which is given in section III, nodal EUEs can be utilized to determine where to implement a DG unit. Higher values of nodal EUE refer to the weakness of transmission network with providing the load properly at related bus. In this case, evaluation of nodal EUEs in a short term scheduling of generation units and in a peak load curve, can lead to a reasonable result for placement of DG units. Regarding the description of the discussed indices and the aim of the placement of DG units which is improving the reliability of power system, PI can be formulated as a weighted summation of all four indices. In this case, regarding the EUE, it would result in lower expected energy which could not be supplied because of both generation system and transmission network, whilst taking GSF into account makes the placement of DG units more effective from the line congestion point of view. GSF based placement would lead to a lower active power flow on transmission lines which would also lessen the risk of contingencies besides the more free capacity. This would make the power transmission more secure with less contributed risk. Besides reliability consideration, MLCs and nodal prices guarantee the economically efficient placement of DG units. Reliability based PIs for optimal allocation of DG units can be expressed as follows:

Table 2 Required parameters of the PSO and BPSO algorithms. PSO setting parameters

∑ Wi × Unb,i

where 4

∑ Wi

= 1 and 0 < Wi < 1 ∀ i = 1,2, 3,4

i=1

Unb,1 =

(∑

)

−gsfnb, j / max { −SGSF }

j ∈ SN

(30)

(31)

Unb,2 = LMPnb/ max {SLMP }

(32)

Unb,3 = −MLCnb/ max { −SMLC }

(33)

Unb,4 = EUEnb/max {SEUE }

(34)

Itmax

Pamax

range

2.8

1.2

300

30

0.7

Pωmin

Pωmax

Itmax

Pamax

rate

0.1

0.85

300

30

0.1

At each hour, the required operation reserve considered as 10 percent of the load. Using the intelligent search methods, reliability evaluations and minimization of objective function are implemented. In addition, dominant failure state sampling and the scheduling of generation units carried out using the BPSO. Also, the participation of consumers in DR programs is investigated using the PSO. Energy storage systems can be used for future works [46,47]. Table 2 provides the information of required parameters in the utilized algorithms. In this paper, four scenarios are discussed which are symbolized by S0, S1, S2 and S3 as provided in Table 3. To solve the optimization problem, the particle swarm optimization (PSO) method is used problem which is a versatile population-based optimization technique, in many respects similar to evolutionary algorithms. In PSO method, the particles that represent potential solutions move around in the phase space with a velocity updated by the particle’s own experience and the experience of the particle’s neighbors or the experience of the whole swarm. On the other hand, population of the PSO method allows greater diversity and exploration over a single population. Also, the momentum effects on particle movement can allow faster convergence and more variety/diversity in search trajectories which makes a proper method to solve the problem. PIs are sorted in descending order as it is shown in Figs. 2 and 3. Buses with no generation unit and those of 138 kV voltage level are suitable candidates for DG placement. While no DR programs are considered, buses 4, 9 and 10 would be chosen for DG placement. DG placement considering DR programs would result in choosing buses 3, 9 and 10. Taking the effect of load reduction through DR programs into the evaluation has changed the optimum locations for DGs. As it was discussed before, the PIs are designated to consist of both economic and reliability aspects of power system operation. In this paper, power system operation is assumed to be in peak load day therefore, improvements of operational indices through optimal placement of DG units and DR implementation can be a verification of the proposed method. Nodal prices (NPs) are shown in Fig. 4 for each scenario. As it is obvious in Fig. 4, implementing DR programs solely, would result in increase of NPs while, operation with DGs and DGs beside DR programs would reduce NPs. Increasing of NPs in the presence of DR programs is because of decommiting of some small generation units near load points. This would cause farther large units to generate sufficient power to meet the demand. As the NP is a combination of cost of congestion besides generation marginal cost and cost of marginal loss, supplying load points by farther generation units would increase the NPs because of increases in line flows and line

(29)

i=1

c2

BPSO setting parameters

4

PInb =

c1

The weighting coefficients Wi can be assigned by different values to insist the importance of placement purpose. The load buses are ranked in descending order of PIs with the first node in the order as the best candidate for DG unit placement. It should be noticed that a load bus with a generation unit installed on it is not considered as a candidate bus.

Table 3 Description of scenarios.

6. Numerical analysis As said before, IEEE Reliability Test System (RTS-79) is considered for numerical analysis of the proposed methods [45]. Three DGs with total rated capacity of 25 MW should be allocated based on PIs. It should be noted that considered type of DG is a power only unit (e.g. micro-turbine) which generates power by consuming any type of fuel. 6

Scenario #

Description

S0 S1 S2 S3

operation operation operation operation S1

with no DR (DER) with DR with optimally placed DGs based on S0 with both DR and optimally placed DGs (DERs) based on

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percentage. Inclusion of DG units on optimum buses based on PIs has resulted in reduction of flow in transmission lines. It is because of the effect of power injection through DG units and the constitution of the proposed PI. The free capacity of transmission network is reduced while DR programs are considered in operation as it is presented in Table 4. No need for small generation units near the load points and supplying the load points from farther large generation units is the reason. This would also affect the loss of transmission lines as it is presented in Table 4. It may seem that the effects of DR programs are exaggerated in this paper, and this type of load reduction cannot be achievable. However, the results can pave the way for more systematic and technical consideration for taking the most advantages of DR programs as the enabling technologies are emerging into power system broadly. Numerical results show the effectiveness of both DR programs and DG units for reinforcement of power system. But, the effects of large load reduction through DR programs which are expectable in near future should be evaluated by considering several network constraints. As the conventional generation units are designated to supply the load firstly, reduction in load points may result in improper operation of generation system because of monetary reasons. This problem can be smoothening by applying some new regulatory decisions from software point of view and emerging technologies such as DGs and storage systems from hardware point of view.

Fig. 2. Sorted load bussed based on Placement Indices without DR.

7. Conclusion Fig. 3. Sorted load bussed based on Placement Indices with DR.

In this paper, optimal placement of DG units in the transmission systems was carried out based on a new placement index. The effectiveness of the proposed placement index was shown in four operation scenarios. The operation of power system was carried out through UC problem. Both the UC problem in the presence of DG and DR, and the reliability evaluation are carried out through an improved BPSO, while load reduction through DR programs was assessed by PSO. The numerical results illustrated some problems due to implementation of DR programs solely. An IEEE RTS-79 is used to evaluate the effectiveness of proposed allocation method. also, four operational scenarios are discussed as follows; operation with no DR (DERs), operation with DR, operation with optimally placed DGs based on first scenario and operation with both DR and optimally placed DGs (DERs) based on second scenario. According to the obtained results, more reliable operation of power systems can be attain in the presence of both DR and optimally placed DG units due to the flexibility in scheduling of DG units which can fulfill some of the network requirements in a more reliable manner. In addition, integration of DR and DG can lead to a further economic operational condition. This conclusion can be even more highlighted by means of some regulatory decisions in the field of DR programs and DG operation.

Fig. 4. Nodal prices at peak hour in different scenarios.

losses. The effects of DERs in each scenario on EUE are represented in Fig. 5. Reliability improvements through load reduction of DR programs and power injection of DG units are noticeable. The best situation is achieved through scenario S3. The last column of Table 4 represents a reliability index. Eportion is the percentage of total EUE to total energy consumption in the system. It reflects a sensible view about the reliable operation of power system. Enhancements in reliability through DERs are clear in Table 4. Load reduction through DR programs besides generation from optimally placed DG units has resulted in a more reliable operation condition. The generated power by generation units should supply the load points through transmission lines. Holding the power flow of a transmission line in predefined limits is of significant responsibilities of ISOs. Power flows in transmission lines without DERs are represented in Fig. 6. The values are expressed as the percentage of lines rated capacity. The most under stressed ones are lines 10, 11 and 23. It is expected to reach to a better condition while DERs implemented but numerical results do not match the expectations completely. Operation with DR programs in scenario S1 has resulted in rising of line flow as it is shown in Fig. 7. The values of Fig. 7 are the deviation of power flows of transmission lines in scenarios S1, S2 and S3 which are represented in

Conflict of interest None.

Fig. 5. Nodal total EUEs in different scenarios. 7

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Table 4 : Comparison between several operational parameters. Scenario

Operation cost ($)

Cost of DR ($)

Cost of DGs ($)

Loss (MWh)

Free capacity of transmission network (MVA)

Eportion (%)

Without DER S1 S2 S3

1,118,615.82 1,092,067.73 1,109,005.83 1,095,890.89

– 261,815.5 – 227,580.5

– – 13,283.2 8521.25

715.9 824.9 674.3 796.7

955.1 903.8 977.8 916.5

0.946 0.049 0.058 0.025

Fig. 6. Flows of lines at peak hour without any DERs in the network.

Fig. 7. Deviation from base case corresponding with flows of lines in different scenarios.

Appendix A Population based intelligent search Population-based intelligent search (PIS) methods have been developed to solve large complex and nonlinear optimization problems and are focused on reducing computational cost and finding near optimal solutions to practical problems. They also alleviate huge mathematical formulation and are applicable to a wide range of engineering programming problems. PIS methods are classified as evolutionary nature-inspired algorithms which are based on successive iterations. In this paper, an improved BPSO is utilized to schedule the generation units in short term operation problem as well as for Reliability evaluation. A problem coordinated PSO is applied to determine the proper load curtailment by consumers through DR programs. (A.1) Particle Swarm Optimization (PSO) James Kennedy and Russel Eberhart introduced the particle Swarm Optimization (PSO) in 1995 which is a nature inspired evolutionary optimization algorithm. In order to optimize the multidimensional problems, the social behavior of organisms such as bird flocking and fish schooling is simulated by this technique. As an optimization method, the PSO provides a search procedure based on population in which individuals and called particles change their positions with the time. The particles fly around in a multidimensional search space and during the flight, each particle adapts its position according to its own and other particles experiences, to get the best position encountered by itself and its neighbors. Usually, the PSO is easy to implement because of few required parameters to be adjusted. As said before, each particle flies with a dynamically adjusted velocity according to its own and neighbors’ experiences. Eqs. (A.1) and (A.2) provide the position and velocity of each particle, respectively.

x i, it = x i, it − 1 + Vi, it

(A.1)

−range Vi, it = w × Vi, it − 1 + C1 × rand1 × (pbesti, it − 1 − x i, it − 1) + C2 × rand2 × (gbestit − 1 − x i, it − 1) × ⎡1 + × (Ite − 1)⎤ MaxIte ⎣ ⎦

(A.2)

8

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Fig. A1. Flowchart of the proposed BPSO method.

(A.3) Binary particle swarm optimization In order to modify classical version of the PSO algorithm to be applicable in discrete space problems, several methods are provided. For example, the ability of searching in a discrete space is provided by the Binary PSO (BPSO). In this paper, the BPSO is applied which is developed based on the corporation of GA and PSO [42]. In this algorithm, bits of a binary string are used to determine the velocity and position of particles. The algorithm consists of three main steps namely are mutation, reproduction, and crossover expressed in Fig. A1 using blocks a, b and c. Note that these steps are derived from the GA. In this paper, mutation and crossover are represented in new velocity and position updating method. In all iterations, particles positions (which can be assumed as each chromosome in each generation) are updated based on the following logical operators:

x i, it − 1 ⟵x i, it − 1 ⊕ vi, it it = 1,2, …, itmax , i = 1,2, …, Pamax

(A.3)

vi, it = ω¯ i, it − 1 + ωi, it − 1 ⋅ (c1 ⋅ (pbesti, it − 1 ⊕ x i, it − 1) + c2⋅(gbestit − 1 ⊕ x i . it − 1))

(A.4)

Pωit

(A.5)

= Pω, max × exp {−λp × (it −

ln λp =

(

Pω, max Pω, min

1)rate }

it = 1,2, … , itmax

)

(itmax − 1)rate

(A.6)

In PSO structure, by using (A.4) it can be assumed as both mutation and crossover between chromosomes with respect to both global and local optimums are defined. Some type of mutation operator is implemented here to improve the search ability of BPSO. ωi, it is the inertial vector of the ith particle which is a random N-length binary vector, whose components are ‘0’ with the probability Pωit . Pωit is a very important parameter in the proposed BPSO approach which is called inertial probability and bits in ωi, it are’ 0’ with the probability Pωit . Inertial probability can be defined as a decreasing parameter with the respect of number of iterations as addressed in Ref. [42]. Inertial probability results in exploring the search space more effectively. The parameter rate in (A.5) helps the searching ability of the algorithm by decelerating loosing information on local optimums. Finally, appropriate stopping criteria, setting parameters s, and adequate number of particles should be utilized based on the type of the optimization problem.

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