Scholarly article on topic 'Exploration of dispatch model integrating wind generators and electric vehicles'

Exploration of dispatch model integrating wind generators and electric vehicles Academic research paper on "Materials engineering"

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{"Unit commitment" / "Economic dispatch" / "Wind integration" / "PEV fleet" / "Imbalance cost" / "Smart charging"}

Abstract of research paper on Materials engineering, author of scientific article — A.N.M.M. Haque, A.U.N. Ibn Saif, P.H. Nguyen, S.S. Torbaghan

Abstract In recent years, the share of renewable energy sources (RES) in the electricity generation mix has been expanding rapidly. However, limited predictability of the RES poses challenges for traditional scheduling and dispatching mechanisms based on unit commitment (UC) and economic dispatch (ED). This paper presents an advanced UC-ED model to incorporate wind generators as RES-based units alongside conventional centralized generators. In the proposed UC-ED model, an imbalance cost is introduced reflecting the wind generation uncertainty along with the marginal generation cost. The proposed UC-ED model aims to utilize the flexibility of fleets of plug-in electric vehicles (PEVs) to optimally compensate for the wind generation uncertainty. A case study with 15 conventional units and 3 wind farms along with a fixed-sized PEV fleet demonstrates that shifting of PEV fleets charging at times of high wind availability realizes generation cost savings. Nevertheless, the operational cost saving incurred by controlled charging appears to diminish when dispatched wind energy becomes considerably larger than the charging energy of PEV fleets. Further analysis of the results reveals that the effectiveness of PEV control strategy in terms of CO2 emission reduction is strongly coupled with generation mix and the proposed control strategy is favored in cases where less pollutant-based plants like nuclear and hydro power are profoundly dominant.

Academic research paper on topic "Exploration of dispatch model integrating wind generators and electric vehicles"

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Applied Energy

journal homepage: www.elsevier.com/locate/apenergy

Exploration of dispatch model integrating wind generators and electric vehicles

A.N.M.M. Haque *, A.U.N. Ibn Saif, P.H. Nguyen, S.S. Torbaghan

Department of Electrical Engineering, Eindhoven University of Technology, Den Dolech 2, 5612AZ Eindhoven, The Netherlands

HIGHLIGHTS

• A novel business model for the BRPs is analyzed.

• Imbalance cost of wind generation is considered in the UC-ED model.

• Smart charging of EVs is included into the UC-ED problem to mitigate the imbalance cost.

• Effects of smart charging on generation cost, CO2 emissions and total network load are assessed.

ARTICLE INFO ABSTRACT

In recent years, the share of renewable energy sources (RES) in the electricity generation mix has been expanding rapidly. However, limited predictability of the RES poses challenges for traditional scheduling and dispatching mechanisms based on unit commitment (UC) and economic dispatch (ED). This paper presents an advanced UC-ED model to incorporate wind generators as RES-based units alongside conventional centralized generators. In the proposed UC-ED model, an imbalance cost is introduced reflecting the wind generation uncertainty along with the marginal generation cost. The proposed UC-ED model aims to utilize the flexibility of fleets of plug-in electric vehicles (PEVs) to optimally compensate for the wind generation uncertainty. A case study with 15 conventional units and 3 wind farms along with a fixed-sized PEV fleet demonstrates that shifting of PEV fleets charging at times of high wind availability realizes generation cost savings. Nevertheless, the operational cost saving incurred by controlled charging appears to diminish when dispatched wind energy becomes considerably larger than the charging energy of PEV fleets. Further analysis of the results reveals that the effectiveness of PEV control strategy in terms of CO2 emission reduction is strongly coupled with generation mix and the proposed control strategy is favored in cases where less pollutant-based plants like nuclear and hydro power are profoundly dominant.

© 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://

creativecommons.org/licenses/by/4.0/).

CrossMark

Article history:

Received 29 April 2016

Received in revised form 6 September 2016

Accepted 26 September 2016

Keywords: Unit commitment Economic dispatch Wind integration PEV fleet Imbalance cost Smart charging

1. Introduction

Electrical power systems are facing fundamental changes for integrating significant amounts of renewable energy sources (RES) as well as new forms of energy consumption like Plug-in Electric Vehicles (PEVs). The intermittency and unpredictability of the RES-based generation units together with the stochastic behavior of PEVs have significant impact on two of the most important aspects of system balancing, namely Unit Commitment (UC) and Economic Dispatch (ED). Traditionally, the objective of UC-ED is to minimize the total operational cost over the scheduling

* Corresponding author. E-mail address: a.n.m.m.haque@tue.nl (A.N.M.M. Haque).

time period while satisfying system load demand and other generation unit constraints [1,2]. Nowadays, the additional uncertainty associated with RES like wind needs to be considered [3,4], while exploiting the flexibility offered by large-scale integration of PEVs.

A large body of literature has been developed aiming at incorporating wind generation and PEVs into the UC-ED process. An approach is presented in [5] to evaluate the potential of electric vehicles (EVs) to reduce the amount of non-wind generation considering the intermittent nature of wind power. Studies have also been focused on Vehicle to Grid (V2G) operations to provide regulation and reserve services and promote a higher penetration level of wind energy into the overall generation mix [6-13]. Moreover, the possibility of emission reduction with intelligent UC with V2G is evaluated in a number of studies [14,15]. Another UC as explored in [16] includes EVs and evaluates the contribution of

http://dx.doi.org/10.1016/j.apenergy.2016.09.078 0306-2619/© 2016 The Authors. Published by Elsevier Ltd.

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Nomenclature

indices Pw,max maximum limit of generation of wind generator farm

i index for generation unit rrdown ramp-down limit of conventional generator

j index for days RRup ramp-up limit of conventional generator

k index for time step

l index for up and down time Variables

C cost function for the conventional generation unit

Parameters CPEV charging optimization function of the PEV cluster

gch charging efficiency CW;0 overestimation imbalance cost function of wind farm

gd driving consumption of PEV CW;U underestimation imbalance cost function of wind farm

d distance driven by a PEV Cw cost function for the wind farm

MD minimum down time of conventional generation unit 0i probability of overestimation

MU minimum up time of conventional generation unit Pc generated power of conventional unit

Nc number of conventional generation units Pev charging power of PEV cluster

Nk number of time steps Pw scheduled wind power of wind farm

Nw number of wind farms s binary variable denoting start-up mode of conventional

npev number of PEV clusters units

PEV,max maximum charging power of PEV cluster sh binary variable denoting shut-down mode of conven-

PEV,min minimum charging power of PEV cluster tional units

Pload value of non-PEV load Ui probability of underestimation

Pmax maximum limit of conventional generation unit x binary variable denoting online mode of conventional

Pmin minimum limit of conventional generation unit units

Pw,av actual wind power from wind generator farm

controlled EV charging and cross-border transmission capacity to reduce dispatch costs, curtailment of wind power and the need for energy storage. A multi-period framework of controlled EV charging is proposed in [17] incorporating a day-ahead dispatch with a real-time control of PEV fleet charging for peak load reduction in the distribution networks. The real-time dispatch mitigates the imbalance from the day-ahead dispatch caused by the uncertainties associated with wind generation and PEV driving patterns. A similar two-stage stochastic economic dispatch problem formulation is proposed in [13], that investigates smart Grid to Vehicle (G2V) and Vehicle to Grid (V2G) mechanisms in the contexts of the Iberian transmission network. The problem of smart control of PHEV charging to balance the fluctuation of wind power is approached from the perspectives of a Balance Responsible Party (BRP) and a Smart Distribution Company (SDC) in [18,19] respectively. As highlighted in [18], the BRP is assumed to alleviate the imbalance in its portfolio resulting from the forecast errors of the large share of wind generation through a controllable plug-in hybrid electric vehicle (PHEV) fleet. On the other hand, the SDC in [19] calculates day-ahead hourly electricity prices and communicates the prices to the PEV owners in order to reduce the monthly electricity bills. A number of market-based demand response approaches have also been presented to tackle the uncertainties associated with the intermittent DG units [20-23].

Basically, uncertainty with wind power generation results in the ramping up and down of expensive online generators to compensate for the deficit and excess prediction of wind power respectively. The ramping capabilities need to be within the physical constraints of the non-wind generation units. Under these circumstances, the large penetration of PEV fleets in the transport sector can play a crucial role with its flexibility in the charging process. Due to the typical driving pattern of PEV owners and PEV battery specifications, the charging of PEV offers a reasonable degree of flexibility by scheduling the charging process within an acceptable time scope. Thus, PEV becomes a suitable nominee for demand response and can be deployed to accommodate the variability and uncertainty caused by wind power [24].

The recent introduction of the Universal Smart Energy Framework (USEF) enables a BRP to optimize its portfolio more efficiently by procuring the flexibility from the small-scale prosumers like PEV owners [25]. In this regard, the electric mobility is identified as a notable source of flexibility in the network, since the success of the EVs depends on the availability of the public charging facilities. Based on the current European market developments, a business model of the charging station operator (CSO) has also been proposed in line with the roles of Aggregator in the distribution network. Hence, the flexibility from controlled charging of a large number of EVs can be effectively used to mitigate the imbalance from the forecast errors of wind generation.

This paper proposes a UC-ED model which incorporates wind power generators along with the fleets of PEV from the perspective of a BRP. The main scientific contributions of the paper are as follows:

• Costs and benefits associated with the imbalance of the wind power are considered while integrating the dispatch cost of wind into the UC-ED model.

• A smart PEV charging scheme has been devised in order to mitigate the imbalance cost of the BRP resulting from the deviations of the predicted wind generation. The charging power is considered as a decision variable of the UC-ED problem to shift the charging load to the instants when significant wind generation is expected.

• The effects of smart charging on generation cost, CO2 emissions and total system load are critically analyzed.

The remainder of the paper is organized as follows: Section 2 presents the overview of the emerging UC-ED model, Section 3 describes the constituents of the proposed model, the optimization problem of the model is detailed in Section 4, while Section 5 provides the description of the test scenario and the assumptions adopted. Finally, simulation results are presented and analyzed in Section 6, before summarizing and concluding with Section 7.

2. Emerging UC-ED model

2.1. Background

In the liberalized electricity markets, a BRP is responsible for actively balancing supply and demand for its portfolio of producers and consumers. The BRP forecasts the required energy supply and demand of its portfolio and seeks the most economical solution to maintain the balance. The requested amount of energy can usually be sourced either by directly dispatching power plants with contractual agreements or by trading in various energy markets. Therefore, UC-ED plays a significant role in order to minimize the total operating cost of the wide range of power plants in the portfolio of a BRP [18,26-28].

For conventional generation units, the important aspects in the UC-ED model are start-up cost, shut-down cost, fuel cost, minimum up and down time, ramping up and down limits of generation units, and other technical constraints. In case of wind generators, the operating cost is negligible due to no fuel cost. However, the cost associated with wind power forecasting error plays a key factor and must be taken into account in the UC-ED model. If the proportion of wind power is very low in the portfolio of the BRP compared to the controllable conventional generating units, it is possible to consider wind power as negative load along with other system loads. The controllable conventional generation units can then be optimized in order to minimize the operating cost while satisfying load demand and operational constraints. Hence, the cost linked with wind power forecasting error can be left out from optimization decision variables [16,29].

However, the extensive penetration of wind power introduces a high degree of uncertainty which necessitates considering the expected cost associated with wind power forecasting error in the UC-ED optimization problem. Understanding the current consideration regarding UC-ED problem with large-scale wind power, this work extends further with a proposition aligned with the business model described in USEF [25] regarding the utilization of the flexibility in PEV charging by incorporating it in the UC-ED model.

2.2. A new business model

The Universal Smart Energy Framework (USEF) aims to adapt the conventional approach of power system and electricity market operations into a fully integrated system with emerging market roles like aggregators and energy service companies (ESCos) facilitated with advanced ICT infrastructure. As highlighted in Fig. 1, this shift of paradigm leads to versatile interactions among different entities involved in the energy value chain. For instance, the possibility of demand response by load shifting and management of local generation facilitates new means to enhance the flexibility in the whole energy system. In one hand, this enables the distribution system operators (DSOs) to use the flexibility offered by the prosumers for network capacity management [30-32], while on the other hand the BRPs can be benefited with active balancing at different timescales [25].

For a BRP's operation, UC-ED is usually performed ahead of the actual time of operation upon receiving the forecasted demand from customers, aggregators and charging station operators (CSO). The PEV aggregator or CSO also provides expected charging flexibility schedule indicating the time span during which charging energy of PEV fleets can be adjusted. Apart from the forecasted demand and PEV flexibility schedules, information of the supply side such as generator specifications, fuel cost, forecasted wind data, forecasted imbalance price are also required for the UC-ED model. In other words, a BRP utilizes the UC-ED model which optimizes both generation portfolio and PEV fleets charging with an objective of minimizing the overall expected generation cost while ensuring optimal usage of wind power for PEV fleets charging [16,18].

Thus, this work incorporates the interaction among three stakeholders in the value chain: (1) a BRP with both conventional and wind generators in its portfolio; (2) non-EV electricity consumers, representing end-users of electricity who usually participate in the market through intermediate selling parties known as energy suppliers; and (3) PEV aggregators or CSO, representing owners of the charging spots for PEV. The PEV aggregators can engage in short-term and long-term contracts with the BRP to offer the flexibility considering the driving patterns, priorities and specifications of the PEV fleets.

Fig. 1. Interaction among different entities within USEF compliant network and energy market.

3. Constituents of the UC-ED model

The focus of this work is to develop a suitable UC-ED model for a BRP with a considerable share of wind generation in its portfolio along with conventional generating units in order to minimize the overall generation cost. A large fleet of PEV is considered as the source of flexibility for scheduling their charging instants when the wind generation is considerably higher. The following subsections describe the key constituents of the UC-ED model associated with wind power and PEV fleet charging.

3.1. Wind power forecasting

Different forecasting techniques are used to predict the wind speed and resulting wind power [33-37]. This paper expresses wind speed forecasting in terms of Weibull probability distribution function (PDF) and translates it into wind power PDF for the UC-ED model [33].

The principal cost associated with wind power is the imbalance cost, originated from the deviation of injected wind power at realtime from the forecasted amount used in the day-ahead UC. The BRP attempts to mitigate this deviation by rescheduling other generation units within its portfolio. An imbalance settlement price is charged by the TSO in case the deviation cannot be sufficiently minimized by the BRP. The imbalance settlement price depends on the volume of system imbalance and the bids on the balancing market. The regulatory framework of the settlement also differs from country to country [38-40]. Since the UC-ED calculation is performed way ahead of the real-time operation, the imbalance settlement price used in the dispatch model requires to be forecasted. Determination of the imbalance price is a wide research topic and is regarded out of the scope of this paper. In this research, the forecasting procedure of the imbalance price is simplified by decoupling it from real balancing market dynamics and as discussed in [41], a linear relationship is assumed between the probability of forecast error and the average imbalance cost. This price is incorporated in the UC-ED model in terms of wind power forecasting error and will be termed as the wind power forecasting error (WPFE) price throughout the remainder of the paper.

Artificial Neural Network (ANN) has been widely used as an efficient forecasting tool in power systems research [34,42-44]. An ANN-based technique is used to forecast the probabilities of underestimation and overestimation which represent the probability of surplus and shortage of wind generation respectively. Since the performance of ANN based forecasting tool is dependent on pattern recognition, the tool needs to be trained with the most recent data before prediction. The forecasting tool is trained with two inputs as follows:

(1) aggregated wind generation error, (Perr = Prealized - Pforecasted) induced by the all the wind generators in the BRP's portfolio that acts as an external input,

(2) the principal inputs- artificial underestimation and overesti-mation chances which have been derived from wind generation error training dataset on the basis of the following set of equations:

PerrJ-Pavg

uavg ' umin

Oi = 1 - ui

if Perr;i p Pavg + Pr

('umax — uavg^j + uavg if Pavg + Pr > Perr,i p Pavg

Pavg-Perr;i| (u _u if p > p . > p _p pr \uavg umm) 11 1 avg > 1 err,i > 1 avg 1 r

err,i 6 Pavg Pr

(1) (2)

where ui and oi are artificial underestimation and overestimation chances respectively at i-th instant of training horizon. umax and umin are maximum and minimum limits of artificial underestimation chances. Perr i is the wind generation error at i-th instant of training horizon and Pavg Pr are median and standard deviation of all wind generation errors in the entire training horizon; uavg represents the artificial underestimation chance corresponding to Pavg.

Once trained, the tool generates underestimation and overesti-mation chances for the forecasting horizon. Afterwards, forecasted underestimation (uk) and overestimation (ok) chances of each forecasted instants are multiplied with mean underestimation (Pwu) and overestimation (Pwo) imbalance prices respectively to determine the expected underestimation (awu k) and overestimation (awo ;k) WPFE price of k-th instant of the forecasting horizon [41]. The expected WPFE prices are subsequently used in the UC-ED model. It is important to note that, the length of forecasting horizon and optimization horizon (of UC-ED) are the same having equal time steps to ensure that the WPFE prices have been evaluated for each time step of the optimization horizon.

3.2. PEV charging and discharging

In order to incorporate the PEV into the UC-ED problem, it is necessary to deal with PEV charging and discharging model that takes into account both vehicle parameters such as battery specifications and driving pattern. Charging of PEV battery is related with the battery charging power and charging efficiency. While the charging power is related to vehicle specification and grid constraints, the charging efficiency depends on inverter inefficiency and other losses in the battery. Therefore, the charged energy Echarge can be expressed as:

Echarge = gchPEVDt

where Dt PEV and gch denote the duration of charging, charging power and overall charging efficiency of PEV respectively.

Contrary to charging, discharging of PEV battery is dependent on driving consumption and driving pattern. If the battery capacity is U kW h and vehicle specification tests show that it can travel a range of S km, the driving consumption can be taken as gd = S/U(km/kW h). So discharging energy, Edischarge can be expressed as,

discharge :

where d represents driving behavior expressed in distance of driven kilometers. For simplicity, gd is regarded as constant, since battery specifications are regarded beyond the scope of the study.

In this work, the charging possibility of a PEV is initiated after the last arrival of the day and flexibility of charging schedule stretches up to the first departure time of the next day. The priority is given to PEV charging by imposing restrain that discharged energy content (due to driving) of each PEV in a particular day should be restored by charging before the departure time of the next day. For a certain day, j comprising k number of time steps having duration of Dt, the above described relation of the i-th PEV can be expressed as follows,

'Z'kTfr .dik

—'"■=* departure j

= J2 gchPE

The charging power, PEV ik of the PEV is bounded by upper and lower limits, Pmax and Pmin respectively.

In this paper, PEV charging power PEVik is considered as the optimization decision variable in the UC-ED model in order to facilitate controlled charging. The case of controlled charging is

Table 1

PEV specifications.

Parameters Value

Maximum charging power, Pmax 2 kW

Minimum charging power, Pmin 0.05 kW

Charging efficiency, gch 1

Driving consumption, gd 0.2 kW h/km

compared against an uncontrolled charging case where the PEV starts charging just after the last arrival of the day with a constant charging power. None of the PEV parameters are therefore considered as optimization decision variables in case of uncontrolled charging. The PEV specification is listed in Table 1.

3.3. Clustering of PEV fleets for optimization

Since the PEV charging power is considered as an optimization decision variable, it is computationally over-burdening to take into account each individual PEV in the optimization problem. However, the driving pattern of each PEV owner needs to be considered in the model to have a close representation of the real scenario. This necessitates clustering a group of PEVs together so that driving patterns of all the clusters together approximately represent the driving pattern of member PEVs.

A synthetic driving profile from a large dataset of original driving data (18,000 individual drivers) has been constructed for the Dutch case and presented in [16]. The PEV fleet is divided into 25 equal sized PEV clusters by means of a K-means clustering algorithm and the synthetic driving profiles consist of first departure time, last arrival time and travelled distance of each PEV cluster for a day. The clustered profiles have been shown to closely represent the behavior of the original driving pattern. Thus it allows to keep the number of PEVs in the optimization problem limited and computationally manageable.

4. Problem formulation for the proposed UC-ED model

The proposed UC-ED problem presented in this paper optimizes the selection and output of conventional and wind generators along with the charging power of PEV fleets. The mathematical model is formulated as a mixed-integer programming (MIP) problem where the objective is to minimize the expected generation cost and to schedule the PEV charging during times of high wind generation.

4.1. Objective function

As shown in (6), the objective function of the UC-ED problem is formulated for minimizing the overall cost associated with the generation and forecasting errors along with the cost of PEV charging.

Nk / Nc Nw

P P mpn x s £ ECKPcAik) +EC«,s,i(pwsik)

Pc,s,ikSwsjk,PEV,ik-Aik;sik k= 1 \ i=1 i= 1

^ ]Cw,u,i(Pw,s,ik-Pw,av,ik} ^ ,o,i(Pw,s,ik-Pw,av,ik)

i=1 i=1 Npev \ +£ CpEV,i(PpEV,ik)J (6)

The first term of the objective function represents costs related to centralized thermal generation units such as fuel cost and startup cost. Second term depicts the direct cost of wind power generation. Third and fourth terms are related to the costs involved in forecasting errors of wind generation.

The cost function of conventional generators consists of the fuel cost, which is a second order function [1,2] and startup cost for restarting an uncommitted thermal generation unit. This can be mathematically expressed as,

Ci(Pc,s,ik) = FC(Pcf,ik)Xik + SUisik = (piPlsik + QiPc,s,ik + r^Xik + SUisik

where pi,qi and ri are cost coefficients of i-th conventional generator and can be obtained from the input - output curves of the generators and are dependent on the particular types of fuel used. SUi denotes the start-up cost of the i-th conventional generator.

A linear cost function will be assumed for the generated wind power. As shown in (8), wind generation does not have any fuel cost and mostly accounts for the payback cost assigned by the BRP.

^W ; i(PW ; ^ - ^P-^

where s, is the direct cost coefficient for the i-th wind farm.

When the generated wind power is more than the scheduled quantity, additional wind power is sold at a reduced price compared to the day-ahead market price. Therefore, the imbalance cost will be linearly related to the difference between the available and scheduled wind power.

CW;U ,i{P1

W S ; l 1 1 W ; aV ; i

) — aw,u ,k{Pw,av ,ik Pw,s,ik)

where awu k denotes expected underestimation WPFE price at time step k.

The overestimation imbalance cost is due to the less available wind power than the scheduled amount. Hence, the shortage of power must be compensated by running expensive generators or purchased from the TSO at a higher price.

ik PW s i ik1 Pw i av i ik - PW s i ik Pw i av i ik

where aw,o,k is the expected overestimation WPFE price at time step k.

Both the expected underestimation and overestimation WPFE prices are estimated using the forecasting procedure discussed in Section 3. Furthermore, due to the stochastic nature of the generated wind power, it is also necessary to include the PDF of wind power of each wind farm in the expressions of underestimation/o verestimation imbalance cost [33]. This can be achieved by taking the integral over the PDF of the wind power random variable, Pw av ik in (9) and (10) within appropriate limits.

Cw,u,ik(Pw,s,ik; Pw,av,ik) ~ aw,u,k(Pw,av,ik — Pw,s,ik)

= aw,uk fPw>"" (Pi - Pws,i)f(Pi)dPi (11)

Cw i o i ik(Pw ,s i ik1 Pw i av, ik) — aw, o, k(Pw ,s, ik Pw, av, ik)

- Ow,o,k iW" (Pwsi - Pif (Pi)dPi (12)

where f (Pi) is the wind power PDF of i-th wind farm from Weibull distribution.

The PEV charging function CPEVj(PEV,ik) requires to be defined in order to shift as much charging energy as possible to time instants when the probability of the generated wind power is higher. The optimization of charging power of PEV clusters is done by exploring the flexibility of PEV fleets charging within the boundary imposed by several PEV constraints. Thus the charging power of PEV fleets will be increased when the wind power is expected to be underestimated. On the other hand, charging power will be reduced in case of overestimation of wind power. The PEV charging optimization function can therefore be formulated as,

CPEV, i(PEV, ik) —

aw,o ,k + aw,u ,k

PEV ik

Thus the final objective function can be written as:

/ iNC \\ '"£FC(Pc_s ,ik)Xik + SU,s,k

min V"

.'I, . Par .X:i, S.i. _

Pc ,s ,ik ,Pw ,s, ik ,PEV, ik ,xik ,sik

siPw,s,i

^ ]aw,u,k{Pw,av,ik - Pw,s,ik) i—1 Nw

^ ]aw,o,k{Pw,s,ik - Pw,av,ik) i—1

I \ ' awto ,k p

+ Ow,0 k+«w,uk EV,ik

sik - shik — xik - xik_1

4.2.6. PEV cluster charge balance constraints

PEV charging requirement is governed by the fact that the discharged energy content of each PEV cluster in a particular day must be charged back before the departure time on the following day.

(^'k—Tfr dik>

—departure j

— X] gchPEV,ikDt

4.2.7. PEV cluster charging power limits

The aggregated charging power of the PEV clusters are bound within an acceptable range.

6 Pev ik 6 Pn

4.2. Constraints

4.2.1. Power balance constraints

The power generated from all the scheduled units must satisfy total network load, charging power of PEV clusters and network losses. However, network losses are kept out of the scope of this paper and therefore discarded from the constraints. The power balance constraint can thus be shown as, Nc Nw Npev

P c s ik + Pw s ik = Pload k + PEV ik i=1

Pc s ik i—1

4.2.2. Generator limits constraints

Each of the conventional and wind generators need to satisfy the maximum limit constraints of generated power output. The maximum output power is thus considered in terms of the constraint as,

Pi,min 6 Pcs,ik 6 Pi,max (16)

0 6 Pw,s,ik 6 Pw ,i,max

4.2.3. Ramp rate limit constraints

Due to physical limitations the change of power output of each thermal generator is subject to ramping up and down constraints signifying how rapidly the output of the generator can be changed.

Pc,s,ik - Pc,s,i(k-1) 6 RRlJPi Pc,s,i(k-1) - Pc,s,ik 6 RR-DOWNi

where RRUPiand RRDOWNidenote the generator up and down ramp rates respectively.

4.2.4. Minimum up/down time

There is a predefined minimum time determining how long a generation unit is required to remain on or off after being committed or released respectively.

Sil 6 Xik

l—k-MUi k

shil 6 1 - xik

l—k-MDi

4.2.5. Generator transition state

This constraint is imposed to ensure consistency among different states like online, start-up and shut-down modes of each generation unit while executing the optimization process.

5. Simulation setup

The simulation of the proposed UC-ED model is performed in the MATLAB environment. Both of the PEV charging optimization and UC-ED model were developed in MATLAB using the open-source optimization modeling language, YALMIP [45]. The mixed-integer optimization problem is solved with the GUROBI optimization solver.1

5.1. Test scenario

The simulation is performed for a period of two days with a time resolution of 15 min which is used for scheduling and settlement of 'E-programs' of Dutch market participants and usually termed as Program Time Unit (PTU).2 For the remainder of the paper, PTU will be used to refer time resolutions.

Fifteen conventional thermal generation units of different fuel types- nuclear, coal, natural gas and oil are used in the model. The specifications of the considered thermal units are shown in Table 2. In addition, three fictitious wind farms, two offshore and one onshore, are also considered in the generation portfolio. Two important issues regarding wind power generation are parameters of Weibull distribution and wind turbine characteristics. Parameters of Weibull distribution depend on the coastal location and the shape of the terrain on the ground, hub height, and the stability of air. Besides, power curves of different wind turbines vary from one another in terms of attributes like rated power, cut-in speed, rated speed and cut-out speed. To create a model simple yet effective, power curves of five most popular wind turbines in the Netherlands are aggregated. Parameters obtained from aggregated power curve are listed in Table 3. Weibull parameters for each wind farm are calculated from historical wind measurements of 2-5 years from meteorological system of Energy research Centre of the Netherlands (ECN).3 The two offshore wind farms are considered to be located in Petten and OWEZ while the onshore farm is in Emmen. The Weibull parameters are then translated into the average hub height of aggregated power curve to retain uniformity in model.

Load data used in the model has been taken from the Dutch TSO Tennet for the first two days of January, 2014.4 The load demand values are scaled in the simulation setup to fit the considered number of generation units. PEV profiles are added to the network load in

1 http://www.gurobi.com.

2 http://www.tennet.org/english.

3 http://www.ecn.nl/home.

4 http://www.tennet.org/english/operational_management/export_data.aspx.

Table 2

Specifications of the generation units.

Generation unit Full-load efficiency (%) Pi,max (MW) Pi,min (MW)

Nuclear 35 1050 600

Coal-fired 40 1220 490

CCGT Unit 1 58 275 150

CCGT Unit 2 58 205 110

Oil-fired 44 600 200

Gas fired Unit 1 45 63 35

Gas-fired Unit 2 45 116 60

Gas-fired Unit 3 45 178 90

Gas-fired Unit 4 45 55 30

Gas-fired Unit 5 45 60 30

Gas-fired Unit 6 45 46 25

Gas-fired Unit 7 45 142 75

Gas-fired Unit 8 45 385 190

Gas-fired Unit 9 45 610 300

Gas-fired Unit 10 45 240 120

Ramp up/down (MW/h) pi (€/MW2 h) qt (€/MW h) n (€/h) SUi (€)

2100 0.0016 16.678 2301.7 120,082

1830 0.00169 23.534 3244.6 69,190.8

825 0.0263 36.106 2906.5 8123.9

615 0.0353 36.106 2166.7 5957.5

1260 0.00712 44.253 3300.6 8850.6

81.9 0.07659 49.711 391.8 869.9

150.8 0.04160 49.711 721.3 1491.3

231.4 0.02711 49.711 1106.8 2237.0

71.5 0.08774 49.711 342.01 745.7

78 0.08043 49.711 373.11 745.7

59.8 0.10491 49.711 286.05 621.4

184.6 0.03399 49.711 883.02 1864.2

500.5 0.01253 49.711 2394.0 4722.6

793 0.00791 49.711 3793.2 7456.7

312 0.02011 49.711 1492.4 2982.7

Table 3

Typical values of aggregated wind power.

Parameter Value

Rated power 3 MW

Cut-in speed 4.5 m/s

Rated speed 16.25 m/s

Cut-out speed 25 m/s

Average hub height 86 m

order to evaluate the impacts of PEV charging. In line with the expected number of PEV in Dutch case, 0.2 million PEVs have been considered in this work with a possible peak charging power of 400 MW (in the unlikely case of all the PEVs charging with maximum power). The synthetic driving profile, number of PEVs and PEV specifications in this paper results in a total required charging energy of 1263.5 MW h per day.

Historical aggregated wind generation error, Perror is required to train the forecasting tool to generate WPFE price, where, Perror = Prealized - Pforecasted. Realized and forecasted wind generation data of 15 min resolution have been accumulated from German TSO Amprion5 and assumed to be similar for the Dutch case. The forecasting tool is trained with the data of one month immediately prior to the time when UC-ED is performed to maintain the desired level of accuracy. The average underestimation and overestimation imbalance price (Pwu ,Pwo) used in the simulation are mean down regulating and up regulating price of Dutch imbalance market with values of 15.49 €/MWh and 73.56 €/MWh respectively [29].

5.2. Overview of assumptions

Important assumptions adopted in the work are listed as follows:

• System is considered lossless.

• Only the PEV fleet is considered as the flexible load in the portfolio. That is to say, the non-PEV electricity demand is considered unresponsive to price and wind generation.

• While performing simulation with different wind penetration level, the non-PEV demand profile, capacity of thermal generation and number of PEVs are kept fixed.

• The level of wind penetration is considerably larger than the charging energy of PEV fleets.

• The aggregated power curve used for wind forecasting is considered as piecewise linear.

5 http://amprion.net/en/wind-feed-in.

6. Simulation results and analysis

UC-ED simulation is performed for two consecutive days starting from 00:15 h on 1st January 2014. The data used for training of the forecasting tool extends from 12:00 h of December 1, 2013 to 11:45 h of December 31, 2013 (total 2880 PTUs).

The dispatch profiles of the generating units for the simulated time frame for an installed wind capacity of 522 MW are shown in Fig. 2. The nuclear unit is dispatched at the maximum output throughout the simulation time whereas due to the relatively higher fuel cost and high ramping capability, the coal-fired generation unit adjusts its output to follow the demand pattern. The wind farms are also dispatched throughout the simulation time with varying outputs dictated by forecasted wind generation and expected underestimation and overestimation WPFE prices. The variable nature of wind generation aggravates the demand fluctuation forcing the online controllable thermal generation units to adjust their output more frequently and rapidly. Additional expensive generation units are also dispatched to supply the peak loads during the evening.

6.1. PEV charging strategies

The controlled charging strategy aims to shift the charging power of the PEV fleet to time instants when wind power output is deemed high while satisfying constraints related to the PEV clusters. As shown in Fig. 3, charging power in uncontrolled case is not correlated with wind power availability. PEV owners begin charging immediately after arriving home in the late afternoon and early evening (almost coinciding with the peak demand), and the charging loads are served by expensive, gas and oil-fired generators. 81.38% of the PEV charging energy is completed by 24:00 h of the day of arrival (PTU No. 96) although almost all the clusters are accessible for charging till 08:30 h of the next day (PTU No. 130). On the other hand, controlled charging utilizes the unexplored time as the charging schedule starts before 10:00 h (PTU No. 40) to exploit the high expected wind generation. Similar incident is manifested again at 04:00 h to 09:30 h on second day (PTU No. 112-134). Fluctuation in PEV charging also follows the variation in the dispatched wind power. For example, sudden drops of generated power from all three wind farms are reflected in dips of charging power of the PEVs at 06:15-07:00 h of first simulation day (PTU No. 25-28) and at 05:45 h of second day (PTU No. 116119). The effect of controlled charging on total dispatch cost over the simulated two days is shown in Table 4.

20 40 60 80 100 120 140 160 180 192

Time samples (PTU)

Fig. 2. Generation dispatch for two days with 522 MW of installed wind capacity.

Dispatched wind power

20 40 60 80 100 120 140 160 180 192

Aggregated PEV charging power

20 40 60 80 100 120 140 160 180 192

Time samples (PTU)

Fig. 3. Dispatched wind power, number of clusters of PEV available for charging and total charging power of the PEVs throughout the simulation time.

6.2. Installed wind capacity vs. cost

The impact of installed wind capacity on the dispatch cost is shown in Table 5. The expected dispatch cost is calculated for two days with varying degree of wind generation keeping the aggregated demand profile, number of PEVs and specifications of the thermal generators fixed. The expected dispatch cost increases with increased penetration of wind generation due to the incorporated imbalance cost terms (Eqs. (9) and (10)) in the UC-ED model. The imbalance cost becomes more dominant with growing penetration, resulting in a higher expected dispatch cost. This effect of imbalance cost cannot be realized if the imbalance cost due to

Table 4

Dispatch costs for different charging strategies.

Scenario Dispatch cost (million €) Cost saving (million €)

Uncontrolled charging 98.87 0.326

Controlled charging 98.53

wind forecasting error is not considered in the UC-ED model and forecasted wind generation is considered as a negative load. Thus the estimation of imbalance cost in the UC-ED calculation helps the BRP to take additional measures like controlled PEV charging for cost saving.

Table 5

Impact of installed wind capacity on dispatch cost.

Installed wind capacity Cost for different charging Cost saving

(MW) methods (million €) (million €)

Uncontrolled Controlled

300 19.50 19.09 0.405

324 19.99 19.58 0.411

450 23.16 22.67 0.489

522 25.57 25.07 0.500

594 28.27 27.78 0.487

879 40.54 40.09 0.457

1080 57.10 56.66 0.447

1413 85.90 85.61 0.287

1530 98.87 98.53 0.326

1800 130.4 130.1 0.276

Table 6

Impact of charging strategy on generation mix.

Fuel type Overall output (MW h)a Reduction (%)

Uncontrolled charging Controlled charging

Gas 9428.66 8620.91 8.567

Oil 4279.49 3503.060 18.143

Coal 49710.99 50288.187 -1.161

Nuclear 49243.63 50103.886 -1.747

Wind 22156.00 22302.75 -0.662

a With installed wind capacity of 1530 MW.

Since the charging energy of the PEV fleets has been kept constant, the effect of controlled charging on cost saving declines with increasing installed wind capacity. Up to 522 MW of installed wind capacity, charging energy of the PEV fleet remains of the same order as the dispatched wind energy, resulting in a significant cost saving by controlled charging. However, with higher wind penetration, the peak load is partially supplied by the wind generators causing in a smaller contribution of expensive generators like gas

and oil. Therefore, cost saving incurred by controlled charging diminishes with increasing wind power as the saving usually occurs by shifting of charging load from expensive peak load generators to cheap base load generators.

The slight shift in savings for 1530 MW is originated predominantly from the start-up costs of peak load generators for that particular installed capacity. Additional generators need to start up during the peak hours to supply the PEV charging demand. This start-up cost contributes in higher cost saving in the above stated controlled charging case of 1530 MW. For all other cases from 1080 MW to 1800 MW the aggregated start-up costs between two charging scenarios remain relatively close.

6.3. Effect on CO2 emissions

The relation between the generation fuel mix and charging strategies is significant in order to explain the effects on the overall CO2 emission. Table 6 summarizes the generated output of different types of units for both of the charging strategies when the installed wind capacity is 1530 MW. As controlled charging notably shifts the PEV charging load during high wind generation, use of expensive generation units are largely avoided. Consequently, nuclear and coal-fired plants (the base load plants) need to increase their generated output.

Although the increased output of the coal-fired plants will result in a higher CO2 emission for the BRP, net emission will be strongly coupled with the generation mix in the portfolio of the BRP. For instance, the proposed control strategy will be favored in cases where less pollutant based plants like nuclear and hydro are profoundly dominant compared to coal power plants.

The change of wind energy in Table 6 indicates the reduction of wind curtailment with the controlled charging strategy. Wind curtailment is feasible when cost of wind (mostly expected imbalance costs) is high compared to the thermal generation units. Curtailment is also an economically and technically preferable option for avoiding the shutdown and restarting of thermal plants.

pi 400 S

■S 200 o

pi 400

■S 200 c

4000 3500

¡3 3000 g

Dispatched wind power

Wind Farm 1 Wind Farm 2 Wind Farm 3

■!.................»T.......I......................................I-

60 80 100 120 Aggregated PEV charging power

180 192

80 100 120 Total network load

180 192

Uncontr illed -Control ed

—" i —

80 100 120 Time Samples (PTU)

180 192

Fig. 4. Dispatched wind power, total charging power of the PEVs along with the total network load during the simulation time.

Table 7

Dispatch cost and cost savings in different seasons.

Dispatch cost (million €) Cost savings (million €)

Uncontrolled Controlled

Winter 98.87 98.53 0.326

Spring 101.413 101.178 0.235

Summer 99.044 98.935 0.109

Autumn 103.800 103.524 0.276

6.4. Effect on peak load

With uncontrolled charging, the bulk of PEV charging takes place in the late afternoon and early evening when most of the PEV owners finish last trip of the day. As shown in Fig. 4, this results in a higher peak load at 18:15 h (PTU No. 73 and 169). However, the peak charging power of the PEV fleet in uncontrolled case is lower than the controlled case even though the maximum allowed charging power is 400 MW for both of the cases. The charging power for uncontrolled charging depends on the arrival time of the PEV clusters and number of clusters available for charging at that time. On the other hand, for controlled charging, the consumed power not only depends on the number of clusters present at that particular time but also on the availability of the generated wind power.

Since in uncontrolled charging no control strategy is applied, some of the PEV clusters with early arrival time and low travelled distance start and finish charging before the arrival of rest of the PEV clusters. On the contrary, the PEV clusters in controlled case do not start charging right after their arrival, instead the charging process is shifted to the instants when high wind power is expected. That is why charging usually occurs at instants when most of the clusters are accessible for charging resulting in a higher peak load. While the increased load may cause congestions in network assets e.g. transformers and cables, this can be avoided by lowering the maximum allowable charging power for PEV in the optimization problem.

6.5. Season-wise cost savings

In addition to the two winter days explained in Section 6.1, the effect of controlled charging is evaluated for the same time horizon during the weekdays in spring, summer and autumn keeping the generator types and driving pattern same. The resulting dispatch costs and cost savings realized through controlled charging for these cases are depicted in Table 7.

Due to the availability of a higher wind speed, a relatively improved cost savings is realized in winter. Higher wind generation also reduces the need of expensive generators resulting in a lower dispatch cost compared to the cases in spring and autumn. Although the dispatch cost is lower in summer due to the lower overall loads, cost savings are considerably lower as the available wind speed is much lower than in other seasons.

7. Conclusions

The focus of this work has been to develop a suitable UC-ED model from the perspectives of a BRP with a large share of wind generation in its portfolio. The model considers PEV fleet charging as an efficient approach for circumventing the imbalance cost from the wind generators. Integration of a controlled charging strategy realizes lower dispatch cost and reduced wind power curtailment compared to the uncontrolled charging. The cost savings result from more PEVs being charged by wind generation thus avoiding the use of more expensive gas and oil-based generators. However,

the relationship between cost savings and controlled charging become loosely coupled when the dispatched wind energy exceeds the required charging energy by a large margin. The proposed approach is also efficient in terms of reduction of CO2 emission when less pollutant-based plants are dominant in the portfolio of the BRP. Based on the two-day simulation in an Intel Core i7 computer with 8 GB of RAM, the controlled charging case requires a simulation time of approximately 287 min compared to 175 min for the uncontrolled case.

In this work, the WPFE price is calculated assuming a simplified linear relationship between the probability of forecast error and the average imbalance cost. In reality, a non-linear relationship exists involving the day-ahead dispatch price as well. Thus, the model can be further upgraded by including an improved forecasting method and a more realistic prediction mechanism of the WPFE price. However, the same formulation of the optimization problem and the solver can still be used to solve the resulting MINLP problem. The sensitivity of the uncertain parameters on the final objective will also have to be evaluated. A more detailed analysis is warranted considering the seasonal variations in wind speed, domestic and commercial loads, other types of local generation units like solar PV and micro-CHPs and recent developments in the demand side such as demand response mechanisms. Future research in this topic can also be directed to integrating uncommitted wind generators for participating in the intra-day balancing market. Since the proposed model uses PEV charging as an optimization decision variable, effects of related forecasting errors of charging demand and flexibility on dispatch cost can also be integrated into the model.

Acknowledgments

This work is partially funded by the NWO URSES project DISPATCH.

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