Power system planning with high renewable energy penetration considering demand response

Nomenclature

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B.Sets Ωn d DR,Set of available time periods of d-th DR at load node n Ω ILΩTL,Sets of interrupted DR and transferred DR Ω LΩCL,Sets of all transmission lines and candidate lines satisfying Ω ⊆Ω CL L LS LE Ω Ω n n,Sets of lines starting from node n and lines ending at node n ΩGi Set of thermal units belonging to type i C.Parameters Maximum quantity of DR IC IC IC IC,Dn t d DR Lim,,,,,Unit investment cost of conventional power plant,energy storage,and candidate transmission lines C C G W B CL g w b l,,Start-up cost and operational cost of thermal power plants per kW C C G SU G i g n d n d DR DR,,,,+ -,Penalty cost of load curtailment per kW C C Incentive cost of the increased and decreased DRs per kW Cap Cap,,+ -,n d n d DR DR,,,Maximum capacity of conventional power plants and VRE CapbB ,Lim Maximum capacity of energy storage G Lim W Lim,,g w βEnergy Re Normalized renewable penetration target Dn t Load,Load demand α α Cur Cur,Load Res Rate of load and renewable generation curtailment ωW w,t Percentage of hourly available VRE FlMax Capacity of transmission line l αG RdαG Ru,,Normalized ramp capability coefficient λi I ,Min Minimum output level of thermal units,g g I ON I Off,,T T,i i Minimum up and down time periods of thermal units,λ Coefficient of the minimum and initial states of charge in the energy storage ηb B Ini Hb b B Charging/discharging efficiency of storage D.Variables D D DR DR,,,,,+n t d n t d-,， Decreased and increased quantity of interrupted DR and transferred DR,,Planning capacity of conventional power plant,VRE,and energy storage xlCL Binary variable of candidate lines P P G W B Cap Cap Cap g w b G W,,,g t w t Scheduled generation output of thermal units and VRE plants LCur n ,t Load curtailment P P dis cha b t b t,,,Scheduled charging and discharging power of energy storage L Power flow of line l at time t θ θ Fl ,t l t l t ( ),( ),+,- Voltage angle at the starting and ending nodes of line l,,Online,start-up,and shut down of the thermal units Eb t O SU SD I I I,,,i t i t i t B,State of charge in energy storage

0 Introduction

There is a broad scientific consensus that a high penetration of renewable energy resources for developing low-carbon energy systems will become an important and common trend in the coming decades [1-3].Owing to the limits imposed by natural rainfalls and geographic topologies on hydropower development,variable renewable energy (VRE),such as wind power (WP) and solar photovoltaic (PV),will be the major contributor to achieve high renewable penetration and keep rapid growth with significant cost reduction in the future [4,5].According to IRENA’s latest data,the cumulative capacity of global WP increased from 180.85 GW in 2010 to 622.70 GW in 2019,while the PV installed capacity increased from 40.27 GW in 2010 to 580.16 GW in 2019 [6].Some countries such as Denmark and Ireland are already operating a power grid with more than 20% annual electricity demand satisfied by VRE generation.China plans to achieve annual VRE generation penetration over 15% by 2020 and over 60% by 2050 [8].

It is well known that the electricity production of VRE highly depends on the weather conditions and thus involves large variability,uncertainty,and low-capacity credit.This gives rise to significant challenges for power system operation and planning [9].The primary technical challenge is the fact that VRE generation does not match the electricity demand because of its undispatch ability,which leads to strong variation and uncertainty in the net load [10].PV power,in particular,has zero production during the night but generates large ramps in the sunrise and sunset periods,which leads to the well-known ‘duck-curve’ problem[11].Although achieving high renewable penetration implies a number of challenges for system operation and planning,there are also many solutions that can provide the operational flexibility needed to handle such challenges.The flexibility retrofit of thermal power plants can reduce the minimum loading ratio [12].Transmission reinforcement is required to enlarge the balance zone and share the reserve capacity [13].Energy storage can temporally shift VRE production to make it coincide with the load demand as much as possible [14],while the demand response (DR)plays a similar role by shifting the load demand [15].Another technology that improves the characteristics of net load is to replace VRE with controllable renewable energy technology,such as concentrating solar power [16].

Evidently,the performance and cost of different solutions vary.It is important to explore the optimal portfolio to satisfy the flexibility requirement for a renewable-dominated system and the role of each flexibility source.In this study,we propose a stochastic investment planning model that considers the DR to explore its role in responding to high penetration of VRE.

Many previous studies focused on the optimal generation portfolio [17],transmission planning [18],and storage requirements [19]to integrate a high share of renewable generation [20-22].However,most of them just deemed the load as a fixed demand profile,and few of them considered the participation of the DR and evaluated the potential that DR flexibility could provide to the power system.Thus,the above studies,such as [17-22],neglected the benefit of load demand flexibility and over-estimated the energy storage demand.

Concerning DR flexibility,some studies pointed out that it provides significant economic benefit on the electric grid expansion [23,24].Ref.[25]evaluated the benefits of DR based on a long-term investment model considering priceelastic demand.The results suggest that DR can result in environmental benefits not only by reducing the energy use,but also by facilitating the integration of renewable energy.Ref.[26]also incorporated DR into a transmission expansion and a planning scheme using a teaching learningbased optimization method.Ref.[27]used electric vehicles(EVs) as a demand flexibility,and an interval-stochastic programming method was proposed to solve the generation and transmission planning problem.Ref.[28]constructed a detailed flexible EV load model and integrated it into a generation expansion model.Considering the multiple flexibilities of the demand load,Ref.[29]proposed a distributed generation (DG) planning model coordinating the demand flexibility,in which the DG expansion plan and the behavior of consumers in DR programs are co-optimized for maximizing the social welfare and the integration of renewable generation.Ref.[30]considered the transferred DR and proposed a stochastic planning model to obtain a flexible and reliable generation-expansion scheme taking the uncertainty of loads and renewable generation into account.However,most of the above studies considered only one type of DR and incorporated only two or three flexible elements,including DR,in the power-system planning problem with VRE.

In this study,four flexible elements,i.e.,generation,transmission lines,storage,and DR,were all considered,and a stochastic power-system planning model with VRE is proposed.Two types of DR,namely interrupted DR and transferred DR,were modeled to express the diversity of DR flexibility.Chronological load and renewable generation curves with 8760 hours within a whole year were reduced to 4 weekly scenarios to accelerate the optimization.In addition,clustered unit commitment constraints to accommodate the variability of renewables were incorporated.Case studies based on the IEEE RTS-96 system are reported to demonstrate the effectiveness of the proposed method.

The major contributions of this study can be summarized as follows:

(1) Development of a stochastic planning model to optimize the generation portfolio,transmission expansion,and energy storage requirement for a power system to integrate high shares of renewable energy with DR.

(2) Model of the flexibility and diversity of different types of DR in the planning optimization.

(3) An empirical analysis based on a modified IEEERTS-96 system.The benefit of DR flexibility is evaluated,and its potential to avoid storage investment is analyzed.

The remainder of this paper is organized as follows.Section 1 presents the DR model in detail and proposes a power-system planning model considering DR.Section 2 discusses the results of the case studies.Finally,the conclusions are summarized in Section 3.

1 Model Formulation

In this section,we first analyze the flexibility of the demand response and establish a mathematical model incorporating different types of DR to express its operational characteristics.Then,we propose a planning model integrating DR flexibility to optimize the portfolio of generation,transmission lines expansion,and storage requirement with the objective of minimizing the overall economic cost.This model incorporates a yearly operation simulation of power systems with an hour resolution.The flexible operation behaviors of conventional thermal power plants,energy storage systems,and DR in response to the uncertainty and variability of VRE are considered.

1.1 DR flexibility model

DR will become an important part in the future electricity market [31].Instead of a fixed load profile,DR could provide more flexibility in reacting to the fluctuation of VRE by adjusting the load demand.In general,adjustable electric demand can be divided into two categories:interrupted load and transferred load [32].As shown in Fig.1,the interrupted load could be shed/increased during certain periods.For instance,this is the case of controllable lighting.The transferred load is the demand that could be shifted from one period to any other instant or period.In addition,concerning the transferred load,we should keep the demand in all available intervals constant.A typical example is an EV.

Fig.1 Interrupted and transferred DRs

Hence,in this study,we categorized DR into two types according to the classification of the adjustable electric demand,namely interrupted DR and transferred DR.In addition,we also considered different DR mechanisms by introducing an index d to describe the diversity of DR.This diversity is reflected in different DR settings,such as different DR available periods.

Therefore,the DR operation flexibility can be described through the constraints (1) and (2).Constraint (1) limits each type of DR at any available periodto its maximum valuewhere n,t ,d represents the load node,time,and the category of DR settings,andare the decreased and increased quantities of DR at any available time.Constraint (2) ensures the demand balance of the transferred DR.

We further considered the effect of DR and integrated it into the following planning model.From the perspective of the power system,to encourage consumers to achieve DR and provide flexibility to the power system,the DR subsidy mechanism is applied,i.e.,the system will pay the incentive subsidy according to the consumers’ DR.For the interrupted and transferred DRs,consumers will respond to the subsidy to decrease/increase the load demand at any available time.Evidently,the subsidy for interrupted DR is higher than that for the transferred DR because the interrupted DR provides more flexibility than the transferred DR.Thus,the incentive cost produced by the DR subsidies can be written in a compact form:

1.2 Planning model considering DR

The proposed model structure is shown in Fig.2.Investment decisions related to generation capacity,storage requirement,and transmission lines are made at the first stage,and an hourly chronological operation simulation for a full year including 8760 hours is performed at the second stage to estimate the annual operating cost.For the operation simulation,four types of technical operating constraints are considered,namely common generation dispatch,operational flexibility,energy storage operation,and DR flexibility.

The objective function formulated by (4) minimizes the sum of the investment cost,denoted by and the operating cost,denoted byThe investment cost consists of two parts:the generation investment,which is calculated by (5),and the expansion cost of transmission lines,which is represented by (6).The annual operating cost is estimated by (7),including the start-stop cost of thermal power plants,fuel cost,load curtailment cost,and the incentive cost of DR.The carbon emission and renewable curtailment costs are not considered.

Fig.2 Structure of the generation capacity planning model

whererepresent the unit investment cost of thermal power,energy storage,VRE plants,and transmission lines,respectively; xlCL represents the candidate lines; CiG ,SU and CgG are the start-stop cost and fuel cost of thermal power plants,respectively; CVoLL is the value of the load loss; are variables;are the planning capacity of thermal power,energy storage,and VRE plants; is the start-up capacity of the thermal units; is the thermal power generation; and is the load curtailment quantity.

The first stage sets the constraints on determining the investment decisions related to generation and transmission lines.Constraint (8) limits the maximum installed capacity of each generation type.Constraint (9) represents the renewable penetration target,which requires that the value of of the overall electricity load be supplied by renewables.denotes the given load demand curve,and is the variable representing renewable generation.Specifically,the case withequal to 100% indicates a fully renewable electric power system.Constraint (10)represents the generation adequacy requirement,which indicates that the loss of load is less than the value of for the total load.In this study,we set to 0.01%.Constraint (11) limits the renewable curtailment to the maximum permitted ratio is the percentage of hourly available renewable generation.

The second stage sets the constraints for the power system production simulation.Constraint (12) represents the power balance at each node,ensuring that the scheduled generation is equal to the load demand under DR.Constraint(13) requires that the loss of the load is less than the load demand at each node.

where are variables denoting the discharging and charging power of energy storage devices,respectively,andis the variable of the line power flow.

For transmission lines,(14) and (15) express the DC power flow of the candidate and installed lines,respectively,where M is a large enough constant.If xlCL =0,(14) holds at any time; if xlCL =1,the constraint of the candidate lines will be the same as that of the installed lines specified in(15).Constraint (16) limits the power flow at each line to its corresponding transmission capacity FlMax; θn ,t is the phaseangle variable.

For VRE units,constraint (17) ensures that the renewable generation output does not exceed the forecasting production.

For conventional thermal power units,the traditional investment model generally employs the following simplified operation model formulated by (18) and (19).The former limits the thermal generation to its capacity,whereas the latter represents the ramp limit of thermal units; is the hourly ramp up/down rate of thermal power.However,it is assumed that thermal units are regarded as perfectly flexible to dispatch generation from zero to the power capacity by ignoring the unit commitment schedules.

Therefore,in addition to constraints (18) and (19),operational flexibility constraints (20-25) are incorporated into the planning model to simulate the flexible operation behavior of thermal power units.Specifically,thermal units are aggregated into NI types based on similar generation characteristics.The continuous variables are introduced to denote the aggregated generation,on-line capacity,start-up capacity,and shutdown capacity of the thermal unit type i at time period t.Constraint (20) links the aggregated generation with the individual generation of thermal units.Constraint (21) limits the on-line capacity to the corresponding power capacity.Constraint (22) formulates the minimum loading limits,showing that the generation output of thermal units cannot be lower than the minimum loading of on-line capacity.Constraint (23) formulates the relationship between online capacity and start-up/shut-down decisions.Constraints(24) and (25) represent the limit of the minimum start-up/shut-down time period of the thermal units.Constraint (24)shows that all the start-up capacity during the past periods will continue online at period t.Constraint (25)shows that all the shut-down capacity during the past periods will remain offline at period t.

For storage devices,(26) limits the charging and discharging rates of storage.Constraint (27) represents the energy balance of storage and introduces a coefficient ηbB to model the energy exchange loss.is the state of charge(SOC) variable.Constraint (28) limits the SOC of storage to the discharging duration hour HbB.Constraint (29) ensures that the SOC of storage returns to the initial level λbIni at the end of the year.The corresponding investment capacity CapbB is optimized.

Constraints (1-29) configure the generation capacity planning model toward a high renewable penetration level.It is a large-scale linear programming model that can be easily implemented and solved using common optimization solvers,such as CPLEX and LINGO.

2 Case Study

2.1 Basic data

In this section,an empirical analysis based on a modified IEEE-RTS-96 system is provided.As illustrated in Fig.3,the capacity of all the units must be optimized.The candidate transmission lines are represented by red dashed lines.The cost performance and maximum installed capacity of each type of generation are summarized in Table1.Cost estimation data were obtained from NREL’s technical report for the U.S.power system in 2050 [32].

To address the computation intractability,the chronological characteristics of the load and VRE generations in a whole year were reduced into 4 weekly scenarios.The load profile is illustrated in Fig.4(a) with a maximum load of 2850 MW,and the variations of the renewable resources are displayed in Fig.4(b).For DR flexibility,we assume that the load in each scenario could be interrupted and transferred.The related settings are displayed in Table2.

Fig.3 Modified IEEE-RTS-96 system

The aim of the whole system is to minimize the overall economic cost.The curtailment of the load was set to be less than 0.02% given a punishment of 2.0 $/kW.The total renewable curtailment was limited to 5%.According to these values,four basic cases are displayed,namely without DR (Case I),with DR (Case II),with DR but without considering the energy storage (Case III),and with high incentive-cost DR (Case IV).All the cases were solved by CPLEX on a PC with an Intel Core i7/2.3 GHz processor and 16 GB of RAM.

Table1 Generation capacity and cost estimation

Annualized Investment Cost/($/kW-yr)Operating Cost/($/MWh)Maximum Capacity/MW Thermal 250 25 76 Gas 100 46 155 Nuclear 365 10 400 Wind 260 0 800 PV 220 0 800 Storage 160 0 400

Fig.4 Load and renewable profiles in four weekly scenarios

Table2 DR flexibility settings

Maximum Amount Time Duration Incentive Cost(Increase)Incentive Cost(Decrease) Nodes Interrupted DR (Case I -III) 100 MW 50～80 h 0.1 $/kW 0.5 $/kW 1,2,3,4,5,6,7,8,9 Transferred DR (Case I -III) 100 MW 1～168 h 0.1 $/kW 0.2 $/kW 10,13,14,15,16,18,19,20 Interrupted DR (Case IV) 100 MW 50～80 h 0.5 $/kW 1.0 $/kW 1,2,3,4,5,6,7,8,9 Transferred DR (Case IV) 100 MW 1～168 h 0.2 $/kW 0.4 $/kW 10,13,14,15,16,18,19,20

Table3 Cost performance of IEEE-RTS-96 system for different cases

Case I Case II Case III Case IV Total Cost / $ 1.23×109 1.17×109 1.21×109 1.21×109 Operation Cost/Incentive Cost / $ 3.24×108 3.05×108/2.23×107 3.35×108/1.17×108 3.19×108/2.02×107 Investment Cost / $ 9.05×108 8.46×108 8.03×108 8.71×108 Storage Cost / $ 1.03×108 5.71×107 0 8.08×107 Solving time / s 859.06 986.54 799.85 985.36

2.2 Results

As illustrated in Fig.5 and Table3,the consideration of DR in the planning model provides more flexibility to the power system and requires more transmission lines to achieve energy exchange.Hence,a slight increase was introduced in the expansion investment of the transmission lines in Case II.However,owing to DR flexibility,the operation cost in Case II reduces by approximately 6%compared with that in Case I.The computation time for each case is provided in the last line of Table3.

Fig.5 Expansion of optimized transmission lines

Meanwhile,the optimized generation and storage capacity displayed in Fig.6 show that the flexibility of DR could replace a part of the flexibility of the energy storage,which saves nearly 45% of the energy storage capacity.This is also the reason that the total investment cost is reduced in Case II.Above all,the total cost decreases by a 5%considering DR.

Fig.6 Optimized generation and storage capacity in Cases I-III

As illustrated in Table4,without DR,there is approximately 577 MWh unplanned load curtailment in the system,while in Case II,the load flexibility is improved by the DR mechanism and the load curtailment reduces to zero.The generation curtailment slightly increases in Case II because we only limited the curtailment rate instead of optimizing the generation consumption.

Table4 Load and generation curtailment in Cases I and II

Case I Case II Load curtailment / MWh 577 0 Gen.curtailment / MWh 1030 1200

Fig.7 displays the optimized generation and load profile considering DR flexibility.Instead of the load curtailment,interrupted and transferred DRs provide more flexibility to satisfy the system’s energy balance and reduce the fluctuation of the demand curve.The maximum load reduces from 2850 MW to 2785 MW,whereas the maximum peakvalley difference decreases by approximately 5%.Fig.7(b) displays the energy and power balance in the winter considering DR.Integrating DR flexibility into planning model,the actual load profile is relatively moderate.

In addition,we used the node’s marginal price to express the capability of the DR and choose Nodes 5,13,20,and 24 as an example,which is displayed in Fig.8.Owing to DR flexibilities,the marginal price at each node sharply decreases and the maximum marginal price reduces by approximately 80% at Node 5.

The above cases confirm that the DR can provide more flexibility to the system besides conventional power plants and energy storage.Next,we will further demonstrate that the DR can avoid only a part of the storage investment cost,and the effect of the energy storage cannot be replaced by DR in Case III.

Fig.7 Optimal generation and load profile considering DR

The optimized cost for Case III is illustrated in Table3.Compared to Case I,the total cost has a slight decrease,but it is still higher than Case II.In addition,as illustrated in Fig.6,owing to the loss of storage,much of the energy storage’s flexibility is transferred to the conventional power plants,causing a significant increase in the proportion of the conventional power plants of nearly 30%.Hence,DR flexibility can replace a part of storage flexibility to avoid storage investment.

Compared to Case II,Case IV has a higher subsidy for different DR flexibility.From the system side,a higher subsidy will lead to a loss of some economic benefits from DR flexibility.Hence,as shown in Table3,the economic cost will increase.The quantities of the DR present a significant decrease,as illustrated in TableV.

Table5 Quantities for different DRs in Cases II and IV

Case II Case IV Interrupt DR/MWh 200.48 80.91 Transferred DR/MWh 5422.2 2981.6

2.3 DR with different load distributions

In this section,we explore the effectiveness of the DR with different load distributions.In the above cases,the load at each node has the same distribution.However,in reality,the load curve could be of different types; this is the case,for instance,for commercial and residential loads.Hence,we used two distributions to express diversity.Nodes 1-9 have one load distribution (Type 1); the remaining load nodes have another one (Type 2).Both types are displayed in Fig.9.We also introduced two subcases to show the adaptiveness of the DR mechanism,as illustrated in Table6.

Table6 Parameter settings in Case V

Case V.1 Case V.2 Type 1 Interrupted DR Transferred DR Type 2 Transferred DR Interrupted DR

As shown in Table7,compared to Case V.2,Case V.1 has lower economic cost because the utilization of the DR flexibility in Case V.1 is more efficient.According to the characteristic of the load curve displayed in Fig.9,the variation of the Type-1 load curve is volatile and the peakvalley difference of the Type-2 load curve is relatively larger.Thus,the interrupted DR is appropriate for the Type-1 load curve,and the transferred DR matches the Type-2 load curve,which coincides with the settings in Case V.1.

Fig.8 Marginal prices of Nodes 5,13,20,and 24 in Cases I and II

Fig.9 Load curve with different distributions

Table7 Cost of Case IV

Case IV.1 Case IV.2 Total Cost/$ 5.44×108 5.46×108 Investment Cost/$ 3.58×108 3.69×108 Incentive Cost/$ 6.64×106 5.49×106

Fig.10 displays the generation capacity and storage requirements of these two subcases.Fig.11 shows a comparison of the marginal price at Nodes 3 and 20 for these two subcases.

Fig.10 Generation portfolio in Case V

Fig.11 Marginal prices in Case IV

3 Conclusions

In this study,we analyzed the flexibility and benefit of the DR based on a stochastic investment planning model.Two types of DR,namely interrupted DR and transferred DR,were modeled.An empirical analysis based on a modified IEEE-RTS-96 system was performed.The results demonstrate the effectiveness of the proposed model and indicate that DR flexibility has a significant benefit in avoiding storage investment.

Acknowledgements

This work is jointly supported by Youth Program of National Natural Science Foundation of China (No.51907100) and Technical Program of Global Energy Interconnection Group Co.,Ltd (No.1100/2020-75001B).

Declaration of Competing Interest

We declare that we have no conflict of interest.