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Distribution grid with distributed energy resources: impact, control, and design

Xue Han Supervisor: Sr. Scientist Henrik W. Bindner Energy System Operation and Management (ESOM), Center for Electric Power and Energy (CEE) Risø, Roskilde, Denmark 7th June, 2016

07 June 2016 DTU Electrical Engineering, Technical University of Denmark

Outline

Introduction

Distribution grid observability

DER integration issues and its flexibility

Distributed control and design metrics

Hierarchical voltage control scheme

Final remarks

2

Introduction

Control System


Introduction

3


Trends in power and energy systems

4

• Environmental concerns • Global efforts on achieving energy system sustainability

• Trends

– 1. Physical electricity/power system with DERs – 2. Monitoring and control of power system

Introduction


I: DERs in the physical systems

Simple diagram of electricity grids.

5

Source: “Final report on the August 14, 2003 blackout in the United States and Canada,” U.S.-Canada Power System Outage Task Force , Tech. Rep., 2008. [Online]. Available: http://energy.gov/oe/

Introduction

Generation Transmission Distribution Consumption


Distribution

+

DERs

I: DERs in the physical systems

6

Simple diagram of future electricity grids.

Introduction


Challenges and opportunities I

• Grid impacts: – Congestions of grid components & voltage drop. – Reduction on base load & voltage rise (bidirectional power flow). – New load patterns & uncertainty (when, where, and what).

• Contribution from distributed energy resources: – Power inverter with additional functionalities – Energy storage in different forms

7

Introduction

Net load

0 Time of a day

Original load Original load + HPs Original load + HPs + EVs Original load + HPs + EVs + PVs


II: Smart grid and system unbundling • Enhancing the monitoring and communication infrastructure • Establishing liberalized markets to better utilize different technologies • Recognizing the flexibility on the demand side

8

TSO/DSO Demand side management system

Market

Commercial market player Other relevant player

Introduction


Challenges and opportunities II • Aggregate the flexibility from DERs to provide system services that can

solve distribution grid operational issues

• Small scale & large number & different technologies and characteristics New aggregation and control paradigms

9

Time of a day

Loading

100% loading

70% loading

Introduction

Voltage magnitude

Length of the feeder

Darker curves: original profile; Lighter curves: expected profile with the activation of service


Exploit the flexibility from DERs • Distribution grid observability and operational issues • Modelling the flexibility of different DER technologies • Aggregation and control system design

– Design requirement – Control algorithm design

10

Control System

Introduction



11

Control System


Motivation • Maximize the information extracted from additional meters with a unit of

expense (€)

12

The observed Danish LV feeder



Sources of measurements • Sources of measurements to improve the grid observability:

– Pseudo measurements – historical annual consumption (𝐸𝐸annual MWh ), load templates (𝑠𝑠), nominal voltage value(𝑈𝑈nom)

– Smart meters at customer side – load(𝐸𝐸hourly (kWh)), 𝑈𝑈 – Remote meters at grid side – 𝑈𝑈, 𝐼𝐼,𝑃𝑃flow

13


Existing knowledge

Source from the field


Evaluation procedure

14

Traditional state estimation

0 measurement

Real state

All measurements of the feeder

Real state

All measurements of the feeder

Estimated state

Combinations of measurements

Error

Initial state-estimation error

Error

state-estimation errors

Comparison

Reduced error

𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 1

𝑛𝑛 ∙ 𝑡𝑡end� �

𝑒𝑒𝑒𝑒𝑒𝑒trad,𝑚𝑚,𝑡𝑡 − 𝑒𝑒𝑒𝑒𝑒𝑒𝑚𝑚,𝑡𝑡

𝑒𝑒𝑒𝑒𝑒𝑒trad,𝑚𝑚,𝑡𝑡

𝑡𝑡end

𝑡𝑡=1

𝑛𝑛

𝑚𝑚=1

Grid Model

Cable parameters, customer info

Smart meter (load)

Load template (load)

Remote meter (𝑃𝑃flow,𝑈𝑈, 𝐼𝐼)

Smart meter (𝑈𝑈)


How much better the grid states is calculated comparing to the results from traditional approach:

𝑒𝑒𝑒𝑒𝑒𝑒trad,𝑚𝑚,𝑡𝑡

𝑒𝑒𝑒𝑒𝑒𝑒𝑚𝑚,𝑡𝑡

+ −


Simulation results I

15

1 Reference scenario: only using pseudo measurements

2 Smart meter: Power injection & voltage at Node 9 (~7% of the total load)


4 Full observation: using all collected measurements


0%10%20%30%40%50%60%70%80%90%

100%

Reference SM 9 SM 6 Full Obs

accyUaccyP


Simulation results II

16






0%10%20%30%40%50%60%70%80%90%

100%


accyUaccyP


Simulation results III

17






0%10%20%30%40%50%60%70%80%90%

100%


accyUaccyP


Simulation results IV

18






0%10%20%30%40%50%60%70%80%90%

100%


accyUaccyP


0%10%20%30%40%50%60%70%80%90%

100%

Reference SM 6 RM 2 Full Obs

accyUaccyP

Simulation results V

19



3 Remote meter: Power flow (3 channels) & voltage at Node 2




0%10%20%30%40%50%60%70%80%90%

100%

Reference SM all RM all Full Obs

accyUaccyP

Simulation results VI

20


2 All smart meter measurements

3 All remote meter measurements




0%10%20%30%40%50%60%70%80%90%

100%

Reference SM all RM all Full Obs

accyUaccyP

Simulation results VII

21


2 All smart meter measurements

3 All remote meter measurements




Summary

22

• Different combinations of measurements are used for calculating the improved accuracy.

• More information can be extracted from a single remote meter than from a single smart meter

• More cost effective to collect measurements from smart meters than installing an additional remote meter

• Additional value of new data source: – Voltage quality monitoring, outage alarm – Load categorization and profile modelling – Grid modelling and grid operation status

Publications: X. Han, S. You, F. Thordarson, D. V. Tackie, S. M. Ostberg, O. M. Pedersen, H. W. Bindner, and N. C. Nordentoft, “Real-time measurements and their effects on state estimation of distribution power system,” in Proc. 4th IEEE PES Innovative Smart Grid Technologies Europe (ISGT-Europe’13). IEEE, Oct. 2013.

P. D. Cajar, X. Han, H. W. Bindner, O. M. Pedersen, F. Thordarson, et al., Monitoring of the load on the distribution grid. Tech report. 2014, iPower Consortium.



DER integration issues and flexibility

23

Control System


Distributed energy resources • Photovoltaic (PV) panel

• Electric vehicle (EV)

• Electric space heating

24


EV

Drivi

ng p

atte

rn

Charing control logic

charge Charing power

Energy to charge

Flexibility

House

Thermostat

𝑇𝑇in

Heating power

Flexibility

𝑇𝑇out

𝑃𝑃

𝑄𝑄

0

Active power production

Active & reactive power production

𝑆𝑆max

Flexibility: • Active power to curtail • Reactive power cap/ind

𝜃𝜃𝑃𝑃𝑃𝑃


Simulation platform

25



Grid impacts • Danish scenario 2030: PV (32.1%), EV (35.6%), HP (9.1%)* • A real Danish 10kV MV distribution feeder:

– 31 nodes, 31 lines, 40 customers (grouped at MV/LV transformer) • Congestion of transformers and cables during the winter • Significant voltage drop during the winter • Voltage rise with high penetration PVs during the summer (73.8%)

26


* Penetration rate is derived as the ratio between the total rated power of DERs and the original peak load value.

Load

ing

[%]

Time [hour] Time [hour]

Vol

tage

[kV

]


Summary • Different DERs

– types of technologies – operational characteristics – flexibility capabilities

• The grid impacts of DERs – Congestion of lines and transformers – Voltage rise and voltage drop in light and heavy load conditions

27


Publications: X. Han, F. Sossan, H. W. Bindner, S. You, H. Hansen, and P. D. Cajar, “Load kick-back effects due to activation of demand response in view of distribution grid operation,” in Proc. 5th IEEE PES Innovative Smart Grid Technologies Europe (ISGT-Europe’14). IEEE, Oct. 2014.

X. Han, H. W. Bindner, H. Hansen, K. S. Rasmussen, P. D. Cajar, Y. Ding, and D. V. Tackie, “Identification of kick-back from normal situations due to activation of flexible demand,” iPower Consortium, Tech. Rep., 2014.



28

Control System


Motivation • A large number of heterogeneous

and geographically dispersed active units.

• Power distribution grid is conventionally designed to be passive.

• The complexity of a centralized control solution based on this traditional control paradigm is significant and does not scale well.

29



Control categorization

30


HV

MV

LV

Control interaction

Load PV Transformer

Centralized Decentralized vertical horizontal

Distributed

Interaction in other control layers Control center Control element Database

Determinate Iterative Centralized shared memory

Peer-to-peer


Design criteria

31

• Regulatory, economic, or technical requirements of the control system • The first step to answer which one is the best solution.


Control objective

Controllable components

Physical grid

Performance constraints and

metrics

Budget

BEST


Summary • A clear definition and categorization of “distributed control”

– the composition of control elements and their relationship • Design criteria

– represent the requirements in the design phase – indicate the performance in the evaluation phase

• Tool to find the best solution by matching – The feature that a control algorithm provides – The problem performance requirement (+ budget)

32


Publications: X. Han, K. Heussen, O. Gehrke, H.W. Bindner, and B. Kroposki, “Methodology to Evaluate Distributed Control Strategies used in Distributed Energy Resource Applications,” submitted to IEEE Trans. Smart Grid. IEEE. (under 2nd round iteration)

X. Han, A. M. Kosek, D. E. M. Bondy, H. W. Bindner, S. You, D. V. Tackie, J. Mehmedalic, and F. Thordarson, “Assessment of distribution grid voltage control strategies in view of deployment,” in Proc. 2nd IEEE International Workshop on Intelligent Energy Systems (IWIES’14). IEEE, Oct. 2014.



33

Control System


Problem formulation • Distribution grid service: congestion management & voltage support • Flexibility from DERs: small scale & large number & different

technologies • Flexible setup that accounts for…

– Power system and DERs: availability of flexibility, the amount, and the location

– Software and communication network: failures at hardware and software

– System services: when, where, which one, how much… • Multiple stakeholders:

– DER owner / customer – Aggregator – DSO

34



Controller design requirements • Resilience to changes and failures, such as …

– A new DER is added into the system – Some DERs want to subscribe to a new service – A computer / a communication link fails

• Single point connection to Aggregator / DSO

– A hierarchical control structure (D-V)

• Frequent and fast updates and response to events (Determinate)

• Different DER technologies – Generic flexibility interface

35



Hierarchical control framework

36


Supervisory Controller

Local Controller

Hierarchy builder

Unit Controller

LC

SC

UC UC

LC

UC UC

Grid info

DSO


• Redundant design: all the computers attached to DER units have a copy of the coordination algorithm.

• The control hierarchy is built via an election process, such that the units in the same group elect the coordinator based on certain properties.

• Election happens when – A significant player (coordinator) in the control hierarchy is lost – A new DER joins the system

Hierarchical control framework II

37



Generic flexibility interface

38


Under charging

Rated power

Battery capacity

Actual power to consume

Target SOC at target time

Electric vehicle

Unit Controller

Current power consumption

Power planning to consume Flexibility & willingness (bidirectional)

Dispatch setpoint

UC Data

UC Set


Optimal dispatch algorithm • Utility function

• Optimization variable 𝑥𝑥: – Vector of the flexibility to be activated of each DER

• Constraints: – Flexibility capacity – Power flow constraints

• Weighting factors: – 𝛼𝛼 for cost of flexibility – 𝛽𝛽 for thermal loss of cables – 𝛾𝛾 for voltage deviation from 𝑈𝑈ref

39


min𝑥𝑥

𝛼𝛼 ∙ � cost𝑖𝑖 ∙ 𝑥𝑥𝑖𝑖∈𝑅𝑅DER

+ � 𝛽𝛽(𝑘𝑘,𝑙𝑙) ∙𝜕𝜕𝑃𝑃 𝑘𝑘,𝑙𝑙

loss

𝜕𝜕𝑆𝑆 ∙ 𝑆𝑆flex(𝑥𝑥)(𝑘𝑘,𝑙𝑙)∈𝑅𝑅line

+ 𝛾𝛾 ∙ � 𝑈𝑈𝑘𝑘(𝑥𝑥) − 𝑈𝑈ref 2

𝑘𝑘∈𝑅𝑅node

𝜕𝜕𝑃𝑃(𝑘𝑘,𝑙𝑙)loss

𝜕𝜕𝑆𝑆: sensitivity factor between power loss at

line (𝑘𝑘, 𝑙𝑙) and apparent power injection vector 𝑆𝑆

𝑆𝑆flex(𝑥𝑥), 𝑈𝑈𝑘𝑘(𝑥𝑥): linear relation between aggregated flexibility / node voltage and 𝑥𝑥.

𝑅𝑅DER, 𝑅𝑅line, and 𝑅𝑅node: set of DERs, cables, and nodes in the test grid.


Case study

40


External Grid

Node 0 Node 3

8 kW

Node 1

8 kW

Line1 (1050m)

Node 2

10 kW 8 kW

Line2 (725m)

8 kW

Line3 (375m)

8 kW 8 kW 8 kW


Simulation results • Voltage profile (1-minute resolution)

41

• Cable loading profile (first line)

𝑈𝑈3 > 𝑈𝑈3min

25.04 1.72

𝑆𝑆(0,1) > 𝑆𝑆(0,1)max

10.56 0.06

Ref. Ctrl.

Vol

tage

at

last

nod

e [p

.u.]

Time [hour] 0 8 16 24 32 40 48 56 64 72

Slack bus Ref. scenario Service scenario

1.04

1.02

1.00

0.98

0.96

0.94

App

aren

t po

wer

flo

w [

kW]

Ref. scenario Service scenario 20

15

10

5

0

Time [hour] 0 8 16 24 32 40 48 56 64 72

Proportion of the period when the constraint is violated [%]


Large scale implementation design I • Introduction of “coordination zone”

– Simplify the location information & enable aggregation approach – Grouping DERs according to their electrical distance from each other – Sufficient number of DER units in the zone to provide flexibility

42



Large scale implementation design II • Scenario 1: reference, without any control scheme • Scenario 2: decentralized autonomous control scheme • Scenario 3: Hierarchical control scheme with implementation of

“coordination zone”

43

Cum

ulat

ive

dist

ribu

tion

of

sam

ples

in t

he s

imul

atio

n pe

riod


Interaction with On-load Tap-changer • Conventionally, tap change is triggered by voltage magnitude violation. • In this setup

– Voltage magnitude – Cost of flexibility

• Simulation results

44


Total cost Overall loss No. of actions

Traditional OLTC - 1 9

Only flexibility 1 0.86 -

OLTC + flexibility 0.91 0.82 4

OLTC (50% cost) + flexibility 0.76 0.83 7


Summary • Hierarchical control scheme that has the following features

– Redundant design + hierarchy builder – Generic flexibility interface – Modular functions – Introducing incentive signals to reflect the real values

• Some realistic factors regarding its implementation are considered – The information sharing between stakeholders – DER location information in a large scale implementation – The interaction between flexibility and active grid assets

45


Publications: X. Han, A. M. Kosek, O. Gehrke, H. W. Bindner, and D. Kullmann, “Activate distributed energy resources’ services: Hierarchical voltage controller as an application,” in Proc. IEEE PES Transmission & Distribution Conference and Exposition 2014. IEEE, Apr. 2014.

X. Han, H. Bindner, J. Mehmedalic, and D. Tackie, “Hybrid control scheme for distributed energy resource management in a market context,” in Proc. IEEE PES General Meeting Conference & Exposition 2015. IEEE, Jul. 2015.

X. Han, H. Bindner, J. Mehmedalic, and D. Tackie, “Coordinated voltage control scheme for distribution grid with on-load tap-changer and distributed energy resources in a market context,” in Proc. IEEE Industrial Electronics Society Annual Conference 2015. IEEE, Nov. 2015.


Final remarks

46


Major contribution • The observability against cost of field measurements in LV feeder is

examined. Smart meters are proven to be the most cost effective solution.

• A simulation platform is built including the grid models, DER models and corresponding future scenarios.

• DER integration issues are examined in simulations. – Congestion of grid components – Voltage rise / drop

• A tool set is developed to assist the design and evaluation of distributed control strategies.

• A hierarchical control scheme is proposed to enable the flexibility services, and to explore the value of flexibility from DERs.

• To facilitate the hierarchical control scheme in a realistic environment, some implementation issues

– the operational information disclosure – the relation with grid assets

47

Final remarks


Future work • More advanced mathematical methods

– machine learning – adaptive control

• The interactions between controlled areas – DSO and DSO – TSO and DSOs

• The impacts of – delays in the process – loss of information – failure of the control elements

48

Final remarks


List of relevant publications • X. Han, S. You, F. Thordarson, D. V. Tackie, S. M. Ostberg, O. M. Pedersen, H. W. Bindner, and N. C.

Nordentoft, “Real-time measurements and their effects on state estimation of distribution power system,” in Proc. 4th IEEE PES Innovative Smart Grid Technologies Europe (ISGT-Europe’13). IEEE, Oct. 2013.

• X. Han, F. Sossan, H. W. Bindner, S. You, H. Hansen, and P. D. Cajar, “Load kick-back effects due to activation of demand response in view of distribution grid operation,” in Proc. 5th IEEE PES Innovative Smart Grid Technologies Europe (ISGT-Europe’14). IEEE, Oct. 2014.

• X. Han, S. You, and H. W. Bindner, “Critical Kick-back Mitigation Through Improved Design of Demand Response,” submitted to Applied Thermal Engineering. Elsevier.

• X. Han, K. Heussen, O. Gehrke, H.W. Bindner, and B. Kroposki, “Methodology to Evaluate Distributed Control Strategies used in Distributed Energy Resource Applications,” submitted to IEEE Trans. Smart Grid. IEEE.

• X. Han, A. M. Kosek, D. E. M. Bondy, H. W. Bindner, S. You, D. V. Tackie, J. Mehmedalic, and F. Thordarson, “Assessment of distribution grid voltage control strategies in view of deployment,” in Proc. 2nd IEEE International Workshop on Intelligent Energy Systems (IWIES’14). IEEE, Oct. 2014.

• X. Han, A. M. Kosek, O. Gehrke, H. W. Bindner, and D. Kullmann, “Activate distributed energy resources’ services: Hierarchical voltage controller as an application,” in Proc. IEEE PES Transmission & Distribution Conference and Exposition 2014. IEEE, Apr. 2014.

• X. Han, H. Bindner, J. Mehmedalic, and D. Tackie, “Hybrid control scheme for distributed energy resource management in a market context,” in Proc. IEEE PES General Meeting Conference & Exposition 2015. IEEE, Jul. 2015.

• X. Han, H. Bindner, J. Mehmedalic, and D. Tackie, “Coordinated voltage control scheme for distribution grid with on-load tap-changer and distributed energy resources in a market context,” in Proc. IEEE Industrial Electronics Society Annual Conference 2015. IEEE, Nov. 2015.

49


Thanks for listening. Questions and comments

50

The PhD project is financially supported by iPower – a Strategic Platform for Innovation and Research within Intelligent Electricity (SPIR).

Special thanks to: Henrik Bindner for his guidance, and SYSLAB team for their support.

Distribution grid with distributed energy resources: impact, control, and design


Backup slides

51


Distributed energy resource (DER) • Small scale • Installed at the end-users in the distribution grid • Able to adjust their production or consumption if demanded by external

instances. • The adjustable portion is referred to as flexibility.

52


Kick-back effect (background) • Demand response program • Example: Time-of-use pricing, a variable rate structure that charges for

energy depending on the time of day and the season

• Identical control signal to all the DERs with homogeneous features • Congestion of grid

– local problem – failure of pricing scheme design

53

Source: Southern California Edison, ISO.


0 10 20 30 40 50 60 70

Kick-back effect (phenomenon) • DERs: temporarily synchronous behaviour when resuming their normal

operation states after the controlled period

54

Load curtailing

Kick back

12

8

4

0

Time [hour]

Pow

er [

MW

]

5000 heat pumps


Kick-back effect (dynamic behaviour)

55

0 10 20 30 40 50 60 70

Time [hour]

Pow

er [

MW

]



56

0 10 20 30 40 50 60 70

Time [hour]

Pow

er [

MW

]



57

0 10 20 30 40 50 60 70

Time [hour]

Pow

er [

MW

]



58

0 10 20 30 40 50 60 70

Time [hour]

Pow

er [

MW

]



59

0 10 20 30 40 50 60 70

Time [hour]

Pow

er [

MW

]



60

0 10 20 30 40 50 60 70

Time [hour]

Pow

er [

MW

]


Willingness of the DER owner • Cost to activate flexibility willingness of the DER owner • General consideration of cost:

– Reactive power from DERs < curtailing power consumption < curtailing power production

• Cost curve of flexibility from electric space heating:

61

Temperature

Cost 𝑇𝑇indoor

𝑎𝑎down

𝑎𝑎up

𝑎𝑎max


Sensitivity analysis • Weighting factors

62

Scenario Cost(𝛼𝛼) Loss(𝛽𝛽) Voltage(𝛾𝛾) Comments

1 1 1 1000 Voltage dominant

2 1 1 1 Balanced condition

3 1 1000 1 Loss dominant

2 3


Information disclosure between stakeholders

63

Balance Responsible Consumer (Retailer)

DSO Aggregator

Modified from D. E. Bondy, A. Thavlov, J. B. Tougaard, K. Heussen, Method for Ancillary Service Modeling and Performance Assessment, submitted to “IEEE Transactions on Smart Grid”.

Consumer/ DER owner

Asset management service

Energy service

Flexibility service

Pow

er d

eliv

ery

serv

ice


Information disclosure between stakeholders

64

Balance Responsible Consumer (Retailer)

DSO Aggregator

Modified from D. E. Bondy, A. Thavlov, J. B. Tougaard, K. Heussen, Method for Ancillary Service Modeling and Performance Assessment, submitted to “IEEE Transactions on Smart Grid”.

Consumer/ DER owner

Control & management related asset states

Flexibility service information

Energy consumption

Asset states

Grid states


• 0 ≤ ∆𝑃𝑃PV+ (𝑡𝑡) ≤ 𝑃𝑃PV(𝑡𝑡) • 0 ≤ ∆𝑄𝑄PV

+,−(𝑡𝑡) ≤ 𝑃𝑃PV 𝑡𝑡 − ∆𝑃𝑃PV+ 𝑡𝑡 ∙ tan (𝜃𝜃PF)

• 𝑃𝑃PV 𝑡𝑡 − ∆𝑃𝑃PV+ 𝑡𝑡 2 + ∆𝑄𝑄PV+,−(𝑡𝑡)

2≤ 𝑆𝑆PVmax

2

DER models (PV)

65

𝑃𝑃

𝑄𝑄

0

𝑆𝑆max

Flexibility:

0,∆𝑃𝑃PV+ (𝑡𝑡) , ∆𝑄𝑄PV− (𝑡𝑡),∆𝑄𝑄PV+ (𝑡𝑡)

𝜃𝜃𝑃𝑃𝑃𝑃 𝑃𝑃PVactual 𝑡𝑡 ∆𝑃𝑃PV+ (𝑡𝑡) is the active power production that a PV can be curtailed.

𝑃𝑃PV(𝑡𝑡) is the active power production that a PV can produce now.

∆𝑄𝑄PV+,−(𝑡𝑡) is reactive power production and

consumption a PV can provide.

𝑆𝑆PVmax is the capacity of the PV inverter, and 𝜃𝜃PF is the maximal power factor that the inverter allows.

𝑃𝑃PVactual 𝑡𝑡 𝑄𝑄PVactual 𝑡𝑡

𝑃𝑃PV(𝑡𝑡)


DER models (EV)

• 𝑃𝑃EVe2m 𝑡𝑡 = 1𝜂𝜂e2m

𝐷𝐷 ∙ 𝑎𝑎𝑐𝑐𝑛𝑛𝑐𝑐e2d/∆𝑡𝑡

• 𝑃𝑃EVch 𝑡𝑡 = 𝑂𝑂 ∙ 𝜂𝜂𝑐𝑐2𝑐𝑐 ∙ 𝑃𝑃EV 𝑡𝑡 , 0 ≤ 𝑃𝑃EV 𝑡𝑡 ≤ 𝑃𝑃EVmax

• 𝐸𝐸d 𝑡𝑡 + 1 = 𝐸𝐸d 𝑡𝑡 + 𝑃𝑃EVch 𝑡𝑡 − 𝑃𝑃EVe2m 𝑡𝑡 ∆𝑡𝑡

• 𝐸𝐸𝑡𝑡leaved = 0

• 𝑂𝑂 = 𝑐𝑐lack ∙ 𝑐𝑐home ∙ 𝑐𝑐order • 𝑐𝑐order = 1 − 1 − 𝑐𝑐grid 1 − 𝑐𝑐owner

• 𝑐𝑐owner = �1,𝐸𝐸d 𝑡𝑡 ≤ 𝜂𝜂𝑐𝑐2𝑐𝑐 ∙ 𝑃𝑃EVmax ∙ 𝑡𝑡leave − 𝑡𝑡 /∆𝑡𝑡 0, elsewise

• 𝑐𝑐lack = �1,𝐸𝐸d 𝑡𝑡 > 0 0, elsewise

• 𝑐𝑐home = �1, 𝑡𝑡arrive ≤ 𝑡𝑡 ≤ 𝑡𝑡leave 0, elsewise

• �0 ≤ ∆𝑃𝑃EV− (𝑡𝑡) ≤ 𝑃𝑃EVmax(𝑡𝑡), 𝑡𝑡𝑎𝑎𝑙𝑙 < 𝑡𝑡𝑐𝑐 ∆𝑃𝑃EV− (𝑡𝑡) = 0, 𝑡𝑡𝑎𝑎𝑙𝑙 ≥ 𝑡𝑡𝑐𝑐

66

EV

Drivi

ng p

atte

rn

Charing control logic

charge

𝑃𝑃EVe2m(𝑡𝑡) is the consumed electric power by driving the distance 𝐷𝐷. and 𝑎𝑎𝑐𝑐𝑛𝑛𝑐𝑐e2d is the ratio between energy and distance.

𝜂𝜂𝑒𝑒2𝑚𝑚 and 𝜂𝜂𝑐𝑐2𝑐𝑐 are consumption and charging efficiencies.

𝑃𝑃EVch 𝑡𝑡 is charged power, and 𝑃𝑃EV 𝑡𝑡 is the charging power.

𝐸𝐸d is the daily energy consumption of an EV, and by the time when the EV leave 𝑡𝑡leave, 𝐸𝐸𝑡𝑡leave

d should be 0.

𝑐𝑐grid

𝐸𝐸d 𝑡𝑡 + 1 𝑃𝑃EVch 𝑡𝑡

∆𝑃𝑃EV− , 0


DER models (electric space heating)

• 𝑇𝑇in 𝑡𝑡 + 1 = 𝐴𝐴 ∙ 𝑇𝑇in 𝑡𝑡 + 𝐶𝐶0 ∙ 𝑃𝑃HPheat(𝑡𝑡) ∙ ∆𝑡𝑡 + 𝐶𝐶1𝑇𝑇out 𝑡𝑡 • 𝑃𝑃HPheat 𝑡𝑡 = 𝑃𝑃HP(𝑡𝑡) ∙ 𝐶𝐶𝑂𝑂𝑃𝑃 ∙ 𝑐𝑐state(𝑡𝑡)

• 𝑐𝑐state(𝑡𝑡) = �0,𝑇𝑇in(𝑡𝑡) ≥ 𝑇𝑇inmax

1,𝑇𝑇in(𝑡𝑡) ≤ 𝑇𝑇inmin

𝑐𝑐state 𝑡𝑡 − 1 ∙ 𝑐𝑐grid, otherwise

• 𝑃𝑃HP(𝑡𝑡) = �0,𝑇𝑇in(𝑡𝑡) ≥ 𝑇𝑇inmax

𝑃𝑃HPmax,𝑇𝑇in(𝑡𝑡) ≤ 𝑇𝑇inmin

𝑃𝑃HP(𝑡𝑡 − 1), otherwise

• � ∆𝑃𝑃HP+ 𝑡𝑡 = 𝑃𝑃HP 𝑡𝑡 , if 𝑐𝑐state 𝑡𝑡 = 0∆𝑃𝑃HP− 𝑡𝑡 = 𝑃𝑃HPmax − 𝑃𝑃HP 𝑡𝑡 , if 𝑐𝑐state 𝑡𝑡 = 1

67

House

Thermostat

𝑇𝑇in

𝑇𝑇out 𝑃𝑃HP(𝑡𝑡)

∆𝑃𝑃HP− (𝑡𝑡),∆𝑃𝑃HP+ (𝑡𝑡) 𝑐𝑐grid

𝑇𝑇in(𝑡𝑡) is the indoor temperature, and 𝑇𝑇out 𝑡𝑡 is the outdoor temperature.

𝐴𝐴,𝐶𝐶0,𝐶𝐶1 are thermal parameters which form the thermostatic model of a building.

𝑃𝑃HPheat(𝑡𝑡) is the heating power output from the heat pump, and 𝑃𝑃HP(𝑡𝑡) is the electric power consumed by the heat pump, in which the coefficient of the heat conversion is 𝐶𝐶𝑂𝑂𝑃𝑃.

𝑐𝑐state is the thermostatic control state.


Assumptions • The external grid is treated as a voltage source (constant magnitude and voltage

angle) with infinite capacity. • The correlations of load and DER behaviours are ignored. Their time-series profiles

are independent from each other. • The loading and capacity of grid assets (e.g., cables and transformers) are fixed

and not dependent on the temperature. • The operation of switches and breakers is not considered. • Synchronized measurements from various locations are collected to estimate the

grid and DER states. • The grid states are all observable. • No delay is considered in the actuation of control decisions, nor at computing and

communicating dispatch set-points. • The power factor is not limited in the PV inverters, and the capacity of inverters is

oversized. • Aggregated cost value is calculated by taking the weighted average of costs from

individual DERs. • The predicted values of external inputs for the next time instant use the current

measured / estimated values. • If infeasible solutions are calculated from the controllers, the set-points will not be

updated.

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