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Modelling of Active Distribution Networks for Power System Restoration Studies
10th IFAC Symposium on Control of Power and Energy Systems 10th IFAC Symposium on Control of Power and Energy Systems Tokyo, Japan, September 2018of Power and Energy Systems Control 10th IFAC Symposium on 4-6, Tokyo, Japan, September 4-6, 2018 Available online at www.sciencedirect.com 10th IFAC Symposium on 4-6, Control Tokyo, Japan, September 2018of Power and Energy Systems Tokyo, Japan, September 4-6, 2018
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IFAC PapersOnLine 51-28 (2018) 558–563
Modelling of Active Distribution Networks Modelling of Active Distribution Networks Modelling of Active Distribution Networks for Power System Restoration Studies Modelling of Active Distribution Networks for Power System Restoration Studies for Power System Restoration Studies for Power System Restoration Studies Gustav Lammert ∗∗ Alexander Klingmann ∗∗
Gustav Lammert Klingmann ∗ ∗ ∗ ∗ ∗∗ ∗ Alexander ∗ Lammert Alexander Christian Hachmann ıo LafferteKlingmann Gustav ∗ Dar´ ∗ Holger Becker ∗∗ ∗ ∗ Christian Hachmann Dar´ ıo Lafferte Becker ∗ ∗ ∗∗ ∗ ∗∗ ∗,∗∗ ∗ Dar´ ∗ Holger ∗∗ Gustav Lammert Alexander Klingmann Christian Hachmann ıo Lafferte Holger Becker Tina Paschedag Wolfram Heckmann Martin Braun ∗ ∗∗ ∗,∗∗ ∗ ∗ ∗∗ Tina Paschedag Wolfram Heckmann Martin Braun ∗ ∗∗ ∗ Wolfram ∗,∗∗ Christian Hachmann Dar´ ıo Lafferte∗∗ Holger Tina Paschedag Heckmann Martin Becker Braun ∗,∗∗ ∗ ∗∗ ∗ Tina Paschedag Wolfram Heckmann Martin Braun ∗,∗∗ University of Kassel, Kassel, Germany ∗ University of Kassel, Kassel, Germany ∗ ∗∗ ∗ University of Kassel, Kassel,Germany Germany Fraunhofer IEE, Kassel, ∗ ∗∗ IEE, ∗∗ ∗∗ Fraunhofer University of Kassel, Kassel,Germany Germany Fraunhofer IEE, Kassel, Kassel, Germany E-Mail: [email protected] ∗∗ E-Mail: [email protected] Fraunhofer IEE, Kassel, Germany E-Mail: [email protected] E-Mail: [email protected] Abstract: This paper presents an aggregated model of Active Distribution Networks (ADNs) Abstract: This paper presents an model of Distribution Networks (ADNs) Abstract: This paper system presentsrestoration an aggregated aggregated model of Active Active Distribution Networks (ADNs) appropriate for power studies. The ADN considers aggregated loads and appropriate for power system restoration studies. The ADN considers aggregated loads and Abstract: This paper system presents an aggregated model of Active Distribution Networks (ADNs) appropriate forgeneration, power restoration studies. The ADN considers aggregated loads and inverter based such as wind and photovoltaic generation. The load model incorinverter based generation, suchrestoration as wind and photovoltaic generation. The load model incorappropriate forgeneration, power system studies. The ADN considersThe aggregated loads and inverter based such as wind and photovoltaic load model incorporates: i) time series data for consumption; ii) voltage andgeneration. frequency dependency; iii) under dependency; iii) under porates: i) time series data for consumption; ii) voltage and frequency inverter based generation, such as wind and photovoltaic generation. The load model incorporates: i)load timeshedding; series data consumption; ii) voltage frequency dependency; iii) under frequency iv)for disconnection behavior; andand v) cold load pick-up. The generation frequency iv) disconnection behavior; and v) cold load The porates:considers: i)load timeshedding; series data consumption; ii) voltage and frequency dependency; iii) under frequency load shedding; iv)for disconnection behavior; and v) frequency cold load pick-up. pick-up. The generation generation model i) time series data for generation; ii) over active power reduction; model considers: i) time series data generation; ii) over frequency active power reduction; frequency load shedding; iv) disconnection behavior; and v) model cold load pick-up. Thephenomena generation model considers: i)and time data for for behavior. generation; ii) over frequency active power reduction; iii) disconnection; iv)series reconnection The ADN covers dynamic iii) disconnection; iv) reconnection behavior. The model covers dynamic model considers: i)and time data generation; ii)ADN over frequency active powerphenomena reduction; iii)the disconnection; and iv) reconnection The ADN covers phenomena in time scale of tens ofseries seconds upfor tobehavior. several minutes withmodel the focus on dynamic frequency dynamics. in the time scale of tens of seconds up to several minutes with the focus on frequency dynamics. iii) disconnection; and iv) reconnection behavior. The ADN model covers dynamic phenomena in the time scale of tens of seconds up to several minutes with the focus on frequency Moreover, the model was tested in several case studies and shows adequate dynamic dynamics. behavior. Moreover, model was in several case shows adequate dynamic behavior. in the timethe scale of tens seconds to several minutesand with the focus on frequency Moreover, the model wasoftested tested in up several case studies studies and shows adequate dynamic dynamics. behavior. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Moreover, the model was tested in several case studies and shows adequate dynamic behavior. Keywords: Under frequency load shedding, blackout, cold load pick-up, black start, island Keywords: Under frequency load shedding, blackout, cold load pick-up, black start, island Keywords: Under frequency shedding, blackout, cold load pick-up, black start, island operation, frequency control,load dynamic equivalent, aggregation, inverter based generation. operation, frequency control,load dynamic equivalent, aggregation, inverter based based generation. Keywords: frequency Under frequency shedding, blackout, cold load pick-up, black start, island operation, control, dynamic equivalent, aggregation, inverter generation. operation, frequency control, dynamic equivalent, aggregation, inverter based generation. 1. INTRODUCTION and IBG, as depicted in Fig. 1 (b). The aggregated load 1. and IBG, as in 1 (b). aggregated 1. INTRODUCTION INTRODUCTION and IBG, as depicted depicted in Fig. Fig. (b). The The aggregated load load model considers: i) time series1 data for consumption; ii) model considers: i) time series data for consumption; ii) INTRODUCTION and IBG, as frequency depicted in Fig. (b). iii) The aggregated load considers: i) time series1 data for Under consumption; ii) voltage and dependency; Frequency Recognizing that 1.power system blackouts are likely to model voltage and frequency dependency; iii) Under Frequency Recognizing that power system blackouts are likely to modelShedding considers: i) time series data iii) for Under consumption; ii) and frequency dependency; Frequency Load (UFLS); iv) disconnection behavior; and Recognizing that power system blackouts measures are likelythat to voltage occur, it is prudent to consider the necessary Shedding (UFLS);dependency; iv) disconnection behavior; and v) v) occur, it is prudent to consider the necessary measures that voltage andPick-Up frequency iii) Under Frequency Recognizing that power system blackouts (IEEE, are likely to Load Load (UFLS); iv) disconnection behavior; and v) Cold Shedding Load (CLPU). The aggregated IBG model occur, ittheir is prudent tointensity consider the duration necessary measures that reduce extent, and 2014). Cold Load Pick-Up (CLPU). The aggregated IBG model reduce their extent, intensity and duration (IEEE, 2014). Shedding (UFLS); iv) disconnection behavior; and v) occur, is prudent consider the necessary measures that Load Cold Loadi) Pick-Up (CLPU). Thegeneration; aggregated IBG model involves: time series data for ii) over frereduce extent,tointensity and duration (IEEE, 2014). One ofittheir the promising measures is the utilization of Active of Active i) time series data generation; ii) over freOne of the measures is the utilization Cold Load (CLPU). The aggregated IBG model reduce extent, intensity and duration (IEEE, 2014). involves: involves: i) Pick-Up time series data for for ii) over frequency active power reduction; iii)generation; disconnection; and iv) One of their the promising promising measures is utilization of Active Distribution Networks (ADNs) to the support the restoration quency power reduction; disconnection; and iv) Distribution Networks (ADNs) to support the restoration involves:active i) time series data foriii) ii) over One of the promising measures is utilization of Active quency active power reduction; iii)generation; disconnection; and freiv) reconnection behavior. The model is for Distribution Networks (ADNs) to the support the blackout restoration process, the system from or behavior. The ADN ADN model is adequate adequate for process, bringing bringing the power power system from the the blackout or reconnection quency active power reduction; iii) disconnection; and iv) Distribution Networks (ADNs) to support the restoration Thestudies ADN model is adequate for power systembehavior. restoration considering long-term process, bringing the power theasblackout emergency state back to thesystem normalfrom state, shown or in reconnection power system restoration studies considering long-term emergency state back to the normal state, as shown in reconnection behavior. The ADN model is adequate for process, bringing the power system from the blackout or power system restoration studies considering long-term emergency state back to host the normal shown in dynamics in the time scale of tens of seconds up to several Fig. 1 (a). These ADNs Inverter state, BasedasGeneration in time scale of tens seconds to Fig. 1 These ADNs Inverter Based power system restoration studies long-term emergency state and back to host the normal state, asGeneration shown in dynamics dynamics in the the time of tens of ofconsidering seconds up upThe to several several minutes with the focusscale on frequency dynamics. model Fig. 1 (a). (a). These ADNs host Inverter Based Generation (IBG), i.e., wind PhotoVoltaic (PV) generation. Howminutes with the focus on frequency dynamics. The model (IBG), i.e., wind and PhotoVoltaic (PV) generation. Howdynamics in the scale of tens of seconds upThe to several Fig. 1the (a). Theseand ADNs host Inverter Based Generation thetime focusgrid on forming frequency dynamics. model does notwith incorporate capabilities. (IBG), i.e., wind PhotoVoltaic (PV) generation. How- minutes ever, incorporation of IBG into the restoration process ever, the incorporation of IBG into (PV) the restoration process does not incorporate grid forming capabilities. minutes with the focus on frequency dynamics. The model (IBG), i.e., wind and PhotoVoltaic generation. However, the incorporation of operators. IBG into the restoration process does not incorporate grid forming capabilities. is challenging for system The remainder of thegrid paper is organized as follows. Secis challenging for system operators. does not incorporate forming capabilities. ever, the incorporation of IBG into the restoration process is challenging for system operators. The remainder of paper is as follows. SecThe of the thethe paper is organized organized as of follows. Section 2remainder duly discusses dynamic behavior the aggreIn practice, negative model is systemload operators. In challenging practice, aa for negative load model is is still still used used by by system system tion 2 duly discusses the dynamic behavior of the aggreThe remainder of the paper is organized as follows. Secdulymodel. discusses the dynamic behavior of the aggregated2 load Section 3 presents the aggregated IBG In practice, negativeIBG loadinmodel still used by system operators to arepresent powerissystem stability stud- tion gated load model. Section 33 presents the aggregated IBG operators to represent IBG in power system stability studtion 2 duly discusses the dynamic behavior of the aggreIn practice, a negative load model is still used by system gated load model. Section presents the aggregated IBG operators to represent IBG inOn power stability stud- model and its functions. Section 4 shows the case studies. ies (Lammert et al., 2017). the system other hand, different and its functions. Section 44 shows case studies. ies (Lammert et 2017). On the other hand, different gated load model. Section 3drawn presents the the aggregated IBG operators to represent IBG in power stability stud- model model and its functions. Section shows the case studies. Finally, the conclusions are in Section 5. ies (Lammert et al., al., 2017). On the system other hand, different methods exist that describe the dynamic behavior of ADNs Finally, the conclusions are drawn in Section 5. methods exist that describe the dynamic behavior of ADNs model and its functions. Section 4 shows the case ies (Lammert etdisturbances al., 2017).the On(Maqbool the other hand, different Finally, the conclusions are drawn in Section 5. studies. methods exist that describe dynamic behavior of ADNs studying small et al., 2016) or studying exist small disturbances (Maqbool et al., 2016) or the conclusions are drawn in Section 5. External methods describe the (Maqbool dynamic of ADNs studying smallthat disturbances et al., Neverthe2016) or Finally, large disturbances (Chaspierre et al., behavior 2017). NORMAL External system large disturbances (Chaspierre et al., 2017). NevertheNORMAL External External studying small disturbances (Maqbool et al., 2016) or system large disturbances less, for power system restorationetstudies IBG Nevertheis usually NORMAL (Chaspierre al., 2017). NORMAL system External system less, for power system restoration studies IBG is usually large for disturbances (Chaspierre etstudies al., 2017). NevertheNORMAL less, power restoration IBG is usually neglected, whichsystem is shown by a comprehensive review given system HV RESTORATION neglected, which is shown by a comprehensive review given HV less,(IEEE, for power system restoration studies is usually neglected, which isFurthermore, shown by a comprehensive given HV in 2014). recent workIBG onreview restoration RESTORATION HV Step-down RESTORATION in (IEEE, 2014). Furthermore, recent work on restoration RESTORATION neglected, which is shown by a comprehensive review given in (IEEE, in 2014). Furthermore, recent on restoration Step-down HV dynamics Germany is focused on work gas turbines (Ertransformer RESTORATION Step-down dynamics in Germany is on gas (ErStep-down transformer in (IEEE, 2014). Furthermore, recent work on(Weber restoration ALERT dynamics Germany is focused focused on plants gas turbines turbines (Erlich et al., in 2012) or pumped-storage and transformer Step-down transformer ALERT lich et al., 2012) or pumped-storage plants (Weber and dynamics in2012) Germany isnot focused on plants gas turbines (ErALERT lich et al., pumped-storage (Weber and transformerMV Kr¨ uger, 2008) andordoes consider ADNs. These facts ALERT MV Kr¨ 2008) and not consider ADNs. These ALERT MV lichu et motivate al., 2012) ordoes pumped-storage (Weber and MV Kr¨ uger, ger, 2008) and does not consider ADNs. These facts facts highly the work reported in plants this paper. EMERGENCY highly motivate the work reported in this paper. MV IBG EMERGENCY Kr¨ u ger, 2008) and does not consider ADNs. These facts highly motivate the work reported in this paper. IBG EMERGENCY EMERGENCY The new contribution of this paper isinathis detailed model that IBG highly motivate the work reported paper. IBG The new of this model that EMERGENCY Inverter based The new contribution contribution of behavior this paper paperofis is a aandetailed detailed modelADN that describes the dynamic aggregated IBGbased Load BLACKOUT Inverter generation Load describes the dynamic behavior of an aggregated ADN Inverter based BLACKOUT Inverter based The new contribution of this paper is a detailed model that generation describes thepower dynamic behavior of anstudies. aggregated ADN suitable for system restoration In particLoad BLACKOUT Load BLACKOUT generation Active distribution network generation Inverter based suitable for power system restoration studies. In particdescribes thepower dynamic behavior oftheanaggregation aggregated ADN Active distributionLoad network BLACKOUT suitable system restoration studies. In of particular, the for ADN model incorporates load generation Active distribution (a) (b) Active distribution network network ular, the ADN model incorporates the aggregation of load suitable for power system restoration studies. In partic(a) (b) ular, the ADN model incorporates the aggregation of load Active distribution network The work was supported by the German Federal Ministry for (a) (b) (a) (b) ular, the ADN model incorporates the aggregation of load The work was supported by the German Federal Ministry for Fig. 1. (a) Power (a) system states (ENTSO-E, (b) 2015). Economic Affairs Energybywithin the framework the project The work was and supported the German FederalofMinistry for Fig. 1. (a) Power system states (ENTSO-E, 2015). Economic Affairs and Energy within the framework of the project Fig. (b) 1. (a) Power system states 2015). Aggregated model of the(ENTSO-E, ADN. Netz:Kraft (FKZ: 0325776J). The work was and supported the German FederalofMinistry for Economic Affairs Energybywithin the framework the project Aggregated model of ADN. Netz:Kraft (FKZ: 0325776J). Fig. (b) 1. (a) Power system states 2015). (b) Aggregated model of the the(ENTSO-E, ADN. Economic Affairs Energy within the framework of the project Netz:Kraft (FKZ: and 0325776J). (b) Aggregated model of the ADN. Netz:Kraft (FKZ: 0325776J). 2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
Copyright © 2018 IFAC 558 Copyright 2018 responsibility IFAC 558Control. Peer review©under of International Federation of Automatic Copyright © 2018 IFAC 558 10.1016/j.ifacol.2018.11.762 Copyright © 2018 IFAC 558
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2. LOAD MODEL
559
P0 Time series
Load model
Q0
2.1 Overview
P
Eqs. (1)–(5) V Measurements f
2.2 Time series of consumption
50.0
If available, time series data of the consumption can be provided to the load model using the input signals for active and reactive power, P0 and Q0 , respectively. As for some power system restoration studies the time scale of interest is several minutes or even hours, the consideration of time series data is important. A representative example using time series data for the consumption is shown in Fig. 3 from t = 0 s to t = 500 s (interval 1).
The voltage and frequency dependencies of the aggregated load are considered in the exponential load model according to (Van Cutsem and Vournas, 2008): α V · (1 + kpf · ∆f ) (1) Pexp = P0 V0 β V · (1 + kqf · ∆f ) (2) Qexp = Q0 V0 where Pexp and Qexp are the active and reactive power, respectively, consumed by the load at the bus voltage V . P0 and Q0 are the active and reactive power, respectively, under the reference voltage V0 , also referred to as the initial operating conditions. The exponents α and β depend on the type of load. The parameters kpf and kqf describe the frequency dependency of the load. The parameter values for the voltage and frequency dependency are based on (Milanovi´c et al., 2013) and listed in Table 1. A typical example of load frequency dependency is shown in Fig. 3 from t = 500 s to t = 833 s (interval 2). 2.4 Under frequency load shedding For cases with a major frequency drop in the system, an automatic UFLS scheme is an effective measure to prevent a further frequency decrease and a system collapse (ENTSO-E, 2015). As large frequency deviations can occur during the restoration process, the UFLS scheme might be considered for investigations. An algorithm for the implementation of the UFLS scheme is shown in Fig. 4. In (ENTSO-E, 2015), 6 load shedding steps are defined, which can be seen in line 2 of the algorithm. Starting from load shedding step 6, the reduced load demand PUFLS is calculated in line 5, until n = 0 is reached. The parameter values for the UFLS scheme are based on (ENTSO-E, 2015) and listed in Table 1. An illustrative example of the UFLS scheme is shown in Fig. 3 from t = 833 s to t = 1133 s (interval 3). 559
f1
49.0
f6 48.0
fdisc
47.0
f
20.0 1
15.0 P [MW]
2.3 Voltage and frequency dependency
Grid Q
Fig. 2. Block diagram of the load model.
f [Hz]
The load represents the aggregate consumption of the underlaying grids. The block diagram of the load model is depicted in Fig. 2 and the inputs are time series (P0 , Q0 ) and measurement (V, f ) signals. The outputs are active and reactive power (P, Q) signals interfaced with the grid. Within the load model block various functions are implemented (see Sections 2.2–2.7).
& Figs. 4–5
2
3
4
10.0
1 2 3 4 5
5.0 0.0 0
500
1,000
1,500
P0 P
5
Time series f dependency UFLS Disconnection CLPU
2,000
2,500
3,000
t [s]
Fig. 3. Load behavior during frequency deviations. 2.5 Disconnection If the frequency further decreases and the UFLS scheme is not sufficient, the load is entirely disconnected from the network, which is usually done manually by the system operator. This disconnection function is implemented as: PLoad,disc = 0
(3)
where PLoad,disc is the active power demand of the load, which is set to zero when the frequency limit for the total load disconnection fdisc is reached. The disconnection settings for the aggregated load model consider the requirements for the UFLS scheme stated in (ENTSOE, 2015) and are listed in Table 1. For the illustration of the load disconnection behavior, an example is depicted in Fig. 3 from t = 1333 s to t = 1500 s (interval 4). 1: procedure Under frequency load shedding 2: n := 6 3: repeat 4: if f < fn then n 5: PUFLS := Pexp · 1 − P i=1 i 6: else 7: n := n − 1 8: endif 9: until n = 0 10: end procedure
Fig. 4. Algorithm for under frequency load shedding.
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Table 1. Parameters of load and inverter based generation model Model
Mode Voltage and frequency dependency
Load
Under frequency load shedding
Disconnection Cold load pick-up Over frequency active power reduction
Disconnection Inverter based generation Reconnection
Needs
Description
Symbol
Value
Unit
Active power voltage dependency Reactive power voltage dependency Active power frequency dependency Reactive power frequency dependency Load shedding step 1 Load shedding step 2 Load shedding step 3 Load shedding step 4 Load shedding step 5 Load shedding step 6 Disconnected load (of P0 ) step 1 Disconnected load (of P0 ) step 2 Disconnected load (of P0 ) step 3 Disconnected load (of P0 ) step 4 Disconnected load (of P0 ) step 5 Disconnected load (of P0 ) step 6 Total load disconnection Max. value due to cold load pick-up Time constant of cold load pick-up Load reconnection
α β kpf kqf f1 f2 f3 f4 f5 f6 P1 P2 P3 P4 P5 P6 fdisc a τ frec
0.62 0.96 1 1 49.0 48.8 48.6 48.4 48.2 48.1 5 10 10 10 10 5 47.5 1 900 47
[–] [–] [%/Hz] [%/Hz] [Hz] [Hz] [Hz] [Hz] [Hz] [Hz] [%] [%] [%] [%] [%] [%] [Hz] [–] [s] [Hz]
Gradient power reduction High frequency limit power reduction High frequency limit disconnection Low frequency limit disconnection High voltage limit disconnection Low voltage limit disconnection Gradient power reconnection High frequency limit reconnection Low frequency limit reconnection High voltage limit reconnection Low voltage limit reconnection Time duration reconnection
mred fred
40 50.2 51.5 47.5 1.1 0.8 10 50.05 47.5 1.1 0.85 60
[%/Hz] [Hz] [Hz] [Hz] [pu] [pu] [%/min] [Hz] [Hz] [pu] [pu] [s]
fmax,disc fmin,disc Vmax,disc Vmin,disc mrec fmax,rec fmin,rec Vmax,rec Vmin,rec ∆tmin,rec
to be adjusted with the under frequency load shedding scheme.
2.6 Cold load pick-up
2.7 Transition between modes
If the load has been de-energized for several hours or more, the inrush current upon re-energizing the load can be significantly higher than in normal operation, which is called CLPU. The increased CLPU demand is due to: i) the magnetizing inrush currents of the system transformers; ii) the starting transients from induction motors; and iii) the loss of load diversity of process and thermostatically controlled loads (Schneider et al., 2016). As this phenomenon might influence the reconnection behavior of distribution feeders, it should be considered for the restoration process. The most common method of addressing the CLPU is the use of a CLPU curve: PCLPU = Pexp · 1 + a · e−(t−t0 )/τ (4) QCLPU = Qexp · 1 + a · e−(t−t0 )/τ (5)
The different modes can be summarized in a state diagram as shown in Fig. 5 that consists of four states, i.e., Normal, UFLS, Disconnection and CLPU. To change from CLPU to Normal, PCLPU is approximately Pexp . For clarity reasons, only frequency requirements are depicted.
where PCLPU and QCLPU represent the active and reactive power consumption of the aggregated load during the CLPU event, and Pexp and Qexp are the active and reactive power values from the exponential load model (see Section 2.3), respectively. The parameters a and τ represent the peak value and time constant of the CLPU event, respectively, with t0 as the instant of reconnection. The parameter values for the CLPU are based on real measurement data from a German system operator and listed in Table 1. An example of the CLPU is shown in Fig. 3 from t = 1500 s to t = 3000 s (interval 5).
560
f < f1 f ≥ f1
UFLS P := PUFLS
f < fdisc
Normal P := Pexp
f < fdisc
Disconnection P := PLoad,disc f > frec
PCLPU ≈ Pexp
f < fdisc
CLPU P := PCLPU
Fig. 5. State diagram of the load model.
f < f1
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3. INVERTER BASED GENERATION MODEL Time series
3.1 Overview
Pm V
Measurements f
Electrical control Eqs. (6)–(7) & Figs. 8–9
1 1+sTg
Inverter Iqcmd 1
Id Grid Iq
1+sTg
f 52.0 fmax,disc
51.5 51.0 50.5
fred
50.0
3.2 Time series of generation
1
2
3
4
10.0 8.0 P [MW]
Similar to the load model, time series data for the generation can be considered for the IBG model using the input signal for the available active power Pm . As the primary energy source of PV or wind generation varies, sudden changes of active power output might interfere with the restoration process. Therefore, if time series data of generation is available, it should be considered for power system restoration studies. An example using time series data for the generation is illustrated in Fig. 7 from t = 0 s to t = 500 s (interval 1).
Idcmd
Fig. 6. Block diagram of the IBG model.
f [Hz]
The IBG represents an aggregated generation including the underlaying grids. The IBG model is based on the small-scale (distribution-connected) Western Electricity Coordinating Council (WECC) model for PV systems (WECC, 2012) and is extended with additional functions required for the restoration process. The block diagram of the IBG model is shown in Fig. 6 and the inputs of the electrical control block are time series (Pm ) and measurement (V, f ) signals. The outputs are current command (Idcmd , Iqcmd ) signals. From the inverter block the current (Id , Iq ) signals are interfaced with the grid. Within the electrical control block various control modes are included (see Sections 3.2–3.6).
561
6.0 1 Time series
4.0
2 Reduction 2.0
Pm P
3 Disconnection
0.0
4 Reconnection 0
500
1,000
1,500
2,000
t [s]
3.3 Over frequency active power reduction
Fig. 7. IBG behavior during frequency deviations.
Over frequency active power reduction (also known as P (f ) control) is required for IBG in order to counteract over frequencies in the system. The reduced active power output Pred of the IBG model is defined as: Pred (f ) = Pfreeze · (1 − mred · (f − fred )) (6) where Pfreeze is the saved active power value when exceeding the frequency limit for power reduction fred . The parameter mred is the active power reduction gradient. The parameter values for the over frequency active power reduction are based on (VDE, 2011) and listed in Table 1. An example of P (f ) control of IBG is depicted in Fig. 7 from t = 555 s to t = 875 s (interval 2).
3.5 Reconnection
3.4 Disconnection If frequency or voltage limits are violated, the IBG disconnects from the grid due to tripping of the protection system (delay times are neglected). The disconnection behavior of the IBG model is defined as: PIBG,disc = 0 (7) where PIBG,disc denotes the active power output of the IBG model, which is set to zero when limits are exceeded. The parameter values for the voltage and frequency disconnection settings of IBG are based on (VDE, 2011) and listed in Table 1. For the illustration of the IBG disconnection behavior, an example is depicted in Fig. 7 from t = 875 s to t = 1060 s (interval 3). 561
The reconnection behavior of IBG is seen in the algorithm of Fig. 8. Before IBG is allowed to reconnect, grid frequency f has to be within defined limits (normal operating range) for a duration of ∆tmin,rec seconds, as seen in line 2 of the algorithm. When the reconnection condition is fulfilled, two different methods can be distinguished that are usually used for the reconnection behavior (VDE, 2011): i) immediate reconnection with full available power Pm (step) as seen in line 4; or ii) slow linear increase of power starting at time instant trec until available power Pm is reached (ramp) as seen in line 6. For clarity reasons, only frequency reconnection requirements are illustrated in the algorithm of Fig. 8. The parameter values for the ramp reconnection behavior of IBG are based on (VDE, 2011) and listed in Table 1. An example is shown in Fig. 7 from t = 1060 s to t = 1660 s (interval 4). 1: procedure Reconnection 2: if fmin,rec < f (t) < fmax,rec for ∆tmin,rec then 3: if step then 4: Prec (t) := Pm (t) 5: else ramp 6: Prec (t) := Pm (t) · mrec · (t − trec ) 7: until Prec (t) = Pm (t) 8: else 9: Prec (t) := Pdisc 10: end procedure
Fig. 8. Algorithm for the reconnection of IBG.
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4. CASE STUDIES
3.6 Transition between modes The different IBG control modes can be summarized in a state diagram as seen in Fig. 9 that consists of the states Normal, Reduction, Disconnection and Reconnection. For clarity reasons, only frequency requirements are depicted in the diagram. If, for instance, an over frequency event occurs during the reconnection process, the state is changed from Reconnection to Reduction. The transition between these two states is illustrated in detail in Fig. 10. As soon as the frequency falls below the threshold fred at t = 1436 s, the reconnection process is continued until Prec = Pm and the Normal state is reached. fred ≤ f ≤ fmax,disc
Reduction P := Pred
f < fred
fred ≤ f ≤ fmax,disc f < fred
fmax,disc < f
fmax,disc < f Disconnection f > f P := PIBG,disc
Normal P := Pm
4.1 Overview The reported ADN model has been used in various power system restoration studies that are presented briefly in Sections 4.2–4.5. An overview of the studies and the used functions of the load and IBG model is given in Table 2. 4.2 Case 1 In this study the ADN model is investigated on a simple test system as shown in Fig. 1 (b). The dynamic behavior of the combination of load and IBG was analyzed under a given frequency deviation, as seen in Fig. 11. From t = 0 s to t = 1000 s, the frequency dependency of the load and the over frequency active power reduction of the IBG lead to a significant change in the residual load seen by the system operator. At t = 1000 s the UFLS starts acting until half of the load is disconnected. At this time, the generation is higher than the consumption, which results in a slightly negative residual load. After reconnecting the ADN at t = 1500 s, the residual load is dominated by the CLPU phenomenon and the reconnection ramp of IBG.
min,disc
Table 2. Case studies
fmin,rec < f < fmax,rec for ∆tmin,rec
Prec = Pm
fmax,disc < f
Model
Mode
Load
Voltage and frequency dependency Under frequency load shedding Disconnection Cold load pick-up
IBG
Over frequency active power reduction Disconnection Reconnection
fmin,disc > f
Reconnection P := Prec
Fig. 9. State diagram of the IBG model. f 52.0 fmax,disc f [Hz]
f [Hz]
51.5 51.0 50.5
fred
50.0
1
2
3
2
10.0 P [MW]
P [MW]
8.0 6.0 4.0 1 Disconnection 2.0
Pm P
2 Reconnection
0.0
3 Reduction 0
500
1,000
1,500
2,000
t [s]
Case 2 3
4
1
f
51.0 50.5 50.0 49.5 49.0 48.5 48.0 47.5 47.0
fred f1 f6 fdisc and fmin,disc
2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
PLoad PIBG Presidual
0
500
load
1,000
1,500
2,000
2,500
3,000
t [s]
Fig. 10. Over frequency active power reduction during reconnection of IBG. 562
Fig. 11. Load and IBG behavior during frequency deviations.
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4.3 Case 2
563
REFERENCES
In this study the ADN model was used to analyze the impact of over frequency active power reduction of IBG on power system restoration and the details can be found in (Hachmann et al., 2017). The P (f ) control is particularly relevant for the operation of small islands within the distribution system. The results of this study reveal that using the full potential of IBG active power reduction, leads to improved frequency dynamics in small island grids without any impact on the overall system behavior in normal operation. 4.4 Case 3 In this study the ADN model was used to examine black start and island operation of a real distribution grid with significant penetration of renewable resources and the details can be found in (Lafferte et al., 2017). The results of this study show that it is technical feasible to re-energize distribution grids using diesel generators and biogas plants in combination with distributed PV systems in order to support the bottom-up power system restoration process. 4.5 Case 4 In this study the ADN model was used to investigate the impact of IBG and load reconnection on the restoration process within a real distribution system and the details can be found in (Hachmann et al., 2018). Furthermore, IBG is used to control the active power balance and increase the reconnected load within the distribution system without the requirement of additional power from the transmission system. The results of this study give a realistic example on how IBG can accelerate load restoration. 5. CONCLUSIONS This paper presents a detailed model of an aggregated ADN that is adequate for power system restoration studies in the time scale of tens of seconds up to several minutes. The model was developed with the focus on frequency dynamics and control. It includes a combination of aggregated load and IBG. The load model involves: i) time series data for consumption; ii) voltage and frequency dependency (i.e. exponential load model); iii) UFLS; iv) disconnection behavior; and v) CLPU. On the other hand, the aggregated IBG model considers: i) time series data for generation; ii) over frequency active power reduction; iii) disconnection; and iv) reconnection behavior. The ADN model was successfully applied in several case studies with real grid data and shows adequate dynamic behavior. Moreover, the studies reveal that the consideration of ADNs can support the power system restoration process. Finally, the developed ADN model helps system operators to incorporate IBG into their restoration schemes. Future work will also consider the frequency sensitive mode of IBG (i.e. providing primary frequency response). Furthermore, additional voltage control functions of IBG, such as fault ride-through and dynamic voltage support and quasi-stationary voltage control by means of reactive power (i.e. Q(V ) control), are of interest. 563
Chaspierre, G., Panciatici, P., and Van Cutsem, T. (2017). Dynamic Equivalent of a Distribution Grid Hosting Dispersed Photovoltaic Units. In IREP’ 17 Symposium. Espinho, Portugal. ENTSO-E (2015). Policy 5: Emergency Operations. V 3.0. Erlich, I., Demmig, S., Shewarega, F. (2012). Restoration Issues in Large Metropolitan Power Systems: An Example in the Berlin Distribution Grid. In 2012 IEEE Power and Energy Society General Meeting. San Diego, USA. Hachmann, C., Lammert, G., Lafferte, D., and Braun, M. (2017). Power System Restoration and Operation of Island Grids with Frequency Dependent Active Power Control of Distributed Generation. In NEIS Conference. Hamburg, Germany. Hachmann, C., Valov, M., Lammert, G., Heckmann, W., and Braun, M. (2018). Unterst¨ utzung des Netzwiederaufbaus durch Ausregelung der dezentralen Erzeugung im Verteilnetz. In Konferenz Zuk¨ unftige Stromnetze f¨ ur erneuerbare Energien. Berlin, Germany. IEEE Restoration Dynamics Task Force (2014). Power System Restoration Dynamics (Issues, Techniques, Planning, Training & Special Considerations). Technical Paper Compendium. PES-TPC2. Lafferte, D., Klingmann, A., Fetzer, D., Lammert, G., Hachmann, C., Paschedag, T., and Braun, M. (2017). Black Start and Island Operation of Distribution Grids with Significant Penetration of Renewable Resources. In 1st International Conference on Large-Scale Grid Integration of Renewable Energy. New-Delhi, India. Lammert, G., Yamashita, K., Pab´on Ospina, L. D., Renner, H., Mart´ınez Villanueva, S., Pourbeik, P., Ciausiu, F.-E., and Braun, M. (2017). International Industry Practice on Modelling and Dynamic Performance of Inverter Based Generation in Power System Studies. CIGRE Science & Engineering, 8, 25–37. Maqbool, I., Lammert, G., Ishchenko, A., and Braun, M. (2016). Power System Model Reduction with GridConnected Photovoltaic Systems Based on Hankel Norm Approximation. In 6th Solar Integration Workshop. Vienna, Austria. Milanovi´c, J. V., Yamashita, K., Mart´ınez Villanueva, S., ˇ and Korunovi´c, L. M. (2013). International Djoki´c, S. Z., Industry Practice on Power System Load Modeling. IEEE Trans. on Power Systems, 28(3), 3038–3046. Schneider, K. P., Sortomme, E., Venkata, S. S., Miller, M. T., and Ponder, L. (2016). Evaluating the Magnitude and Duration of Cold Load Pick-Up on Residential Distribution Feeders Using Multi-State Load Models. IEEE Trans. on Power Systems, 31(5), 3765–3774. Van Cutsem, T., and Vournas, C. (2008). Voltage Stability of Electric Power Systems. Springer. VDE-AR-N 4105 (2011). Generators Connected to the Low-Voltage Distribution Network – Technical Requirements for the Connection to and Parallel Operation with Low-Voltage Distribution Networks. Weber, H., and Kr¨ uger, M. (2008). Dynamic Investigation of Network Restoration by the Pumped-Storage Plant Markersbach in Germany. In 17th IFAC World Congress. Seoul, Korea. Western Electricity Coordinating Council (WECC) Renewable Energy Modeling Task Force (2012). WECC Solar PV Dynamic Model Specification.
ScienceDirect
IFAC PapersOnLine 51-28 (2018) 558–563
Modelling of Active Distribution Networks Modelling of Active Distribution Networks Modelling of Active Distribution Networks for Power System Restoration Studies Modelling of Active Distribution Networks for Power System Restoration Studies for Power System Restoration Studies for Power System Restoration Studies Gustav Lammert ∗∗ Alexander Klingmann ∗∗
Gustav Lammert Klingmann ∗ ∗ ∗ ∗ ∗∗ ∗ Alexander ∗ Lammert Alexander Christian Hachmann ıo LafferteKlingmann Gustav ∗ Dar´ ∗ Holger Becker ∗∗ ∗ ∗ Christian Hachmann Dar´ ıo Lafferte Becker ∗ ∗ ∗∗ ∗ ∗∗ ∗,∗∗ ∗ Dar´ ∗ Holger ∗∗ Gustav Lammert Alexander Klingmann Christian Hachmann ıo Lafferte Holger Becker Tina Paschedag Wolfram Heckmann Martin Braun ∗ ∗∗ ∗,∗∗ ∗ ∗ ∗∗ Tina Paschedag Wolfram Heckmann Martin Braun ∗ ∗∗ ∗ Wolfram ∗,∗∗ Christian Hachmann Dar´ ıo Lafferte∗∗ Holger Tina Paschedag Heckmann Martin Becker Braun ∗,∗∗ ∗ ∗∗ ∗ Tina Paschedag Wolfram Heckmann Martin Braun ∗,∗∗ University of Kassel, Kassel, Germany ∗ University of Kassel, Kassel, Germany ∗ ∗∗ ∗ University of Kassel, Kassel,Germany Germany Fraunhofer IEE, Kassel, ∗ ∗∗ IEE, ∗∗ ∗∗ Fraunhofer University of Kassel, Kassel,Germany Germany Fraunhofer IEE, Kassel, Kassel, Germany E-Mail: [email protected] ∗∗ E-Mail: [email protected] Fraunhofer IEE, Kassel, Germany E-Mail: [email protected] E-Mail: [email protected] Abstract: This paper presents an aggregated model of Active Distribution Networks (ADNs) Abstract: This paper presents an model of Distribution Networks (ADNs) Abstract: This paper system presentsrestoration an aggregated aggregated model of Active Active Distribution Networks (ADNs) appropriate for power studies. The ADN considers aggregated loads and appropriate for power system restoration studies. The ADN considers aggregated loads and Abstract: This paper system presents an aggregated model of Active Distribution Networks (ADNs) appropriate forgeneration, power restoration studies. The ADN considers aggregated loads and inverter based such as wind and photovoltaic generation. The load model incorinverter based generation, suchrestoration as wind and photovoltaic generation. The load model incorappropriate forgeneration, power system studies. The ADN considersThe aggregated loads and inverter based such as wind and photovoltaic load model incorporates: i) time series data for consumption; ii) voltage andgeneration. frequency dependency; iii) under dependency; iii) under porates: i) time series data for consumption; ii) voltage and frequency inverter based generation, such as wind and photovoltaic generation. The load model incorporates: i)load timeshedding; series data consumption; ii) voltage frequency dependency; iii) under frequency iv)for disconnection behavior; andand v) cold load pick-up. The generation frequency iv) disconnection behavior; and v) cold load The porates:considers: i)load timeshedding; series data consumption; ii) voltage and frequency dependency; iii) under frequency load shedding; iv)for disconnection behavior; and v) frequency cold load pick-up. pick-up. The generation generation model i) time series data for generation; ii) over active power reduction; model considers: i) time series data generation; ii) over frequency active power reduction; frequency load shedding; iv) disconnection behavior; and v) model cold load pick-up. Thephenomena generation model considers: i)and time data for for behavior. generation; ii) over frequency active power reduction; iii) disconnection; iv)series reconnection The ADN covers dynamic iii) disconnection; iv) reconnection behavior. The model covers dynamic model considers: i)and time data generation; ii)ADN over frequency active powerphenomena reduction; iii)the disconnection; and iv) reconnection The ADN covers phenomena in time scale of tens ofseries seconds upfor tobehavior. several minutes withmodel the focus on dynamic frequency dynamics. in the time scale of tens of seconds up to several minutes with the focus on frequency dynamics. iii) disconnection; and iv) reconnection behavior. The ADN model covers dynamic phenomena in the time scale of tens of seconds up to several minutes with the focus on frequency Moreover, the model was tested in several case studies and shows adequate dynamic dynamics. behavior. Moreover, model was in several case shows adequate dynamic behavior. in the timethe scale of tens seconds to several minutesand with the focus on frequency Moreover, the model wasoftested tested in up several case studies studies and shows adequate dynamic dynamics. behavior. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Moreover, the model was tested in several case studies and shows adequate dynamic behavior. Keywords: Under frequency load shedding, blackout, cold load pick-up, black start, island Keywords: Under frequency load shedding, blackout, cold load pick-up, black start, island Keywords: Under frequency shedding, blackout, cold load pick-up, black start, island operation, frequency control,load dynamic equivalent, aggregation, inverter based generation. operation, frequency control,load dynamic equivalent, aggregation, inverter based based generation. Keywords: frequency Under frequency shedding, blackout, cold load pick-up, black start, island operation, control, dynamic equivalent, aggregation, inverter generation. operation, frequency control, dynamic equivalent, aggregation, inverter based generation. 1. INTRODUCTION and IBG, as depicted in Fig. 1 (b). The aggregated load 1. and IBG, as in 1 (b). aggregated 1. INTRODUCTION INTRODUCTION and IBG, as depicted depicted in Fig. Fig. (b). The The aggregated load load model considers: i) time series1 data for consumption; ii) model considers: i) time series data for consumption; ii) INTRODUCTION and IBG, as frequency depicted in Fig. (b). iii) The aggregated load considers: i) time series1 data for Under consumption; ii) voltage and dependency; Frequency Recognizing that 1.power system blackouts are likely to model voltage and frequency dependency; iii) Under Frequency Recognizing that power system blackouts are likely to modelShedding considers: i) time series data iii) for Under consumption; ii) and frequency dependency; Frequency Load (UFLS); iv) disconnection behavior; and Recognizing that power system blackouts measures are likelythat to voltage occur, it is prudent to consider the necessary Shedding (UFLS);dependency; iv) disconnection behavior; and v) v) occur, it is prudent to consider the necessary measures that voltage andPick-Up frequency iii) Under Frequency Recognizing that power system blackouts (IEEE, are likely to Load Load (UFLS); iv) disconnection behavior; and v) Cold Shedding Load (CLPU). The aggregated IBG model occur, ittheir is prudent tointensity consider the duration necessary measures that reduce extent, and 2014). Cold Load Pick-Up (CLPU). The aggregated IBG model reduce their extent, intensity and duration (IEEE, 2014). Shedding (UFLS); iv) disconnection behavior; and v) occur, is prudent consider the necessary measures that Load Cold Loadi) Pick-Up (CLPU). Thegeneration; aggregated IBG model involves: time series data for ii) over frereduce extent,tointensity and duration (IEEE, 2014). One ofittheir the promising measures is the utilization of Active of Active i) time series data generation; ii) over freOne of the measures is the utilization Cold Load (CLPU). The aggregated IBG model reduce extent, intensity and duration (IEEE, 2014). involves: involves: i) Pick-Up time series data for for ii) over frequency active power reduction; iii)generation; disconnection; and iv) One of their the promising promising measures is utilization of Active Distribution Networks (ADNs) to the support the restoration quency power reduction; disconnection; and iv) Distribution Networks (ADNs) to support the restoration involves:active i) time series data foriii) ii) over One of the promising measures is utilization of Active quency active power reduction; iii)generation; disconnection; and freiv) reconnection behavior. The model is for Distribution Networks (ADNs) to the support the blackout restoration process, the system from or behavior. The ADN ADN model is adequate adequate for process, bringing bringing the power power system from the the blackout or reconnection quency active power reduction; iii) disconnection; and iv) Distribution Networks (ADNs) to support the restoration Thestudies ADN model is adequate for power systembehavior. restoration considering long-term process, bringing the power theasblackout emergency state back to thesystem normalfrom state, shown or in reconnection power system restoration studies considering long-term emergency state back to the normal state, as shown in reconnection behavior. The ADN model is adequate for process, bringing the power system from the blackout or power system restoration studies considering long-term emergency state back to host the normal shown in dynamics in the time scale of tens of seconds up to several Fig. 1 (a). These ADNs Inverter state, BasedasGeneration in time scale of tens seconds to Fig. 1 These ADNs Inverter Based power system restoration studies long-term emergency state and back to host the normal state, asGeneration shown in dynamics dynamics in the the time of tens of ofconsidering seconds up upThe to several several minutes with the focusscale on frequency dynamics. model Fig. 1 (a). (a). These ADNs host Inverter Based Generation (IBG), i.e., wind PhotoVoltaic (PV) generation. Howminutes with the focus on frequency dynamics. The model (IBG), i.e., wind and PhotoVoltaic (PV) generation. Howdynamics in the scale of tens of seconds upThe to several Fig. 1the (a). Theseand ADNs host Inverter Based Generation thetime focusgrid on forming frequency dynamics. model does notwith incorporate capabilities. (IBG), i.e., wind PhotoVoltaic (PV) generation. How- minutes ever, incorporation of IBG into the restoration process ever, the incorporation of IBG into (PV) the restoration process does not incorporate grid forming capabilities. minutes with the focus on frequency dynamics. The model (IBG), i.e., wind and PhotoVoltaic generation. However, the incorporation of operators. IBG into the restoration process does not incorporate grid forming capabilities. is challenging for system The remainder of thegrid paper is organized as follows. Secis challenging for system operators. does not incorporate forming capabilities. ever, the incorporation of IBG into the restoration process is challenging for system operators. The remainder of paper is as follows. SecThe of the thethe paper is organized organized as of follows. Section 2remainder duly discusses dynamic behavior the aggreIn practice, negative model is systemload operators. In challenging practice, aa for negative load model is is still still used used by by system system tion 2 duly discusses the dynamic behavior of the aggreThe remainder of the paper is organized as follows. Secdulymodel. discusses the dynamic behavior of the aggregated2 load Section 3 presents the aggregated IBG In practice, negativeIBG loadinmodel still used by system operators to arepresent powerissystem stability stud- tion gated load model. Section 33 presents the aggregated IBG operators to represent IBG in power system stability studtion 2 duly discusses the dynamic behavior of the aggreIn practice, a negative load model is still used by system gated load model. Section presents the aggregated IBG operators to represent IBG inOn power stability stud- model and its functions. Section 4 shows the case studies. ies (Lammert et al., 2017). the system other hand, different and its functions. Section 44 shows case studies. ies (Lammert et 2017). On the other hand, different gated load model. Section 3drawn presents the the aggregated IBG operators to represent IBG in power stability stud- model model and its functions. Section shows the case studies. Finally, the conclusions are in Section 5. ies (Lammert et al., al., 2017). On the system other hand, different methods exist that describe the dynamic behavior of ADNs Finally, the conclusions are drawn in Section 5. methods exist that describe the dynamic behavior of ADNs model and its functions. Section 4 shows the case ies (Lammert etdisturbances al., 2017).the On(Maqbool the other hand, different Finally, the conclusions are drawn in Section 5. studies. methods exist that describe dynamic behavior of ADNs studying small et al., 2016) or studying exist small disturbances (Maqbool et al., 2016) or the conclusions are drawn in Section 5. External methods describe the (Maqbool dynamic of ADNs studying smallthat disturbances et al., Neverthe2016) or Finally, large disturbances (Chaspierre et al., behavior 2017). NORMAL External system large disturbances (Chaspierre et al., 2017). NevertheNORMAL External External studying small disturbances (Maqbool et al., 2016) or system large disturbances less, for power system restorationetstudies IBG Nevertheis usually NORMAL (Chaspierre al., 2017). NORMAL system External system less, for power system restoration studies IBG is usually large for disturbances (Chaspierre etstudies al., 2017). NevertheNORMAL less, power restoration IBG is usually neglected, whichsystem is shown by a comprehensive review given system HV RESTORATION neglected, which is shown by a comprehensive review given HV less,(IEEE, for power system restoration studies is usually neglected, which isFurthermore, shown by a comprehensive given HV in 2014). recent workIBG onreview restoration RESTORATION HV Step-down RESTORATION in (IEEE, 2014). Furthermore, recent work on restoration RESTORATION neglected, which is shown by a comprehensive review given in (IEEE, in 2014). Furthermore, recent on restoration Step-down HV dynamics Germany is focused on work gas turbines (Ertransformer RESTORATION Step-down dynamics in Germany is on gas (ErStep-down transformer in (IEEE, 2014). Furthermore, recent work on(Weber restoration ALERT dynamics Germany is focused focused on plants gas turbines turbines (Erlich et al., in 2012) or pumped-storage and transformer Step-down transformer ALERT lich et al., 2012) or pumped-storage plants (Weber and dynamics in2012) Germany isnot focused on plants gas turbines (ErALERT lich et al., pumped-storage (Weber and transformerMV Kr¨ uger, 2008) andordoes consider ADNs. These facts ALERT MV Kr¨ 2008) and not consider ADNs. These ALERT MV lichu et motivate al., 2012) ordoes pumped-storage (Weber and MV Kr¨ uger, ger, 2008) and does not consider ADNs. These facts facts highly the work reported in plants this paper. EMERGENCY highly motivate the work reported in this paper. MV IBG EMERGENCY Kr¨ u ger, 2008) and does not consider ADNs. These facts highly motivate the work reported in this paper. IBG EMERGENCY EMERGENCY The new contribution of this paper isinathis detailed model that IBG highly motivate the work reported paper. IBG The new of this model that EMERGENCY Inverter based The new contribution contribution of behavior this paper paperofis is a aandetailed detailed modelADN that describes the dynamic aggregated IBGbased Load BLACKOUT Inverter generation Load describes the dynamic behavior of an aggregated ADN Inverter based BLACKOUT Inverter based The new contribution of this paper is a detailed model that generation describes thepower dynamic behavior of anstudies. aggregated ADN suitable for system restoration In particLoad BLACKOUT Load BLACKOUT generation Active distribution network generation Inverter based suitable for power system restoration studies. In particdescribes thepower dynamic behavior oftheanaggregation aggregated ADN Active distributionLoad network BLACKOUT suitable system restoration studies. In of particular, the for ADN model incorporates load generation Active distribution (a) (b) Active distribution network network ular, the ADN model incorporates the aggregation of load suitable for power system restoration studies. In partic(a) (b) ular, the ADN model incorporates the aggregation of load Active distribution network The work was supported by the German Federal Ministry for (a) (b) (a) (b) ular, the ADN model incorporates the aggregation of load The work was supported by the German Federal Ministry for Fig. 1. (a) Power (a) system states (ENTSO-E, (b) 2015). Economic Affairs Energybywithin the framework the project The work was and supported the German FederalofMinistry for Fig. 1. (a) Power system states (ENTSO-E, 2015). Economic Affairs and Energy within the framework of the project Fig. (b) 1. (a) Power system states 2015). Aggregated model of the(ENTSO-E, ADN. Netz:Kraft (FKZ: 0325776J). The work was and supported the German FederalofMinistry for Economic Affairs Energybywithin the framework the project Aggregated model of ADN. Netz:Kraft (FKZ: 0325776J). Fig. (b) 1. (a) Power system states 2015). (b) Aggregated model of the the(ENTSO-E, ADN. Economic Affairs Energy within the framework of the project Netz:Kraft (FKZ: and 0325776J). (b) Aggregated model of the ADN. Netz:Kraft (FKZ: 0325776J). 2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
Copyright © 2018 IFAC 558 Copyright 2018 responsibility IFAC 558Control. Peer review©under of International Federation of Automatic Copyright © 2018 IFAC 558 10.1016/j.ifacol.2018.11.762 Copyright © 2018 IFAC 558
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2. LOAD MODEL
559
P0 Time series
Load model
Q0
2.1 Overview
P
Eqs. (1)–(5) V Measurements f
2.2 Time series of consumption
50.0
If available, time series data of the consumption can be provided to the load model using the input signals for active and reactive power, P0 and Q0 , respectively. As for some power system restoration studies the time scale of interest is several minutes or even hours, the consideration of time series data is important. A representative example using time series data for the consumption is shown in Fig. 3 from t = 0 s to t = 500 s (interval 1).
The voltage and frequency dependencies of the aggregated load are considered in the exponential load model according to (Van Cutsem and Vournas, 2008): α V · (1 + kpf · ∆f ) (1) Pexp = P0 V0 β V · (1 + kqf · ∆f ) (2) Qexp = Q0 V0 where Pexp and Qexp are the active and reactive power, respectively, consumed by the load at the bus voltage V . P0 and Q0 are the active and reactive power, respectively, under the reference voltage V0 , also referred to as the initial operating conditions. The exponents α and β depend on the type of load. The parameters kpf and kqf describe the frequency dependency of the load. The parameter values for the voltage and frequency dependency are based on (Milanovi´c et al., 2013) and listed in Table 1. A typical example of load frequency dependency is shown in Fig. 3 from t = 500 s to t = 833 s (interval 2). 2.4 Under frequency load shedding For cases with a major frequency drop in the system, an automatic UFLS scheme is an effective measure to prevent a further frequency decrease and a system collapse (ENTSO-E, 2015). As large frequency deviations can occur during the restoration process, the UFLS scheme might be considered for investigations. An algorithm for the implementation of the UFLS scheme is shown in Fig. 4. In (ENTSO-E, 2015), 6 load shedding steps are defined, which can be seen in line 2 of the algorithm. Starting from load shedding step 6, the reduced load demand PUFLS is calculated in line 5, until n = 0 is reached. The parameter values for the UFLS scheme are based on (ENTSO-E, 2015) and listed in Table 1. An illustrative example of the UFLS scheme is shown in Fig. 3 from t = 833 s to t = 1133 s (interval 3). 559
f1
49.0
f6 48.0
fdisc
47.0
f
20.0 1
15.0 P [MW]
2.3 Voltage and frequency dependency
Grid Q
Fig. 2. Block diagram of the load model.
f [Hz]
The load represents the aggregate consumption of the underlaying grids. The block diagram of the load model is depicted in Fig. 2 and the inputs are time series (P0 , Q0 ) and measurement (V, f ) signals. The outputs are active and reactive power (P, Q) signals interfaced with the grid. Within the load model block various functions are implemented (see Sections 2.2–2.7).
& Figs. 4–5
2
3
4
10.0
1 2 3 4 5
5.0 0.0 0
500
1,000
1,500
P0 P
5
Time series f dependency UFLS Disconnection CLPU
2,000
2,500
3,000
t [s]
Fig. 3. Load behavior during frequency deviations. 2.5 Disconnection If the frequency further decreases and the UFLS scheme is not sufficient, the load is entirely disconnected from the network, which is usually done manually by the system operator. This disconnection function is implemented as: PLoad,disc = 0
(3)
where PLoad,disc is the active power demand of the load, which is set to zero when the frequency limit for the total load disconnection fdisc is reached. The disconnection settings for the aggregated load model consider the requirements for the UFLS scheme stated in (ENTSOE, 2015) and are listed in Table 1. For the illustration of the load disconnection behavior, an example is depicted in Fig. 3 from t = 1333 s to t = 1500 s (interval 4). 1: procedure Under frequency load shedding 2: n := 6 3: repeat 4: if f < fn then n 5: PUFLS := Pexp · 1 − P i=1 i 6: else 7: n := n − 1 8: endif 9: until n = 0 10: end procedure
Fig. 4. Algorithm for under frequency load shedding.
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Table 1. Parameters of load and inverter based generation model Model
Mode Voltage and frequency dependency
Load
Under frequency load shedding
Disconnection Cold load pick-up Over frequency active power reduction
Disconnection Inverter based generation Reconnection
Needs
Description
Symbol
Value
Unit
Active power voltage dependency Reactive power voltage dependency Active power frequency dependency Reactive power frequency dependency Load shedding step 1 Load shedding step 2 Load shedding step 3 Load shedding step 4 Load shedding step 5 Load shedding step 6 Disconnected load (of P0 ) step 1 Disconnected load (of P0 ) step 2 Disconnected load (of P0 ) step 3 Disconnected load (of P0 ) step 4 Disconnected load (of P0 ) step 5 Disconnected load (of P0 ) step 6 Total load disconnection Max. value due to cold load pick-up Time constant of cold load pick-up Load reconnection
α β kpf kqf f1 f2 f3 f4 f5 f6 P1 P2 P3 P4 P5 P6 fdisc a τ frec
0.62 0.96 1 1 49.0 48.8 48.6 48.4 48.2 48.1 5 10 10 10 10 5 47.5 1 900 47
[–] [–] [%/Hz] [%/Hz] [Hz] [Hz] [Hz] [Hz] [Hz] [Hz] [%] [%] [%] [%] [%] [%] [Hz] [–] [s] [Hz]
Gradient power reduction High frequency limit power reduction High frequency limit disconnection Low frequency limit disconnection High voltage limit disconnection Low voltage limit disconnection Gradient power reconnection High frequency limit reconnection Low frequency limit reconnection High voltage limit reconnection Low voltage limit reconnection Time duration reconnection
mred fred
40 50.2 51.5 47.5 1.1 0.8 10 50.05 47.5 1.1 0.85 60
[%/Hz] [Hz] [Hz] [Hz] [pu] [pu] [%/min] [Hz] [Hz] [pu] [pu] [s]
fmax,disc fmin,disc Vmax,disc Vmin,disc mrec fmax,rec fmin,rec Vmax,rec Vmin,rec ∆tmin,rec
to be adjusted with the under frequency load shedding scheme.
2.6 Cold load pick-up
2.7 Transition between modes
If the load has been de-energized for several hours or more, the inrush current upon re-energizing the load can be significantly higher than in normal operation, which is called CLPU. The increased CLPU demand is due to: i) the magnetizing inrush currents of the system transformers; ii) the starting transients from induction motors; and iii) the loss of load diversity of process and thermostatically controlled loads (Schneider et al., 2016). As this phenomenon might influence the reconnection behavior of distribution feeders, it should be considered for the restoration process. The most common method of addressing the CLPU is the use of a CLPU curve: PCLPU = Pexp · 1 + a · e−(t−t0 )/τ (4) QCLPU = Qexp · 1 + a · e−(t−t0 )/τ (5)
The different modes can be summarized in a state diagram as shown in Fig. 5 that consists of four states, i.e., Normal, UFLS, Disconnection and CLPU. To change from CLPU to Normal, PCLPU is approximately Pexp . For clarity reasons, only frequency requirements are depicted.
where PCLPU and QCLPU represent the active and reactive power consumption of the aggregated load during the CLPU event, and Pexp and Qexp are the active and reactive power values from the exponential load model (see Section 2.3), respectively. The parameters a and τ represent the peak value and time constant of the CLPU event, respectively, with t0 as the instant of reconnection. The parameter values for the CLPU are based on real measurement data from a German system operator and listed in Table 1. An example of the CLPU is shown in Fig. 3 from t = 1500 s to t = 3000 s (interval 5).
560
f < f1 f ≥ f1
UFLS P := PUFLS
f < fdisc
Normal P := Pexp
f < fdisc
Disconnection P := PLoad,disc f > frec
PCLPU ≈ Pexp
f < fdisc
CLPU P := PCLPU
Fig. 5. State diagram of the load model.
f < f1
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3. INVERTER BASED GENERATION MODEL Time series
3.1 Overview
Pm V
Measurements f
Electrical control Eqs. (6)–(7) & Figs. 8–9
1 1+sTg
Inverter Iqcmd 1
Id Grid Iq
1+sTg
f 52.0 fmax,disc
51.5 51.0 50.5
fred
50.0
3.2 Time series of generation
1
2
3
4
10.0 8.0 P [MW]
Similar to the load model, time series data for the generation can be considered for the IBG model using the input signal for the available active power Pm . As the primary energy source of PV or wind generation varies, sudden changes of active power output might interfere with the restoration process. Therefore, if time series data of generation is available, it should be considered for power system restoration studies. An example using time series data for the generation is illustrated in Fig. 7 from t = 0 s to t = 500 s (interval 1).
Idcmd
Fig. 6. Block diagram of the IBG model.
f [Hz]
The IBG represents an aggregated generation including the underlaying grids. The IBG model is based on the small-scale (distribution-connected) Western Electricity Coordinating Council (WECC) model for PV systems (WECC, 2012) and is extended with additional functions required for the restoration process. The block diagram of the IBG model is shown in Fig. 6 and the inputs of the electrical control block are time series (Pm ) and measurement (V, f ) signals. The outputs are current command (Idcmd , Iqcmd ) signals. From the inverter block the current (Id , Iq ) signals are interfaced with the grid. Within the electrical control block various control modes are included (see Sections 3.2–3.6).
561
6.0 1 Time series
4.0
2 Reduction 2.0
Pm P
3 Disconnection
0.0
4 Reconnection 0
500
1,000
1,500
2,000
t [s]
3.3 Over frequency active power reduction
Fig. 7. IBG behavior during frequency deviations.
Over frequency active power reduction (also known as P (f ) control) is required for IBG in order to counteract over frequencies in the system. The reduced active power output Pred of the IBG model is defined as: Pred (f ) = Pfreeze · (1 − mred · (f − fred )) (6) where Pfreeze is the saved active power value when exceeding the frequency limit for power reduction fred . The parameter mred is the active power reduction gradient. The parameter values for the over frequency active power reduction are based on (VDE, 2011) and listed in Table 1. An example of P (f ) control of IBG is depicted in Fig. 7 from t = 555 s to t = 875 s (interval 2).
3.5 Reconnection
3.4 Disconnection If frequency or voltage limits are violated, the IBG disconnects from the grid due to tripping of the protection system (delay times are neglected). The disconnection behavior of the IBG model is defined as: PIBG,disc = 0 (7) where PIBG,disc denotes the active power output of the IBG model, which is set to zero when limits are exceeded. The parameter values for the voltage and frequency disconnection settings of IBG are based on (VDE, 2011) and listed in Table 1. For the illustration of the IBG disconnection behavior, an example is depicted in Fig. 7 from t = 875 s to t = 1060 s (interval 3). 561
The reconnection behavior of IBG is seen in the algorithm of Fig. 8. Before IBG is allowed to reconnect, grid frequency f has to be within defined limits (normal operating range) for a duration of ∆tmin,rec seconds, as seen in line 2 of the algorithm. When the reconnection condition is fulfilled, two different methods can be distinguished that are usually used for the reconnection behavior (VDE, 2011): i) immediate reconnection with full available power Pm (step) as seen in line 4; or ii) slow linear increase of power starting at time instant trec until available power Pm is reached (ramp) as seen in line 6. For clarity reasons, only frequency reconnection requirements are illustrated in the algorithm of Fig. 8. The parameter values for the ramp reconnection behavior of IBG are based on (VDE, 2011) and listed in Table 1. An example is shown in Fig. 7 from t = 1060 s to t = 1660 s (interval 4). 1: procedure Reconnection 2: if fmin,rec < f (t) < fmax,rec for ∆tmin,rec then 3: if step then 4: Prec (t) := Pm (t) 5: else ramp 6: Prec (t) := Pm (t) · mrec · (t − trec ) 7: until Prec (t) = Pm (t) 8: else 9: Prec (t) := Pdisc 10: end procedure
Fig. 8. Algorithm for the reconnection of IBG.
IFAC CPES 2018 562 Tokyo, Japan, September 4-6, 2018
Gustav Lammert et al. / IFAC PapersOnLine 51-28 (2018) 558–563
4. CASE STUDIES
3.6 Transition between modes The different IBG control modes can be summarized in a state diagram as seen in Fig. 9 that consists of the states Normal, Reduction, Disconnection and Reconnection. For clarity reasons, only frequency requirements are depicted in the diagram. If, for instance, an over frequency event occurs during the reconnection process, the state is changed from Reconnection to Reduction. The transition between these two states is illustrated in detail in Fig. 10. As soon as the frequency falls below the threshold fred at t = 1436 s, the reconnection process is continued until Prec = Pm and the Normal state is reached. fred ≤ f ≤ fmax,disc
Reduction P := Pred
f < fred
fred ≤ f ≤ fmax,disc f < fred
fmax,disc < f
fmax,disc < f Disconnection f > f P := PIBG,disc
Normal P := Pm
4.1 Overview The reported ADN model has been used in various power system restoration studies that are presented briefly in Sections 4.2–4.5. An overview of the studies and the used functions of the load and IBG model is given in Table 2. 4.2 Case 1 In this study the ADN model is investigated on a simple test system as shown in Fig. 1 (b). The dynamic behavior of the combination of load and IBG was analyzed under a given frequency deviation, as seen in Fig. 11. From t = 0 s to t = 1000 s, the frequency dependency of the load and the over frequency active power reduction of the IBG lead to a significant change in the residual load seen by the system operator. At t = 1000 s the UFLS starts acting until half of the load is disconnected. At this time, the generation is higher than the consumption, which results in a slightly negative residual load. After reconnecting the ADN at t = 1500 s, the residual load is dominated by the CLPU phenomenon and the reconnection ramp of IBG.
min,disc
Table 2. Case studies
fmin,rec < f < fmax,rec for ∆tmin,rec
Prec = Pm
fmax,disc < f
Model
Mode
Load
Voltage and frequency dependency Under frequency load shedding Disconnection Cold load pick-up
IBG
Over frequency active power reduction Disconnection Reconnection
fmin,disc > f
Reconnection P := Prec
Fig. 9. State diagram of the IBG model. f 52.0 fmax,disc f [Hz]
f [Hz]
51.5 51.0 50.5
fred
50.0
1
2
3
2
10.0 P [MW]
P [MW]
8.0 6.0 4.0 1 Disconnection 2.0
Pm P
2 Reconnection
0.0
3 Reduction 0
500
1,000
1,500
2,000
t [s]
Case 2 3
4
1
f
51.0 50.5 50.0 49.5 49.0 48.5 48.0 47.5 47.0
fred f1 f6 fdisc and fmin,disc
2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
PLoad PIBG Presidual
0
500
load
1,000
1,500
2,000
2,500
3,000
t [s]
Fig. 10. Over frequency active power reduction during reconnection of IBG. 562
Fig. 11. Load and IBG behavior during frequency deviations.
IFAC CPES 2018 Tokyo, Japan, September 4-6, 2018
Gustav Lammert et al. / IFAC PapersOnLine 51-28 (2018) 558–563
4.3 Case 2
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REFERENCES
In this study the ADN model was used to analyze the impact of over frequency active power reduction of IBG on power system restoration and the details can be found in (Hachmann et al., 2017). The P (f ) control is particularly relevant for the operation of small islands within the distribution system. The results of this study reveal that using the full potential of IBG active power reduction, leads to improved frequency dynamics in small island grids without any impact on the overall system behavior in normal operation. 4.4 Case 3 In this study the ADN model was used to examine black start and island operation of a real distribution grid with significant penetration of renewable resources and the details can be found in (Lafferte et al., 2017). The results of this study show that it is technical feasible to re-energize distribution grids using diesel generators and biogas plants in combination with distributed PV systems in order to support the bottom-up power system restoration process. 4.5 Case 4 In this study the ADN model was used to investigate the impact of IBG and load reconnection on the restoration process within a real distribution system and the details can be found in (Hachmann et al., 2018). Furthermore, IBG is used to control the active power balance and increase the reconnected load within the distribution system without the requirement of additional power from the transmission system. The results of this study give a realistic example on how IBG can accelerate load restoration. 5. CONCLUSIONS This paper presents a detailed model of an aggregated ADN that is adequate for power system restoration studies in the time scale of tens of seconds up to several minutes. The model was developed with the focus on frequency dynamics and control. It includes a combination of aggregated load and IBG. The load model involves: i) time series data for consumption; ii) voltage and frequency dependency (i.e. exponential load model); iii) UFLS; iv) disconnection behavior; and v) CLPU. On the other hand, the aggregated IBG model considers: i) time series data for generation; ii) over frequency active power reduction; iii) disconnection; and iv) reconnection behavior. The ADN model was successfully applied in several case studies with real grid data and shows adequate dynamic behavior. Moreover, the studies reveal that the consideration of ADNs can support the power system restoration process. Finally, the developed ADN model helps system operators to incorporate IBG into their restoration schemes. Future work will also consider the frequency sensitive mode of IBG (i.e. providing primary frequency response). Furthermore, additional voltage control functions of IBG, such as fault ride-through and dynamic voltage support and quasi-stationary voltage control by means of reactive power (i.e. Q(V ) control), are of interest. 563
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