Volt/var Chain Process*

Schultis, Daniel-Leon; Ilo, Albana

doi:10.1007/978-3-030-81530-1_4

Daniel-Leon Schultis³ &
Albana Ilo³

Part of the book series: Power Systems ((POWSYS))

353 Accesses

Abstract

The massive connection of renewable and distributed generation and the electrification of other sectors give rise to new challenges and opportunities that call for an adaption of the traditional Volt/var control schemes. Recently introduced cosφ(P)- and Q(U)-control of photovoltaic inverters and on-load tap changers in distribution substations to mitigate voltage limit violations provoke massive technical and social problems. This chapter conducts a comprehensive and systematic holistic study to analyse the Volt/var behaviour on the medium- and low voltage levels, focusing on high-medium and medium-low voltage grid boundaries. The recently emerged and newly introduced control strategies are considered. Their evaluation shows that the X(U)-control in radial structures combined with Q-Autarkic customer plants maintains voltage limits reliably, effectively, and efficiently, while preserving the interests of all involved stakeholders. It also clarifies that voltage limits do not remain constant throughout the day, introducing the concept of "boundary voltage limits" for the first time. Additional, practical modelling steps are suggested.

Simplicity is the ultimate sophistication.

—Leonardo da Vinci

*Author: Daniel-Leon Schultis and Albana Ilo

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Notes

1.
Machine-side VSC, DC link capacitor, and grid-side VSC.
2.
Series reactive power contribution is sometimes used in distribution level to secure the supply of factories against voltage dips [79].
3.
These constraints apply exclusively to the boundary node between Grid-Link_1 and Grid-Link_2.
4.
RDPs are commonly used in industrial CPs.
5.
Positive algebraic sign for reactive power absorptions.
6.
The following parameters that correspond to a LV overhead line with a length of 100 m are used: U_nom = 230 V, R = 0.03264 Ω, X = 0.03557 Ω.
7.
Positive algebraic sign for active power injection and reactive power absorption.

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TU Wien, Vienna, Austria
Daniel-Leon Schultis & Albana Ilo

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Appendices

Appendix

A.4.1 Behaviour of Different Link-Grids

This appendix catalogues the simulated behaviour of all Link-Grids listed in Table 4.5 under different Volt/var control strategies and for the case without any Volt/var control. The rural residential CP_Link-Grid and the rural LV_Link-Grid are calculated for both spiky and smooth load profiles at the CP level. Meanwhile, all other Link-Grids are simulated only for the smoothed load profiles.

Table 4.5 Overview of the simulated Link-Grids

Full size table

4.2.1 A.4.1.1 Spiky Load Profiles

CP level

Rural residential CP_Link-Grid connected to LV level

The model of the rural residential CP_Link-Grid is specified in Fig. 4.95; Its behaviour without any Volt/var control is depicted in Fig. 4.96; And its behaviour with the different Volt/var controls is shown in Fig. 4.97. Furthermore, Fig. 4.98 presents the behaviour of the rural residential CP_Link-Grid for cases A, B, and C.

CP structure	Equivalent device model	SMPS, motors, resistive, lighting
	Producer model	One photovoltaic system
	Storage model	One electric vehicle charger
Equivalent device model	Daily energy consumption	4.25 kWh
	Max. active power consumption	4.46 kW
	Max. reactive power consumption	0.65 kvar
	Max. reactive power production	0.16 kvar
	ZIP coefficients	Time-invariant
	References	[10, 37]
Producer model	Daily energy production	23.14 kWh
	Max. active power production	5.00 kW
	Reactive power contribution	According to Volt/var control strategy
	References	[41]
Storage model	Daily energy consumption	1.85 kWh
	Max. active power consumption	3.7 kW
	ZIP coefficients	Time-invariant
	References	[37, 64]

Control strategy	$Q_{t}^{LV - CP}$ (kvar)
Control strategy	Case A	Case B	Case C
None	−0.0044	0.0182	−0.0131
cosφ(P)	−0.0044	2.4395	−0.0131
Q(U)	1.2056	−1.1918	−0.0131
CP_Q-Autarky	0.0000	0.0000	0.0000

Control strategy	$Q_{t}^{CP - Dev}$ (kvar)
Control strategy	Case A	Case B	Case C
None	−0.0044	0.0182	−0.0131
cosφ(P)	−0.0044	0.0182	−0.0131
Q(U)	−0.0044	0.0182	−0.0131
CP_Q-Autarky	−0.0044	0.0182	−0.0131

Control strategy	$Q_{t}^{CP - Pr}$ (kvar)
Control strategy	Case A	Case B	Case C
None	0.0000	0.0000	0.0000
cosφ(P)	0.0000	2.4213	0.0000
Q(U)	1.2100	−1.2100	0.0000
CP_Q-Autarky	0.0044	−0.0182	0.0131

LV level

Rural LV_Link-Grid

The model of the rural LV_Link-Grid is specified in Fig. 4.99; Its behaviour without any Volt/var control is depicted in Figs. 4.100 and 4.101; And its behaviour with the different Volt/var controls is shown in Figs. 4.102 to 4.104. Furthermore, Figs. 4.105 to 4.107 present the behaviour of the rural LV_Link-Grid for cases A, B, and C.

DTR	Rating:		400 kVA
	Nominal voltage		Primary	21.0 kV
	Nominal voltage		Secondary	0.42 kV
	Short circuit voltage		Total	3.7%
	Short circuit voltage		Resistive part	1.0%
Feeders	Nominal voltage			0.4 kV
	Number of feeders			4
	Total line length			6.335 km
	Total cable share			58.64%
	Feeder length		Maximal	1.630 km
	Feeder length		Minimal	0.565 km
Control parameters	OLTC		Upper voltage limit	0.990 p.u
			Lower voltage limit	0.950 p.u
			Min./mid/max. tap positions	1/3/5
			Additional voltage per tap	2.5%
	X(U)		Upper voltage limit	1.09 p.u
	X(U)		Lower voltage limit	0.91 p.u
Connected lumped models	Link-Grids	CP	Residential with spiky load profiles	61

Control strategy	$Q_{t}^{MV - LV}$ (kvar)
Control strategy	Case A	Case B	Case C
None	1.1849	23.7847	3.7581
cosφ(P)	1.1849	178.2922	3.7581
Q(U)	37.8057	36.1168	3.7581
X(U)	1.1849	23.7847	3.7583
X(U)+	−0.1576	16.6295	0.0536
OLTC	1.0427	23.4057	3.5752
OLTC+	−0.1403	16.6295	0.0682

Control strategy	$Q_{\Sigma ,t}^{LV - CP}$ (kvar)
Control strategy	Case A	Case B	Case C
None	1.3421	7.0678	3.6998
cosφ(P)	1.3421	154.0554	3.6998
Q(U)	37.6942	19.1260	3.6998
X(U)	1.3421	7.0678	3.6998
X(U)+	0.0000	0.0000	0.0000
OLTC	1.1826	7.4946	3.5024
OLTC+	0.0000	0.0000	0.0000

Control strategy	$Q_{\Sigma ,t}^{LV}$ (kvar)
Control strategy	Case A	Case B	Case C
None	−0.1572	16.7169	0.0585
cosφ(P)	−0.1572	24.2372	0.0585
Q(U)	0.1115	16.9907	0.0585
X(U)	−0.1572	16.7169	0.0585
X(U)+	−0.1576	16.6295	0.0536
OLTC	−0.1399	15.9111	0.0729
OLTC+	−0.1403	16.6295	0.0682

Control strategy	$\Delta P_{t}^{LV}$ (kW)
Control strategy	Case A	Case B	Case C
None	0.0250	17.1154	0.2402
cosφ(P)	0.0250	24.9791	0.2402
Q(U)	0.2931	17.6844	0.2402
X(U)	0.0250	17.1154	0.2402
X(U)+	0.0245	17.0116	0.2350
OLTC	0.0254	16.3134	0.2475
OLTC+	0.0250	17.0116	0.2426

Control strategy	$Loading_{t}^{DTR}$(%)
Control strategy	Case A	Case B	Case C
None	1.9979	68.0621	7.2600
cosφ(P)	1.9979	80.9169	7.2600
Q(U)	9.2271	68.3151	7.2600
X(U)	1.9979	68.0621	7.2600
X(U)+	1.9786	67.9281	7.2011
OLTC	1.9188	68.1371	7.1809
OLTC+	1.9033	67.9281	7.1269

4.2.2 A.4.1.2 Smoothed Load Profiles

CP level

Rural residential CP_Link-Grid connected to LV level

The model of the rural residential CP_Link-Grid is specified in Fig. 4.108; Its behaviour without any Volt/var control is depicted in Fig. 4.109; And its behaviour with the different Volt/var controls is shown in Fig. 4.110. Furthermore, Fig. 4.111 present the behaviour of the rural residential CP_Link-Grid for cases A, B, and C.

CP structure	Equivalent device model	SMPS, motors, resistive, lighting
	Producer model	One photovoltaic system
	Storage model	One electric vehicle charger
Equivalent device model	Daily energy consumption	20.75 kWh
	Max. active power consumption^*	1.37 kW
	Max. reactive power consumption	0.22 kvar
	Max. reactive power production	0.07 kvar
	ZIP coefficients	Time-variant
	References	[58]
Producer model	Daily energy production	31.37 kWh
	Max. active power production	5.00 kW
	Reactive power contribution	According to Volt/var control strategy
	References	[41]
Storage model	Daily energy consumption	3.51 kWh
	Max. active power consumption	0.30 kW
	ZIP coefficients	Time-invariant
	References	[6, 64]

^aThis value is derived from the maximal active power flow through the DTR of the rural LV_Link-Grid measured throughout 2016

Control strategy	$Q_{t}^{LV - CP}$ (kvar)
Control strategy	Case A	Case B	Case C
None	0.1791	0.1406	−0.0656
cosφ(P)	0.1791	2.5622	−0.0656
Q(U)	1.3891	−1.0694	−0.0656
CP_Q-Autarky	0.0000	0.0000	0.0000

Control strategy	$Q_{t}^{CP - Dev}$(kvar)
Control strategy	Case A	Case B	Case C
None	0.1791	0.1406	−0.0656
cosφ(P)	0.1791	0.1406	−0.0656
Q(U)	0.1791	0.1406	−0.0656
CP_Q-Autarky	0.1791	0.1406	−0.0656

Control strategy	$Q_{t}^{CP - Pr}$(kvar)
Control strategy	Case A	Case B	Case C
None	0.0000	0.0000	0.0000
cosφ(P)	0.0000	2.4215	0.0000
Q(U)	1.2100	−1.2100	0.0000
CP_Q-Autarky	-0.1791	−0.1406	0.0656

Urban residential CP_Link-Grid connected to LV level.

The model of the urban residential CP_Link-Grid is specified in Fig. 4.112; Its behaviour without any Volt/var control is depicted in Fig. 4.113; And its behaviour with the different Volt/var controls is shown in Fig. 4.114. Furthermore, Fig. 4.115 present the behaviour of the urban residential CP_Link-Grid for cases A, B, and C.

CP structure	Equivalent device model	SMPS, motors, resistive, lighting
	Producer model	One photovoltaic system
	Storage model	One electric vehicle charger
Equivalent device model	Daily energy consumption	29.73 kWh
	Max. active power consumption^a	1.96 kW
	Max. reactive power consumption	0.32 kvar
	Max. reactive power production	0.10 kvar
	ZIP coefficients	Time-variant
	References	[58]
Producer model	Daily energy production	31.37 kWh
	Max. active power production	5.00 kW
	Reactive power contribution	According to Volt/var control strategy
	References	[41]
Storage model	Daily energy consumption	3.51 kWh
	Max. active power consumption	0.30 kW
	ZIP coefficients	Time-invariant
	References	[6, 64]

^aThis value is derived from the maximal active power flow through the DTR of the urban LV_Link-Grid measured throughout 2016

Control strategy	$Q_{t}^{LV - CP}$(kvar)
Control strategy	Case A	Case B	Case C
None	0.2566	0.2015	−0.0940
cosφ(P)	0.2566	2.6230	−0.0940
Q(U)	1.4666	−1.0085	−0.0940
CP_Q-Autarky	0.0000	0.0000	0.0000

Control strategy	$Q_{t}^{CP - Dev}$(kvar)
Control strategy	Case A	Case B	Case C
None	0.2566	0.2015	−0.0940
cosφ(P)	0.2566	0.2015	−0.0940
Q(U)	0.2566	0.2015	−0.0940
CP_Q-Autarky	0.2566	0.2015	−0.0940

Control strategy	$Q_{t}^{CP - Pr}$ (kvar)
Control strategy	Case A	Case B	Case C
None	0.0000	0.0000	0.0000
cosφ(P)	0.0000	2.4215	0.0000
Q(U)	1.2100	−1.2100	0.0000
CP_Q-Autarky	−0.2566	−0.2015	0.0940

Commercial CP_Link-Grid connected to MV level.

The model of the commercial CP_Link-Grid is specified in Fig. 4.116; Its behaviour without any Volt/var control is depicted in Fig. 4.117; And its behaviour with the different Volt/var controls is shown in Fig. 4.118. Furthermore, Fig. 4.119 present the behaviour of the commercial CP_Link-Grid for cases A, B, and C.

CP structure	Equivalent device model	SMPS, motors, resistive, lighting
	Producer model	One photovoltaic system
	Storage model	Three electric vehicle chargers
Equivalent device model	Daily energy consumption	690.25 kWh
	Max. active power consumption	50 kW
	Power factor	0.90 inductive
	ZIP coefficients	Time-invariant
	References	[12] and [10]
Producer model	Daily energy production	313.65 kWh
	Max. active power production	50 kW
	Reactive power contribution	According to Volt/var control strategy
	References	[41]
Storage model	Daily energy consumption	46.03 kWh
	Max. active power consumption	4.41 kW
	ZIP coefficients	Time-invariant
	References	[6, 64]

Control strategy	$Q_{t}^{MV - CP}$ (kvar)
Control strategy	Case A	Case B	Case C
None	6.9423	19.5685	11.3008
cosφ(P)	6.9423	43.7842	11.3008
Q(U)	19.0423	7.4685	11.3008
CP_Q-Autarky	0.0000	0.0000	0.0000

Control strategy	$Q_{t}^{CP - Dev}$ (kvar)
Control strategy	Case A	Case B	Case C
None	6.9423	19.5685	11.3008
cosφ(P)	6.9423	19.5685	11.3008
Q(U)	6.9423	19.5685	11.3008
CP_Q-Autarky	6.9423	19.5685	11.3008

Control strategy	$Q_{t}^{CP - Pr}$ (kvar)
Control strategy	Case A	Case B	Case C
None	0.0000	0.0000	0.0000
cosφ(P)	0.0000	24.2158	0.0000
Q(U)	12.1000	−12.1000	0.0000
CP_Q-Autarky	−6.9423	−19.5685	−11.3008

Industrial CP_Link-Grid connected to MV level

The model of the industrial CP_Link-Grid is specified in Fig. 4.120; Its behaviour without any Volt/var control is depicted in Fig. 4.121; And its behaviour with the different Volt/var controls is shown in Fig. 4.122. Furthermore, Fig. 4.123 present the behaviour of the industrial CP_Link-Grid for cases A, B, and C.

CP structure	Equivalent device model	SMPS, motors, resistive, lighting
CP structure	Producer model	One photovoltaic system
Equivalent device model	Daily energy consumption	118.44 MWh
	Max. active power consumption^a	8 MW
	Power factor	0.90 inductive
	ZIP coefficients	Time-invariant
	References	[12] and [10]
Producer model	Daily energy production	1.88 MWh
	Max. active power production	300 kW
	Reactive power contribution	According to Volt/var control strategy
	References	[41]

^aThis value corresponds to the billing demand of the two industrial customers connected to the large MV_Link-Grid

Control strategy	$Q_{t}^{MV - CP}$ (kvar)
Control strategy	Case A	Case B	Case C
None	1676.7231	3267.1158	1518.3498
cosφ(P)	1676.7231	3412.4081	1518.3498
Q(U)	1749.3231	3194.5158	1518.3498
CP_Q-Autarky	0.0000	0.0000	0.0000

Control strategy	$Q_{t}^{CP - Dev}$ (kvar)
Control strategy	Case A	Case B	Case C
None	1676.7231	3267.1158	1518.3498
cosφ(P)	1676.7231	3267.1158	1518.3498
Q(U)	1676.7231	3267.1158	1518.3498
CP_Q-Autarky	1676.7231	3267.1158	1518.3498

Control strategy	$Q_{t}^{CP - Pr}$ (kvar)
Control strategy	Case A	Case B	Case C
None	0.0000	0.0000	0.0000
cosφ(P)	0.0000	145.2922	0.0000
Q(U)	72.6000	−72.6000	0.0000
CP_Q-Autarky	−1676.7231	−3267.1158	−1518.3498

LV level

Rural LV_Link-Grid

The model of the rural LV_Link-Grid is specified in Fig. 4.124; Its behaviour without any Volt/var control is depicted in Figs. 4.125 and 4.126; And its behaviour with the different Volt/var controls is shown in Figs. 4.127 to 4.129. Furthermore, Figs. 4.130 to 4.132 present the behaviour of the rural LV_Link-Grid for cases A, B, and C.

DTR	Rating:		400 kVA
	Nominal voltage		Primary	21.0 kV
	Nominal voltage		Secondary	0.42 kV
	Short circuit voltage		Total	3.7%
	Short circuit voltage		Resistive part	1.0%
Feeders	Nominal voltage			0.4 kV
	Number of feeders			4
	Total line length			6.335 km
	Total cable share			58.64%
	Feeder length		Maximal	1.630 km
	Feeder length		Minimal	0.565 km
Control parameters	OLTC		Upper voltage limit	0.990 p.u
			Lower voltage limit	0.950 p.u
			Min./mid/max. tap positions	1/3/5
			Additional voltage per tap	2.5%
	X(U)		Upper voltage limit	1.09 p.u
	X(U)		Lower voltage limit	0.91 p.u
Connected lumped models	Link-Grids	CP	Rural residential with smoothed load profiles	61

Control strategy	$Q_{t}^{MV - LV}$(kvar)
Control strategy	Case A	Case B	Case C
None	11.2117	24.7847	−2.5265
cosφ(P)	11.2117	179.6204	−2.5265
Q(U)	26.0203	35.2988	−4.0817
X(U)	11.2117	24.7847	−2.5265
X(U)+	0.5220	15.1919	1.1476
OLTC	10.4582	24.7847	−2.0585
OLTC+	0.5354	15.1919	1.1833

Control strategy	$Q_{\Sigma ,t}^{LV - CP}$(kvar)
Control strategy	Case A	Case B	Case C
None	10.6646	9.4851	−3.6763
cosφ(P)	10.6646	156.6212	−3.6763
Q(U)	25.3810	19.7681	−5.2365
X(U)	10.6646	9.4851	−3.6763
X(U)+	0.0000	0.0000	0.0000
OLTC	9.8987	9.4851	−3.2434
OLTC+	0.0000	0.0000	0.0000

Control strategy	$Q_{\Sigma ,t}^{LV}$(kvar)
Control strategy	Case A	Case B	Case C
None	0.5471	15.2995	1.1498
cosφ(P)	0.5471	22.9992	1.1498
Q(U)	0.6393	15.5307	1.1547
X(U)	0.5471	15.2995	1.1498
X(U)+	0.5220	15.1919	1.1476
OLTC	0.5595	15.2995	1.1850
OLTC+	0.5354	15.1919	1.1833

Control strategy	$\Delta P_{t}^{LV}$(kW)
Control strategy	Case A	Case B	Case C
None	0.7643	15.9688	1.3885
cosφ(P)	0.7643	23.9166	1.3885
Q(U)	0.8266	16.4398	1.3990
X(U)	0.7643	15.9688	1.3885
X(U)+	0.7388	15.8581	1.3859
OLTC	0.7601	15.9688	1.4179
OLTC+	0.7356	15.8581	1.4159

Control strategy	$Loading_{t}^{DTR}$(%)
Control strategy	Case A	Case B	Case C
None	13.7426	64.0142	18.4742
cosφ(P)	13.7426	77.9572	18.4742
Q(U)	14.8192	64.2656	18.4987
X(U)	13.7426	64.0142	18.4742
X(U)+	13.5088	63.8105	18.4553
OLTC	13.0492	64.0142	18.2095
OLTC+	12.8352	63.8105	18.1956

Urban LV_Link-Grid

The model of the urban LV_Link-Grid is specified in Fig. 4.133; Its behaviour without any Volt/var control is depicted in Figs. 4.134 and 4.135; And its behaviour with the different Volt/var controls is shown in Figs. 4.136 to 4.138. Furthermore, Figs. 4.139 to 4.141 present the behaviour of the urban LV_Link-Grid for cases A, B, and C.

DTR	Rating:		800 kVA
	Nominal voltage		Primary	20.0 kV
	Nominal voltage		Secondary	0.4 kV
	Short circuit voltage		Total	4.0%
	Short circuit voltage		Resistive part	1.0%
Feeders	Nominal voltage			0.4 kV
	Number of feeders			9
	Total line length			12.815 km
	Total cable share			96.14%
	Feeder length		Maximal	1.270 km
	Feeder length		Minimal	0.305 km
Control parameters	OLTC		Upper voltage limit	1.025 p.u
			Lower voltage limit	0.950 p.u
			Min./mid/max. tap positions	1/3/5
			Additional voltage per tap	2.5%
	X(U)		Upper voltage limit	1.09 p.u
	X(U)		Lower voltage limit	0.91 p.u
Connected lumped models	Link-Grids	CP	Urban residential with smoothed load profiles	175

Control strategy	$Q_{t}^{MV - LV}$(kvar)
Control strategy	Case A	Case B	Case C
None	46.5923	72.0637	−9.8095
cosφ(P)	46.5923	512.9641	−9.8095
Q(U)	75.7565	66.6676	−12.6388
X(U)	46.5923	72.0638	−9.8093
X(U)+	2.7900	33.6598	5.1902
OLTC	44.9710	72.0637	−9.8095
OLTC+	2.8048	33.6598	5.1902

Control strategy	$Q_{\Sigma ,t}^{LV - CP}$(kvar)
Control strategy	Case A	Case B	Case C
None	43.6756	38.0601	−15.0114
cosφ(P)	43.6756	459.8271	−15.0114
Q(U)	72.6505	32.7091	−17.8544
X(U)	43.6756	38.0601	−15.0114
X(U)+	0.0000	0.0000	0.0000
OLTC	42.0423	38.0601	−15.0114
OLTC+	0.0000	0.0000	0.0000

Control strategy	$Q_{\Sigma ,t}^{LV}$(kvar)
Control strategy	Case A	Case B	Case C
None	2.9167	34.0037	5.2021
cosφ(P)	2.9167	53.1370	5.2021
Q(U)	3.1061	33.9585	5.2156
X(U)	2.9167	34.0037	5.2021
X(U)+	2.7900	33.6598	5.1902
OLTC	2.9287	34.0037	5.2021
OLTC+	2.8048	33.6598	5.1902

Control strategy	$\Delta P_{t}^{LV}$(kW)
Control strategy	Case A	Case B	Case C
None	3.4914	34.0481	5.7219
cosφ(P)	3.4914	53.0728	5.7219
Q(U)	3.6255	34.0269	5.7424
X(U)	3.4914	34.0481	5.7219
X(U)+	3.3684	33.7011	5.7095
OLTC	3.4750	34.0481	5.7219
OLTC+	3.3547	33.7011	5.7095

Control strategy	$Loading_{t}^{DTR}$(%)
Control strategy	Case A	Case B	Case C
None	27.6187	87.0541	35.3063
cosφ(P)	27.6187	108.3297	35.3063
Q(U)	28.4914	86.9772	35.3293
X(U)	27.6188	87.0541	35.3063
X(U)+	27.1280	86.6339	35.2651
OLTC	26.8802	87.0541	35.3063
OLTC+	26.4107	86.6339	35.2651

MV level

Small MV_Link-Grid

The model of the small MV_Link-Grid is specified in Fig. 4.142; Its behaviour without any Volt/var control is depicted in Figs. 4.143 and 4.144; And its behaviour with the different Volt/var controls is shown in Figs. 4.145 and 4.146. Furthermore, Figs. 4.147 and 4.148 present the behaviour of the small MV_Link-Grid for cases A, B, and C.

Feeders	Nominal voltage			20 kV
	Number of feeders			4
	Total line length			158.46 km
	Total cable share			70.62%
	Feeder length		Maximal	25.90 km
			Minimal	14.82 km
Connected lumped models	Link-Grids	CP	Commercial with smoothed load profiles	90
		LV	Rural for smoothed load profiles in CP level	49
			Urban for smoothed load profiles in CP level	4

Control strategy	$Q_{t}^{HV - MV}$ (kvar)
Control strategy	Case A	Case B	Case C
None	−3166.4324	−274.0876	−3158.5634
cosφ(P)	−3166.4324	11,546.7229	−3158.5634
Q(U)	−1928.1602	1511.9364	−3710.0295
X(U)	−3166.4318	248.7131	−3158.5616
X(U)+	−4477.5800	−2081.4525	−3933.1527
OLTC	−3212.9555	−263.6931	−3145.0208
OLTC+	−4481.5044	−2784.5875	−3932.6640

Control strategy	$Q_{\Sigma ,t}^{MV - CP}$ (kvar)
Control strategy	Case A	Case B	Case C
None	618.4366	1853.2531	999.4724
cosφ(P)	618.4366	3974.8352	999.4724
Q(U)	1453.9913	1515.7483	1001.1713
X(U)	618.4366	1848.5563	999.4724
X(U)+	0.0000	0.0000	0.0000
OLTC	618.9152	1853.2941	999.5357
OLTC+	0.0000	0.0000	0.0000

Control strategy	$Q_{\Sigma ,t}^{MV - LV}$ (kvar)
Control strategy	Case A	Case B	Case C
None	727.8706	1475.6636	−147.5860
cosφ(P)	727.8706	10,826.4782	−147.5860
Q(U)	1127.1403	3552.6617	−702.6286
X(U)	727.8711	1990.3126	−147.5842
X(U)+	36.8124	1528.7827	78.0662
OLTC	685.6193	1484.7638	−133.5151
OLTC+	37.5357	834.2631	79.2284

Control strategy	$Q_{\Sigma ,t}^{MV}$ (kvar)
Control strategy	Case A	Case B	Case C
None	−4512.7396	−3603.0043	−4010.4498
cosφ(P)	−4512.7396	−3254.5905	−4010.4498
Q(U)	−4509.2919	−3556.4736	−4008.5722
X(U)	−4512.7396	−3590.1558	−4010.4497
X(U)+	−4514.3924	−3610.2352	−4011.2189
OLTC	−4517.4900	−3601.7510	−4011.0413
OLTC+	−4519.0401	−3618.8506	−4011.8923

Control strategy	$\Delta P_{t}^{MV}$ (kW)
Control strategy	Case A	Case B	Case C
None	65.6263	522.4462	125.4512
cosφ(P)	65.6263	822.7866	125.4512
Q(U)	56.7900	546.8396	137.9468
X(U)	65.6263	527.0487	125.4512
X(U)+	81.2532	529.9529	134.0752
OLTC	62.9133	524.2177	124.9212
OLTC+	78.1092	535.3583	133.5975

Large MV_Link-Grid

The model of the large MV_Link-Grid is specified in Fig. 4.149; Its behaviour without any Volt/var control is depicted in Figs. 4.150 and 4.151; And its behaviour with the different Volt/var controls is shown in Figs. 4.152 and 4.153. Furthermore, Figs. 4.154 and 4.155 present the behaviour of the large MV_Link-Grid for cases A, B, and C.

Feeders	Nominal voltage			20 kV
	Number of feeders			6
	Total line length			267.151 km
	Total cable share			74.66%
	Feeder length		Maximal	46.10 km
			Minimal	2.00 km
Connected lumped models	Link-Grids	CP	Commercial with smoothed load profiles	143
			Industrial with smoothed load profiles	2
		LV	Rural for smoothed load profiles in CP level	45
			Urban for smoothed load profiles in CP level	11
	Producers	Hydroelectric power plants	400 kW^a	2
			300 kW^a	1
			100 kW^a	11
			60 kW^a	1

^aThe hydroelectric power plants are modelled as voltage-independent PQ node-elements. They constantly inject 70% of their maximal active power production over the entire time horizon. They do not contribute any reactive power. Their upper and lower BVLs are set to 1.1 and 0.9 p.u. for the complete simulated time horizon.

Control strategy	$Q_{t}^{HV - MV}$ (kvar)
Control strategy	Case A	Case B	Case C
None	−2178.3268	5323.0076	−2288.3236
cosφ(P)	−2178.3268	21,186.5807	−2288.3236
Q(U)	112.0730	6399.8174	−2589.4373
X(U)	−2178.3260	5519.1924	−2288.3210
X(U)+	−7480.6020	−4754.2448	−6577.2863
OLTC	−2234.5103	5326.7501	−2272.0105
OLTC+	−7484.4610	−5144.4723	−6576.9824

Control strategy	$Q_{\Sigma ,t}^{MV - CP}$(kvar)
Control strategy	Case A	Case B	Case C
None	4333.0964	9521.7222	4601.8610
cosφ(P)	4333.0964	13,099.2043	4601.8610
Q(U)	5899.0375	9067.4411	4604.0249
X(U)	4333.0964	9514.0736	4601.8610
X(U)+	0.0000	0.0000	0.0000
OLTC	4334.1894	9521.7074	4601.9296
OLTC+	0.0000	0.0000	0.0000

Control strategy	$Q_{\Sigma ,t}^{MV - LV}$(kvar)
Control strategy	Case A	Case B	Case C
None	1015.8510	1887.8723	−212.1237
cosφ(P)	1015.8510	13,708.7961	−212.1237
Q(U)	1720.6532	3389.1906	−514.2476
X(U)	1015.8518	2083.9526	−212.1211
X(U)+	54.1633	1398.7258	109.2150
OLTC	963.1898	1891.4090	−195.2761
OLTC+	54.9485	1011.2246	110.7794

Control strategy	$Q_{\Sigma ,t}^{MV}$(kvar)
Control strategy	Case A	Case B	Case C
None	−7527.2742	−6086.5869	−6678.0609
cosφ(P)	−7527.2742	−5621.4196	−6678.0609
Q(U)	−7507.6177	−6056.8143	−6679.2146
X(U)	−7527.2742	−6078.8338	−6678.0609
X(U)+	−7534.7653	−6152.9706	−6686.5013
OLTC	−7531.8895	−6086.3663	−6678.6640
OLTC+	−7539.4095	−6155.6969	−6687.7617

Control strategy	$Q_{\Sigma ,t}^{MV - Pr}$(kvar)
Control strategy	Case A	Case B	Case C
None	0.0000	0.0000	0.0000
cosφ(P)	0.0000	0.0000	0.0000
Q(U)	0.0000	0.0000	0.0000
X(U)	0.0000	0.0000	0.0000
X(U)+	0.0000	0.0000	0.0000
OLTC	0.0000	0.0000	0.0000
OLTC+	0.0000	0.0000	0.0000

Control strategy	$\Delta P_{t}^{MV}$(kW)
Control strategy	Case A	Case B	Case C
None	83.1072	536.9832	144.1819
cosφ(P)	83.1072	846.0916	144.1819
Q(U)	52.6137	538.5407	149.2351
X(U)	83.1072	536.4634	144.1819
X(U)+	121.4523	554.7991	181.1443
OLTC	81.9192	537.2434	143.6320
OLTC+	119.6531	572.3173	180.3358

A.4.2 Volt/var Control Parametrisation

This appendix discusses the Q(U) and OLTC parametrisation impact on the LV_Link-Grid's behaviour in detail.

4.3.1 A.4.2.1 Impact of Q(U) Parametrisation

The Q(U)-control characteristic must be adequately set to widen the $BVL_{t}^{MV - LV}$ sufficiently, while avoiding unnecessary reactive power flows and oscillations. The maximal impact on the voltage is achieved when all PV inverters connected to the LV_Link-Grid contribute their maximal reactive power, either all in inductive or all in capacitive mode. However, the high reactive power flow increases the grid loss and the loading and propagates up to the superordinate MV_Link-Grid. Therefore, the characteristic should be set with a high slope gradient and a wide dead band to minimise the reactive power flows. But, too high slope gradients may lead to oscillations [39]. Figure 4.156 shows two control characteristics used to analyse the impact of Q(U) parametrisation on the behaviour of the rural LV_Link-Grid: Default and customised. The default characteristic is used in Sect. 4.7 to compare the different Volt/var control strategies and yields the results shown in Fig. 4.66b. The customised characteristic is parametrised to maximise the permissible voltage range at the BLiN^MV−LV of the rural LV_Link-Grid for the given scenario while keeping the reactive power flows as low as possible; A higher slope gradient is used in this case.

The methodology used to customise the Q(U)-characteristic is illustrated in Fig. 4.157. The goal is that all PV inverters contribute their maximal reactive power only when voltage limit violations occur. Simulating the scenario with smoothed load profiles defined in Sect. 4.7.2.1 for the customised characteristic yields the upper and lower $BVL_{t}^{MV - LV}$ shown in Fig. 4.157a. The minimal boundary voltage that leads to upper limit violations within the LV_Link-Grid is 1.03 p.u. and appears at 12:10. Meanwhile, at 18:00 occurs the maximum boundary voltage that leads to lower limit violations, i.e. 0.9125 p.u.

These two points are decisive for the control parametrisation, and the corresponding voltage profiles are shown in Fig. 4.157b. The difference between the MV-LV boundary voltage, which is marked by a grey cross, and the voltage at the feeder beginning, results from the voltage drop over the DTR. Regarding the case with a lower limit violation, the inverters’ capacitive behaviour increases the voltage along the feeders with overhead line share. In contrast, the voltage still decreases at the pure cable feeder due to the high active power consumption. For both cases, the BLiN^LV−CP (which are also the connection nodes of the PV systems) with the lowest and highest voltage values are highlighted with green colour. It is clear to see in Fig. 4.157c that all inverters contribute their maximal reactive power (hatched part of the characteristic). When the voltage at the BLiN^MV−LV comes closer to its nominal value, no limits are violated, and some of the inverters reduce their var contribution, thus avoiding unnecessary reactive power flows.

The customised Q(U)-characteristic is an idealised case, as the CP power contributions are unknown in reality and vary for each day. But, it enables to theoretically analyse the optimal performance of the control strategy and the impact of its parametrisation on the grid behaviour. Figure 4.158 shows the daily Volt/var behaviour of the rural LV_Link-Grid with Q(U)-control for both characteristics.

In comparison, the customised characteristic allows for higher MV-LV boundary voltages around midday and significantly increases the reactive power flows within a wide area of the voltage–time-plane. However, the inductive and capacitive areas, as well as the $BVL_{t}^{MV - LV}$, maintain their fundamental shape independently of the exact parametrisation. The reactive power flows over the BLiN^MV−LV are compared for both Q(U)-characteristics in Table 4.6.

Table 4.6 Reactive power flow over the BLiN^MV−LV of the rural LV_Link-Grid for smoothed load profiles at the CP level, different cases and distinct Q(U)-characteristics

Full size table

4.3.2 A.4.2.2 Impact of OLTC Parametrisation

The OLTC maintains the voltage at the secondary bus bar of the DTR within a predefined voltage band, which must be adequately set to guarantee limit compliance at the LV level. The ideal parameters are found for the rural LV_Link-Grid and the defined scenario by excluding the DTR from the grid model, setting the BLiN^MV−LV to its secondary bus bar, and calculating the upper and lower $BVL_{t}^{MV - LV}$ of the resulting model for the case without any Volt/var control, Fig. 4.159.

This analysis shows that no voltage limit violations occur within the LV grid when the secondary voltage stays within 0.95 and 0.99 p.u.; These values represent the adequate OLTC parameters. To study the impact of inadequate parameters, the wider voltage band between 0.94 and 1.00 p.u. is also considered in the following simulations.

The OLTC parametrisation impact is analysed by calculating the lumped model of the rural LV_Link-Grid according to Fig. 4.124 for both settings. Using the adequate OLTC parameters yields the results shown in Fig. 4.160a. The original $BVL_{t}^{MV - LV}$, i.e. those without any Volt/var control, are shifted mainly in parallel, without affecting the reactive power exchange significantly. When inadequate parameters are used, the $BVL_{t}^{MV - LV}$ are also shifted in parallel, and additionally, upper and lower limit violation islands occur in the voltage–time-plane, Fig. 4.160b. An increase of the MV-LV boundary voltage eliminates the upper limit violations at the LV level in the upper islands. In the lower ones, a reduction of the boundary voltage eliminates the lower limit violations.

To clarify the limit violation islands’ occurrence, Fig. 4.161 enlarges the limit violation islands and shows the voltage profiles of all feeders of the rural LV_Link-Grid with inadequate OLTC parameters at 18:00 for three different MV-LV boundary voltages: 0.9575 p.u. (case X), 0.9475 p.u. (case Y), and 0.9375 p.u. (case Z).

In case X, the mid-position of the tap (3/5) is sufficient to maintain the voltage at the feeder beginning in the predefined band, which is set between 0.94 and 1.00 p.u. When the MV-LV boundary voltage decreases by 0.01 p.u., the CPs located at the feeder end violate their lower limit, case Y. Meanwhile, the voltage at the feeder beginning is 0.944 p.u., thus no change of the tap position is required. When the MV-LV boundary voltage further decreases, the tap changes its position to 4/5, eliminating the violations of the lower voltage limit, case Z.

A.4.3 Volt/var control evaluation

This appendix provides the detailed definitions of the evaluation criteria used in Sect. 4.8 and the normalisation procedure used to enable their illustration within the evaluation hexagon.

4.4.1 A.4.3.1 Definition of Technical Evaluation Criteria

The technical criteria are calculated for the (U, t)-plane spanned by the simulated time horizon of 24 h and by the MV-LV boundary voltages between 0.9 and 1.1 p.u. (see Fig. 4.79). For brevity, the MV-LV boundary voltage ($U_{t}^{MV - LV}$) is denoted just as U in Eqs. (4.49)–(4.52).

Voltage limit violations

The voltage limit violation index (VI) is calculated for the regarded zone within the (U, t)-plane according to Eq. (4.49).

$$VI_{U,t} = \frac{1}{{N^{nodes} }}\left( {{ }\mathop \sum \limits_{j = 1}^{{m_{U,t} }} \left( {\frac{{U_{U,t}^{{\overline{viol} ,j}} }}{{U_{nom}^{LV} }} - 1.1{\text{ p}}{\text{.u}}{.}} \right) + \mathop \sum \limits_{j = 1}^{{n_{U,t} }} \left( {0.9{\text{ p}}{\text{.u}}{.} - \frac{{U_{U,t}^{{\underline{viol} ,j}} }}{{U_{nom}^{LV} }}} \right)} \right)$$

(4.49a)

$$VI = \mathop \sum \limits_{\forall t} \mathop \sum \limits_{\forall U} VI_{U,t}$$

(4.49b)

where U and t are the MV-LV boundary voltage and the instant of time, respectively;$N^{nodes}$ is the total number of LV grid nodes; $m_{U,t}$ is the number of the LV grid nodes that violate the upper voltage limit; $n_{U,t}$ is the number of the LV grid nodes that violate the lower voltage limit;${ }U_{U,t}^{{\overline{viol} ,j}}$ are the voltages of the LV grid nodes that violate the upper voltage limit; $U_{U,t}^{{\underline{viol} ,j}}$ are the voltages of the LV grid nodes that violate the lower voltage limit; And $U_{nom}^{LV}$ is the nominal voltage of the LV level.

MV-LV reactive power exchange.

The MV-LV reactive energy exchange ($E^{Q}$) is calculated for the regarded (U, t)-plane according to Eq. (4.50) without considering the flow direction.

$$E^{Q} = { }\Delta t\cdot\mathop \sum \limits_{\forall t} \mathop \sum \limits_{\forall U} \left| {Q_{U,t}^{MV - LV} } \right|$$

(4.50)

where $\Delta t = 10\,{\text{min}}$ is the temporal resolution of the load profiles; And $Q_{U,t}^{MV - LV}$ is the reactive power flow through the MV-LV boundary node.

Active power loss

The energy loss ($\Delta E$) is calculated for the regarded (U, t)-plane according to Eq. (4.51).

$$\Delta E = { }\Delta t\cdot\mathop \sum \limits_{\forall t} \mathop \sum \limits_{\forall U} \Delta P_{U,t}^{LV}$$

(4.51)

where $\Delta P_{U,t}^{LV}$ is the active power loss within the LV_Link-Grid.

DTR loading

The average DTR loading ($Loading^{DTR,avg}$) is calculated for the regarded (U, t)-plane according to Eq. (4.52).

$$Loading^{DTR,avg} = { }\frac{1}{{N^{t} \cdot N^{U} }} \cdot \mathop \sum \limits_{\forall t} \mathop \sum \limits_{\forall U} Loading_{U,t}^{DTR}$$

(4.52)

where $N^{U}$, $N^{t}$ are the numbers of MV-LV boundary voltages and instants of time, respectively, within the regarded (U,t)-plane.

4.4.2 A.4.3.2 Calculation of the Evaluation Hexagon Data

The evaluation criteria defined in Sect. A.4.3.1 are calculated for each control setup (indexed with c) and both LV_Link-Grids (indexed with g) catalogued in Sect. A.4.1.2. Firstly, the evaluation hexagon is calculated for each LV_Link-Grid separately, and secondly, a common hexagon is calculated to enable the compact presentation of the final evaluation results.

Calculation of the separate hexagons

The technical evaluation criteria are normalised according to Eq. (4.53) to enable their illustration in a common chart. The resulting normalised evaluation criteria lie within the interval [0, 1] and do not have any physical unit.

$$VI_{c,g}^{norm} = { }\frac{{VI_{c,g} }}{{\mathop {\max }\limits_{c} \left( {VI_{c,g} } \right)}}$$

(4.53a)

$$E_{c,g}^{Q,norm} = { }\frac{{E_{c,g}^{Q} }}{{\mathop {\max }\limits_{c} \left( {E_{c,g}^{Q} } \right)}}$$

(4.53b)

$$\Delta E_{c,g}^{norm} = { }\frac{{\Delta E_{c,g} }}{{\mathop {\max }\limits_{c} \left( {\Delta E_{c,g} } \right)}}$$

(4.53c)

$$Loading_{c,g}^{DTR,avg,norm} = { }\frac{{Loading_{c,g}^{DTR,avg} }}{{\mathop {\max }\limits_{c} \left( {Loading_{c,g}^{DTR,avg} } \right)}}$$

(4.53d)

where $VI_{c,g}^{norm}$, $E_{c,g}^{Q,norm}$, $\Delta E_{c,g}^{norm}$, $Loading_{c,g}^{DTR,avg,norm}$ are the normalised values of the evaluation criteria of the control setup c and the LV_Link-Grid g (rural or urban).

Calculation of the common hexagon

The results of both LV_Link-Grids are superimposed according to Eq. (4.54) to enable the compact presentation of the evaluation.

$$VI_{c}^{norm} = { }\frac{{VI_{c,rural}^{norm} + VI_{c,urban}^{norm} }}{2}$$

(4.54a)

$$E_{c}^{Q,norm} = { }\frac{{E_{c,rural}^{Q,norm} + E_{c,urban}^{Q,norm} }}{2}$$

(4.54b)

$$\Delta E_{c}^{norm} = { }\frac{{\Delta E_{c,rural}^{norm} + \Delta E_{c,urban}^{norm} }}{2}$$

(4.54c)

$$Loading_{c}^{DTR,avg,norm} = { }\frac{{Loading_{c,rural}^{DTR,avg,norm} + Loading_{c,urban}^{DTR,avg,norm} }}{2}$$

(4.54d)

where $VI_{c}^{norm}$, $E_{c}^{Q,norm}$, $\Delta E_{c}^{norm}$, $Loading_{c}^{DTR,avg,norm}$ are the normalised and superimposed values of the evaluation criteria for the control setup c, which are plotted in the common evaluation hexagon.

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Schultis, DL., Ilo, A. (2022). Volt/var Chain Process*. In: A Holistic Solution for Smart Grids based on LINK– Paradigm. Power Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-81530-1_4

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DOI: https://doi.org/10.1007/978-3-030-81530-1_4
Published: 19 November 2021
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-81529-5
Online ISBN: 978-3-030-81530-1
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Appendices

Appendix

A.4.1 Behaviour of Different Link-Grids

4.2.1 A.4.1.1 Spiky Load Profiles

CP level

LV level

4.2.2 A.4.1.2 Smoothed Load Profiles

CP level

LV level

MV level

A.4.2 Volt/var Control Parametrisation

4.3.1 A.4.2.1 Impact of Q(U) Parametrisation

4.3.2 A.4.2.2 Impact of OLTC Parametrisation

A.4.3 Volt/var control evaluation

4.4.1 A.4.3.1 Definition of Technical Evaluation Criteria

4.4.2 A.4.3.2 Calculation of the Evaluation Hexagon Data

Calculation of the separate hexagons

Calculation of the common hexagon

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