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Laboratório de Eletrônica Industrial e Energias Renováveis

Research Group

Prof. Ricardo Lúcio Março / 2017Prof. Ricardo Lúcio Outubro / 2018 1

Virtual Impedance Approach for Power Flow Control

Ricardo LúcioLEIER/CT/DEE/UFRN

http://www.leier.ct.ufrn.br



Outline

1. Motivation

2. DG Power Converters

3. Power Flow Control

4. Virtual Impedance Concept

5. Main Features of Virtual Impedance Approach

6. Voltage Grid Supporting for Grid-feeding converters



Motivation

• The modern power system organized by microgrids has improvedreliability, sustainability, and efficiency;

• Distributed generation based on renewable energy and energy storagehas planed new horizons;

• Renewable energy systems are non-dispatchable sources of energywhich could result in stability issues;

• DG systems interconnect to the grid via power converters which enablespower flow control.

• Microgrids have higher R/X ratio producing power flow coupling termsreducing the effectiveness of conventional droop control techniques;

• Virtual impedance concept could modify the R/X ratio of microgrids andovercome the drawbacks due to the P/Q couplings terms



Classification of DG Power Converters• DG converters can be classified as grid-feeding, grid-forming and grid-

supporting.

Grid-feeding injects activeand reactive power to theenergized grid.

Grid-forming sets voltageamplitude and frequency ofmicrogrid.

Controlled current sourcewith high internal impedance.

Controlled voltage source withlow internal impedance.

- Grid-forming can operate in both grid-connected or islanded modes.



Classification of DG Power Converters• Grid-supporting includes the features of grid feeding and grid forming

converters.

Voltage and frequency supporting can be included in CCS-based grid-supporting.

The main objective is todeliver proper PQ flow.

Contribution to theregulation of the gridfrequency and voltage.

- CVS grid-supporting can not operate in islanded mode.

Requires at least one gridforming to operate.



Classification of DG Power Converters• Grid-supporting includes the features of grid feeding and grid forming

converters.

Active and reactive power regulation can be included in CVS-based grid-supporting.

The main objective is toregulate grid voltage andfrequency

Contribution to the PQpower sharing among grid-forming power converters.

- CVS Grid-forming can operate in both grid-connected or islanded modes.



Power Flow Control• In general, the power flow control between DGs and microgrids employs

droop control approaches.

Considering the use of grid-forming converters, the active and reactivepowers delivered are

𝑃𝑓 =𝑉𝑓

𝑅𝑔2 + 𝑋𝑔

2 𝑅𝑔 𝑉𝑓 − 𝑉𝑔𝑐𝑜𝑠𝛿 + 𝑋𝑔𝑉𝑔𝑠𝑖𝑛𝛿

𝑄𝑓 =𝑉𝑓

𝑅𝑔2 + 𝑋𝑔

2 −𝑅𝑔𝑉𝑔𝑠𝑖𝑛𝛿 + 𝑋𝑔 𝑉𝑓 − 𝑉𝑔𝑐𝑜𝑠𝛿

• Inductive grid:

𝑃𝑓 ≈𝑉𝑓

𝑋𝑔𝑉𝑔𝑠𝑖𝑛𝛿 ⇒ 𝛿 ≈

𝑋𝑔𝑃𝑓

𝑉𝑓𝑉𝑔

𝑄𝑓 ≈𝑉𝑓

𝑋𝑔𝑉𝑓 − 𝑉𝑔𝑐𝑜𝑠𝛿 ⇒ 𝑉𝑓 − 𝑉𝑔 ≈

𝑋𝑔𝑄𝑓

𝑉𝑓

Relationship between powerangle and active power, as well as,voltage difference and reactivepower.



Power Flow Control• Based on the relationships P- and Q-V, it is possible to define the

following droop control expressions:

𝑓𝑔 − 𝑓𝑔∗ = −𝐷𝑝 𝑃𝑔 − 𝑃𝑔

∗

Droop functions are valid only for inductive networks, they fail formicrogrids (high R/X ratio);

Poor voltage regulation of critical loads with the application of reactivepower control;

Load-dependent frequency deviation; Poor power sharing among DGs due to unequal output impedances

between DGs and loads.

𝑉𝑔 − 𝑉𝑔∗ = −𝐷𝑞 𝑄𝑔 − 𝑄𝑔

∗

• Conventional droop control approaches present the following drawbacks:



Power Flow Control• Different control methods can be used for improving the power flow

control and overcome the PQ coupling terms.

1. Voltage Power Droop (VPD)/Frequency Reactive Boost (FQB);2. Reactive Power-Differential Q-V’ Droop Control;3. Angle Droop Control;4. Virtual Frame Transformation;5. Virtual Impedance Method;6. Adaptive Droop Control;7. Virtual Inertia-Based Droop Control.

• Improved droop methods:

Virtual impedance can modify the profile of the gird impedance; Adaptive droop approaches can overcome possible grid impedance

variations; Virtual inertia-based droop control can contribute to microgrid stability.



Virtual Impedance Concept• Two virtual impedance loops can be employed to shape the DG output

impedance:1. Inner Virtual Impedance, which modifies the output of

current/voltage regulator;2. Outer Virtual Impedance, which modifies the reference current

voltage of the Dg control system.• Considering the DG based on grid-feeding control structure:



Virtual Impedance Concept• Block diagram of grid-feeding current control loop:

• Blocks Yg(s) and Yf(s) are the open-loop transfer functions of DG outputcurrents and output admittance of the LCL filter;

• Gd(s) models the voltage source converter (VSC);• Yv(s) and Gv(s) are the outer and inner virtual impedance;• Ri(s) is the transfer function of the current controller.



Virtual Impedance Concept• The closed-loop transfer function without virtual impedance approaches is

𝐼𝑔𝑠 𝑠 = 𝑌𝑓𝑐 𝑠 𝐼𝑔

𝑠∗ 𝑠 − 𝑌𝑔𝑐 𝑠 𝑉𝑔𝑠 𝑠 ,

𝑌𝑔𝑐 𝑠 =𝑌𝑔 𝑠

1 + 𝑅𝑖 𝑠 𝐺𝑑 𝑠 𝑌𝑓 𝑠,

𝑌𝑓𝑐 𝑠 =𝑅𝑖 𝑠 𝐺𝑑 𝑠 𝑌𝑓 𝑠

1 + 𝑅𝑖 𝑠 𝐺𝑑 𝑠 𝑌𝑓 𝑠,

where:

is the closed-loop transfer functionof the DG output current, and:

refers to the closed-loop system admittance.

• The voltage source inverter is modeled by the Padé approximation given by

𝐺𝑑 𝑠 =2 − 𝜏𝑎𝑠

2 + 𝜏𝑎𝑠, in which 𝜏𝑎 = 1.5𝑇𝑠.



Virtual Impedance Concept• The insertion of the outer virtual impedance block Yv(s) results in


𝑠∗ 𝑠 −

𝑌𝑔𝑐 𝑠 + 𝑌𝑓𝑐(𝑠)𝑌𝑣(𝑠) 𝑉𝑔𝑠 𝑠

• The outer virtual admittancecontroller Yv(s) causes nomodifications on Yfc(s).

• Yv(s) synthesizes and admittance𝑌𝑣𝑐 𝑠 = 𝑌𝑓𝑐 𝑠 𝑌𝑣 𝑠 .

• Yvc(s) corresponds to a newcircuit branch interconnected inparallel to the systemadmittance.



Virtual Impedance Concept• Physical interpretation of the virtual impedance insertion in the DG

Virtual impedance modifies the standard reference current Ig* by

inserting a parallel branch YfcYv; The effect of the virtual impedance correspond to add a Ig = Iv to the

DG controlled output current. The effectiveness of virtual impedance depends on the VSI power

availability.𝐼𝑔 − 𝐼𝑣 = 𝐼𝑔

′ < 𝐼𝑔(𝑟𝑎𝑡𝑖𝑛𝑔)



Virtual Impedance Concept• The transfer function of the DG control system with the inclusion of inner

virtual impedance results in


𝑠∗ 𝑠 − 𝑌𝑔𝑐 𝑠 𝑉𝑔𝑠 𝑠 ,

𝑌𝑓𝑐 𝑠 =𝑅𝑖 𝑠 𝐺𝑑 𝑠 𝑌𝑓 𝑠

1 + 𝑅𝑖 𝑠 + 𝐺𝑣(𝑠) 𝐺𝑑(𝑠)𝑌𝑓 𝑠,

where:

is the closed-loop transfer functionof the DG output current, and:

𝑌𝑔𝑐 𝑠 =𝑌𝑔 𝑠

1 + 𝑅𝑖 𝑠 + 𝐺𝑣(𝑠) 𝐺𝑑(𝑠)𝑌𝑓 𝑠,

refers to the closed-loop system admittance.

The characteristic polynomial of the closed-loop transfer function was modified by the inclusion of term 𝐺𝑣𝐺𝑑𝑌𝑓



Features of Virtual Impedance Approach• The use of virtual impedance can contribute for improving the DG power

flow control and stability, which main features are

1. Virtual impedance implementation corresponds to the execution ofcontrol algorithm or direct complex manipulations;

2. Derivative procedure employed by implementing virtual reactance canbe avoided by using steady-state approach.

3. Reactance elements can be implemented without losses to the DG;4. Positive and negative resistances, capacitance and inductance can be

implemented;5. The resultant interconnection grid impedance can be decoupled;

• In general, the outer virtual impedance is used for power flow control andshape the interconnection grid impedance.

Inner virtual impedance can be also useful for emulating virtual inertia and provide damping effects.



Voltage Supporting for Grid-feeding Converters• Grid-feeding converters are controlled current sources based on LCL-VSC

and these main function is to deliver power to the grid.

LCL-VSC DG systems can also provide voltage supporting to the grid.

• Based on the equivalent circuit of LCL-VSC, it is possible to define asuitable virtual impedance YfcYv to driven the PCC voltage.

• For voltage supporting, it is possible to use virtual inductance or virtualcapacitance.

The value of the required virtual inductance/capacitance depends on the knowledge of PCC equivalent impedance.





• If the virtual capacitance is the choice for the implementation, its valuecan determined as

𝐶𝑣 =𝑞𝑟𝑒𝑞

3𝑉𝑔𝑛2 𝜔𝑔

with - limit imposed by the VSC power rating.𝑞𝑟 < 𝑆𝑟2 − 𝑝𝑔

2

Simple solution but ineffective due the inherent intermittent behavior of the microgrids.





• The uncertainties behavior of the microgrid could be overcome by usingdroop functions as follows

𝐶𝑣,𝑚𝑎𝑥 =𝑞𝑚𝑎𝑥

3𝑉𝑔𝑛2 𝜔𝑔

𝑞𝑚𝑎𝑥 = 𝑆𝑟2 − 𝑝𝑔

2

The voltage error can be normalized and associated to the grid codes.

𝑉𝑔 − 𝑉𝑔∗ = −𝐷𝑞 𝐶𝑣,𝑚𝑎𝑥 − 𝐶𝑣,𝑚𝑖𝑛

With , restricted to the power limit

• The use of the power availability of LCL-VSC addresses adaptive feature tothe virtual impedance control approach.

The implementation of the virtual capacitance by using the PCC voltage asinput results in derivative calculus procedure.

To overcome the derivative procedure, steady-state complex manipulationcan be employed.



Voltage Supporting for Grid-feeding Converters• Block diagram of the DG control system of LCL-VSC Dg with voltage grid

supporting.

In which, the virtual impedance block realize the following calculus

𝐼𝑣𝑠 = 𝑗𝜔𝑔𝐶𝑣𝑉𝑔

𝑠

The control system is implemented on the stationary reference frame.



Final Comments• The following control approaches can be employed for implementing the

virtual impedance for power flow control:

Model-based control schemes:• Adaptive control approaches – MRAC and APPC.• Variable structure control strategies – VS-MRAC and VS-APPC.

Non standard control schemes:• Variable control structures – Sliding Mode – SM.• Hybrid control strategies – SM-PI and DSM-PI.

• For accomplishing the required effectiveness of power flow control, it ispossible to integrate grid impedance estimation techniques like:

Grid impedance estimation schemes:• Passive approaches – Phasor estimation, RLS, Kalman filter.• Active approaches – signal injection with DFT and SDWPT analysis.



•Thank You!

•Questions?

virtual impedance approach for power flow controlcoral.ufsm.br/sepoc/sepoc2018/arquivos/... ·...

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