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Integrated control design of converters in power electronics embedded grids

Prof. Pericle Zanchetta

Power Electronics, Machines and control (PEMC) Group Faculty of Engineering

University of Nottingham – UK

ENER 2019 – University of Talca, Chile

Research Team

Prof. Pericle Zanchetta Prof. Patrick Wheeler Dr. Andrea Formentini

David Dewar

PhD student

Kang Li

PhD student

Power electronics in microgrids

• Large penetration of renewables in

the power system • Several power converters operating

in the same network • Each power converter has local

intelligence and control

The complex interactions

between control loops require

accurate design methods

More Electric Aircraft power distribution

The electrical system on aircraft

is supplied by a fixed voltage,

variable frequency generator.

AC and DC grids at different

voltage levels are generated

from the main distribution grid

by means of power electronics

systems.

Highlighted, the 400Hz grid is

main supply to many non-

propulsive loads, which need

more power converters.

Proposed solution:

Design system controls with full consideration to all system dynamics and sub-

system interactive behaviour.

Optimal Performance across sub-systems achieved.

Mitigation of sub-system interactions.

Reduction in required cross-controller communication through decentralized

approach.

These power electronics subsystems tend to interact with each other in an

undesired way.

To mitigate interactions, usually large passive filters are installed between

subsystems. THIS INCREASES WEIGHT, VOLUME and DECREASES

EFFICIENCY

Integrated Global control design

Analysed Test System (aircraft 400Hz)

A standard 3-phase active Voltage Source

Inverter (VSI).

LCR Filter connected to the output, and fed

by solid DC source on its input.

This generates the 3-phase grid @ Nominal

400Hz

A standard 3-phase active front end (AFE)

rectifier.

LR filter on 3-phase input. DC-Link

capacitor across output terminals.

The load (RL) can consist of either resistive

loads or a Constant Power Loads (CPL).

VSI System Modelling

In AC systems, the common approach to controller

design is to use the DQ reference frame.

The expressions for the VSI in DQ frame can be

represented in the state-space as:

vsi vsi vsi vsi vsi vsi vsi

vsi vsi vsi

x A x B u G d

y C x

d

vsi

q

mu

m

ad

vsi

aq

Id

I

𝑥𝑣𝑠𝑖 = 𝐼𝑖𝑑 𝑉𝑐𝑑 𝐼𝑖𝑞 𝑉𝑐𝑞 𝑇

AFE System Modelling

The expressions for the AFE in DQ frame can

be represented in the state-space as indicated

below

𝑥 𝑎𝑓𝑒 = 𝐴𝑎𝑓𝑒𝑥𝑎𝑓𝑒 + 𝐵𝑎𝑓𝑒𝑢𝑎𝑓𝑒 + 𝐺𝑎𝑓𝑒𝑑𝑎𝑓𝑒

𝑦𝑎𝑓𝑒 = 𝐶𝑎𝑓𝑒𝑥𝑎𝑓𝑒

cd

afe

cq

Vd

V

𝑥𝑎𝑓𝑒 = 𝐼𝑎𝑑 𝐼𝑎𝑞 𝑉𝑑𝑐𝑎𝑇

𝑢𝑎𝑓𝑒 =𝑝𝑑𝑝𝑞

H2 Global Optimization

A multivariable state feedback approach, and in particular H2 Optimal Control, was

chosen as the control design method for such a system with many interacting states.

1. H2 control is relatively simple to tune, in order to get the desired dynamic

performance across all states.

2. It has very close roots to Robust controls in that the use of Lyapunov functions are

employed to verify stability of the system. Also a version of this controller

synthesis called H2/H∞ could be applied if further system robustification is desired.

3. Wide variety of mathematical software tools can be used to synthesise this

control.

4. Design is simple and well understood. To the designer, only the knowledge of the

state-space system is required to develop this control.

H2 Global Optimization Controller Synthesis

P state-space plant of the system

to be controlled.

K global optimal controller to be

found.

x state of the system

u system inputs

y system outputs

w plant disturbances

z performance output

During the design, disturbances are generally

neglected, thus D11 , D21 are set to 0.

D22 is the feedforward matrix, and as no

feedforward is incorporated, it is also set to 0.

B1 is disturbance input matrix. As all states can be

influenced, it is therefore the identity matrix.

C2 is a matrix which describes all measurable

states. As all states can be measured directly,

this is made an identity matrix.

C1 & D12 are the tuning terms.

H2 Global Optimization Integral States and Inputs

𝑥 = 𝐼𝑖𝑑 𝑉𝑐𝑑 𝐼𝑖𝑞 𝑉𝑐𝑞 𝐼𝑎𝑑 𝐼𝑎𝑞 𝑉𝑑𝑐𝑎 𝝎𝑽𝒄𝒅𝝎𝑽𝒄𝒒

𝝎𝑰𝒊𝒒 𝝎𝑽𝒅𝒄𝒂

𝑇

It is important for systems to achieve zero-steady state error for critical control terms.

Integral states (ωx) are then incorporated as system states.

These states are used to force the smallest errors to the reference demands to be

corrected by the control over time.

𝑢 = 𝑚𝑑 𝑚𝑞 𝑝𝑑 𝑝𝑞

The inputs to the system are the modulation indexes defined as such in DQ frame

m → VSI duty, p → AFE Duty.

The aim of the optimization is to produce a

stable set of feedback gains to minimize

the effects an outside disturbance has on

overall the performance on the system.

H2 Controller Design – Problem Matrices

𝐴 =𝐴𝑣𝑠𝑖 𝐴𝑐𝑣

𝐴𝑐𝑎 𝐴𝑎𝑓𝑒

Avsi and Aafe details the state equation of the VSI and AFE, including integral

states for zero steady state error

Acv and Aca details the coupling terms between VSI and AFE

Bvsi and Bafe details the input equations equation of the VSI and AFE

𝐵2 =𝐵𝑣𝑠𝑖 00 𝐵𝑎𝑓𝑒

H2 Controller Design – Notional System

The control scheme for the H2 is nothing special as opposed to other controllers.

However, to avoid direct communication being required between converters, a

decentralized controller is a must.

Therefore, K in the optimization is constrained to take the form as shown.

This ensures each control is optimized to the system as a whole by H2 , but also each

control is dependant only on its states.

𝐾 =𝑲𝑽𝑺𝑰 00 𝑲𝑨𝑭𝑬

Experimental results

VSI AFE

C 10µF Cdc 100µF

R 300mΩ Ra 0.8Ω

L 1mH La 565µH

Vdci 290V Pl 1kW

Reference Values

Vcd-ref 100* 2 V Iaq-ref 0A

Vcq-ref 0V Vdc-ref 400V

fswitching 10kHz

fsample 20kHz

AC Grid Frequency

f 400Hz

H2 Controller Design Experimental Performance

At 0.05s, a 1kW step load is applied

across the AFE output terminals.

The dynamics of the H2 control in the

DQ frame are shown to be very fast,

with only slight overshoot across each

of the states.

1. DC-Link voltage dropped only 13V.

2. VSI voltages has a minor transient

of 3V, but the grid voltages are held

stiff. As expected from grid

generator.

3. The whole system reaches

equilibrium subject to large

disturbance after only 5ms.

System Scalability

The H2 controller synthesis allows easy integration of multiple other sub-systems to

be optimized to the global system

Requirements:

Expansion of states to incorporate new subsystem behaviour, and new inputs to

the system (Simple expansion of A and B matrices)

Expansion of the gain matrix K - Simple addition of new constraints to K for an

additional independent controller

System Scalability – Scaled Up Matrices

Green terms define new AFE being incorporated onto the grid

Please note for simplicity, the PLL has not been included in these state equations.

System Scalability – Performance

Systems can

run

independently

Little

interaction

between

subsystems

Fast dynamic

responses

Step loads on AFE1 of 1kW at 0.011s, and on AFE2 of 500W at 0.041s.

System Scalability – Comparison with PI

Vcd and Vcq

experience

noticeable

transient

fluctuations

interactions

can be

observed

across all

states during

transients

Clearly show

H2

improvement Step loads on AFE1 of 1kW at 0.011s, and on AFE2 of 500W at 0.041s.

Optimal H2 Controller Synthesis by System Identification

Optimization of converter in an a

pre-existent grid

System parameters could

be unknown

Other converter controllers

may have unknown

performances

Likely industrial implementation of the H2 Decentralized Controller

System identification

Newly installed converter can send out voltage and current perturbations

Analyse the systems transfer function characteristics to estimate a state-space

representation of system

Optimize controller using H2 based on estimated system response.

Optimal H2 Controller Synthesis by System Identification

Pseudo Random binary signals are injected from the VSI into the AFE to ideally

simulate an infinite frequency range. AFE input voltages and currents are recorded.

Transfer functions including cross-coupling terms are then obtained

State-space representations of the Transfer functions can then be extrapolated.

Optimal H2 Controller Synthesis by System Identification - Performance

Control synthesised from the

identification of the

experimental setup

outperforms the control

optimized with the nominal

model.

Where commercial system

parameters are not be

available, the process of

system identification allows

global optimal controls to be

developed when integrating

converters into unknown

electrical systems. Blue – VSI independently optimized H2 Red – VSI optimized with Nominal AFE

Yellow – VSI optimized with identified AFE

Conclusions

The H2 Optimization Technique has shown performance improvement over traditional

control methods

Increased Robustness

Faster Dynamic Performance

Maintain stability and performance under smaller passive filters (System

weight reduction)

Expandability to additional sub-systems and loads

Having developed a working system, one can easily expand on the optimization

matrices to incorporate additional subsystems

Each subsystem shares the effects of interaction mitigation and Increased

Performance and robustness

Applicability on a larger size grid

Inclusion of PLL in the control optimization

Proved implementation into real practical applications, with impedance estimation