Distributed Control of Inverter-Based Power Grids · 2019-05-29 · Distributed Control of Inverter-Based Power Grids John W. Simpson-Porco ESIF Workshop: Frontiers in Distributed

Distributed Control of Inverter-Based Power Grids

John W. Simpson-Porco

ESIF Workshop: Frontiers in Distributed Optimization & Control of Sustainable Power Systems

Co-Authors: Florian Dörfler (ETH) and Francesco Bullo (UCSB)

January 26th, 2016

(commons.wikimedia.org, mapssite.blogspot.com)

What are the control strategies?

Electricity & The Power Grid

Electricity is the foundation of technological civilization

Hierarchical grid: generate/transmit/consume

Challenges: multi-scale, need reliability + performance

1 / 22

What are the control strategies?

Electricity & The Power Grid

Electricity is the foundation of technological civilization

Hierarchical grid: generate/transmit/consume

Challenges: multi-scale, need reliability + performance

1 / 22 (commons.wikimedia.org, mapssite.blogspot.com)

http:mapssite.blogspot.comhttp:commons.wikimedia.org

What are the control strategies?

Electricity & The Power Grid

Electricity is the foundation of technological civilization

Hierarchical grid: generate/transmit/consume

Challenges: multi-scale, need reliability + performance

1 / 22 (commons.wikimedia.org, mapssite.blogspot.com)

http:mapssite.blogspot.comhttp:commons.wikimedia.org

Electricity & The Power Grid

Electricity is the foundation of technological civilization

Hierarchical grid: generate/transmit/consume

Challenges: multi-scale, need reliability + performance

What are the control strategies?

1 / 22 (commons.wikimedia.org, mapssite.blogspot.com)

http:mapssite.blogspot.comhttp:commons.wikimedia.org

Bulk Power System Control Architecture & Objectives Hierarchy by spatial/temporal scales and physics

3. Tertiary control (offline) Goal: optimize operation Strategy: centralized & forecast

2. Secondary control (minutes) Goal: restore frequency Strategy: centralized

1. Primary control (real-time) Goal: stabilize freq. and volt. Strategy: decentralized

Q: Is this hierarchical architecture still appropriate

for new applications?

2 / 22

Bulk Power System Control Architecture & Objectives Hierarchy by spatial/temporal scales and physics

3. Tertiary control (offline) Goal: optimize operation Strategy: centralized & forecast

2. Secondary control (minutes) Goal: restore frequency Strategy: centralized

1. Primary control (real-time) Goal: stabilize freq. and volt. Strategy: decentralized

Q: Is this hierarchical architecture still appropriate

for new applications?

2 / 22

Bulk Power System Control Architecture & Objectives Hierarchy by spatial/temporal scales and physics

3. Tertiary control (offline) Goal: optimize operation Strategy: centralized & forecast

2. Secondary control (minutes) Goal: restore frequency Strategy: centralized

1. Primary control (real-time) Goal: stabilize freq. and volt. Strategy: decentralized

Q: Is this hierarchical architecture still appropriate

for new applications?

2 / 22

Bulk Power System Control Architecture & Objectives Hierarchy by spatial/temporal scales and physics

3. Tertiary control (offline) Goal: optimize operation Strategy: centralized & forecast

2. Secondary control (minutes) Goal: restore frequency Strategy: centralized

1. Primary control (real-time) Goal: stabilize freq. and volt. Strategy: decentralized

Q: Is this hierarchical architecture still appropriate

for new applications?

2 / 22

(Electronic Component News)

Two Major Trends Trend 1: Physical Volatility

(New York Magazine)

1

2

bulk distributed generation, regulation (33 by 2020 in CA, GEA in ON)

growing demand & old infrastructure

⇒ lowered inertia & robustness margins

sensors, actuators & grid-edge resources (PMUs, FACTS, flexible loads)

control of cyber-physical systems

Trend 2: Technological Advances

1

2

⇒ cyber-coordination layer for smart grid

3 / 22

1

Two Major Trends Trend 1: Physical Volatility

(New York Magazine)

1

2

bulk distributed generation, regulation (33 by 2020 in CA, GEA in ON)

growing demand & old infrastructure

⇒ lowered inertia & robustness margins

Trend 2: Technological Advances

sensors, actuators & grid-edge resources (PMUs, FACTS, flexible loads)

2 control of cyber-physical systems

(Electronic Component News) 3 / 22

⇒ cyber-coordination layer for smart grid

Outline

Introduction & Project Samples

Distributed Control in Microgrids Primary Control Tertiary Control Secondary Control

3 / 22

Relevant Publications

J. W. Simpson-Porco, F. Dörfler, and F. Bullo. Voltage stabilization in microgrids via quadratic droop control. IEEE

Transactions on Automatic Control, May 2015. Note: Conditionally accepted.

J. W. Simpson-Porco, F. Dörfler, and F. Bullo. Voltage Collapse in Complex Power Grids. February 2015. Note:

Accepted.

J. W. Simpson-Porco, Q. Shafiee, F. Dörfler, J. C. Vasquez, J. M. Guerrero, and F. Bullo. Secondary Frequency and

Voltage Control in Islanded Microgrids via Distributed Averaging. IEEE Transactions on Industrial Electronics, 62(11):7025-7038, 2015.

F. Dörfler, J. W. Simpson-Porco, and F. Bullo. Breaking the Hierarchy: Distributed Control & Economic Optimality in

Microgrids. IEEE Transactions on Control of Network Systems. Note: To Appear.

J. W. Simpson-Porco, F. Dörfler, and F. Bullo. Synchronization and Power-Sharing for Droop-Controlled Inverters in

Islanded Microgrids. Automatica, 49(9):2603-2611, 2013.

Research supported by

4 / 22

Project Samples: Voltage Control/Collapse Quadratic Droop Control (TAC) Voltage Collapse (Nat. Comms.)

Optimal Distrib. Volt/Var (CDC) Collapse W.A.M. (TSG)

5 / 22

Outline

Introduction & Project Samples

Distributed Control in Microgrids Primary Control Tertiary Control Secondary Control

5 / 22

Microgrids

Structure • low-voltage, small footprint • grid-connected or islanded • autonomously managed

Applications • hospitals, military, campuses, large

vehicles, & isolated communities

Benefits • naturally distributed for renewables • scalable, efficient & redundant

Operational challenges • low inertia & uncertainty • plug’n’play & no central authority

6 / 22

Microgrids

Structure • low-voltage, small footprint • grid-connected or islanded • autonomously managed

Applications • hospitals, military, campuses, large

vehicles, & isolated communities

Benefits • naturally distributed for renewables • scalable, efficient & redundant

Operational challenges • low inertia & uncertainty • plug’n’play & no central authority

6 / 22

• active power: Pi =�

j BijEiEj sin(θi − θj) + GijEiEj cos(θi − θj)• reactive power: Qi = −

�j BijEiEj cos(θi − θj) + GijEiEj sin(θi − θj)

Modeling I: AC circuits

1

2

3

4

5

6

Loads ( ) and Inverters ( )

Quasi-Synchronous: ω c ω∗ ⇒ Vi = Ei e jθi

Load Model: Constant powers Pi ∗ , Q∗ i

Coupling Laws: Kirchoff and Ohm: Yij = Gij + jBij

Line Characteristics: Gij /Bij = const. (today, lossless Gij = 0)

Decoupling: Pi ≈ Pi (θ) & Qi ≈ Qi (E ) (normal operating conditions)

7 / 22

Modeling I: AC circuits

1

2

3

4

Loads ( ) and Inverters ( )

Quasi-Synchronous: ω c ω∗ ⇒ Vi = Ei e jθi

Load Model: Constant powers Pi ∗ , Q∗ i

Coupling Laws: Kirchoff and Ohm: Yij = Gij + jBij

5 Line Characteristics: Gij /Bij = const. (today, lossless Gij = 0)

6 Decoupling: Pi ≈ Pi (θ) & Qi ≈ Qi (E ) (normal operating conditions)

• active power: Pi = �

j Bij Ei Ej sin(θi − θj ) + Gij Ei Ej cos(θi − θj ) • reactive power: Qi = −

� j Bij Ei Ej cos(θi − θj ) + Gij Ei Ej sin(θi − θj )

7 / 22

• active power: Pi =�

j BijEiEj sin(θi − θj) + GijEiEj cos(θi − θj)• reactive power: Qi = −

�j BijEiEj cos(θi − θj) + GijEiEj sin(θi − θj)

Modeling I: AC circuits

1

2

Loads ( ) and Inverters ( )

Quasi-Synchronous: ω c ω∗ ⇒ Vi = Ei e jθi

3 Load Model: Constant powers Pi ∗ , Q∗ i

4

5

6

Coupling Laws: Kirchoff and Ohm: Yij = Gij + jBij

Line Characteristics: Gij /Bij = const. (today, lossless Gij = 0)

Decoupling: Pi ≈ Pi (θ) & Qi ≈ Qi (E ) (normal operating conditions)

7 / 22

Modeling I: AC circuits

1

2

3

4

5

6

Loads ( ) and Inverters ( )

Quasi-Synchronous: ω c ω∗ ⇒ Vi = Ei e jθi

Load Model: Constant powers Pi ∗ , Q∗ i

Coupling Laws: Kirchoff and Ohm: Yij = Gij + jBij

Line Characteristics: Gij /Bij = const. (today, lossless Gij = 0)

Decoupling: Pi ≈ Pi (θ) & Qi ≈ Qi (E ) (normal operating conditions)

• trigonometric active power flow: Pi (θ) = �

j Bij sin(θi − θj ) • quadratic reactive power flow: Qi (E ) = −

� j Bij Ei Ej

7 / 22

ωi = ufreqi , τi Ėi = u

volti

Modeling II: Inverter-interfaced sources also applies to frequency-responsive loads

Power inverters are . . .

interface between AC grid and DC or variable AC sources

operated as controllable ideal voltage sources

}DC }PWM LCL }Assumptions:

• Fast, stable inner/outer loops (voltage/current/impedance)

• Good harmonic filtering • Balanced 3-phase operation

8 / 22

Modeling II: Inverter-interfaced sources also applies to frequency-responsive loads

Power inverters are . . .

interface between AC grid and DC or variable AC sources

operated as controllable ideal voltage sources

ωi = ufreq i , τi Ėi = u

volt i

Eei(θ+ωt)

}DC }PWM LCL }Assumptions:

• Fast, stable inner/outer loops (voltage/current/impedance)

• Good harmonic filtering • Balanced 3-phase operation

8 / 22

Open-Loop System & Control Objectives Frequency Open-Loop Voltage Open-Loop

Inverter Dynamics (i ∈ I):Inverter Dynamics (i ∈ I):

ωi = θ̇i = ufreq i

Pi (θ) = Bij sin(θi − θj )

j

τi Ėi = u volt i

Qi (E ) = − Bij Ei Ej

j

Power Balance: (i ∈ L)Power Balance (i ∈ L):

0 = P ∗ i −

j Bij sin(θi − θj ) 0 = Q ∗ i +

j Bij Ei Ej

Primary Control Objectives: 1

2

3

Stabilization: Ensure stable frequency/voltage dynamics

Balance: Balance supply/demand for variable loads

Load Sharing: Power injections proportional to unit capacities 9 / 22

Open-Loop System & Control Objectives Frequency Open-Loop Voltage Open-Loop

Inverter Dynamics (i ∈ I):Inverter Dynamics (i ∈ I):

ωi = θ̇i = ufreq i

Pi (θ) = Bij sin(θi − θj )j

τi Ėi = u volt i

Qi (E ) = − Bij Ei Ejj

Power Balance: (i ∈ L)Power Balance (i ∈ L):

0 = P ∗ i − j Bij sin(θi − θj ) 0 = Q ∗ i + j

Bij Ei Ej

Primary Control Objectives: 1

2

3

Stabilization: Ensure stable frequency/voltage dynamics

Balance: Balance supply/demand for variable loads

Load Sharing: Power injections proportional to unit capacities 9 / 22

Open-Loop System & Control Objectives Frequency Open-Loop Voltage Open-Loop

Inverter Dynamics (i ∈ I):Inverter Dynamics (i ∈ I):

ωi = θ̇i = ufreq i

Pi (θ) = Bij sin(θi − θj )j

τi Ėi = u volt i

Qi (E ) = − Bij Ei Ejj

Power Balance: (i ∈ L)Power Balance (i ∈ L):

0 = P ∗ i − j Bij sin(θi − θj ) 0 = Q ∗ i + j

Bij Ei Ej

Primary Control Objectives:

Stabilization: Ensure stable frequency/voltage dynamics

Balance: Balance supply/demand for variable loads

Load Sharing: Power injections proportional to unit capacities

1

2

3

9 / 22

Open-Loop System & Control Objectives Frequency Open-Loop Voltage Open-Loop

Inverter Dynamics (i ∈ I):Inverter Dynamics (i ∈ I):

ωi = θ̇i = ufreq i

Pi (θ) = Bij sin(θi − θj )j

τi Ėi = u volt i

Qi (E ) = − Bij Ei Ejj

Power Balance: (i ∈ L)Power Balance (i ∈ L):

0 = P ∗ i − j Bij sin(θi − θj ) 0 = Q ∗ i + j

Bij Ei Ej

Primary Control Objectives: 1

2

3

Stabilization: Ensure stable frequency/voltage dynamics

Balance: Balance supply/demand for variable loads

Load Sharing: Power injections proportional to unit capacities 9 / 22

Frequency Droop Control

ωi = ω∗ −miPi (θ)

Primary Droop Control “Grid-forming” decentralized control

Key Idea: emulate generator speed & AVR control

10 / 22

Primary Droop Control “Grid-forming” decentralized control

Key Idea: emulate generator speed & AVR control

Frequency Droop Control Voltage Droop Control

ωi = ω∗ − mi Pi (θ) τi Ėi = −(Ei − E ∗) − ni Qi (E )

10 / 22

Primary Droop Control “Grid-forming” decentralized control

Key Idea: emulate generator speed & AVR control

Frequency Droop Control Quad. Voltage Droop Control

ωi = ω∗ − mi Pi (θ) τi Ėi = −Ei (Ei −E ∗)−ni Qi (E )

10 / 22

� Spring Network Interpretations of Equilibria

Frequency Droop Control Voltage Droop Control

0 = P∗ i − j Bij sin(θi − θj ) �

0 = Qi ∗ + j Bij Ei Ej

11 / 22

� Spring Network Interpretations of Equilibria

Frequency Droop Control Voltage Droop Control

0 = P∗ i − j Bij sin(θi − θj ) �

0 = Qi ∗ + j Bij Ei Ej

11 / 22

Spring Network Interpretations of Equilibria

Frequency Droop Control Voltage Droop Control

0 = P∗ i − �

j Bij sin(θi − θj ) 0 = Q∗ i + �

j Bij Ei Ej

11 / 22

Spring Network Interpretations of Equilibria

Frequency Droop Control Voltage Droop Control

0 = P∗ i − �

j Bij sin(θi − θj ) 0 = Q∗ i + �

j Bij Ei Ej

11 / 22

Droop Control Stability Conditions Frequency Droop Control

0 = P ∗ i −

j Bij sin(θi − θj )

θ̇i = −mi

j Bij sin(θi − θj )

Theorem: Frequency Stability (JWSP, FD, & FB ’12)

∃! loc. exp. stable angle equilibrium θeq iff

(A†P)ij Bij

< 1

for all edges (i , j) of microgrid.

Voltage Droop Control

0 = Q ∗ i +

j Bij Ei Ej

τi Ėi = −Ei (Ei − E ∗ ) + ni

j Bij Ei Ej

Theorem: Voltage Stability (JWSP, FD, & FB ’15)

∃! loc. exp. stable voltage equilibrium point Eeq if

4 (E ∗)2 (B

−1 LL QL)i < 1

for all load nodes i of microgrid.

Tight and Sufficient Necessary and Sufficient 12 / 22

Droop Control Stability Conditions Frequency Droop Control

0 = P ∗ i − j Bij sin(θi − θj )

θ̇i = −mi j Bij sin(θi − θj )

Theorem: Frequency Stability (JWSP, FD, & FB ’12)

∃! loc. exp. stable angle equilibrium θeq iff

(A†P)ij Bij

< 1

for all edges (i , j) of microgrid.

Voltage Droop Control

0 = Q ∗ i + j Bij Ei Ej

τi Ėi = −Ei (Ei − E ∗ ) + ni j Bij Ei Ej

Theorem: Voltage Stability (JWSP, FD, & FB ’15)

∃! loc. exp. stable voltage equilibrium point Eeq if

4 (E ∗)2 (B

−1 LL QL)i < 1

for all load nodes i of microgrid.

Tight and Sufficient Necessary and Sufficient 12 / 22

Droop Control Stability Conditions Frequency Droop Control

0 = P ∗ i − j Bij sin(θi − θj )

θ̇i = −mi j Bij sin(θi − θj )

Theorem: Frequency Stability (JWSP, FD, & FB ’12)

∃! loc. exp. stable angle equilibrium θeq iff

(A†P)ij Bij

< 1

for all edges (i , j) of microgrid.

Voltage Droop Control

0 = Q ∗ i + j Bij Ei Ej

τi Ėi = −Ei (Ei − E ∗ ) + ni j Bij Ei Ej

Theorem: Voltage Stability (JWSP, FD, & FB ’15)

∃! loc. exp. stable voltage equilibrium point Eeq if

4 (E ∗)2 (B

−1 LL QL)i < 1

for all load nodes i of microgrid.

Tight and Sufficient Necessary and Sufficient 12 / 22

Droop Control Stability Conditions Frequency Droop Control

0 = P ∗ i − j Bij sin(θi − θj )

θ̇i = −mi j Bij sin(θi − θj )

Theorem: Frequency Stability (JWSP, FD, & FB ’12)

∃! loc. exp. stable angle equilibrium θeq iff

(A†P)ij Bij

< 1

for all edges (i , j) of microgrid.

Voltage Droop Control

0 = Q ∗ i + j Bij Ei Ej

τi Ėi = −Ei (Ei − E ∗ ) + ni j Bij Ei Ej

Theorem: Voltage Stability (JWSP, FD, & FB ’15)

∃! loc. exp. stable voltage equilibrium point Eeq if

4 (E ∗)2 (B

−1 LL QL)i < 1

for all load nodes i of microgrid.

Tight and Sufficient Necessary and Sufficient 12 / 22

Open Primary Control Problems

1 Coupled equilibrium and stability analysis

2 New controllers for Gij /Bij constant=

3 Basins of attraction

4 Limits of decentralized control

13 / 22

minimize θ∈Tn f (θ) =1

2 invertersαi [Pi (θ)]

2

subject to

load power balance: 0 = P∗i − Pi (θ)branch flow constraints: |θi − θj | ≤ γij < π/2inverter injection constraints: Pi (θ) ∈

�0,P i�

Variations: general strictly convex & differentiable cost.

Conventional: Offline, Centralized, Model & Load Forecast

Plug-and-play Microgrid: On-line, decentralized, no model, no forecasts

Result: Droop = decentralized primal algorithm for this problem.

Economic dispatch minimize the total cost of generation

14 / 22

Conventional: Offline, Centralized, Model & Load Forecast

Plug-and-play Microgrid: On-line, decentralized, no model, no forecasts

Result: Droop = decentralized primal algorithm for this problem.

Economic dispatch minimize the total cost of generation

minimize θ∈Tn f (θ) = 1 2 inverters

αi [Pi (θ)]2

subject to

load power balance: 0 = P ∗ i − Pi (θ) branch flow constraints: |θi − θj | ≤ γij < π/2 inverter injection constraints: Pi (θ) ∈

� 0, P i �

Variations: general strictly convex & differentiable cost.

14 / 22

Plug-and-play Microgrid: On-line, decentralized, no model, no forecasts

Result: Droop = decentralized primal algorithm for this problem.

Economic dispatch minimize the total cost of generation

minimize θ∈Tn f (θ) = 1 2 inverters

αi [Pi (θ)]2

subject to

load power balance: 0 = P ∗ i − Pi (θ) branch flow constraints: |θi − θj | ≤ γij < π/2 inverter injection constraints: Pi (θ) ∈

� 0, P i �

Variations: general strictly convex & differentiable cost.

Conventional: Offline, Centralized, Model & Load Forecast

14 / 22

Result: Droop = decentralized primal algorithm for this problem.

Economic dispatch minimize the total cost of generation

minimize θ∈Tn f (θ) = 1 2 inverters

αi [Pi (θ)]2

subject to

load power balance: 0 = P ∗ i − Pi (θ) branch flow constraints: |θi − θj | ≤ γij < π/2 inverter injection constraints: Pi (θ) ∈

� 0, P i �

Variations: general strictly convex & differentiable cost.

Conventional: Offline, Centralized, Model & Load Forecast

Plug-and-play Microgrid: On-line, decentralized, no model, no forecasts

14 / 22

Economic dispatch minimize the total cost of generation

minimize θ∈Tn f (θ) = 1 2 inverters

αi [Pi (θ)]2

subject to

load power balance: 0 = P ∗ i − Pi (θ) branch flow constraints: |θi − θj | ≤ γij < π/2 inverter injection constraints: Pi (θ) ∈

� 0, P i �

Variations: general strictly convex & differentiable cost.

Conventional: Offline, Centralized, Model & Load Forecast

Plug-and-play Microgrid: On-line, decentralized, no model, no forecasts

Result: Droop = decentralized primal algorithm for this problem.

14 / 22

centralized &

not applicable

in microgrids

does not maintain

load sharing or

economic optimality

What about distributed secondary control strategies?

Secondary frequency control in power networks Problem: steady-state frequency deviation (ωss = ω∗)

Solution: integral control on frequency error

15 / 22

centralized &

not applicable

in microgrids

does not maintain

load sharing or

economic optimality

What about distributed secondary control strategies?

Secondary frequency control in power networks Problem: steady-state frequency deviation (ωss = ω∗)

Solution: integral control on frequency error

Interconnected Systems Isolated Systems

• Centralized automatic • Decentralized PI control generation control (AGC) (isochronous mode)

control

area

remainder

control

areas

PT

PL

Ptie

PG

15 / 22

does not maintain

load sharing or

economic optimality

What about distributed secondary control strategies?

Secondary frequency control in power networks Problem: steady-state frequency deviation (ωss = ω∗)

Solution: integral control on frequency error

Interconnected Systems Isolated Systems

• Centralized automatic generation control (AGC)

control

area

remainder

control

areas

PT

PL

Ptie

PG

centralized &

not applicable

in microgrids

• Decentralized PI control (isochronous mode)

15 / 22

does not maintain

load sharing or

economic optimality

What about distributed secondary control strategies?

Secondary frequency control in power networks Problem: steady-state frequency deviation (ωss = ω∗)

Solution: integral control on frequency error

Interconnected Systems Isolated Systems

• Centralized automatic generation control (AGC)

control

area

remainder

control

areas

PT

PL

Ptie

PG

centralized &

not applicable

in microgrids

• Decentralized PI control (isochronous mode) 342 Power System Dynamics

−−

−

−

+

++

R

ωref ∆ω

ω

Pm

Pref

KA

∆PωKωs

1s

Σ Σ

Σ

Figure 9.8 Supplementary control added to the turbine governing system.

shown by the dashed line, consists of an integrating element which adds a control signal !Pω that isproportional to the integral of the speed (or frequency) error to the load reference point. This signalmodifies the value of the setting in the Pref circuit thereby shifting the speed–droop characteristicin the way shown in Figure 9.7.

Not all the generating units in a system that implements decentralized control need be equippedwith supplementary loops and participate in secondary control. Usually medium-sized units areused for frequency regulation while large base load units are independent and set to operate at a pre-scribed generation level. In combined cycle gas and steam turbine power plants the supplementarycontrol may affect only the gas turbine or both the steam and the gas turbines.

In an interconnected power system consisting of a number of different control areas, secondarycontrol cannot be decentralized because the supplementary control loops have no information as towhere the power imbalance occurs so that a change in the power demand in one area would resultin regulator action in all the other areas. Such decentralized control action would cause undesirablechanges in the power flows in the tie-lines linking the systems and the consequent violation of thecontracts between the cooperating systems. To avoid this, centralized secondary control is used.

In interconnected power systems, AGC is implemented in such a way that each area, or subsystem,has its own central regulator. As shown in Figure 9.9, the power system is in equilibrium if, for eacharea, the total power generation PT, the total power demand PL and the net tie-line interchangepower Ptie satisfy the condition

PT − (PL + Ptie) = 0. (9.8)

The objective of each area regulator is to maintain frequency at the scheduled level (frequencycontrol) and to maintain net tie-line interchanges from the given area at the scheduled values (tie-line control). If there is a large power balance disturbance in one subsystem (caused for example bythe tripping of a generating unit), then regulators in each area should try to restore the frequencyand net tie-line interchanges. This is achieved when the regulator in the area where the imbalanceoriginated enforces an increase in generation equal to the power deficit. In other words, eacharea regulator should enforce an increased generation covering its own area power imbalance andmaintain planned net tie-line interchanges. This is referred to as the non-intervention rule.

controlarea

remaindercontrolareas

PT

PL

Ptie

Figure 9.9 Power balance of a control area.

15 / 22

What about distributed secondary control strategies?

Secondary frequency control in power networks Problem: steady-state frequency deviation (ωss = ω∗)

Solution: integral control on frequency error

Interconnected Systems Isolated Systems

generation control (AGC)

control

area

remainder

control

areas

PT

PL

Ptie

PG

centralized

&

not applicable

in microgrids

• Centralized automatic • Decentralized PI control (isochronous mode) 342 Power System Dynamics

−−

−

−

+

++

R

ωref ∆ω

ω

Pm

Pref

KA

∆PωKωs

1s

Σ Σ

Σ

Figure 9.8 Supplementary control added to the turbine governing system.

shown by the dashed line, consists of an integrating element which adds a control signal !Pω that isproportional to the integral of the speed (or frequency) error to the load reference point. This signalmodifies the value of the setting in the Pref circuit thereby shifting the speed–droop characteristicin the way shown in Figure 9.7.

Not all the generating units in a system that implements decentralized control need be equippedwith supplementary loops and participate in secondary control. Usually medium-sized units areused for frequency regulation while large base load units are independent and set to operate at a pre-scribed generation level. In combined cycle gas and steam turbine power plants the supplementarycontrol may affect only the gas turbine or both the steam and the gas turbines.

In an interconnected power system consisting of a number of different control areas, secondarycontrol cannot be decentralized because the supplementary control loops have no information as towhere the power imbalance occurs so that a change in the power demand in one area would resultin regulator action in all the other areas. Such decentralized control action would cause undesirablechanges in the power flows in the tie-lines linking the systems and the consequent violation of thecontracts between the cooperating systems. To avoid this, centralized secondary control is used.

In interconnected power systems, AGC is implemented in such a way that each area, or subsystem,has its own central regulator. As shown in Figure 9.9, the power system is in equilibrium if, for eacharea, the total power generation PT, the total power demand PL and the net tie-line interchangepower Ptie satisfy the condition

PT − (PL + Ptie) = 0. (9.8)

The objective of each area regulator is to maintain frequency at the scheduled level (frequencycontrol) and to maintain net tie-line interchanges from the given area at the scheduled values (tie-line control). If there is a large power balance disturbance in one subsystem (caused for example bythe tripping of a generating unit), then regulators in each area should try to restore the frequencyand net tie-line interchanges. This is achieved when the regulator in the area where the imbalanceoriginated enforces an increase in generation equal to the power deficit. In other words, eacharea regulator should enforce an increased generation covering its own area power imbalance andmaintain planned net tie-line interchanges. This is referred to as the non-intervention rule.

controlarea

remaindercontrolareas

PT

PL

Ptie

Figure 9.9 Power balance of a control area.

does notload

maintainsharing

or

economic

optimality

15 / 22

What about distributed secondary control strategies?

Centralized automaticgeneration control (AGC)

• Decentralized PI(isochronous mode)

centralized &

not applicable

in microgrids

does not maintain

load sharing or

economic optimality

Secondary frequency control in power networks Problem: steady-state frequency deviation (ωss = ω∗)

Solution: integral control on frequency error

Interconnected Systems

•

Isolated Systems

control 342 Power System Dynamics

−−

−

−

+

++

R

ωref ∆ω

ω

Pm

Pref

KA

∆PωKωs

1s

Σ Σ

Σ

Figure 9.8 Supplementary control added to the turbine governing system.

shown by the dashed line, consists of an integrating element which adds a control signal !Pω that isproportional to the integral of the speed (or frequency) error to the load reference point. This signalmodifies the value of the setting in the Pref circuit thereby shifting the speed–droop characteristicin the way shown in Figure 9.7.

Not all the generating units in a system that implements decentralized control need be equippedwith supplementary loops and participate in secondary control. Usually medium-sized units areused for frequency regulation while large base load units are independent and set to operate at a pre-scribed generation level. In combined cycle gas and steam turbine power plants the supplementarycontrol may affect only the gas turbine or both the steam and the gas turbines.

In an interconnected power system consisting of a number of different control areas, secondarycontrol cannot be decentralized because the supplementary control loops have no information as towhere the power imbalance occurs so that a change in the power demand in one area would resultin regulator action in all the other areas. Such decentralized control action would cause undesirablechanges in the power flows in the tie-lines linking the systems and the consequent violation of thecontracts between the cooperating systems. To avoid this, centralized secondary control is used.

In interconnected power systems, AGC is implemented in such a way that each area, or subsystem,has its own central regulator. As shown in Figure 9.9, the power system is in equilibrium if, for eacharea, the total power generation PT, the total power demand PL and the net tie-line interchangepower Ptie satisfy the condition

PT − (PL + Ptie) = 0. (9.8)

The objective of each area regulator is to maintain frequency at the scheduled level (frequencycontrol) and to maintain net tie-line interchanges from the given area at the scheduled values (tie-line control). If there is a large power balance disturbance in one subsystem (caused for example bythe tripping of a generating unit), then regulators in each area should try to restore the frequencyand net tie-line interchanges. This is achieved when the regulator in the area where the imbalanceoriginated enforces an increase in generation equal to the power deficit. In other words, eacharea regulator should enforce an increased generation covering its own area power imbalance andmaintain planned net tie-line interchanges. This is referred to as the non-intervention rule.

controlarea

remaindercontrolareas

PT

PL

Ptie

Figure 9.9 Power balance of a control area.

Centralized control

15 / 22

Secondary frequency control in power networks Problem: steady-state frequency deviation (ωss = ω∗)

Solution: integral control on frequency error

Interconnected Systems Isolated Systems

generation control (AGC)

control

area

remainder

control

areas

PT

PL

Ptie

PG

centralized

&

not applicable

in microgrids

• Centralized automatic • Decentralized PI control (isochronous mode) 342 Power System Dynamics

−−

−

−

+

++

R

ωref ∆ω

ω

Pm

Pref

KA

∆PωKωs

1s

Σ Σ

Σ

Figure 9.8 Supplementary control added to the turbine governing system.

shown by the dashed line, consists of an integrating element which adds a control signal !Pω that isproportional to the integral of the speed (or frequency) error to the load reference point. This signalmodifies the value of the setting in the Pref circuit thereby shifting the speed–droop characteristicin the way shown in Figure 9.7.

Not all the generating units in a system that implements decentralized control need be equippedwith supplementary loops and participate in secondary control. Usually medium-sized units areused for frequency regulation while large base load units are independent and set to operate at a pre-scribed generation level. In combined cycle gas and steam turbine power plants the supplementarycontrol may affect only the gas turbine or both the steam and the gas turbines.

In an interconnected power system consisting of a number of different control areas, secondarycontrol cannot be decentralized because the supplementary control loops have no information as towhere the power imbalance occurs so that a change in the power demand in one area would resultin regulator action in all the other areas. Such decentralized control action would cause undesirablechanges in the power flows in the tie-lines linking the systems and the consequent violation of thecontracts between the cooperating systems. To avoid this, centralized secondary control is used.

In interconnected power systems, AGC is implemented in such a way that each area, or subsystem,has its own central regulator. As shown in Figure 9.9, the power system is in equilibrium if, for eacharea, the total power generation PT, the total power demand PL and the net tie-line interchangepower Ptie satisfy the condition

PT − (PL + Ptie) = 0. (9.8)

The objective of each area regulator is to maintain frequency at the scheduled level (frequencycontrol) and to maintain net tie-line interchanges from the given area at the scheduled values (tie-line control). If there is a large power balance disturbance in one subsystem (caused for example bythe tripping of a generating unit), then regulators in each area should try to restore the frequencyand net tie-line interchanges. This is achieved when the regulator in the area where the imbalanceoriginated enforces an increase in generation equal to the power deficit. In other words, eacharea regulator should enforce an increased generation covering its own area power imbalance andmaintain planned net tie-line interchanges. This is referred to as the non-intervention rule.

controlarea

remaindercontrolareas

PT

PL

Ptie

Figure 9.9 Power balance of a control area.

does notload

maintainsharing

or

economic

optimality

What about distributed secondary control strategies? 15 / 22

�

Distributed Averaging PI (DAPI) Frequency Control

ωi = ω ∗ − mi Pi (θ) − Ωi

ki Ω̇i = (ωi − ω ∗ )− j ⊆ inverters

aij · (Ωi − Ωj )

1

2

no tuning, no model dependence

weak comm. requirements

3 maintains load sharing (share burden of sec. control)

Simple & Intuitive

Theorem: Stability of DAPI [JWSP, FD, & FB, ’13]

DAPI-Controlled System Stable

Droop-Controlled System Stable

(grid-conscious sec. control) 16 / 22

�

Distributed Averaging PI (DAPI) Frequency Control

ωi = ω ∗ − mi Pi (θ) − Ωi

ki Ω̇i = (ωi − ω ∗ )− j ⊆ inverters

aij · (Ωi − Ωj )

1

2

3

no tuning, no model dependence

weak comm. requirements

maintains load sharing (share burden of sec. control)

Simple & Intuitive

Theorem: Stability of DAPI [JWSP, FD, & FB, ’13]

DAPI-Controlled System Stable

Droop-Controlled System Stable

(grid-conscious sec. control) 16 / 22

�

Distributed Averaging PI (DAPI) Frequency Control

ωi = ω ∗ − mi Pi (θ) − Ωi

ki Ω̇i = (ωi − ω ∗ )− j ⊆ inverters

aij · (Ωi − Ωj )

1

2

3

no tuning, no model dependence

weak comm. requirements

maintains load sharing (share burden of sec. control)

Simple & Intuitive

Theorem: Stability of DAPI [JWSP, FD, & FB, ’13]

DAPI-Controlled System Stable

Droop-Controlled System Stable

(grid-conscious sec. control) 16 / 22

�

Distributed Averaging PI (DAPI) Frequency Control

ωi = ω ∗ − mi Pi (θ) − Ωi

ki Ω̇i = (ωi − ω ∗ )− j ⊆ inverters

aij · (Ωi − Ωj )

1

2

3

no tuning, no model dependence

weak comm. requirements Theorem: Stability of DAPI

maintains load sharing [JWSP, FD, & FB, ’13] (share burden of sec. control) DAPI-Controlled System Stable

Droop-Controlled System Stable Simple & Intuitive

(grid-conscious sec. control) 16 / 22

�

Distributed Averaging PI (DAPI) Frequency Control

ωi = ω ∗ − mi Pi (θ) − Ωi

ki Ω̇i = (ωi − ω ∗ )− j ⊆ inverters

aij · (Ωi − Ωj )

1

2

3

no tuning, no model dependence

weak comm. requirements Theorem: Stability of DAPI

maintains load sharing [JWSP, FD, & FB, ’13] (share burden of sec. control) DAPI-Controlled System Stable

Droop-Controlled System Stable Simple & Intuitive

(grid-conscious sec. control) 16 / 22

� �

� �

Distributed Averaging PI (DAPI) Voltage Control [TIE ’15]

Problem: steady-state voltage deviations (Ei = E ∗)i Goals: Voltage regulation Ei → E ∗, “load” sharing Qi /Q∗ = Qj /Q∗ i i j

Bad News: These goals are fundamentally conflicting.

We propose a heuristic compromise.

τi Ėi = −(Ei − Ei ∗ ) − ni Qi (E ) − ei Qi Qj

κi ėi = βi (Ei − Ei ∗ )− bij · − Qi ∗ Qj ∗ j ⊆ inverters

Tuning Intuition:

1

2

βi >> j bij =⇒ voltage regulation βi

� �

� �

Distributed Averaging PI (DAPI) Voltage Control [TIE ’15]

Problem: steady-state voltage deviations (Ei = E ∗)i Goals: Voltage regulation Ei → E ∗, “load” sharing Qi /Q∗ = Qj /Q∗ i i j

Bad News: These goals are fundamentally conflicting.

We propose a heuristic compromise.

τi Ėi = −(Ei − Ei ∗ ) − ni Qi (E ) − ei Qi Qj

κi ėi = βi (Ei − Ei ∗ )− bij · − Qi ∗ Qj ∗ j ⊆ inverters

Tuning Intuition:

1

2

βi >> j bij =⇒ voltage regulation βi

� �

� �

Distributed Averaging PI (DAPI) Voltage Control [TIE ’15]

Problem: steady-state voltage deviations (Ei = E ∗)i Goals: Voltage regulation Ei → E ∗, “load” sharing Qi /Q∗ = Qj /Q∗ i i j

Bad News: These goals are fundamentally conflicting.

We propose a heuristic compromise.

τi Ėi = −(Ei − Ei ∗ ) − ni Qi (E ) − ei Qi Qj

κi ėi = βi (Ei − Ei ∗ )− bij · − Qi ∗ Qj ∗ j ⊆ inverters

Tuning Intuition:

1

2

βi >> j bij =⇒ voltage regulation βi

� �

� �

Distributed Averaging PI (DAPI) Voltage Control [TIE ’15]

Problem: steady-state voltage deviations (Ei = E ∗)i Goals: Voltage regulation Ei → E ∗, “load” sharing Qi /Q∗ = Qj /Q∗ i i j

Bad News: These goals are fundamentally conflicting.

We propose a heuristic compromise.

τi Ėi = −(Ei − E ∗ i ) − ni Qi (E ) − ei

κi ėi = βi (Ei − E ∗ i )− j ⊆ inverters

bij · Qi Q∗ i

− Qj Q∗ j

Tuning Intuition:

1

2

βi >> j bij =⇒ voltage regulation βi

� �

� �

Distributed Averaging PI (DAPI) Voltage Control [TIE ’15]

Problem: steady-state voltage deviations (Ei = E ∗)i Goals: Voltage regulation Ei → E ∗, “load” sharing Qi /Q∗ = Qj /Q∗ i i j

Bad News: These goals are fundamentally conflicting.

We propose a heuristic compromise.

τi Ėi = −(Ei − E ∗ i ) − ni Qi (E ) − ei

κi ėi = βi (Ei − E ∗ i )− j ⊆ inverters

bij · Qi Q∗ i

− Qj Q∗ j

Tuning Intuition:

1

2

βi >> j bij =⇒ voltage regulation βi

From Hierarchical Control to DAPI Control flat hierarchy, distributed, no time-scale separations, & model-free

18 / 22

From Hierarchical Control to DAPI Control flat hierarchy, distributed, no time-scale separations, & model-free

18 / 22

1 t < 7: Droop Control

2 t = 7: DAPI Control

3 t = 22: Remove Load 2

4 t = 36: Attach Load 2

Experimental Validation of DAPI Control Experiments @ Aalborg University Intelligent Microgrid Laboratory

DCSource

LCLfilter

DCSource

LCLfilter

DCSource

LCLfilter

4DG

DCSource

LCLfilter

1DG

2DG 3DG

Load1 Load2

12Z

23Z

34Z

1Z 2Z

19 / 22

Experimental Validation of DAPI Control Experiments @ Aalborg University Intelligent Microgrid Laboratory

DCSource

LCLfilter

DCSource

LCLfilter

DCSource

LCLfilter

4DG

DCSource

LCLfilter

1DG

2DG 3DG

Load1 Load2

12Z

23Z

34Z

1Z 2Z

1 t < 7: Droop Control 2 t = 7: DAPI Control 3 t = 22: Remove Load 2 4 t = 36: Attach Load 2

19 / 22

Experimental Validation of DAPI Control Experiments @ Aalborg University Intelligent Microgrid Laboratory

DCSource

LCLfilter

DCSource

LCLfilter

DCSource

LCLfilter

4DG

DCSource

LCLfilter

1DG

2DG 3DG

Load1 Load2

12Z

23Z

34Z

1Z 2Z

1 t < 7: Droop Control 2 t = 7: DAPI Control 3 t = 22: Remove Load 2 4 t = 36: Attach Load 2

19 / 22

Summary

Distributed Inverter Control • Primary control stability • Distributed PI controllers • Primary/tertiary connections • Extensive validation

Future Work • More detailed models • More systematic designs • H2 performance • Monitoring ⇐⇒ Feedback

DCSource

LCLfilter

DCSource

LCLfilter

DCSource

LCLfilter

4DG

DCSource

LCLfilter

1DG

2DG 3DG

Load1 Load2

12Z

23Z

34Z

1Z 2Z

20 / 22

Acknowledgements

Florian Dörfler Francesco Bullo Qobad Shafiee Josep Guerrero

Marco Todescato Basilio Gentile Ruggero Carli Sandro Zampieri 21 / 22

Question Time

http://engr.ucsb.edu/~johnwsimpsonporco/ [email protected]

http://engr.ucsb.edu/~johnwsimpsonporco/http://engr.ucsb.edu/~johnwsimpsonporco/mailto:[email protected]

supplementary slides

An incomplete literature review of a busy field

ntwk with unknown disturbances ∪ integral control ∪ distributed averaging

all-to-all source frequency & injection averaging [Q. Shafiee, J. Vasquez, & J. Guerrero, ’13] & [H. Liang, B. Choi, W. Zhuang, & X. Shen, ’13] & [M. Andreasson, D. V. Dimarogonas, K. H. Johansson, & H. Sandberg, ’12]

optimality w.r.t. economic dispatch [E. Mallada & S. Low, ’13] & [M. Andreasson, D. V. Dimarogonas, K. H. Johansson, & H. Sandberg, ’13] & [X. Zhang and A. Papachristodoulou, ’13] & [N. Li, L. Chen, C. Zhao & S. Low ’13]

ratio consensus & dispatch [S.T. Cady, A. Garcıa-Domınguez, & C.N. Hadjicostis, ’13]

load balancing in Port-Hamiltonian networks [J. Wei & A. Van der Schaft, ’13]

passivity-based network cooperation and flow optimization [M. Bürger, D. Zelazo, & F. Allgöwer, ’13, M. Bürger & C. de Persis ’13, He Bai & S.Y. Shafi ’13]

distributed PI avg optimization [G. Droge, H. Kawashima, & M. Egerstedt, ’13]

PI avg consensus [R. Freeman, P. Yang, & K. Lynch ’06] & [M. Zhu & S. Martinez ’10]

decentralized “practical” integral control [N. Ainsworth & S. Grijalva, ’13]

� �DAPI Voltage Control – Performance [TIE ’15]

τi Ėi = −(Ei − E ∗ ) − ni Qi (E ) − ei

κi ėi = βi (Ei − E ∗ i )− j ⊆ inverters

bij · Qi Q∗ i

− Qj Q∗ j

Introduction & Project SamplesDistributed Control in MicrogridsPrimary ControlTertiary ControlSecondary Control