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