EE533 Power System Operations

1
EE533 Power System Operations

• Network Security Analysis

2
Power Flow Model and Studies

• Describes steady state behavior of system
• Specific topology and load
• Power flow problem
• Given topology, loads, generator schedules and
  control settings
• Find all phasor voltages
• Device loading, losses, and other quantities can
  be determined once voltages are known

3
Power Flow Model and Studies

• Describes steady state behavior of system
• Specific topology and load
• Power flow problem
• Given topology, loads, generator schedules and
  control settings
• Find all phasor voltages
• Device loading, losses, and other quantities can
  be determined once voltages are known

4
Power Flow Model and Studies

• Used operation in operations planning to
• Determine base case for each operating period
• Generator schedules
• Interchange and control settings
• So that
• Credible contingencies do not move system past
  alert state
• Also define operating procedure to return from
  alert to normal after contingency
• Used on-line to
• Monitor and alarm through contingency analysis
  with real time data
• Manage congestion (SCOPF)

5
Power Flow Model and Studies

• Variants
• Inertial Load Flow
• Immediately upon disturbance (Line trip)
• Generator internal voltages/angles are frozen
• LTCs are frozen, power electronics/relays may
  react
• System electromechanical transients and
  fast-acting controllers
• Governor load flow
• If a generator trips lost power will be
  distributed by governors
• Interchange and control settings
• Response of slower controllers
• Conventional Load Flow

Offline dynamic studies used to monitor these
6
Power Flow Model and Studies

• Advanced

Security Constrained Optimal Power Flow
7
Power Flow Problem

• Component Models

• Generators
• Modeled as ideal current source
• Described by desire real power (MW) and Terminal
  Voltage Magnitude(V)
• Constrained by capability curve
• Lines and two-winding Transformers
• PI model
• Constrained by thermal rating(s)
• Power Electronic Devices
• Detailed steady-state models

8
Power Flow Problem

• Component Models

• Capacitors/Reactors
• Constant Impedance
• Load
• Constant KVA
• Polynomial Model for voltage dependence
• Special consideration for operations breaker
  oriented mode
• A line fault can outage two lines
• Breaker status and Topology Processor must
  maintain
• correct real-time model

Breaker open (maintenance)
Line 2 now Open at one end
These breakers clear Fault at X to open Line 1
Line 2
X
Line 1
9
Power Flow Problem

• Network Model
• Admittance Matrix
• I Y V

j
k
I Nx1 vector of bus currents I1,
I2,..Ik,..,Im,.. IN injected into bus by
loads, generators, and other components V
Nx1 vector of line to neutral voltages V1,
V2,..Vk,..,Vm,..VN in positive sequence (per
phase model)
Ik
Im
N bus network
Y NxN admittance matrix Ykk Sum of admittances
of at node k Ykj -Sum of admittances of
elements from node k directly to node j
10
Power Flow Problem
j

• Network Model
• Admittance Matrix
• I Y V

k
Ik
Im
N bus network

• Steady State Power Balance

KCL and Complex power injected into bus k
11
Power Flow Problem

• Steady State Power Balance

j
Complex power injected into bus k Polar Form
Vk Vk/dk YkjYkj /?k
k
Ik
Im
N bus network
12
Power Flow Problem

• Mathematical Formulation

Given Y Sk at load buses
Vk at buses with generators Pk at buses
with generators1
j
k
Ik
Im
N bus network
Find V 1 Cannot specify all Pk
13
Power Flow Problem

• Mathematical Formulation Slack Bus

j
k
Ik
Im
N bus network
Equations are Dependent ? Pk Ploss ? Qk
Qloss Can add any constant to all ds since
equations involve dk-dj ? Pk
Ploss ? Qk Qloss Cannot specify all Pks
14
Power Flow Problem

• Mathematical Formulation Slack Bus

j
Can add any constant to all ds since equations
involve dk-dj
k
Ik
Im
Select a generator bus m as SLACK Let dm 0
phasor reference Drop Pm equation
N bus network
Physical slack is provided by the Governors and
is Distribute over all Generators
15
Power Flow Problem

• Mathematical Formulation General bus
  classification
• and Equation reduction

j
k
Ik
Generator or Voltage Controlled V and P given
Q and d unknown Load P and Q given V and d
unknown Slack V and d0 given P and Q unknown
Im
N bus network
16
Power Flow Problem

• Mathematical Formulation General bus
  classification
• and Equation reduction

j
k
Ik
Generator or Voltage Controlled V and P given
Q and d unknown Load P and Q given V and d
unknown Slack V and d0 given P and Q unknown
Im
N bus network
17
Power Flow Problem

• Mathematical Formulation General bus
  classification
• and Equation reduction
• Ng Generators 1 slack Nl loads
• NgNL unknown d
• NL unknown V
• Select NG2NL equations
• NGNL P equations
• NL Q equations
• All V, d known after solution
• Calculate remaining

j
k
Ik
Im
N bus network
18
Power Flow Problem

• Mathematical Formulation

j
k
Ik
Im
N bus network
NG2NL Unknowns LHS Given Some known V, d in RHS
19
Power Flow Problem

• Mathematical Formulation

j
k
Ik
Im
N bus network
NG2Nl Equations LHS Given Some known V, d in
RHS NG2NL Unknowns V, d
20
Power Flow Problem

• PF, OPF and SCOPF

Power Flow (PF) Solve f(X) 0 where f(x)
denote the power flow Equations Optimal Power
Flow Min z(x) -- usually, fuel and OM cost as
in ED f(x) 0 -- PF Equations H(x) 0 --
Limits, e.g., generator and line
capacities
j
k
Ik
Im
N bus network
21
Power Flow Problem

• PF, OPF and SCOPF

N bus network
j
Security Constrained OPF
k
Ik
Min z(x) -- usually, fuel and OM cost
as in ED f(x) 0 f1(x1)0
f2(x2)0 . -- PF Equations H1(x) 0
H1(x1) 0 H2(x2) 0 -- Limits
g1(x,x1) 0 g2(x,x2) 0 --
Coupling Constraints e.g. Generator power
change from base case lt some limt

Im
Base Contingency Contingency
Case 1 2
22
Power Flow Problem

• PF, OPF and SCOPF
• PF Solution
• Most common
• Full Newton (Planning)
• Fast decoupled(Operations)
• Others
• Gauss
• Quadratic
• OPF and SCOPF
• Most Common Successive LP
• Second Order Solution KT
• Others Gradient
• Relaxation

N bus network
j
Im