Muons

Voltage control within a specified range of limits and capacitor switching are an effective means of minimizing loss and improving voltage profiles and deferred construction and maintenance costs in the end within the reliability and power-quality constraints of the system. Voltage/VAr control considers multiphase unbalanced distribution system operation, dispersed generation, and control equipment in the large system. In distribution auto-mation, functions using voltage/VAr control options must maintain proper

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communication between planning problems like the decision to install capac-itors, and recognizing the cost benefit analysis.

5.3.1 Methods of Voltage/VAr in Distribution Automation

Several methods have been used for voltage/VAr control over the years, including:

• Decoupled formulation with a linear voltage-regulator problem and capacitor-switching problem can be solved interactively using a lin-ear and nonlinlin-ear optimization

• OPF-based reactive-power dispatching aimed at minimizing power losses by optimal placement of capacitors

• A proposed linear-programming-based method that minimizes losses by changing transformer tap setting and VAr injection

• A mixed-integer programming model that solves the problem of voltage/VAr control using the principle of recursive linear programming

• Several other techniques that use linear power flow to break the overall problem into a master-capacitor switching problem and slave-capacitor operation problem given the switching schedule (based on the Dantzig-Wolfe decomposition principle for a multi-area reactive-power-planning problem)

• A three-phase power-flow program that accounts for the distributed loads by approximating their effects on nodal voltage via equivalent lumped nodes; this method is also capable of accounting for dis-persed generation, tap controls, and shunt capacitor switching

• A contingency-secured approach for voltage-profile improvements to bridge the gap between VAr planning and VAr dispatching

• A rule-based system combined with standard linear programming to solve the voltage/VAr control problem

• Other intelligent systems such as fuzzy logic, genetic algorithm, and their hybrids for voltage/VAr control that have been developed and tested successfully to keep the computational burden within possible limits

5.3.2 Evaluation of Methods Used for Voltage/VAr Control

1. Voltage/VAr control using optimization methods and intelligent sys-tems and their hybrids have been applied to this complex problem.

2. Optimization methods include linear programming, nonlinear pro-gramming, and mixed-integer programming using the principles of

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decomposition for the full AC OPF. Heuristic approaches have been used to get around the discrete variable used for selecting switching capacitors.

3. Rule-based evolutionary programming in combination with OPF based on efficient algorithms, such as interior-point OPF, is an option for designing a future efficient voltage/VAr control problem.

5.3.3 Modeling of Voltage/VAr Control Options

The VAr control problem is modeled as a large-scale, complex, nonlinear combinational problem. The decision on capacitor switching has to be mod-eled as a discrete variable. The sequence of switching in size and site has to be properly modeled for a given optimization method.

5.3.4 Formulation of Voltage/VAr

This includes the integrated voltage/VAr with the load-management prob-lem to improve efficiency given the following four objectives:

1. Customer-outage cost

Minimum outage cost = (5.1)

where

X_ik = level of curtailable load selection of type k at bus i (p.u. MW) PCki = maximum curtailable MW of type k at the ith bus (p.u. MW) CC_k = curtailment cost of customer type k ($/p.u. MW)

2. Loss minimization

The objective of the loss minimization function is given by

Min I²r = (5.2)

3. Load balancing

(5.3) X_ik PC_ki CC_k

i

× ×

( )

∑

r P Q

ij V

ij

ij ij

∑

Max S S

i i max

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where

Pij, Qij = transfer power (branch i-j at p.u.) V_i = voltage of bus i (p.u.)

4. Multiple objective function

Z = Min[a + b – c] (5.4)

5.3.5 System Operating Constraints These include

Branch flow equations:

Yi+1 = fi+1(Yi) (5.5) where

(5.6)

Branch flow takes into account the recursive relationships between the suc-cessive nodes in the radial distribution system. The demand in P_D, Q_D also have an interruptible component, which is the load-management control options X. In addition, the reactive power equation has the capacity switch-ing option Q_s.

Voltage limits/current limits:

The voltage and current limits are given as

(5.7)

(5.8) Capacitor control limits:

(5.9) Curtailable load-control limits:

P_i×X ≤Pc_ki (5.10)

Qi×Xki≤Qcki (5.11)

Yi= ⎡⎣⎢P Q VD D X Qk s i⎤ , , ², , ,δ⎦⎥

V_i^min ≤V_i ≤V_i^max

I_ij^min ≤ I_ij ≤ I_ij^max

Qs_i^min<Qs_i≤Qs_i^max

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5.3.6 Methodology

The mathematical optimization problem in Equations 5.5 to 5.11 falls into the class of nonlinear mixed-integer programming problems. We use an easier method to overcome the computational challenges. The hybrid artifi-cial intelligence optimization scheme gets around the problem’s computa-tional challenges. They are used for:

• Off-line plan: use the feasible MIP (mixed-integer programming method) from Equations 5.5 to 5.11

• On-line execution

Use expert systems in real time to handle the optimization of:

• Discrete variables (selections of capacitor switching, load-manage-ment options)

• Operation development

The online artificial intelligence (AI) methodology uses the following steps:

1. Develop knowledge base from the off-line mode using the optimi-zation model.

2. Perform real-time data acquisition on load, network, and topology (in real-time model).

3. Access the knowledge base to detect dispatch functions, load-man-agement options, and capacitor switching under specific load con-ditions (in real time).

4. Invoke the rule base to ensure that the load management and capac-itor switching are within limits.

5. Reform load flow to check violations of network constraints.

5.4 Fault Detection (Distribution Automation Function)