Voltage Regulator Constraints with Zero r and x Values in LinDist3flow

[irfanUK22]

Howdy,
I am Irfan Ullah, a graduate student at Texas A&M University, working under the guidance of Dr. Karen Butler-Purry at Texas A&M, and collaborating with Dr. Russell Bent, Art Barnes, and Harsha Nagarajan. My research focuses on Black Start Restoration (BSR) in power distribution systems. I have implemented BSR using PowerModelsDistribution (PMD) and PowerModelsONM (ONM). This work utilizes the linearized voltage regulator constraints from ONM.

This pull request addresses an issue in the linearized voltage drop constraint (PowerModelsONM.jl/src/form/lindistflow.jl: line 306-364) that arises due to how the voltage regulator operates. Specifically:
• If the voltage regulator regulates the voltage at the load center:
The r and x settings are non-zero (e.g., in the IEEE 123 Node system).
• If the voltage regulator regulates the voltage at the node it is connected to:
The r and x settings are zero (e.g., in the Iowa State 240 Node system).

Background:
• In the IEEE 123 Node system, where the voltage is regulated at the load center and r and x are non-zero, the linearized voltage regulator constraints (including the commented-out part) worked perfectly. I successfully tested the BSR formulation on this system without encountering issues.

• However, in the Iowa State 240 Node system, the voltage is regulated at the node itself, resulting in r = 0 and x = 0. This causes:

w_drop = 2 * r * p_to[idx] + 2 * x * q_to[idx] #PowerModelsONM.jl/src/form/lindistflow.jl: line 413)

becoming a constant zero (w_drop = 0).
• The relaxation function IM.relaxation_product (defined in PowerModelsONM.jl/src/core/base.jl, line 110) requires a valid expression for w_drop. When w_drop = 0, the function fails, causing an error.

Proposed Solution:

To handle the case where r = 0 and x = 0, the following adjustments are proposed:
1. Define w_drop as:
w_drop = 2 * r * p_to[idx] + 2 * x * q_to[idx]

2. Check if w_drop equals zero:

if r == 0 && x == 0
w_drop_z_block = w_drop # Direct assignment without relaxation
# Skip relaxation for (w_drop, z_block)
else
w_drop_z_block = @variable(pm.model, base_name="w_drop_z_block") # Create new variable
IM.relaxation_product(pm, w_drop, z_block, w_drop_z_block) # Apply relaxation
End

3. Return w_drop_z_block.

Implementation Notes:
• This solution ensures that:
○ Relaxation is only applied when w_drop is a valid expression.
○ Direct assignment is used when w_drop = 0, preventing errors in the relaxation function.
• The modification is made in the linearized voltage drop constraint (lindistflow.jl, line 343).
• The proposed changes have been validated:
○ IEEE 123 Node system: The constraints were uncommented and tested; they worked fine since r and x are non-zero.
○ Iowa State 240 Node system: The issue was resolved with the proposed adjustments.

	Thank you 
	
	
	Best Regrads
	Irfan Ullah 
	Texas A&M University 

Dec 12 Pull Request .pptx