We will look at load and renewable expansion where transient stability becomes the limiting factor.

Base Model

We start with the base model used in the transient stability exercise. From now on, we assume that you have done that exercise.

Design Objective

We assume that the load in the system will grow substantially and we want to meet the load with renewable (wind) generation. We won’t be adding any new transmission lines to the system, so the new loads would be met with new generation and perhaps upgraded transmission lines.

Step 1: Understanding the Limits of the Existing System

Start with the system in the transient stability exercise. We want to understand what the limit of the system is under various contingencies.

  1. Enumerate all possible line outages (we looked at one in the exercise), and study the transient stability behavior. We need a metric to quantify how stable the system is. A simple and commonly used metric is the following ratio: \(S=\max_{t \geq 0} \max_{i,j} \frac{\delta_i (t)-\delta_j (t)}{2\pi}.\) This ratio measures the largest angle separation between any pair of buses throughout the transient. Assuming the fault clearing time as given the the exercise, find and record what this number is.

  2. One way to stress the system is to have a longer fault clearing time, since this can be thought as the system ``drifting’’ further away from its base state. Find a fault clearing time that would lead to large angle swings. Can you find a time that would lead to \(S \geq \frac{1}{4} = \frac{\pi/4}{2\pi}\), which is often seen as a sign of the system becoming unstable.

  3. We want to push the load to a point where the power flow problem is not solvable anymore. Note, this is not a dynamic phenomena. Because there is more than one load, there is not a unique way to increase the load. There are two common approaches. The first one is to multiple all load by a factor (larger than 1), the second is to pick a load and just increase that particular load (you can pick any one you want). Try both and report when power flow stop converging.

Step 2: Adding a Wind Power Plant

  1. The wind power plant models are built into PSAT. You can take a look at some of the included case files, for example, d_014_dyn_wind.mdl in the PSAT test folder. Add a wind power plant to your system.
  2. Using the load values you found in Step 1.3, find the minimum size of the wind turbine you need to install such that the power flow problem is solvable.
  3. We want to dynamic performance to not degrade when load increases and a wind plant is added. There are several ways to do this, from adding damping and inertia to the existing synchronous generators, adding synthetic inertia and damping to wind, to just increasing the output of wind power. Using the following cost for damping and inertia constants: every 10% increase of the base value for the synchronous generator cost $10,000, and for the wind turbine, every 10% increase from base value cost $15,000. Find the most cost efficient way to achieve the same dynamic performance as the base system we started with.
  4. You should submit two files: 1) a short report describing all the values you chose and your reasoning behind it. For example, if you chose to have more damping than inertia, why is that? 2) The simulink file such that I can reproduce your results in PSAT.