Load-Tap-Changing Transformers and Voltage Control

Jonas Kersulis

January 25, 2017

http://kersulis.github.io/presentations/498lecture2

1. Motivation

  • LTCs control voltage online.
  • Renewable generation fluctuations may strain them.
  • LTCs are expensive and complicated.

Load Tap Changing (LTC) Transformer: a big piece of hardware

LTC: more than meets the eye

This is a tap changer.

It can vary the transformer turns ratio online.

Role of LTCs

  • Respond to voltage fluctuations online.
  • Generation fluctuations typically known.
  • Load fluctuations known well by now too.

Problem: Weather fluctuations not known.

So LTCs still play a crucial role.

Unfortunately, they are

  1. Expensive
  2. Discrete
  3. A major cause of system failure

Issue 1: cost

Source

Issue 1: cost

Ibid.

Issue 1: cost

Ibid.

Issue 2: discrete behavior

Continuous signal, discrete device. We need

  • Delays
  • Deadbands
  • Coordination

Details later.

Issue 3: system failure

The IEEE testing standard considers LTC lifespan to be 50k tap operations.

Tap-changer failure most likely cause of medium-voltage transformer failure. Source

2. Modeling

Consider this simple network.

  • Far left: the grid
  • Next: substation LTC
  • Then: connection to wind and a distribution feeder
  • Far right: distribution LTC

LTC configuration basics

LTC Models

Wait, what's a DLTC? Where do time constants come from?

Consider two LTC models:

  • DLTC: definite delay, counts time outside deadband
  • ITLC: inverse delay, integrates deviation from deadband

DLTC Model

\begin{align} \\ \\ \\ d(t) &= \begin{cases} 1 & \mbox{if } \Delta V(t) > DB \\ -1 & \mbox{if } \Delta V(t) < -DB \\ 0 & \mbox{otherwise} \end{cases} \\ \\ \\ \\ \\ \\ c(t) &= \begin{cases} c(t-\Delta t) + \Delta t & \mbox{if } d(t) = 1 \mbox{ and } c(t-\Delta t) \geq 0 \\ c(t-\Delta t) - \Delta t & \mbox{if } d(t) = -1 \mbox{ and } c(t-\Delta t) \leq 0 \\ 0 & \mbox{otherwise} \end{cases} \\ \\ \\ \\ \\ \\ T(t) &= \begin{cases} T(t-\Delta t) + 1 & \mbox{if } d(t) = 1 \mbox{ and } c(t) > C \\ T(t-\Delta t) - 1 & \mbox{if } d(t) = -1 \mbox{ and } c(t) < -C \\ T(t-\Delta t) & \mbox{otherwise, and when $T$ at limit} \end{cases} \end{align}

ILTC Model

\begin{align} \\ \\ \\ \frac{de(t)}{dt} &= \begin{cases} \frac{1}{\tau}(\Delta V(t) - DB) &\mbox{if }\Delta V(t) > DB \\ \frac{1}{\tau}(\Delta V(t) + DB) &\mbox{if }\Delta V(t) < -DB \end{cases} \\ \\ \\ \\ \\ \\ e(t) &= \begin{cases} e(t-\Delta t) + \frac{de(t)}{dt}\Delta t \qquad\mbox{if }T(t) = T(t-\Delta t) \\ 0 \qquad\mbox{otherwise, and when $V$ in deadband} \\ \end{cases} \\\\ \\ \\ \\ \\ \\ T(t) &= \begin{cases} T(t-\Delta t) + 1 &\mbox{if }e(t) > \alpha \\ T(t-\Delta t) - 1 &\mbox{if }e(t) < -\alpha \\ T(t-\Delta t) &\mbox{otherwise, and when $T$ at limit} \end{cases} \end{align}

3. LTC Research Overview

Ideas:

  • Monitor
  • Modify and control
  • Optimize existing controller behavior

Monitor

Lots of work in this area at University of Queensland.

  • Paper insulation samples (Dr. Daniel Martin)
  • Tank vibration signal analysis (Lakshitha Naranpanawe)
  • Machine learning on oil samples (gas content), thermal and acoustic samples (Dr. Hui Ma)

Modify and control

Common objectives:

  • Minimize losses (difficult!)
  • Minimize tap operations (enumerate?)
  • Prevent undesirable interactions (hunting, voltage regulator runaway)

Common constraints:

  • Power balance
  • Voltage limits
  • Branch flow constraints (even thermal limits)
  • Transformer capacity limits (reverse limit $<$ forward limit)
  • Tap limits
  • Renewable generation constraints (voltage regulation limits)

Hybrid dynamics. Heuristics and assumptions everywhere!

In the literature

Agalgaonkar et al.: Day-ahead LTC and PV control.

  • Objective: fix LTC and PV inverter setpoints to minimize tap operations. \begin{align} f &= \left(\overbrace{W_c}^\text{tap count wt.} \underbrace{\sum_{t=2}^{N}\sum_{T=1}^{N_{tr}} \lvert \text{Tap}_{t,T} - \text{Tap}_{t-1,T} \rvert}_\text{total taps}\right) + \left( \overbrace{W_r}^\text{extreme tap wt.} \underbrace{\sum_{t=1}^{N} \lvert P_t \rvert}_\text{penalty function}\right), \end{align} where \begin{align} P_t &\geq 0 \\ P_t &\geq p_1\text{Tap}_t + p_2 \\ P_t &\geq p_3\text{Tap}_t + p_4, \end{align} and $p_1-p_4$ are penalty function parameters.
  • Constraints: many (good example of thoroughness)

Issues and assumptions

  • Reliant on day-ahead PV forecasts
  • Assumes LTC setpoints are controllable
  • Assumes communication between LTCs and solar PV
  • Interior-point method

Also in the literature

Park et al.: Day-ahead STATCOM dispatch

  • Objective: dispatch STATCOMs a day in advance, allow LTCs and VRs to act semi-autonomously. \begin{align} \min J &= \overbrace{w_L\sum_{t=1}^{24}L_t}^\text{loss term} + \overbrace{w_V\sum_{t=1}^{24}\sum_{n=1}^{N}D_{n,t}}^\text{voltage deviation term} \\ & \text{subject to:} \\ V_\text{min} &< V_{n,t} < V_\text{max}\quad\forall n \\ &\sum_{t=2}^{24} \lvert \text{Tap}_{p,t} - \text{Tap}_{p,t-1}\rvert \leq MK_{T_p}\quad\forall p \\ &\sum_{t=2}^{24}\lvert C_{q,t}\oplus C_{q,t-1}\vert \leq MK_{C_q} \quad\forall q \end{align}
  • LTCs and VRs use capacitor dispatch to fix setpoints in advance

    • Issues and assumptions

    • Communication requirements
    • Getting stuck with yesterday's forecast
    • Reliance on genetic algorithm

    4. Optimization setup

    Optimize existing controller behavior

    Rationale:

    • Long time before new devices take over or existing LTCs are retrofitted
    • Communication is hard

    Combine

    • Test network
    • Parameters introduced previously
    • NREL wind and solar data

    Illustrate

    • Subtransmission/distribution tradeoff
    • Parameter sensitivity

    Big idea: explore interaction between LTCs and renewables

    Especially impact of renewable voltage regulation on LTC tapping

    NREL data

    NREL's Wind Prospector provides simulated power data at 100m, assuming site-appropriate turbine power curves.

    • Take one year of data at max. resolution (5 min)
    • Interpolate to obtain 1-min data
    • Similar process for NREL solar PV data

    Ready for simulation.

    • Let $P_g$ be NREL wind or solar data
    • Let $Q_g$ be limited to $[-Q_g^{lim},Q_g^{lim}]$
      • Bus 1 begins as PV (voltage specified)
      • If reactive power limit encountered, switch to PQ bus

    Simulation

    Let's first examine extreme cases:

    • Case 1: loose renewable regulation, $Q_g^{lim}=0$
    • Case 2: tight regulation, $Q_g^{lim}=\infty$

    Tapping tradeoff

    Time to get a bigger picture

    • Sweep through many values of $Q_g^{lim}$
    • Simulate for one year at one minute resolution
    • Count LTC taps and plot distribution vs. subtransmission
    • Total taps decrease as renewable regulation tightens
    • But the subtransmission LTC taps more

    One more level

    • Visualize sensitivity to LTC setpoint
    • Overlay multiple tradeoff curves

    Conclusions

    • LTCs continue to play a key role in power systems.
    • Rise in renewables threatens LTC lifespan.
    • We can influence tapping behavior without controlling an LTC directly.
    • Renewable voltage regulation balances active power fluctuation effects between distribution and subtransmission LTCs.
    • The trade-off is nuanced even for simple networks.
    • Understanding relationships between parameters is key to developing algorithms for general networks.