Holomorphic Embedding Load Flow Method (HELMTM)

Algorithm Development for NASA Intelligent Power Control

Bradley C. Glenn, Ph.D.

Gridquant Technologies LLC Bob Stuart, Ross Harding

Grupo AIA Antonio Trias, Ph.D., Regina Llopis Rivas, Ph.D., José Luis Marín, Ph.D.

Battelle Memorial Institute Frank E. Jakob, Jeff Keip

Introduction

• Team background

• Relevance of HELMTM pertaining to the NASA Intelligent Autonomous Control Architecture

• HELMTM Overview

• Vision and results of Phase I and Phase II of SBIR

• Commercialization of Technology to NASA and non-NASA Applications

Source of picture: NASA, “Overview of Intelligent Power Controller Development for Human Deep Space Exploration”, IECEC 2014 Cleveland, Ohio

Current Events relating to Space Power Systems

Intelligent Autonomous Control Architecture

From Soeder, James F. et al.” Overview of Intelligent Power Controller Development for Human Deep Space Exploration”, Presented to IECEC 2014 Cleveland, Ohio

HELM™ Overview

Current methods: lack of convergence, need initial seed solution

• Holomorphic Embedding Load Flow Method

• Direct, constructive solution to powerflow equations

• Non-iterative and deterministic, unlike traditional methods

• Uses a fundamentally new mathematical approach

• Based on Complex Analysis: Analytic Continuation, not numerical continuation or Homotopy

• New measures of distance to collapse (Sigma indicators)

• This new PF engine is the key enabler of a new class of software applications for decision support in grid operations

• Applications can now reliably perform massive search on the state-space of the system. Analogous to GPS sat-nav.

• They run in parallel to existing tools – act as expert operator support in online mode

• They work in terms of the actual SCADA actions, not idealized or simplified models

Some Common misconceptions of HELM™ • Not the same as the Series Load Flow Method

• Holomorphic Embedding method is somewhat related to these ideas, but with one key difference: the Series Load Flow uses real variables and HELM complex variables

• Not numerical Homotopy continuation

• Homotopy methods compute the powerflow solution along a parameterized curve, but only exploit continuity and single differentiability.

• Therefore the path-following steps still use numerical iteration to track the solution (N-R is typically used as the “corrector” in the predictor-corrector steps)

• The power series are not an approximation!

• For Holomorphic functions (==complex analytic), the power series is the function

• Many holomorphic functions are actually defined via their power series (e.g. ez)

• Padé approximants (in this case) are not an approximation!

• The beauty of HELM is that voltages become an algebraic curve of the embedding parameter. For these class of functions, Stahl’s theorem applies.

• This means that the near-diagonal sequence of Padé approximants of the power series are guaranteed to converge

• Moreover the theorem states that they converge outside the radius of convergence of the power series, in the maximal domain possible. Therefore they provide the maximal analytic continuation.

• This last bit provides completeness to the method: when the solution exists, the Padé sequence will converge to it; when the solution does not exist, the sequence oscillates.

HELM™ Power Flow not the Entire Story • AGORA: an intelligent REAL-TIME

and MODEL-BASED tools for the Transmission/Distribution Operator

• State Estimation is a process that cleanses, corrects bad sensor data, and reconstructs missing data, based on the powerflow equations and other methods

• In AC grids, HELM™ methodology influenced the development of a whole new State Estimation technique. It uses the holomorphic power flow calculation, as well as several other local electric tests, as a critical way to enhance the resilience of State Estimation in the presence of bad or missing data.

AIA Load Flow

Contingency Analysis

State Estimator

RT Simulator

PV/QV Curves

OPF

Restoration Solver

Lim. Viol. Solver

SCADA

Vision of HELM for Autonomous Space Power Systems • Extend existing AC load flow, state estimation, and

optimal power flow to DC and Microgrids, all necessary for full autonomy

• Perfect method using models and operational data from actual components on International Space Station and Orion Spacecraft

• Working with Aerojet Rocketdyne, PC Krause, and NASA engineers

• Extend to potential NASA Commercial Applications • Solar Electric Propulsion

• Extend to Non-NASA Commerical Applications • DC or AC-Microgrids

Extension to DC system components

Nonlinear Behavior of Components

• The nonlinear behavior of components results in multiple equilibrium points. The actual equilibrium state is determined by the stability of the equilibrium points

HELM DC results for solar PV array

The DC-based HELMTM power flow demonstrated on the simplified spacecraft power system the ability to find the desirable and stable region for equilibrium.

if

Diode Example and importance of non- iterative power flow algorithm

Virtanen, J., “Numerical Circuit Design Methods” (course S-553210), Aalto University. URL: http://radio.aalto.fi/en/contact/personnel/jarmo_virtanen/

Newton-Raphson fractal for the three-bus model, at moderate stress (second example)

POTENTIAL NASA COMMERCIAL APPLICATIONS • Reliable and fast State Estimator that will improve grid

observability

• Optimization algorithms for load management under variable load demand and constrained capacity

• Control-based applications

• Auto-healing modules providing optimal (power-flow checked) action sequences for reconfiguration, in order to minimize brownouts and blackouts

• Provide the building blocks for a truly autonomous power system, a pre-requisite for successful deep space missions requiring long-term operation with minimal human intervention

• Envision that the first NASA system to receive the benefits of this effort will be Solar Electric Propulsion (SEP)

POTENTIAL NON-NASA COMMERCIAL and Terrestrial Applications Spin-Offs

Source of Picture: Soeder, James F., et al. “Application of Autonomous Spacecraft Power Control Technology to Terrestrial Microrgrids”; July 28 – 30, 2014, 12th International Energy Conversion Engineering Conference

• Part of Phase I Project was to demonstrate technology for terrestrial microgrids

• A microgrid is a group of connected loads and distributed generation resources within clearly defined electrical boundaries that acts as a single controllable entity with respect to the main grid.

• A microgrid can connect and disconnect from the gird to enable it to operate in both the grid connected and “island” mode.

• Because of the land available for renewable energy resources and critical infrastructure, military bases are excellent candidates for microgrids.

• Emerging microgrids will require more robust software

NASA SBIR DC-HELM Commercialization approach One of the team members, Battelle is “in the business of innovation” (Tagline)

They accomplish that by assembling inter-disciplinary, multi-faceted teams to solve

customer problems through funded contract research projects

− In doing so Battelle seeks synergies and adjacencies for a technology than can

- Adapt technology from synergistic areas -- find existing solutions

- Inject developed technology into adjacent areas – create additional value streams

For NASA, the project team is exploring the use of the DC-HELM algorithm for other

applications such as electric aircraft propulsion, ocean ship power, stationary DC

microgrids, renewable energy integration, and related fields involving terrestrial power

systems

− As the team identifies project opportunities to apply the algorithm in other areas, the

funding from those clients may be used as cost sharing to attract extended and

expanded funds for the NASA SBIR Phase 2 “DC HELM” project thus accelerating its

development and value to a greater number of customers

2015 EnergyTech 1