Distributed Smart Energy Systems

IfA Open House - 3 December 2018

New technologies for power generation from renewable energy sources

Ready for 100% renewables?

What is mature?

What is not?

  • Microgeneration technology
  • Primary source diversification
  • Incentives and policies
  • Enterprises and investors
  • Real-time grid operation
  • A technology to interconnect renewable sources
  • A study of the stability/performance of the system

The Smart Grid challenge:

innovate the largest machine ever built by man

Virtual inertia for

increased frequency stability

Traditional grid:

massive mechanical inertia that automatically compensates for power imbalance

Future grid:

larger power imbalance
less mechanical inertia
one solution:
virtual inertia

Virtual inertia = real energy storage + power converter

\displaystyle \min \int_0^\infty \left( \sum_{ij} \alpha_{ij} (\theta_i(t) - \theta_j(t))^2 + \sum_i \beta_i \dot \theta_i(t)^2 \right) dt
min⁡∫0∞(∑ijαij(θi(t)−θj(t))2+∑iβiθ˙i(t)2)dt\displaystyle \min \int_0^\infty \left( \sum_{ij} \alpha_{ij} (\theta_i(t) - \theta_j(t))^2 + \sum_i \beta_i \dot \theta_i(t)^2 \right) dt
\displaystyle M_i \ddot \theta_i + D_i \dot \theta_i = {P_i}^\text{in} - {P_i}^\text{out}
Miθ¨i+Diθ˙i=Piin−Piout\displaystyle M_i \ddot \theta_i + D_i \dot \theta_i = {P_i}^\text{in} - {P_i}^\text{out}

Swing eq.

Goal:

Advanced methods for numerical optimization

Analysis of a zero-inertia grid:
phasor-free models

Most power system models implicitly assume

quasi-sinusoidal operation at the nominal frequency

We need a model without these assumptions!

Synchronous generators

Power
converters

A port-Hamiltonian model for the power grid:

  • explicit modeling of energy balance
  • network of subsystems
  • powerful tools for the analysis of the interconnection

A model for the design of new generation of grid controllers

Mathematical modeling

Synchronization in a zero-inertia grid:
virtual oscillators

How to synchronize power inverters?

Do we need to emulate synchronous generators? 

Emerging limit cycles in nonlinear systems!

Nonlinear control design

Real-time power flow optimization

Typical grid optimization problem

\displaystyle \min_{v, \theta, p, q} \sum_i c_i(p_i)
min⁡v,θ,p,q∑ici(pi)\displaystyle \min_{v, \theta, p, q} \sum_i c_i(p_i)

sum of power generation costs

{p_i}^\text{min} \le {p_i} \le {p_i}^\text{max}
pimin≤pi≤pimax{p_i}^\text{min} \le {p_i} \le {p_i}^\text{max}
{v_i}^\text{min} \le {v_i} \le {v_i}^\text{max}
vimin≤vi≤vimax{v_i}^\text{min} \le {v_i} \le {v_i}^\text{max}

power generation limits

voltage contraints

\sqrt{{p_i}^2 + {q_i}^2} \le {s_i}^\text{max}
pi2+qi2≤simax\sqrt{{p_i}^2 + {q_i}^2} \le {s_i}^\text{max}

thermal generator limits

v_i \sum_j v_i (g_{ij} \cos (\theta_i -\theta_j) + b_{ij} \sin (\theta_i -\theta_j) ) = p_i
vi∑jvi(gijcos⁡(θi−θj)+bijsin⁡(θi−θj))=piv_i \sum_j v_i (g_{ij} \cos (\theta_i -\theta_j) + b_{ij} \sin (\theta_i -\theta_j) ) = p_i
v_i \sum_j v_i (g_{ij} \sin (\theta_i -\theta_j) - b_{ij} \cos (\theta_i -\theta_j) ) = q_i
vi∑jvi(gijsin⁡(θi−θj)−bijcos⁡(θi−θj))=qiv_i \sum_j v_i (g_{ij} \sin (\theta_i -\theta_j) - b_{ij} \cos (\theta_i -\theta_j) ) = q_i

power flow eq's!

A highly nonconvex manifold!

 

Geometric methods for iterative optimization

Optimization theory

Questions?

Distributed control

Optimization theory

Nonlinear control design

Mathematical modeling

Advanced methods for numerical optimization

Distributed Smart Energy Systems

Distributed Smart Energy Systems

By Saverio Bolognani

Distributed Smart Energy Systems

A short presentation for the IfA Open House

  • 2,000

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