1. Voltage Control in Power Systems: Preliminary Results T. Geyer, G. Ferrari-Trecate, T. Geyer, G. Ferrari-Trecate, M. Morari Automatic Control Laboratory Swiss Federal Institute of Technology (ETH) in collaboration with Mats Larsson ABB

2. Power system: overview Generator 1:  infinite bus Generator 2:  generates limited power Capacitor bank:  stabilizes power system Transformer:  steps down voltage  controls load voltage Load:  consumes power Network:  connects components

3. Power system: overview (ctd.) hybrid system:  discrete manipulated variables  logic and finite state machine  nonlinearities  pwa functions 3 major submodels:  generator 2  transformer  load

4. Hybrid model dimensions:  2 ordinary diff. equations  1 finite state machine  29 algebraic equations:  11 linear, 18 nonlinear  6 states:  2 continuous, 4 discrete  4 manipulated variables:  1 continuous, 3 discrete model available:  in modelica  as pwa discrete-time approx. in MLD form  and ?

5.  control objectives:  stabilizeV 4m (cont.)  min. load shedding s L (disc.)  manipulated variables:  ultc voltage reference: V 4m,ref (cont.)  capacitor switching: s C (disc.)  load shedding: s L (disc.)  disturbance:  line outage (disc.) Control problem

6. Optimal Control Problem Subject to  Dynamics (in MLD form):  Soft constraints on bus voltages :

7. Receding Horizon Control  Optimize at time t (with new measurements)  Only apply the first optimal move u(t)  Repeat the whole optimization at time t +1  Advantage of on-line optimization: Feedback!

8. Tuning of Cost Function  Violation of soft constraints is penalized by:  Choose weight R on u such that: No constraint violation:nominal control: > ultc voltage reference > capacitor bank Constraint violation:emergency control: > all controls including load-shedding

9. Preliminary Results

10. Conclusions  Control problem:  MPC is able to stabilize the load voltage V 4m with N=2 and T s =15sec without using load-shedding  solution time 8sec..2min (PC with 1GHz)  but: there remains a control error  Outlook:  observer  model reduction  reachability analysis  large-scale problem