Effects of Panel Orientation on Solar Integration into Electric Grids by M. Doroshenko ISS4E Lab, University of Waterloo

Problem Definition Increasing solar penetration leads to Duck Curve Curtailment caused by over-generation bad because solar is expensive both CAPEX and FIT Stability problems reverse flows and balance loss Ramping evening ramp (sunset) micro weather variations macro weather variations

Why is Ramping Bad? Ramping leads to increased thermal power plant cycling “Cycling refers to the operation of electric generating units at varying load levels, including … load following … in response to changes in system [net] load requirements”[1] Estimating impact (WWSIS) Renewables “increase annual cycling costs by $35-$157 million, or 13%-24%, across the Western Interconnection” [2] Negligible in comparison to fuel displaced by renewables ($7 billion) Emissions associated with cycling are estimated to be negligible as well Still, there might be some potential for financial improvement 1) N Kumar, P Besuner, S Lefton, D Agan, and D Hilleman. Power plant cycling costs. Contract, 303: , )

Idea What parameters of solar panels can be manipulated to alleviate the aforementioned problems? What if changing panel orientation can help? installation stage only Mechanism: East- and West-facing panels may cut the peaks and flatten the ramps

Positioning Parameters Orientation angle between the panel’s normal and the South also called azimuth angle Tilt angle between the panel and the horizontal plane not crucial in the current research

Model Formulation Single agent independent system operator (e.g. IESO) Linear programming model objective: minimize expenditures and emissions Iterative vs Basic Approach simulation is repeated several times solar installed capacity is aggregated over time Advantages: dynamic solar penetration easy to adjust for multi-agent modeling Many simplifying assumptions: to be explored later

Model Formulation: Overview Objective: Balance constraint: Incremental constraint: *non-negativity constraints are not presented

Model Formulation: Objective Variables: q j – quantity of panels with orientation j to be installed (J=13) G i – aggregate conventional generation at time i (I=8760) Parameters: γ i,j – solar power production level for time i and orientation j (HOMER) r j – feed-in tariff imposed for orientation j ( ∀ j: r j =25 cents/kWh) p i – price of thermal power imposed for time i ( ∀ i: p i =5 cents/kWh) λ – carbon tax factor (monetized control knob)

Model Formulation: Constraints Variables: q j – quantity of panels with orientation j to be installed (J=13) G i – aggregate conventional generation at time i (I=8760) Parameters: H i – aggregate load at time i (22.8 kW max, scaled down from IESO) e j – existing panels with orientation j at this iteration (aggregated over time) Q – incremental limit per step (10 panels per year) γ i,j – solar power production level for time i and orientation j (HOMER)

Incremental and Aggregate View

Analysis Curtailing minimized due to the objective As solar penetration grows, model no longer deems South optimal: 110 panels South further 64 panels are placed facing East and West increasing generation during morning and evening avoidance of high curtailing during afternoon If λ≤20 cents/kWh – no solar installed more economical to use thermal Growth of λ results in increased curtailing Summer Profile (λ=30) Winter Profile (λ=30)

Future Work Current limitations Single-agent model Stick only – rigid orientation requirement set by ISO No carrot – no financial incentives for owners to diversify orientation Did not address ramping/cycling yet Plan Debug the multi-objective model Introduce variables pertinent to cycling Collect real data from installation on campus

Conclusion The model demonstrates value of orientation diversification curtailing is minimized even though cycling is not taken into account diversification occurs once solar penetration reaches the level of load Challengers Sun-following installations (tracking systems) Storage systems High capital costs

Q&A

Technical Stuff Homer data based on the assumption that all orientations have the same tilt optimal tilt for given latitude when facing South However, this tilt may not be optimal for panels facing East or West Real data will be collected from panels with tilt of 15° 5 orientations will be available