Photovoltaic energy system with value function optimization
A photovoltaic energy system includes a photovoltaic field configured to convert solar energy into electrical energy, a power inverter configured to control an electric power output of the photovoltaic field, and a controller. The controller can determine optimal power setpoints for the power inverter by optimizing a value function that includes a penalty cost for failing to comply with a ramp rate limit and photovoltaic revenue.
1. A photovoltaic energy system comprising:
a photovoltaic field configured to convert solar energy into electrical energy;
a power inverter configured to control an electric power output of the photovoltaic field;
a battery; and
a controller configured to determine optimal power setpoints for the power inverter by optimizing a value function that includes a penalty cost for failing to comply with a ramp rate limit, photovoltaic revenue as a function of the optimal power setpoints, a cost of battery capacity loss, and battery operating cost as a function of the optimal power setpoints,
wherein the controller is configured to estimate the penalty cost of failing to comply with the ramp rate limit as a function of a number of noncompliance events and an amount by which an actual rate of change of the electric power output exceeds the ramp rate limit.
2. The photovoltaic energy system of claim 1 , wherein the power inverter is configured to control the power output of the photovoltaic field to an energy grid.
3. The photovoltaic energy system of claim 1 , wherein the power inverter is configured to convert a direct current (DC) output of the photovoltaic field into an alternating current (AC) output and provide the AC output to an energy grid, the AC output defining an electric power output of the photovoltaic energy system.
4. The photovoltaic energy system of claim 1 , wherein the controller is configured to determine a set of optimal power setpoints for the power inverter at each of a plurality of time steps within a prediction window.
5. The photovoltaic energy system of claim 1 , wherein the controller is configured to estimate the photovoltaic revenue as a function of an electric power output to an energy grid resulting from the optimal power setpoints and a price of the electric power output to the energy grid.
6. The photovoltaic energy system of claim 1 , wherein the controller is configured to optimize the value function over a prediction window comprising a plurality of time steps;
wherein the value function is a summation of the photovoltaic revenue and the penalty cost at each of the plurality of time steps.
7. A photovoltaic energy system comprising:
a photovoltaic field configured to convert solar energy into electrical energy;
a first power inverter configured to control an electric power output of the photovoltaic field;
a battery;
a second power inverter configured to control an electric power output of the battery; and
a controller configured to determine optimal power setpoints for the first power inverter and the second power inverter by optimizing a value function that includes a penalty cost for failing to comply with a ramp rate limit, a cost of battery capacity loss, and battery operating cost as a function of the optimal power setpoints,
wherein the controller is configured to estimate the penalty cost of failing to comply with the ramp rate limit as a function of a number of noncompliance events and an amount by which an actual rate of change of the electric power output exceeds the ramp rate limit.
8. The photovoltaic energy system of claim 7 , wherein the first power inverter is configured to control the electric power output of the photovoltaic field to an energy grid and the second power inverter is configured to control the electric power output of the battery to the energy grid.
9. The photovoltaic energy system of claim 7 , wherein the first and second power inverters are configured to convert a direct current (DC) output of the photovoltaic field and the battery into an alternating current (AC) output and provide the AC outputs to an energy grid, the AC outputs defining a total electric power output of the photovoltaic energy system.
10. The photovoltaic energy system of claim 7 , wherein the battery is configured to store at least a portion of the electrical energy generated by the photovoltaic field;
wherein the controller is configured to adjust a total electric power output of the photovoltaic energy system using electrical energy from the battery to supplement the electric power output of the photovoltaic field.
11. The photovoltaic energy system of claim 7 , wherein the controller is configured to estimate the battery operating cost as a function of at least one of:
cost of charging the battery;
cost of discharging the battery; and
heat generation from the battery.
12. The photovoltaic energy system of claim 7 , wherein the value function further comprises at least one of:
estimated revenue from an electric power output of the photovoltaic energy system to an energy grid;
estimated cost of failing to comply with a ramp rate limit; and
electric power losses within at least one of the first power inverter and the second power inverter.
13. The photovoltaic energy system of claim 7 , wherein the controller is configured to determine a set of optimal power setpoints for the first power inverter and the second power inverter at each of a plurality of time steps within a prediction window.
14. A renewable energy system comprising:
a renewable energy field configured to convert a renewable energy source into electrical energy;
a first power inverter configured to control a power output of the renewable energy field;
a battery;
a second power inverter configured to control a power output of the battery; and
a controller configured to determine optimal power setpoints for the first power inverter and the second power inverter by optimizing a value function that includes a penalty cost for failing to comply with a ramp rate limit, a cost of battery capacity loss, and battery operating cost as a function of the optimal power setpoints,
wherein the controller is configured to estimate the penalty cost of failing to comply with the ramp rate limit as a function of a number of noncompliance events and an amount by which an actual rate of change of the electric power output exceeds the ramp rate limit.
15. The renewable energy system of claim 14 , wherein the renewable energy field comprises at least one of a photovoltaic field, a wind turbine field, a hydroelectric field, a tidal energy field, and a geothermal energy field.
16. The renewable energy system of claim 14 , wherein the first power inverter is configured to control the electric power output of the renewable energy field to an energy grid and the second power inverter is configured to control the electric power output of the battery to the energy grid.
17. The renewable energy system of claim 14 , wherein the battery is configured to store at least a portion of the electrical energy generated by the renewable energy field;
wherein the controller is configured to adjust a total electric power output of the renewable energy system using electrical energy from the battery to supplement the electric power output of the renewable energy field.
18. The renewable energy system of claim 14 , wherein the controller is configured to estimate the battery operating cost as a function of at least one of:
cost of charging the battery;
cost of discharging the battery; and
heat generation from the battery.
19. The renewable energy system of claim 14 , wherein the controller is configured to determine a set of optimal power setpoints for the first power inverter and the second power inverter at each of a plurality of time steps within a prediction window.