To solve the challenge with the simplified optimization method, we propose an adaptive MPC method. It involves adjusting the number of cost functions calculated by system states to ensure dynamic performance with low computational burden. To solve the problem that the classical method has a higher switching frequency, an adaptive hybrid predictive control framework is proposed. It involves adjusting the SM insertion number through the PR controller to obtain the adjustment amount for the SM inputs. It adds to the selected optimal candidate combination for current predictive control to obtain the ideal SM insertion combination . By controlling the threshold , the SM insertion adjustment amount is adjusted to reduce the change in switching frequency.
4.1. The Proposed Adaptive MPC
This work proposes an adaptive MPC to ensure fast dynamic performance. In this method, the candidate insertion number combinations are automatically adjusted according to system operation modes, achieving good adaptation for both steady and transient states. As shown in
Figure 4, at the stage of predictive current control, the system operation modes are distinguished between steady and transient states. If the system is operating in a steady state, three insertion number combinations (
,
), (
,
), and (
,
) are considered in the cost function of grid current. Once the cost function values of the three candidate combinations are all larger than the threshold
, it indicates that the system is operating in a transient state. Next, two additional candidate combinations (
,
and
,
) are calculated to shorten the optimization steps and improve the dynamic performance. As shown in
Figure 3, during the steady state, there are still only three candidate combinations considered in the cost function calculations. However, when the system reference suddenly changes, the proposed method calculates more combinations for the SM inputs, which improves the dynamic performance of the system. In summary, this method has low computational complexity in the steady state and only adds two to four cost function calculations in the transient state, effectively balancing computational complexity and dynamic tracking performance. Algorithm 1 is the proposed system state judgment algorithm.
Algorithm 1 State judgment in phase current control. |
- 1:
function A1 , ), (, ), (, ), - 2:
if && && then - 3:
Calculate (, ), (, ); - 4:
else - 5:
(, )=99999; - 6:
(, )=99999; - 7:
end if - 8:
Output: , , , , ; - 9:
end function
|
4.2. Proposed PR Circulating Current and Capacitor Voltage Fluctuation Suppression Controller
The simplified optimization hybrid predictive control framework can effectively suppress circulating current and capacitor voltage fluctuation, but it increases switching frequency and energy loss. To solve the problem, we maintained one switch state per cycle and developed an adaptive hybrid predictive control framework. We added a PR controller that modifies the SM insertion number instead of the duty cycle without increasing the switching frequency. When the system is in a steady state, the range of adjustment for the SMs is small, and when the system is in a transient state, is expanded to suppress circulating current and capacitor voltage fluctuation.
First, the candidate combinations are selected in the predictive current control. The candidate combination (
,
) is the optimal candidate combination in the grid current control. When the cost function of the candidate combination is higher than the threshold value of
, the system is in a transient state, and in the opposite case, it is in a steady state.
Figure 4 shows the improved hybrid control framework. Algorithm 2 is the algorithm for controlling the limit of SM input adjustment. Algorithm 3 is the proposed algorithm for selecting a circulating current reference based on control objectives.
Algorithm 2 State judgment in circulating current control. |
- 1:
function A2 ((, ), , ) - 2:
if < then - 3:
limit && ; - 4:
else - 5:
limit && ; - 6:
end if - 7:
Output: ; - 8:
end function
|
Algorithm 3 State judgment in capacitor voltage control. |
- 1:
function A3 (, , N, ,,) - 2:
if
then - 3:
let ; - 4:
else - 5:
let ; - 6:
end if - 7:
Output: ; - 8:
end function
|
Step 1: In the predictive current control, as before, the current tracking is achieved based on Equation (
8). Then, the cost function is minimized to select the optimal SM insertion number
for the current stage.
Step 2: In the PR-based control loop, the circulating current and circulating current reference are calculated and sent to the PR controller.
Step 3: The output of the PR controller is the corrected value for the SM insertion number, which effectively suppresses the circulating current through .
Step 4: Finally, the controller adds the SM insertion number
to the correction value
for the SM insertion number, considering the circulating current (the ideal SM insertion number is shown in Equations (14) and (15)). Then, the sorting algorithm balances the capacitor voltage and output switching signals.
By taking the derivative of Equations (12) and (13), it can be seen that the amplitude of the circulating current and capacitor voltage is inversely proportional when . When is constant, and the capacitor voltage is the smallest. When and , the capacitor voltage fluctuation is the smallest. When and , the circulating current is the smallest. Due to the quarter-cycle difference between the peak values of the circulating current and capacitor voltage, the peak values of the circulating current and capacitor voltage fluctuation can be suppressed separately by changing the reference of the circulating current. When the circulating current reaches its peak, it is suppressed, and the capacitor voltage fluctuation is not severe. The reverse is also true.
1: If , it means that the capacitor voltage fluctuation is greater than the circulating current deviation, and the system is in a transient state; excessive deviation in the capacitor voltage fluctuation from the reference requires priority control. Then, we use a outer loop PR controller to obtain and to ensure the control quality of the capacitor voltage fluctuation control.
2: If , it means that the capacitor voltage fluctuation is greater than the deviation in the circulating current, and the system is in a steady state; the capacitor voltage fluctuation does not deviate excessively from the reference. Then, we use a outer loop PR controller to obtain and to ensure the control quality of the predictive current control.
3: If , it means that the circulating current is greater than the capacitor voltage fluctuation deviation, and the system is in a transient state; excessive deviation in the circulating current from the reference requires priority control. We set and to ensure the control quality of the circulating current control.
4: If , it means that the circulating current is greater than the capacitor voltage fluctuation deviation, and the system is in a steady state; the circulating current does not deviate excessively from the reference. We set and to ensure the control quality of the predictive current control.
The proposed adaptive hybrid predictive control framework maintains the same combination of switch outputs during each control cycle and has a lower switching frequency than the hybrid MPC with a PR controller. Due to the difference of one quarter of a cycle between the peak value of the circulating current and capacitor voltage, controlling the current reference and coordinating the current and capacitor voltage according to operating conditions can reduce the peak of the circulating current and capacitor voltage. Additionally, this method has better circulating current and capacitor voltage suppression abilities. This is because the output of the PR control is the correction value for the SM insertion number rather than the duty cycle. When the circulating current deviation is severe, the range of action of the PR controller is increased to enhance the circulating current and capacitor voltage fluctuation control performance. Conversely, the range of the PR controller is reduced to enhance the current control performance.