Adaptive Power Control Method for Distributed Generators in DC Microgrids

The model-free control strategy based on the adaptive observer is presented to manage load power distribution for distributed generators in DC microgrids. By dynamically linearizing the modeling of the microgrid system, the model-free secondary control signal is designed to coordinate the distributed power sources, so that the load power is distributed proportionally to the rated capacity. In addition, the desired output voltage is introduced to restore the system bus voltage. The control scheme cannot depend on the structural details of the object system, which is structurally simple and easily implemented. Finally, the feasibility of the proposed data-driven scheme is demonstrated through case test results based on the RTDS experimental platform.


Introduction
Microgrids allow for the effective integration of distributed generators (DGs), which are an important development direction for future smart grids [1].With the rapid development of DC supplies like photovoltaics, energy storage devices, and fuel cells, and the proliferation of DC loads like LED illumination and electrical mobility, DC microgrids have attracted much attention and research from scholars due to their low costs and minimal losses, as well as eliminating the need to consider reactive power compensation and frequency stability.
Hierarchical control is the main control approach for microgrids.Among them, primary control is droop control and secondary control is used to compensate for voltage deviation and energy distribution errors arising from the main droop control [2].The secondary optimal regulation of the microgrid can improve the system operating efficiency and power quality.In addition, model information such as system structure and system order of the actual nonlinear controlled system is unknown, making it difficult to establish an accurate mathematical model.Data-driven model-free control uses historical sampling data to estimate the controlled object model, does not rely on system model information, and has a simple control structure, which is already widely used in areas such as autonomous driving, motor control, and traffic control [3,4].
This study proposes a model-free secondary strategy with an adaptive observer for distributed generators in DC microgrids.A dynamic linearisation model is established by using the measurement data, and a model-free control strategy is further designed to achieve load power distribution according to rated capacity and system bus voltage recovery.The proposed data-driven control scheme does not require a priori knowledge of the controlled system with simple structure and high robustness.In addition, the feasibility of the proposed strategy is demonstrated through an example study.

DC microgrid Structure
A typical microgrid configuration is illustrated in Fig. 1, containing a DC bus, DGs (including PV and energy storage units), and loads.In a DC microgrid, the DGs are usually attached to the public bus in a direct shunt connection.

traditional droop control
The energy distribution among the converters is controlled using the conventional droop function, where the V-P droop control is expressed as follows: where oi V is the output voltage, ref V is the rated voltage of the DC bus, i m is the droop factor, and oi P is the output power.
The conventional droop control method cannot ensure that each DG precisely distributes the load power according to its rated capacity, and the inherent voltage deviation reduces the quality of the supply voltage of the DC microgrid system.

Model-free secondary control strategy
To achieve system voltage stability and accurate power distribution, a distributed secondary strategy is suggested.Every converter gets driven directly from the droop function, and the overall control scheme is illustrated in Fig. 2.Then, a secondary input i n is designed to be added to the main droop Function (1), i.e. ( ) ( ( ), ( )) y V P  is the system output vector and ( ) ꞏ f is an unknown system model parameter.Measuring the DG output voltage and power online, Equation ( 3) is discretized as ( 1) ( ( ), ( 1), , ( ), ( ), ( 1), , ( )) where d is an unknown positive integer representing the order of the system.Equation ( 4) can be equivalently converted to an incremental form of the data model by partial form linearisation under typical constraints [5].
, there must exist a pseudo-partial derivative (PPD) matrix ( ) i k Φ that allows Equation ( 4) to be converted to ( 1) ( ) ( ) where , and L is the dynamic linearisation constant.
The partial form linearised Equation ( 5) of the microgrid system is an equivalent data model whose existence can be demonstrated by a rigorous mathematical analysis process [6].
Prior to designing the controller, an adaptive observer is proposed to estimate the parameters ( ) i k Φ .Measuring the voltage and power of DGs, the ith observer is structured as follows: ( is the output estimation error, ˆ( ) i k y is the system output estimate, ˆ( ) i k Φ is the estimate of the PPD matrix, and i K is the matrix of observer gains with satisfying i i F I K   .
Combining Equation ( 5) and Equation ( 6), the output estimation error is given by ( 1) ( ) ( ) ( ) where ( ) ( ) ( ) is the estimation error of the PPD matrix.Then, the adaptive update rate of the PPD matrix is expressed by , and 0 i   is a weighting coefficient to constrain the variation range of PPD estimates.Thus, the PPD adaptive observer for Equation ( 5) is shown as According to Equation (9), the model-free secondary controller is as follows: is the desired output of the system, 0   is the weighting factor, and  is a finite constant used to limit the variation rate of the control input.
In the proposed model-free second control method, the desired output voltage is the nominal voltage and the desired output power * / ( ) oi ratei ratei oi P P P P    .Through the dynamic adjustment of the desired output of DGs, the precise energy distribution and voltage stabilization of the microgrid are achieved, thus ensuring the steady operation of the entire system.

Experimental analysis
To prove the feasibility of the proposed method based on the adaptive observer, a DC microgrid system with three parallel DGs (DG1, DG2, and DG3) and three loads is built based on the RTDS experimental platform, as illustrated in Fig. 3.The specific system parameters are shown in Table 1.
Table 1 System Parameters Parameter Symbol Value Rated power of DG1

Case 1: load power distribution
The effectiveness of the proposed strategy is verified in Case 1 by the power distribution during steady state operation of the system.During 0-2 s, the system operates in the conventional droop control state.
As can be seen from Fig. 4 (a), the load power distribution among the DGs cannot be proportionally distributed due to the influence of line impedance.At t=2s, the DGs switch to the proposed model-free control scheme.In the proposed scheme, the controller dynamically adjusts the actual output power of each DG by the desired output power to achieve an accurate proportional distribution of load power.At the same time, the desired output voltage is introduced to control the converter outlet side voltage to restore the bus voltage to the rated system voltage, as shown in Fig. 4 (b) and Fig. 4 (c).

Conclusion
A model-free secondary control scheme for distributed generators in DC microgrids is suggested to provide accurate energy distribution and system voltage recovery.The model-free controller is designed by dynamic linearisation modeling, which is robust and easy to implement.The test results based on the RTDS experimental platform demonstrate that the proposed method is feasible and able to guarantee the stable operation of the microgrid system.

Fig. 2
Fig. 2 Secondary control structure diagramFrom the microgrid system illustrated in Fig.2, an input-output data model of the following form can be developed.

Fig. 3
Fig. 3 System block diagram based on RTDS

Fig. 4 Fig. 5
Fig. 4 Operational results of load power distribution with the proposed control strategy 4.2.Case 2: Load-side power fluctuations This example verifies the effectiveness of the proposed model-free secondary control by the power fluctuations on the load side.During 0-5 s, only Load 1 works normally on the load side of the system.At t=5s, Load 2 is connected on the load side.In addition, Load 3 is connected on the load side at t=10s.The system operation results under load-side power fluctuation are shown in Fig. 5.It can be seen from Fig. 5 (a) that the load power can be distributed in proportion to the rated capacity under the proposed control strategy, regardless of the load variations.Moreover, the bus voltage fluctuates within a reasonable voltage range during load-side power fluctuations, as shown in Fig. 5 (b) and Fig. 5 (c).