Adaptive Bidirectional Droop Control Strategy for Hybrid AC-DC Port Microgrids

Abstract

To solve the problem that the interlinking converter of hybrid AC-DC port microgrids cannot satisfy optimal control under multiple operating conditions, an adaptive bidirectional droop control strategy of the interlinking converter in the islanding hybrid microgrid is proposed. Based on the normalization method, the AC frequency and DC voltage are uniformly controlled. The priority of AC microgrid frequency control and DC microgrid voltage control in bidirectional droop control is determined by adaptive weight coefficients, so that the interlinking converter preferentially supports the side with a larger deviation of AC frequency or DC voltage, which ensures that the frequency and voltage of both sides are maintained within the optimal range. The action dead band is designed to optimize the starting conditions and reduce unnecessary actions of the interlinking converter. A small signal model of the system is established, and the stability of the proposed control strategy is verified by root locus analysis.

3.1 Introduction

Port Electric-thermal microgrid is one of the typical applications of integrated energy systems. Its integrates the supply, conversion, and storage equipment in electric and thermal energy flows based on users’ electrical and thermal demands, and to coordinate and optimize protection and control methods to achieve economical and reliable operation [1,2,3,4]. With the increasingly diverse energy needs of industrial, commercial, and residential users supplied by microgrids, there exist more complex multi-energy couplings, such as energy cascade utilization, which poses difficulties for energy optimization management of electric thermal microgrids [4, 5]. Energy cascade utilization is an effective method to improve energy utilization efficiency and supply quality. It is an important direction in current research on energy optimization management of electric-thermal microgrids [6,7,8].

AC-DC hybrid microgrid mainly consists of AC microgrid, DC microgrid and microgrids interlinking converter (MIC). The MIC is the core device to balance the power of both microgrids, which can coordinate the control of AC and DC microgrids to achieve bi-directional power mutual aid and optimal stability. MIC not only ensures the stable and efficient operation of hybrid microgrid under different operating conditions, but also further improves the capacity of renewable energy consumption. As a bridge for AC-DC power exchange, the interconverter plays a key role in maintaining the stability of the system frequency and voltage [9,10,11,12], and the design of suitable interconverter control strategy becomes an important research content in the development of hybrid AC-DC microgrid.

AC-DC hybrid microgrid interconverters need to regulate AC frequency and DC voltage simultaneously, and the traditional active droop method, which only considers single-side quantities, is no longer applicable. By improving the traditional droop control equations or studying the coupling relationship between AC frequency and DC voltage, scholars have proposed bidirectional power control strategies that can regulate AC frequency and DC voltage simultaneously [13,14,15,16]. The literature [17, 18] unifies the droop characteristics of AC side and DC side for bidirectional droop control of microgrid interconnection converter based on typical hybrid microgrid structure through the scalarization process. In [19], the droop relationship between frequency and voltage squared is introduced for control through the energy conservation relationship on the AC and DC sides. The literature [20] analyzed the linear coupling relationship between AC frequency and DC voltage by virtual inertia and virtual capacitance characteristics, and also obtained the droop relationship between AC frequency and DC voltage squared. To further improve the stability of hybrid AC-DC microgrid, literature [21] proposed an improved inner-loop control strategy for microgrid interconnection converter based on disturbance observation link, and literature [22, 23] provided inertia support for frequency and voltage based on virtual synchronous motor control strategy to improve the system anti-disturbance capability. Literature [24] proposed a control strategy for microgrid interconnection converter with AC-DC microgrid internal energy storage device to improve the overall energy management capability of hybrid microgrid. In the literature [25], an AC-DC microgrid two-layer optimization method is proposed, which incorporates secondary regulation and DG generation cost optimization control strategies based on bidirectional droop control of the interconnection converter. In the literature [17,18,19,20,21,22,23,24,25], a unified droop control based on the scalarization method or linking the AC frequency and DC voltage from the energy balance perspective is performed for the control of microgrid interconnection converters to realize the bidirectional control of power between AC and DC microgrids. However, in the process of power regulation of hybrid microgrid with islanded operation, there is often a conflict between AC frequency optimization and DC voltage optimization due to the limitation of adjustable DG power regulation capability, and the aforementioned literature is based on fixed droop coefficient or proportional coefficient to regulate the power between AC and DC sub-microgrids without considering the regulation priority between AC frequency and DC voltage. Due to the different amount of DG access, the strength of the AC-DC sub-micro-network's ability to stabilize frequency and voltage will also change. The two-way droop control strategy based on fixed coefficients will lead to larger frequency or voltage deviations when load changes occur on the weaker side of the AC-DC sub-micro-network, which cannot give full play to the support role of the strong micro-network to the weak micro-network, and the frequency and voltage equalization effect is poor.

To solve the above problems, this chapter proposes an interconverter adaptive bidirectional droop control strategy with the control objective of balancing and compensating the AC frequency and DC voltage deviations of the hybrid microgrid. In order to reduce the combined deviation of AC frequency and DC voltage, the adaptive value of the weight coefficient is proposed to ensure that the MIC gives priority to the quantity with larger deviation in the active dynamic regulation process. Set the start-up deadband to avoid the non-essential operation of the interconverter. Establish the small-signal model of the interconnection converter and analyze the influence of the control parameters on the system stability. A typical AC-DC hybrid microgrid system is established in the PSCAD/EMTDC simulation platform and RT-LAB experimental platform to verify the effectiveness and reliability of the proposed control strategy.

3.2 Hybrid Microgrid and Its Interlinking Converter

3.2.1 AC-DC Hybrid Microgrid

The typical topology of a hybrid AC/DC microgrid is shown in Fig. 3.1. The AC microgrid and DC microgrid are interconnected at the bus through an interlinking converter, allowing for flexible power flow between the two grids. By controlling the interlinking converter, power can flow bidirectionally between the AC microgrid and DC microgrid. The entire hybrid microgrid system is connected to the public AC grid through a point of common coupling (PCC), enabling seamless switching between grid-connected and islanded modes.

Fig. 3.1

Typical hybrid AC/DC interconnected microgrids

The hybrid microgrid with both AC and DC components adopts a peer-to-peer control mode, which does not require communication and can meet the requirement of plug-and-play for both distributed generators (DGs) and loads. The controllable DGs within the AC microgrid jointly maintain the stability of AC bus frequency and voltage according to the P − f and Q − U_ac droop characteristics outlined in Eq. (3.1).

$$\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {f = f_{0} - K_{fi} \left( {P_{i} - P_{0i} } \right)} \\ {U_{{{\text{ac}}}} = U_{{{\text{ac}}0}} - K_{qi} \left( {Q_{i} - Q_{0i} } \right)} \\ \end{array} } \right.} \\ \end{array}$$

(3.1)

Among them, the subscript i represents the index of the AC DG, P_i represents the active power output of DG i, P_0i represents the active power output of DG i under rated conditions, f₀ is the power frequency, f is the current operating frequency of the AC microgrid, K_fi is the frequency droop coefficient, Q_i represents the reactive power output of DG i, Q_0i represents the reactive power output of DG i under rated conditions, U_ac0 is the rated AC voltage, U_ac is the current voltage of the AC microgrid, and K_qi is the voltage droop coefficient. In order to achieve load sharing, the droop coefficients K_fi and K_qi are inversely proportional to the capacity of DG i.

The controllable distributed generators (DGs) in the DC microgrid collectively maintain the stability of the DC bus voltage according to the droop relationship of Eq. (3.2) for P-U_dc.

$$\begin{array}{*{20}c} {U_{{{\text{dc}}}} = U_{{{\text{dc}}0}} - K_{uj} \left( {P_{j} - P_{0j} } \right)} \\ \end{array}$$

(3.2)

where the subscript j represents the index of the DC distributed generation (DG), P_j represents the active power output of DG_j, P_0j represents the output power of DG_j under rated conditions, U_dc0 represents the rated DC voltage, U_dc represents the current operating voltage of the DC microgrid, and K_uj represents the droop coefficient of the DC voltage. In order to achieve load sharing, the droop coefficient K_uj is inversely proportional to the capacity of DG_j.

3.2.2 The Structure of Hybrid Microgrid Interlinking Converter

The microgrid interlinking converter adopts voltage source converter (VSC) structure, and the topology is shown in Fig. 3.2, where the meanings of the variables are as follows: U_abc and i_abc are the three-phase voltage and current on the AC side of the converter, E_abc is the three-phase voltage of the AC bus, L_ac is the total inductance of the filter and line between the AC side of the converter and the AC bus, C_dc is the DC filter capacitor, U_dc and i_dc are the voltage and current of the DC side of the converter, respectively, and P_MIC is the active power exchanged between the AC and DC microgrids, and the analysis below takes the inverting direction as the positive power direction.

Fig. 3.2

Topological structure of the MIC

The microgrid interlinking converter of the microgrid adopts a voltage source converter (VSC) structure, as shown in Fig. 3.2. The meanings of the variables are as follows: U_abc and i_abc are the three-phase voltage and current on the converter's AC side, E_abc is the three-phase voltage of the AC bus, L_ac is the total inductance of the filter and line between the converter’s AC side and the AC bus, C_dc is the DC filter capacitor, U_dc and i_dc are the voltage and current on the converter’s DC side, P_MIC is the active power exchanged between the AC and DC microgrids. The analysis in the following text is based on the inverter direction as the positive power direction.

There is no reactive power balance issue in a DC microgrid, and the interlinking converter does not need to control the reactive power on the DC side. This chapter only discusses the impact of the active power control strategy of the interlinking converter on the frequency stability of the AC microgrid and the voltage stability of the DC microgrid under islanding operation mode.

3.3 Bidirectional Adaptive Droop Control Strategy for Interlinking Converter

3.3.1 Bidirectional Droop Control Targets

The interlinking converter, in the operation of an AC/DC hybrid microgrid island, coordinates the magnitude of the AC frequency deviation and the DC voltage deviation by controlling the active power between the AC and DC microgrids. To simplify the analysis, line impedance is ignored, and the relationship between power variation in the AC/DC sub-microgrids with load changes can be expressed as Eq. (3.3).

$$\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\mathop \sum \limits_{i = 1}^{m} P_{i} = \mathop \sum \limits_{i = 1}^{m} P_{0i} + \Delta P_{{{\text{load\_AC}}}} - P_{{{\text{MIC}}}} } \\ {\mathop \sum \limits_{j = 1}^{n} P_{j} = \mathop \sum \limits_{j = 1}^{n} P_{0j} + \Delta P_{{{\text{load\_DC}}}} + P_{{{\text{MIC}}}} } \\ \end{array} } \right.} \\ \end{array}$$

(3.3)

where m and n are the number of controllable DGs in the AC microgrid and DC microgrid, respectively. ΔP_{load_AC} and ΔP_{load_DC} are the incremental loads of the AC load and DC load respectively. Substituting Eqs. (3.1) and (3.2) into Eq. (3.3) yields the variations in AC frequency and DC voltage, as shown in Eq. (3.4).

$$\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {\Delta f = f - f_{0} = - \frac{{\Delta P_{{{\text{load\_AC}}}} - P_{{{\text{MIC}}}} }}{{\mathop \sum \nolimits_{i = 1}^{m} \frac{1}{{K_{fi} }}}}} \\ {\Delta U_{{{\text{dc}}}} = U_{{{\text{dc}}}} - U_{{{\text{dc}}0}} = - \frac{{\Delta P_{{{\text{load\_DC}}}} + P_{{{\text{MIC}}}} }}{{\mathop \sum \nolimits_{j = 1}^{n} \frac{1}{{K_{uj} }}}}} \\ \end{array} } \right.} \\ \end{array}$$

(3.4)

From Eq. (3.4), it can be seen that the deviation between the AC frequency and the DC voltage is related to the magnitude of the load change, the power transmitted by the interlinking converter, and the load-carrying capacity of the AC/DC hybrid microgrid itself. If the interlinking converter does not participate in power regulation, different load changes or the strength of the microgrid can cause a large deviation in either AC frequency or DC voltage, while the other quantity has a small deviation. When the load change is large or the microgrid is weak, the quantity with a large deviation in frequency and voltage will exceed the allowable range, affecting the safe and stable operation of the hybrid microgrid system.

The power control strategy for interlinking converters in a hybrid microgrid can provide power support from the side with smaller AC frequency or DC voltage deviation to the other side, ensuring that both AC frequency and DC voltage stay within limits. In order to quantitatively describe the impact of frequency and voltage deviations on the stability of the hybrid microgrid, a comprehensive deviation index called the Global Variation Index (G_vi) is defined as shown in Eq. (3.5) [24].

$$\begin{array}{*{20}c} {G_{{{\text{vi}}}} = \left( {\frac{\Delta f}{{f_{max} - f_{min} }}} \right)^{2} + \left( {\frac{{\Delta U_{{{\text{dc}}}} }}{{U_{{{\text{dcmax}}}} - U_{{{\text{dcmin}}}} }}} \right)^{2} } \\ \end{array}$$

(3.5)

where f_max and f_min are the maximum and minimum frequencies allowed for AC sub-microgrid, U_dcmax and U_dcmin are the maximum and minimum voltages allowed for DC sub-microgrid, respectively. The objective is to obtain the active reference value of the interlinking converter based on the current AC frequency and DC voltage of the hybrid microgrid system, and to make the hybrid microgrid to achieve a smaller active reference value under different load changes, DG switching, and AC and DC microgrid strengths and weaknesses by adaptive parameter droop control without communication. The adaptive parameter droop control enables the hybrid microgrid to achieve a small integrated deviation under different conditions of load variation, DG switching and AC/DC microgrid strength.

3.3.2 Adaptive Bidirectional Droop Control Strategy

To standardize the dimensions and simplify control, normalization is first applied to the AC frequency and DC voltage [18], as shown in Eq. (3.6).

$$\begin{array}{*{20}l} {\left\{ {\begin{array}{*{20}c} {f_{pu} = \frac{{f - 0.5\left( {f_{max} + f_{min} } \right)}}{{0.5\left( {f_{max} - f_{min} } \right)}}} \\ {U_{dc.pu} = \frac{{U_{dc} - 0.5\left( {U_{dcmax} + U_{dcmin} } \right)}}{{0.5\left( {U_{dcmax} - U_{dcmin} } \right)}}} \\ \end{array} } \right.} \\ \end{array}$$

(3.6)

where f_pu is the normalized AC frequency and U_dc.pu is the normalized DC voltage. After the normalization process, the frequency and voltage of the hybrid microgrid are unified to a range of [−1, 1] when normally allowed.

The power response of the interlinking converter to the AC/DC sub-microgrid can be obtained based on the “active power-frequency” droop relationship and the “active power-DC voltage” droop relationship. The difference power is the power reference value of the interlinking converter, with the inverter direction taken as the reference of positive direction, as shown in Eq. (3.7).

$$\begin{array}{*{20}c} {P = P_{0} - K \cdot f_{{{\text{pu}}}} + K \cdot U_{{{\text{dc.pu}}}} } \\ \end{array}$$

(3.7)

where K is the droop coefficient, which can be set based on the maximum power P_max of the interlinking converter [17], or adjusted according to actual operational requirements [23].

The control strategy of Eq. (3.7) implements bidirectional control of active power for the interlinking converter in the microgrid based on the droop relationship between AC and DC. However, this strategy cannot effectively adjust the priority of AC frequency and DC voltage response in different operating states due to the fixed droop coefficient. To address this, Eq. (3.8) is derived by introducing an adjustable weighting coefficient l into the equation.

$$\begin{array}{*{20}c} {P = P_{0} - \lambda \cdot K \cdot f_{{{\text{pu}}}} + \left( {1 - \lambda } \right) \cdot K \cdot U_{{{\text{dc.pu}}}} } \\ \end{array}$$

(3.8)

The range of variation for the weighting coefficient λ is (0, 1). By adjusting λ, the priority of power support between the AC and DC sides can be coordinated, ensuring a balanced compensation for AC frequency and DC voltage during disturbances.

To ensure the safe and reliable operation of an independent AC/DC microgrid, priority should be given to provide power support to the side with larger AC frequency or DC voltage deviations. By optimizing the power exchange between the two sides of the interlinking converter, the balance and compensation for AC frequency and DC voltage deviations can be achieved, thereby better ensuring the overall performance of the system. When the frequency deviation (f_pu) is greater than the DC voltage deviation (U_dc.pu), power is supported from the DC side to the AC side, ensuring that the AC frequency is adjusted according to the P − f_pu droop relationship. Conversely, when the power deviation (f_pu) is smaller than the DC voltage deviation (U_dc.pu), power is supported from the AC side to the DC side, ensuring that the DC voltage is adjusted according to the P − U_dc.pu droop relationship. Therefore, the weighting coefficient $\lambda$ is positively correlated with the AC frequency deviation and negatively correlated with the DC voltage deviation.

To adapt to different scenarios, λ is set to have sufficient sensitivity to both AC frequency and DC voltage deviations.

$$\begin{array}{*{20}l} {\lambda = \left\{ {\begin{array}{*{20}c} {\frac{{\left| {f_{pu} } \right|^{n} }}{{\left| {f_{pu} } \right|^{n} + \left| {U_{dc.pu} } \right|^{n} }},\left| {f_{pu} } \right| > \varepsilon or \left| {U_{dc.pu} } \right| > \varepsilon } \\ {0.5,\left| {f_{pu} } \right| < \varepsilon and \left| {U_{dc.pu} } \right| < \varepsilon } \\ \end{array} } \right.} \\ \end{array}$$

(3.9)

In the equation, ε represents a small value for optimal selection according to the microgrid operation requirements. In this text, e is set to 0.05. When the normalized AC frequency deviation and DC voltage deviation are within 5%, the weighting factor for the droop control on both sides is not adjusted, and in this case, λ is set to 0.5. The variation of λ with different values of n is shown in Fig. 3.3.

Fig. 3.3

Diagram of the variation of λ with n

From Fig. 3.3, it can be seen that when n is set to 1, the change in λ is too gradual, making it difficult to achieve optimal control of support power when f_pu and U_dc.pu have significant deviations. When n has a large value, the change in λ is too rapid, and the support power becomes too sensitive to fluctuations in f_pu and U_dc.pu, which can easily lead to control instability.

In order to give λ a certain adaptive ability to the deviation of f_pu and U_dc.pu, while avoiding the instability caused by λ being too sensitive to the changes of f_pu and U_dc.pu, by setting n = 2 in Eq. (3.9), the method for determining the adaptive weighting coefficients of λ is obtained as shown in Eq. (3.10).

$$\begin{array}{*{20}l} {\lambda = \left\{ {\begin{array}{*{20}c} {\frac{{f_{{{\text{pu}}}}^{2} }}{{f_{{{\text{pu}}}}^{2} + U_{\text{dc.pu}}^{2} }},\left| {f_{{{\text{pu}}}} } \right| > \varepsilon {\text{ or }}\left| {U_{{{\text{dc.pu}}}} } \right| > \varepsilon } \\ {0.5,\left| {f_{{{\text{pu}}}} \left| { \le \varepsilon {\text{ and }}} \right|U_{{{\text{dc.pu}}}}} \right| \le \varepsilon } \\ \end{array} } \right.} \\ \end{array}$$

(3.10)

Substituting Eq. (3.10) into Eq. (3.8), the adaptive bidirectional droop control equation can be obtained as shown in Eq. (3.11).

$$\begin{array}{*{20}l} {P = \left\{ {\begin{array}{*{20}c} {P_{0} - K \cdot \frac{{f_{{{\text{pu}}}}^{3} - U_{{{\text{dc.pu}}}}^{3} }}{{f_{{{\text{pu}}}}^{2} + U_{{{\text{dc.pu}}}}^{2} }},\left| {f_{{{\text{pu}}}} } \right| > \varepsilon {\text{ or }}\left| {U_{{{\text{dc.pu}}}} } \right| > \varepsilon } \\ {P_{0} - 0.5 \cdot K \cdot \left( {f_{{{\text{pu}}}} - U_{{{\text{dc.pu}}}} } \right),\left| {f_{{{\text{pu}}}} \left| { \le \varepsilon {\text{ and }}} \right|U_{{{\text{dc.pu}}}} } \right| \le \varepsilon } \\ \end{array} } \right.} \\ \end{array}$$

(3.11)

The control equation can achieve the control effect shown in Table 3.1. The adaptive bidirectional droop control strategy prioritizes the side with larger deviations in AC frequency and DC voltage, and smoothly transitions between P − f_pu droop control and P − U_dc.pu droop control, without causing any impact during the control strategy switching process. Since both AC frequency and DC voltage can be directly measured at the interface of the microgrid interlinking converter, this method does not require communication and is suitable for the plug-and-play requirements of microgrids.

Table 3.1 Adaptive bidirectional droop control characteristics

When Δf is large, priority is given to maintaining f within the normal operating range through the P − f droop relationship. When ΔU_dc is large, priority is given to maintaining U_dc within the normal operating range through the P − U_dc droop relationship. This achieves adaptive adjustment of the deviation.

The active reference values of the MIC under different conditions are shown in Fig. 3.4. The equation for adaptive bidirectional droop control is a binary function, and its function graph is the characteristic surface of P_ref in the spatial coordinate system with respect to f_pu and U_dc.pu. Based on the relative size relationship between normalized frequency and voltage, the operating range can be divided into four quadrants.

Fig. 3.4

Reference power of MIC in different situations

• (1) Quadrant I: f_pu > 0 and U_dc.pu < 0. In this case, there is an excess of power in the AC microgrid and a shortage of power in the DC microgrid. The interlinking converter operates in rectifier mode, providing power support from the AC microgrid to the DC microgrid.

• (2) Quadrant II: f_pu > 0, U_dc.pu > 0. In this case, both the AC and DC sub-microgrids have power surplus. The interlinking converter operates in standby, rectifier, or inverter mode based on the relative magnitudes of the AC frequency and DC voltage, reducing overall deviation.

• (3) Quadrant III: f_pu < 0, U_dc.pu > 0. In this case, there is a shortage of power in the AC sub-microgrid, while the power in the DC sub-microgrid is surplus. The interlinking converter operates in the inverter mode, providing power support from the DC sub-microgrid to the AC sub-microgrid.

• (4) Quadrant IV: f_pu < 0, U_dc.pu < 0. In this case, both AC and DC microgrids have a power deficit. Interlinking converters operate in standby, rectifier, or inverter mode based on the relative sizes of the AC frequency and DC voltage, reducing the overall deviation.

The above analysis demonstrates that the proposed adaptive bidirectional droop control strategy can achieve bidirectional power flow based on the magnitude of the AC frequency and DC voltage deviation. Furthermore, when there is a conflict between AC frequency control and DC voltage control, it can prioritize compensating the side with larger deviation in order to reduce the overall deviation.

3.3.3 Start-Up Conditions

The real-time variation of DG and load within the hybrid microgrid can lead to small-scale fluctuations in active power, even when the system is operating stably. In order to prevent frequent operation of the interlinking converter during steady-state operation, a deadband is required as a start-up condition in practical applications.

By factoring Eq. (3.11), we obtain Eq. (3.12):

$$\begin{array}{*{20}c} {P = P_{0} - K^{\prime}\left( {f_{{{\text{pu}}}} - U_{{{\text{dc.pu}}}} } \right)} \\ \end{array}$$

(3.12)

where K′ is the adaptive bidirectional droop coefficient, which can be expressed as:

$$\begin{array}{*{20}l} {K^{\prime} = \left\{ {\begin{array}{*{20}c} {\frac{{f_{{{\text{pu}}}}^{2} + f_{{{\text{pu}}}} \cdot U_{{{\text{dc.pu}}}} + U_{{{\text{dc.pu}}}}^{2} }}{{f_{{{\text{pu}}}}^{2} + U_{{{\text{dc.pu}}}}^{2} }} \cdot K,\left| {f_{{{\text{pu}}}} } \right| > \varepsilon {\text{ or }}\left| {U_{{{\text{dc.pu}}}} } \right| > \varepsilon } \\ {0.5 \cdot K,\left| {f_{{{\text{pu}}}} \left| { \le \varepsilon {\text{ and }}} \right|U_{{{\text{dc.pu}}}} } \right| \le \varepsilon } \\ \end{array} } \right.} \\ \end{array}$$

(3.13)

In Eq. (3.12), (f_pu − U_dc.pu) can be regarded as a new bidirectional droop control input variable, with a range of [−2, 2]. The magnitude of (f_pu − U_dc.pu) determines the active power regulation direction of the interlinking converter. The interlinking converter should remain in idle state under the following two conditions: (1) both the AC frequency and DC voltage are near their rated values. (2) there is power surplus or deficit in both the AC subgrid and DC subgrid (i.e., quadrant II or quadrant IV in Fig. 3.3), and the relative deviation of AC frequency and DC voltage is close in magnitude. These two conditions can be unified as (f_pu − U_dc.pu) ≈ 0. Based on the above analysis, Eq. (3.11) can be improved as Eq. (3.14).

$$\begin{array}{*{20}c} {P = \left\{ {\begin{array}{*{20}c} { - K^{\prime} \cdot \frac{{f_{{{\text{pu}}}} - U_{{{\text{dc.pu}}}} - D}}{2 - D}, f_{{{\text{pu}}}} - U_{{{\text{dc.pu}}}} > D} \\ {{0, } - D < f_{{{\text{pu}}}} - U_{{{\text{dc.pu}}}} < D} \\ { - K^{\prime} \cdot \frac{{f_{{{\text{pu}}}} - U_{{{\text{dc.pu}}}} + D}}{2 - D}, f_{{{\text{pu}}}} - U_{{{\text{dc.pu}}}} < - D} \\ \end{array} } \right.} \\ \end{array}$$

(3.14)

where D is the action deadband, and in this text, D = ε = 0.05. The characteristics of droop control before and after improvement are shown in Fig. 3.5.

Fig. 3.5

Curve of droop control characteristic

The interlinking converter does not transfer power in the deadband and remains in standby mode. It only starts when the normalized deviation between the AC frequency and the DC voltage (f_pu − U_dc.pu) exceeds the deadband range, thus avoiding frequent device actions.

3.4 Small-Signal Modeling and Stability Analysis of Interlinking Converter

The adaptive bidirectional droop control strategy is based on the control of the interlinking converter in a hybrid microgrid using AC frequency and DC voltage. Different droop coefficients K and weight coefficients λ may have an impact on the stability of the hybrid microgrid system, and only when the coefficients are within a reasonable range can the stable operation of the hybrid microgrid system be ensured. In this section, the influence of changes in the droop coefficient and weight coefficient values on the stability of the system is studied using eigenvalue analysis.

The adaptive bidirectional droop control strategy takes the normalized AC frequency (f_pu) and the DC voltage (U_dc.pu) as inputs, and the active power (P) of the interlinking converter as the output. The active power reference value is obtained by linearizing Eq. (3.8) as shown in Eq. (3.15).

$$\begin{array}{*{20}c} {\Delta P_{{{\text{ref}}}} = - \lambda \cdot K \cdot \Delta f_{{{\text{pu}}}} + \left( {1 - \lambda } \right) \cdot K \cdot \Delta U_{{{\text{dc.pu}}}} } \\ \end{array}$$

(3.15)

The power decoupling double closed-loop control of the microgrid interlinking converter is implemented in the dq coordinate system. The power outer loop adopts PI control, while the current inner loop has a much wider bandwidth than the power outer loop and can be simplified as an inertial element [26]. Its transfer function is shown in Eq. (3.16).

$$\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {G_{{{\text{PI}}}} \left( s \right) = k_{p} + \frac{{k_{i} }}{s}} \\ {G_{c} \left( s \right) = \frac{1}{{1 + T_{s} \cdot s}}} \\ \end{array} } \right.} \\ \end{array}$$

(3.16)

where k_p and k_i are the proportional and integral coefficients respectively, and T_s is the switching period of the interlinking converter.

The active power angle relationship on the AC side of an interlinking converter is written as:

$$\begin{array}{*{20}c} {P = \frac{{U_{{{\text{ac}}}} \cdot E}}{{X_{L} }}\delta } \\ \end{array}$$

(3.17)

where X_L is the total impedance between the AC output of the interlinking converter and the AC bus, and δ is the phase angle difference between the converter and the AC bus.

The relationship between the DC side power of the interlinking converter is:

$$\begin{array}{*{20}c} {P = U_{{{\text{dc}}}} \left( {I_{{{\text{dc}}}} - C_{{{\text{dc}}}} \frac{{dU_{{{\text{dc}}}} }}{dt}} \right)} \\ \end{array}$$

(3.18)

The transfer functions for active power of the interlinking converter with respect to AC frequency and DC voltage, obtained by linearizing Eqs. (3.17) and (3.18), are shown in Eq. (3.19).

$$\begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {G_{{\text{f}}} \left( s \right) = \frac{{X_{{\text{L}}} \cdot s}}{{2\pi \cdot U_{{{\text{ac}}}} \cdot E}}} \\ {G_{{{\text{Udc}}}} \left( s \right) = \frac{1}{{I_{{{\text{dc}}}} - C_{{{\text{dc}}}} \cdot U_{{{\text{dc}}}} \cdot s}}} \\ \end{array} } \right.} \\ \end{array}$$

(3.19)

According to Eqs. (3.15)–(3.19), the small signal model of the interlinking converter closed-loop system can be obtained, as shown in Fig. 3.6. The influence of the droop coefficient K and the weight coefficient λ on the distribution of system eigenvalues is studied separately, and the root locus is plotted as shown in Fig. 3.7.

Fig. 3.6

Small-signal model of close-loop system

Fig. 3.7

Locus of eigenvalues for close-loop system

Figure 3.7a shows the root locus plot as the droop coefficient K increases from 0 to 5, and Fig. 3.7b shows the root locus plot as the weighting coefficient λ increases from 0 to 1. The characteristic roots of the closed-loop system are all located in the left half-plane of the imaginary axis, indicating system stability under small disturbances. The distribution of dominant poles in the complex plane changes with variations in K and λ, thereby affecting the dynamic response characteristics. Based on the stability analysis results in this chapter and existing stability analysis conclusions for AC/DC microgrids [12], it can be concluded that within the specified range, the droop coefficient K and weighting coefficient λ can satisfy the stability requirements of the system during normal operation.

The weight coefficient λ of the adaptive bidirectional droop control strategy varies actively within the range of (0, 1), aiming to reduce the comprehensive deviation index and achieve better AC frequency and DC voltage balance while ensuring system stability. To prevent the interlinking converter from overloading, the value of the droop coefficient K should not exceed the maximum value of the interlinking converter capacity. At the same time, to fully utilize the bidirectional power regulation capability, the droop coefficient K can be chosen as the interlinking converter capacity S_MIC.

3.5 Simulations

A hybrid microgrid simulation model in PSCAD/EMTDC software is built as shown in Fig. 3.1. The AC microgrid consists of two controllable power sources DG1 and DG2 with P-f control, and one uncontrollable power source DG3 with PQ control. The DC microgrid consists of two controllable power sources DG4 and DG5 with P-U_dc control, and one uncontrollable power source DG6 with PQ control. The system parameters are shown in Table 3.2. The rated value of the AC and DC loads is 0.6 MW, and the initial active power for each DG is 0.3 MW with an initial output of 0.1 MW. The power is balanced within the AC and DC microgrids, and the power transfer through the interlinking converter is 0.

Table 3.2 System parameters

3.5.1 Scenario 1: Load Variation

To verify the effectiveness of the proposed adaptive bidirectional droop control strategy in responding to changes in AC and DC loads and maintaining stable AC frequency and DC voltage, different scenarios were set up including unilateral load changes, simultaneous load changes on both sides, etc. At the initial moment, DG1 ~ 6 were all put into operation, and both AC and DC loads are 0.3 MW.

• (1) Scenario 1.1: Load Variation in One Side

The AC load increases to 0.6 MW at 2 s, the DC load also increases to 0.6 MW at 4 s, and the AC load returns to 0.3 MW at 6 s. The simulation results are shown in Fig. 3.8.

Fig. 3.8

Simulation results of scenario 1.1

As shown in Fig. 3.8, at the beginning, the AC frequency and DC voltage are both close to their rated values, and the interlinking converter is in standby mode. At 2 s, the AC load increases, causing the AC frequency to drop, and the interlinking converter operates in the inverter mode. At 4 s, the DC load increases, causing the DC voltage to drop. At this point, the power shortage in the AC and DC microgrid is equal, and adjusting the power on either side will increase the overall deviation value. The interlinking converter is in standby mode. At 6 s, the AC load recovers, but there is a power shortage on the DC side, and the interlinking converter operates in rectifier mode. The above results show that the proposed strategy can effectively respond to changes in AC and DC loads, balance the power between AC and DC, avoid excessive deviation in AC frequency or DC voltage, and keep them within the allowable range.

• (2) Scenario 1.2: Bilateral Load Variation

The mixed microgrid experiences changes in both AC and DC loads, which may result in complementary or repulsive (reducing the frequency or voltage deviation on one side, while increasing the deviation on the other side) AC and DC power. Therefore, an interlinking converter is required to coordinate the bidirectional power based on the deviation values of AC frequency and DC voltage. Different scenarios of changes in AC and DC loads were simulated, and the steady-state values of AC frequency, DC voltage, and active power of the interlinking converter were recorded. The simulation results are shown in Table 3.3.

Table 3.3 Simulation results of scenario 1-2

According to Table 3.3, an increase in load is positive and a decrease in load is negative. The active power of the interlinking converter is positive for inversion and negative for rectification. Therefore, the following conclusions can be drawn: (1) When the load of AC and DC changes in a complementary manner, the interlinking converter can provide support from the surplus side to the deficient side in controlling power. (2) When the load of AC and DC increases or decreases simultaneously, there is a contradiction between optimizing AC frequency and optimizing DC voltage. If the power change on both sides is equal, adjusting the power on either side will increase the overall deviation, and the interlinking converter will operate in standby mode. (3) If the power change on AC and DC is not equal, the side with larger deviation is more likely to exceed the limit. In this case, the interlinking converter adaptively provides power support to the side with larger deviation to reduce the overall deviation. The above analysis shows that the proposed method can adaptively adjust the power and direction of the interlinking converter based on the relative deviation of AC frequency and DC voltage, ensuring that both AC frequency and DC voltage remain stable within the optimal range.

3.5.2 Scenario 2: DG Output Change or on/off Switch

The changes in DG output or the switching of DGs may cause power imbalance and changes in load capacity in a hybrid microgrid. In such scenarios, the strong microgrid should provide power support to the weak microgrid. To validate the effectiveness of the proposed method in this scenario, simulations were conducted for both uncontrollable DG output changes and controllable DG switching.

• (1) Scenario 2.1: Uncontrollable Output Variation of DG

At the initial moment, both AC and DC loads are at 0.3 MW. DG1 ~ 6 are all in operation, with non-controllable DG3 and DG6 generating 0.1 MW each. At 2 s, the output of AC DG3 increases to 0.2 MW, and at 4 s, the output of DC DG6 also increases to 0.2 MW. At 6 s, the output of AC DG3 returns to 0.1 MW. The simulation results are shown in Fig. 3.9.

Fig. 3.9

Simulation results of scenario 2.1

As shown in Fig. 3.9, the response characteristics of uncontrollable DG are similar to load variations. However, since uncontrollable DGs are generally renewable energy sources, their output has fluctuating characteristics, leading to fluctuations in frequency and voltage. The adaptive bidirectional droop control strategy can balance the uncontrollable DG power between the AC and DC sides, which is beneficial for improving the capacity of renewable energy integration.

• (2) Scenario 2.2: Adjustable DG Switching

At the initial moment, both the AC and DC loads are 0.3 MW, and controllable DG1, DG2, DG4, and DG5 are put into operation. At 2 s, DC DG5 is disconnected; at 4 s, AC DG2 is disconnected; at 6 s, DC DG5 is reconnected to the grid. The simulation results are shown in Fig. 3.10.

Fig. 3.10

Simulation results of scenario 2.2

As shown in Fig. 3.10, at 2 s, the voltage drops and the DC microgrid weakens due to the disconnection of DG5. At this time, the interlinking converter operates in rectifier mode. At 4 s, the AC DG2 is also disconnected, and the strength of the AC and DC microgrids decreases, as well as the power deficit. The interlinking converter switches to standby mode. At 6 s, the DC DG5 is reconnected, with a weak AC grid and a strong DC grid, and the interlinking converter operates in inverter mode. The above results indicate that the interlinking converter, using adaptive bidirectional droop control strategy, can meet the requirements of flexible integration of DG, improve the mutual support capability of AC and DC DG, and fully exert the power support function of AC and DC DG in hybrid microgrid.

The simulation results of scenario 1 and scenario 2 demonstrate that the proposed adaptive bidirectional droop control strategy can effectively regulate the bidirectional power between AC and DC microgrids in various operating scenarios, such as load variations, changes in distributed generation (DG) output, or switching. It balances the AC frequency and DC voltage deviation, and enhances the power regulation capability of the hybrid AC/DC microgrid.

3.6 RT-LAB Simulation Verification

The RT-LAB semi-physical simulation platform is built, as shown in Fig. 3.11, to verify the performance of the proposed adaptive bidirectional droop control strategy. The platform includes the RT-LAB OP7000 hardware simulated real-time simulator, the FPGA controller of XILINX FPGA ZYNQ7020, the AN706 controller sampling module with a maximum sampling frequency of 200 K, and the waveform measurement using Tektronix MSO44 oscilloscope.

Fig. 3.11

RT-LAB hardware in loop simulation experiment platform

A real-time simulator has been built in which a hybrid AC/DC microgrid and an interlinking converter model are included, with parameters as shown in Table 3.2. The control strategy is implemented in a hardware simulation using an FPGA controller. The interlinking converter voltage and current on both sides are sampled through the AN706 board connected to the RTLAB AO board. The adaptive bidirectional droop control is carried out in the FPGA controller, and the control signals for the interlinking converter switches are generated. The control signals are inputted through the RTLAB DI board connected to the AN706 board, forming a closed-loop simulation.

The effectiveness of the proposed adaptive bidirectional droop control strategy is verified through a semi-physical simulation in different strong and weak situations of AC/DC hybrid microgrids. The load capacity of the microgrid varies with the adjustable DG penetration level in AC/DC hybrid microgrids, and load changes in weak microgrids are more likely to cause significant deviations or even exceeding limits in frequency and DC voltage. In such cases, a stronger microgrid is required to provide more power support to a weaker microgrid. To verify the effectiveness of the proposed strategy in the above situations, the power response characteristics of the interlinking converter during load changes with different DG penetration levels in AC/DC microgrids are simulated, and the proposed method is compared with the fixed coefficient bidirectional droop method.

3.6.1 Scenario 1: Weak AC Microgrid and Strong DC Microgrid

At the initial moment, the AC and DC loads are both 0.3 MW. Only DG1 is put into operation in the AC microgrid, while DG4 and DG5 are put into operation in the DC microgrid. The initial power of each DG has been set to achieve source-load balance within the AC/DC microgrid. At 2 s, the AC load increases to 0.6 MW, and at 6 s, the DC load also increases to 0.6 MW. The experimental results are shown in Fig. 3.12.

Fig. 3.12

Experimental results of scenario 1

As shown in Fig. 3.12, the AC load increases between 2 and 6 s, and only DG1 in the AC microgrid has a weak load capacity. Adjusting it according to the traditional fixed coefficient method would result in a significant drop in AC frequency. However, using the adaptive coefficient control method proposed in this chapter can deliver more supporting power to the AC microgrid. Compared to the traditional method, the power transmission increases by 0.038 MW and the overall deviation decreases by 28.7%. After 6 s, both the AC and DC loads increase to 0.6 MW. Although the power deficit is equal between AC and DC, the AC microgrid is weaker and experiences a greater frequency drop. The method proposed in this chapter can adaptively provide more power support to the AC side. Compared to the traditional method, the power transmission increases by 0.019 MW and the overall deviation decreases by 9.8%.

3.6.2 Scenario 2: Strong AC Microgrid and Weak DC Microgrid

At the initial moment, the AC and DC loads were both 0.3 MW. AC microgrid DG1 and DG2 were put into operation, while only DG4 was put into operation in the DC microgrid. The initial power of each DG has been set to ensure source-load balance within the AC-DC microgrid. At 2 s, the DC load increased to 0.6 MW, and at 6 s, the AC load also increased to 0.6 MW. The experimental results are shown in Fig. 3.13.

Fig. 3.13

Experimental results of scenario 2

As shown in Fig. 3.13, during the 2~6 s period, the DC load increases and only DG4 in the DC microgrid has a weaker load capacity. Adjusting it using the traditional fixed coefficient method would result in a significant voltage drop. However, by using the adaptive coefficient control method proposed in this chapter, more support power can be provided to the DC microgrid. Compared to the traditional method, the power transmission is increased by 0.035 MW and the overall deviation is reduced by 32.6%. After 6 s, both the AC and DC loads increase to 0.6 MW. Although the shortfall in AC and DC power is equal, the DC microgrid is weaker and experiences more voltage drop. The proposed method can adaptively provide more power support to the DC side. Compared to the traditional method, the power transmission is increased by 0.017 MW and the overall deviation is reduced by 9.3%.

The results of the semi-physical simulation verification show that using the adaptive bidirectional droop control strategy can achieve better compensation effects for both AC frequency and DC voltage balance. Combining theoretical analysis and simulation, the results indicate that the proposed strategy can fully utilize the power mutual assistance capability between microgrids and achieve power optimization distribution under various operating states with source and load fluctuations in the AC/DC microgrid.

3.7 Conclusion

The interlinking converter is a core device for flexible interconnection between AC microgrids and DC microgrids, playing a key role in balancing power between AC and DC microgrids and improving frequency and voltage stability. In response to the problem that traditional bidirectional droop control strategies cannot dynamically adjust the priority of AC frequency control and DC voltage control, An adaptive bidirectional droop control strategy for the interlinking converter is proposed in this chapter, which dynamically adjusts the adaptive weighting coefficient based on the deviation of AC frequency and DC voltage to achieve a balanced compensation for AC frequency and DC voltage deviation, and effectively reducing the overall deviation index of the AC/DC microgrid. Through theoretical analysis, simulation, and experimental verification, the following main conclusions are drawn:

• (1) When dealing with fluctuations in AC or DC loads, the proposed adaptive bidirectional droop control strategy enables bidirectional power flow between AC and DC side, fully leveraging the power mutual assistance capability between AC and DC microgrids and maintaining frequency and voltage within the optimal range.

• (2) The proposed strategy does not require communication, making it convenient for plug-and-play of distributed energy sources and improving the flexibility of hybrid microgrid systems. By setting a deadband as the activation condition, frequent actions of the interlinking converter are avoided, thus the system reliability is enhanced.

• (3) Compared to traditional bidirectional power droop control strategies, the proposed method exhibits better balance of AC frequency and DC voltage in hybrid microgrids with varying strengths. It also optimizes the control for the side with larger power imbalance, effectively improving the reliability and stability of the hybrid microgrid system.