Mathematical Model and Analysis of Bidirectional

DC-DC for Microgrid Application

Power System Analysis
Digital Assignment 1
BEEE306P

Navya Kukreja Snehasree Senthilkumar Anuj Verma

22BEE0093 22BEE0163 22BEE0197

1 Literature Survey Overview

1.1 Review and Comparative Study of Bi-Directional DC-DC
Converters
This paper presents a overview of bi-directional DC-DC converters and their application,
focusing on the different topologies of non-isolated and isolated bidirectional DC-DC
converters. It discusses the factors considered for classification of these converters, such as
merits and demerits, features and complexity. [8]

1.2 Topologies and Control Schemes of Bidirectional DC–DC

Power Converters: An Overview
This paper provides a comprehensive explanation of different topologies of bi-directional
DC-DC converters, discussing it’s advantages and disadvantages. It also discusses various
control schemes such as PID control, fuzzy logic control, digital control and more. Along
with this, the paper reviews five switching strategies. [2]

1.3 A 98.3% Efficient GaN Isolated Bidirectional DC–DC

Converter for DC Microgrid Energy Storage System
Applications
This paper explains recent research, and proposes GaN-based bidirectional DC-DC
converter instead of Si superjunction MOSFETs in ZVS topolgies for ESS application.
This allows the converter achieve higher efficiency, higher power density and wider
input/output voltage range. [12]

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1.4 Power exchange among microgrids using modular-isolated
bidirectional DC–DC converter
This paper explores the use of a modular-isolated bidirectional DC-DC converter for power
exchange between a DC microgrid and a DC distribution network. It proposes a power
management strategy that facilitates surplus power sharing among microgrids and
maintains stable operation even during network islanding. The research includes
experimental validation of the converter’s operation and software simulations of a
PV-based microgrid under various conditions. [3]

1.5 A Survey of Bi-directional DC-DC Converters for

Transportation Electrification and Microgrid Applications
This paper provides elucidation on different bi-directional DC-DC converters with a focus
on the application of these topolgies in different areas such as electric vehicles, micrgrids,
etc. The paper also highlights the versatility of dual active bridge converters through a
simulation and graph. [10]

2 Microgrid and DC Microgrid

A microgrid (MG) is a localized energy system that integrates distributed energy resources.
It allows power to be exchanged between a main grid, a battery, and (often renewable)
sources. [7]

2.1 DCMG and ACMG comparison

• DC microgrids (DCMGs) offer more efficient interconnection of distributed energy
resources, ESS, and sensitive loads than ACMG.

• This is due to the elimination of AC-DC and DC-AC conversion stages, which incur
losses. Many renewable energy sources, like solar photovoltaic (PV) panels, and
energy storage systems (ESS), like batteries, generate or store energy in DC form. By
utilizing a DC bus, these resources can be directly integrated, reducing the need for
multiple conversion steps and improving overall system efficiency.

• Modern electronic loads often operate on DC power, making DCMGs a more direct
and efficient solution for these applications.

• The absence of frequency and reactive power control in DCMGs simplifies control
strategies and enhances system stability, making them particularly advantageous for
remote or isolated areas where efficient power delivery is critical. [1]

2
 Figure 1: DCMG, courtesy of [1]

2.2 Bidirectional DC-to-DC Converters in MG

In a DC Microgrid (DCMG), a bidirectional DC/DC converter serves as an interface,
enabling both the storage of energy from renewable sources like PV arrays and the retrieval
of stored energy from devices such as batteries. [3] [4]
Bidirectional DC-DC converters offers several key advantages within DCMGs:
• Facilitates Inter-Microgrid Power Exchange: These converters enable seamless
power exchange between microgrids connected via a common DC bus and a
sophisticated cyber communication network. This allows for dynamic load balancing
and optimizes resource utilization across the network. [3]
• Enables Power Sharing Between Neighboring DCMGs: By connecting
neighbouring DCMGs, bidirectional converters allow for direct power transfer,
improving resilience and reliability, especially during islanded operation or periods of
high demand. [3]
• Ensures Bidirectional Power Flow and Voltage Stability: These converters
maintain a balanced power supply and demand by facilitating bidirectional power
flow. This stabilizes DC voltages within the microgrid, even under varying load
conditions or fluctuating renewable energy generation. [3]
• Supports Load-Shedding Prevention and Enhanced Reliability: By enabling
the sharing of surplus power with overloaded microgrids, bidirectional DC-DC
converters can prevent or minimize load shedding, thereby improving the reliability of
the distribution network. [3]

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3 Different converter types
Prior to choosing our topic as ”Bidirectional DC-DC Converter,” we looked at various
types of converters [6] [5] [9]. Here are our findings.

Converter type Advantages Drawbacks

Two-Level VSI (DC-AC) Simple, low-cost High harmonics, low
Converts DC to AC for microgrid integration. efficiency at high
voltage
Multilevel Inverter (DC-AC) Low harmonics, high Complex, expensive
Generates AC from multiple DC voltage levels, efficiency
reducing harmonics.
Bidirectional DC-DC Efficient energy Complex control,
Manages energy storage by enabling storage, grid stability potential instability
charging/discharging.
Grid-Forming Inverter Enables islanding, Costly, complex
Provides voltage/frequency reference for reliable control
islanded microgrids.
Grid-Supporting Converter Improves Requires precise
Regulates active/reactive power for grid voltage/frequency coordination
stability. stability
Interlinking Converter (AC-DC) Enables hybrid grids, Expensive, high
Connects AC and DC microgrid sections for flexible maintenance
power exchange.

Table 1: Overview of different types of converters

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4 Different topologies of DC-DC converters
Let us examine a few different topologies of DC-DC converters. [10]
We shall measure complexity by component count, indicated as the number of switches,
inductors, and capacitors in the system. For example, an entry of S = 2, L = 1, C = 3
means that the system uses:

• Two switches

• One inductor

• Three capacitors

Topology Complexity Applications

Two Quadrant Buck Boost Converter S=2 EV charging
Buck mode during charging and boost mode during L=1
discharging C=1
Four Quadrant Buck Boost Converter S=2 Renewable energy
Provides buck and boost mode of power flow while L=1 systems, EV
charging and discharging C=1
Dual Active Bridge Converter S=8 Microgrid, automotive
Consists of two bridges – left and right bridge act as L=1 applications, battery
fully controlled inverter and rectifier respectively C=1 charging, more-electric
aircraft
CLLC Converter S=8 Transportation
Uses resonant capacitor to overcome high voltage stress L=1 electrification, energy
on switching devices and lowers EMI C=2 storage systems
Series Resonant DC-DC Converter with S=8 Charging of PHEV
Clamped Capacitor Voltage L=2
Clamping diodes provide current limiting during short C=1
circuit and are connected across resonant capacitor for
protection
LCLC Resonant Converter S=8 Renewable Energy
Used for wide input voltage application as converter has L=2 Storage System, EV
sharp voltage gain C=4

Table 2: Overview of different topologies

5
5 Different control schemers for DC-DC converters
Let us examine a few different control schemes for DC-DC converters. [2]

Scheme Applications Merits Demerits

PID Smart grids, EVs, fuel Low cost, reliable. Low efficiency, poor
Simple, robust cells transient response.
voltage/current
regulation.
Sliding Mode DC motor control, Robust, fast response. Needs accurate
Forces system to a stand-alone DC parameters.
sliding surface; robust networks, energy
to disturbances. storage.
Dynamic Evolution Ultra-capacitor storage High performance, no Complex duty cycle
Minimizes voltage drop with fuel cells. model needed. calculation.
after load changes,
model-free.
Model Predictive DC power, batteries, Fast response, simple. Limited to linear
Predicts behaviour, hybrid powertrains. models.
optimizes actions.
Fuzzy PV lighting, energy Handles non- Relies on expert
Uses fuzzy logic for storage, motor drives. linearities, robust. knowledge.
uncertainties.
Digital Control Energy storage, EVs, Flexible, fault Complex, needs
Flexible control with DC distribution monitoring. processing power.
processors
Boundary Control Buck/boost Fast, stable. Sensitive to parameter
Time-optimal, fast converters. variations.
transient response.

Table 3: Overview of different control schemes

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6 Two-quadrant buck and boost non-isolated
converter
We chose to model this converter, for the following reasons:

• It provides bidirectional power flow, making it suitable for charging.

• Having both step-up and step-down ability can help handle supply instabilities.

• It is a simple, therefore cheap, topology

• It can provide high efficiency due to continuous current conduction mode and dual
operation mode. [8]

Figure 2: Two-quadrant non-isolated buck and boost converter, courtesy of [2]

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We can mathematically model this with state-space equations. Our derivation for these
equations is attached at the end of our report. [11]

6.1 In buck mode

 R 1 
PT  
− 0 0 0
i˙L  L L
   
 il 1  
˙
 1  
0  VBT
VH  =  0 − 0  VH  +  RDBCH  V
CH RDB

   DB
V˙L  VL 1
 1 
1 0
0 − RBT CL
CL RBT CL

6.2 In boost mode

 R 1 1 
PT  
− − 0 0
˙ L L L  il
   
iL  1  
1 1 
0  VBT
V˙H  =  −
 
 CH − 0  VH  +  RDBCH  V
CH RDB

  DB
V˙L 1  VL 1
 1 
0 − 0
CL RBT CL RBT CL

8
References
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[2] Saman A. Gorji, Hosein G. Sahebi, Mehran Ektesabi, and Ahmad B. Rad. Topologies
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[3] Reza Haghmaram, Farzad Sedaghati, and Reza Ghafarpour. Power exchange among
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[9] Wenlong Ming. Power electronic converters for microgrids. In Nick Jenkins, editor,
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