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1766077

2032年全釩液流電池市場預測：按電池組件、材料類型、應用、最終用戶和地區進行的全球分析

Vanadium Redox Flow Battery Market Forecasts to 2032 - Global Analysis By Battery Component (Electrolyte, Stack Frame, Flow Frame, Tanks, Pumps and Pipes), Material Type, Application, End User and By Geography
出版日期: | 出版商: Stratistics Market Research Consulting | 英文 200+ Pages | 商品交期: 2-3個工作天內

價格

據 Stratistics MRC 稱，全球釩液流電池市場預計在 2025 年達到 3.663 億美元，到 2032 年將達到 11.326 億美元，預測期內的複合年成長率為 17.5%。釩液流電池 (VRFB) 是一種可充電液流電池，它將能量儲存在含有不同氧化態釩離子的液體電解質中。與傳統電池不同，VRFB 透過將電解儲存在外部罐中來實現功率和能量分離，從而實現獨立縮放。這種設計具有出色的可擴展性、長循環壽命（15,000-20,000 次循環）、由於電解不易燃而具有高安全性以及最小的自放電。 VRFB 特別適合大規模、長時間能源儲存應用，例如電網穩定和可再生能源整合。

根據世界經濟論壇預測，2022年全球電動車銷量將比2021年成長55%，達到1,050萬輛。

可再生能源整合

太陽能和風能等可再生能源的普及正在加速全釩液流電池 (VRFB) 產業的發展。由於這些能源來源的波動性，VRFB 為大規模能源儲存提供了可靠的選擇，從而實現穩定的電力供應。 VRFB 使用壽命長、可擴展，並且能夠管理頻繁的充放電循環，使其成為電網穩定和可再生能源整合的理想選擇。全球市場對 VRFB 的採用源自於對永續能源系統日益成長的需求。

初期投資高

高昂的初始投資是全釩液流電池 (VRFB) 市場成長的主要障礙。系統安裝、釩電解和基礎設施建設相關的前期成本明顯高於其他電池技術。這種經濟負擔阻礙了小型能源供應商和新興市場採用 VRFB 解決方案，儘管 VRFB 具有長期性能優勢，但其廣泛應用仍受到阻礙，並減緩了整體市場的擴張。

技術進步

技術進步在很大程度上推動了全釩液流電池 (VRFB) 市場的成長。電解配方、電池組設計和系統整合的創新提高了 VRFB 的能源效率、儲存容量和使用壽命。這些改進使 VRFB 適用於大規模可再生能源儲存和電網穩定。此外，自動化和遠端監控系統的進步降低了營運成本並提高了系統可靠性。因此，VRFB 在公用事業規模和工業應用中的吸引力日益增強，刺激了市場擴張。

釩成本和供應風險

由於高成本且供應風險高，全釩液流電池 (VRFB) 市場正面臨負面影響和限制。價格波動、全球供應商有限以及地緣政治依賴給製造商和投資者帶來了不確定性。這些挑戰推高了生產成本，並降低了 VRFB 相對於其他電池技術的競爭力。因此，計劃開發商對採用 VRFB 猶豫不決，這可能會阻礙其大規模部署和發展。

COVID-19的影響

新冠疫情最初擾亂了全釩液流電池 (VRFB) 市場，原因是供應鏈中斷、工業活動放緩以及可再生能源計劃延期。製造業放緩和物流限制阻礙了零件供應。然而，隨著各國政府優先投資綠色能源以促進經濟復甦，市場開始復甦，這刺激了對全釩液流電池 (VRFB) 等長壽命能源儲存解決方案的需求。這項轉變凸顯了該技術在疫情後永續能源基礎設施中所扮演的角色。

預計研究機構部門將成為預測期內最大的部門

隨著持續創新和技術進步，科學研究機構正在不斷提升電池的效率、可擴展性和使用壽命。材料最佳化和成本降低策略的努力，使釩電池更具商業性可行性。此外，學術界和產業界之間的緊密合作正在加速產品開發和部署，促進釩電池在全球電網規模能源儲存、可再生能源併網和脫碳計畫中的更廣泛應用。

預計雙極板部分將在預測期內實現最高的複合年成長率

在預測期內，由於系統效率和耐用性的提高，雙極板領域預計將實現最高成長率。雙極板在均勻電流分配和降低內阻方面發揮關鍵作用，從而提高能量輸出並延長電池壽命。石墨複合材料和導電聚合物等材料的進步降低了成本並提高了性能，從而推動了它們在大規模能源儲存應用中的應用，並推動了公共產業和工業領域的市場成長。

比最大的地區

由於可再生能源投資和電網現代化計劃的不斷增加，預計亞太地區將在預測期內佔據最大的市場佔有率。中國、日本和韓國等國家正積極採用大規模能源儲存解決方案，以支持其清潔能源目標並確保電網穩定。政府激勵措施、快速工業化以及對不間斷電源日益成長的需求進一步推動了市場擴張。該地區強大的製造業基礎也促進了釩電池技術的開發和部署。

複合年成長率最高的地區

預計北美地區在預測期內將實現最高的複合年成長率，因為該地區專注於能源儲存技術以提高電網穩定性並實現脫碳目標，從而增加了對釩電解液電池的需求。技術發展、法律規範和政府獎勵都在推動其在商業和公共產業領域的應用。此外，關鍵企業和研究機構的存在正在刺激技術創新，從而推動北美整體市場的成長。

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  • 公司簡介
    • 對其他市場參與企業（最多 3 家公司）進行全面分析
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  • 地理細分
    • 根據客戶興趣對主要國家進行市場估計、預測和複合年成長率（註：基於可行性檢查）
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    • 透過產品系列、地理分佈和策略聯盟對主要企業基準化分析

目錄

第1章執行摘要

第2章 前言

  • 概述
  • 相關利益者
  • 研究範圍
  • 調查方法
    • 資料探勘
    • 數據分析
    • 數據檢驗
    • 研究途徑
  • 研究材料
    • 主要研究資料
    • 二手研究資料
    • 先決條件

第3章市場走勢分析

  • 介紹
  • 驅動程式
  • 限制因素
  • 機會
  • 威脅
  • 應用分析
  • 最終用戶分析
  • 新興市場
  • COVID-19的影響

第4章 波特五力分析

  • 供應商的議價能力
  • 買家的議價能力
  • 替代品的威脅
  • 新進入者的威脅
  • 競爭對手之間的競爭

5. 全球全釩液流電池市場（按電瓶組件）

  • 介紹
  • 電解質
  • 堆疊框架
  • 流動框架
  • 坦克
  • 泵浦
  • 管道

6. 全球釩液流電池市場（依材料類型）

  • 介紹
  • 釩電解
  • 離子交換膜
  • 電極
  • 雙極板
  • 集電器
  • 其他

7. 全球釩液流電池市場（依應用）

  • 介紹
  • 公用事業規模的能源儲存
  • 離網電力系統
  • 電動車充電站
  • 工業備用電源
  • 可再生能源整合
  • 其他

8. 全球釩液流電池市場（依最終用戶）

  • 介紹
  • 公共產業
  • 商業和工業
  • 住宅
  • 軍隊
  • 研究所
  • 其他

9. 全球釩液流電池市場（按地區）

  • 介紹
  • 北美洲
    • 美國
    • 加拿大
    • 墨西哥
  • 歐洲
    • 德國
    • 英國
    • 義大利
    • 法國
    • 西班牙
    • 其他歐洲國家
  • 亞太地區
    • 日本
    • 中國
    • 印度
    • 澳洲
    • 紐西蘭
    • 韓國
    • 其他亞太地區
  • 南美洲
    • 阿根廷
    • 巴西
    • 智利
    • 南美洲其他地區
  • 中東和非洲
    • 沙烏地阿拉伯
    • 阿拉伯聯合大公國
    • 卡達
    • 南非
    • 其他中東和非洲地區

第10章 重大進展

  • 協議、夥伴關係、合作和合資企業
  • 收購與合併
  • 新產品發布
  • 業務擴展
  • 其他關鍵策略

第11章 公司概況

  • VRB Energy Inc.
  • Invinity Energy Systems
  • Sumitomo Electric Industries, Ltd.
  • H2, Inc.
  • Rongke Power
  • UniEnergy Technologies
  • StorEn Technologies Inc.
  • VoltStorage
  • Avalon Battery
  • Redflow Limited
  • Sinergy Flow Srl
  • Solibra Energy Storage Technologies GmbH
  • VanadiumCorp Resource Inc.
  • VFlow Tech
  • Volterion
  • Primus Power
  • Dalian Rongke Power Company, Ltd.
  • Largo Inc.
Product Code: SMRC29932

According to Stratistics MRC, the Global Vanadium Redox Flow Battery Market is accounted for $366.3 million in 2025 and is expected to reach $1132.6 million by 2032 growing at a CAGR of 17.5% during the forecast period. A Vanadium Redox Flow Battery (VRFB) is a type of rechargeable flow battery that stores energy in liquid electrolytes containing vanadium ions in different oxidation states. Unlike traditional batteries, VRFBs decouple power and energy by storing electrolytes in external tanks, allowing for independent scaling. This design provides exceptional scalability, long cycle life (15,000-20,000 cycles), high safety due to non-flammable electrolytes, and minimal self-discharge. VRFBs are particularly well-suited for large-scale, long-duration energy storage applications like grid stabilization and renewable energy integration.

According to the World Economic Forum, global sales of electric vehicles (EVs) increased by 55% reaching a total of 10.5 million in 2022 from 2021.

Market Dynamics:

Driver:

Renewable Energy Integration

The incorporation of renewable energy sources such as solar and wind is accelerating the growth of the Vanadium Redox Flow Battery (VRFB) industry. Due to the erratic nature of these energy sources, VRFBs provide a dependable option for large-scale energy storage, allowing for a steady supply of electricity. They are perfect for grid stability and renewable integration because of their extended lifespan, scalability, and capacity to manage frequent charge-discharge cycles. The introduction of VRFBs in international markets is being driven by the rising need for sustainable energy systems.

Restraint:

High Upfront Investment

High upfront investment poses a significant barrier to the growth of the Vanadium Redox Flow Battery (VRFB) market. The initial costs associated with system installation, vanadium electrolyte, and infrastructure development are considerably higher compared to other battery technologies. This financial burden discourages small-scale energy providers and emerging markets from adopting VRFB solutions, thereby hindering widespread deployment and slowing the market's overall expansion despite its long-term performance advantages.

Opportunity:

Technological Advancements

Technological advancements are significantly propelling the growth of the Vanadium Redox Flow Battery (VRFB) market. Innovations in electrolyte formulations, stack designs, and system integration have enhanced energy efficiency, storage capacity, and lifespan of VRFBs. These improvements make them more suitable for large-scale renewable energy storage and grid stabilization. Additionally, advancements in automation and remote monitoring systems reduce operational costs and improve system reliability. As a result, VRFBs are becoming increasingly attractive for utility-scale and industrial applications, fueling market expansion.

Threat:

Vanadium Cost & Supply Risk

The Vanadium Redox Flow Battery (VRFB) market faces a negative and hindering impact due to the high cost and supply risk of vanadium. Price volatility, limited global suppliers, and geopolitical dependencies create uncertainty for manufacturers and investors. These challenges increase production costs and reduce the competitiveness of VRFBs compared to other battery technologies. As a result, project developers may hesitate to adopt VRFBs, hindering large-scale deployment and market growth.

Covid-19 Impact

The Covid-19 pandemic initially disrupted the Vanadium Redox Flow Battery (VRFB) market due to supply chain interruptions, reduced industrial activities, and delays in renewable energy projects. Manufacturing slowdowns and restricted logistics hampered component availability. However, the market began recovering as governments emphasized green energy investments for economic revival, boosting demand for long-duration energy storage solutions like VRFBs. This shift highlighted the technology's role in sustainable energy infrastructure post-pandemic.

The research institutions segment is expected to be the largest during the forecast period

The research institutions segment is expected to account for the largest market share during the forecast period, due to continuous innovation and technological advancements, these institutions are enhancing battery efficiency, scalability, and lifespan. Their efforts in material optimization and cost-reduction strategies are making VRFBs more commercially viable. Additionally, strong collaborations between academia and industry are accelerating product development and deployment, fostering greater adoption of VRFBs in grid-scale energy storage, renewable integration, and decarbonization initiatives worldwide.

The bipolar plates segment is expected to have the highest CAGR during the forecast period

Over the forecast period, the bipolar plates segment is predicted to witness the highest growth rate because it enhances system efficiency and durability. These plates play a critical role in enabling uniform current distribution and minimizing internal resistance, leading to improved energy output and extended battery life. Advances in materials such as graphite composites and conductive polymers are reducing costs and increasing performance, thus boosting adoption in large-scale energy storage applications and accelerating market growth across utility and industrial sectors.

Region with largest share:

During the forecast period, the Asia Pacific region is expected to hold the largest market share due to rising investments in renewable energy and grid modernization initiatives. Countries like China, Japan, and South Korea are actively adopting large-scale energy storage solutions to support clean energy targets and ensure grid stability. Government incentives, rapid industrialization, and increasing demand for uninterrupted power supply are further propelling market expansion. The region's robust manufacturing base also contributes to the development and deployment of VRFB technology

Region with highest CAGR:

Over the forecast period, the North America region is anticipated to exhibit the highest CAGR, because of the region's strong focus on energy storage technologies to improve grid stability and meet decarbonization goals, demand for VRFBs has increased. Technological developments, enabling regulatory frameworks, and government incentives are all promoting adoption in the commercial and utility sectors. Furthermore, innovation is being fostered by the presence of important businesses and research institutions, which is accelerating the market's overall growth in North America.

Key players in the market

Some of the key players profiled in the Vanadium Redox Flow Battery Market include VRB Energy Inc., Invinity Energy Systems, Sumitomo Electric Industries, Ltd., H2, Inc., Rongke Power, UniEnergy Technologies, StorEn Technologies Inc., VoltStorage, Avalon Battery, Redflow Limited, Sinergy Flow S.r.l., Solibra Energy Storage Technologies GmbH, VanadiumCorp Resource Inc., VFlow Tech, Volterion, Primus Power, Dalian Rongke Power Company, Ltd. and Largo Inc.

Key Developments:

In April 2025, ABB and Sumitomo Corporation have signed a Memorandum of Understanding, aimed at jointly exploring solutions for decarbonizing mining machinery. The partnership focuses on fleet electrification-specifically, the integration of overhead "trolley assist" systems to power haul trucks-and seeks to deliver net-zero emissions solutions at mine sites.

In February 2025, Sumitomo Electric Industries, Ltd. has signed a construction subcontract with Energieanlagen Ramonat GmbH, for construction work, including the installation of 525 kV high-voltage direct current (DC) cross-linked polyethylene (XLPE) cables in the German Korridor B project 49.

Battery Components Covered:

  • Electrolyte
  • Stack Frame
  • Flow Frame
  • Tanks
  • Pumps
  • Pipes

Material Types Covered:

  • Vanadium Electrolyte
  • Ion Exchange Membranes
  • Electrodes
  • Bipolar Plates
  • Current Collectors
  • Other Material Types

Applications Covered:

  • Utility-Scale Energy Storage
  • Off-Grid Power Systems
  • EV Charging Stations
  • Industrial Backup Power
  • Renewable Energy Integration
  • Other Applications

End Users Covered:

  • Utilities
  • Commercial & Industrial
  • Residential
  • Military
  • Research Institutions
  • Other End Users

Regions Covered:

  • North America
    • US
    • Canada
    • Mexico
  • Europe
    • Germany
    • UK
    • Italy
    • France
    • Spain
    • Rest of Europe
  • Asia Pacific
    • Japan
    • China
    • India
    • Australia
    • New Zealand
    • South Korea
    • Rest of Asia Pacific
  • South America
    • Argentina
    • Brazil
    • Chile
    • Rest of South America
  • Middle East & Africa
    • Saudi Arabia
    • UAE
    • Qatar
    • South Africa
    • Rest of Middle East & Africa

What our report offers:

  • Market share assessments for the regional and country-level segments
  • Strategic recommendations for the new entrants
  • Covers Market data for the years 2022, 2023, 2024, 2026, and 2030
  • Market Trends (Drivers, Constraints, Opportunities, Threats, Challenges, Investment Opportunities, and recommendations)
  • Strategic recommendations in key business segments based on the market estimations
  • Competitive landscaping mapping the key common trends
  • Company profiling with detailed strategies, financials, and recent developments
  • Supply chain trends mapping the latest technological advancements

Free Customization Offerings:

All the customers of this report will be entitled to receive one of the following free customization options:

  • Company Profiling
    • Comprehensive profiling of additional market players (up to 3)
    • SWOT Analysis of key players (up to 3)
  • Regional Segmentation
    • Market estimations, Forecasts and CAGR of any prominent country as per the client's interest (Note: Depends on feasibility check)
  • Competitive Benchmarking
    • Benchmarking of key players based on product portfolio, geographical presence, and strategic alliances

Table of Contents

1 Executive Summary

2 Preface

  • 2.1 Abstract
  • 2.2 Stake Holders
  • 2.3 Research Scope
  • 2.4 Research Methodology
    • 2.4.1 Data Mining
    • 2.4.2 Data Analysis
    • 2.4.3 Data Validation
    • 2.4.4 Research Approach
  • 2.5 Research Sources
    • 2.5.1 Primary Research Sources
    • 2.5.2 Secondary Research Sources
    • 2.5.3 Assumptions

3 Market Trend Analysis

  • 3.1 Introduction
  • 3.2 Drivers
  • 3.3 Restraints
  • 3.4 Opportunities
  • 3.5 Threats
  • 3.6 Application Analysis
  • 3.7 End User Analysis
  • 3.8 Emerging Markets
  • 3.9 Impact of Covid-19

4 Porters Five Force Analysis

  • 4.1 Bargaining power of suppliers
  • 4.2 Bargaining power of buyers
  • 4.3 Threat of substitutes
  • 4.4 Threat of new entrants
  • 4.5 Competitive rivalry

5 Global Vanadium Redox Flow Battery Market, By Battery Component

  • 5.1 Introduction
  • 5.2 Electrolyte
  • 5.3 Stack Frame
  • 5.4 Flow Frame
  • 5.5 Tanks
  • 5.6 Pumps
  • 5.7 Pipes

6 Global Vanadium Redox Flow Battery Market, By Material Type

  • 6.1 Introduction
  • 6.2 Vanadium Electrolyte
  • 6.3 Ion Exchange Membranes
  • 6.4 Electrodes
  • 6.5 Bipolar Plates
  • 6.6 Current Collectors
  • 6.7 Other Material Types

7 Global Vanadium Redox Flow Battery Market, By Application

  • 7.1 Introduction
  • 7.2 Utility-Scale Energy Storage
  • 7.3 Off-Grid Power Systems
  • 7.4 EV Charging Stations
  • 7.5 Industrial Backup Power
  • 7.6 Renewable Energy Integration
  • 7.7 Other Applications

8 Global Vanadium Redox Flow Battery Market, By End User

  • 8.1 Introduction
  • 8.2 Utilities
  • 8.3 Commercial & Industrial
  • 8.4 Residential
  • 8.5 Military
  • 8.6 Research Institutions
  • 8.7 Other End Users

9 Global Vanadium Redox Flow Battery Market, By Geography

  • 9.1 Introduction
  • 9.2 North America
    • 9.2.1 US
    • 9.2.2 Canada
    • 9.2.3 Mexico
  • 9.3 Europe
    • 9.3.1 Germany
    • 9.3.2 UK
    • 9.3.3 Italy
    • 9.3.4 France
    • 9.3.5 Spain
    • 9.3.6 Rest of Europe
  • 9.4 Asia Pacific
    • 9.4.1 Japan
    • 9.4.2 China
    • 9.4.3 India
    • 9.4.4 Australia
    • 9.4.5 New Zealand
    • 9.4.6 South Korea
    • 9.4.7 Rest of Asia Pacific
  • 9.5 South America
    • 9.5.1 Argentina
    • 9.5.2 Brazil
    • 9.5.3 Chile
    • 9.5.4 Rest of South America
  • 9.6 Middle East & Africa
    • 9.6.1 Saudi Arabia
    • 9.6.2 UAE
    • 9.6.3 Qatar
    • 9.6.4 South Africa
    • 9.6.5 Rest of Middle East & Africa

10 Key Developments

  • 10.1 Agreements, Partnerships, Collaborations and Joint Ventures
  • 10.2 Acquisitions & Mergers
  • 10.3 New Product Launch
  • 10.4 Expansions
  • 10.5 Other Key Strategies

11 Company Profiling

  • 11.1 VRB Energy Inc.
  • 11.2 Invinity Energy Systems
  • 11.3 Sumitomo Electric Industries, Ltd.
  • 11.4 H2, Inc.
  • 11.5 Rongke Power
  • 11.6 UniEnergy Technologies
  • 11.7 StorEn Technologies Inc.
  • 11.8 VoltStorage
  • 11.9 Avalon Battery
  • 11.10 Redflow Limited
  • 11.11 Sinergy Flow S.r.l.
  • 11.12 Solibra Energy Storage Technologies GmbH
  • 11.13 VanadiumCorp Resource Inc.
  • 11.14 VFlow Tech
  • 11.15 Volterion
  • 11.16 Primus Power
  • 11.17 Dalian Rongke Power Company, Ltd.
  • 11.18 Largo Inc.

List of Tables

  • Table 1 Global Vanadium Redox Flow Battery Market Outlook, By Region (2024-2032) ($MN)
  • Table 2 Global Vanadium Redox Flow Battery Market Outlook, By Battery Component (2024-2032) ($MN)
  • Table 3 Global Vanadium Redox Flow Battery Market Outlook, By Electrolyte (2024-2032) ($MN)
  • Table 4 Global Vanadium Redox Flow Battery Market Outlook, By Stack Frame (2024-2032) ($MN)
  • Table 5 Global Vanadium Redox Flow Battery Market Outlook, By Flow Frame (2024-2032) ($MN)
  • Table 6 Global Vanadium Redox Flow Battery Market Outlook, By Tanks (2024-2032) ($MN)
  • Table 7 Global Vanadium Redox Flow Battery Market Outlook, By Pumps (2024-2032) ($MN)
  • Table 8 Global Vanadium Redox Flow Battery Market Outlook, By Pipes (2024-2032) ($MN)
  • Table 9 Global Vanadium Redox Flow Battery Market Outlook, By Material Type (2024-2032) ($MN)
  • Table 10 Global Vanadium Redox Flow Battery Market Outlook, By Vanadium Electrolyte (2024-2032) ($MN)
  • Table 11 Global Vanadium Redox Flow Battery Market Outlook, By Ion Exchange Membranes (2024-2032) ($MN)
  • Table 12 Global Vanadium Redox Flow Battery Market Outlook, By Electrodes (2024-2032) ($MN)
  • Table 13 Global Vanadium Redox Flow Battery Market Outlook, By Bipolar Plates (2024-2032) ($MN)
  • Table 14 Global Vanadium Redox Flow Battery Market Outlook, By Current Collectors (2024-2032) ($MN)
  • Table 15 Global Vanadium Redox Flow Battery Market Outlook, By Other Material Types (2024-2032) ($MN)
  • Table 16 Global Vanadium Redox Flow Battery Market Outlook, By Application (2024-2032) ($MN)
  • Table 17 Global Vanadium Redox Flow Battery Market Outlook, By Utility-Scale Energy Storage (2024-2032) ($MN)
  • Table 18 Global Vanadium Redox Flow Battery Market Outlook, By Off-Grid Power Systems (2024-2032) ($MN)
  • Table 19 Global Vanadium Redox Flow Battery Market Outlook, By EV Charging Stations (2024-2032) ($MN)
  • Table 20 Global Vanadium Redox Flow Battery Market Outlook, By Industrial Backup Power (2024-2032) ($MN)
  • Table 21 Global Vanadium Redox Flow Battery Market Outlook, By Renewable Energy Integration (2024-2032) ($MN)
  • Table 22 Global Vanadium Redox Flow Battery Market Outlook, By Other Applications (2024-2032) ($MN)
  • Table 23 Global Vanadium Redox Flow Battery Market Outlook, By End User (2024-2032) ($MN)
  • Table 24 Global Vanadium Redox Flow Battery Market Outlook, By Utilities (2024-2032) ($MN)
  • Table 25 Global Vanadium Redox Flow Battery Market Outlook, By Commercial & Industrial (2024-2032) ($MN)
  • Table 26 Global Vanadium Redox Flow Battery Market Outlook, By Residential (2024-2032) ($MN)
  • Table 27 Global Vanadium Redox Flow Battery Market Outlook, By Military (2024-2032) ($MN)
  • Table 28 Global Vanadium Redox Flow Battery Market Outlook, By Research Institutions (2024-2032) ($MN)
  • Table 29 Global Vanadium Redox Flow Battery Market Outlook, By Other End Users (2024-2032) ($MN)

Note: Tables for North America, Europe, APAC, South America, and Middle East & Africa Regions are also represented in the same manner as above.